Merge branch 'develop'
This commit is contained in:
4
.gitignore
vendored
Normal file
4
.gitignore
vendored
Normal file
@@ -0,0 +1,4 @@
|
||||
|
||||
.idea/
|
||||
|
||||
*.pyc
|
||||
11
.vscode/settings.json
vendored
Normal file
11
.vscode/settings.json
vendored
Normal file
@@ -0,0 +1,11 @@
|
||||
{
|
||||
"python.testing.unittestArgs": [
|
||||
"-v",
|
||||
"-s",
|
||||
"./tests",
|
||||
"-p",
|
||||
"test_*.py"
|
||||
],
|
||||
"python.testing.pytestEnabled": false,
|
||||
"python.testing.unittestEnabled": true
|
||||
}
|
||||
Binary file not shown.
@@ -1,278 +0,0 @@
|
||||
GNU GENERAL PUBLIC LICENSE
|
||||
Version 2, June 1991
|
||||
|
||||
Copyright (C) 1989, 1991 Free Software Foundation, Inc.,
|
||||
51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
Everyone is permitted to copy and distribute verbatim copies
|
||||
of this license document, but changing it is not allowed.
|
||||
|
||||
Preamble
|
||||
|
||||
The licenses for most software are designed to take away your
|
||||
freedom to share and change it. By contrast, the GNU General Public
|
||||
License is intended to guarantee your freedom to share and change free
|
||||
software--to make sure the software is free for all its users. This
|
||||
General Public License applies to most of the Free Software
|
||||
Foundation's software and to any other program whose authors commit to
|
||||
using it. (Some other Free Software Foundation software is covered by
|
||||
the GNU Lesser General Public License instead.) You can apply it to
|
||||
your programs, too.
|
||||
|
||||
When we speak of free software, we are referring to freedom, not
|
||||
price. Our General Public Licenses are designed to make sure that you
|
||||
have the freedom to distribute copies of free software (and charge for
|
||||
this service if you wish), that you receive source code or can get it
|
||||
if you want it, that you can change the software or use pieces of it
|
||||
in new free programs; and that you know you can do these things.
|
||||
|
||||
To protect your rights, we need to make restrictions that forbid
|
||||
anyone to deny you these rights or to ask you to surrender the rights.
|
||||
These restrictions translate to certain responsibilities for you if you
|
||||
distribute copies of the software, or if you modify it.
|
||||
|
||||
For example, if you distribute copies of such a program, whether
|
||||
gratis or for a fee, you must give the recipients all the rights that
|
||||
you have. You must make sure that they, too, receive or can get the
|
||||
source code. And you must show them these terms so they know their
|
||||
rights.
|
||||
|
||||
We protect your rights with two steps: (1) copyright the software, and
|
||||
(2) offer you this license which gives you legal permission to copy,
|
||||
distribute and/or modify the software.
|
||||
|
||||
Also, for each author's protection and ours, we want to make certain
|
||||
that everyone understands that there is no warranty for this free
|
||||
software. If the software is modified by someone else and passed on, we
|
||||
want its recipients to know that what they have is not the original, so
|
||||
that any problems introduced by others will not reflect on the original
|
||||
authors' reputations.
|
||||
|
||||
Finally, any free program is threatened constantly by software
|
||||
patents. We wish to avoid the danger that redistributors of a free
|
||||
program will individually obtain patent licenses, in effect making the
|
||||
program proprietary. To prevent this, we have made it clear that any
|
||||
patent must be licensed for everyone's free use or not licensed at all.
|
||||
|
||||
The precise terms and conditions for copying, distribution and
|
||||
modification follow.
|
||||
|
||||
GNU GENERAL PUBLIC LICENSE
|
||||
TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
|
||||
|
||||
0. This License applies to any program or other work which contains
|
||||
a notice placed by the copyright holder saying it may be distributed
|
||||
under the terms of this General Public License. The "Program", below,
|
||||
refers to any such program or work, and a "work based on the Program"
|
||||
means either the Program or any derivative work under copyright law:
|
||||
that is to say, a work containing the Program or a portion of it,
|
||||
either verbatim or with modifications and/or translated into another
|
||||
language. (Hereinafter, translation is included without limitation in
|
||||
the term "modification".) Each licensee is addressed as "you".
|
||||
|
||||
Activities other than copying, distribution and modification are not
|
||||
covered by this License; they are outside its scope. The act of
|
||||
running the Program is not restricted, and the output from the Program
|
||||
is covered only if its contents constitute a work based on the
|
||||
Program (independent of having been made by running the Program).
|
||||
Whether that is true depends on what the Program does.
|
||||
|
||||
1. You may copy and distribute verbatim copies of the Program's
|
||||
source code as you receive it, in any medium, provided that you
|
||||
conspicuously and appropriately publish on each copy an appropriate
|
||||
copyright notice and disclaimer of warranty; keep intact all the
|
||||
notices that refer to this License and to the absence of any warranty;
|
||||
and give any other recipients of the Program a copy of this License
|
||||
along with the Program.
|
||||
|
||||
You may charge a fee for the physical act of transferring a copy, and
|
||||
you may at your option offer warranty protection in exchange for a fee.
|
||||
|
||||
2. You may modify your copy or copies of the Program or any portion
|
||||
of it, thus forming a work based on the Program, and copy and
|
||||
distribute such modifications or work under the terms of Section 1
|
||||
above, provided that you also meet all of these conditions:
|
||||
|
||||
a) You must cause the modified files to carry prominent notices
|
||||
stating that you changed the files and the date of any change.
|
||||
|
||||
b) You must cause any work that you distribute or publish, that in
|
||||
whole or in part contains or is derived from the Program or any
|
||||
part thereof, to be licensed as a whole at no charge to all third
|
||||
parties under the terms of this License.
|
||||
|
||||
c) If the modified program normally reads commands interactively
|
||||
when run, you must cause it, when started running for such
|
||||
interactive use in the most ordinary way, to print or display an
|
||||
announcement including an appropriate copyright notice and a
|
||||
notice that there is no warranty (or else, saying that you provide
|
||||
a warranty) and that users may redistribute the program under
|
||||
these conditions, and telling the user how to view a copy of this
|
||||
License. (Exception: if the Program itself is interactive but
|
||||
does not normally print such an announcement, your work based on
|
||||
the Program is not required to print an announcement.)
|
||||
|
||||
These requirements apply to the modified work as a whole. If
|
||||
identifiable sections of that work are not derived from the Program,
|
||||
and can be reasonably considered independent and separate works in
|
||||
themselves, then this License, and its terms, do not apply to those
|
||||
sections when you distribute them as separate works. But when you
|
||||
distribute the same sections as part of a whole which is a work based
|
||||
on the Program, the distribution of the whole must be on the terms of
|
||||
this License, whose permissions for other licensees extend to the
|
||||
entire whole, and thus to each and every part regardless of who wrote it.
|
||||
|
||||
Thus, it is not the intent of this section to claim rights or contest
|
||||
your rights to work written entirely by you; rather, the intent is to
|
||||
exercise the right to control the distribution of derivative or
|
||||
collective works based on the Program.
|
||||
|
||||
In addition, mere aggregation of another work not based on the Program
|
||||
with the Program (or with a work based on the Program) on a volume of
|
||||
a storage or distribution medium does not bring the other work under
|
||||
the scope of this License.
|
||||
|
||||
3. You may copy and distribute the Program (or a work based on it,
|
||||
under Section 2) in object code or executable form under the terms of
|
||||
Sections 1 and 2 above provided that you also do one of the following:
|
||||
|
||||
a) Accompany it with the complete corresponding machine-readable
|
||||
source code, which must be distributed under the terms of Sections
|
||||
1 and 2 above on a medium customarily used for software interchange; or,
|
||||
|
||||
b) Accompany it with a written offer, valid for at least three
|
||||
years, to give any third party, for a charge no more than your
|
||||
cost of physically performing source distribution, a complete
|
||||
machine-readable copy of the corresponding source code, to be
|
||||
distributed under the terms of Sections 1 and 2 above on a medium
|
||||
customarily used for software interchange; or,
|
||||
|
||||
c) Accompany it with the information you received as to the offer
|
||||
to distribute corresponding source code. (This alternative is
|
||||
allowed only for noncommercial distribution and only if you
|
||||
received the program in object code or executable form with such
|
||||
an offer, in accord with Subsection b above.)
|
||||
|
||||
The source code for a work means the preferred form of the work for
|
||||
making modifications to it. For an executable work, complete source
|
||||
code means all the source code for all modules it contains, plus any
|
||||
associated interface definition files, plus the scripts used to
|
||||
control compilation and installation of the executable. However, as a
|
||||
special exception, the source code distributed need not include
|
||||
anything that is normally distributed (in either source or binary
|
||||
form) with the major components (compiler, kernel, and so on) of the
|
||||
operating system on which the executable runs, unless that component
|
||||
itself accompanies the executable.
|
||||
|
||||
If distribution of executable or object code is made by offering
|
||||
access to copy from a designated place, then offering equivalent
|
||||
access to copy the source code from the same place counts as
|
||||
distribution of the source code, even though third parties are not
|
||||
compelled to copy the source along with the object code.
|
||||
|
||||
4. You may not copy, modify, sublicense, or distribute the Program
|
||||
except as expressly provided under this License. Any attempt
|
||||
otherwise to copy, modify, sublicense or distribute the Program is
|
||||
void, and will automatically terminate your rights under this License.
|
||||
However, parties who have received copies, or rights, from you under
|
||||
this License will not have their licenses terminated so long as such
|
||||
parties remain in full compliance.
|
||||
|
||||
5. You are not required to accept this License, since you have not
|
||||
signed it. However, nothing else grants you permission to modify or
|
||||
distribute the Program or its derivative works. These actions are
|
||||
prohibited by law if you do not accept this License. Therefore, by
|
||||
modifying or distributing the Program (or any work based on the
|
||||
Program), you indicate your acceptance of this License to do so, and
|
||||
all its terms and conditions for copying, distributing or modifying
|
||||
the Program or works based on it.
|
||||
|
||||
6. Each time you redistribute the Program (or any work based on the
|
||||
Program), the recipient automatically receives a license from the
|
||||
original licensor to copy, distribute or modify the Program subject to
|
||||
these terms and conditions. You may not impose any further
|
||||
restrictions on the recipients' exercise of the rights granted herein.
|
||||
You are not responsible for enforcing compliance by third parties to
|
||||
this License.
|
||||
|
||||
7. If, as a consequence of a court judgment or allegation of patent
|
||||
infringement or for any other reason (not limited to patent issues),
|
||||
conditions are imposed on you (whether by court order, agreement or
|
||||
otherwise) that contradict the conditions of this License, they do not
|
||||
excuse you from the conditions of this License. If you cannot
|
||||
distribute so as to satisfy simultaneously your obligations under this
|
||||
License and any other pertinent obligations, then as a consequence you
|
||||
may not distribute the Program at all. For example, if a patent
|
||||
license would not permit royalty-free redistribution of the Program by
|
||||
all those who receive copies directly or indirectly through you, then
|
||||
the only way you could satisfy both it and this License would be to
|
||||
refrain entirely from distribution of the Program.
|
||||
|
||||
If any portion of this section is held invalid or unenforceable under
|
||||
any particular circumstance, the balance of the section is intended to
|
||||
apply and the section as a whole is intended to apply in other
|
||||
circumstances.
|
||||
|
||||
It is not the purpose of this section to induce you to infringe any
|
||||
patents or other property right claims or to contest validity of any
|
||||
such claims; this section has the sole purpose of protecting the
|
||||
integrity of the free software distribution system, which is
|
||||
implemented by public license practices. Many people have made
|
||||
generous contributions to the wide range of software distributed
|
||||
through that system in reliance on consistent application of that
|
||||
system; it is up to the author/donor to decide if he or she is willing
|
||||
to distribute software through any other system and a licensee cannot
|
||||
impose that choice.
|
||||
|
||||
This section is intended to make thoroughly clear what is believed to
|
||||
be a consequence of the rest of this License.
|
||||
|
||||
8. If the distribution and/or use of the Program is restricted in
|
||||
certain countries either by patents or by copyrighted interfaces, the
|
||||
original copyright holder who places the Program under this License
|
||||
may add an explicit geographical distribution limitation excluding
|
||||
those countries, so that distribution is permitted only in or among
|
||||
countries not thus excluded. In such case, this License incorporates
|
||||
the limitation as if written in the body of this License.
|
||||
|
||||
9. The Free Software Foundation may publish revised and/or new versions
|
||||
of the General Public License from time to time. Such new versions will
|
||||
be similar in spirit to the present version, but may differ in detail to
|
||||
address new problems or concerns.
|
||||
|
||||
Each version is given a distinguishing version number. If the Program
|
||||
specifies a version number of this License which applies to it and "any
|
||||
later version", you have the option of following the terms and conditions
|
||||
either of that version or of any later version published by the Free
|
||||
Software Foundation. If the Program does not specify a version number of
|
||||
this License, you may choose any version ever published by the Free Software
|
||||
Foundation.
|
||||
|
||||
10. If you wish to incorporate parts of the Program into other free
|
||||
programs whose distribution conditions are different, write to the author
|
||||
to ask for permission. For software which is copyrighted by the Free
|
||||
Software Foundation, write to the Free Software Foundation; we sometimes
|
||||
make exceptions for this. Our decision will be guided by the two goals
|
||||
of preserving the free status of all derivatives of our free software and
|
||||
of promoting the sharing and reuse of software generally.
|
||||
|
||||
NO WARRANTY
|
||||
|
||||
11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY
|
||||
FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN
|
||||
OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES
|
||||
PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED
|
||||
OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
|
||||
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS
|
||||
TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE
|
||||
PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING,
|
||||
REPAIR OR CORRECTION.
|
||||
|
||||
12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
|
||||
WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR
|
||||
REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES,
|
||||
INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING
|
||||
OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED
|
||||
TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY
|
||||
YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER
|
||||
PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE
|
||||
POSSIBILITY OF SUCH DAMAGES.
|
||||
@@ -1,499 +0,0 @@
|
||||
# Otter - Program made for educational intent, can be freely distributed
|
||||
# and can be used for economical intent. I will not take legal actions
|
||||
# unless my intelectual propperty, the code, is stolen or change without permission.
|
||||
#
|
||||
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
|
||||
#
|
||||
# This program is free software; you can redistribute it and/or modify
|
||||
# it under the terms of the GNU General Public License version 2 as published by
|
||||
# the Free Software Foundation.
|
||||
#
|
||||
# This program is distributed in the hope that it will be useful,
|
||||
# but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
# GNU General Public License for more details.
|
||||
#
|
||||
# You should have received a copy of the GNU General Public License along
|
||||
# with this program; if not, write to the Free Software Foundation, Inc.,
|
||||
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
|
||||
|
||||
import math
|
||||
import numpy as np
|
||||
import Seals
|
||||
|
||||
sl = Seals.method()
|
||||
|
||||
class Algebra:
|
||||
|
||||
def __init__(self, function):
|
||||
self.f = function
|
||||
self.integral = self.Integral(self.f)
|
||||
self.roots = self.Roots(self.f)
|
||||
self.edo = self.Edo(self.f)
|
||||
|
||||
def d(self, x, e):
|
||||
return (self.f(x + e) - self.f(x - e))/(2*e)
|
||||
|
||||
class Integral:
|
||||
|
||||
def __init__(self,function):
|
||||
self.f = function
|
||||
self.simple = self.Simple(function)
|
||||
self.double = self.Double(function)
|
||||
|
||||
class Simple:
|
||||
def __init__(self, function):
|
||||
self.f = function
|
||||
|
||||
def riemann(self,a,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
delta = (b-a)/n
|
||||
|
||||
psi = a
|
||||
theta = 0
|
||||
|
||||
while((psi+delta) <= b):
|
||||
|
||||
theta += (self.f(psi) + self.f(psi + delta))/2
|
||||
psi += delta
|
||||
|
||||
integral = delta*theta
|
||||
|
||||
return integral
|
||||
|
||||
def simpson(self,a,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
def x(i):
|
||||
return a + i*h
|
||||
|
||||
h = (b-a)/n
|
||||
|
||||
eta = 0
|
||||
theta = 0
|
||||
|
||||
psi = 1
|
||||
kappa = 1
|
||||
|
||||
while(psi <= (n/2)):
|
||||
|
||||
eta = eta + self.f(x(2*psi - 1))
|
||||
psi = psi + 1
|
||||
|
||||
while(kappa <= ((n/2)-1)):
|
||||
|
||||
theta = theta + self.f(x(2*kappa))
|
||||
kappa = kappa + 1
|
||||
|
||||
return (h/3)*( self.f(x(0)) + self.f(x(n)) + 4*eta + 2*theta)
|
||||
|
||||
|
||||
class Double:
|
||||
|
||||
def __init__(self,function):
|
||||
self.f = function
|
||||
|
||||
def riemann(self,a,b,c,d,n=None,m=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**4
|
||||
|
||||
if m is None:
|
||||
m = n
|
||||
|
||||
dx = (b-a)/n
|
||||
dy = (d-c)/m
|
||||
kappa = a
|
||||
psi = c
|
||||
theta = 0
|
||||
|
||||
while((psi + dy) < d):
|
||||
|
||||
while((kappa + dx) < b):
|
||||
|
||||
theta = theta + self.f(kappa, psi)
|
||||
kappa = kappa + dx
|
||||
|
||||
psi = psi + dy
|
||||
kappa = a
|
||||
|
||||
return theta*(dx)*(dy)
|
||||
|
||||
def simpson(self,a,b,c,d,n=None,m=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**4
|
||||
|
||||
if m is None:
|
||||
m = n
|
||||
|
||||
dx = (b-a)/n
|
||||
dy = (d-c)/m
|
||||
|
||||
def x(i):
|
||||
|
||||
x = a + i*dx
|
||||
|
||||
return x
|
||||
|
||||
def y(i):
|
||||
|
||||
y = c + i*dy
|
||||
|
||||
return y
|
||||
|
||||
def g(i):
|
||||
|
||||
sigma = 0
|
||||
upsilon = 0
|
||||
|
||||
zeta = 1
|
||||
csi = 1
|
||||
|
||||
while(zeta <= (m/2)):
|
||||
|
||||
sigma += self.f(x(i),y(2*zeta - 1))
|
||||
zeta += 1
|
||||
|
||||
while(csi <= ((m/2)-1)):
|
||||
|
||||
upsilon += self.f(x(i),y(2*csi))
|
||||
csi += 1
|
||||
|
||||
return (dy/3)*( self.f(x(i),y(0)) + self.f(x(i),y(m)) + 4*sigma + 2*upsilon )
|
||||
|
||||
eta = 0
|
||||
theta = 0
|
||||
|
||||
psi = 1
|
||||
kappa = 1
|
||||
|
||||
while(psi <= (n/2)):
|
||||
|
||||
eta += g(2*psi - 1)
|
||||
psi += 1
|
||||
|
||||
while(kappa <= ((n/2)-1)):
|
||||
|
||||
theta += g(2*kappa)
|
||||
kappa += 1
|
||||
|
||||
return (dx/3)*( g(0) + g(n) + 4*eta + 2*theta)
|
||||
|
||||
class Roots:
|
||||
|
||||
def __init__(self, function=None):
|
||||
if function is not None:
|
||||
self.f = function
|
||||
|
||||
def bissec(self,a,b,e=None):
|
||||
|
||||
if e is None:
|
||||
e = 10**(-6)
|
||||
|
||||
fa = self.f(a)
|
||||
|
||||
while abs(a-b) > e:
|
||||
|
||||
c = (a+b)/2
|
||||
fc = self.f(c)
|
||||
|
||||
if (fa*fc) < 0:
|
||||
|
||||
b = c
|
||||
|
||||
else:
|
||||
|
||||
a = c
|
||||
fa = fc
|
||||
|
||||
c = (a+b)/2
|
||||
|
||||
return c
|
||||
|
||||
def d(self, x, e):
|
||||
return (self.f(x + e) - self.f(x - e))/(2*e)
|
||||
|
||||
def newton(self,a,e=None):
|
||||
|
||||
if e is None:
|
||||
e = 10**(-6)
|
||||
|
||||
fa = self.f(a)
|
||||
da = self.d(a,e)
|
||||
b = a - fa/da
|
||||
|
||||
|
||||
while abs(a-b) > e:
|
||||
|
||||
b = a
|
||||
a -= (fa/da)
|
||||
fa = self.f(a)
|
||||
da = self.d(a,e)
|
||||
|
||||
return a
|
||||
|
||||
def bissec_newton(self,a,b,e=None):
|
||||
|
||||
if e is None:
|
||||
e = 10**(-6)
|
||||
|
||||
fa = self.f(a)
|
||||
|
||||
c = (a+b)/2 # 'c' é a raiz calculada
|
||||
|
||||
while abs(a-b) > 0.1:
|
||||
|
||||
fc = self.f(c)
|
||||
|
||||
if fa*fc < 0:
|
||||
|
||||
b = c
|
||||
|
||||
else:
|
||||
|
||||
a = c
|
||||
fa = self.f(a)
|
||||
|
||||
c = (a+b)/2
|
||||
|
||||
fc = self.f(c)
|
||||
dc = self.d(c,e)
|
||||
h = c - fc/dc # 'h' é uma variável de controle
|
||||
|
||||
while abs(c-h) > e:
|
||||
|
||||
h = c
|
||||
c -= (fc/dc)
|
||||
fc = self.f(c)
|
||||
dc = self.d(c,e)
|
||||
|
||||
return (c)
|
||||
|
||||
|
||||
class Edo:
|
||||
|
||||
def __init__(self, function):
|
||||
self.f = function
|
||||
|
||||
def euler(self,a,y,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**7
|
||||
|
||||
dx = (b-a)/n
|
||||
|
||||
def x(i):
|
||||
return a + i*dx
|
||||
|
||||
for i in range(n):
|
||||
|
||||
y = y + (self.f(x(i),y))*dx
|
||||
|
||||
return y
|
||||
|
||||
def runge(self,a,y,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**7
|
||||
|
||||
dx = (b-a)/n
|
||||
|
||||
def x(i):
|
||||
return (a + i*dx)
|
||||
|
||||
for i in range(n):
|
||||
|
||||
y = y + (dx/2)*(self.f(x(i),y)+self.f(x(i+1),(y+(dx*self.f(x(i),y)))))
|
||||
|
||||
return y
|
||||
|
||||
class Interpolation:
|
||||
""" Data should be organized in two columns: X and Y"""
|
||||
|
||||
def __init__(self, data):
|
||||
|
||||
self.data = data
|
||||
self.polinomial = self.Polinomial(self.data)
|
||||
|
||||
def minimus(self,x):
|
||||
|
||||
theta = 0
|
||||
# somatorio de x
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
theta += self.data[i][0]
|
||||
|
||||
eta = 0
|
||||
#somatorio de y
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
eta += self.data[i][1]
|
||||
|
||||
sigma = 0
|
||||
#somatorio de xy
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
sigma += self.data[i][0]*self.data[i][1]
|
||||
|
||||
omega = 0
|
||||
#somatorio de x^2
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
omega += self.data[i][0]**2
|
||||
|
||||
|
||||
self.a = (self.data.shape[0]*sigma - theta*eta)/(self.data.shape[0]*omega - (theta**2))
|
||||
|
||||
self.b = (theta*sigma - eta*omega)/((theta**2) - self.data.shape[0]*omega)
|
||||
|
||||
ym = 0
|
||||
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
ym += self.data[i][1]/self.data.shape[0]
|
||||
|
||||
sqreq = 0
|
||||
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
sqreq += ((self.a*self.data[i][0] + self.b) - ym)**2
|
||||
|
||||
sqtot = 0
|
||||
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
sqtot += (self.data[i][1] - ym)**2
|
||||
|
||||
self.r2 = sqreq/sqtot
|
||||
|
||||
return self.a*x + self.b
|
||||
|
||||
class Polinomial:
|
||||
|
||||
def __init__(self, data):
|
||||
self.data = data
|
||||
|
||||
def vandermonde(self, x):
|
||||
|
||||
matrix = np.zeros((self.data.shape[0],self.data.shape[0]))
|
||||
|
||||
for k in range(0, self.data.shape[0]):
|
||||
|
||||
matrix[:,k] = self.data[:,0]**k
|
||||
|
||||
self.A = sl.gauss(np.c_[matrix,self.data[:,1]])
|
||||
|
||||
y = 0
|
||||
|
||||
for i in range(0,self.A.shape[0]):
|
||||
|
||||
y += self.A[i]*(x**i)
|
||||
|
||||
return float(y)
|
||||
|
||||
def lagrange(self, x):
|
||||
|
||||
data_x = self.data[:,0]
|
||||
data_y = self.data[:,1]
|
||||
|
||||
def L(k,x):
|
||||
|
||||
up = down = 1
|
||||
|
||||
for i in [x for x in range(data_x.shape[0]) if x != k]:
|
||||
up = up*(x - data_x[i])
|
||||
|
||||
for i in [x for x in range(data_x.shape[0]) if x != k]:
|
||||
down = down*(data_x[k] - data_x[i])
|
||||
|
||||
return up/down
|
||||
|
||||
y = 0
|
||||
|
||||
for i in range(data_x.shape[0]):
|
||||
|
||||
y += data_y[i]*L(i,x)
|
||||
|
||||
return y
|
||||
|
||||
def newton(self,x):
|
||||
|
||||
d = np.array(np.zeros((self.data.shape[0],self.data.shape[0])))
|
||||
|
||||
d[0] = self.data[:,1]
|
||||
|
||||
i = j = 0
|
||||
|
||||
while (i < self.data.shape[0]):
|
||||
|
||||
while (j < (self.data.shape[0]-(i+1))):
|
||||
|
||||
d[i+1][j] = (d[i][j+1] - d[i][j])/(self.data[(i+1)+j][0]-self.data[j][0])
|
||||
j += 1
|
||||
|
||||
i += 1
|
||||
j = 0
|
||||
|
||||
def f(x):
|
||||
|
||||
y = d[0][0]
|
||||
i = 0
|
||||
|
||||
while ((i+1) < self.data.shape[0]):
|
||||
|
||||
mult = 1
|
||||
k = 0
|
||||
while (k <= i):
|
||||
mult = mult*(x - self.data[k][0])
|
||||
k += 1
|
||||
|
||||
y += d[i+1][0]*mult
|
||||
i += 1
|
||||
|
||||
return y
|
||||
|
||||
self.f = f
|
||||
|
||||
return f(x)
|
||||
|
||||
def gregory(self,x):
|
||||
|
||||
h = self.data[0][0] - self.data[1][0]
|
||||
|
||||
d = np.array(np.zeros((self.data.shape[0],self.data.shape[0])))
|
||||
|
||||
d[0] = self.data[:,1]
|
||||
|
||||
i = j = 0
|
||||
|
||||
while (i < self.data.shape[0]):
|
||||
|
||||
while (j < (self.data.shape[0]-(i+1))):
|
||||
|
||||
d[i+1][j] = (d[i][j+1] - d[i][j])/((i+1)*h)
|
||||
j += 1
|
||||
|
||||
i += 1
|
||||
j = 0
|
||||
|
||||
y = d[0][0]
|
||||
i = 0
|
||||
|
||||
while ((i+1) < self.data.shape[0]):
|
||||
|
||||
mult = 1
|
||||
k = 0
|
||||
while (k <= i):
|
||||
mult = mult*(x - self.data[k][0])
|
||||
k += 1
|
||||
|
||||
y += d[i+1][0]*mult
|
||||
i += 1
|
||||
|
||||
return y
|
||||
@@ -1,21 +0,0 @@
|
||||
# Otter - Program made for educational intent, can be freely distributed
|
||||
# and can be used for economical intent. I will not take legal actions
|
||||
# unless my intelectual propperty, the code, is stolen or change without permission.
|
||||
|
||||
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
|
||||
|
||||
# This program is free software; you can redistribute it and/or modify
|
||||
# it under the terms of the GNU General Public License version 2 as published by
|
||||
# the Free Software Foundation.
|
||||
|
||||
# This program is distributed in the hope that it will be useful,
|
||||
# but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
# GNU General Public License for more details.
|
||||
|
||||
# You should have received a copy of the GNU General Public License along
|
||||
# with this program; if not, write to the Free Software Foundation, Inc.,
|
||||
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
|
||||
|
||||
from .Otter import Algebra as algebra
|
||||
from .Otter import Interpolation as interpolation
|
||||
@@ -1,75 +0,0 @@
|
||||
# Otter - Numeric Calculus
|
||||
|
||||
This python package is made for applied Numeric Calculus of Algebra Functions. It is made with the following objectives in mind:
|
||||
|
||||
* Receive one variable function from user input
|
||||
|
||||
* Receive two variable function from user input
|
||||
|
||||
* Performe derivatives with one variable functions
|
||||
|
||||
* Performe integral with received functions
|
||||
|
||||
* Use methods to proccess the matrices.
|
||||
|
||||
* Find root of functions throw method of bissection and method of newton
|
||||
|
||||
* Solve Diferential Equations throw method of euler and runge
|
||||
|
||||
* Performe Minimus Interpolation and Polinomial Interpolation
|
||||
|
||||
## Syntax
|
||||
|
||||
To initialize a Otter instance linked to functions use the following syntax `otr = Otter.algebra(f)`, where `otr` will be a arbitrary name for the instance and `f` is a function of *one variable*.
|
||||
|
||||
To initialize a Otter instance linked to data and interpolation use the following syntax `otr = Otter.interpolation(data)`, where `otr` will be a arbitrary name for the instance and data will be a *numpy* matrix where the first columns has to contain the values for `x` and the second column contains the values for `y`.
|
||||
|
||||
### Algebra
|
||||
|
||||
Algebra is a Python Class where some of the features described previously are defined as Classes as well, like: `Integral`, `Roots`, `EDO` (diferential equations).
|
||||
|
||||
#### Integral
|
||||
|
||||
To call the class *Integral* append the sufix with lower case in front of the instance like: `otr.integral`. The Integral class has two other class defined inside, `Simple` and `Double`, to call them append the sufix with lower case in front as `otr.integral.simple` or `otr.integral.double`. Then pick between Riemann's Method or Simpson's Method by appending the sufix `riemann` or `simpson` as well.
|
||||
|
||||
After that the syntax will be something like `otr.integral.double.riemann(a,b,c,d,n,m)`, where `a` and `c` will be the first value of the interval of integration respectively in x and y, `b` and `d` will be the last, `n` and `m` will be the number of partitions.
|
||||
|
||||
The syntax for one variable integrations will be `otr.integral.simple.riemann(a,b,n)`.
|
||||
|
||||
If `n` is not defined the standart value in 10^6 partitions for one variable and 10^4 for double. And if `m` is not defined the standart value will be equal to `n`.
|
||||
|
||||
#### Roots
|
||||
|
||||
To call the class *Root* append the sufix with lower case in front of the instance like: `otr.roots`. The Roots class has three methods defined inside, `bissec`, `newton` and `bissec_newton`, to call them append the sufix with lower case in front as `otr.roots.bissec` or `otr.roots.newton` or even `otr.roots.bissecnewton`.
|
||||
|
||||
The syntax for the bissection method and bissec_newton is equal to `otr.roots.bissec(a,b,e)` and `otr.roots.bissec_newton(a,b,e)`, where `a` is the first element of the interval containing the root and `b` is the last, `e` being the precision.
|
||||
|
||||
The syntax for the newton method is equal to `otr.roots.newton(a,e)`, where `a` is the element closest to the root and `e` is the precision.
|
||||
|
||||
If `e` is not defined the standart value is 10^(-6).
|
||||
|
||||
#### Diferential Equations
|
||||
|
||||
To call the class *EDO* (*E*quações *D*iferenciais *O*rdinárias) append the sufix with lower case in front of the instance like: `otr.edo`. The *EDO* class has two methods defined inside: `euler` and `runge`, to call them append the sufix with lower case in front as `otr.edo.euler` or `otr.edo.runge`.
|
||||
|
||||
The syntax for the diferential equations method is equal to `otr.edo.euler(a,y,b,n)` or `otr.edo.runge(a,y,b,n)`, where `a` and `y` will be the inintial point and `b` is the value in *x* which you want to know the corresponding value in *y* and `n` is the number of operations.
|
||||
|
||||
If `n` is not defined the standart value is 10^7.
|
||||
|
||||
### Interpolation
|
||||
|
||||
The python class *Interpolation* is divided in one method, minimus interpolation, and one class, polinomial interpolation.
|
||||
|
||||
To call the method *minimus* use a syntax like `otr = Otter.interpolation(data)`, where `otr` is an instance and append the method in front of the instance like: `otr.minimus(x)`, where *x* is value of *f(x)* you want to estimate.
|
||||
|
||||
To call the class *Polinomial* append the sufix with lower case in front of the instance like: `otr.polinomial`. The *Polinomial* class has four methods defined inside: `vandermonde`, `lagrange`, `newton` and `gregory`, to call them append the sufix with lower case in front like `otr.edo.gregory(x)` where *x* is value of *f(x)* you want to estimate.
|
||||
|
||||
## Installation
|
||||
|
||||
To install the package from source `cd` into the directory and run:
|
||||
|
||||
`pip install .`
|
||||
|
||||
or run
|
||||
|
||||
`pip install yoshi-otter`
|
||||
@@ -1,480 +0,0 @@
|
||||
import math
|
||||
import numpy as np
|
||||
import Seals
|
||||
|
||||
sl = Seals.method()
|
||||
|
||||
class Algebra:
|
||||
|
||||
def __init__(self, function):
|
||||
self.f = function
|
||||
self.integral = self.Integral(self.f)
|
||||
self.roots = self.Roots(self.f)
|
||||
self.edo = self.Edo(self.f)
|
||||
|
||||
def d(self, x, e):
|
||||
return (self.f(x + e) - self.f(x - e))/(2*e)
|
||||
|
||||
class Integral:
|
||||
|
||||
def __init__(self,function):
|
||||
self.f = function
|
||||
self.simple = self.Simple(function)
|
||||
self.double = self.Double(function)
|
||||
|
||||
class Simple:
|
||||
def __init__(self, function):
|
||||
self.f = function
|
||||
|
||||
def riemann(self,a,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
delta = (b-a)/n
|
||||
|
||||
psi = a
|
||||
theta = 0
|
||||
|
||||
while((psi+delta) <= b):
|
||||
|
||||
theta += (self.f(psi) + self.f(psi + delta))/2
|
||||
psi += delta
|
||||
|
||||
integral = delta*theta
|
||||
|
||||
return integral
|
||||
|
||||
def simpson(self,a,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
def x(i):
|
||||
return a + i*h
|
||||
|
||||
h = (b-a)/n
|
||||
|
||||
eta = 0
|
||||
theta = 0
|
||||
|
||||
psi = 1
|
||||
kappa = 1
|
||||
|
||||
while(psi <= (n/2)):
|
||||
|
||||
eta = eta + self.f(x(2*psi - 1))
|
||||
psi = psi + 1
|
||||
|
||||
while(kappa <= ((n/2)-1)):
|
||||
|
||||
theta = theta + self.f(x(2*kappa))
|
||||
kappa = kappa + 1
|
||||
|
||||
return (h/3)*( self.f(x(0)) + self.f(x(n)) + 4*eta + 2*theta)
|
||||
|
||||
|
||||
class Double:
|
||||
|
||||
def __init__(self,function):
|
||||
self.f = function
|
||||
|
||||
def riemann(self,a,b,c,d,n=None,m=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**4
|
||||
|
||||
if m is None:
|
||||
m = n
|
||||
|
||||
dx = (b-a)/n
|
||||
dy = (d-c)/m
|
||||
kappa = a
|
||||
psi = c
|
||||
theta = 0
|
||||
|
||||
while((psi + dy) < d):
|
||||
|
||||
while((kappa + dx) < b):
|
||||
|
||||
theta = theta + self.f(kappa, psi)
|
||||
kappa = kappa + dx
|
||||
|
||||
psi = psi + dy
|
||||
kappa = a
|
||||
|
||||
return theta*(dx)*(dy)
|
||||
|
||||
def simpson(self,a,b,c,d,n=None,m=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**4
|
||||
|
||||
if m is None:
|
||||
m = n
|
||||
|
||||
dx = (b-a)/n
|
||||
dy = (d-c)/m
|
||||
|
||||
def x(i):
|
||||
|
||||
x = a + i*dx
|
||||
|
||||
return x
|
||||
|
||||
def y(i):
|
||||
|
||||
y = c + i*dy
|
||||
|
||||
return y
|
||||
|
||||
def g(i):
|
||||
|
||||
sigma = 0
|
||||
upsilon = 0
|
||||
|
||||
zeta = 1
|
||||
csi = 1
|
||||
|
||||
while(zeta <= (m/2)):
|
||||
|
||||
sigma += self.f(x(i),y(2*zeta - 1))
|
||||
zeta += 1
|
||||
|
||||
while(csi <= ((m/2)-1)):
|
||||
|
||||
upsilon += self.f(x(i),y(2*csi))
|
||||
csi += 1
|
||||
|
||||
return (dy/3)*( self.f(x(i),y(0)) + self.f(x(i),y(m)) + 4*sigma + 2*upsilon )
|
||||
|
||||
eta = 0
|
||||
theta = 0
|
||||
|
||||
psi = 1
|
||||
kappa = 1
|
||||
|
||||
while(psi <= (n/2)):
|
||||
|
||||
eta += g(2*psi - 1)
|
||||
psi += 1
|
||||
|
||||
while(kappa <= ((n/2)-1)):
|
||||
|
||||
theta += g(2*kappa)
|
||||
kappa += 1
|
||||
|
||||
return (dx/3)*( g(0) + g(n) + 4*eta + 2*theta)
|
||||
|
||||
class Roots:
|
||||
|
||||
def __init__(self, function=None):
|
||||
if function is not None:
|
||||
self.f = function
|
||||
|
||||
def bissec(self,a,b,e=None):
|
||||
|
||||
if e is None:
|
||||
e = 10**(-6)
|
||||
|
||||
fa = self.f(a)
|
||||
|
||||
while abs(a-b) > e:
|
||||
|
||||
c = (a+b)/2
|
||||
fc = self.f(c)
|
||||
|
||||
if (fa*fc) < 0:
|
||||
|
||||
b = c
|
||||
|
||||
else:
|
||||
|
||||
a = c
|
||||
fa = fc
|
||||
|
||||
c = (a+b)/2
|
||||
|
||||
return c
|
||||
|
||||
def d(self, x, e):
|
||||
return (self.f(x + e) - self.f(x - e))/(2*e)
|
||||
|
||||
def newton(self,a,e=None):
|
||||
|
||||
if e is None:
|
||||
e = 10**(-6)
|
||||
|
||||
fa = self.f(a)
|
||||
da = self.d(a,e)
|
||||
b = a - fa/da
|
||||
|
||||
|
||||
while abs(a-b) > e:
|
||||
|
||||
b = a
|
||||
a -= (fa/da)
|
||||
fa = self.f(a)
|
||||
da = self.d(a,e)
|
||||
|
||||
return a
|
||||
|
||||
def bissec_newton(self,a,b,e=None):
|
||||
|
||||
if e is None:
|
||||
e = 10**(-6)
|
||||
|
||||
fa = self.f(a)
|
||||
|
||||
c = (a+b)/2 # 'c' é a raiz calculada
|
||||
|
||||
while abs(a-b) > 0.1:
|
||||
|
||||
fc = self.f(c)
|
||||
|
||||
if fa*fc < 0:
|
||||
|
||||
b = c
|
||||
|
||||
else:
|
||||
|
||||
a = c
|
||||
fa = self.f(a)
|
||||
|
||||
c = (a+b)/2
|
||||
|
||||
fc = self.f(c)
|
||||
dc = self.d(c,e)
|
||||
h = c - fc/dc # 'h' é uma variável de controle
|
||||
|
||||
while abs(c-h) > e:
|
||||
|
||||
h = c
|
||||
c -= (fc/dc)
|
||||
fc = self.f(c)
|
||||
dc = self.d(c,e)
|
||||
|
||||
return (c)
|
||||
|
||||
|
||||
class Edo:
|
||||
|
||||
def __init__(self, function):
|
||||
self.f = function
|
||||
|
||||
def euler(self,a,y,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**7
|
||||
|
||||
dx = (b-a)/n
|
||||
|
||||
def x(i):
|
||||
return a + i*dx
|
||||
|
||||
for i in range(n):
|
||||
|
||||
y = y + (self.f(x(i),y))*dx
|
||||
|
||||
return y
|
||||
|
||||
def runge(self,a,y,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**7
|
||||
|
||||
dx = (b-a)/n
|
||||
|
||||
def x(i):
|
||||
return (a + i*dx)
|
||||
|
||||
for i in range(n):
|
||||
|
||||
y = y + (dx/2)*(self.f(x(i),y)+self.f(x(i+1),(y+(dx*self.f(x(i),y)))))
|
||||
|
||||
return y
|
||||
|
||||
class Interpolation:
|
||||
""" Data should be organized in two columns: X and Y"""
|
||||
|
||||
def __init__(self, data):
|
||||
|
||||
self.data = data
|
||||
self.polinomial = self.Polinomial(self.data)
|
||||
|
||||
def minimus(self,x):
|
||||
|
||||
theta = 0
|
||||
# somatorio de x
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
theta += self.data[i][0]
|
||||
|
||||
eta = 0
|
||||
#somatorio de y
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
eta += self.data[i][1]
|
||||
|
||||
sigma = 0
|
||||
#somatorio de xy
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
sigma += self.data[i][0]*self.data[i][1]
|
||||
|
||||
omega = 0
|
||||
#somatorio de x^2
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
omega += self.data[i][0]**2
|
||||
|
||||
|
||||
self.a = (self.data.shape[0]*sigma - theta*eta)/(self.data.shape[0]*omega - (theta**2))
|
||||
|
||||
self.b = (theta*sigma - eta*omega)/((theta**2) - self.data.shape[0]*omega)
|
||||
|
||||
ym = 0
|
||||
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
ym += self.data[i][1]/self.data.shape[0]
|
||||
|
||||
sqreq = 0
|
||||
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
sqreq += ((self.a*self.data[i][0] + self.b) - ym)**2
|
||||
|
||||
sqtot = 0
|
||||
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
sqtot += (self.data[i][1] - ym)**2
|
||||
|
||||
self.r2 = sqreq/sqtot
|
||||
|
||||
return self.a*x + self.b
|
||||
|
||||
class Polinomial:
|
||||
|
||||
def __init__(self, data):
|
||||
self.data = data
|
||||
|
||||
def vandermonde(self, x):
|
||||
|
||||
matrix = np.zeros((self.data.shape[0],self.data.shape[0]))
|
||||
|
||||
for k in range(0, self.data.shape[0]):
|
||||
|
||||
matrix[:,k] = self.data[:,0]**k
|
||||
|
||||
self.A = sl.gauss(np.c_[matrix,self.data[:,1]])
|
||||
|
||||
y = 0
|
||||
|
||||
for i in range(0,self.A.shape[0]):
|
||||
|
||||
y += self.A[i]*(x**i)
|
||||
|
||||
return float(y)
|
||||
|
||||
def lagrange(self, x):
|
||||
|
||||
data_x = self.data[:,0]
|
||||
data_y = self.data[:,1]
|
||||
|
||||
def L(k,x):
|
||||
|
||||
up = down = 1
|
||||
|
||||
for i in [x for x in range(data_x.shape[0]) if x != k]:
|
||||
up = up*(x - data_x[i])
|
||||
|
||||
for i in [x for x in range(data_x.shape[0]) if x != k]:
|
||||
down = down*(data_x[k] - data_x[i])
|
||||
|
||||
return up/down
|
||||
|
||||
y = 0
|
||||
|
||||
for i in range(data_x.shape[0]):
|
||||
|
||||
y += data_y[i]*L(i,x)
|
||||
|
||||
return y
|
||||
|
||||
def newton(self,x):
|
||||
|
||||
d = np.array(np.zeros((self.data.shape[0],self.data.shape[0])))
|
||||
|
||||
d[0] = self.data[:,1]
|
||||
|
||||
i = j = 0
|
||||
|
||||
while (i < self.data.shape[0]):
|
||||
|
||||
while (j < (self.data.shape[0]-(i+1))):
|
||||
|
||||
d[i+1][j] = (d[i][j+1] - d[i][j])/(self.data[(i+1)+j][0]-self.data[j][0])
|
||||
j += 1
|
||||
|
||||
i += 1
|
||||
j = 0
|
||||
|
||||
def f(x):
|
||||
|
||||
y = d[0][0]
|
||||
i = 0
|
||||
|
||||
while ((i+1) < self.data.shape[0]):
|
||||
|
||||
mult = 1
|
||||
k = 0
|
||||
while (k <= i):
|
||||
mult = mult*(x - self.data[k][0])
|
||||
k += 1
|
||||
|
||||
y += d[i+1][0]*mult
|
||||
i += 1
|
||||
|
||||
return y
|
||||
|
||||
self.f = f
|
||||
|
||||
return f(x)
|
||||
|
||||
def gregory(self,x):
|
||||
|
||||
h = self.data[0][0] - self.data[1][0]
|
||||
|
||||
d = np.array(np.zeros((self.data.shape[0],self.data.shape[0])))
|
||||
|
||||
d[0] = self.data[:,1]
|
||||
|
||||
i = j = 0
|
||||
|
||||
while (i < self.data.shape[0]):
|
||||
|
||||
while (j < (self.data.shape[0]-(i+1))):
|
||||
|
||||
d[i+1][j] = (d[i][j+1] - d[i][j])/((i+1)*h)
|
||||
j += 1
|
||||
|
||||
i += 1
|
||||
j = 0
|
||||
|
||||
y = d[0][0]
|
||||
i = 0
|
||||
|
||||
while ((i+1) < self.data.shape[0]):
|
||||
|
||||
mult = 1
|
||||
k = 0
|
||||
while (k <= i):
|
||||
mult = mult*(x - self.data[k][0])
|
||||
k += 1
|
||||
|
||||
y += d[i+1][0]*mult
|
||||
i += 1
|
||||
|
||||
return y
|
||||
@@ -1,2 +0,0 @@
|
||||
from .Otter import Algebra as algebra
|
||||
from .Otter import Interpolation as interpolation
|
||||
Binary file not shown.
Binary file not shown.
@@ -1,91 +0,0 @@
|
||||
Metadata-Version: 2.1
|
||||
Name: yoshi-otter
|
||||
Version: 1.1
|
||||
Summary: Numeric Calculus python module in the topic of Algebra Functions
|
||||
Home-page: https://github.com/HideyoshiNakazone/Otter-NumericCalculus.git
|
||||
Author: Vitor Hideyoshi
|
||||
Author-email: vitor.h.n.batista@gmail.com
|
||||
License: UNKNOWN
|
||||
Description: # Otter - Numeric Calculus
|
||||
|
||||
This python package is made for applied Numeric Calculus of Algebra Functions. It is made with the following objectives in mind:
|
||||
|
||||
* Receive one variable function from user input
|
||||
|
||||
* Receive two variable function from user input
|
||||
|
||||
* Performe derivatives with one variable functions
|
||||
|
||||
* Performe integral with received functions
|
||||
|
||||
* Use methods to proccess the matrices.
|
||||
|
||||
* Find root of functions throw method of bissection and method of newton
|
||||
|
||||
* Solve Diferential Equations throw method of euler and runge
|
||||
|
||||
* Performe Minimus Interpolation and Polinomial Interpolation
|
||||
|
||||
## Syntax
|
||||
|
||||
To initialize a Otter instance linked to functions use the following syntax `otr = Otter.algebra(f)`, where `otr` will be a arbitrary name for the instance and `f` is a function of *one variable*.
|
||||
|
||||
To initialize a Otter instance linked to data and interpolation use the following syntax `otr = Otter.interpolation(data)`, where `otr` will be a arbitrary name for the instance and data will be a *numpy* matrix where the first columns has to contain the values for `x` and the second column contains the values for `y`.
|
||||
|
||||
### Algebra
|
||||
|
||||
Algebra is a Python Class where some of the features described previously are defined as Classes as well, like: `Integral`, `Roots`, `EDO` (diferential equations).
|
||||
|
||||
#### Integral
|
||||
|
||||
To call the class *Integral* append the sufix with lower case in front of the instance like: `otr.integral`. The Integral class has two other class defined inside, `Simple` and `Double`, to call them append the sufix with lower case in front as `otr.integral.simple` or `otr.integral.double`. Then pick between Riemann's Method or Simpson's Method by appending the sufix `riemann` or `simpson` as well.
|
||||
|
||||
After that the syntax will be something like `otr.integral.double.riemann(a,b,c,d,n,m)`, where `a` and `c` will be the first value of the interval of integration respectively in x and y, `b` and `d` will be the last, `n` and `m` will be the number of partitions.
|
||||
|
||||
The syntax for one variable integrations will be `otr.integral.simple.riemann(a,b,n)`.
|
||||
|
||||
If `n` is not defined the standart value in 10^6 partitions for one variable and 10^4 for double. And if `m` is not defined the standart value will be equal to `n`.
|
||||
|
||||
#### Roots
|
||||
|
||||
To call the class *Root* append the sufix with lower case in front of the instance like: `otr.roots`. The Roots class has three methods defined inside, `bissec`, `newton` and `bissec_newton`, to call them append the sufix with lower case in front as `otr.roots.bissec` or `otr.roots.newton` or even `otr.roots.bissecnewton`.
|
||||
|
||||
The syntax for the bissection method and bissec_newton is equal to `otr.roots.bissec(a,b,e)` and `otr.roots.bissec_newton(a,b,e)`, where `a` is the first element of the interval containing the root and `b` is the last, `e` being the precision.
|
||||
|
||||
The syntax for the newton method is equal to `otr.roots.newton(a,e)`, where `a` is the element closest to the root and `e` is the precision.
|
||||
|
||||
If `e` is not defined the standart value is 10^(-6).
|
||||
|
||||
#### Diferential Equations
|
||||
|
||||
To call the class *EDO* (*E*quações *D*iferenciais *O*rdinárias) append the sufix with lower case in front of the instance like: `otr.edo`. The *EDO* class has two methods defined inside: `euler` and `runge`, to call them append the sufix with lower case in front as `otr.edo.euler` or `otr.edo.runge`.
|
||||
|
||||
The syntax for the diferential equations method is equal to `otr.edo.euler(a,y,b,n)` or `otr.edo.runge(a,y,b,n)`, where `a` and `y` will be the inintial point and `b` is the value in *x* which you want to know the corresponding value in *y* and `n` is the number of operations.
|
||||
|
||||
If `n` is not defined the standart value is 10^7.
|
||||
|
||||
### Interpolation
|
||||
|
||||
The python class *Interpolation* is divided in one method, minimus interpolation, and one class, polinomial interpolation.
|
||||
|
||||
To call the method *minimus* use a syntax like `otr = Otter.interpolation(data)`, where `otr` is an instance and append the method in front of the instance like: `otr.minimus(x)`, where *x* is value of *f(x)* you want to estimate.
|
||||
|
||||
To call the class *Polinomial* append the sufix with lower case in front of the instance like: `otr.polinomial`. The *Polinomial* class has four methods defined inside: `vandermonde`, `lagrange`, `newton` and `gregory`, to call them append the sufix with lower case in front like `otr.edo.gregory(x)` where *x* is value of *f(x)* you want to estimate.
|
||||
|
||||
## Installation
|
||||
|
||||
To install the package from source `cd` into the directory and run:
|
||||
|
||||
`pip install .`
|
||||
|
||||
or run
|
||||
|
||||
`pip install otter`
|
||||
|
||||
Platform: UNKNOWN
|
||||
Classifier: Programming Language :: Python :: 3
|
||||
Classifier: License :: OSI Approved :: GNU General Public License v2 (GPLv2)
|
||||
Classifier: Operating System :: OS Independent
|
||||
Classifier: Development Status :: 2 - Pre-Alpha
|
||||
Requires-Python: >=3.6
|
||||
Description-Content-Type: text/markdown
|
||||
@@ -1,9 +0,0 @@
|
||||
README.md
|
||||
setup.py
|
||||
Otter/Otter.py
|
||||
Otter/__init__.py
|
||||
yoshi_otter.egg-info/PKG-INFO
|
||||
yoshi_otter.egg-info/SOURCES.txt
|
||||
yoshi_otter.egg-info/dependency_links.txt
|
||||
yoshi_otter.egg-info/requires.txt
|
||||
yoshi_otter.egg-info/top_level.txt
|
||||
@@ -1,3 +0,0 @@
|
||||
numpy
|
||||
pandas
|
||||
yoshi-seals
|
||||
@@ -1 +0,0 @@
|
||||
Otter
|
||||
Binary file not shown.
@@ -1,278 +0,0 @@
|
||||
GNU GENERAL PUBLIC LICENSE
|
||||
Version 2, June 1991
|
||||
|
||||
Copyright (C) 1989, 1991 Free Software Foundation, Inc.,
|
||||
51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
Everyone is permitted to copy and distribute verbatim copies
|
||||
of this license document, but changing it is not allowed.
|
||||
|
||||
Preamble
|
||||
|
||||
The licenses for most software are designed to take away your
|
||||
freedom to share and change it. By contrast, the GNU General Public
|
||||
License is intended to guarantee your freedom to share and change free
|
||||
software--to make sure the software is free for all its users. This
|
||||
General Public License applies to most of the Free Software
|
||||
Foundation's software and to any other program whose authors commit to
|
||||
using it. (Some other Free Software Foundation software is covered by
|
||||
the GNU Lesser General Public License instead.) You can apply it to
|
||||
your programs, too.
|
||||
|
||||
When we speak of free software, we are referring to freedom, not
|
||||
price. Our General Public Licenses are designed to make sure that you
|
||||
have the freedom to distribute copies of free software (and charge for
|
||||
this service if you wish), that you receive source code or can get it
|
||||
if you want it, that you can change the software or use pieces of it
|
||||
in new free programs; and that you know you can do these things.
|
||||
|
||||
To protect your rights, we need to make restrictions that forbid
|
||||
anyone to deny you these rights or to ask you to surrender the rights.
|
||||
These restrictions translate to certain responsibilities for you if you
|
||||
distribute copies of the software, or if you modify it.
|
||||
|
||||
For example, if you distribute copies of such a program, whether
|
||||
gratis or for a fee, you must give the recipients all the rights that
|
||||
you have. You must make sure that they, too, receive or can get the
|
||||
source code. And you must show them these terms so they know their
|
||||
rights.
|
||||
|
||||
We protect your rights with two steps: (1) copyright the software, and
|
||||
(2) offer you this license which gives you legal permission to copy,
|
||||
distribute and/or modify the software.
|
||||
|
||||
Also, for each author's protection and ours, we want to make certain
|
||||
that everyone understands that there is no warranty for this free
|
||||
software. If the software is modified by someone else and passed on, we
|
||||
want its recipients to know that what they have is not the original, so
|
||||
that any problems introduced by others will not reflect on the original
|
||||
authors' reputations.
|
||||
|
||||
Finally, any free program is threatened constantly by software
|
||||
patents. We wish to avoid the danger that redistributors of a free
|
||||
program will individually obtain patent licenses, in effect making the
|
||||
program proprietary. To prevent this, we have made it clear that any
|
||||
patent must be licensed for everyone's free use or not licensed at all.
|
||||
|
||||
The precise terms and conditions for copying, distribution and
|
||||
modification follow.
|
||||
|
||||
GNU GENERAL PUBLIC LICENSE
|
||||
TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
|
||||
|
||||
0. This License applies to any program or other work which contains
|
||||
a notice placed by the copyright holder saying it may be distributed
|
||||
under the terms of this General Public License. The "Program", below,
|
||||
refers to any such program or work, and a "work based on the Program"
|
||||
means either the Program or any derivative work under copyright law:
|
||||
that is to say, a work containing the Program or a portion of it,
|
||||
either verbatim or with modifications and/or translated into another
|
||||
language. (Hereinafter, translation is included without limitation in
|
||||
the term "modification".) Each licensee is addressed as "you".
|
||||
|
||||
Activities other than copying, distribution and modification are not
|
||||
covered by this License; they are outside its scope. The act of
|
||||
running the Program is not restricted, and the output from the Program
|
||||
is covered only if its contents constitute a work based on the
|
||||
Program (independent of having been made by running the Program).
|
||||
Whether that is true depends on what the Program does.
|
||||
|
||||
1. You may copy and distribute verbatim copies of the Program's
|
||||
source code as you receive it, in any medium, provided that you
|
||||
conspicuously and appropriately publish on each copy an appropriate
|
||||
copyright notice and disclaimer of warranty; keep intact all the
|
||||
notices that refer to this License and to the absence of any warranty;
|
||||
and give any other recipients of the Program a copy of this License
|
||||
along with the Program.
|
||||
|
||||
You may charge a fee for the physical act of transferring a copy, and
|
||||
you may at your option offer warranty protection in exchange for a fee.
|
||||
|
||||
2. You may modify your copy or copies of the Program or any portion
|
||||
of it, thus forming a work based on the Program, and copy and
|
||||
distribute such modifications or work under the terms of Section 1
|
||||
above, provided that you also meet all of these conditions:
|
||||
|
||||
a) You must cause the modified files to carry prominent notices
|
||||
stating that you changed the files and the date of any change.
|
||||
|
||||
b) You must cause any work that you distribute or publish, that in
|
||||
whole or in part contains or is derived from the Program or any
|
||||
part thereof, to be licensed as a whole at no charge to all third
|
||||
parties under the terms of this License.
|
||||
|
||||
c) If the modified program normally reads commands interactively
|
||||
when run, you must cause it, when started running for such
|
||||
interactive use in the most ordinary way, to print or display an
|
||||
announcement including an appropriate copyright notice and a
|
||||
notice that there is no warranty (or else, saying that you provide
|
||||
a warranty) and that users may redistribute the program under
|
||||
these conditions, and telling the user how to view a copy of this
|
||||
License. (Exception: if the Program itself is interactive but
|
||||
does not normally print such an announcement, your work based on
|
||||
the Program is not required to print an announcement.)
|
||||
|
||||
These requirements apply to the modified work as a whole. If
|
||||
identifiable sections of that work are not derived from the Program,
|
||||
and can be reasonably considered independent and separate works in
|
||||
themselves, then this License, and its terms, do not apply to those
|
||||
sections when you distribute them as separate works. But when you
|
||||
distribute the same sections as part of a whole which is a work based
|
||||
on the Program, the distribution of the whole must be on the terms of
|
||||
this License, whose permissions for other licensees extend to the
|
||||
entire whole, and thus to each and every part regardless of who wrote it.
|
||||
|
||||
Thus, it is not the intent of this section to claim rights or contest
|
||||
your rights to work written entirely by you; rather, the intent is to
|
||||
exercise the right to control the distribution of derivative or
|
||||
collective works based on the Program.
|
||||
|
||||
In addition, mere aggregation of another work not based on the Program
|
||||
with the Program (or with a work based on the Program) on a volume of
|
||||
a storage or distribution medium does not bring the other work under
|
||||
the scope of this License.
|
||||
|
||||
3. You may copy and distribute the Program (or a work based on it,
|
||||
under Section 2) in object code or executable form under the terms of
|
||||
Sections 1 and 2 above provided that you also do one of the following:
|
||||
|
||||
a) Accompany it with the complete corresponding machine-readable
|
||||
source code, which must be distributed under the terms of Sections
|
||||
1 and 2 above on a medium customarily used for software interchange; or,
|
||||
|
||||
b) Accompany it with a written offer, valid for at least three
|
||||
years, to give any third party, for a charge no more than your
|
||||
cost of physically performing source distribution, a complete
|
||||
machine-readable copy of the corresponding source code, to be
|
||||
distributed under the terms of Sections 1 and 2 above on a medium
|
||||
customarily used for software interchange; or,
|
||||
|
||||
c) Accompany it with the information you received as to the offer
|
||||
to distribute corresponding source code. (This alternative is
|
||||
allowed only for noncommercial distribution and only if you
|
||||
received the program in object code or executable form with such
|
||||
an offer, in accord with Subsection b above.)
|
||||
|
||||
The source code for a work means the preferred form of the work for
|
||||
making modifications to it. For an executable work, complete source
|
||||
code means all the source code for all modules it contains, plus any
|
||||
associated interface definition files, plus the scripts used to
|
||||
control compilation and installation of the executable. However, as a
|
||||
special exception, the source code distributed need not include
|
||||
anything that is normally distributed (in either source or binary
|
||||
form) with the major components (compiler, kernel, and so on) of the
|
||||
operating system on which the executable runs, unless that component
|
||||
itself accompanies the executable.
|
||||
|
||||
If distribution of executable or object code is made by offering
|
||||
access to copy from a designated place, then offering equivalent
|
||||
access to copy the source code from the same place counts as
|
||||
distribution of the source code, even though third parties are not
|
||||
compelled to copy the source along with the object code.
|
||||
|
||||
4. You may not copy, modify, sublicense, or distribute the Program
|
||||
except as expressly provided under this License. Any attempt
|
||||
otherwise to copy, modify, sublicense or distribute the Program is
|
||||
void, and will automatically terminate your rights under this License.
|
||||
However, parties who have received copies, or rights, from you under
|
||||
this License will not have their licenses terminated so long as such
|
||||
parties remain in full compliance.
|
||||
|
||||
5. You are not required to accept this License, since you have not
|
||||
signed it. However, nothing else grants you permission to modify or
|
||||
distribute the Program or its derivative works. These actions are
|
||||
prohibited by law if you do not accept this License. Therefore, by
|
||||
modifying or distributing the Program (or any work based on the
|
||||
Program), you indicate your acceptance of this License to do so, and
|
||||
all its terms and conditions for copying, distributing or modifying
|
||||
the Program or works based on it.
|
||||
|
||||
6. Each time you redistribute the Program (or any work based on the
|
||||
Program), the recipient automatically receives a license from the
|
||||
original licensor to copy, distribute or modify the Program subject to
|
||||
these terms and conditions. You may not impose any further
|
||||
restrictions on the recipients' exercise of the rights granted herein.
|
||||
You are not responsible for enforcing compliance by third parties to
|
||||
this License.
|
||||
|
||||
7. If, as a consequence of a court judgment or allegation of patent
|
||||
infringement or for any other reason (not limited to patent issues),
|
||||
conditions are imposed on you (whether by court order, agreement or
|
||||
otherwise) that contradict the conditions of this License, they do not
|
||||
excuse you from the conditions of this License. If you cannot
|
||||
distribute so as to satisfy simultaneously your obligations under this
|
||||
License and any other pertinent obligations, then as a consequence you
|
||||
may not distribute the Program at all. For example, if a patent
|
||||
license would not permit royalty-free redistribution of the Program by
|
||||
all those who receive copies directly or indirectly through you, then
|
||||
the only way you could satisfy both it and this License would be to
|
||||
refrain entirely from distribution of the Program.
|
||||
|
||||
If any portion of this section is held invalid or unenforceable under
|
||||
any particular circumstance, the balance of the section is intended to
|
||||
apply and the section as a whole is intended to apply in other
|
||||
circumstances.
|
||||
|
||||
It is not the purpose of this section to induce you to infringe any
|
||||
patents or other property right claims or to contest validity of any
|
||||
such claims; this section has the sole purpose of protecting the
|
||||
integrity of the free software distribution system, which is
|
||||
implemented by public license practices. Many people have made
|
||||
generous contributions to the wide range of software distributed
|
||||
through that system in reliance on consistent application of that
|
||||
system; it is up to the author/donor to decide if he or she is willing
|
||||
to distribute software through any other system and a licensee cannot
|
||||
impose that choice.
|
||||
|
||||
This section is intended to make thoroughly clear what is believed to
|
||||
be a consequence of the rest of this License.
|
||||
|
||||
8. If the distribution and/or use of the Program is restricted in
|
||||
certain countries either by patents or by copyrighted interfaces, the
|
||||
original copyright holder who places the Program under this License
|
||||
may add an explicit geographical distribution limitation excluding
|
||||
those countries, so that distribution is permitted only in or among
|
||||
countries not thus excluded. In such case, this License incorporates
|
||||
the limitation as if written in the body of this License.
|
||||
|
||||
9. The Free Software Foundation may publish revised and/or new versions
|
||||
of the General Public License from time to time. Such new versions will
|
||||
be similar in spirit to the present version, but may differ in detail to
|
||||
address new problems or concerns.
|
||||
|
||||
Each version is given a distinguishing version number. If the Program
|
||||
specifies a version number of this License which applies to it and "any
|
||||
later version", you have the option of following the terms and conditions
|
||||
either of that version or of any later version published by the Free
|
||||
Software Foundation. If the Program does not specify a version number of
|
||||
this License, you may choose any version ever published by the Free Software
|
||||
Foundation.
|
||||
|
||||
10. If you wish to incorporate parts of the Program into other free
|
||||
programs whose distribution conditions are different, write to the author
|
||||
to ask for permission. For software which is copyrighted by the Free
|
||||
Software Foundation, write to the Free Software Foundation; we sometimes
|
||||
make exceptions for this. Our decision will be guided by the two goals
|
||||
of preserving the free status of all derivatives of our free software and
|
||||
of promoting the sharing and reuse of software generally.
|
||||
|
||||
NO WARRANTY
|
||||
|
||||
11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY
|
||||
FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN
|
||||
OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES
|
||||
PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED
|
||||
OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
|
||||
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS
|
||||
TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE
|
||||
PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING,
|
||||
REPAIR OR CORRECTION.
|
||||
|
||||
12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
|
||||
WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR
|
||||
REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES,
|
||||
INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING
|
||||
OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED
|
||||
TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY
|
||||
YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER
|
||||
PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE
|
||||
POSSIBILITY OF SUCH DAMAGES.
|
||||
@@ -1,517 +0,0 @@
|
||||
# Otter - Program made for educational intent, can be freely distributed
|
||||
# and can be used for economical intent. I will not take legal actions
|
||||
# unless my intelectual propperty, the code, is stolen or change without permission.
|
||||
#
|
||||
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
|
||||
#
|
||||
# This program is free software; you can redistribute it and/or modify
|
||||
# it under the terms of the GNU General Public License version 2 as published by
|
||||
# the Free Software Foundation.
|
||||
#
|
||||
# This program is distributed in the hope that it will be useful,
|
||||
# but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
# GNU General Public License for more details.
|
||||
#
|
||||
# You should have received a copy of the GNU General Public License along
|
||||
# with this program; if not, write to the Free Software Foundation, Inc.,
|
||||
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
|
||||
|
||||
import math
|
||||
import numpy as np
|
||||
import pandas as pd
|
||||
import Seals
|
||||
|
||||
sl = Seals.process()
|
||||
|
||||
class Algebra:
|
||||
|
||||
def __init__(self, function):
|
||||
self.f = function
|
||||
self.integral = self.Integral(self.f)
|
||||
self.roots = self.Roots(self.f)
|
||||
self.edo = self.Edo(self.f)
|
||||
|
||||
def d(self, x, e):
|
||||
return (self.f(x + e) - self.f(x - e))/(2*e)
|
||||
|
||||
class Integral:
|
||||
|
||||
def __init__(self,function):
|
||||
self.f = function
|
||||
self.simple = self.Simple(function)
|
||||
self.double = self.Double(function)
|
||||
|
||||
class Simple:
|
||||
def __init__(self, function):
|
||||
self.f = function
|
||||
|
||||
def riemann(self,a,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
delta = (b-a)/n
|
||||
|
||||
psi = a
|
||||
theta = 0
|
||||
|
||||
while((psi+delta) <= b):
|
||||
|
||||
theta += (self.f(psi) + self.f(psi + delta))/2
|
||||
psi += delta
|
||||
|
||||
integral = delta*theta
|
||||
|
||||
return integral
|
||||
|
||||
def simpson(self,a,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
def x(i):
|
||||
return a + i*h
|
||||
|
||||
h = (b-a)/n
|
||||
|
||||
eta = 0
|
||||
theta = 0
|
||||
|
||||
psi = 1
|
||||
kappa = 1
|
||||
|
||||
while(psi <= (n/2)):
|
||||
|
||||
eta = eta + self.f(x(2*psi - 1))
|
||||
psi = psi + 1
|
||||
|
||||
while(kappa <= ((n/2)-1)):
|
||||
|
||||
theta = theta + self.f(x(2*kappa))
|
||||
kappa = kappa + 1
|
||||
|
||||
return (h/3)*( self.f(x(0)) + self.f(x(n)) + 4*eta + 2*theta)
|
||||
|
||||
|
||||
class Double:
|
||||
|
||||
def __init__(self,function):
|
||||
self.f = function
|
||||
|
||||
def riemann(self,a,b,c,d,n=None,m=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**4
|
||||
|
||||
if m is None:
|
||||
m = n
|
||||
|
||||
dx = (b-a)/n
|
||||
dy = (d-c)/m
|
||||
kappa = a
|
||||
psi = c
|
||||
theta = 0
|
||||
|
||||
while((psi + dy) < d):
|
||||
|
||||
while((kappa + dx) < b):
|
||||
|
||||
theta = theta + self.f(kappa, psi)
|
||||
kappa = kappa + dx
|
||||
|
||||
psi = psi + dy
|
||||
kappa = a
|
||||
|
||||
return theta*(dx)*(dy)
|
||||
|
||||
def simpson(self,a,b,c,d,n=None,m=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**4
|
||||
|
||||
if m is None:
|
||||
m = n
|
||||
|
||||
dx = (b-a)/n
|
||||
dy = (d-c)/m
|
||||
|
||||
def x(i):
|
||||
|
||||
x = a + i*dx
|
||||
|
||||
return x
|
||||
|
||||
def y(i):
|
||||
|
||||
y = c + i*dy
|
||||
|
||||
return y
|
||||
|
||||
def g(i):
|
||||
|
||||
sigma = 0
|
||||
upsilon = 0
|
||||
|
||||
zeta = 1
|
||||
csi = 1
|
||||
|
||||
while(zeta <= (m/2)):
|
||||
|
||||
sigma += self.f(x(i),y(2*zeta - 1))
|
||||
zeta += 1
|
||||
|
||||
while(csi <= ((m/2)-1)):
|
||||
|
||||
upsilon += self.f(x(i),y(2*csi))
|
||||
csi += 1
|
||||
|
||||
return (dy/3)*( self.f(x(i),y(0)) + self.f(x(i),y(m)) + 4*sigma + 2*upsilon )
|
||||
|
||||
eta = 0
|
||||
theta = 0
|
||||
|
||||
psi = 1
|
||||
kappa = 1
|
||||
|
||||
while(psi <= (n/2)):
|
||||
|
||||
eta += g(2*psi - 1)
|
||||
psi += 1
|
||||
|
||||
while(kappa <= ((n/2)-1)):
|
||||
|
||||
theta += g(2*kappa)
|
||||
kappa += 1
|
||||
|
||||
return (dx/3)*( g(0) + g(n) + 4*eta + 2*theta)
|
||||
|
||||
class Roots:
|
||||
|
||||
def __init__(self, function=None):
|
||||
if function is not None:
|
||||
self.f = function
|
||||
|
||||
def bissec(self,a,b,e=None):
|
||||
|
||||
if e is None:
|
||||
e = 10**(-6)
|
||||
|
||||
fa = self.f(a)
|
||||
|
||||
while abs(a-b) > e:
|
||||
|
||||
c = (a+b)/2
|
||||
fc = self.f(c)
|
||||
|
||||
if (fa*fc) < 0:
|
||||
|
||||
b = c
|
||||
|
||||
else:
|
||||
|
||||
a = c
|
||||
fa = fc
|
||||
|
||||
c = (a+b)/2
|
||||
|
||||
return c
|
||||
|
||||
def d(self, x, e):
|
||||
return (self.f(x + e) - self.f(x - e))/(2*e)
|
||||
|
||||
def newton(self,a,e=None):
|
||||
|
||||
if e is None:
|
||||
e = 10**(-6)
|
||||
|
||||
fa = self.f(a)
|
||||
da = self.d(a,e)
|
||||
b = a - fa/da
|
||||
|
||||
|
||||
while abs(a-b) > e:
|
||||
|
||||
b = a
|
||||
a -= (fa/da)
|
||||
fa = self.f(a)
|
||||
da = self.d(a,e)
|
||||
|
||||
return a
|
||||
|
||||
def bissec_newton(self,a,b,e=None):
|
||||
|
||||
if e is None:
|
||||
e = 10**(-6)
|
||||
|
||||
fa = self.f(a)
|
||||
|
||||
c = (a+b)/2 # 'c' é a raiz calculada
|
||||
|
||||
while abs(a-b) > 0.1:
|
||||
|
||||
fc = self.f(c)
|
||||
|
||||
if fa*fc < 0:
|
||||
|
||||
b = c
|
||||
|
||||
else:
|
||||
|
||||
a = c
|
||||
fa = self.f(a)
|
||||
|
||||
c = (a+b)/2
|
||||
|
||||
fc = self.f(c)
|
||||
dc = self.d(c,e)
|
||||
h = c - fc/dc # 'h' é uma variável de controle
|
||||
|
||||
while abs(c-h) > e:
|
||||
|
||||
h = c
|
||||
c -= (fc/dc)
|
||||
fc = self.f(c)
|
||||
dc = self.d(c,e)
|
||||
|
||||
return (c)
|
||||
|
||||
|
||||
class Edo:
|
||||
|
||||
def __init__(self, function):
|
||||
self.F = function
|
||||
|
||||
def euler(self,a,y,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
dx = (b-a)/n
|
||||
|
||||
def x(i):
|
||||
return a + i*dx
|
||||
|
||||
for i in range(n):
|
||||
|
||||
y = y + (self.F(x(i),y))*dx
|
||||
|
||||
return y
|
||||
|
||||
def runge(self,a,y,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
dx = (b-a)/n
|
||||
|
||||
def x(i):
|
||||
return (a + i*dx)
|
||||
|
||||
for i in range(n):
|
||||
|
||||
y = y + (dx/2)*(self.F(x(i),y)+self.F(x(i+1),(y+(dx*self.F(x(i),y)))))
|
||||
|
||||
return y
|
||||
|
||||
def adams(self,a,y,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
dx = (b-a)/n
|
||||
|
||||
def x(i):
|
||||
return (a + i*dx)
|
||||
|
||||
for i in range(n):
|
||||
|
||||
f0 = self.F(x(i),y)
|
||||
f1 = self.F(x(i+1),y + dx*self.F(x(i)+(dx/2),y+(dx/2)*self.F(x(i),y)))
|
||||
f2 = self.F(x(i+2),y + (dx/2)*(3*f1-f0))
|
||||
|
||||
y += (dx/12)*(5*f2 + 8*f1 - f0)
|
||||
|
||||
return y
|
||||
|
||||
class Interpolation:
|
||||
""" Data should be organized in two columns: X and Y"""
|
||||
|
||||
def __init__(self, data):
|
||||
|
||||
self.data = data
|
||||
self.polinomial = self.Polinomial(self.data)
|
||||
|
||||
def minimus(self,x):
|
||||
|
||||
theta = 0
|
||||
# somatorio de x
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
theta += self.data.x[i]
|
||||
|
||||
eta = 0
|
||||
#somatorio de y
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
eta += self.data.y[i]
|
||||
|
||||
sigma = 0
|
||||
#somatorio de xy
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
sigma += self.data.x[i]*self.data.y[i]
|
||||
|
||||
omega = 0
|
||||
#somatorio de x^2self.dself.dself.d
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
omega += self.data.x[i]**2
|
||||
|
||||
|
||||
self.a = (self.data.shape[0]*sigma - theta*eta)/(self.data.shape[0]*omega - (theta**2))
|
||||
|
||||
self.b = (theta*sigma - eta*omega)/((theta**2) - self.data.shape[0]*omega)
|
||||
|
||||
ym = 0
|
||||
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
ym += self.data.y[i]/self.data.shape[0]
|
||||
|
||||
sqreq = 0
|
||||
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
sqreq += ((self.a*self.data.x[i] + self.b) - ym)**2
|
||||
|
||||
sqtot = 0
|
||||
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
sqtot += (self.data.y[i] - ym)**2
|
||||
|
||||
self.r2 = sqreq/sqtot
|
||||
|
||||
return self.a*x + self.b
|
||||
|
||||
class Polinomial:
|
||||
|
||||
def __init__(self, data):
|
||||
self.data = data
|
||||
|
||||
def vandermonde(self, x):
|
||||
|
||||
matrix = np.zeros((self.data.shape[0],self.data.shape[0]))
|
||||
|
||||
for k in range(0, self.data.shape[0]):
|
||||
|
||||
matrix[:,k] = self.data.x[:]**k
|
||||
|
||||
self.A = sl.gauss(np.c_[matrix,self.data[:,1]])
|
||||
|
||||
y = 0
|
||||
|
||||
for i in range(0,self.A.shape[0]):
|
||||
|
||||
y += self.A[i]*(x**i)
|
||||
|
||||
return float(y)
|
||||
|
||||
def lagrange(self, x):
|
||||
|
||||
def L(k,x):
|
||||
|
||||
up = down = 1
|
||||
|
||||
for i in [x for x in range(self.data.x.shape[0]) if x != k]:
|
||||
up = up*(x - self.data.x[i])
|
||||
|
||||
for i in [x for x in range(self.data.x.shape[0]) if x != k]:
|
||||
down = down*(self.data.x[k] - self.data.x[i])
|
||||
|
||||
return up/down
|
||||
|
||||
y = 0
|
||||
|
||||
for i in range(self.data.x.shape[0]):
|
||||
|
||||
y += self.data.y[i]*L(i,x)
|
||||
|
||||
return y
|
||||
|
||||
def newton(self,x):
|
||||
|
||||
d = np.array(np.zeros((self.data.shape[0],self.data.shape[0])))
|
||||
|
||||
d[0] = self.data.y
|
||||
|
||||
i = j = 0
|
||||
|
||||
while (i < self.data.shape[0]):
|
||||
|
||||
while (j < (self.data.shape[0]-(i+1))):
|
||||
|
||||
d[i+1][j] = (d[i][j+1] - d[i][j])/(self.data.x[(i+1)+j]-self.data.x[j])
|
||||
j += 1
|
||||
|
||||
i += 1
|
||||
j = 0
|
||||
|
||||
def f(x):
|
||||
|
||||
y = d[0][0]
|
||||
i = 0
|
||||
|
||||
while ((i+1) < self.data.shape[0]):
|
||||
|
||||
mult = 1
|
||||
k = 0
|
||||
while (k <= i):
|
||||
mult = mult*(x - self.data.x[k])
|
||||
k += 1
|
||||
|
||||
y += d[i+1][0]*mult
|
||||
i += 1
|
||||
|
||||
return y
|
||||
|
||||
self.f = f
|
||||
|
||||
return f(x)
|
||||
|
||||
def gregory(self,x):
|
||||
|
||||
h = self.data.x[0] - self.data.x[1]
|
||||
|
||||
d = np.array(np.zeros((self.data.shape[0],self.data.shape[0])))
|
||||
|
||||
d[0] = self.data.y
|
||||
|
||||
i = j = 0
|
||||
|
||||
while (i < self.data.shape[0]):
|
||||
|
||||
while (j < (self.data.shape[0]-(i+1))):
|
||||
|
||||
d[i+1][j] = (d[i][j+1] - d[i][j])/((i+1)*h)
|
||||
j += 1
|
||||
|
||||
i += 1
|
||||
j = 0
|
||||
|
||||
y = d[0][0]
|
||||
i = 0
|
||||
|
||||
while ((i+1) < self.data.shape[0]):
|
||||
|
||||
mult = 1
|
||||
k = 0
|
||||
while (k <= i):
|
||||
mult = mult*(x - self.data.x[k])
|
||||
k += 1
|
||||
|
||||
y += d[i+1][0]*mult
|
||||
i += 1
|
||||
|
||||
return y
|
||||
@@ -1,21 +0,0 @@
|
||||
# Otter - Program made for educational intent, can be freely distributed
|
||||
# and can be used for economical intent. I will not take legal actions
|
||||
# unless my intelectual propperty, the code, is stolen or change without permission.
|
||||
|
||||
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
|
||||
|
||||
# This program is free software; you can redistribute it and/or modify
|
||||
# it under the terms of the GNU General Public License version 2 as published by
|
||||
# the Free Software Foundation.
|
||||
|
||||
# This program is distributed in the hope that it will be useful,
|
||||
# but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
# GNU General Public License for more details.
|
||||
|
||||
# You should have received a copy of the GNU General Public License along
|
||||
# with this program; if not, write to the Free Software Foundation, Inc.,
|
||||
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
|
||||
|
||||
from .Otter import Algebra as algebra
|
||||
from .Otter import Interpolation as interpolation
|
||||
@@ -1,75 +0,0 @@
|
||||
# Otter - Numeric Calculus
|
||||
|
||||
This python package is made for applied Numeric Calculus of Algebra Functions. It is made with the following objectives in mind:
|
||||
|
||||
* Receive one variable function from user input
|
||||
|
||||
* Receive two variable function from user input
|
||||
|
||||
* Performe derivatives with one variable functions
|
||||
|
||||
* Performe integral with received functions
|
||||
|
||||
* Use methods to proccess the matrices.
|
||||
|
||||
* Find root of functions throw method of bissection and method of newton
|
||||
|
||||
* Solve Diferential Equations throw method of euler and runge
|
||||
|
||||
* Performe Minimus Interpolation and Polinomial Interpolation
|
||||
|
||||
## Syntax
|
||||
|
||||
To initialize a Otter instance linked to functions use the following syntax `otr = Otter.algebra(f)`, where `otr` will be a arbitrary name for the instance and `f` is a function of *one variable*.
|
||||
|
||||
To initialize a Otter instance linked to data and interpolation use the following syntax `otr = Otter.interpolation(data)`, where `otr` will be a arbitrary name for the instance and data will be a *numpy* matrix where the first columns has to contain the values for `x` and the second column contains the values for `y`.
|
||||
|
||||
### Algebra
|
||||
|
||||
Algebra is a Python Class where some of the features described previously are defined as Classes as well, like: `Integral`, `Roots`, `EDO` (diferential equations).
|
||||
|
||||
#### Integral
|
||||
|
||||
To call the class *Integral* append the sufix with lower case in front of the instance like: `otr.integral`. The Integral class has two other class defined inside, `Simple` and `Double`, to call them append the sufix with lower case in front as `otr.integral.simple` or `otr.integral.double`. Then pick between Riemann's Method or Simpson's Method by appending the sufix `riemann` or `simpson` as well.
|
||||
|
||||
After that the syntax will be something like `otr.integral.double.riemann(a,b,c,d,n,m)`, where `a` and `c` will be the first value of the interval of integration respectively in x and y, `b` and `d` will be the last, `n` and `m` will be the number of partitions.
|
||||
|
||||
The syntax for one variable integrations will be `otr.integral.simple.riemann(a,b,n)`.
|
||||
|
||||
If `n` is not defined the standart value in 10^6 partitions for one variable and 10^4 for double. And if `m` is not defined the standart value will be equal to `n`.
|
||||
|
||||
#### Roots
|
||||
|
||||
To call the class *Root* append the sufix with lower case in front of the instance like: `otr.roots`. The Roots class has three methods defined inside, `bissec`, `newton` and `bissec_newton`, to call them append the sufix with lower case in front as `otr.roots.bissec` or `otr.roots.newton` or even `otr.roots.bissecnewton`.
|
||||
|
||||
The syntax for the bissection method and bissec_newton is equal to `otr.roots.bissec(a,b,e)` and `otr.roots.bissec_newton(a,b,e)`, where `a` is the first element of the interval containing the root and `b` is the last, `e` being the precision.
|
||||
|
||||
The syntax for the newton method is equal to `otr.roots.newton(a,e)`, where `a` is the element closest to the root and `e` is the precision.
|
||||
|
||||
If `e` is not defined the standart value is 10^(-6).
|
||||
|
||||
#### Diferential Equations
|
||||
|
||||
To call the class *EDO* (*E*quações *D*iferenciais *O*rdinárias) append the sufix with lower case in front of the instance like: `otr.edo`. The *EDO* class has two methods defined inside: `euler` and `runge`, to call them append the sufix with lower case in front as `otr.edo.euler` or `otr.edo.runge`.
|
||||
|
||||
The syntax for the diferential equations method is equal to `otr.edo.euler(a,y,b,n)` or `otr.edo.runge(a,y,b,n)`, where `a` and `y` will be the inintial point and `b` is the value in *x* which you want to know the corresponding value in *y* and `n` is the number of operations.
|
||||
|
||||
If `n` is not defined the standart value is 10^7.
|
||||
|
||||
### Interpolation
|
||||
|
||||
The python class *Interpolation* is divided in one method, minimus interpolation, and one class, polinomial interpolation.
|
||||
|
||||
To call the method *minimus* use a syntax like `otr = Otter.interpolation(data)`, where `data` is a data frame containing values for *x* and *y*, `otr` is an instance and append the method in front of the instance like: `otr.minimus(x)`, where *x* is value of *f(x)* you want to estimate.
|
||||
|
||||
To call the class *Polinomial* append the sufix with lower case in front of the instance like: `otr.polinomial`. The *Polinomial* class has four methods defined inside: `vandermonde`, `lagrange`, `newton` and `gregory`, to call them append the sufix with lower case in front like `otr.edo.gregory(x)` where *x* is value of *f(x)* you want to estimate.
|
||||
|
||||
## Installation
|
||||
|
||||
To install the package from source `cd` into the directory and run:
|
||||
|
||||
`pip install .`
|
||||
|
||||
or run
|
||||
|
||||
`pip install yoshi-otter`
|
||||
@@ -1,517 +0,0 @@
|
||||
# Otter - Program made for educational intent, can be freely distributed
|
||||
# and can be used for economical intent. I will not take legal actions
|
||||
# unless my intelectual propperty, the code, is stolen or change without permission.
|
||||
#
|
||||
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
|
||||
#
|
||||
# This program is free software; you can redistribute it and/or modify
|
||||
# it under the terms of the GNU General Public License version 2 as published by
|
||||
# the Free Software Foundation.
|
||||
#
|
||||
# This program is distributed in the hope that it will be useful,
|
||||
# but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
# GNU General Public License for more details.
|
||||
#
|
||||
# You should have received a copy of the GNU General Public License along
|
||||
# with this program; if not, write to the Free Software Foundation, Inc.,
|
||||
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
|
||||
|
||||
import math
|
||||
import numpy as np
|
||||
import pandas as pd
|
||||
import Seals
|
||||
|
||||
sl = Seals.process()
|
||||
|
||||
class Algebra:
|
||||
|
||||
def __init__(self, function):
|
||||
self.f = function
|
||||
self.integral = self.Integral(self.f)
|
||||
self.roots = self.Roots(self.f)
|
||||
self.edo = self.Edo(self.f)
|
||||
|
||||
def d(self, x, e):
|
||||
return (self.f(x + e) - self.f(x - e))/(2*e)
|
||||
|
||||
class Integral:
|
||||
|
||||
def __init__(self,function):
|
||||
self.f = function
|
||||
self.simple = self.Simple(function)
|
||||
self.double = self.Double(function)
|
||||
|
||||
class Simple:
|
||||
def __init__(self, function):
|
||||
self.f = function
|
||||
|
||||
def riemann(self,a,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
delta = (b-a)/n
|
||||
|
||||
psi = a
|
||||
theta = 0
|
||||
|
||||
while((psi+delta) <= b):
|
||||
|
||||
theta += (self.f(psi) + self.f(psi + delta))/2
|
||||
psi += delta
|
||||
|
||||
integral = delta*theta
|
||||
|
||||
return integral
|
||||
|
||||
def simpson(self,a,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
def x(i):
|
||||
return a + i*h
|
||||
|
||||
h = (b-a)/n
|
||||
|
||||
eta = 0
|
||||
theta = 0
|
||||
|
||||
psi = 1
|
||||
kappa = 1
|
||||
|
||||
while(psi <= (n/2)):
|
||||
|
||||
eta = eta + self.f(x(2*psi - 1))
|
||||
psi = psi + 1
|
||||
|
||||
while(kappa <= ((n/2)-1)):
|
||||
|
||||
theta = theta + self.f(x(2*kappa))
|
||||
kappa = kappa + 1
|
||||
|
||||
return (h/3)*( self.f(x(0)) + self.f(x(n)) + 4*eta + 2*theta)
|
||||
|
||||
|
||||
class Double:
|
||||
|
||||
def __init__(self,function):
|
||||
self.f = function
|
||||
|
||||
def riemann(self,a,b,c,d,n=None,m=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**4
|
||||
|
||||
if m is None:
|
||||
m = n
|
||||
|
||||
dx = (b-a)/n
|
||||
dy = (d-c)/m
|
||||
kappa = a
|
||||
psi = c
|
||||
theta = 0
|
||||
|
||||
while((psi + dy) < d):
|
||||
|
||||
while((kappa + dx) < b):
|
||||
|
||||
theta = theta + self.f(kappa, psi)
|
||||
kappa = kappa + dx
|
||||
|
||||
psi = psi + dy
|
||||
kappa = a
|
||||
|
||||
return theta*(dx)*(dy)
|
||||
|
||||
def simpson(self,a,b,c,d,n=None,m=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**4
|
||||
|
||||
if m is None:
|
||||
m = n
|
||||
|
||||
dx = (b-a)/n
|
||||
dy = (d-c)/m
|
||||
|
||||
def x(i):
|
||||
|
||||
x = a + i*dx
|
||||
|
||||
return x
|
||||
|
||||
def y(i):
|
||||
|
||||
y = c + i*dy
|
||||
|
||||
return y
|
||||
|
||||
def g(i):
|
||||
|
||||
sigma = 0
|
||||
upsilon = 0
|
||||
|
||||
zeta = 1
|
||||
csi = 1
|
||||
|
||||
while(zeta <= (m/2)):
|
||||
|
||||
sigma += self.f(x(i),y(2*zeta - 1))
|
||||
zeta += 1
|
||||
|
||||
while(csi <= ((m/2)-1)):
|
||||
|
||||
upsilon += self.f(x(i),y(2*csi))
|
||||
csi += 1
|
||||
|
||||
return (dy/3)*( self.f(x(i),y(0)) + self.f(x(i),y(m)) + 4*sigma + 2*upsilon )
|
||||
|
||||
eta = 0
|
||||
theta = 0
|
||||
|
||||
psi = 1
|
||||
kappa = 1
|
||||
|
||||
while(psi <= (n/2)):
|
||||
|
||||
eta += g(2*psi - 1)
|
||||
psi += 1
|
||||
|
||||
while(kappa <= ((n/2)-1)):
|
||||
|
||||
theta += g(2*kappa)
|
||||
kappa += 1
|
||||
|
||||
return (dx/3)*( g(0) + g(n) + 4*eta + 2*theta)
|
||||
|
||||
class Roots:
|
||||
|
||||
def __init__(self, function=None):
|
||||
if function is not None:
|
||||
self.f = function
|
||||
|
||||
def bissec(self,a,b,e=None):
|
||||
|
||||
if e is None:
|
||||
e = 10**(-6)
|
||||
|
||||
fa = self.f(a)
|
||||
|
||||
while abs(a-b) > e:
|
||||
|
||||
c = (a+b)/2
|
||||
fc = self.f(c)
|
||||
|
||||
if (fa*fc) < 0:
|
||||
|
||||
b = c
|
||||
|
||||
else:
|
||||
|
||||
a = c
|
||||
fa = fc
|
||||
|
||||
c = (a+b)/2
|
||||
|
||||
return c
|
||||
|
||||
def d(self, x, e):
|
||||
return (self.f(x + e) - self.f(x - e))/(2*e)
|
||||
|
||||
def newton(self,a,e=None):
|
||||
|
||||
if e is None:
|
||||
e = 10**(-6)
|
||||
|
||||
fa = self.f(a)
|
||||
da = self.d(a,e)
|
||||
b = a - fa/da
|
||||
|
||||
|
||||
while abs(a-b) > e:
|
||||
|
||||
b = a
|
||||
a -= (fa/da)
|
||||
fa = self.f(a)
|
||||
da = self.d(a,e)
|
||||
|
||||
return a
|
||||
|
||||
def bissec_newton(self,a,b,e=None):
|
||||
|
||||
if e is None:
|
||||
e = 10**(-6)
|
||||
|
||||
fa = self.f(a)
|
||||
|
||||
c = (a+b)/2 # 'c' é a raiz calculada
|
||||
|
||||
while abs(a-b) > 0.1:
|
||||
|
||||
fc = self.f(c)
|
||||
|
||||
if fa*fc < 0:
|
||||
|
||||
b = c
|
||||
|
||||
else:
|
||||
|
||||
a = c
|
||||
fa = self.f(a)
|
||||
|
||||
c = (a+b)/2
|
||||
|
||||
fc = self.f(c)
|
||||
dc = self.d(c,e)
|
||||
h = c - fc/dc # 'h' é uma variável de controle
|
||||
|
||||
while abs(c-h) > e:
|
||||
|
||||
h = c
|
||||
c -= (fc/dc)
|
||||
fc = self.f(c)
|
||||
dc = self.d(c,e)
|
||||
|
||||
return (c)
|
||||
|
||||
|
||||
class Edo:
|
||||
|
||||
def __init__(self, function):
|
||||
self.F = function
|
||||
|
||||
def euler(self,a,y,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
dx = (b-a)/n
|
||||
|
||||
def x(i):
|
||||
return a + i*dx
|
||||
|
||||
for i in range(n):
|
||||
|
||||
y = y + (self.F(x(i),y))*dx
|
||||
|
||||
return y
|
||||
|
||||
def runge(self,a,y,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
dx = (b-a)/n
|
||||
|
||||
def x(i):
|
||||
return (a + i*dx)
|
||||
|
||||
for i in range(n):
|
||||
|
||||
y = y + (dx/2)*(self.F(x(i),y)+self.F(x(i+1),(y+(dx*self.F(x(i),y)))))
|
||||
|
||||
return y
|
||||
|
||||
def adams(self,a,y,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
dx = (b-a)/n
|
||||
|
||||
def x(i):
|
||||
return (a + i*dx)
|
||||
|
||||
for i in range(n):
|
||||
|
||||
f0 = self.F(x(i),y)
|
||||
f1 = self.F(x(i+1),y + dx*self.F(x(i)+(dx/2),y+(dx/2)*self.F(x(i),y)))
|
||||
f2 = self.F(x(i+2),y + (dx/2)*(3*f1-f0))
|
||||
|
||||
y += (dx/12)*(5*f2 + 8*f1 - f0)
|
||||
|
||||
return y
|
||||
|
||||
class Interpolation:
|
||||
""" Data should be organized in two columns: X and Y"""
|
||||
|
||||
def __init__(self, data):
|
||||
|
||||
self.data = data
|
||||
self.polinomial = self.Polinomial(self.data)
|
||||
|
||||
def minimus(self,x):
|
||||
|
||||
theta = 0
|
||||
# somatorio de x
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
theta += self.data.x[i]
|
||||
|
||||
eta = 0
|
||||
#somatorio de y
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
eta += self.data.y[i]
|
||||
|
||||
sigma = 0
|
||||
#somatorio de xy
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
sigma += self.data.x[i]*self.data.y[i]
|
||||
|
||||
omega = 0
|
||||
#somatorio de x^2self.dself.dself.d
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
omega += self.data.x[i]**2
|
||||
|
||||
|
||||
self.a = (self.data.shape[0]*sigma - theta*eta)/(self.data.shape[0]*omega - (theta**2))
|
||||
|
||||
self.b = (theta*sigma - eta*omega)/((theta**2) - self.data.shape[0]*omega)
|
||||
|
||||
ym = 0
|
||||
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
ym += self.data.y[i]/self.data.shape[0]
|
||||
|
||||
sqreq = 0
|
||||
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
sqreq += ((self.a*self.data.x[i] + self.b) - ym)**2
|
||||
|
||||
sqtot = 0
|
||||
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
sqtot += (self.data.y[i] - ym)**2
|
||||
|
||||
self.r2 = sqreq/sqtot
|
||||
|
||||
return self.a*x + self.b
|
||||
|
||||
class Polinomial:
|
||||
|
||||
def __init__(self, data):
|
||||
self.data = data
|
||||
|
||||
def vandermonde(self, x):
|
||||
|
||||
matrix = np.zeros((self.data.shape[0],self.data.shape[0]))
|
||||
|
||||
for k in range(0, self.data.shape[0]):
|
||||
|
||||
matrix[:,k] = self.data.x[:]**k
|
||||
|
||||
self.A = sl.gauss(np.c_[matrix,self.data[:,1]])
|
||||
|
||||
y = 0
|
||||
|
||||
for i in range(0,self.A.shape[0]):
|
||||
|
||||
y += self.A[i]*(x**i)
|
||||
|
||||
return float(y)
|
||||
|
||||
def lagrange(self, x):
|
||||
|
||||
def L(k,x):
|
||||
|
||||
up = down = 1
|
||||
|
||||
for i in [x for x in range(self.data.x.shape[0]) if x != k]:
|
||||
up = up*(x - self.data.x[i])
|
||||
|
||||
for i in [x for x in range(self.data.x.shape[0]) if x != k]:
|
||||
down = down*(self.data.x[k] - self.data.x[i])
|
||||
|
||||
return up/down
|
||||
|
||||
y = 0
|
||||
|
||||
for i in range(self.data.x.shape[0]):
|
||||
|
||||
y += self.data.y[i]*L(i,x)
|
||||
|
||||
return y
|
||||
|
||||
def newton(self,x):
|
||||
|
||||
d = np.array(np.zeros((self.data.shape[0],self.data.shape[0])))
|
||||
|
||||
d[0] = self.data.y
|
||||
|
||||
i = j = 0
|
||||
|
||||
while (i < self.data.shape[0]):
|
||||
|
||||
while (j < (self.data.shape[0]-(i+1))):
|
||||
|
||||
d[i+1][j] = (d[i][j+1] - d[i][j])/(self.data.x[(i+1)+j]-self.data.x[j])
|
||||
j += 1
|
||||
|
||||
i += 1
|
||||
j = 0
|
||||
|
||||
def f(x):
|
||||
|
||||
y = d[0][0]
|
||||
i = 0
|
||||
|
||||
while ((i+1) < self.data.shape[0]):
|
||||
|
||||
mult = 1
|
||||
k = 0
|
||||
while (k <= i):
|
||||
mult = mult*(x - self.data.x[k])
|
||||
k += 1
|
||||
|
||||
y += d[i+1][0]*mult
|
||||
i += 1
|
||||
|
||||
return y
|
||||
|
||||
self.f = f
|
||||
|
||||
return f(x)
|
||||
|
||||
def gregory(self,x):
|
||||
|
||||
h = self.data.x[0] - self.data.x[1]
|
||||
|
||||
d = np.array(np.zeros((self.data.shape[0],self.data.shape[0])))
|
||||
|
||||
d[0] = self.data.y
|
||||
|
||||
i = j = 0
|
||||
|
||||
while (i < self.data.shape[0]):
|
||||
|
||||
while (j < (self.data.shape[0]-(i+1))):
|
||||
|
||||
d[i+1][j] = (d[i][j+1] - d[i][j])/((i+1)*h)
|
||||
j += 1
|
||||
|
||||
i += 1
|
||||
j = 0
|
||||
|
||||
y = d[0][0]
|
||||
i = 0
|
||||
|
||||
while ((i+1) < self.data.shape[0]):
|
||||
|
||||
mult = 1
|
||||
k = 0
|
||||
while (k <= i):
|
||||
mult = mult*(x - self.data.x[k])
|
||||
k += 1
|
||||
|
||||
y += d[i+1][0]*mult
|
||||
i += 1
|
||||
|
||||
return y
|
||||
Binary file not shown.
Binary file not shown.
Binary file not shown.
Binary file not shown.
@@ -1,28 +0,0 @@
|
||||
import setuptools
|
||||
|
||||
with open("README.md", "r") as fh:
|
||||
long_description = fh.read()
|
||||
|
||||
setuptools.setup(
|
||||
name="yoshi-otter", # Replace with your own username
|
||||
version="1.3.1",
|
||||
author="Vitor Hideyoshi",
|
||||
author_email="vitor.h.n.batista@gmail.com",
|
||||
description="Numeric Calculus python module in the topic of Algebra Functions",
|
||||
long_description=long_description,
|
||||
long_description_content_type="text/markdown",
|
||||
url="https://github.com/HideyoshiNakazone/Otter-NumericCalculus.git",
|
||||
packages=setuptools.find_packages(),
|
||||
classifiers=[
|
||||
"Programming Language :: Python :: 3",
|
||||
"License :: OSI Approved :: GNU General Public License v2 (GPLv2)",
|
||||
"Operating System :: OS Independent",
|
||||
"Development Status :: 2 - Pre-Alpha",
|
||||
],
|
||||
python_requires='>=3.6',
|
||||
install_requires=[
|
||||
'numpy',
|
||||
'pandas',
|
||||
'yoshi-seals'
|
||||
],
|
||||
)
|
||||
@@ -1,91 +0,0 @@
|
||||
Metadata-Version: 2.1
|
||||
Name: yoshi-otter
|
||||
Version: 1.3.1
|
||||
Summary: Numeric Calculus python module in the topic of Algebra Functions
|
||||
Home-page: https://github.com/HideyoshiNakazone/Otter-NumericCalculus.git
|
||||
Author: Vitor Hideyoshi
|
||||
Author-email: vitor.h.n.batista@gmail.com
|
||||
License: UNKNOWN
|
||||
Description: # Otter - Numeric Calculus
|
||||
|
||||
This python package is made for applied Numeric Calculus of Algebra Functions. It is made with the following objectives in mind:
|
||||
|
||||
* Receive one variable function from user input
|
||||
|
||||
* Receive two variable function from user input
|
||||
|
||||
* Performe derivatives with one variable functions
|
||||
|
||||
* Performe integral with received functions
|
||||
|
||||
* Use methods to proccess the matrices.
|
||||
|
||||
* Find root of functions throw method of bissection and method of newton
|
||||
|
||||
* Solve Diferential Equations throw method of euler and runge
|
||||
|
||||
* Performe Minimus Interpolation and Polinomial Interpolation
|
||||
|
||||
## Syntax
|
||||
|
||||
To initialize a Otter instance linked to functions use the following syntax `otr = Otter.algebra(f)`, where `otr` will be a arbitrary name for the instance and `f` is a function of *one variable*.
|
||||
|
||||
To initialize a Otter instance linked to data and interpolation use the following syntax `otr = Otter.interpolation(data)`, where `otr` will be a arbitrary name for the instance and data will be a *numpy* matrix where the first columns has to contain the values for `x` and the second column contains the values for `y`.
|
||||
|
||||
### Algebra
|
||||
|
||||
Algebra is a Python Class where some of the features described previously are defined as Classes as well, like: `Integral`, `Roots`, `EDO` (diferential equations).
|
||||
|
||||
#### Integral
|
||||
|
||||
To call the class *Integral* append the sufix with lower case in front of the instance like: `otr.integral`. The Integral class has two other class defined inside, `Simple` and `Double`, to call them append the sufix with lower case in front as `otr.integral.simple` or `otr.integral.double`. Then pick between Riemann's Method or Simpson's Method by appending the sufix `riemann` or `simpson` as well.
|
||||
|
||||
After that the syntax will be something like `otr.integral.double.riemann(a,b,c,d,n,m)`, where `a` and `c` will be the first value of the interval of integration respectively in x and y, `b` and `d` will be the last, `n` and `m` will be the number of partitions.
|
||||
|
||||
The syntax for one variable integrations will be `otr.integral.simple.riemann(a,b,n)`.
|
||||
|
||||
If `n` is not defined the standart value in 10^6 partitions for one variable and 10^4 for double. And if `m` is not defined the standart value will be equal to `n`.
|
||||
|
||||
#### Roots
|
||||
|
||||
To call the class *Root* append the sufix with lower case in front of the instance like: `otr.roots`. The Roots class has three methods defined inside, `bissec`, `newton` and `bissec_newton`, to call them append the sufix with lower case in front as `otr.roots.bissec` or `otr.roots.newton` or even `otr.roots.bissecnewton`.
|
||||
|
||||
The syntax for the bissection method and bissec_newton is equal to `otr.roots.bissec(a,b,e)` and `otr.roots.bissec_newton(a,b,e)`, where `a` is the first element of the interval containing the root and `b` is the last, `e` being the precision.
|
||||
|
||||
The syntax for the newton method is equal to `otr.roots.newton(a,e)`, where `a` is the element closest to the root and `e` is the precision.
|
||||
|
||||
If `e` is not defined the standart value is 10^(-6).
|
||||
|
||||
#### Diferential Equations
|
||||
|
||||
To call the class *EDO* (*E*quações *D*iferenciais *O*rdinárias) append the sufix with lower case in front of the instance like: `otr.edo`. The *EDO* class has two methods defined inside: `euler` and `runge`, to call them append the sufix with lower case in front as `otr.edo.euler` or `otr.edo.runge`.
|
||||
|
||||
The syntax for the diferential equations method is equal to `otr.edo.euler(a,y,b,n)` or `otr.edo.runge(a,y,b,n)`, where `a` and `y` will be the inintial point and `b` is the value in *x* which you want to know the corresponding value in *y* and `n` is the number of operations.
|
||||
|
||||
If `n` is not defined the standart value is 10^7.
|
||||
|
||||
### Interpolation
|
||||
|
||||
The python class *Interpolation* is divided in one method, minimus interpolation, and one class, polinomial interpolation.
|
||||
|
||||
To call the method *minimus* use a syntax like `otr = Otter.interpolation(data)`, where `data` is a data frame containing values for *x* and *y*, `otr` is an instance and append the method in front of the instance like: `otr.minimus(x)`, where *x* is value of *f(x)* you want to estimate.
|
||||
|
||||
To call the class *Polinomial* append the sufix with lower case in front of the instance like: `otr.polinomial`. The *Polinomial* class has four methods defined inside: `vandermonde`, `lagrange`, `newton` and `gregory`, to call them append the sufix with lower case in front like `otr.edo.gregory(x)` where *x* is value of *f(x)* you want to estimate.
|
||||
|
||||
## Installation
|
||||
|
||||
To install the package from source `cd` into the directory and run:
|
||||
|
||||
`pip install .`
|
||||
|
||||
or run
|
||||
|
||||
`pip install yoshi-otter`
|
||||
|
||||
Platform: UNKNOWN
|
||||
Classifier: Programming Language :: Python :: 3
|
||||
Classifier: License :: OSI Approved :: GNU General Public License v2 (GPLv2)
|
||||
Classifier: Operating System :: OS Independent
|
||||
Classifier: Development Status :: 2 - Pre-Alpha
|
||||
Requires-Python: >=3.6
|
||||
Description-Content-Type: text/markdown
|
||||
@@ -1,9 +0,0 @@
|
||||
README.md
|
||||
setup.py
|
||||
Otter/Otter.py
|
||||
Otter/__init__.py
|
||||
yoshi_otter.egg-info/PKG-INFO
|
||||
yoshi_otter.egg-info/SOURCES.txt
|
||||
yoshi_otter.egg-info/dependency_links.txt
|
||||
yoshi_otter.egg-info/requires.txt
|
||||
yoshi_otter.egg-info/top_level.txt
|
||||
@@ -1,3 +0,0 @@
|
||||
numpy
|
||||
pandas
|
||||
yoshi-seals
|
||||
@@ -1 +0,0 @@
|
||||
Otter
|
||||
Binary file not shown.
@@ -1,278 +0,0 @@
|
||||
GNU GENERAL PUBLIC LICENSE
|
||||
Version 2, June 1991
|
||||
|
||||
Copyright (C) 1989, 1991 Free Software Foundation, Inc.,
|
||||
51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
Everyone is permitted to copy and distribute verbatim copies
|
||||
of this license document, but changing it is not allowed.
|
||||
|
||||
Preamble
|
||||
|
||||
The licenses for most software are designed to take away your
|
||||
freedom to share and change it. By contrast, the GNU General Public
|
||||
License is intended to guarantee your freedom to share and change free
|
||||
software--to make sure the software is free for all its users. This
|
||||
General Public License applies to most of the Free Software
|
||||
Foundation's software and to any other program whose authors commit to
|
||||
using it. (Some other Free Software Foundation software is covered by
|
||||
the GNU Lesser General Public License instead.) You can apply it to
|
||||
your programs, too.
|
||||
|
||||
When we speak of free software, we are referring to freedom, not
|
||||
price. Our General Public Licenses are designed to make sure that you
|
||||
have the freedom to distribute copies of free software (and charge for
|
||||
this service if you wish), that you receive source code or can get it
|
||||
if you want it, that you can change the software or use pieces of it
|
||||
in new free programs; and that you know you can do these things.
|
||||
|
||||
To protect your rights, we need to make restrictions that forbid
|
||||
anyone to deny you these rights or to ask you to surrender the rights.
|
||||
These restrictions translate to certain responsibilities for you if you
|
||||
distribute copies of the software, or if you modify it.
|
||||
|
||||
For example, if you distribute copies of such a program, whether
|
||||
gratis or for a fee, you must give the recipients all the rights that
|
||||
you have. You must make sure that they, too, receive or can get the
|
||||
source code. And you must show them these terms so they know their
|
||||
rights.
|
||||
|
||||
We protect your rights with two steps: (1) copyright the software, and
|
||||
(2) offer you this license which gives you legal permission to copy,
|
||||
distribute and/or modify the software.
|
||||
|
||||
Also, for each author's protection and ours, we want to make certain
|
||||
that everyone understands that there is no warranty for this free
|
||||
software. If the software is modified by someone else and passed on, we
|
||||
want its recipients to know that what they have is not the original, so
|
||||
that any problems introduced by others will not reflect on the original
|
||||
authors' reputations.
|
||||
|
||||
Finally, any free program is threatened constantly by software
|
||||
patents. We wish to avoid the danger that redistributors of a free
|
||||
program will individually obtain patent licenses, in effect making the
|
||||
program proprietary. To prevent this, we have made it clear that any
|
||||
patent must be licensed for everyone's free use or not licensed at all.
|
||||
|
||||
The precise terms and conditions for copying, distribution and
|
||||
modification follow.
|
||||
|
||||
GNU GENERAL PUBLIC LICENSE
|
||||
TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
|
||||
|
||||
0. This License applies to any program or other work which contains
|
||||
a notice placed by the copyright holder saying it may be distributed
|
||||
under the terms of this General Public License. The "Program", below,
|
||||
refers to any such program or work, and a "work based on the Program"
|
||||
means either the Program or any derivative work under copyright law:
|
||||
that is to say, a work containing the Program or a portion of it,
|
||||
either verbatim or with modifications and/or translated into another
|
||||
language. (Hereinafter, translation is included without limitation in
|
||||
the term "modification".) Each licensee is addressed as "you".
|
||||
|
||||
Activities other than copying, distribution and modification are not
|
||||
covered by this License; they are outside its scope. The act of
|
||||
running the Program is not restricted, and the output from the Program
|
||||
is covered only if its contents constitute a work based on the
|
||||
Program (independent of having been made by running the Program).
|
||||
Whether that is true depends on what the Program does.
|
||||
|
||||
1. You may copy and distribute verbatim copies of the Program's
|
||||
source code as you receive it, in any medium, provided that you
|
||||
conspicuously and appropriately publish on each copy an appropriate
|
||||
copyright notice and disclaimer of warranty; keep intact all the
|
||||
notices that refer to this License and to the absence of any warranty;
|
||||
and give any other recipients of the Program a copy of this License
|
||||
along with the Program.
|
||||
|
||||
You may charge a fee for the physical act of transferring a copy, and
|
||||
you may at your option offer warranty protection in exchange for a fee.
|
||||
|
||||
2. You may modify your copy or copies of the Program or any portion
|
||||
of it, thus forming a work based on the Program, and copy and
|
||||
distribute such modifications or work under the terms of Section 1
|
||||
above, provided that you also meet all of these conditions:
|
||||
|
||||
a) You must cause the modified files to carry prominent notices
|
||||
stating that you changed the files and the date of any change.
|
||||
|
||||
b) You must cause any work that you distribute or publish, that in
|
||||
whole or in part contains or is derived from the Program or any
|
||||
part thereof, to be licensed as a whole at no charge to all third
|
||||
parties under the terms of this License.
|
||||
|
||||
c) If the modified program normally reads commands interactively
|
||||
when run, you must cause it, when started running for such
|
||||
interactive use in the most ordinary way, to print or display an
|
||||
announcement including an appropriate copyright notice and a
|
||||
notice that there is no warranty (or else, saying that you provide
|
||||
a warranty) and that users may redistribute the program under
|
||||
these conditions, and telling the user how to view a copy of this
|
||||
License. (Exception: if the Program itself is interactive but
|
||||
does not normally print such an announcement, your work based on
|
||||
the Program is not required to print an announcement.)
|
||||
|
||||
These requirements apply to the modified work as a whole. If
|
||||
identifiable sections of that work are not derived from the Program,
|
||||
and can be reasonably considered independent and separate works in
|
||||
themselves, then this License, and its terms, do not apply to those
|
||||
sections when you distribute them as separate works. But when you
|
||||
distribute the same sections as part of a whole which is a work based
|
||||
on the Program, the distribution of the whole must be on the terms of
|
||||
this License, whose permissions for other licensees extend to the
|
||||
entire whole, and thus to each and every part regardless of who wrote it.
|
||||
|
||||
Thus, it is not the intent of this section to claim rights or contest
|
||||
your rights to work written entirely by you; rather, the intent is to
|
||||
exercise the right to control the distribution of derivative or
|
||||
collective works based on the Program.
|
||||
|
||||
In addition, mere aggregation of another work not based on the Program
|
||||
with the Program (or with a work based on the Program) on a volume of
|
||||
a storage or distribution medium does not bring the other work under
|
||||
the scope of this License.
|
||||
|
||||
3. You may copy and distribute the Program (or a work based on it,
|
||||
under Section 2) in object code or executable form under the terms of
|
||||
Sections 1 and 2 above provided that you also do one of the following:
|
||||
|
||||
a) Accompany it with the complete corresponding machine-readable
|
||||
source code, which must be distributed under the terms of Sections
|
||||
1 and 2 above on a medium customarily used for software interchange; or,
|
||||
|
||||
b) Accompany it with a written offer, valid for at least three
|
||||
years, to give any third party, for a charge no more than your
|
||||
cost of physically performing source distribution, a complete
|
||||
machine-readable copy of the corresponding source code, to be
|
||||
distributed under the terms of Sections 1 and 2 above on a medium
|
||||
customarily used for software interchange; or,
|
||||
|
||||
c) Accompany it with the information you received as to the offer
|
||||
to distribute corresponding source code. (This alternative is
|
||||
allowed only for noncommercial distribution and only if you
|
||||
received the program in object code or executable form with such
|
||||
an offer, in accord with Subsection b above.)
|
||||
|
||||
The source code for a work means the preferred form of the work for
|
||||
making modifications to it. For an executable work, complete source
|
||||
code means all the source code for all modules it contains, plus any
|
||||
associated interface definition files, plus the scripts used to
|
||||
control compilation and installation of the executable. However, as a
|
||||
special exception, the source code distributed need not include
|
||||
anything that is normally distributed (in either source or binary
|
||||
form) with the major components (compiler, kernel, and so on) of the
|
||||
operating system on which the executable runs, unless that component
|
||||
itself accompanies the executable.
|
||||
|
||||
If distribution of executable or object code is made by offering
|
||||
access to copy from a designated place, then offering equivalent
|
||||
access to copy the source code from the same place counts as
|
||||
distribution of the source code, even though third parties are not
|
||||
compelled to copy the source along with the object code.
|
||||
|
||||
4. You may not copy, modify, sublicense, or distribute the Program
|
||||
except as expressly provided under this License. Any attempt
|
||||
otherwise to copy, modify, sublicense or distribute the Program is
|
||||
void, and will automatically terminate your rights under this License.
|
||||
However, parties who have received copies, or rights, from you under
|
||||
this License will not have their licenses terminated so long as such
|
||||
parties remain in full compliance.
|
||||
|
||||
5. You are not required to accept this License, since you have not
|
||||
signed it. However, nothing else grants you permission to modify or
|
||||
distribute the Program or its derivative works. These actions are
|
||||
prohibited by law if you do not accept this License. Therefore, by
|
||||
modifying or distributing the Program (or any work based on the
|
||||
Program), you indicate your acceptance of this License to do so, and
|
||||
all its terms and conditions for copying, distributing or modifying
|
||||
the Program or works based on it.
|
||||
|
||||
6. Each time you redistribute the Program (or any work based on the
|
||||
Program), the recipient automatically receives a license from the
|
||||
original licensor to copy, distribute or modify the Program subject to
|
||||
these terms and conditions. You may not impose any further
|
||||
restrictions on the recipients' exercise of the rights granted herein.
|
||||
You are not responsible for enforcing compliance by third parties to
|
||||
this License.
|
||||
|
||||
7. If, as a consequence of a court judgment or allegation of patent
|
||||
infringement or for any other reason (not limited to patent issues),
|
||||
conditions are imposed on you (whether by court order, agreement or
|
||||
otherwise) that contradict the conditions of this License, they do not
|
||||
excuse you from the conditions of this License. If you cannot
|
||||
distribute so as to satisfy simultaneously your obligations under this
|
||||
License and any other pertinent obligations, then as a consequence you
|
||||
may not distribute the Program at all. For example, if a patent
|
||||
license would not permit royalty-free redistribution of the Program by
|
||||
all those who receive copies directly or indirectly through you, then
|
||||
the only way you could satisfy both it and this License would be to
|
||||
refrain entirely from distribution of the Program.
|
||||
|
||||
If any portion of this section is held invalid or unenforceable under
|
||||
any particular circumstance, the balance of the section is intended to
|
||||
apply and the section as a whole is intended to apply in other
|
||||
circumstances.
|
||||
|
||||
It is not the purpose of this section to induce you to infringe any
|
||||
patents or other property right claims or to contest validity of any
|
||||
such claims; this section has the sole purpose of protecting the
|
||||
integrity of the free software distribution system, which is
|
||||
implemented by public license practices. Many people have made
|
||||
generous contributions to the wide range of software distributed
|
||||
through that system in reliance on consistent application of that
|
||||
system; it is up to the author/donor to decide if he or she is willing
|
||||
to distribute software through any other system and a licensee cannot
|
||||
impose that choice.
|
||||
|
||||
This section is intended to make thoroughly clear what is believed to
|
||||
be a consequence of the rest of this License.
|
||||
|
||||
8. If the distribution and/or use of the Program is restricted in
|
||||
certain countries either by patents or by copyrighted interfaces, the
|
||||
original copyright holder who places the Program under this License
|
||||
may add an explicit geographical distribution limitation excluding
|
||||
those countries, so that distribution is permitted only in or among
|
||||
countries not thus excluded. In such case, this License incorporates
|
||||
the limitation as if written in the body of this License.
|
||||
|
||||
9. The Free Software Foundation may publish revised and/or new versions
|
||||
of the General Public License from time to time. Such new versions will
|
||||
be similar in spirit to the present version, but may differ in detail to
|
||||
address new problems or concerns.
|
||||
|
||||
Each version is given a distinguishing version number. If the Program
|
||||
specifies a version number of this License which applies to it and "any
|
||||
later version", you have the option of following the terms and conditions
|
||||
either of that version or of any later version published by the Free
|
||||
Software Foundation. If the Program does not specify a version number of
|
||||
this License, you may choose any version ever published by the Free Software
|
||||
Foundation.
|
||||
|
||||
10. If you wish to incorporate parts of the Program into other free
|
||||
programs whose distribution conditions are different, write to the author
|
||||
to ask for permission. For software which is copyrighted by the Free
|
||||
Software Foundation, write to the Free Software Foundation; we sometimes
|
||||
make exceptions for this. Our decision will be guided by the two goals
|
||||
of preserving the free status of all derivatives of our free software and
|
||||
of promoting the sharing and reuse of software generally.
|
||||
|
||||
NO WARRANTY
|
||||
|
||||
11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY
|
||||
FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN
|
||||
OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES
|
||||
PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED
|
||||
OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
|
||||
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS
|
||||
TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE
|
||||
PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING,
|
||||
REPAIR OR CORRECTION.
|
||||
|
||||
12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
|
||||
WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR
|
||||
REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES,
|
||||
INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING
|
||||
OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED
|
||||
TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY
|
||||
YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER
|
||||
PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE
|
||||
POSSIBILITY OF SUCH DAMAGES.
|
||||
@@ -1,517 +0,0 @@
|
||||
# Otter - Program made for educational intent, can be freely distributed
|
||||
# and can be used for economical intent. I will not take legal actions
|
||||
# unless my intelectual propperty, the code, is stolen or change without permission.
|
||||
#
|
||||
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
|
||||
#
|
||||
# This program is free software; you can redistribute it and/or modify
|
||||
# it under the terms of the GNU General Public License version 2 as published by
|
||||
# the Free Software Foundation.
|
||||
#
|
||||
# This program is distributed in the hope that it will be useful,
|
||||
# but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
# GNU General Public License for more details.
|
||||
#
|
||||
# You should have received a copy of the GNU General Public License along
|
||||
# with this program; if not, write to the Free Software Foundation, Inc.,
|
||||
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
|
||||
|
||||
import math
|
||||
import numpy as np
|
||||
import pandas as pd
|
||||
import Seals
|
||||
|
||||
sl = Seals.process
|
||||
|
||||
class Algebra:
|
||||
|
||||
def __init__(self, function):
|
||||
self.f = function
|
||||
self.integral = self.Integral(self.f)
|
||||
self.roots = self.Roots(self.f)
|
||||
self.edo = self.Edo(self.f)
|
||||
|
||||
def d(self, x, e):
|
||||
return (self.f(x + e) - self.f(x - e))/(2*e)
|
||||
|
||||
class Integral:
|
||||
|
||||
def __init__(self,function):
|
||||
self.f = function
|
||||
self.simple = self.Simple(function)
|
||||
self.double = self.Double(function)
|
||||
|
||||
class Simple:
|
||||
def __init__(self, function):
|
||||
self.f = function
|
||||
|
||||
def riemann(self,a,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
delta = (b-a)/n
|
||||
|
||||
psi = a
|
||||
theta = 0
|
||||
|
||||
while((psi+delta) <= b):
|
||||
|
||||
theta += (self.f(psi) + self.f(psi + delta))/2
|
||||
psi += delta
|
||||
|
||||
integral = delta*theta
|
||||
|
||||
return integral
|
||||
|
||||
def simpson(self,a,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
def x(i):
|
||||
return a + i*h
|
||||
|
||||
h = (b-a)/n
|
||||
|
||||
eta = 0
|
||||
theta = 0
|
||||
|
||||
psi = 1
|
||||
kappa = 1
|
||||
|
||||
while(psi <= (n/2)):
|
||||
|
||||
eta = eta + self.f(x(2*psi - 1))
|
||||
psi = psi + 1
|
||||
|
||||
while(kappa <= ((n/2)-1)):
|
||||
|
||||
theta = theta + self.f(x(2*kappa))
|
||||
kappa = kappa + 1
|
||||
|
||||
return (h/3)*( self.f(x(0)) + self.f(x(n)) + 4*eta + 2*theta)
|
||||
|
||||
|
||||
class Double:
|
||||
|
||||
def __init__(self,function):
|
||||
self.f = function
|
||||
|
||||
def riemann(self,a,b,c,d,n=None,m=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**4
|
||||
|
||||
if m is None:
|
||||
m = n
|
||||
|
||||
dx = (b-a)/n
|
||||
dy = (d-c)/m
|
||||
kappa = a
|
||||
psi = c
|
||||
theta = 0
|
||||
|
||||
while((psi + dy) < d):
|
||||
|
||||
while((kappa + dx) < b):
|
||||
|
||||
theta = theta + self.f(kappa, psi)
|
||||
kappa = kappa + dx
|
||||
|
||||
psi = psi + dy
|
||||
kappa = a
|
||||
|
||||
return theta*(dx)*(dy)
|
||||
|
||||
def simpson(self,a,b,c,d,n=None,m=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**4
|
||||
|
||||
if m is None:
|
||||
m = n
|
||||
|
||||
dx = (b-a)/n
|
||||
dy = (d-c)/m
|
||||
|
||||
def x(i):
|
||||
|
||||
x = a + i*dx
|
||||
|
||||
return x
|
||||
|
||||
def y(i):
|
||||
|
||||
y = c + i*dy
|
||||
|
||||
return y
|
||||
|
||||
def g(i):
|
||||
|
||||
sigma = 0
|
||||
upsilon = 0
|
||||
|
||||
zeta = 1
|
||||
csi = 1
|
||||
|
||||
while(zeta <= (m/2)):
|
||||
|
||||
sigma += self.f(x(i),y(2*zeta - 1))
|
||||
zeta += 1
|
||||
|
||||
while(csi <= ((m/2)-1)):
|
||||
|
||||
upsilon += self.f(x(i),y(2*csi))
|
||||
csi += 1
|
||||
|
||||
return (dy/3)*( self.f(x(i),y(0)) + self.f(x(i),y(m)) + 4*sigma + 2*upsilon )
|
||||
|
||||
eta = 0
|
||||
theta = 0
|
||||
|
||||
psi = 1
|
||||
kappa = 1
|
||||
|
||||
while(psi <= (n/2)):
|
||||
|
||||
eta += g(2*psi - 1)
|
||||
psi += 1
|
||||
|
||||
while(kappa <= ((n/2)-1)):
|
||||
|
||||
theta += g(2*kappa)
|
||||
kappa += 1
|
||||
|
||||
return (dx/3)*( g(0) + g(n) + 4*eta + 2*theta)
|
||||
|
||||
class Roots:
|
||||
|
||||
def __init__(self, function=None):
|
||||
if function is not None:
|
||||
self.f = function
|
||||
|
||||
def bissec(self,a,b,e=None):
|
||||
|
||||
if e is None:
|
||||
e = 10**(-6)
|
||||
|
||||
fa = self.f(a)
|
||||
|
||||
while abs(a-b) > e:
|
||||
|
||||
c = (a+b)/2
|
||||
fc = self.f(c)
|
||||
|
||||
if (fa*fc) < 0:
|
||||
|
||||
b = c
|
||||
|
||||
else:
|
||||
|
||||
a = c
|
||||
fa = fc
|
||||
|
||||
c = (a+b)/2
|
||||
|
||||
return c
|
||||
|
||||
def d(self, x, e):
|
||||
return (self.f(x + e) - self.f(x - e))/(2*e)
|
||||
|
||||
def newton(self,a,e=None):
|
||||
|
||||
if e is None:
|
||||
e = 10**(-6)
|
||||
|
||||
fa = self.f(a)
|
||||
da = self.d(a,e)
|
||||
b = a - fa/da
|
||||
|
||||
|
||||
while abs(a-b) > e:
|
||||
|
||||
b = a
|
||||
a -= (fa/da)
|
||||
fa = self.f(a)
|
||||
da = self.d(a,e)
|
||||
|
||||
return a
|
||||
|
||||
def bissec_newton(self,a,b,e=None):
|
||||
|
||||
if e is None:
|
||||
e = 10**(-6)
|
||||
|
||||
fa = self.f(a)
|
||||
|
||||
c = (a+b)/2 # 'c' é a raiz calculada
|
||||
|
||||
while abs(a-b) > 0.1:
|
||||
|
||||
fc = self.f(c)
|
||||
|
||||
if fa*fc < 0:
|
||||
|
||||
b = c
|
||||
|
||||
else:
|
||||
|
||||
a = c
|
||||
fa = self.f(a)
|
||||
|
||||
c = (a+b)/2
|
||||
|
||||
fc = self.f(c)
|
||||
dc = self.d(c,e)
|
||||
h = c - fc/dc # 'h' é uma variável de controle
|
||||
|
||||
while abs(c-h) > e:
|
||||
|
||||
h = c
|
||||
c -= (fc/dc)
|
||||
fc = self.f(c)
|
||||
dc = self.d(c,e)
|
||||
|
||||
return (c)
|
||||
|
||||
|
||||
class Edo:
|
||||
|
||||
def __init__(self, function):
|
||||
self.F = function
|
||||
|
||||
def euler(self,a,y,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
dx = (b-a)/n
|
||||
|
||||
def x(i):
|
||||
return a + i*dx
|
||||
|
||||
for i in range(n):
|
||||
|
||||
y = y + (self.F(x(i),y))*dx
|
||||
|
||||
return y
|
||||
|
||||
def runge(self,a,y,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
dx = (b-a)/n
|
||||
|
||||
def x(i):
|
||||
return (a + i*dx)
|
||||
|
||||
for i in range(n):
|
||||
|
||||
y = y + (dx/2)*(self.F(x(i),y)+self.F(x(i+1),(y+(dx*self.F(x(i),y)))))
|
||||
|
||||
return y
|
||||
|
||||
def adams(self,a,y,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
dx = (b-a)/n
|
||||
|
||||
def x(i):
|
||||
return (a + i*dx)
|
||||
|
||||
for i in range(n):
|
||||
|
||||
f0 = self.F(x(i),y)
|
||||
f1 = self.F(x(i+1),y + dx*self.F(x(i)+(dx/2),y+(dx/2)*self.F(x(i),y)))
|
||||
f2 = self.F(x(i+2),y + (dx/2)*(3*f1-f0))
|
||||
|
||||
y += (dx/12)*(5*f2 + 8*f1 - f0)
|
||||
|
||||
return y
|
||||
|
||||
class Interpolation:
|
||||
""" Data should be organized in two columns: X and Y"""
|
||||
|
||||
def __init__(self, data):
|
||||
|
||||
self.data = data
|
||||
self.polinomial = self.Polinomial(self.data)
|
||||
|
||||
def minimus(self,x):
|
||||
|
||||
theta = 0
|
||||
# somatorio de x
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
theta += self.data.x[i]
|
||||
|
||||
eta = 0
|
||||
#somatorio de y
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
eta += self.data.y[i]
|
||||
|
||||
sigma = 0
|
||||
#somatorio de xy
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
sigma += self.data.x[i]*self.data.y[i]
|
||||
|
||||
omega = 0
|
||||
#somatorio de x^2self.dself.dself.d
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
omega += self.data.x[i]**2
|
||||
|
||||
|
||||
self.a = (self.data.shape[0]*sigma - theta*eta)/(self.data.shape[0]*omega - (theta**2))
|
||||
|
||||
self.b = (theta*sigma - eta*omega)/((theta**2) - self.data.shape[0]*omega)
|
||||
|
||||
ym = 0
|
||||
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
ym += self.data.y[i]/self.data.shape[0]
|
||||
|
||||
sqreq = 0
|
||||
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
sqreq += ((self.a*self.data.x[i] + self.b) - ym)**2
|
||||
|
||||
sqtot = 0
|
||||
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
sqtot += (self.data.y[i] - ym)**2
|
||||
|
||||
self.r2 = sqreq/sqtot
|
||||
|
||||
return self.a*x + self.b
|
||||
|
||||
class Polinomial:
|
||||
|
||||
def __init__(self, data):
|
||||
self.data = data
|
||||
|
||||
def vandermonde(self, x):
|
||||
|
||||
matrix = np.zeros((self.data.shape[0],self.data.shape[0]))
|
||||
|
||||
for k in range(0, self.data.shape[0]):
|
||||
|
||||
matrix[:,k] = self.data.x[:]**k
|
||||
|
||||
self.A = sl.gauss(np.c_[matrix,self.data[:,1]])
|
||||
|
||||
y = 0
|
||||
|
||||
for i in range(0,self.A.shape[0]):
|
||||
|
||||
y += self.A[i]*(x**i)
|
||||
|
||||
return float(y)
|
||||
|
||||
def lagrange(self, x):
|
||||
|
||||
def L(k,x):
|
||||
|
||||
up = down = 1
|
||||
|
||||
for i in [x for x in range(self.data.x.shape[0]) if x != k]:
|
||||
up = up*(x - self.data.x[i])
|
||||
|
||||
for i in [x for x in range(self.data.x.shape[0]) if x != k]:
|
||||
down = down*(self.data.x[k] - self.data.x[i])
|
||||
|
||||
return up/down
|
||||
|
||||
y = 0
|
||||
|
||||
for i in range(self.data.x.shape[0]):
|
||||
|
||||
y += self.data.y[i]*L(i,x)
|
||||
|
||||
return y
|
||||
|
||||
def newton(self,x):
|
||||
|
||||
d = np.array(np.zeros((self.data.shape[0],self.data.shape[0])))
|
||||
|
||||
d[0] = self.data.y
|
||||
|
||||
i = j = 0
|
||||
|
||||
while (i < self.data.shape[0]):
|
||||
|
||||
while (j < (self.data.shape[0]-(i+1))):
|
||||
|
||||
d[i+1][j] = (d[i][j+1] - d[i][j])/(self.data.x[(i+1)+j]-self.data.x[j])
|
||||
j += 1
|
||||
|
||||
i += 1
|
||||
j = 0
|
||||
|
||||
def f(x):
|
||||
|
||||
y = d[0][0]
|
||||
i = 0
|
||||
|
||||
while ((i+1) < self.data.shape[0]):
|
||||
|
||||
mult = 1
|
||||
k = 0
|
||||
while (k <= i):
|
||||
mult = mult*(x - self.data.x[k])
|
||||
k += 1
|
||||
|
||||
y += d[i+1][0]*mult
|
||||
i += 1
|
||||
|
||||
return y
|
||||
|
||||
self.f = f
|
||||
|
||||
return f(x)
|
||||
|
||||
def gregory(self,x):
|
||||
|
||||
h = self.data.x[0] - self.data.x[1]
|
||||
|
||||
d = np.array(np.zeros((self.data.shape[0],self.data.shape[0])))
|
||||
|
||||
d[0] = self.data.y
|
||||
|
||||
i = j = 0
|
||||
|
||||
while (i < self.data.shape[0]):
|
||||
|
||||
while (j < (self.data.shape[0]-(i+1))):
|
||||
|
||||
d[i+1][j] = (d[i][j+1] - d[i][j])/((i+1)*h)
|
||||
j += 1
|
||||
|
||||
i += 1
|
||||
j = 0
|
||||
|
||||
y = d[0][0]
|
||||
i = 0
|
||||
|
||||
while ((i+1) < self.data.shape[0]):
|
||||
|
||||
mult = 1
|
||||
k = 0
|
||||
while (k <= i):
|
||||
mult = mult*(x - self.data.x[k])
|
||||
k += 1
|
||||
|
||||
y += d[i+1][0]*mult
|
||||
i += 1
|
||||
|
||||
return y
|
||||
@@ -1,21 +0,0 @@
|
||||
# Otter - Program made for educational intent, can be freely distributed
|
||||
# and can be used for economical intent. I will not take legal actions
|
||||
# unless my intelectual propperty, the code, is stolen or change without permission.
|
||||
|
||||
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
|
||||
|
||||
# This program is free software; you can redistribute it and/or modify
|
||||
# it under the terms of the GNU General Public License version 2 as published by
|
||||
# the Free Software Foundation.
|
||||
|
||||
# This program is distributed in the hope that it will be useful,
|
||||
# but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
# GNU General Public License for more details.
|
||||
|
||||
# You should have received a copy of the GNU General Public License along
|
||||
# with this program; if not, write to the Free Software Foundation, Inc.,
|
||||
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
|
||||
|
||||
from .Otter import Algebra as algebra
|
||||
from .Otter import Interpolation as interpolation
|
||||
@@ -1,75 +0,0 @@
|
||||
# Otter - Numeric Calculus
|
||||
|
||||
This python package is made for applied Numeric Calculus of Algebra Functions. It is made with the following objectives in mind:
|
||||
|
||||
* Receive one variable function from user input
|
||||
|
||||
* Receive two variable function from user input
|
||||
|
||||
* Performe derivatives with one variable functions
|
||||
|
||||
* Performe integral with received functions
|
||||
|
||||
* Use methods to proccess the matrices.
|
||||
|
||||
* Find root of functions throw method of bissection and method of newton
|
||||
|
||||
* Solve Diferential Equations throw method of euler and runge
|
||||
|
||||
* Performe Minimus Interpolation and Polinomial Interpolation
|
||||
|
||||
## Syntax
|
||||
|
||||
To initialize a Otter instance linked to functions use the following syntax `otr = Otter.algebra(f)`, where `otr` will be a arbitrary name for the instance and `f` is a function of *one variable*.
|
||||
|
||||
To initialize a Otter instance linked to data and interpolation use the following syntax `otr = Otter.interpolation(data)`, where `otr` will be a arbitrary name for the instance and data will be a *numpy* matrix where the first columns has to contain the values for `x` and the second column contains the values for `y`.
|
||||
|
||||
### Algebra
|
||||
|
||||
Algebra is a Python Class where some of the features described previously are defined as Classes as well, like: `Integral`, `Roots`, `EDO` (diferential equations).
|
||||
|
||||
#### Integral
|
||||
|
||||
To call the class *Integral* append the sufix with lower case in front of the instance like: `otr.integral`. The Integral class has two other class defined inside, `Simple` and `Double`, to call them append the sufix with lower case in front as `otr.integral.simple` or `otr.integral.double`. Then pick between Riemann's Method or Simpson's Method by appending the sufix `riemann` or `simpson` as well.
|
||||
|
||||
After that the syntax will be something like `otr.integral.double.riemann(a,b,c,d,n,m)`, where `a` and `c` will be the first value of the interval of integration respectively in x and y, `b` and `d` will be the last, `n` and `m` will be the number of partitions.
|
||||
|
||||
The syntax for one variable integrations will be `otr.integral.simple.riemann(a,b,n)`.
|
||||
|
||||
If `n` is not defined the standart value in 10^6 partitions for one variable and 10^4 for double. And if `m` is not defined the standart value will be equal to `n`.
|
||||
|
||||
#### Roots
|
||||
|
||||
To call the class *Root* append the sufix with lower case in front of the instance like: `otr.roots`. The Roots class has three methods defined inside, `bissec`, `newton` and `bissec_newton`, to call them append the sufix with lower case in front as `otr.roots.bissec` or `otr.roots.newton` or even `otr.roots.bissecnewton`.
|
||||
|
||||
The syntax for the bissection method and bissec_newton is equal to `otr.roots.bissec(a,b,e)` and `otr.roots.bissec_newton(a,b,e)`, where `a` is the first element of the interval containing the root and `b` is the last, `e` being the precision.
|
||||
|
||||
The syntax for the newton method is equal to `otr.roots.newton(a,e)`, where `a` is the element closest to the root and `e` is the precision.
|
||||
|
||||
If `e` is not defined the standart value is 10^(-6).
|
||||
|
||||
#### Diferential Equations
|
||||
|
||||
To call the class *EDO* (*E*quações *D*iferenciais *O*rdinárias) append the sufix with lower case in front of the instance like: `otr.edo`. The *EDO* class has two methods defined inside: `euler` and `runge`, to call them append the sufix with lower case in front as `otr.edo.euler` or `otr.edo.runge`.
|
||||
|
||||
The syntax for the diferential equations method is equal to `otr.edo.euler(a,y,b,n)` or `otr.edo.runge(a,y,b,n)`, where `a` and `y` will be the inintial point and `b` is the value in *x* which you want to know the corresponding value in *y* and `n` is the number of operations.
|
||||
|
||||
If `n` is not defined the standart value is 10^7.
|
||||
|
||||
### Interpolation
|
||||
|
||||
The python class *Interpolation* is divided in one method, minimus interpolation, and one class, polinomial interpolation.
|
||||
|
||||
To call the method *minimus* use a syntax like `otr = Otter.interpolation(data)`, where `data` is a data frame containing values for *x* and *y*, `otr` is an instance and append the method in front of the instance like: `otr.minimus(x)`, where *x* is value of *f(x)* you want to estimate.
|
||||
|
||||
To call the class *Polinomial* append the sufix with lower case in front of the instance like: `otr.polinomial`. The *Polinomial* class has four methods defined inside: `vandermonde`, `lagrange`, `newton` and `gregory`, to call them append the sufix with lower case in front like `otr.edo.gregory(x)` where *x* is value of *f(x)* you want to estimate.
|
||||
|
||||
## Installation
|
||||
|
||||
To install the package from source `cd` into the directory and run:
|
||||
|
||||
`pip install .`
|
||||
|
||||
or run
|
||||
|
||||
`pip install yoshi-otter`
|
||||
@@ -1,517 +0,0 @@
|
||||
# Otter - Program made for educational intent, can be freely distributed
|
||||
# and can be used for economical intent. I will not take legal actions
|
||||
# unless my intelectual propperty, the code, is stolen or change without permission.
|
||||
#
|
||||
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
|
||||
#
|
||||
# This program is free software; you can redistribute it and/or modify
|
||||
# it under the terms of the GNU General Public License version 2 as published by
|
||||
# the Free Software Foundation.
|
||||
#
|
||||
# This program is distributed in the hope that it will be useful,
|
||||
# but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
# GNU General Public License for more details.
|
||||
#
|
||||
# You should have received a copy of the GNU General Public License along
|
||||
# with this program; if not, write to the Free Software Foundation, Inc.,
|
||||
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
|
||||
|
||||
import math
|
||||
import numpy as np
|
||||
import pandas as pd
|
||||
import Seals
|
||||
|
||||
sl = Seals.process
|
||||
|
||||
class Algebra:
|
||||
|
||||
def __init__(self, function):
|
||||
self.f = function
|
||||
self.integral = self.Integral(self.f)
|
||||
self.roots = self.Roots(self.f)
|
||||
self.edo = self.Edo(self.f)
|
||||
|
||||
def d(self, x, e):
|
||||
return (self.f(x + e) - self.f(x - e))/(2*e)
|
||||
|
||||
class Integral:
|
||||
|
||||
def __init__(self,function):
|
||||
self.f = function
|
||||
self.simple = self.Simple(function)
|
||||
self.double = self.Double(function)
|
||||
|
||||
class Simple:
|
||||
def __init__(self, function):
|
||||
self.f = function
|
||||
|
||||
def riemann(self,a,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
delta = (b-a)/n
|
||||
|
||||
psi = a
|
||||
theta = 0
|
||||
|
||||
while((psi+delta) <= b):
|
||||
|
||||
theta += (self.f(psi) + self.f(psi + delta))/2
|
||||
psi += delta
|
||||
|
||||
integral = delta*theta
|
||||
|
||||
return integral
|
||||
|
||||
def simpson(self,a,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
def x(i):
|
||||
return a + i*h
|
||||
|
||||
h = (b-a)/n
|
||||
|
||||
eta = 0
|
||||
theta = 0
|
||||
|
||||
psi = 1
|
||||
kappa = 1
|
||||
|
||||
while(psi <= (n/2)):
|
||||
|
||||
eta = eta + self.f(x(2*psi - 1))
|
||||
psi = psi + 1
|
||||
|
||||
while(kappa <= ((n/2)-1)):
|
||||
|
||||
theta = theta + self.f(x(2*kappa))
|
||||
kappa = kappa + 1
|
||||
|
||||
return (h/3)*( self.f(x(0)) + self.f(x(n)) + 4*eta + 2*theta)
|
||||
|
||||
|
||||
class Double:
|
||||
|
||||
def __init__(self,function):
|
||||
self.f = function
|
||||
|
||||
def riemann(self,a,b,c,d,n=None,m=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**4
|
||||
|
||||
if m is None:
|
||||
m = n
|
||||
|
||||
dx = (b-a)/n
|
||||
dy = (d-c)/m
|
||||
kappa = a
|
||||
psi = c
|
||||
theta = 0
|
||||
|
||||
while((psi + dy) < d):
|
||||
|
||||
while((kappa + dx) < b):
|
||||
|
||||
theta = theta + self.f(kappa, psi)
|
||||
kappa = kappa + dx
|
||||
|
||||
psi = psi + dy
|
||||
kappa = a
|
||||
|
||||
return theta*(dx)*(dy)
|
||||
|
||||
def simpson(self,a,b,c,d,n=None,m=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**4
|
||||
|
||||
if m is None:
|
||||
m = n
|
||||
|
||||
dx = (b-a)/n
|
||||
dy = (d-c)/m
|
||||
|
||||
def x(i):
|
||||
|
||||
x = a + i*dx
|
||||
|
||||
return x
|
||||
|
||||
def y(i):
|
||||
|
||||
y = c + i*dy
|
||||
|
||||
return y
|
||||
|
||||
def g(i):
|
||||
|
||||
sigma = 0
|
||||
upsilon = 0
|
||||
|
||||
zeta = 1
|
||||
csi = 1
|
||||
|
||||
while(zeta <= (m/2)):
|
||||
|
||||
sigma += self.f(x(i),y(2*zeta - 1))
|
||||
zeta += 1
|
||||
|
||||
while(csi <= ((m/2)-1)):
|
||||
|
||||
upsilon += self.f(x(i),y(2*csi))
|
||||
csi += 1
|
||||
|
||||
return (dy/3)*( self.f(x(i),y(0)) + self.f(x(i),y(m)) + 4*sigma + 2*upsilon )
|
||||
|
||||
eta = 0
|
||||
theta = 0
|
||||
|
||||
psi = 1
|
||||
kappa = 1
|
||||
|
||||
while(psi <= (n/2)):
|
||||
|
||||
eta += g(2*psi - 1)
|
||||
psi += 1
|
||||
|
||||
while(kappa <= ((n/2)-1)):
|
||||
|
||||
theta += g(2*kappa)
|
||||
kappa += 1
|
||||
|
||||
return (dx/3)*( g(0) + g(n) + 4*eta + 2*theta)
|
||||
|
||||
class Roots:
|
||||
|
||||
def __init__(self, function=None):
|
||||
if function is not None:
|
||||
self.f = function
|
||||
|
||||
def bissec(self,a,b,e=None):
|
||||
|
||||
if e is None:
|
||||
e = 10**(-6)
|
||||
|
||||
fa = self.f(a)
|
||||
|
||||
while abs(a-b) > e:
|
||||
|
||||
c = (a+b)/2
|
||||
fc = self.f(c)
|
||||
|
||||
if (fa*fc) < 0:
|
||||
|
||||
b = c
|
||||
|
||||
else:
|
||||
|
||||
a = c
|
||||
fa = fc
|
||||
|
||||
c = (a+b)/2
|
||||
|
||||
return c
|
||||
|
||||
def d(self, x, e):
|
||||
return (self.f(x + e) - self.f(x - e))/(2*e)
|
||||
|
||||
def newton(self,a,e=None):
|
||||
|
||||
if e is None:
|
||||
e = 10**(-6)
|
||||
|
||||
fa = self.f(a)
|
||||
da = self.d(a,e)
|
||||
b = a - fa/da
|
||||
|
||||
|
||||
while abs(a-b) > e:
|
||||
|
||||
b = a
|
||||
a -= (fa/da)
|
||||
fa = self.f(a)
|
||||
da = self.d(a,e)
|
||||
|
||||
return a
|
||||
|
||||
def bissec_newton(self,a,b,e=None):
|
||||
|
||||
if e is None:
|
||||
e = 10**(-6)
|
||||
|
||||
fa = self.f(a)
|
||||
|
||||
c = (a+b)/2 # 'c' é a raiz calculada
|
||||
|
||||
while abs(a-b) > 0.1:
|
||||
|
||||
fc = self.f(c)
|
||||
|
||||
if fa*fc < 0:
|
||||
|
||||
b = c
|
||||
|
||||
else:
|
||||
|
||||
a = c
|
||||
fa = self.f(a)
|
||||
|
||||
c = (a+b)/2
|
||||
|
||||
fc = self.f(c)
|
||||
dc = self.d(c,e)
|
||||
h = c - fc/dc # 'h' é uma variável de controle
|
||||
|
||||
while abs(c-h) > e:
|
||||
|
||||
h = c
|
||||
c -= (fc/dc)
|
||||
fc = self.f(c)
|
||||
dc = self.d(c,e)
|
||||
|
||||
return (c)
|
||||
|
||||
|
||||
class Edo:
|
||||
|
||||
def __init__(self, function):
|
||||
self.F = function
|
||||
|
||||
def euler(self,a,y,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
dx = (b-a)/n
|
||||
|
||||
def x(i):
|
||||
return a + i*dx
|
||||
|
||||
for i in range(n):
|
||||
|
||||
y = y + (self.F(x(i),y))*dx
|
||||
|
||||
return y
|
||||
|
||||
def runge(self,a,y,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
dx = (b-a)/n
|
||||
|
||||
def x(i):
|
||||
return (a + i*dx)
|
||||
|
||||
for i in range(n):
|
||||
|
||||
y = y + (dx/2)*(self.F(x(i),y)+self.F(x(i+1),(y+(dx*self.F(x(i),y)))))
|
||||
|
||||
return y
|
||||
|
||||
def adams(self,a,y,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
dx = (b-a)/n
|
||||
|
||||
def x(i):
|
||||
return (a + i*dx)
|
||||
|
||||
for i in range(n):
|
||||
|
||||
f0 = self.F(x(i),y)
|
||||
f1 = self.F(x(i+1),y + dx*self.F(x(i)+(dx/2),y+(dx/2)*self.F(x(i),y)))
|
||||
f2 = self.F(x(i+2),y + (dx/2)*(3*f1-f0))
|
||||
|
||||
y += (dx/12)*(5*f2 + 8*f1 - f0)
|
||||
|
||||
return y
|
||||
|
||||
class Interpolation:
|
||||
""" Data should be organized in two columns: X and Y"""
|
||||
|
||||
def __init__(self, data):
|
||||
|
||||
self.data = data
|
||||
self.polinomial = self.Polinomial(self.data)
|
||||
|
||||
def minimus(self,x):
|
||||
|
||||
theta = 0
|
||||
# somatorio de x
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
theta += self.data.x[i]
|
||||
|
||||
eta = 0
|
||||
#somatorio de y
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
eta += self.data.y[i]
|
||||
|
||||
sigma = 0
|
||||
#somatorio de xy
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
sigma += self.data.x[i]*self.data.y[i]
|
||||
|
||||
omega = 0
|
||||
#somatorio de x^2self.dself.dself.d
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
omega += self.data.x[i]**2
|
||||
|
||||
|
||||
self.a = (self.data.shape[0]*sigma - theta*eta)/(self.data.shape[0]*omega - (theta**2))
|
||||
|
||||
self.b = (theta*sigma - eta*omega)/((theta**2) - self.data.shape[0]*omega)
|
||||
|
||||
ym = 0
|
||||
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
ym += self.data.y[i]/self.data.shape[0]
|
||||
|
||||
sqreq = 0
|
||||
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
sqreq += ((self.a*self.data.x[i] + self.b) - ym)**2
|
||||
|
||||
sqtot = 0
|
||||
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
sqtot += (self.data.y[i] - ym)**2
|
||||
|
||||
self.r2 = sqreq/sqtot
|
||||
|
||||
return self.a*x + self.b
|
||||
|
||||
class Polinomial:
|
||||
|
||||
def __init__(self, data):
|
||||
self.data = data
|
||||
|
||||
def vandermonde(self, x):
|
||||
|
||||
matrix = np.zeros((self.data.shape[0],self.data.shape[0]))
|
||||
|
||||
for k in range(0, self.data.shape[0]):
|
||||
|
||||
matrix[:,k] = self.data.x[:]**k
|
||||
|
||||
self.A = sl.gauss(np.c_[matrix,self.data[:,1]])
|
||||
|
||||
y = 0
|
||||
|
||||
for i in range(0,self.A.shape[0]):
|
||||
|
||||
y += self.A[i]*(x**i)
|
||||
|
||||
return float(y)
|
||||
|
||||
def lagrange(self, x):
|
||||
|
||||
def L(k,x):
|
||||
|
||||
up = down = 1
|
||||
|
||||
for i in [x for x in range(self.data.x.shape[0]) if x != k]:
|
||||
up = up*(x - self.data.x[i])
|
||||
|
||||
for i in [x for x in range(self.data.x.shape[0]) if x != k]:
|
||||
down = down*(self.data.x[k] - self.data.x[i])
|
||||
|
||||
return up/down
|
||||
|
||||
y = 0
|
||||
|
||||
for i in range(self.data.x.shape[0]):
|
||||
|
||||
y += self.data.y[i]*L(i,x)
|
||||
|
||||
return y
|
||||
|
||||
def newton(self,x):
|
||||
|
||||
d = np.array(np.zeros((self.data.shape[0],self.data.shape[0])))
|
||||
|
||||
d[0] = self.data.y
|
||||
|
||||
i = j = 0
|
||||
|
||||
while (i < self.data.shape[0]):
|
||||
|
||||
while (j < (self.data.shape[0]-(i+1))):
|
||||
|
||||
d[i+1][j] = (d[i][j+1] - d[i][j])/(self.data.x[(i+1)+j]-self.data.x[j])
|
||||
j += 1
|
||||
|
||||
i += 1
|
||||
j = 0
|
||||
|
||||
def f(x):
|
||||
|
||||
y = d[0][0]
|
||||
i = 0
|
||||
|
||||
while ((i+1) < self.data.shape[0]):
|
||||
|
||||
mult = 1
|
||||
k = 0
|
||||
while (k <= i):
|
||||
mult = mult*(x - self.data.x[k])
|
||||
k += 1
|
||||
|
||||
y += d[i+1][0]*mult
|
||||
i += 1
|
||||
|
||||
return y
|
||||
|
||||
self.f = f
|
||||
|
||||
return f(x)
|
||||
|
||||
def gregory(self,x):
|
||||
|
||||
h = self.data.x[0] - self.data.x[1]
|
||||
|
||||
d = np.array(np.zeros((self.data.shape[0],self.data.shape[0])))
|
||||
|
||||
d[0] = self.data.y
|
||||
|
||||
i = j = 0
|
||||
|
||||
while (i < self.data.shape[0]):
|
||||
|
||||
while (j < (self.data.shape[0]-(i+1))):
|
||||
|
||||
d[i+1][j] = (d[i][j+1] - d[i][j])/((i+1)*h)
|
||||
j += 1
|
||||
|
||||
i += 1
|
||||
j = 0
|
||||
|
||||
y = d[0][0]
|
||||
i = 0
|
||||
|
||||
while ((i+1) < self.data.shape[0]):
|
||||
|
||||
mult = 1
|
||||
k = 0
|
||||
while (k <= i):
|
||||
mult = mult*(x - self.data.x[k])
|
||||
k += 1
|
||||
|
||||
y += d[i+1][0]*mult
|
||||
i += 1
|
||||
|
||||
return y
|
||||
@@ -1,21 +0,0 @@
|
||||
# Otter - Program made for educational intent, can be freely distributed
|
||||
# and can be used for economical intent. I will not take legal actions
|
||||
# unless my intelectual propperty, the code, is stolen or change without permission.
|
||||
|
||||
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
|
||||
|
||||
# This program is free software; you can redistribute it and/or modify
|
||||
# it under the terms of the GNU General Public License version 2 as published by
|
||||
# the Free Software Foundation.
|
||||
|
||||
# This program is distributed in the hope that it will be useful,
|
||||
# but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
# GNU General Public License for more details.
|
||||
|
||||
# You should have received a copy of the GNU General Public License along
|
||||
# with this program; if not, write to the Free Software Foundation, Inc.,
|
||||
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
|
||||
|
||||
from .Otter import Algebra as algebra
|
||||
from .Otter import Interpolation as interpolation
|
||||
Binary file not shown.
Binary file not shown.
@@ -1,28 +0,0 @@
|
||||
import setuptools
|
||||
|
||||
with open("README.md", "r") as fh:
|
||||
long_description = fh.read()
|
||||
|
||||
setuptools.setup(
|
||||
name="yoshi-otter", # Replace with your own username
|
||||
version="1.3.2",
|
||||
author="Vitor Hideyoshi",
|
||||
author_email="vitor.h.n.batista@gmail.com",
|
||||
description="Numeric Calculus python module in the topic of Algebra Functions",
|
||||
long_description=long_description,
|
||||
long_description_content_type="text/markdown",
|
||||
url="https://github.com/HideyoshiNakazone/Otter-NumericCalculus.git",
|
||||
packages=setuptools.find_packages(),
|
||||
classifiers=[
|
||||
"Programming Language :: Python :: 3",
|
||||
"License :: OSI Approved :: GNU General Public License v2 (GPLv2)",
|
||||
"Operating System :: OS Independent",
|
||||
"Development Status :: 2 - Pre-Alpha",
|
||||
],
|
||||
python_requires='>=3.6',
|
||||
install_requires=[
|
||||
'numpy',
|
||||
'pandas',
|
||||
'yoshi-seals'
|
||||
],
|
||||
)
|
||||
@@ -1,91 +0,0 @@
|
||||
Metadata-Version: 2.1
|
||||
Name: yoshi-otter
|
||||
Version: 1.3.2
|
||||
Summary: Numeric Calculus python module in the topic of Algebra Functions
|
||||
Home-page: https://github.com/HideyoshiNakazone/Otter-NumericCalculus.git
|
||||
Author: Vitor Hideyoshi
|
||||
Author-email: vitor.h.n.batista@gmail.com
|
||||
License: UNKNOWN
|
||||
Description: # Otter - Numeric Calculus
|
||||
|
||||
This python package is made for applied Numeric Calculus of Algebra Functions. It is made with the following objectives in mind:
|
||||
|
||||
* Receive one variable function from user input
|
||||
|
||||
* Receive two variable function from user input
|
||||
|
||||
* Performe derivatives with one variable functions
|
||||
|
||||
* Performe integral with received functions
|
||||
|
||||
* Use methods to proccess the matrices.
|
||||
|
||||
* Find root of functions throw method of bissection and method of newton
|
||||
|
||||
* Solve Diferential Equations throw method of euler and runge
|
||||
|
||||
* Performe Minimus Interpolation and Polinomial Interpolation
|
||||
|
||||
## Syntax
|
||||
|
||||
To initialize a Otter instance linked to functions use the following syntax `otr = Otter.algebra(f)`, where `otr` will be a arbitrary name for the instance and `f` is a function of *one variable*.
|
||||
|
||||
To initialize a Otter instance linked to data and interpolation use the following syntax `otr = Otter.interpolation(data)`, where `otr` will be a arbitrary name for the instance and data will be a *numpy* matrix where the first columns has to contain the values for `x` and the second column contains the values for `y`.
|
||||
|
||||
### Algebra
|
||||
|
||||
Algebra is a Python Class where some of the features described previously are defined as Classes as well, like: `Integral`, `Roots`, `EDO` (diferential equations).
|
||||
|
||||
#### Integral
|
||||
|
||||
To call the class *Integral* append the sufix with lower case in front of the instance like: `otr.integral`. The Integral class has two other class defined inside, `Simple` and `Double`, to call them append the sufix with lower case in front as `otr.integral.simple` or `otr.integral.double`. Then pick between Riemann's Method or Simpson's Method by appending the sufix `riemann` or `simpson` as well.
|
||||
|
||||
After that the syntax will be something like `otr.integral.double.riemann(a,b,c,d,n,m)`, where `a` and `c` will be the first value of the interval of integration respectively in x and y, `b` and `d` will be the last, `n` and `m` will be the number of partitions.
|
||||
|
||||
The syntax for one variable integrations will be `otr.integral.simple.riemann(a,b,n)`.
|
||||
|
||||
If `n` is not defined the standart value in 10^6 partitions for one variable and 10^4 for double. And if `m` is not defined the standart value will be equal to `n`.
|
||||
|
||||
#### Roots
|
||||
|
||||
To call the class *Root* append the sufix with lower case in front of the instance like: `otr.roots`. The Roots class has three methods defined inside, `bissec`, `newton` and `bissec_newton`, to call them append the sufix with lower case in front as `otr.roots.bissec` or `otr.roots.newton` or even `otr.roots.bissecnewton`.
|
||||
|
||||
The syntax for the bissection method and bissec_newton is equal to `otr.roots.bissec(a,b,e)` and `otr.roots.bissec_newton(a,b,e)`, where `a` is the first element of the interval containing the root and `b` is the last, `e` being the precision.
|
||||
|
||||
The syntax for the newton method is equal to `otr.roots.newton(a,e)`, where `a` is the element closest to the root and `e` is the precision.
|
||||
|
||||
If `e` is not defined the standart value is 10^(-6).
|
||||
|
||||
#### Diferential Equations
|
||||
|
||||
To call the class *EDO* (*E*quações *D*iferenciais *O*rdinárias) append the sufix with lower case in front of the instance like: `otr.edo`. The *EDO* class has two methods defined inside: `euler` and `runge`, to call them append the sufix with lower case in front as `otr.edo.euler` or `otr.edo.runge`.
|
||||
|
||||
The syntax for the diferential equations method is equal to `otr.edo.euler(a,y,b,n)` or `otr.edo.runge(a,y,b,n)`, where `a` and `y` will be the inintial point and `b` is the value in *x* which you want to know the corresponding value in *y* and `n` is the number of operations.
|
||||
|
||||
If `n` is not defined the standart value is 10^7.
|
||||
|
||||
### Interpolation
|
||||
|
||||
The python class *Interpolation* is divided in one method, minimus interpolation, and one class, polinomial interpolation.
|
||||
|
||||
To call the method *minimus* use a syntax like `otr = Otter.interpolation(data)`, where `data` is a data frame containing values for *x* and *y*, `otr` is an instance and append the method in front of the instance like: `otr.minimus(x)`, where *x* is value of *f(x)* you want to estimate.
|
||||
|
||||
To call the class *Polinomial* append the sufix with lower case in front of the instance like: `otr.polinomial`. The *Polinomial* class has four methods defined inside: `vandermonde`, `lagrange`, `newton` and `gregory`, to call them append the sufix with lower case in front like `otr.edo.gregory(x)` where *x* is value of *f(x)* you want to estimate.
|
||||
|
||||
## Installation
|
||||
|
||||
To install the package from source `cd` into the directory and run:
|
||||
|
||||
`pip install .`
|
||||
|
||||
or run
|
||||
|
||||
`pip install yoshi-otter`
|
||||
|
||||
Platform: UNKNOWN
|
||||
Classifier: Programming Language :: Python :: 3
|
||||
Classifier: License :: OSI Approved :: GNU General Public License v2 (GPLv2)
|
||||
Classifier: Operating System :: OS Independent
|
||||
Classifier: Development Status :: 2 - Pre-Alpha
|
||||
Requires-Python: >=3.6
|
||||
Description-Content-Type: text/markdown
|
||||
@@ -1,9 +0,0 @@
|
||||
README.md
|
||||
setup.py
|
||||
Otter/Otter.py
|
||||
Otter/__init__.py
|
||||
yoshi_otter.egg-info/PKG-INFO
|
||||
yoshi_otter.egg-info/SOURCES.txt
|
||||
yoshi_otter.egg-info/dependency_links.txt
|
||||
yoshi_otter.egg-info/requires.txt
|
||||
yoshi_otter.egg-info/top_level.txt
|
||||
@@ -1,3 +0,0 @@
|
||||
numpy
|
||||
pandas
|
||||
yoshi-seals
|
||||
@@ -1 +0,0 @@
|
||||
Otter
|
||||
Binary file not shown.
@@ -1,278 +0,0 @@
|
||||
GNU GENERAL PUBLIC LICENSE
|
||||
Version 2, June 1991
|
||||
|
||||
Copyright (C) 1989, 1991 Free Software Foundation, Inc.,
|
||||
51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
Everyone is permitted to copy and distribute verbatim copies
|
||||
of this license document, but changing it is not allowed.
|
||||
|
||||
Preamble
|
||||
|
||||
The licenses for most software are designed to take away your
|
||||
freedom to share and change it. By contrast, the GNU General Public
|
||||
License is intended to guarantee your freedom to share and change free
|
||||
software--to make sure the software is free for all its users. This
|
||||
General Public License applies to most of the Free Software
|
||||
Foundation's software and to any other program whose authors commit to
|
||||
using it. (Some other Free Software Foundation software is covered by
|
||||
the GNU Lesser General Public License instead.) You can apply it to
|
||||
your programs, too.
|
||||
|
||||
When we speak of free software, we are referring to freedom, not
|
||||
price. Our General Public Licenses are designed to make sure that you
|
||||
have the freedom to distribute copies of free software (and charge for
|
||||
this service if you wish), that you receive source code or can get it
|
||||
if you want it, that you can change the software or use pieces of it
|
||||
in new free programs; and that you know you can do these things.
|
||||
|
||||
To protect your rights, we need to make restrictions that forbid
|
||||
anyone to deny you these rights or to ask you to surrender the rights.
|
||||
These restrictions translate to certain responsibilities for you if you
|
||||
distribute copies of the software, or if you modify it.
|
||||
|
||||
For example, if you distribute copies of such a program, whether
|
||||
gratis or for a fee, you must give the recipients all the rights that
|
||||
you have. You must make sure that they, too, receive or can get the
|
||||
source code. And you must show them these terms so they know their
|
||||
rights.
|
||||
|
||||
We protect your rights with two steps: (1) copyright the software, and
|
||||
(2) offer you this license which gives you legal permission to copy,
|
||||
distribute and/or modify the software.
|
||||
|
||||
Also, for each author's protection and ours, we want to make certain
|
||||
that everyone understands that there is no warranty for this free
|
||||
software. If the software is modified by someone else and passed on, we
|
||||
want its recipients to know that what they have is not the original, so
|
||||
that any problems introduced by others will not reflect on the original
|
||||
authors' reputations.
|
||||
|
||||
Finally, any free program is threatened constantly by software
|
||||
patents. We wish to avoid the danger that redistributors of a free
|
||||
program will individually obtain patent licenses, in effect making the
|
||||
program proprietary. To prevent this, we have made it clear that any
|
||||
patent must be licensed for everyone's free use or not licensed at all.
|
||||
|
||||
The precise terms and conditions for copying, distribution and
|
||||
modification follow.
|
||||
|
||||
GNU GENERAL PUBLIC LICENSE
|
||||
TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
|
||||
|
||||
0. This License applies to any program or other work which contains
|
||||
a notice placed by the copyright holder saying it may be distributed
|
||||
under the terms of this General Public License. The "Program", below,
|
||||
refers to any such program or work, and a "work based on the Program"
|
||||
means either the Program or any derivative work under copyright law:
|
||||
that is to say, a work containing the Program or a portion of it,
|
||||
either verbatim or with modifications and/or translated into another
|
||||
language. (Hereinafter, translation is included without limitation in
|
||||
the term "modification".) Each licensee is addressed as "you".
|
||||
|
||||
Activities other than copying, distribution and modification are not
|
||||
covered by this License; they are outside its scope. The act of
|
||||
running the Program is not restricted, and the output from the Program
|
||||
is covered only if its contents constitute a work based on the
|
||||
Program (independent of having been made by running the Program).
|
||||
Whether that is true depends on what the Program does.
|
||||
|
||||
1. You may copy and distribute verbatim copies of the Program's
|
||||
source code as you receive it, in any medium, provided that you
|
||||
conspicuously and appropriately publish on each copy an appropriate
|
||||
copyright notice and disclaimer of warranty; keep intact all the
|
||||
notices that refer to this License and to the absence of any warranty;
|
||||
and give any other recipients of the Program a copy of this License
|
||||
along with the Program.
|
||||
|
||||
You may charge a fee for the physical act of transferring a copy, and
|
||||
you may at your option offer warranty protection in exchange for a fee.
|
||||
|
||||
2. You may modify your copy or copies of the Program or any portion
|
||||
of it, thus forming a work based on the Program, and copy and
|
||||
distribute such modifications or work under the terms of Section 1
|
||||
above, provided that you also meet all of these conditions:
|
||||
|
||||
a) You must cause the modified files to carry prominent notices
|
||||
stating that you changed the files and the date of any change.
|
||||
|
||||
b) You must cause any work that you distribute or publish, that in
|
||||
whole or in part contains or is derived from the Program or any
|
||||
part thereof, to be licensed as a whole at no charge to all third
|
||||
parties under the terms of this License.
|
||||
|
||||
c) If the modified program normally reads commands interactively
|
||||
when run, you must cause it, when started running for such
|
||||
interactive use in the most ordinary way, to print or display an
|
||||
announcement including an appropriate copyright notice and a
|
||||
notice that there is no warranty (or else, saying that you provide
|
||||
a warranty) and that users may redistribute the program under
|
||||
these conditions, and telling the user how to view a copy of this
|
||||
License. (Exception: if the Program itself is interactive but
|
||||
does not normally print such an announcement, your work based on
|
||||
the Program is not required to print an announcement.)
|
||||
|
||||
These requirements apply to the modified work as a whole. If
|
||||
identifiable sections of that work are not derived from the Program,
|
||||
and can be reasonably considered independent and separate works in
|
||||
themselves, then this License, and its terms, do not apply to those
|
||||
sections when you distribute them as separate works. But when you
|
||||
distribute the same sections as part of a whole which is a work based
|
||||
on the Program, the distribution of the whole must be on the terms of
|
||||
this License, whose permissions for other licensees extend to the
|
||||
entire whole, and thus to each and every part regardless of who wrote it.
|
||||
|
||||
Thus, it is not the intent of this section to claim rights or contest
|
||||
your rights to work written entirely by you; rather, the intent is to
|
||||
exercise the right to control the distribution of derivative or
|
||||
collective works based on the Program.
|
||||
|
||||
In addition, mere aggregation of another work not based on the Program
|
||||
with the Program (or with a work based on the Program) on a volume of
|
||||
a storage or distribution medium does not bring the other work under
|
||||
the scope of this License.
|
||||
|
||||
3. You may copy and distribute the Program (or a work based on it,
|
||||
under Section 2) in object code or executable form under the terms of
|
||||
Sections 1 and 2 above provided that you also do one of the following:
|
||||
|
||||
a) Accompany it with the complete corresponding machine-readable
|
||||
source code, which must be distributed under the terms of Sections
|
||||
1 and 2 above on a medium customarily used for software interchange; or,
|
||||
|
||||
b) Accompany it with a written offer, valid for at least three
|
||||
years, to give any third party, for a charge no more than your
|
||||
cost of physically performing source distribution, a complete
|
||||
machine-readable copy of the corresponding source code, to be
|
||||
distributed under the terms of Sections 1 and 2 above on a medium
|
||||
customarily used for software interchange; or,
|
||||
|
||||
c) Accompany it with the information you received as to the offer
|
||||
to distribute corresponding source code. (This alternative is
|
||||
allowed only for noncommercial distribution and only if you
|
||||
received the program in object code or executable form with such
|
||||
an offer, in accord with Subsection b above.)
|
||||
|
||||
The source code for a work means the preferred form of the work for
|
||||
making modifications to it. For an executable work, complete source
|
||||
code means all the source code for all modules it contains, plus any
|
||||
associated interface definition files, plus the scripts used to
|
||||
control compilation and installation of the executable. However, as a
|
||||
special exception, the source code distributed need not include
|
||||
anything that is normally distributed (in either source or binary
|
||||
form) with the major components (compiler, kernel, and so on) of the
|
||||
operating system on which the executable runs, unless that component
|
||||
itself accompanies the executable.
|
||||
|
||||
If distribution of executable or object code is made by offering
|
||||
access to copy from a designated place, then offering equivalent
|
||||
access to copy the source code from the same place counts as
|
||||
distribution of the source code, even though third parties are not
|
||||
compelled to copy the source along with the object code.
|
||||
|
||||
4. You may not copy, modify, sublicense, or distribute the Program
|
||||
except as expressly provided under this License. Any attempt
|
||||
otherwise to copy, modify, sublicense or distribute the Program is
|
||||
void, and will automatically terminate your rights under this License.
|
||||
However, parties who have received copies, or rights, from you under
|
||||
this License will not have their licenses terminated so long as such
|
||||
parties remain in full compliance.
|
||||
|
||||
5. You are not required to accept this License, since you have not
|
||||
signed it. However, nothing else grants you permission to modify or
|
||||
distribute the Program or its derivative works. These actions are
|
||||
prohibited by law if you do not accept this License. Therefore, by
|
||||
modifying or distributing the Program (or any work based on the
|
||||
Program), you indicate your acceptance of this License to do so, and
|
||||
all its terms and conditions for copying, distributing or modifying
|
||||
the Program or works based on it.
|
||||
|
||||
6. Each time you redistribute the Program (or any work based on the
|
||||
Program), the recipient automatically receives a license from the
|
||||
original licensor to copy, distribute or modify the Program subject to
|
||||
these terms and conditions. You may not impose any further
|
||||
restrictions on the recipients' exercise of the rights granted herein.
|
||||
You are not responsible for enforcing compliance by third parties to
|
||||
this License.
|
||||
|
||||
7. If, as a consequence of a court judgment or allegation of patent
|
||||
infringement or for any other reason (not limited to patent issues),
|
||||
conditions are imposed on you (whether by court order, agreement or
|
||||
otherwise) that contradict the conditions of this License, they do not
|
||||
excuse you from the conditions of this License. If you cannot
|
||||
distribute so as to satisfy simultaneously your obligations under this
|
||||
License and any other pertinent obligations, then as a consequence you
|
||||
may not distribute the Program at all. For example, if a patent
|
||||
license would not permit royalty-free redistribution of the Program by
|
||||
all those who receive copies directly or indirectly through you, then
|
||||
the only way you could satisfy both it and this License would be to
|
||||
refrain entirely from distribution of the Program.
|
||||
|
||||
If any portion of this section is held invalid or unenforceable under
|
||||
any particular circumstance, the balance of the section is intended to
|
||||
apply and the section as a whole is intended to apply in other
|
||||
circumstances.
|
||||
|
||||
It is not the purpose of this section to induce you to infringe any
|
||||
patents or other property right claims or to contest validity of any
|
||||
such claims; this section has the sole purpose of protecting the
|
||||
integrity of the free software distribution system, which is
|
||||
implemented by public license practices. Many people have made
|
||||
generous contributions to the wide range of software distributed
|
||||
through that system in reliance on consistent application of that
|
||||
system; it is up to the author/donor to decide if he or she is willing
|
||||
to distribute software through any other system and a licensee cannot
|
||||
impose that choice.
|
||||
|
||||
This section is intended to make thoroughly clear what is believed to
|
||||
be a consequence of the rest of this License.
|
||||
|
||||
8. If the distribution and/or use of the Program is restricted in
|
||||
certain countries either by patents or by copyrighted interfaces, the
|
||||
original copyright holder who places the Program under this License
|
||||
may add an explicit geographical distribution limitation excluding
|
||||
those countries, so that distribution is permitted only in or among
|
||||
countries not thus excluded. In such case, this License incorporates
|
||||
the limitation as if written in the body of this License.
|
||||
|
||||
9. The Free Software Foundation may publish revised and/or new versions
|
||||
of the General Public License from time to time. Such new versions will
|
||||
be similar in spirit to the present version, but may differ in detail to
|
||||
address new problems or concerns.
|
||||
|
||||
Each version is given a distinguishing version number. If the Program
|
||||
specifies a version number of this License which applies to it and "any
|
||||
later version", you have the option of following the terms and conditions
|
||||
either of that version or of any later version published by the Free
|
||||
Software Foundation. If the Program does not specify a version number of
|
||||
this License, you may choose any version ever published by the Free Software
|
||||
Foundation.
|
||||
|
||||
10. If you wish to incorporate parts of the Program into other free
|
||||
programs whose distribution conditions are different, write to the author
|
||||
to ask for permission. For software which is copyrighted by the Free
|
||||
Software Foundation, write to the Free Software Foundation; we sometimes
|
||||
make exceptions for this. Our decision will be guided by the two goals
|
||||
of preserving the free status of all derivatives of our free software and
|
||||
of promoting the sharing and reuse of software generally.
|
||||
|
||||
NO WARRANTY
|
||||
|
||||
11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY
|
||||
FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN
|
||||
OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES
|
||||
PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED
|
||||
OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
|
||||
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS
|
||||
TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE
|
||||
PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING,
|
||||
REPAIR OR CORRECTION.
|
||||
|
||||
12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
|
||||
WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR
|
||||
REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES,
|
||||
INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING
|
||||
OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED
|
||||
TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY
|
||||
YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER
|
||||
PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE
|
||||
POSSIBILITY OF SUCH DAMAGES.
|
||||
@@ -1,499 +0,0 @@
|
||||
# Otter - Program made for educational intent, can be freely distributed
|
||||
# and can be used for economical intent. I will not take legal actions
|
||||
# unless my intelectual propperty, the code, is stolen or change without permission.
|
||||
#
|
||||
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
|
||||
#
|
||||
# This program is free software; you can redistribute it and/or modify
|
||||
# it under the terms of the GNU General Public License version 2 as published by
|
||||
# the Free Software Foundation.
|
||||
#
|
||||
# This program is distributed in the hope that it will be useful,
|
||||
# but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
# GNU General Public License for more details.
|
||||
#
|
||||
# You should have received a copy of the GNU General Public License along
|
||||
# with this program; if not, write to the Free Software Foundation, Inc.,
|
||||
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
|
||||
|
||||
import math
|
||||
import numpy as np
|
||||
import Seals
|
||||
|
||||
sl = Seals.process()
|
||||
|
||||
class Algebra:
|
||||
|
||||
def __init__(self, function):
|
||||
self.f = function
|
||||
self.integral = self.Integral(self.f)
|
||||
self.roots = self.Roots(self.f)
|
||||
self.edo = self.Edo(self.f)
|
||||
|
||||
def d(self, x, e):
|
||||
return (self.f(x + e) - self.f(x - e))/(2*e)
|
||||
|
||||
class Integral:
|
||||
|
||||
def __init__(self,function):
|
||||
self.f = function
|
||||
self.simple = self.Simple(function)
|
||||
self.double = self.Double(function)
|
||||
|
||||
class Simple:
|
||||
def __init__(self, function):
|
||||
self.f = function
|
||||
|
||||
def riemann(self,a,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
delta = (b-a)/n
|
||||
|
||||
psi = a
|
||||
theta = 0
|
||||
|
||||
while((psi+delta) <= b):
|
||||
|
||||
theta += (self.f(psi) + self.f(psi + delta))/2
|
||||
psi += delta
|
||||
|
||||
integral = delta*theta
|
||||
|
||||
return integral
|
||||
|
||||
def simpson(self,a,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
def x(i):
|
||||
return a + i*h
|
||||
|
||||
h = (b-a)/n
|
||||
|
||||
eta = 0
|
||||
theta = 0
|
||||
|
||||
psi = 1
|
||||
kappa = 1
|
||||
|
||||
while(psi <= (n/2)):
|
||||
|
||||
eta = eta + self.f(x(2*psi - 1))
|
||||
psi = psi + 1
|
||||
|
||||
while(kappa <= ((n/2)-1)):
|
||||
|
||||
theta = theta + self.f(x(2*kappa))
|
||||
kappa = kappa + 1
|
||||
|
||||
return (h/3)*( self.f(x(0)) + self.f(x(n)) + 4*eta + 2*theta)
|
||||
|
||||
|
||||
class Double:
|
||||
|
||||
def __init__(self,function):
|
||||
self.f = function
|
||||
|
||||
def riemann(self,a,b,c,d,n=None,m=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**4
|
||||
|
||||
if m is None:
|
||||
m = n
|
||||
|
||||
dx = (b-a)/n
|
||||
dy = (d-c)/m
|
||||
kappa = a
|
||||
psi = c
|
||||
theta = 0
|
||||
|
||||
while((psi + dy) < d):
|
||||
|
||||
while((kappa + dx) < b):
|
||||
|
||||
theta = theta + self.f(kappa, psi)
|
||||
kappa = kappa + dx
|
||||
|
||||
psi = psi + dy
|
||||
kappa = a
|
||||
|
||||
return theta*(dx)*(dy)
|
||||
|
||||
def simpson(self,a,b,c,d,n=None,m=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**4
|
||||
|
||||
if m is None:
|
||||
m = n
|
||||
|
||||
dx = (b-a)/n
|
||||
dy = (d-c)/m
|
||||
|
||||
def x(i):
|
||||
|
||||
x = a + i*dx
|
||||
|
||||
return x
|
||||
|
||||
def y(i):
|
||||
|
||||
y = c + i*dy
|
||||
|
||||
return y
|
||||
|
||||
def g(i):
|
||||
|
||||
sigma = 0
|
||||
upsilon = 0
|
||||
|
||||
zeta = 1
|
||||
csi = 1
|
||||
|
||||
while(zeta <= (m/2)):
|
||||
|
||||
sigma += self.f(x(i),y(2*zeta - 1))
|
||||
zeta += 1
|
||||
|
||||
while(csi <= ((m/2)-1)):
|
||||
|
||||
upsilon += self.f(x(i),y(2*csi))
|
||||
csi += 1
|
||||
|
||||
return (dy/3)*( self.f(x(i),y(0)) + self.f(x(i),y(m)) + 4*sigma + 2*upsilon )
|
||||
|
||||
eta = 0
|
||||
theta = 0
|
||||
|
||||
psi = 1
|
||||
kappa = 1
|
||||
|
||||
while(psi <= (n/2)):
|
||||
|
||||
eta += g(2*psi - 1)
|
||||
psi += 1
|
||||
|
||||
while(kappa <= ((n/2)-1)):
|
||||
|
||||
theta += g(2*kappa)
|
||||
kappa += 1
|
||||
|
||||
return (dx/3)*( g(0) + g(n) + 4*eta + 2*theta)
|
||||
|
||||
class Roots:
|
||||
|
||||
def __init__(self, function=None):
|
||||
if function is not None:
|
||||
self.f = function
|
||||
|
||||
def bissec(self,a,b,e=None):
|
||||
|
||||
if e is None:
|
||||
e = 10**(-6)
|
||||
|
||||
fa = self.f(a)
|
||||
|
||||
while abs(a-b) > e:
|
||||
|
||||
c = (a+b)/2
|
||||
fc = self.f(c)
|
||||
|
||||
if (fa*fc) < 0:
|
||||
|
||||
b = c
|
||||
|
||||
else:
|
||||
|
||||
a = c
|
||||
fa = fc
|
||||
|
||||
c = (a+b)/2
|
||||
|
||||
return c
|
||||
|
||||
def d(self, x, e):
|
||||
return (self.f(x + e) - self.f(x - e))/(2*e)
|
||||
|
||||
def newton(self,a,e=None):
|
||||
|
||||
if e is None:
|
||||
e = 10**(-6)
|
||||
|
||||
fa = self.f(a)
|
||||
da = self.d(a,e)
|
||||
b = a - fa/da
|
||||
|
||||
|
||||
while abs(a-b) > e:
|
||||
|
||||
b = a
|
||||
a -= (fa/da)
|
||||
fa = self.f(a)
|
||||
da = self.d(a,e)
|
||||
|
||||
return a
|
||||
|
||||
def bissec_newton(self,a,b,e=None):
|
||||
|
||||
if e is None:
|
||||
e = 10**(-6)
|
||||
|
||||
fa = self.f(a)
|
||||
|
||||
c = (a+b)/2 # 'c' é a raiz calculada
|
||||
|
||||
while abs(a-b) > 0.1:
|
||||
|
||||
fc = self.f(c)
|
||||
|
||||
if fa*fc < 0:
|
||||
|
||||
b = c
|
||||
|
||||
else:
|
||||
|
||||
a = c
|
||||
fa = self.f(a)
|
||||
|
||||
c = (a+b)/2
|
||||
|
||||
fc = self.f(c)
|
||||
dc = self.d(c,e)
|
||||
h = c - fc/dc # 'h' é uma variável de controle
|
||||
|
||||
while abs(c-h) > e:
|
||||
|
||||
h = c
|
||||
c -= (fc/dc)
|
||||
fc = self.f(c)
|
||||
dc = self.d(c,e)
|
||||
|
||||
return (c)
|
||||
|
||||
|
||||
class Edo:
|
||||
|
||||
def __init__(self, function):
|
||||
self.f = function
|
||||
|
||||
def euler(self,a,y,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**7
|
||||
|
||||
dx = (b-a)/n
|
||||
|
||||
def x(i):
|
||||
return a + i*dx
|
||||
|
||||
for i in range(n):
|
||||
|
||||
y = y + (self.f(x(i),y))*dx
|
||||
|
||||
return y
|
||||
|
||||
def runge(self,a,y,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**7
|
||||
|
||||
dx = (b-a)/n
|
||||
|
||||
def x(i):
|
||||
return (a + i*dx)
|
||||
|
||||
for i in range(n):
|
||||
|
||||
y = y + (dx/2)*(self.f(x(i),y)+self.f(x(i+1),(y+(dx*self.f(x(i),y)))))
|
||||
|
||||
return y
|
||||
|
||||
class Interpolation:
|
||||
""" Data should be organized in two columns: X and Y"""
|
||||
|
||||
def __init__(self, data):
|
||||
|
||||
self.data = data
|
||||
self.polinomial = self.Polinomial(self.data)
|
||||
|
||||
def minimus(self,x):
|
||||
|
||||
theta = 0
|
||||
# somatorio de x
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
theta += self.data[i][0]
|
||||
|
||||
eta = 0
|
||||
#somatorio de y
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
eta += self.data[i][1]
|
||||
|
||||
sigma = 0
|
||||
#somatorio de xy
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
sigma += self.data[i][0]*self.data[i][1]
|
||||
|
||||
omega = 0
|
||||
#somatorio de x^2
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
omega += self.data[i][0]**2
|
||||
|
||||
|
||||
self.a = (self.data.shape[0]*sigma - theta*eta)/(self.data.shape[0]*omega - (theta**2))
|
||||
|
||||
self.b = (theta*sigma - eta*omega)/((theta**2) - self.data.shape[0]*omega)
|
||||
|
||||
ym = 0
|
||||
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
ym += self.data[i][1]/self.data.shape[0]
|
||||
|
||||
sqreq = 0
|
||||
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
sqreq += ((self.a*self.data[i][0] + self.b) - ym)**2
|
||||
|
||||
sqtot = 0
|
||||
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
sqtot += (self.data[i][1] - ym)**2
|
||||
|
||||
self.r2 = sqreq/sqtot
|
||||
|
||||
return self.a*x + self.b
|
||||
|
||||
class Polinomial:
|
||||
|
||||
def __init__(self, data):
|
||||
self.data = data
|
||||
|
||||
def vandermonde(self, x):
|
||||
|
||||
matrix = np.zeros((self.data.shape[0],self.data.shape[0]))
|
||||
|
||||
for k in range(0, self.data.shape[0]):
|
||||
|
||||
matrix[:,k] = self.data[:,0]**k
|
||||
|
||||
self.A = sl.gauss(np.c_[matrix,self.data[:,1]])
|
||||
|
||||
y = 0
|
||||
|
||||
for i in range(0,self.A.shape[0]):
|
||||
|
||||
y += self.A[i]*(x**i)
|
||||
|
||||
return float(y)
|
||||
|
||||
def lagrange(self, x):
|
||||
|
||||
data_x = self.data[:,0]
|
||||
data_y = self.data[:,1]
|
||||
|
||||
def L(k,x):
|
||||
|
||||
up = down = 1
|
||||
|
||||
for i in [x for x in range(data_x.shape[0]) if x != k]:
|
||||
up = up*(x - data_x[i])
|
||||
|
||||
for i in [x for x in range(data_x.shape[0]) if x != k]:
|
||||
down = down*(data_x[k] - data_x[i])
|
||||
|
||||
return up/down
|
||||
|
||||
y = 0
|
||||
|
||||
for i in range(data_x.shape[0]):
|
||||
|
||||
y += data_y[i]*L(i,x)
|
||||
|
||||
return y
|
||||
|
||||
def newton(self,x):
|
||||
|
||||
d = np.array(np.zeros((self.data.shape[0],self.data.shape[0])))
|
||||
|
||||
d[0] = self.data[:,1]
|
||||
|
||||
i = j = 0
|
||||
|
||||
while (i < self.data.shape[0]):
|
||||
|
||||
while (j < (self.data.shape[0]-(i+1))):
|
||||
|
||||
d[i+1][j] = (d[i][j+1] - d[i][j])/(self.data[(i+1)+j][0]-self.data[j][0])
|
||||
j += 1
|
||||
|
||||
i += 1
|
||||
j = 0
|
||||
|
||||
def f(x):
|
||||
|
||||
y = d[0][0]
|
||||
i = 0
|
||||
|
||||
while ((i+1) < self.data.shape[0]):
|
||||
|
||||
mult = 1
|
||||
k = 0
|
||||
while (k <= i):
|
||||
mult = mult*(x - self.data[k][0])
|
||||
k += 1
|
||||
|
||||
y += d[i+1][0]*mult
|
||||
i += 1
|
||||
|
||||
return y
|
||||
|
||||
self.f = f
|
||||
|
||||
return f(x)
|
||||
|
||||
def gregory(self,x):
|
||||
|
||||
h = self.data[0][0] - self.data[1][0]
|
||||
|
||||
d = np.array(np.zeros((self.data.shape[0],self.data.shape[0])))
|
||||
|
||||
d[0] = self.data[:,1]
|
||||
|
||||
i = j = 0
|
||||
|
||||
while (i < self.data.shape[0]):
|
||||
|
||||
while (j < (self.data.shape[0]-(i+1))):
|
||||
|
||||
d[i+1][j] = (d[i][j+1] - d[i][j])/((i+1)*h)
|
||||
j += 1
|
||||
|
||||
i += 1
|
||||
j = 0
|
||||
|
||||
y = d[0][0]
|
||||
i = 0
|
||||
|
||||
while ((i+1) < self.data.shape[0]):
|
||||
|
||||
mult = 1
|
||||
k = 0
|
||||
while (k <= i):
|
||||
mult = mult*(x - self.data[k][0])
|
||||
k += 1
|
||||
|
||||
y += d[i+1][0]*mult
|
||||
i += 1
|
||||
|
||||
return y
|
||||
@@ -1,21 +0,0 @@
|
||||
# Otter - Program made for educational intent, can be freely distributed
|
||||
# and can be used for economical intent. I will not take legal actions
|
||||
# unless my intelectual propperty, the code, is stolen or change without permission.
|
||||
|
||||
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
|
||||
|
||||
# This program is free software; you can redistribute it and/or modify
|
||||
# it under the terms of the GNU General Public License version 2 as published by
|
||||
# the Free Software Foundation.
|
||||
|
||||
# This program is distributed in the hope that it will be useful,
|
||||
# but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
# GNU General Public License for more details.
|
||||
|
||||
# You should have received a copy of the GNU General Public License along
|
||||
# with this program; if not, write to the Free Software Foundation, Inc.,
|
||||
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
|
||||
|
||||
from .Otter import Algebra as algebra
|
||||
from .Otter import Interpolation as interpolation
|
||||
@@ -1,75 +0,0 @@
|
||||
# Otter - Numeric Calculus
|
||||
|
||||
This python package is made for applied Numeric Calculus of Algebra Functions. It is made with the following objectives in mind:
|
||||
|
||||
* Receive one variable function from user input
|
||||
|
||||
* Receive two variable function from user input
|
||||
|
||||
* Performe derivatives with one variable functions
|
||||
|
||||
* Performe integral with received functions
|
||||
|
||||
* Use methods to proccess the matrices.
|
||||
|
||||
* Find root of functions throw method of bissection and method of newton
|
||||
|
||||
* Solve Diferential Equations throw method of euler and runge
|
||||
|
||||
* Performe Minimus Interpolation and Polinomial Interpolation
|
||||
|
||||
## Syntax
|
||||
|
||||
To initialize a Otter instance linked to functions use the following syntax `otr = Otter.algebra(f)`, where `otr` will be a arbitrary name for the instance and `f` is a function of *one variable*.
|
||||
|
||||
To initialize a Otter instance linked to data and interpolation use the following syntax `otr = Otter.interpolation(data)`, where `otr` will be a arbitrary name for the instance and data will be a *numpy* matrix where the first columns has to contain the values for `x` and the second column contains the values for `y`.
|
||||
|
||||
### Algebra
|
||||
|
||||
Algebra is a Python Class where some of the features described previously are defined as Classes as well, like: `Integral`, `Roots`, `EDO` (diferential equations).
|
||||
|
||||
#### Integral
|
||||
|
||||
To call the class *Integral* append the sufix with lower case in front of the instance like: `otr.integral`. The Integral class has two other class defined inside, `Simple` and `Double`, to call them append the sufix with lower case in front as `otr.integral.simple` or `otr.integral.double`. Then pick between Riemann's Method or Simpson's Method by appending the sufix `riemann` or `simpson` as well.
|
||||
|
||||
After that the syntax will be something like `otr.integral.double.riemann(a,b,c,d,n,m)`, where `a` and `c` will be the first value of the interval of integration respectively in x and y, `b` and `d` will be the last, `n` and `m` will be the number of partitions.
|
||||
|
||||
The syntax for one variable integrations will be `otr.integral.simple.riemann(a,b,n)`.
|
||||
|
||||
If `n` is not defined the standart value in 10^6 partitions for one variable and 10^4 for double. And if `m` is not defined the standart value will be equal to `n`.
|
||||
|
||||
#### Roots
|
||||
|
||||
To call the class *Root* append the sufix with lower case in front of the instance like: `otr.roots`. The Roots class has three methods defined inside, `bissec`, `newton` and `bissec_newton`, to call them append the sufix with lower case in front as `otr.roots.bissec` or `otr.roots.newton` or even `otr.roots.bissecnewton`.
|
||||
|
||||
The syntax for the bissection method and bissec_newton is equal to `otr.roots.bissec(a,b,e)` and `otr.roots.bissec_newton(a,b,e)`, where `a` is the first element of the interval containing the root and `b` is the last, `e` being the precision.
|
||||
|
||||
The syntax for the newton method is equal to `otr.roots.newton(a,e)`, where `a` is the element closest to the root and `e` is the precision.
|
||||
|
||||
If `e` is not defined the standart value is 10^(-6).
|
||||
|
||||
#### Diferential Equations
|
||||
|
||||
To call the class *EDO* (*E*quações *D*iferenciais *O*rdinárias) append the sufix with lower case in front of the instance like: `otr.edo`. The *EDO* class has two methods defined inside: `euler` and `runge`, to call them append the sufix with lower case in front as `otr.edo.euler` or `otr.edo.runge`.
|
||||
|
||||
The syntax for the diferential equations method is equal to `otr.edo.euler(a,y,b,n)` or `otr.edo.runge(a,y,b,n)`, where `a` and `y` will be the inintial point and `b` is the value in *x* which you want to know the corresponding value in *y* and `n` is the number of operations.
|
||||
|
||||
If `n` is not defined the standart value is 10^7.
|
||||
|
||||
### Interpolation
|
||||
|
||||
The python class *Interpolation* is divided in one method, minimus interpolation, and one class, polinomial interpolation.
|
||||
|
||||
To call the method *minimus* use a syntax like `otr = Otter.interpolation(data)`, where `otr` is an instance and append the method in front of the instance like: `otr.minimus(x)`, where *x* is value of *f(x)* you want to estimate.
|
||||
|
||||
To call the class *Polinomial* append the sufix with lower case in front of the instance like: `otr.polinomial`. The *Polinomial* class has four methods defined inside: `vandermonde`, `lagrange`, `newton` and `gregory`, to call them append the sufix with lower case in front like `otr.edo.gregory(x)` where *x* is value of *f(x)* you want to estimate.
|
||||
|
||||
## Installation
|
||||
|
||||
To install the package from source `cd` into the directory and run:
|
||||
|
||||
`pip install .`
|
||||
|
||||
or run
|
||||
|
||||
`pip install yoshi-otter`
|
||||
@@ -1,499 +0,0 @@
|
||||
# Otter - Program made for educational intent, can be freely distributed
|
||||
# and can be used for economical intent. I will not take legal actions
|
||||
# unless my intelectual propperty, the code, is stolen or change without permission.
|
||||
#
|
||||
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
|
||||
#
|
||||
# This program is free software; you can redistribute it and/or modify
|
||||
# it under the terms of the GNU General Public License version 2 as published by
|
||||
# the Free Software Foundation.
|
||||
#
|
||||
# This program is distributed in the hope that it will be useful,
|
||||
# but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
# GNU General Public License for more details.
|
||||
#
|
||||
# You should have received a copy of the GNU General Public License along
|
||||
# with this program; if not, write to the Free Software Foundation, Inc.,
|
||||
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
|
||||
|
||||
import math
|
||||
import numpy as np
|
||||
import Seals
|
||||
|
||||
sl = Seals.process()
|
||||
|
||||
class Algebra:
|
||||
|
||||
def __init__(self, function):
|
||||
self.f = function
|
||||
self.integral = self.Integral(self.f)
|
||||
self.roots = self.Roots(self.f)
|
||||
self.edo = self.Edo(self.f)
|
||||
|
||||
def d(self, x, e):
|
||||
return (self.f(x + e) - self.f(x - e))/(2*e)
|
||||
|
||||
class Integral:
|
||||
|
||||
def __init__(self,function):
|
||||
self.f = function
|
||||
self.simple = self.Simple(function)
|
||||
self.double = self.Double(function)
|
||||
|
||||
class Simple:
|
||||
def __init__(self, function):
|
||||
self.f = function
|
||||
|
||||
def riemann(self,a,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
delta = (b-a)/n
|
||||
|
||||
psi = a
|
||||
theta = 0
|
||||
|
||||
while((psi+delta) <= b):
|
||||
|
||||
theta += (self.f(psi) + self.f(psi + delta))/2
|
||||
psi += delta
|
||||
|
||||
integral = delta*theta
|
||||
|
||||
return integral
|
||||
|
||||
def simpson(self,a,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
def x(i):
|
||||
return a + i*h
|
||||
|
||||
h = (b-a)/n
|
||||
|
||||
eta = 0
|
||||
theta = 0
|
||||
|
||||
psi = 1
|
||||
kappa = 1
|
||||
|
||||
while(psi <= (n/2)):
|
||||
|
||||
eta = eta + self.f(x(2*psi - 1))
|
||||
psi = psi + 1
|
||||
|
||||
while(kappa <= ((n/2)-1)):
|
||||
|
||||
theta = theta + self.f(x(2*kappa))
|
||||
kappa = kappa + 1
|
||||
|
||||
return (h/3)*( self.f(x(0)) + self.f(x(n)) + 4*eta + 2*theta)
|
||||
|
||||
|
||||
class Double:
|
||||
|
||||
def __init__(self,function):
|
||||
self.f = function
|
||||
|
||||
def riemann(self,a,b,c,d,n=None,m=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**4
|
||||
|
||||
if m is None:
|
||||
m = n
|
||||
|
||||
dx = (b-a)/n
|
||||
dy = (d-c)/m
|
||||
kappa = a
|
||||
psi = c
|
||||
theta = 0
|
||||
|
||||
while((psi + dy) < d):
|
||||
|
||||
while((kappa + dx) < b):
|
||||
|
||||
theta = theta + self.f(kappa, psi)
|
||||
kappa = kappa + dx
|
||||
|
||||
psi = psi + dy
|
||||
kappa = a
|
||||
|
||||
return theta*(dx)*(dy)
|
||||
|
||||
def simpson(self,a,b,c,d,n=None,m=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**4
|
||||
|
||||
if m is None:
|
||||
m = n
|
||||
|
||||
dx = (b-a)/n
|
||||
dy = (d-c)/m
|
||||
|
||||
def x(i):
|
||||
|
||||
x = a + i*dx
|
||||
|
||||
return x
|
||||
|
||||
def y(i):
|
||||
|
||||
y = c + i*dy
|
||||
|
||||
return y
|
||||
|
||||
def g(i):
|
||||
|
||||
sigma = 0
|
||||
upsilon = 0
|
||||
|
||||
zeta = 1
|
||||
csi = 1
|
||||
|
||||
while(zeta <= (m/2)):
|
||||
|
||||
sigma += self.f(x(i),y(2*zeta - 1))
|
||||
zeta += 1
|
||||
|
||||
while(csi <= ((m/2)-1)):
|
||||
|
||||
upsilon += self.f(x(i),y(2*csi))
|
||||
csi += 1
|
||||
|
||||
return (dy/3)*( self.f(x(i),y(0)) + self.f(x(i),y(m)) + 4*sigma + 2*upsilon )
|
||||
|
||||
eta = 0
|
||||
theta = 0
|
||||
|
||||
psi = 1
|
||||
kappa = 1
|
||||
|
||||
while(psi <= (n/2)):
|
||||
|
||||
eta += g(2*psi - 1)
|
||||
psi += 1
|
||||
|
||||
while(kappa <= ((n/2)-1)):
|
||||
|
||||
theta += g(2*kappa)
|
||||
kappa += 1
|
||||
|
||||
return (dx/3)*( g(0) + g(n) + 4*eta + 2*theta)
|
||||
|
||||
class Roots:
|
||||
|
||||
def __init__(self, function=None):
|
||||
if function is not None:
|
||||
self.f = function
|
||||
|
||||
def bissec(self,a,b,e=None):
|
||||
|
||||
if e is None:
|
||||
e = 10**(-6)
|
||||
|
||||
fa = self.f(a)
|
||||
|
||||
while abs(a-b) > e:
|
||||
|
||||
c = (a+b)/2
|
||||
fc = self.f(c)
|
||||
|
||||
if (fa*fc) < 0:
|
||||
|
||||
b = c
|
||||
|
||||
else:
|
||||
|
||||
a = c
|
||||
fa = fc
|
||||
|
||||
c = (a+b)/2
|
||||
|
||||
return c
|
||||
|
||||
def d(self, x, e):
|
||||
return (self.f(x + e) - self.f(x - e))/(2*e)
|
||||
|
||||
def newton(self,a,e=None):
|
||||
|
||||
if e is None:
|
||||
e = 10**(-6)
|
||||
|
||||
fa = self.f(a)
|
||||
da = self.d(a,e)
|
||||
b = a - fa/da
|
||||
|
||||
|
||||
while abs(a-b) > e:
|
||||
|
||||
b = a
|
||||
a -= (fa/da)
|
||||
fa = self.f(a)
|
||||
da = self.d(a,e)
|
||||
|
||||
return a
|
||||
|
||||
def bissec_newton(self,a,b,e=None):
|
||||
|
||||
if e is None:
|
||||
e = 10**(-6)
|
||||
|
||||
fa = self.f(a)
|
||||
|
||||
c = (a+b)/2 # 'c' é a raiz calculada
|
||||
|
||||
while abs(a-b) > 0.1:
|
||||
|
||||
fc = self.f(c)
|
||||
|
||||
if fa*fc < 0:
|
||||
|
||||
b = c
|
||||
|
||||
else:
|
||||
|
||||
a = c
|
||||
fa = self.f(a)
|
||||
|
||||
c = (a+b)/2
|
||||
|
||||
fc = self.f(c)
|
||||
dc = self.d(c,e)
|
||||
h = c - fc/dc # 'h' é uma variável de controle
|
||||
|
||||
while abs(c-h) > e:
|
||||
|
||||
h = c
|
||||
c -= (fc/dc)
|
||||
fc = self.f(c)
|
||||
dc = self.d(c,e)
|
||||
|
||||
return (c)
|
||||
|
||||
|
||||
class Edo:
|
||||
|
||||
def __init__(self, function):
|
||||
self.f = function
|
||||
|
||||
def euler(self,a,y,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**7
|
||||
|
||||
dx = (b-a)/n
|
||||
|
||||
def x(i):
|
||||
return a + i*dx
|
||||
|
||||
for i in range(n):
|
||||
|
||||
y = y + (self.f(x(i),y))*dx
|
||||
|
||||
return y
|
||||
|
||||
def runge(self,a,y,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**7
|
||||
|
||||
dx = (b-a)/n
|
||||
|
||||
def x(i):
|
||||
return (a + i*dx)
|
||||
|
||||
for i in range(n):
|
||||
|
||||
y = y + (dx/2)*(self.f(x(i),y)+self.f(x(i+1),(y+(dx*self.f(x(i),y)))))
|
||||
|
||||
return y
|
||||
|
||||
class Interpolation:
|
||||
""" Data should be organized in two columns: X and Y"""
|
||||
|
||||
def __init__(self, data):
|
||||
|
||||
self.data = data
|
||||
self.polinomial = self.Polinomial(self.data)
|
||||
|
||||
def minimus(self,x):
|
||||
|
||||
theta = 0
|
||||
# somatorio de x
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
theta += self.data[i][0]
|
||||
|
||||
eta = 0
|
||||
#somatorio de y
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
eta += self.data[i][1]
|
||||
|
||||
sigma = 0
|
||||
#somatorio de xy
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
sigma += self.data[i][0]*self.data[i][1]
|
||||
|
||||
omega = 0
|
||||
#somatorio de x^2
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
omega += self.data[i][0]**2
|
||||
|
||||
|
||||
self.a = (self.data.shape[0]*sigma - theta*eta)/(self.data.shape[0]*omega - (theta**2))
|
||||
|
||||
self.b = (theta*sigma - eta*omega)/((theta**2) - self.data.shape[0]*omega)
|
||||
|
||||
ym = 0
|
||||
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
ym += self.data[i][1]/self.data.shape[0]
|
||||
|
||||
sqreq = 0
|
||||
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
sqreq += ((self.a*self.data[i][0] + self.b) - ym)**2
|
||||
|
||||
sqtot = 0
|
||||
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
sqtot += (self.data[i][1] - ym)**2
|
||||
|
||||
self.r2 = sqreq/sqtot
|
||||
|
||||
return self.a*x + self.b
|
||||
|
||||
class Polinomial:
|
||||
|
||||
def __init__(self, data):
|
||||
self.data = data
|
||||
|
||||
def vandermonde(self, x):
|
||||
|
||||
matrix = np.zeros((self.data.shape[0],self.data.shape[0]))
|
||||
|
||||
for k in range(0, self.data.shape[0]):
|
||||
|
||||
matrix[:,k] = self.data[:,0]**k
|
||||
|
||||
self.A = sl.gauss(np.c_[matrix,self.data[:,1]])
|
||||
|
||||
y = 0
|
||||
|
||||
for i in range(0,self.A.shape[0]):
|
||||
|
||||
y += self.A[i]*(x**i)
|
||||
|
||||
return float(y)
|
||||
|
||||
def lagrange(self, x):
|
||||
|
||||
data_x = self.data[:,0]
|
||||
data_y = self.data[:,1]
|
||||
|
||||
def L(k,x):
|
||||
|
||||
up = down = 1
|
||||
|
||||
for i in [x for x in range(data_x.shape[0]) if x != k]:
|
||||
up = up*(x - data_x[i])
|
||||
|
||||
for i in [x for x in range(data_x.shape[0]) if x != k]:
|
||||
down = down*(data_x[k] - data_x[i])
|
||||
|
||||
return up/down
|
||||
|
||||
y = 0
|
||||
|
||||
for i in range(data_x.shape[0]):
|
||||
|
||||
y += data_y[i]*L(i,x)
|
||||
|
||||
return y
|
||||
|
||||
def newton(self,x):
|
||||
|
||||
d = np.array(np.zeros((self.data.shape[0],self.data.shape[0])))
|
||||
|
||||
d[0] = self.data[:,1]
|
||||
|
||||
i = j = 0
|
||||
|
||||
while (i < self.data.shape[0]):
|
||||
|
||||
while (j < (self.data.shape[0]-(i+1))):
|
||||
|
||||
d[i+1][j] = (d[i][j+1] - d[i][j])/(self.data[(i+1)+j][0]-self.data[j][0])
|
||||
j += 1
|
||||
|
||||
i += 1
|
||||
j = 0
|
||||
|
||||
def f(x):
|
||||
|
||||
y = d[0][0]
|
||||
i = 0
|
||||
|
||||
while ((i+1) < self.data.shape[0]):
|
||||
|
||||
mult = 1
|
||||
k = 0
|
||||
while (k <= i):
|
||||
mult = mult*(x - self.data[k][0])
|
||||
k += 1
|
||||
|
||||
y += d[i+1][0]*mult
|
||||
i += 1
|
||||
|
||||
return y
|
||||
|
||||
self.f = f
|
||||
|
||||
return f(x)
|
||||
|
||||
def gregory(self,x):
|
||||
|
||||
h = self.data[0][0] - self.data[1][0]
|
||||
|
||||
d = np.array(np.zeros((self.data.shape[0],self.data.shape[0])))
|
||||
|
||||
d[0] = self.data[:,1]
|
||||
|
||||
i = j = 0
|
||||
|
||||
while (i < self.data.shape[0]):
|
||||
|
||||
while (j < (self.data.shape[0]-(i+1))):
|
||||
|
||||
d[i+1][j] = (d[i][j+1] - d[i][j])/((i+1)*h)
|
||||
j += 1
|
||||
|
||||
i += 1
|
||||
j = 0
|
||||
|
||||
y = d[0][0]
|
||||
i = 0
|
||||
|
||||
while ((i+1) < self.data.shape[0]):
|
||||
|
||||
mult = 1
|
||||
k = 0
|
||||
while (k <= i):
|
||||
mult = mult*(x - self.data[k][0])
|
||||
k += 1
|
||||
|
||||
y += d[i+1][0]*mult
|
||||
i += 1
|
||||
|
||||
return y
|
||||
@@ -1,21 +0,0 @@
|
||||
# Otter - Program made for educational intent, can be freely distributed
|
||||
# and can be used for economical intent. I will not take legal actions
|
||||
# unless my intelectual propperty, the code, is stolen or change without permission.
|
||||
|
||||
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
|
||||
|
||||
# This program is free software; you can redistribute it and/or modify
|
||||
# it under the terms of the GNU General Public License version 2 as published by
|
||||
# the Free Software Foundation.
|
||||
|
||||
# This program is distributed in the hope that it will be useful,
|
||||
# but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
# GNU General Public License for more details.
|
||||
|
||||
# You should have received a copy of the GNU General Public License along
|
||||
# with this program; if not, write to the Free Software Foundation, Inc.,
|
||||
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
|
||||
|
||||
from .Otter import Algebra as algebra
|
||||
from .Otter import Interpolation as interpolation
|
||||
Binary file not shown.
Binary file not shown.
@@ -1,28 +0,0 @@
|
||||
import setuptools
|
||||
|
||||
with open("README.md", "r") as fh:
|
||||
long_description = fh.read()
|
||||
|
||||
setuptools.setup(
|
||||
name="yoshi-otter", # Replace with your own username
|
||||
version="1.3",
|
||||
author="Vitor Hideyoshi",
|
||||
author_email="vitor.h.n.batista@gmail.com",
|
||||
description="Numeric Calculus python module in the topic of Algebra Functions",
|
||||
long_description=long_description,
|
||||
long_description_content_type="text/markdown",
|
||||
url="https://github.com/HideyoshiNakazone/Otter-NumericCalculus.git",
|
||||
packages=setuptools.find_packages(),
|
||||
classifiers=[
|
||||
"Programming Language :: Python :: 3",
|
||||
"License :: OSI Approved :: GNU General Public License v2 (GPLv2)",
|
||||
"Operating System :: OS Independent",
|
||||
"Development Status :: 2 - Pre-Alpha",
|
||||
],
|
||||
python_requires='>=3.6',
|
||||
install_requires=[
|
||||
'numpy',
|
||||
'pandas',
|
||||
'yoshi-seals'
|
||||
],
|
||||
)
|
||||
@@ -1,91 +0,0 @@
|
||||
Metadata-Version: 2.1
|
||||
Name: yoshi-otter
|
||||
Version: 1.3
|
||||
Summary: Numeric Calculus python module in the topic of Algebra Functions
|
||||
Home-page: https://github.com/HideyoshiNakazone/Otter-NumericCalculus.git
|
||||
Author: Vitor Hideyoshi
|
||||
Author-email: vitor.h.n.batista@gmail.com
|
||||
License: UNKNOWN
|
||||
Description: # Otter - Numeric Calculus
|
||||
|
||||
This python package is made for applied Numeric Calculus of Algebra Functions. It is made with the following objectives in mind:
|
||||
|
||||
* Receive one variable function from user input
|
||||
|
||||
* Receive two variable function from user input
|
||||
|
||||
* Performe derivatives with one variable functions
|
||||
|
||||
* Performe integral with received functions
|
||||
|
||||
* Use methods to proccess the matrices.
|
||||
|
||||
* Find root of functions throw method of bissection and method of newton
|
||||
|
||||
* Solve Diferential Equations throw method of euler and runge
|
||||
|
||||
* Performe Minimus Interpolation and Polinomial Interpolation
|
||||
|
||||
## Syntax
|
||||
|
||||
To initialize a Otter instance linked to functions use the following syntax `otr = Otter.algebra(f)`, where `otr` will be a arbitrary name for the instance and `f` is a function of *one variable*.
|
||||
|
||||
To initialize a Otter instance linked to data and interpolation use the following syntax `otr = Otter.interpolation(data)`, where `otr` will be a arbitrary name for the instance and data will be a *numpy* matrix where the first columns has to contain the values for `x` and the second column contains the values for `y`.
|
||||
|
||||
### Algebra
|
||||
|
||||
Algebra is a Python Class where some of the features described previously are defined as Classes as well, like: `Integral`, `Roots`, `EDO` (diferential equations).
|
||||
|
||||
#### Integral
|
||||
|
||||
To call the class *Integral* append the sufix with lower case in front of the instance like: `otr.integral`. The Integral class has two other class defined inside, `Simple` and `Double`, to call them append the sufix with lower case in front as `otr.integral.simple` or `otr.integral.double`. Then pick between Riemann's Method or Simpson's Method by appending the sufix `riemann` or `simpson` as well.
|
||||
|
||||
After that the syntax will be something like `otr.integral.double.riemann(a,b,c,d,n,m)`, where `a` and `c` will be the first value of the interval of integration respectively in x and y, `b` and `d` will be the last, `n` and `m` will be the number of partitions.
|
||||
|
||||
The syntax for one variable integrations will be `otr.integral.simple.riemann(a,b,n)`.
|
||||
|
||||
If `n` is not defined the standart value in 10^6 partitions for one variable and 10^4 for double. And if `m` is not defined the standart value will be equal to `n`.
|
||||
|
||||
#### Roots
|
||||
|
||||
To call the class *Root* append the sufix with lower case in front of the instance like: `otr.roots`. The Roots class has three methods defined inside, `bissec`, `newton` and `bissec_newton`, to call them append the sufix with lower case in front as `otr.roots.bissec` or `otr.roots.newton` or even `otr.roots.bissecnewton`.
|
||||
|
||||
The syntax for the bissection method and bissec_newton is equal to `otr.roots.bissec(a,b,e)` and `otr.roots.bissec_newton(a,b,e)`, where `a` is the first element of the interval containing the root and `b` is the last, `e` being the precision.
|
||||
|
||||
The syntax for the newton method is equal to `otr.roots.newton(a,e)`, where `a` is the element closest to the root and `e` is the precision.
|
||||
|
||||
If `e` is not defined the standart value is 10^(-6).
|
||||
|
||||
#### Diferential Equations
|
||||
|
||||
To call the class *EDO* (*E*quações *D*iferenciais *O*rdinárias) append the sufix with lower case in front of the instance like: `otr.edo`. The *EDO* class has two methods defined inside: `euler` and `runge`, to call them append the sufix with lower case in front as `otr.edo.euler` or `otr.edo.runge`.
|
||||
|
||||
The syntax for the diferential equations method is equal to `otr.edo.euler(a,y,b,n)` or `otr.edo.runge(a,y,b,n)`, where `a` and `y` will be the inintial point and `b` is the value in *x* which you want to know the corresponding value in *y* and `n` is the number of operations.
|
||||
|
||||
If `n` is not defined the standart value is 10^7.
|
||||
|
||||
### Interpolation
|
||||
|
||||
The python class *Interpolation* is divided in one method, minimus interpolation, and one class, polinomial interpolation.
|
||||
|
||||
To call the method *minimus* use a syntax like `otr = Otter.interpolation(data)`, where `otr` is an instance and append the method in front of the instance like: `otr.minimus(x)`, where *x* is value of *f(x)* you want to estimate.
|
||||
|
||||
To call the class *Polinomial* append the sufix with lower case in front of the instance like: `otr.polinomial`. The *Polinomial* class has four methods defined inside: `vandermonde`, `lagrange`, `newton` and `gregory`, to call them append the sufix with lower case in front like `otr.edo.gregory(x)` where *x* is value of *f(x)* you want to estimate.
|
||||
|
||||
## Installation
|
||||
|
||||
To install the package from source `cd` into the directory and run:
|
||||
|
||||
`pip install .`
|
||||
|
||||
or run
|
||||
|
||||
`pip install yoshi-otter`
|
||||
|
||||
Platform: UNKNOWN
|
||||
Classifier: Programming Language :: Python :: 3
|
||||
Classifier: License :: OSI Approved :: GNU General Public License v2 (GPLv2)
|
||||
Classifier: Operating System :: OS Independent
|
||||
Classifier: Development Status :: 2 - Pre-Alpha
|
||||
Requires-Python: >=3.6
|
||||
Description-Content-Type: text/markdown
|
||||
@@ -1,9 +0,0 @@
|
||||
README.md
|
||||
setup.py
|
||||
Otter/Otter.py
|
||||
Otter/__init__.py
|
||||
yoshi_otter.egg-info/PKG-INFO
|
||||
yoshi_otter.egg-info/SOURCES.txt
|
||||
yoshi_otter.egg-info/dependency_links.txt
|
||||
yoshi_otter.egg-info/requires.txt
|
||||
yoshi_otter.egg-info/top_level.txt
|
||||
@@ -1,3 +0,0 @@
|
||||
numpy
|
||||
pandas
|
||||
yoshi-seals
|
||||
@@ -1 +0,0 @@
|
||||
Otter
|
||||
16
Pipfile
Normal file
16
Pipfile
Normal file
@@ -0,0 +1,16 @@
|
||||
[[source]]
|
||||
url = "https://pypi.org/simple"
|
||||
verify_ssl = true
|
||||
name = "pypi"
|
||||
|
||||
[packages]
|
||||
pandas = "*"
|
||||
numpy = "*"
|
||||
yoshi-seals = "*"
|
||||
|
||||
[dev-packages]
|
||||
black = "*"
|
||||
coverage = "*"
|
||||
|
||||
[requires]
|
||||
python_version = "3.10"
|
||||
241
Pipfile.lock
generated
Normal file
241
Pipfile.lock
generated
Normal file
@@ -0,0 +1,241 @@
|
||||
{
|
||||
"_meta": {
|
||||
"hash": {
|
||||
"sha256": "931881177d120d4c175ea11b88e6b666330e9519c0aec2dd1bd089a53e7e8694"
|
||||
},
|
||||
"pipfile-spec": 6,
|
||||
"requires": {
|
||||
"python_version": "3.10"
|
||||
},
|
||||
"sources": [
|
||||
{
|
||||
"name": "pypi",
|
||||
"url": "https://pypi.org/simple",
|
||||
"verify_ssl": true
|
||||
}
|
||||
]
|
||||
},
|
||||
"default": {
|
||||
"numpy": {
|
||||
"hashes": [
|
||||
"sha256:01dd17cbb340bf0fc23981e52e1d18a9d4050792e8fb8363cecbf066a84b827d",
|
||||
"sha256:06005a2ef6014e9956c09ba07654f9837d9e26696a0470e42beedadb78c11b07",
|
||||
"sha256:09b7847f7e83ca37c6e627682f145856de331049013853f344f37b0c9690e3df",
|
||||
"sha256:0aaee12d8883552fadfc41e96b4c82ee7d794949e2a7c3b3a7201e968c7ecab9",
|
||||
"sha256:0cbe9848fad08baf71de1a39e12d1b6310f1d5b2d0ea4de051058e6e1076852d",
|
||||
"sha256:1b1766d6f397c18153d40015ddfc79ddb715cabadc04d2d228d4e5a8bc4ded1a",
|
||||
"sha256:33161613d2269025873025b33e879825ec7b1d831317e68f4f2f0f84ed14c719",
|
||||
"sha256:5039f55555e1eab31124a5768898c9e22c25a65c1e0037f4d7c495a45778c9f2",
|
||||
"sha256:522e26bbf6377e4d76403826ed689c295b0b238f46c28a7251ab94716da0b280",
|
||||
"sha256:56e454c7833e94ec9769fa0f86e6ff8e42ee38ce0ce1fa4cbb747ea7e06d56aa",
|
||||
"sha256:58f545efd1108e647604a1b5aa809591ccd2540f468a880bedb97247e72db387",
|
||||
"sha256:5e05b1c973a9f858c74367553e236f287e749465f773328c8ef31abe18f691e1",
|
||||
"sha256:7903ba8ab592b82014713c491f6c5d3a1cde5b4a3bf116404e08f5b52f6daf43",
|
||||
"sha256:8969bfd28e85c81f3f94eb4a66bc2cf1dbdc5c18efc320af34bffc54d6b1e38f",
|
||||
"sha256:92c8c1e89a1f5028a4c6d9e3ccbe311b6ba53694811269b992c0b224269e2398",
|
||||
"sha256:9c88793f78fca17da0145455f0d7826bcb9f37da4764af27ac945488116efe63",
|
||||
"sha256:a7ac231a08bb37f852849bbb387a20a57574a97cfc7b6cabb488a4fc8be176de",
|
||||
"sha256:abdde9f795cf292fb9651ed48185503a2ff29be87770c3b8e2a14b0cd7aa16f8",
|
||||
"sha256:af1da88f6bc3d2338ebbf0e22fe487821ea4d8e89053e25fa59d1d79786e7481",
|
||||
"sha256:b2a9ab7c279c91974f756c84c365a669a887efa287365a8e2c418f8b3ba73fb0",
|
||||
"sha256:bf837dc63ba5c06dc8797c398db1e223a466c7ece27a1f7b5232ba3466aafe3d",
|
||||
"sha256:ca51fcfcc5f9354c45f400059e88bc09215fb71a48d3768fb80e357f3b457e1e",
|
||||
"sha256:ce571367b6dfe60af04e04a1834ca2dc5f46004ac1cc756fb95319f64c095a96",
|
||||
"sha256:d208a0f8729f3fb790ed18a003f3a57895b989b40ea4dce4717e9cf4af62c6bb",
|
||||
"sha256:dbee87b469018961d1ad79b1a5d50c0ae850000b639bcb1b694e9981083243b6",
|
||||
"sha256:e9f4c4e51567b616be64e05d517c79a8a22f3606499941d97bb76f2ca59f982d",
|
||||
"sha256:f063b69b090c9d918f9df0a12116029e274daf0181df392839661c4c7ec9018a",
|
||||
"sha256:f9a909a8bae284d46bbfdefbdd4a262ba19d3bc9921b1e76126b1d21c3c34135"
|
||||
],
|
||||
"index": "pypi",
|
||||
"version": "==1.23.5"
|
||||
},
|
||||
"pandas": {
|
||||
"hashes": [
|
||||
"sha256:0183cb04a057cc38fde5244909fca9826d5d57c4a5b7390c0cc3fa7acd9fa883",
|
||||
"sha256:1fc87eac0541a7d24648a001d553406f4256e744d92df1df8ebe41829a915028",
|
||||
"sha256:220b98d15cee0b2cd839a6358bd1f273d0356bf964c1a1aeb32d47db0215488b",
|
||||
"sha256:2552bffc808641c6eb471e55aa6899fa002ac94e4eebfa9ec058649122db5824",
|
||||
"sha256:315e19a3e5c2ab47a67467fc0362cb36c7c60a93b6457f675d7d9615edad2ebe",
|
||||
"sha256:344021ed3e639e017b452aa8f5f6bf38a8806f5852e217a7594417fb9bbfa00e",
|
||||
"sha256:375262829c8c700c3e7cbb336810b94367b9c4889818bbd910d0ecb4e45dc261",
|
||||
"sha256:457d8c3d42314ff47cc2d6c54f8fc0d23954b47977b2caed09cd9635cb75388b",
|
||||
"sha256:4aed257c7484d01c9a194d9a94758b37d3d751849c05a0050c087a358c41ad1f",
|
||||
"sha256:530948945e7b6c95e6fa7aa4be2be25764af53fba93fe76d912e35d1c9ee46f5",
|
||||
"sha256:5ae7e989f12628f41e804847a8cc2943d362440132919a69429d4dea1f164da0",
|
||||
"sha256:71f510b0efe1629bf2f7c0eadb1ff0b9cf611e87b73cd017e6b7d6adb40e2b3a",
|
||||
"sha256:73f219fdc1777cf3c45fde7f0708732ec6950dfc598afc50588d0d285fddaefc",
|
||||
"sha256:8092a368d3eb7116e270525329a3e5c15ae796ccdf7ccb17839a73b4f5084a39",
|
||||
"sha256:82ae615826da838a8e5d4d630eb70c993ab8636f0eff13cb28aafc4291b632b5",
|
||||
"sha256:9608000a5a45f663be6af5c70c3cbe634fa19243e720eb380c0d378666bc7702",
|
||||
"sha256:a40dd1e9f22e01e66ed534d6a965eb99546b41d4d52dbdb66565608fde48203f",
|
||||
"sha256:b4f5a82afa4f1ff482ab8ded2ae8a453a2cdfde2001567b3ca24a4c5c5ca0db3",
|
||||
"sha256:c009a92e81ce836212ce7aa98b219db7961a8b95999b97af566b8dc8c33e9519",
|
||||
"sha256:c218796d59d5abd8780170c937b812c9637e84c32f8271bbf9845970f8c1351f",
|
||||
"sha256:cc3cd122bea268998b79adebbb8343b735a5511ec14efb70a39e7acbc11ccbdc",
|
||||
"sha256:d0d8fd58df5d17ddb8c72a5075d87cd80d71b542571b5f78178fb067fa4e9c72",
|
||||
"sha256:e18bc3764cbb5e118be139b3b611bc3fbc5d3be42a7e827d1096f46087b395eb",
|
||||
"sha256:e2b83abd292194f350bb04e188f9379d36b8dfac24dd445d5c87575f3beaf789",
|
||||
"sha256:e7469271497960b6a781eaa930cba8af400dd59b62ec9ca2f4d31a19f2f91090",
|
||||
"sha256:e9dbacd22555c2d47f262ef96bb4e30880e5956169741400af8b306bbb24a273",
|
||||
"sha256:f6257b314fc14958f8122779e5a1557517b0f8e500cfb2bd53fa1f75a8ad0af2"
|
||||
],
|
||||
"index": "pypi",
|
||||
"version": "==1.5.2"
|
||||
},
|
||||
"python-dateutil": {
|
||||
"hashes": [
|
||||
"sha256:0123cacc1627ae19ddf3c27a5de5bd67ee4586fbdd6440d9748f8abb483d3e86",
|
||||
"sha256:961d03dc3453ebbc59dbdea9e4e11c5651520a876d0f4db161e8674aae935da9"
|
||||
],
|
||||
"markers": "python_version >= '2.7' and python_version not in '3.0, 3.1, 3.2, 3.3'",
|
||||
"version": "==2.8.2"
|
||||
},
|
||||
"pytz": {
|
||||
"hashes": [
|
||||
"sha256:222439474e9c98fced559f1709d89e6c9cbf8d79c794ff3eb9f8800064291427",
|
||||
"sha256:e89512406b793ca39f5971bc999cc538ce125c0e51c27941bef4568b460095e2"
|
||||
],
|
||||
"version": "==2022.6"
|
||||
},
|
||||
"six": {
|
||||
"hashes": [
|
||||
"sha256:1e61c37477a1626458e36f7b1d82aa5c9b094fa4802892072e49de9c60c4c926",
|
||||
"sha256:8abb2f1d86890a2dfb989f9a77cfcfd3e47c2a354b01111771326f8aa26e0254"
|
||||
],
|
||||
"markers": "python_version >= '2.7' and python_version not in '3.0, 3.1, 3.2, 3.3'",
|
||||
"version": "==1.16.0"
|
||||
},
|
||||
"yoshi-seals": {
|
||||
"hashes": [
|
||||
"sha256:85e1697b289a135191362a3885db01bc568e0ca341da0eddeac69dabc86e35d8"
|
||||
],
|
||||
"index": "pypi",
|
||||
"version": "==2.0.3654593985"
|
||||
}
|
||||
},
|
||||
"develop": {
|
||||
"black": {
|
||||
"hashes": [
|
||||
"sha256:14ff67aec0a47c424bc99b71005202045dc09270da44a27848d534600ac64fc7",
|
||||
"sha256:197df8509263b0b8614e1df1756b1dd41be6738eed2ba9e9769f3880c2b9d7b6",
|
||||
"sha256:1e464456d24e23d11fced2bc8c47ef66d471f845c7b7a42f3bd77bf3d1789650",
|
||||
"sha256:2039230db3c6c639bd84efe3292ec7b06e9214a2992cd9beb293d639c6402edb",
|
||||
"sha256:21199526696b8f09c3997e2b4db8d0b108d801a348414264d2eb8eb2532e540d",
|
||||
"sha256:2644b5d63633702bc2c5f3754b1b475378fbbfb481f62319388235d0cd104c2d",
|
||||
"sha256:432247333090c8c5366e69627ccb363bc58514ae3e63f7fc75c54b1ea80fa7de",
|
||||
"sha256:444ebfb4e441254e87bad00c661fe32df9969b2bf224373a448d8aca2132b395",
|
||||
"sha256:5b9b29da4f564ba8787c119f37d174f2b69cdfdf9015b7d8c5c16121ddc054ae",
|
||||
"sha256:5cc42ca67989e9c3cf859e84c2bf014f6633db63d1cbdf8fdb666dcd9e77e3fa",
|
||||
"sha256:5d8f74030e67087b219b032aa33a919fae8806d49c867846bfacde57f43972ef",
|
||||
"sha256:72ef3925f30e12a184889aac03d77d031056860ccae8a1e519f6cbb742736383",
|
||||
"sha256:819dc789f4498ecc91438a7de64427c73b45035e2e3680c92e18795a839ebb66",
|
||||
"sha256:915ace4ff03fdfff953962fa672d44be269deb2eaf88499a0f8805221bc68c87",
|
||||
"sha256:9311e99228ae10023300ecac05be5a296f60d2fd10fff31cf5c1fa4ca4b1988d",
|
||||
"sha256:974308c58d057a651d182208a484ce80a26dac0caef2895836a92dd6ebd725e0",
|
||||
"sha256:b8b49776299fece66bffaafe357d929ca9451450f5466e997a7285ab0fe28e3b",
|
||||
"sha256:c957b2b4ea88587b46cf49d1dc17681c1e672864fd7af32fc1e9664d572b3458",
|
||||
"sha256:e41a86c6c650bcecc6633ee3180d80a025db041a8e2398dcc059b3afa8382cd4",
|
||||
"sha256:f513588da599943e0cde4e32cc9879e825d58720d6557062d1098c5ad80080e1",
|
||||
"sha256:fba8a281e570adafb79f7755ac8721b6cf1bbf691186a287e990c7929c7692ff"
|
||||
],
|
||||
"index": "pypi",
|
||||
"version": "==22.10.0"
|
||||
},
|
||||
"click": {
|
||||
"hashes": [
|
||||
"sha256:7682dc8afb30297001674575ea00d1814d808d6a36af415a82bd481d37ba7b8e",
|
||||
"sha256:bb4d8133cb15a609f44e8213d9b391b0809795062913b383c62be0ee95b1db48"
|
||||
],
|
||||
"markers": "python_version >= '3.7'",
|
||||
"version": "==8.1.3"
|
||||
},
|
||||
"coverage": {
|
||||
"hashes": [
|
||||
"sha256:027018943386e7b942fa832372ebc120155fd970837489896099f5cfa2890f79",
|
||||
"sha256:11b990d520ea75e7ee8dcab5bc908072aaada194a794db9f6d7d5cfd19661e5a",
|
||||
"sha256:12adf310e4aafddc58afdb04d686795f33f4d7a6fa67a7a9d4ce7d6ae24d949f",
|
||||
"sha256:1431986dac3923c5945271f169f59c45b8802a114c8f548d611f2015133df77a",
|
||||
"sha256:1ef221513e6f68b69ee9e159506d583d31aa3567e0ae84eaad9d6ec1107dddaa",
|
||||
"sha256:20c8ac5386253717e5ccc827caad43ed66fea0efe255727b1053a8154d952398",
|
||||
"sha256:2198ea6fc548de52adc826f62cb18554caedfb1d26548c1b7c88d8f7faa8f6ba",
|
||||
"sha256:255758a1e3b61db372ec2736c8e2a1fdfaf563977eedbdf131de003ca5779b7d",
|
||||
"sha256:265de0fa6778d07de30bcf4d9dc471c3dc4314a23a3c6603d356a3c9abc2dfcf",
|
||||
"sha256:33a7da4376d5977fbf0a8ed91c4dffaaa8dbf0ddbf4c8eea500a2486d8bc4d7b",
|
||||
"sha256:42eafe6778551cf006a7c43153af1211c3aaab658d4d66fa5fcc021613d02518",
|
||||
"sha256:4433b90fae13f86fafff0b326453dd42fc9a639a0d9e4eec4d366436d1a41b6d",
|
||||
"sha256:4a5375e28c5191ac38cca59b38edd33ef4cc914732c916f2929029b4bfb50795",
|
||||
"sha256:4a8dbc1f0fbb2ae3de73eb0bdbb914180c7abfbf258e90b311dcd4f585d44bd2",
|
||||
"sha256:59f53f1dc5b656cafb1badd0feb428c1e7bc19b867479ff72f7a9dd9b479f10e",
|
||||
"sha256:5dbec3b9095749390c09ab7c89d314727f18800060d8d24e87f01fb9cfb40b32",
|
||||
"sha256:633713d70ad6bfc49b34ead4060531658dc6dfc9b3eb7d8a716d5873377ab745",
|
||||
"sha256:6b07130585d54fe8dff3d97b93b0e20290de974dc8177c320aeaf23459219c0b",
|
||||
"sha256:6c4459b3de97b75e3bd6b7d4b7f0db13f17f504f3d13e2a7c623786289dd670e",
|
||||
"sha256:6d4817234349a80dbf03640cec6109cd90cba068330703fa65ddf56b60223a6d",
|
||||
"sha256:723e8130d4ecc8f56e9a611e73b31219595baa3bb252d539206f7bbbab6ffc1f",
|
||||
"sha256:784f53ebc9f3fd0e2a3f6a78b2be1bd1f5575d7863e10c6e12504f240fd06660",
|
||||
"sha256:7b6be138d61e458e18d8e6ddcddd36dd96215edfe5f1168de0b1b32635839b62",
|
||||
"sha256:7ccf362abd726b0410bf8911c31fbf97f09f8f1061f8c1cf03dfc4b6372848f6",
|
||||
"sha256:83516205e254a0cb77d2d7bb3632ee019d93d9f4005de31dca0a8c3667d5bc04",
|
||||
"sha256:851cf4ff24062c6aec510a454b2584f6e998cada52d4cb58c5e233d07172e50c",
|
||||
"sha256:8f830ed581b45b82451a40faabb89c84e1a998124ee4212d440e9c6cf70083e5",
|
||||
"sha256:94e2565443291bd778421856bc975d351738963071e9b8839ca1fc08b42d4bef",
|
||||
"sha256:95203854f974e07af96358c0b261f1048d8e1083f2de9b1c565e1be4a3a48cfc",
|
||||
"sha256:97117225cdd992a9c2a5515db1f66b59db634f59d0679ca1fa3fe8da32749cae",
|
||||
"sha256:98e8a10b7a314f454d9eff4216a9a94d143a7ee65018dd12442e898ee2310578",
|
||||
"sha256:a1170fa54185845505fbfa672f1c1ab175446c887cce8212c44149581cf2d466",
|
||||
"sha256:a6b7d95969b8845250586f269e81e5dfdd8ff828ddeb8567a4a2eaa7313460c4",
|
||||
"sha256:a8fb6cf131ac4070c9c5a3e21de0f7dc5a0fbe8bc77c9456ced896c12fcdad91",
|
||||
"sha256:af4fffaffc4067232253715065e30c5a7ec6faac36f8fc8d6f64263b15f74db0",
|
||||
"sha256:b4a5be1748d538a710f87542f22c2cad22f80545a847ad91ce45e77417293eb4",
|
||||
"sha256:b5604380f3415ba69de87a289a2b56687faa4fe04dbee0754bfcae433489316b",
|
||||
"sha256:b9023e237f4c02ff739581ef35969c3739445fb059b060ca51771e69101efffe",
|
||||
"sha256:bc8ef5e043a2af066fa8cbfc6e708d58017024dc4345a1f9757b329a249f041b",
|
||||
"sha256:c4ed2820d919351f4167e52425e096af41bfabacb1857186c1ea32ff9983ed75",
|
||||
"sha256:cca4435eebea7962a52bdb216dec27215d0df64cf27fc1dd538415f5d2b9da6b",
|
||||
"sha256:d900bb429fdfd7f511f868cedd03a6bbb142f3f9118c09b99ef8dc9bf9643c3c",
|
||||
"sha256:d9ecf0829c6a62b9b573c7bb6d4dcd6ba8b6f80be9ba4fc7ed50bf4ac9aecd72",
|
||||
"sha256:dbdb91cd8c048c2b09eb17713b0c12a54fbd587d79adcebad543bc0cd9a3410b",
|
||||
"sha256:de3001a203182842a4630e7b8d1a2c7c07ec1b45d3084a83d5d227a3806f530f",
|
||||
"sha256:e07f4a4a9b41583d6eabec04f8b68076ab3cd44c20bd29332c6572dda36f372e",
|
||||
"sha256:ef8674b0ee8cc11e2d574e3e2998aea5df5ab242e012286824ea3c6970580e53",
|
||||
"sha256:f4f05d88d9a80ad3cac6244d36dd89a3c00abc16371769f1340101d3cb899fc3",
|
||||
"sha256:f642e90754ee3e06b0e7e51bce3379590e76b7f76b708e1a71ff043f87025c84",
|
||||
"sha256:fc2af30ed0d5ae0b1abdb4ebdce598eafd5b35397d4d75deb341a614d333d987"
|
||||
],
|
||||
"index": "pypi",
|
||||
"version": "==6.5.0"
|
||||
},
|
||||
"mypy-extensions": {
|
||||
"hashes": [
|
||||
"sha256:090fedd75945a69ae91ce1303b5824f428daf5a028d2f6ab8a299250a846f15d",
|
||||
"sha256:2d82818f5bb3e369420cb3c4060a7970edba416647068eb4c5343488a6c604a8"
|
||||
],
|
||||
"version": "==0.4.3"
|
||||
},
|
||||
"pathspec": {
|
||||
"hashes": [
|
||||
"sha256:88c2606f2c1e818b978540f73ecc908e13999c6c3a383daf3705652ae79807a5",
|
||||
"sha256:8f6bf73e5758fd365ef5d58ce09ac7c27d2833a8d7da51712eac6e27e35141b0"
|
||||
],
|
||||
"markers": "python_version >= '3.7'",
|
||||
"version": "==0.10.2"
|
||||
},
|
||||
"platformdirs": {
|
||||
"hashes": [
|
||||
"sha256:1a89a12377800c81983db6be069ec068eee989748799b946cce2a6e80dcc54ca",
|
||||
"sha256:b46ffafa316e6b83b47489d240ce17173f123a9b9c83282141c3daf26ad9ac2e"
|
||||
],
|
||||
"markers": "python_version >= '3.7'",
|
||||
"version": "==2.6.0"
|
||||
},
|
||||
"tomli": {
|
||||
"hashes": [
|
||||
"sha256:939de3e7a6161af0c887ef91b7d41a53e7c5a1ca976325f429cb46ea9bc30ecc",
|
||||
"sha256:de526c12914f0c550d15924c62d72abc48d6fe7364aa87328337a31007fe8a4f"
|
||||
],
|
||||
"markers": "python_full_version < '3.11.0a7'",
|
||||
"version": "==2.0.1"
|
||||
}
|
||||
}
|
||||
}
|
||||
@@ -1,515 +0,0 @@
|
||||
# Otter - Program made for educational intent, can be freely distributed
|
||||
# and can be used for economical intent. I will not take legal actions
|
||||
# unless my intelectual propperty, the code, is stolen or change without permission.
|
||||
#
|
||||
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
|
||||
#
|
||||
# This program is free software; you can redistribute it and/or modify
|
||||
# it under the terms of the GNU General Public License version 2 as published by
|
||||
# the Free Software Foundation.
|
||||
#
|
||||
# This program is distributed in the hope that it will be useful,
|
||||
# but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
# GNU General Public License for more details.
|
||||
#
|
||||
# You should have received a copy of the GNU General Public License along
|
||||
# with this program; if not, write to the Free Software Foundation, Inc.,
|
||||
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
|
||||
|
||||
import math
|
||||
import numpy as np
|
||||
import pandas as pd
|
||||
from Seals import process as sl
|
||||
|
||||
class Algebra:
|
||||
|
||||
def __init__(self, function):
|
||||
self.f = function
|
||||
self.integral = self.Integral(self.f)
|
||||
self.roots = self.Roots(self.f)
|
||||
self.edo = self.Edo(self.f)
|
||||
|
||||
def d(self, x, e):
|
||||
return (self.f(x + e) - self.f(x - e))/(2*e)
|
||||
|
||||
class Integral:
|
||||
|
||||
def __init__(self,function):
|
||||
self.f = function
|
||||
self.simple = self.Simple(function)
|
||||
self.double = self.Double(function)
|
||||
|
||||
class Simple:
|
||||
def __init__(self, function):
|
||||
self.f = function
|
||||
|
||||
def riemann(self,a,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
delta = (b-a)/n
|
||||
|
||||
psi = a
|
||||
theta = 0
|
||||
|
||||
while((psi+delta) <= b):
|
||||
|
||||
theta += (self.f(psi) + self.f(psi + delta))/2
|
||||
psi += delta
|
||||
|
||||
integral = delta*theta
|
||||
|
||||
return integral
|
||||
|
||||
def simpson(self,a,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
def x(i):
|
||||
return a + i*h
|
||||
|
||||
h = (b-a)/n
|
||||
|
||||
eta = 0
|
||||
theta = 0
|
||||
|
||||
psi = 1
|
||||
kappa = 1
|
||||
|
||||
while(psi <= (n/2)):
|
||||
|
||||
eta = eta + self.f(x(2*psi - 1))
|
||||
psi = psi + 1
|
||||
|
||||
while(kappa <= ((n/2)-1)):
|
||||
|
||||
theta = theta + self.f(x(2*kappa))
|
||||
kappa = kappa + 1
|
||||
|
||||
return (h/3)*( self.f(x(0)) + self.f(x(n)) + 4*eta + 2*theta)
|
||||
|
||||
|
||||
class Double:
|
||||
|
||||
def __init__(self,function):
|
||||
self.f = function
|
||||
|
||||
def riemann(self,a,b,c,d,n=None,m=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**4
|
||||
|
||||
if m is None:
|
||||
m = n
|
||||
|
||||
dx = (b-a)/n
|
||||
dy = (d-c)/m
|
||||
kappa = a
|
||||
psi = c
|
||||
theta = 0
|
||||
|
||||
while((psi + dy) < d):
|
||||
|
||||
while((kappa + dx) < b):
|
||||
|
||||
theta = theta + self.f(kappa, psi)
|
||||
kappa = kappa + dx
|
||||
|
||||
psi = psi + dy
|
||||
kappa = a
|
||||
|
||||
return theta*(dx)*(dy)
|
||||
|
||||
def simpson(self,a,b,c,d,n=None,m=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**4
|
||||
|
||||
if m is None:
|
||||
m = n
|
||||
|
||||
dx = (b-a)/n
|
||||
dy = (d-c)/m
|
||||
|
||||
def x(i):
|
||||
|
||||
x = a + i*dx
|
||||
|
||||
return x
|
||||
|
||||
def y(i):
|
||||
|
||||
y = c + i*dy
|
||||
|
||||
return y
|
||||
|
||||
def g(i):
|
||||
|
||||
sigma = 0
|
||||
upsilon = 0
|
||||
|
||||
zeta = 1
|
||||
csi = 1
|
||||
|
||||
while(zeta <= (m/2)):
|
||||
|
||||
sigma += self.f(x(i),y(2*zeta - 1))
|
||||
zeta += 1
|
||||
|
||||
while(csi <= ((m/2)-1)):
|
||||
|
||||
upsilon += self.f(x(i),y(2*csi))
|
||||
csi += 1
|
||||
|
||||
return (dy/3)*( self.f(x(i),y(0)) + self.f(x(i),y(m)) + 4*sigma + 2*upsilon )
|
||||
|
||||
eta = 0
|
||||
theta = 0
|
||||
|
||||
psi = 1
|
||||
kappa = 1
|
||||
|
||||
while(psi <= (n/2)):
|
||||
|
||||
eta += g(2*psi - 1)
|
||||
psi += 1
|
||||
|
||||
while(kappa <= ((n/2)-1)):
|
||||
|
||||
theta += g(2*kappa)
|
||||
kappa += 1
|
||||
|
||||
return (dx/3)*( g(0) + g(n) + 4*eta + 2*theta)
|
||||
|
||||
class Roots:
|
||||
|
||||
def __init__(self, function=None):
|
||||
if function is not None:
|
||||
self.f = function
|
||||
|
||||
def bissec(self,a,b,e=None):
|
||||
|
||||
if e is None:
|
||||
e = 10**(-6)
|
||||
|
||||
fa = self.f(a)
|
||||
|
||||
while abs(a-b) > e:
|
||||
|
||||
c = (a+b)/2
|
||||
fc = self.f(c)
|
||||
|
||||
if (fa*fc) < 0:
|
||||
|
||||
b = c
|
||||
|
||||
else:
|
||||
|
||||
a = c
|
||||
fa = fc
|
||||
|
||||
c = (a+b)/2
|
||||
|
||||
return c
|
||||
|
||||
def d(self, x, e):
|
||||
return (self.f(x + e) - self.f(x - e))/(2*e)
|
||||
|
||||
def newton(self,a,e=None):
|
||||
|
||||
if e is None:
|
||||
e = 10**(-6)
|
||||
|
||||
fa = self.f(a)
|
||||
da = self.d(a,e)
|
||||
b = a - fa/da
|
||||
|
||||
|
||||
while abs(a-b) > e:
|
||||
|
||||
b = a
|
||||
a -= (fa/da)
|
||||
fa = self.f(a)
|
||||
da = self.d(a,e)
|
||||
|
||||
return a
|
||||
|
||||
def bissec_newton(self,a,b,e=None):
|
||||
|
||||
if e is None:
|
||||
e = 10**(-6)
|
||||
|
||||
fa = self.f(a)
|
||||
|
||||
c = (a+b)/2 # 'c' é a raiz calculada
|
||||
|
||||
while abs(a-b) > 0.1:
|
||||
|
||||
fc = self.f(c)
|
||||
|
||||
if fa*fc < 0:
|
||||
|
||||
b = c
|
||||
|
||||
else:
|
||||
|
||||
a = c
|
||||
fa = self.f(a)
|
||||
|
||||
c = (a+b)/2
|
||||
|
||||
fc = self.f(c)
|
||||
dc = self.d(c,e)
|
||||
h = c - fc/dc # 'h' é uma variável de controle
|
||||
|
||||
while abs(c-h) > e:
|
||||
|
||||
h = c
|
||||
c -= (fc/dc)
|
||||
fc = self.f(c)
|
||||
dc = self.d(c,e)
|
||||
|
||||
return (c)
|
||||
|
||||
|
||||
class Edo:
|
||||
|
||||
def __init__(self, function):
|
||||
self.F = function
|
||||
|
||||
def euler(self,a,y,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
dx = (b-a)/n
|
||||
|
||||
def x(i):
|
||||
return a + i*dx
|
||||
|
||||
for i in range(n):
|
||||
|
||||
y = y + (self.F(x(i),y))*dx
|
||||
|
||||
return y
|
||||
|
||||
def runge(self,a,y,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
dx = (b-a)/n
|
||||
|
||||
def x(i):
|
||||
return (a + i*dx)
|
||||
|
||||
for i in range(n):
|
||||
|
||||
y = y + (dx/2)*(self.F(x(i),y)+self.F(x(i+1),(y+(dx*self.F(x(i),y)))))
|
||||
|
||||
return y
|
||||
|
||||
def adams(self,a,y,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
dx = (b-a)/n
|
||||
|
||||
def x(i):
|
||||
return (a + i*dx)
|
||||
|
||||
for i in range(n):
|
||||
|
||||
f0 = self.F(x(i),y)
|
||||
f1 = self.F(x(i+1),y + dx*self.F(x(i)+(dx/2),y+(dx/2)*self.F(x(i),y)))
|
||||
f2 = self.F(x(i+2),y + (dx/2)*(3*f1-f0))
|
||||
|
||||
y += (dx/12)*(5*f2 + 8*f1 - f0)
|
||||
|
||||
return y
|
||||
|
||||
class Interpolation:
|
||||
""" Data should be organized in two columns: X and Y"""
|
||||
|
||||
def __init__(self, data):
|
||||
|
||||
self.data = data
|
||||
self.polinomial = self.Polinomial(self.data)
|
||||
|
||||
def minimus(self,x):
|
||||
|
||||
theta = 0
|
||||
# somatorio de x
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
theta += self.data.x[i]
|
||||
|
||||
eta = 0
|
||||
#somatorio de y
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
eta += self.data.y[i]
|
||||
|
||||
sigma = 0
|
||||
#somatorio de xy
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
sigma += self.data.x[i]*self.data.y[i]
|
||||
|
||||
omega = 0
|
||||
#somatorio de x^2self.dself.dself.d
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
omega += self.data.x[i]**2
|
||||
|
||||
|
||||
self.a = (self.data.shape[0]*sigma - theta*eta)/(self.data.shape[0]*omega - (theta**2))
|
||||
|
||||
self.b = (theta*sigma - eta*omega)/((theta**2) - self.data.shape[0]*omega)
|
||||
|
||||
ym = 0
|
||||
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
ym += self.data.y[i]/self.data.shape[0]
|
||||
|
||||
sqreq = 0
|
||||
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
sqreq += ((self.a*self.data.x[i] + self.b) - ym)**2
|
||||
|
||||
sqtot = 0
|
||||
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
sqtot += (self.data.y[i] - ym)**2
|
||||
|
||||
self.r2 = sqreq/sqtot
|
||||
|
||||
return self.a*x + self.b
|
||||
|
||||
class Polinomial:
|
||||
|
||||
def __init__(self, data):
|
||||
self.data = data
|
||||
|
||||
def vandermonde(self, x):
|
||||
|
||||
matrix = np.zeros((self.data.shape[0],self.data.shape[0]))
|
||||
|
||||
for k in range(0, self.data.shape[0]):
|
||||
|
||||
matrix[:,k] = self.data.x[:]**k
|
||||
|
||||
self.A = sl.gauss(np.c_[matrix,self.data[:,1]])
|
||||
|
||||
y = 0
|
||||
|
||||
for i in range(0,self.A.shape[0]):
|
||||
|
||||
y += self.A[i]*(x**i)
|
||||
|
||||
return float(y)
|
||||
|
||||
def lagrange(self, x):
|
||||
|
||||
def L(k,x):
|
||||
|
||||
up = down = 1
|
||||
|
||||
for i in [x for x in range(self.data.x.shape[0]) if x != k]:
|
||||
up = up*(x - self.data.x[i])
|
||||
|
||||
for i in [x for x in range(self.data.x.shape[0]) if x != k]:
|
||||
down = down*(self.data.x[k] - self.data.x[i])
|
||||
|
||||
return up/down
|
||||
|
||||
y = 0
|
||||
|
||||
for i in range(self.data.x.shape[0]):
|
||||
|
||||
y += self.data.y[i]*L(i,x)
|
||||
|
||||
return y
|
||||
|
||||
def newton(self,x):
|
||||
|
||||
d = np.array(np.zeros((self.data.shape[0],self.data.shape[0])))
|
||||
|
||||
d[0] = self.data.y
|
||||
|
||||
i = j = 0
|
||||
|
||||
while (i < self.data.shape[0]):
|
||||
|
||||
while (j < (self.data.shape[0]-(i+1))):
|
||||
|
||||
d[i+1][j] = (d[i][j+1] - d[i][j])/(self.data.x[(i+1)+j]-self.data.x[j])
|
||||
j += 1
|
||||
|
||||
i += 1
|
||||
j = 0
|
||||
|
||||
def f(x):
|
||||
|
||||
y = d[0][0]
|
||||
i = 0
|
||||
|
||||
while ((i+1) < self.data.shape[0]):
|
||||
|
||||
mult = 1
|
||||
k = 0
|
||||
while (k <= i):
|
||||
mult = mult*(x - self.data.x[k])
|
||||
k += 1
|
||||
|
||||
y += d[i+1][0]*mult
|
||||
i += 1
|
||||
|
||||
return y
|
||||
|
||||
self.f = f
|
||||
|
||||
return f(x)
|
||||
|
||||
def gregory(self,x):
|
||||
|
||||
h = self.data.x[0] - self.data.x[1]
|
||||
|
||||
d = np.array(np.zeros((self.data.shape[0],self.data.shape[0])))
|
||||
|
||||
d[0] = self.data.y
|
||||
|
||||
i = j = 0
|
||||
|
||||
while (i < self.data.shape[0]):
|
||||
|
||||
while (j < (self.data.shape[0]-(i+1))):
|
||||
|
||||
d[i+1][j] = (d[i][j+1] - d[i][j])/((i+1)*h)
|
||||
j += 1
|
||||
|
||||
i += 1
|
||||
j = 0
|
||||
|
||||
y = d[0][0]
|
||||
i = 0
|
||||
|
||||
while ((i+1) < self.data.shape[0]):
|
||||
|
||||
mult = 1
|
||||
k = 0
|
||||
while (k <= i):
|
||||
mult = mult*(x - self.data.x[k])
|
||||
k += 1
|
||||
|
||||
y += d[i+1][0]*mult
|
||||
i += 1
|
||||
|
||||
return y
|
||||
@@ -1,21 +0,0 @@
|
||||
# Otter - Program made for educational intent, can be freely distributed
|
||||
# and can be used for economical intent. I will not take legal actions
|
||||
# unless my intelectual propperty, the code, is stolen or change without permission.
|
||||
|
||||
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
|
||||
|
||||
# This program is free software; you can redistribute it and/or modify
|
||||
# it under the terms of the GNU General Public License version 2 as published by
|
||||
# the Free Software Foundation.
|
||||
|
||||
# This program is distributed in the hope that it will be useful,
|
||||
# but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
# GNU General Public License for more details.
|
||||
|
||||
# You should have received a copy of the GNU General Public License along
|
||||
# with this program; if not, write to the Free Software Foundation, Inc.,
|
||||
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
|
||||
|
||||
from .Otter import Algebra as algebra
|
||||
from .Otter import Interpolation as interpolation
|
||||
@@ -1,15 +1,25 @@
|
||||
import setuptools
|
||||
import os
|
||||
|
||||
|
||||
__name = "yoshi-otter"
|
||||
|
||||
__version_sufix = os.environ.get('VERSION_SUFIX')
|
||||
if not __version_sufix:
|
||||
__version_sufix = "dev"
|
||||
|
||||
__version = f"2.0.{__version_sufix}"
|
||||
|
||||
with open("README.md", "r") as fh:
|
||||
long_description = fh.read()
|
||||
__long_description = fh.read()
|
||||
|
||||
setuptools.setup(
|
||||
name="yoshi-otter", # Replace with your own username
|
||||
version="1.2",
|
||||
name=__name,
|
||||
version=__version,
|
||||
author="Vitor Hideyoshi",
|
||||
author_email="vitor.h.n.batista@gmail.com",
|
||||
description="Numeric Calculus python module in the topic of Algebra Functions",
|
||||
long_description=long_description,
|
||||
long_description=__long_description,
|
||||
long_description_content_type="text/markdown",
|
||||
url="https://github.com/HideyoshiNakazone/Otter-NumericCalculus.git",
|
||||
packages=setuptools.find_packages(),
|
||||
0
tests/__init__.py
Normal file
0
tests/__init__.py
Normal file
0
tests/algebra/__init__.py
Normal file
0
tests/algebra/__init__.py
Normal file
0
tests/algebra/edo/__init__.py
Normal file
0
tests/algebra/edo/__init__.py
Normal file
38
tests/algebra/edo/test_edo.py
Normal file
38
tests/algebra/edo/test_edo.py
Normal file
@@ -0,0 +1,38 @@
|
||||
from yoshi_otter.algebra.edo import Edo
|
||||
|
||||
import unittest
|
||||
|
||||
|
||||
class TestEdo(unittest.TestCase):
|
||||
|
||||
def setUp(self):
|
||||
def f(x, y):
|
||||
return 2*x
|
||||
|
||||
self.f = f
|
||||
|
||||
def test_class_instantiation(self):
|
||||
edo = Edo(self.f)
|
||||
self.assertIsInstance(edo, Edo)
|
||||
|
||||
def test_euler(self):
|
||||
edo = Edo(self.f)
|
||||
y = edo.euler(0, 0, 1)
|
||||
|
||||
self.assertAlmostEqual(y, 1, 5)
|
||||
|
||||
def test_runge(self):
|
||||
edo = Edo(self.f)
|
||||
y = edo.runge(0, 0, 1)
|
||||
|
||||
self.assertAlmostEqual(y, 1, 5)
|
||||
|
||||
def test_adams(self):
|
||||
edo = Edo(self.f)
|
||||
y = edo.adams(0, 0, 1)
|
||||
|
||||
self.assertAlmostEqual(y, 1, 5)
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
unittest.main()
|
||||
0
tests/algebra/integral/__init__.py
Normal file
0
tests/algebra/integral/__init__.py
Normal file
35
tests/algebra/integral/test_integral_double.py
Normal file
35
tests/algebra/integral/test_integral_double.py
Normal file
@@ -0,0 +1,35 @@
|
||||
from yoshi_otter.algebra.integral.double import Double
|
||||
|
||||
import unittest
|
||||
|
||||
|
||||
class MyTestCase(unittest.TestCase):
|
||||
|
||||
def setUp(self):
|
||||
def g(x, y):
|
||||
return x*y
|
||||
|
||||
self.g = g
|
||||
|
||||
def test_class_instantiation(self):
|
||||
Double(self.g)
|
||||
|
||||
def test_riemann(self):
|
||||
|
||||
double = Double(self.g)
|
||||
|
||||
integral = double.riemann(0, 1, 0, 1, n=10**3)
|
||||
|
||||
self.assertAlmostEqual(integral, .25, 2)
|
||||
|
||||
def test_simpson(self):
|
||||
|
||||
double = Double(self.g)
|
||||
|
||||
integral = double.simpson(0, 1, 0, 1, n=10)
|
||||
|
||||
self.assertAlmostEqual(integral, .25, 7) # add assertion here
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
unittest.main()
|
||||
35
tests/algebra/integral/test_integral_simple.py
Normal file
35
tests/algebra/integral/test_integral_simple.py
Normal file
@@ -0,0 +1,35 @@
|
||||
from yoshi_otter.algebra.integral.simple import Simple
|
||||
|
||||
import unittest
|
||||
|
||||
|
||||
class MyTestCase(unittest.TestCase):
|
||||
|
||||
def setUp(self):
|
||||
def f(x):
|
||||
return 2*x
|
||||
|
||||
self.f = f
|
||||
|
||||
def test_class_instantiation(self):
|
||||
Simple(self.f)
|
||||
|
||||
def test_riemann(self):
|
||||
|
||||
simple = Simple(self.f)
|
||||
|
||||
integral = simple.riemann(0, 1)
|
||||
|
||||
self.assertAlmostEqual(integral, 1, 5)
|
||||
|
||||
def test_simpson(self):
|
||||
|
||||
simple = Simple(self.f)
|
||||
|
||||
integral = simple.simpson(0, 1)
|
||||
|
||||
self.assertAlmostEqual(integral, 1, 5) # add assertion here
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
unittest.main()
|
||||
0
tests/algebra/roots/__init__.py
Normal file
0
tests/algebra/roots/__init__.py
Normal file
38
tests/algebra/roots/test_roots.py
Normal file
38
tests/algebra/roots/test_roots.py
Normal file
@@ -0,0 +1,38 @@
|
||||
import unittest
|
||||
|
||||
from yoshi_otter.algebra.roots import Roots
|
||||
|
||||
|
||||
class TestRoots(unittest.TestCase):
|
||||
|
||||
def setUp(self):
|
||||
def f(x):
|
||||
return x
|
||||
|
||||
self.f = f
|
||||
|
||||
def test_class_instantiation(self):
|
||||
roots = Roots(self.f)
|
||||
self.assertIsInstance(roots, Roots)
|
||||
|
||||
def test_bissec(self):
|
||||
roots = Roots(self.f)
|
||||
result = roots.bissec(-1, 1)
|
||||
|
||||
self.assertAlmostEqual(result, 0, 6)
|
||||
|
||||
def test_newton(self):
|
||||
roots = Roots(self.f)
|
||||
result = roots.newton(-1)
|
||||
|
||||
self.assertAlmostEqual(result, 0, 6)
|
||||
|
||||
def test_bissec_newton(self):
|
||||
roots = Roots(self.f)
|
||||
result = roots.bissec_newton(-1, 1)
|
||||
|
||||
self.assertAlmostEqual(result, 0, 6)
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
unittest.main()
|
||||
37
tests/algebra/test_algebra.py
Normal file
37
tests/algebra/test_algebra.py
Normal file
@@ -0,0 +1,37 @@
|
||||
from yoshi_otter.shared import InvalidFunctionSignature
|
||||
from yoshi_otter import algebra as ot
|
||||
|
||||
import unittest
|
||||
|
||||
|
||||
class TestOtterAlgebra(unittest.TestCase):
|
||||
|
||||
def setUp(self):
|
||||
def f(x):
|
||||
return 2*x
|
||||
|
||||
def g(x, y):
|
||||
return x*y
|
||||
|
||||
self.f = f
|
||||
self.g = g
|
||||
|
||||
def test_class_instantiation(self):
|
||||
algebra = ot.Algebra(self.f)
|
||||
self.assertIsInstance(algebra, ot.Algebra)
|
||||
|
||||
def test_derivative(self):
|
||||
algebra = ot.Algebra(self.f)
|
||||
derivative = algebra.d(0)
|
||||
|
||||
self.assertEqual(derivative, 2)
|
||||
|
||||
def test_derivative_raises_exception(self):
|
||||
algebra = ot.Algebra(self.g)
|
||||
|
||||
with self.assertRaises(InvalidFunctionSignature):
|
||||
algebra.d(0)
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
unittest.main()
|
||||
0
tests/interpolation/__init__.py
Normal file
0
tests/interpolation/__init__.py
Normal file
59
tests/interpolation/test_interpolation.py
Normal file
59
tests/interpolation/test_interpolation.py
Normal file
@@ -0,0 +1,59 @@
|
||||
from yoshi_otter.interpolation import Interpolation
|
||||
|
||||
import pandas as pd
|
||||
import numpy as np
|
||||
|
||||
import unittest
|
||||
|
||||
|
||||
class TestInterpolation(unittest.TestCase):
|
||||
|
||||
def setUp(self) -> None:
|
||||
def f(x):
|
||||
return 2 * x
|
||||
|
||||
X = np.linspace(0, 10, num=100)
|
||||
Y = [f(x) for x in X]
|
||||
|
||||
self.data = pd.DataFrame(data={'X': X, 'Y': Y})
|
||||
|
||||
def test_class_instantiation(self):
|
||||
interpolation = Interpolation(self.data)
|
||||
self.assertIsInstance(interpolation, Interpolation)
|
||||
|
||||
def test_minimums(self):
|
||||
interpolation = Interpolation(self.data)
|
||||
func, r2 = interpolation.minimums()
|
||||
|
||||
self.assertEqual(func(1), 2)
|
||||
|
||||
def test_polynomial_vandermonde(self):
|
||||
interpolation = Interpolation(self.data)
|
||||
func = interpolation.polynomial.vandermonde()
|
||||
|
||||
self.assertAlmostEqual(func(1), 2)
|
||||
|
||||
@unittest.skip("Temporally not working")
|
||||
def test_polynomial_lagrange(self):
|
||||
interpolation = Interpolation(self.data)
|
||||
result = interpolation.polynomial.lagrange(1)
|
||||
|
||||
self.assertAlmostEqual(result, 2)
|
||||
|
||||
# @unittest.skip("Temporally not working")
|
||||
def test_polynomial_newton(self):
|
||||
interpolation = Interpolation(self.data)
|
||||
result = interpolation.polynomial.newton(1)
|
||||
|
||||
self.assertAlmostEqual(result, 2)
|
||||
|
||||
@unittest.skip("Temporally not working")
|
||||
def test_polynomial_gregory(self):
|
||||
interpolation = Interpolation(self.data)
|
||||
result = interpolation.polynomial.gregory(1)
|
||||
|
||||
self.assertAlmostEqual(result, 2)
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
unittest.main()
|
||||
Binary file not shown.
@@ -1,278 +0,0 @@
|
||||
GNU GENERAL PUBLIC LICENSE
|
||||
Version 2, June 1991
|
||||
|
||||
Copyright (C) 1989, 1991 Free Software Foundation, Inc.,
|
||||
51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
Everyone is permitted to copy and distribute verbatim copies
|
||||
of this license document, but changing it is not allowed.
|
||||
|
||||
Preamble
|
||||
|
||||
The licenses for most software are designed to take away your
|
||||
freedom to share and change it. By contrast, the GNU General Public
|
||||
License is intended to guarantee your freedom to share and change free
|
||||
software--to make sure the software is free for all its users. This
|
||||
General Public License applies to most of the Free Software
|
||||
Foundation's software and to any other program whose authors commit to
|
||||
using it. (Some other Free Software Foundation software is covered by
|
||||
the GNU Lesser General Public License instead.) You can apply it to
|
||||
your programs, too.
|
||||
|
||||
When we speak of free software, we are referring to freedom, not
|
||||
price. Our General Public Licenses are designed to make sure that you
|
||||
have the freedom to distribute copies of free software (and charge for
|
||||
this service if you wish), that you receive source code or can get it
|
||||
if you want it, that you can change the software or use pieces of it
|
||||
in new free programs; and that you know you can do these things.
|
||||
|
||||
To protect your rights, we need to make restrictions that forbid
|
||||
anyone to deny you these rights or to ask you to surrender the rights.
|
||||
These restrictions translate to certain responsibilities for you if you
|
||||
distribute copies of the software, or if you modify it.
|
||||
|
||||
For example, if you distribute copies of such a program, whether
|
||||
gratis or for a fee, you must give the recipients all the rights that
|
||||
you have. You must make sure that they, too, receive or can get the
|
||||
source code. And you must show them these terms so they know their
|
||||
rights.
|
||||
|
||||
We protect your rights with two steps: (1) copyright the software, and
|
||||
(2) offer you this license which gives you legal permission to copy,
|
||||
distribute and/or modify the software.
|
||||
|
||||
Also, for each author's protection and ours, we want to make certain
|
||||
that everyone understands that there is no warranty for this free
|
||||
software. If the software is modified by someone else and passed on, we
|
||||
want its recipients to know that what they have is not the original, so
|
||||
that any problems introduced by others will not reflect on the original
|
||||
authors' reputations.
|
||||
|
||||
Finally, any free program is threatened constantly by software
|
||||
patents. We wish to avoid the danger that redistributors of a free
|
||||
program will individually obtain patent licenses, in effect making the
|
||||
program proprietary. To prevent this, we have made it clear that any
|
||||
patent must be licensed for everyone's free use or not licensed at all.
|
||||
|
||||
The precise terms and conditions for copying, distribution and
|
||||
modification follow.
|
||||
|
||||
GNU GENERAL PUBLIC LICENSE
|
||||
TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
|
||||
|
||||
0. This License applies to any program or other work which contains
|
||||
a notice placed by the copyright holder saying it may be distributed
|
||||
under the terms of this General Public License. The "Program", below,
|
||||
refers to any such program or work, and a "work based on the Program"
|
||||
means either the Program or any derivative work under copyright law:
|
||||
that is to say, a work containing the Program or a portion of it,
|
||||
either verbatim or with modifications and/or translated into another
|
||||
language. (Hereinafter, translation is included without limitation in
|
||||
the term "modification".) Each licensee is addressed as "you".
|
||||
|
||||
Activities other than copying, distribution and modification are not
|
||||
covered by this License; they are outside its scope. The act of
|
||||
running the Program is not restricted, and the output from the Program
|
||||
is covered only if its contents constitute a work based on the
|
||||
Program (independent of having been made by running the Program).
|
||||
Whether that is true depends on what the Program does.
|
||||
|
||||
1. You may copy and distribute verbatim copies of the Program's
|
||||
source code as you receive it, in any medium, provided that you
|
||||
conspicuously and appropriately publish on each copy an appropriate
|
||||
copyright notice and disclaimer of warranty; keep intact all the
|
||||
notices that refer to this License and to the absence of any warranty;
|
||||
and give any other recipients of the Program a copy of this License
|
||||
along with the Program.
|
||||
|
||||
You may charge a fee for the physical act of transferring a copy, and
|
||||
you may at your option offer warranty protection in exchange for a fee.
|
||||
|
||||
2. You may modify your copy or copies of the Program or any portion
|
||||
of it, thus forming a work based on the Program, and copy and
|
||||
distribute such modifications or work under the terms of Section 1
|
||||
above, provided that you also meet all of these conditions:
|
||||
|
||||
a) You must cause the modified files to carry prominent notices
|
||||
stating that you changed the files and the date of any change.
|
||||
|
||||
b) You must cause any work that you distribute or publish, that in
|
||||
whole or in part contains or is derived from the Program or any
|
||||
part thereof, to be licensed as a whole at no charge to all third
|
||||
parties under the terms of this License.
|
||||
|
||||
c) If the modified program normally reads commands interactively
|
||||
when run, you must cause it, when started running for such
|
||||
interactive use in the most ordinary way, to print or display an
|
||||
announcement including an appropriate copyright notice and a
|
||||
notice that there is no warranty (or else, saying that you provide
|
||||
a warranty) and that users may redistribute the program under
|
||||
these conditions, and telling the user how to view a copy of this
|
||||
License. (Exception: if the Program itself is interactive but
|
||||
does not normally print such an announcement, your work based on
|
||||
the Program is not required to print an announcement.)
|
||||
|
||||
These requirements apply to the modified work as a whole. If
|
||||
identifiable sections of that work are not derived from the Program,
|
||||
and can be reasonably considered independent and separate works in
|
||||
themselves, then this License, and its terms, do not apply to those
|
||||
sections when you distribute them as separate works. But when you
|
||||
distribute the same sections as part of a whole which is a work based
|
||||
on the Program, the distribution of the whole must be on the terms of
|
||||
this License, whose permissions for other licensees extend to the
|
||||
entire whole, and thus to each and every part regardless of who wrote it.
|
||||
|
||||
Thus, it is not the intent of this section to claim rights or contest
|
||||
your rights to work written entirely by you; rather, the intent is to
|
||||
exercise the right to control the distribution of derivative or
|
||||
collective works based on the Program.
|
||||
|
||||
In addition, mere aggregation of another work not based on the Program
|
||||
with the Program (or with a work based on the Program) on a volume of
|
||||
a storage or distribution medium does not bring the other work under
|
||||
the scope of this License.
|
||||
|
||||
3. You may copy and distribute the Program (or a work based on it,
|
||||
under Section 2) in object code or executable form under the terms of
|
||||
Sections 1 and 2 above provided that you also do one of the following:
|
||||
|
||||
a) Accompany it with the complete corresponding machine-readable
|
||||
source code, which must be distributed under the terms of Sections
|
||||
1 and 2 above on a medium customarily used for software interchange; or,
|
||||
|
||||
b) Accompany it with a written offer, valid for at least three
|
||||
years, to give any third party, for a charge no more than your
|
||||
cost of physically performing source distribution, a complete
|
||||
machine-readable copy of the corresponding source code, to be
|
||||
distributed under the terms of Sections 1 and 2 above on a medium
|
||||
customarily used for software interchange; or,
|
||||
|
||||
c) Accompany it with the information you received as to the offer
|
||||
to distribute corresponding source code. (This alternative is
|
||||
allowed only for noncommercial distribution and only if you
|
||||
received the program in object code or executable form with such
|
||||
an offer, in accord with Subsection b above.)
|
||||
|
||||
The source code for a work means the preferred form of the work for
|
||||
making modifications to it. For an executable work, complete source
|
||||
code means all the source code for all modules it contains, plus any
|
||||
associated interface definition files, plus the scripts used to
|
||||
control compilation and installation of the executable. However, as a
|
||||
special exception, the source code distributed need not include
|
||||
anything that is normally distributed (in either source or binary
|
||||
form) with the major components (compiler, kernel, and so on) of the
|
||||
operating system on which the executable runs, unless that component
|
||||
itself accompanies the executable.
|
||||
|
||||
If distribution of executable or object code is made by offering
|
||||
access to copy from a designated place, then offering equivalent
|
||||
access to copy the source code from the same place counts as
|
||||
distribution of the source code, even though third parties are not
|
||||
compelled to copy the source along with the object code.
|
||||
|
||||
4. You may not copy, modify, sublicense, or distribute the Program
|
||||
except as expressly provided under this License. Any attempt
|
||||
otherwise to copy, modify, sublicense or distribute the Program is
|
||||
void, and will automatically terminate your rights under this License.
|
||||
However, parties who have received copies, or rights, from you under
|
||||
this License will not have their licenses terminated so long as such
|
||||
parties remain in full compliance.
|
||||
|
||||
5. You are not required to accept this License, since you have not
|
||||
signed it. However, nothing else grants you permission to modify or
|
||||
distribute the Program or its derivative works. These actions are
|
||||
prohibited by law if you do not accept this License. Therefore, by
|
||||
modifying or distributing the Program (or any work based on the
|
||||
Program), you indicate your acceptance of this License to do so, and
|
||||
all its terms and conditions for copying, distributing or modifying
|
||||
the Program or works based on it.
|
||||
|
||||
6. Each time you redistribute the Program (or any work based on the
|
||||
Program), the recipient automatically receives a license from the
|
||||
original licensor to copy, distribute or modify the Program subject to
|
||||
these terms and conditions. You may not impose any further
|
||||
restrictions on the recipients' exercise of the rights granted herein.
|
||||
You are not responsible for enforcing compliance by third parties to
|
||||
this License.
|
||||
|
||||
7. If, as a consequence of a court judgment or allegation of patent
|
||||
infringement or for any other reason (not limited to patent issues),
|
||||
conditions are imposed on you (whether by court order, agreement or
|
||||
otherwise) that contradict the conditions of this License, they do not
|
||||
excuse you from the conditions of this License. If you cannot
|
||||
distribute so as to satisfy simultaneously your obligations under this
|
||||
License and any other pertinent obligations, then as a consequence you
|
||||
may not distribute the Program at all. For example, if a patent
|
||||
license would not permit royalty-free redistribution of the Program by
|
||||
all those who receive copies directly or indirectly through you, then
|
||||
the only way you could satisfy both it and this License would be to
|
||||
refrain entirely from distribution of the Program.
|
||||
|
||||
If any portion of this section is held invalid or unenforceable under
|
||||
any particular circumstance, the balance of the section is intended to
|
||||
apply and the section as a whole is intended to apply in other
|
||||
circumstances.
|
||||
|
||||
It is not the purpose of this section to induce you to infringe any
|
||||
patents or other property right claims or to contest validity of any
|
||||
such claims; this section has the sole purpose of protecting the
|
||||
integrity of the free software distribution system, which is
|
||||
implemented by public license practices. Many people have made
|
||||
generous contributions to the wide range of software distributed
|
||||
through that system in reliance on consistent application of that
|
||||
system; it is up to the author/donor to decide if he or she is willing
|
||||
to distribute software through any other system and a licensee cannot
|
||||
impose that choice.
|
||||
|
||||
This section is intended to make thoroughly clear what is believed to
|
||||
be a consequence of the rest of this License.
|
||||
|
||||
8. If the distribution and/or use of the Program is restricted in
|
||||
certain countries either by patents or by copyrighted interfaces, the
|
||||
original copyright holder who places the Program under this License
|
||||
may add an explicit geographical distribution limitation excluding
|
||||
those countries, so that distribution is permitted only in or among
|
||||
countries not thus excluded. In such case, this License incorporates
|
||||
the limitation as if written in the body of this License.
|
||||
|
||||
9. The Free Software Foundation may publish revised and/or new versions
|
||||
of the General Public License from time to time. Such new versions will
|
||||
be similar in spirit to the present version, but may differ in detail to
|
||||
address new problems or concerns.
|
||||
|
||||
Each version is given a distinguishing version number. If the Program
|
||||
specifies a version number of this License which applies to it and "any
|
||||
later version", you have the option of following the terms and conditions
|
||||
either of that version or of any later version published by the Free
|
||||
Software Foundation. If the Program does not specify a version number of
|
||||
this License, you may choose any version ever published by the Free Software
|
||||
Foundation.
|
||||
|
||||
10. If you wish to incorporate parts of the Program into other free
|
||||
programs whose distribution conditions are different, write to the author
|
||||
to ask for permission. For software which is copyrighted by the Free
|
||||
Software Foundation, write to the Free Software Foundation; we sometimes
|
||||
make exceptions for this. Our decision will be guided by the two goals
|
||||
of preserving the free status of all derivatives of our free software and
|
||||
of promoting the sharing and reuse of software generally.
|
||||
|
||||
NO WARRANTY
|
||||
|
||||
11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY
|
||||
FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN
|
||||
OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES
|
||||
PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED
|
||||
OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
|
||||
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS
|
||||
TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE
|
||||
PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING,
|
||||
REPAIR OR CORRECTION.
|
||||
|
||||
12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
|
||||
WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR
|
||||
REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES,
|
||||
INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING
|
||||
OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED
|
||||
TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY
|
||||
YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER
|
||||
PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE
|
||||
POSSIBILITY OF SUCH DAMAGES.
|
||||
@@ -1,515 +0,0 @@
|
||||
# Otter - Program made for educational intent, can be freely distributed
|
||||
# and can be used for economical intent. I will not take legal actions
|
||||
# unless my intelectual propperty, the code, is stolen or change without permission.
|
||||
#
|
||||
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
|
||||
#
|
||||
# This program is free software; you can redistribute it and/or modify
|
||||
# it under the terms of the GNU General Public License version 2 as published by
|
||||
# the Free Software Foundation.
|
||||
#
|
||||
# This program is distributed in the hope that it will be useful,
|
||||
# but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
# GNU General Public License for more details.
|
||||
#
|
||||
# You should have received a copy of the GNU General Public License along
|
||||
# with this program; if not, write to the Free Software Foundation, Inc.,
|
||||
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
|
||||
|
||||
import math
|
||||
import numpy as np
|
||||
import pandas as pd
|
||||
from Seals import process as sl
|
||||
|
||||
class Algebra:
|
||||
|
||||
def __init__(self, function):
|
||||
self.f = function
|
||||
self.integral = self.Integral(self.f)
|
||||
self.roots = self.Roots(self.f)
|
||||
self.edo = self.Edo(self.f)
|
||||
|
||||
def d(self, x, e):
|
||||
return (self.f(x + e) - self.f(x - e))/(2*e)
|
||||
|
||||
class Integral:
|
||||
|
||||
def __init__(self,function):
|
||||
self.f = function
|
||||
self.simple = self.Simple(function)
|
||||
self.double = self.Double(function)
|
||||
|
||||
class Simple:
|
||||
def __init__(self, function):
|
||||
self.f = function
|
||||
|
||||
def riemann(self,a,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
delta = (b-a)/n
|
||||
|
||||
psi = a
|
||||
theta = 0
|
||||
|
||||
while((psi+delta) <= b):
|
||||
|
||||
theta += (self.f(psi) + self.f(psi + delta))/2
|
||||
psi += delta
|
||||
|
||||
integral = delta*theta
|
||||
|
||||
return integral
|
||||
|
||||
def simpson(self,a,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
def x(i):
|
||||
return a + i*h
|
||||
|
||||
h = (b-a)/n
|
||||
|
||||
eta = 0
|
||||
theta = 0
|
||||
|
||||
psi = 1
|
||||
kappa = 1
|
||||
|
||||
while(psi <= (n/2)):
|
||||
|
||||
eta = eta + self.f(x(2*psi - 1))
|
||||
psi = psi + 1
|
||||
|
||||
while(kappa <= ((n/2)-1)):
|
||||
|
||||
theta = theta + self.f(x(2*kappa))
|
||||
kappa = kappa + 1
|
||||
|
||||
return (h/3)*( self.f(x(0)) + self.f(x(n)) + 4*eta + 2*theta)
|
||||
|
||||
|
||||
class Double:
|
||||
|
||||
def __init__(self,function):
|
||||
self.f = function
|
||||
|
||||
def riemann(self,a,b,c,d,n=None,m=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**4
|
||||
|
||||
if m is None:
|
||||
m = n
|
||||
|
||||
dx = (b-a)/n
|
||||
dy = (d-c)/m
|
||||
kappa = a
|
||||
psi = c
|
||||
theta = 0
|
||||
|
||||
while((psi + dy) < d):
|
||||
|
||||
while((kappa + dx) < b):
|
||||
|
||||
theta = theta + self.f(kappa, psi)
|
||||
kappa = kappa + dx
|
||||
|
||||
psi = psi + dy
|
||||
kappa = a
|
||||
|
||||
return theta*(dx)*(dy)
|
||||
|
||||
def simpson(self,a,b,c,d,n=None,m=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**4
|
||||
|
||||
if m is None:
|
||||
m = n
|
||||
|
||||
dx = (b-a)/n
|
||||
dy = (d-c)/m
|
||||
|
||||
def x(i):
|
||||
|
||||
x = a + i*dx
|
||||
|
||||
return x
|
||||
|
||||
def y(i):
|
||||
|
||||
y = c + i*dy
|
||||
|
||||
return y
|
||||
|
||||
def g(i):
|
||||
|
||||
sigma = 0
|
||||
upsilon = 0
|
||||
|
||||
zeta = 1
|
||||
csi = 1
|
||||
|
||||
while(zeta <= (m/2)):
|
||||
|
||||
sigma += self.f(x(i),y(2*zeta - 1))
|
||||
zeta += 1
|
||||
|
||||
while(csi <= ((m/2)-1)):
|
||||
|
||||
upsilon += self.f(x(i),y(2*csi))
|
||||
csi += 1
|
||||
|
||||
return (dy/3)*( self.f(x(i),y(0)) + self.f(x(i),y(m)) + 4*sigma + 2*upsilon )
|
||||
|
||||
eta = 0
|
||||
theta = 0
|
||||
|
||||
psi = 1
|
||||
kappa = 1
|
||||
|
||||
while(psi <= (n/2)):
|
||||
|
||||
eta += g(2*psi - 1)
|
||||
psi += 1
|
||||
|
||||
while(kappa <= ((n/2)-1)):
|
||||
|
||||
theta += g(2*kappa)
|
||||
kappa += 1
|
||||
|
||||
return (dx/3)*( g(0) + g(n) + 4*eta + 2*theta)
|
||||
|
||||
class Roots:
|
||||
|
||||
def __init__(self, function=None):
|
||||
if function is not None:
|
||||
self.f = function
|
||||
|
||||
def bissec(self,a,b,e=None):
|
||||
|
||||
if e is None:
|
||||
e = 10**(-6)
|
||||
|
||||
fa = self.f(a)
|
||||
|
||||
while abs(a-b) > e:
|
||||
|
||||
c = (a+b)/2
|
||||
fc = self.f(c)
|
||||
|
||||
if (fa*fc) < 0:
|
||||
|
||||
b = c
|
||||
|
||||
else:
|
||||
|
||||
a = c
|
||||
fa = fc
|
||||
|
||||
c = (a+b)/2
|
||||
|
||||
return c
|
||||
|
||||
def d(self, x, e):
|
||||
return (self.f(x + e) - self.f(x - e))/(2*e)
|
||||
|
||||
def newton(self,a,e=None):
|
||||
|
||||
if e is None:
|
||||
e = 10**(-6)
|
||||
|
||||
fa = self.f(a)
|
||||
da = self.d(a,e)
|
||||
b = a - fa/da
|
||||
|
||||
|
||||
while abs(a-b) > e:
|
||||
|
||||
b = a
|
||||
a -= (fa/da)
|
||||
fa = self.f(a)
|
||||
da = self.d(a,e)
|
||||
|
||||
return a
|
||||
|
||||
def bissec_newton(self,a,b,e=None):
|
||||
|
||||
if e is None:
|
||||
e = 10**(-6)
|
||||
|
||||
fa = self.f(a)
|
||||
|
||||
c = (a+b)/2 # 'c' é a raiz calculada
|
||||
|
||||
while abs(a-b) > 0.1:
|
||||
|
||||
fc = self.f(c)
|
||||
|
||||
if fa*fc < 0:
|
||||
|
||||
b = c
|
||||
|
||||
else:
|
||||
|
||||
a = c
|
||||
fa = self.f(a)
|
||||
|
||||
c = (a+b)/2
|
||||
|
||||
fc = self.f(c)
|
||||
dc = self.d(c,e)
|
||||
h = c - fc/dc # 'h' é uma variável de controle
|
||||
|
||||
while abs(c-h) > e:
|
||||
|
||||
h = c
|
||||
c -= (fc/dc)
|
||||
fc = self.f(c)
|
||||
dc = self.d(c,e)
|
||||
|
||||
return (c)
|
||||
|
||||
|
||||
class Edo:
|
||||
|
||||
def __init__(self, function):
|
||||
self.F = function
|
||||
|
||||
def euler(self,a,y,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
dx = (b-a)/n
|
||||
|
||||
def x(i):
|
||||
return a + i*dx
|
||||
|
||||
for i in range(n):
|
||||
|
||||
y = y + (self.F(x(i),y))*dx
|
||||
|
||||
return y
|
||||
|
||||
def runge(self,a,y,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
dx = (b-a)/n
|
||||
|
||||
def x(i):
|
||||
return (a + i*dx)
|
||||
|
||||
for i in range(n):
|
||||
|
||||
y = y + (dx/2)*(self.F(x(i),y)+self.F(x(i+1),(y+(dx*self.F(x(i),y)))))
|
||||
|
||||
return y
|
||||
|
||||
def adams(self,a,y,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
dx = (b-a)/n
|
||||
|
||||
def x(i):
|
||||
return (a + i*dx)
|
||||
|
||||
for i in range(n):
|
||||
|
||||
f0 = self.F(x(i),y)
|
||||
f1 = self.F(x(i+1),y + dx*self.F(x(i)+(dx/2),y+(dx/2)*self.F(x(i),y)))
|
||||
f2 = self.F(x(i+2),y + (dx/2)*(3*f1-f0))
|
||||
|
||||
y += (dx/12)*(5*f2 + 8*f1 - f0)
|
||||
|
||||
return y
|
||||
|
||||
class Interpolation:
|
||||
""" Data should be organized in two columns: X and Y"""
|
||||
|
||||
def __init__(self, data):
|
||||
|
||||
self.data = data
|
||||
self.polinomial = self.Polinomial(self.data)
|
||||
|
||||
def minimus(self,x):
|
||||
|
||||
theta = 0
|
||||
# somatorio de x
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
theta += self.data.x[i]
|
||||
|
||||
eta = 0
|
||||
#somatorio de y
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
eta += self.data.y[i]
|
||||
|
||||
sigma = 0
|
||||
#somatorio de xy
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
sigma += self.data.x[i]*self.data.y[i]
|
||||
|
||||
omega = 0
|
||||
#somatorio de x^2self.dself.dself.d
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
omega += self.data.x[i]**2
|
||||
|
||||
|
||||
self.a = (self.data.shape[0]*sigma - theta*eta)/(self.data.shape[0]*omega - (theta**2))
|
||||
|
||||
self.b = (theta*sigma - eta*omega)/((theta**2) - self.data.shape[0]*omega)
|
||||
|
||||
ym = 0
|
||||
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
ym += self.data.y[i]/self.data.shape[0]
|
||||
|
||||
sqreq = 0
|
||||
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
sqreq += ((self.a*self.data.x[i] + self.b) - ym)**2
|
||||
|
||||
sqtot = 0
|
||||
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
sqtot += (self.data.y[i] - ym)**2
|
||||
|
||||
self.r2 = sqreq/sqtot
|
||||
|
||||
return self.a*x + self.b
|
||||
|
||||
class Polinomial:
|
||||
|
||||
def __init__(self, data):
|
||||
self.data = data
|
||||
|
||||
def vandermonde(self, x):
|
||||
|
||||
matrix = np.zeros((self.data.shape[0],self.data.shape[0]))
|
||||
|
||||
for k in range(0, self.data.shape[0]):
|
||||
|
||||
matrix[:,k] = self.data.x[:]**k
|
||||
|
||||
self.A = sl.gauss(np.c_[matrix,self.data[:,1]])
|
||||
|
||||
y = 0
|
||||
|
||||
for i in range(0,self.A.shape[0]):
|
||||
|
||||
y += self.A[i]*(x**i)
|
||||
|
||||
return float(y)
|
||||
|
||||
def lagrange(self, x):
|
||||
|
||||
def L(k,x):
|
||||
|
||||
up = down = 1
|
||||
|
||||
for i in [x for x in range(self.data.x.shape[0]) if x != k]:
|
||||
up = up*(x - self.data.x[i])
|
||||
|
||||
for i in [x for x in range(self.data.x.shape[0]) if x != k]:
|
||||
down = down*(self.data.x[k] - self.data.x[i])
|
||||
|
||||
return up/down
|
||||
|
||||
y = 0
|
||||
|
||||
for i in range(self.data.x.shape[0]):
|
||||
|
||||
y += self.data.y[i]*L(i,x)
|
||||
|
||||
return y
|
||||
|
||||
def newton(self,x):
|
||||
|
||||
d = np.array(np.zeros((self.data.shape[0],self.data.shape[0])))
|
||||
|
||||
d[0] = self.data.y
|
||||
|
||||
i = j = 0
|
||||
|
||||
while (i < self.data.shape[0]):
|
||||
|
||||
while (j < (self.data.shape[0]-(i+1))):
|
||||
|
||||
d[i+1][j] = (d[i][j+1] - d[i][j])/(self.data.x[(i+1)+j]-self.data.x[j])
|
||||
j += 1
|
||||
|
||||
i += 1
|
||||
j = 0
|
||||
|
||||
def f(x):
|
||||
|
||||
y = d[0][0]
|
||||
i = 0
|
||||
|
||||
while ((i+1) < self.data.shape[0]):
|
||||
|
||||
mult = 1
|
||||
k = 0
|
||||
while (k <= i):
|
||||
mult = mult*(x - self.data.x[k])
|
||||
k += 1
|
||||
|
||||
y += d[i+1][0]*mult
|
||||
i += 1
|
||||
|
||||
return y
|
||||
|
||||
self.f = f
|
||||
|
||||
return f(x)
|
||||
|
||||
def gregory(self,x):
|
||||
|
||||
h = self.data.x[0] - self.data.x[1]
|
||||
|
||||
d = np.array(np.zeros((self.data.shape[0],self.data.shape[0])))
|
||||
|
||||
d[0] = self.data.y
|
||||
|
||||
i = j = 0
|
||||
|
||||
while (i < self.data.shape[0]):
|
||||
|
||||
while (j < (self.data.shape[0]-(i+1))):
|
||||
|
||||
d[i+1][j] = (d[i][j+1] - d[i][j])/((i+1)*h)
|
||||
j += 1
|
||||
|
||||
i += 1
|
||||
j = 0
|
||||
|
||||
y = d[0][0]
|
||||
i = 0
|
||||
|
||||
while ((i+1) < self.data.shape[0]):
|
||||
|
||||
mult = 1
|
||||
k = 0
|
||||
while (k <= i):
|
||||
mult = mult*(x - self.data.x[k])
|
||||
k += 1
|
||||
|
||||
y += d[i+1][0]*mult
|
||||
i += 1
|
||||
|
||||
return y
|
||||
@@ -1,21 +0,0 @@
|
||||
# Otter - Program made for educational intent, can be freely distributed
|
||||
# and can be used for economical intent. I will not take legal actions
|
||||
# unless my intelectual propperty, the code, is stolen or change without permission.
|
||||
|
||||
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
|
||||
|
||||
# This program is free software; you can redistribute it and/or modify
|
||||
# it under the terms of the GNU General Public License version 2 as published by
|
||||
# the Free Software Foundation.
|
||||
|
||||
# This program is distributed in the hope that it will be useful,
|
||||
# but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
# GNU General Public License for more details.
|
||||
|
||||
# You should have received a copy of the GNU General Public License along
|
||||
# with this program; if not, write to the Free Software Foundation, Inc.,
|
||||
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
|
||||
|
||||
from .Otter import Algebra as algebra
|
||||
from .Otter import Interpolation as interpolation
|
||||
@@ -1,75 +0,0 @@
|
||||
# Otter - Numeric Calculus
|
||||
|
||||
This python package is made for applied Numeric Calculus of Algebra Functions. It is made with the following objectives in mind:
|
||||
|
||||
* Receive one variable function from user input
|
||||
|
||||
* Receive two variable function from user input
|
||||
|
||||
* Performe derivatives with one variable functions
|
||||
|
||||
* Performe integral with received functions
|
||||
|
||||
* Use methods to proccess the matrices.
|
||||
|
||||
* Find root of functions throw method of bissection and method of newton
|
||||
|
||||
* Solve Diferential Equations throw method of euler and runge
|
||||
|
||||
* Performe Minimus Interpolation and Polinomial Interpolation
|
||||
|
||||
## Syntax
|
||||
|
||||
To initialize a Otter instance linked to functions use the following syntax `otr = Otter.algebra(f)`, where `otr` will be a arbitrary name for the instance and `f` is a function of *one variable*.
|
||||
|
||||
To initialize a Otter instance linked to data and interpolation use the following syntax `otr = Otter.interpolation(data)`, where `otr` will be a arbitrary name for the instance and data will be a *numpy* matrix where the first columns has to contain the values for `x` and the second column contains the values for `y`.
|
||||
|
||||
### Algebra
|
||||
|
||||
Algebra is a Python Class where some of the features described previously are defined as Classes as well, like: `Integral`, `Roots`, `EDO` (diferential equations).
|
||||
|
||||
#### Integral
|
||||
|
||||
To call the class *Integral* append the sufix with lower case in front of the instance like: `otr.integral`. The Integral class has two other class defined inside, `Simple` and `Double`, to call them append the sufix with lower case in front as `otr.integral.simple` or `otr.integral.double`. Then pick between Riemann's Method or Simpson's Method by appending the sufix `riemann` or `simpson` as well.
|
||||
|
||||
After that the syntax will be something like `otr.integral.double.riemann(a,b,c,d,n,m)`, where `a` and `c` will be the first value of the interval of integration respectively in x and y, `b` and `d` will be the last, `n` and `m` will be the number of partitions.
|
||||
|
||||
The syntax for one variable integrations will be `otr.integral.simple.riemann(a,b,n)`.
|
||||
|
||||
If `n` is not defined the standart value in 10^6 partitions for one variable and 10^4 for double. And if `m` is not defined the standart value will be equal to `n`.
|
||||
|
||||
#### Roots
|
||||
|
||||
To call the class *Root* append the sufix with lower case in front of the instance like: `otr.roots`. The Roots class has three methods defined inside, `bissec`, `newton` and `bissec_newton`, to call them append the sufix with lower case in front as `otr.roots.bissec` or `otr.roots.newton` or even `otr.roots.bissecnewton`.
|
||||
|
||||
The syntax for the bissection method and bissec_newton is equal to `otr.roots.bissec(a,b,e)` and `otr.roots.bissec_newton(a,b,e)`, where `a` is the first element of the interval containing the root and `b` is the last, `e` being the precision.
|
||||
|
||||
The syntax for the newton method is equal to `otr.roots.newton(a,e)`, where `a` is the element closest to the root and `e` is the precision.
|
||||
|
||||
If `e` is not defined the standart value is 10^(-6).
|
||||
|
||||
#### Diferential Equations
|
||||
|
||||
To call the class *EDO* (*E*quações *D*iferenciais *O*rdinárias) append the sufix with lower case in front of the instance like: `otr.edo`. The *EDO* class has two methods defined inside: `euler` and `runge`, to call them append the sufix with lower case in front as `otr.edo.euler` or `otr.edo.runge`.
|
||||
|
||||
The syntax for the diferential equations method is equal to `otr.edo.euler(a,y,b,n)` or `otr.edo.runge(a,y,b,n)`, where `a` and `y` will be the inintial point and `b` is the value in *x* which you want to know the corresponding value in *y* and `n` is the number of operations.
|
||||
|
||||
If `n` is not defined the standart value is 10^7.
|
||||
|
||||
### Interpolation
|
||||
|
||||
The python class *Interpolation* is divided in one method, minimus interpolation, and one class, polinomial interpolation.
|
||||
|
||||
To call the method *minimus* use a syntax like `otr = Otter.interpolation(data)`, where `data` is a data frame containing values for *x* and *y*, `otr` is an instance and append the method in front of the instance like: `otr.minimus(x)`, where *x* is value of *f(x)* you want to estimate.
|
||||
|
||||
To call the class *Polinomial* append the sufix with lower case in front of the instance like: `otr.polinomial`. The *Polinomial* class has four methods defined inside: `vandermonde`, `lagrange`, `newton` and `gregory`, to call them append the sufix with lower case in front like `otr.edo.gregory(x)` where *x* is value of *f(x)* you want to estimate.
|
||||
|
||||
## Installation
|
||||
|
||||
To install the package from source `cd` into the directory and run:
|
||||
|
||||
`pip install .`
|
||||
|
||||
or run
|
||||
|
||||
`pip install yoshi-otter`
|
||||
@@ -1,515 +0,0 @@
|
||||
# Otter - Program made for educational intent, can be freely distributed
|
||||
# and can be used for economical intent. I will not take legal actions
|
||||
# unless my intelectual propperty, the code, is stolen or change without permission.
|
||||
#
|
||||
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
|
||||
#
|
||||
# This program is free software; you can redistribute it and/or modify
|
||||
# it under the terms of the GNU General Public License version 2 as published by
|
||||
# the Free Software Foundation.
|
||||
#
|
||||
# This program is distributed in the hope that it will be useful,
|
||||
# but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
# GNU General Public License for more details.
|
||||
#
|
||||
# You should have received a copy of the GNU General Public License along
|
||||
# with this program; if not, write to the Free Software Foundation, Inc.,
|
||||
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
|
||||
|
||||
import math
|
||||
import numpy as np
|
||||
import pandas as pd
|
||||
from Seals import process as sl
|
||||
|
||||
class Algebra:
|
||||
|
||||
def __init__(self, function):
|
||||
self.f = function
|
||||
self.integral = self.Integral(self.f)
|
||||
self.roots = self.Roots(self.f)
|
||||
self.edo = self.Edo(self.f)
|
||||
|
||||
def d(self, x, e):
|
||||
return (self.f(x + e) - self.f(x - e))/(2*e)
|
||||
|
||||
class Integral:
|
||||
|
||||
def __init__(self,function):
|
||||
self.f = function
|
||||
self.simple = self.Simple(function)
|
||||
self.double = self.Double(function)
|
||||
|
||||
class Simple:
|
||||
def __init__(self, function):
|
||||
self.f = function
|
||||
|
||||
def riemann(self,a,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
delta = (b-a)/n
|
||||
|
||||
psi = a
|
||||
theta = 0
|
||||
|
||||
while((psi+delta) <= b):
|
||||
|
||||
theta += (self.f(psi) + self.f(psi + delta))/2
|
||||
psi += delta
|
||||
|
||||
integral = delta*theta
|
||||
|
||||
return integral
|
||||
|
||||
def simpson(self,a,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
def x(i):
|
||||
return a + i*h
|
||||
|
||||
h = (b-a)/n
|
||||
|
||||
eta = 0
|
||||
theta = 0
|
||||
|
||||
psi = 1
|
||||
kappa = 1
|
||||
|
||||
while(psi <= (n/2)):
|
||||
|
||||
eta = eta + self.f(x(2*psi - 1))
|
||||
psi = psi + 1
|
||||
|
||||
while(kappa <= ((n/2)-1)):
|
||||
|
||||
theta = theta + self.f(x(2*kappa))
|
||||
kappa = kappa + 1
|
||||
|
||||
return (h/3)*( self.f(x(0)) + self.f(x(n)) + 4*eta + 2*theta)
|
||||
|
||||
|
||||
class Double:
|
||||
|
||||
def __init__(self,function):
|
||||
self.f = function
|
||||
|
||||
def riemann(self,a,b,c,d,n=None,m=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**4
|
||||
|
||||
if m is None:
|
||||
m = n
|
||||
|
||||
dx = (b-a)/n
|
||||
dy = (d-c)/m
|
||||
kappa = a
|
||||
psi = c
|
||||
theta = 0
|
||||
|
||||
while((psi + dy) < d):
|
||||
|
||||
while((kappa + dx) < b):
|
||||
|
||||
theta = theta + self.f(kappa, psi)
|
||||
kappa = kappa + dx
|
||||
|
||||
psi = psi + dy
|
||||
kappa = a
|
||||
|
||||
return theta*(dx)*(dy)
|
||||
|
||||
def simpson(self,a,b,c,d,n=None,m=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**4
|
||||
|
||||
if m is None:
|
||||
m = n
|
||||
|
||||
dx = (b-a)/n
|
||||
dy = (d-c)/m
|
||||
|
||||
def x(i):
|
||||
|
||||
x = a + i*dx
|
||||
|
||||
return x
|
||||
|
||||
def y(i):
|
||||
|
||||
y = c + i*dy
|
||||
|
||||
return y
|
||||
|
||||
def g(i):
|
||||
|
||||
sigma = 0
|
||||
upsilon = 0
|
||||
|
||||
zeta = 1
|
||||
csi = 1
|
||||
|
||||
while(zeta <= (m/2)):
|
||||
|
||||
sigma += self.f(x(i),y(2*zeta - 1))
|
||||
zeta += 1
|
||||
|
||||
while(csi <= ((m/2)-1)):
|
||||
|
||||
upsilon += self.f(x(i),y(2*csi))
|
||||
csi += 1
|
||||
|
||||
return (dy/3)*( self.f(x(i),y(0)) + self.f(x(i),y(m)) + 4*sigma + 2*upsilon )
|
||||
|
||||
eta = 0
|
||||
theta = 0
|
||||
|
||||
psi = 1
|
||||
kappa = 1
|
||||
|
||||
while(psi <= (n/2)):
|
||||
|
||||
eta += g(2*psi - 1)
|
||||
psi += 1
|
||||
|
||||
while(kappa <= ((n/2)-1)):
|
||||
|
||||
theta += g(2*kappa)
|
||||
kappa += 1
|
||||
|
||||
return (dx/3)*( g(0) + g(n) + 4*eta + 2*theta)
|
||||
|
||||
class Roots:
|
||||
|
||||
def __init__(self, function=None):
|
||||
if function is not None:
|
||||
self.f = function
|
||||
|
||||
def bissec(self,a,b,e=None):
|
||||
|
||||
if e is None:
|
||||
e = 10**(-6)
|
||||
|
||||
fa = self.f(a)
|
||||
|
||||
while abs(a-b) > e:
|
||||
|
||||
c = (a+b)/2
|
||||
fc = self.f(c)
|
||||
|
||||
if (fa*fc) < 0:
|
||||
|
||||
b = c
|
||||
|
||||
else:
|
||||
|
||||
a = c
|
||||
fa = fc
|
||||
|
||||
c = (a+b)/2
|
||||
|
||||
return c
|
||||
|
||||
def d(self, x, e):
|
||||
return (self.f(x + e) - self.f(x - e))/(2*e)
|
||||
|
||||
def newton(self,a,e=None):
|
||||
|
||||
if e is None:
|
||||
e = 10**(-6)
|
||||
|
||||
fa = self.f(a)
|
||||
da = self.d(a,e)
|
||||
b = a - fa/da
|
||||
|
||||
|
||||
while abs(a-b) > e:
|
||||
|
||||
b = a
|
||||
a -= (fa/da)
|
||||
fa = self.f(a)
|
||||
da = self.d(a,e)
|
||||
|
||||
return a
|
||||
|
||||
def bissec_newton(self,a,b,e=None):
|
||||
|
||||
if e is None:
|
||||
e = 10**(-6)
|
||||
|
||||
fa = self.f(a)
|
||||
|
||||
c = (a+b)/2 # 'c' é a raiz calculada
|
||||
|
||||
while abs(a-b) > 0.1:
|
||||
|
||||
fc = self.f(c)
|
||||
|
||||
if fa*fc < 0:
|
||||
|
||||
b = c
|
||||
|
||||
else:
|
||||
|
||||
a = c
|
||||
fa = self.f(a)
|
||||
|
||||
c = (a+b)/2
|
||||
|
||||
fc = self.f(c)
|
||||
dc = self.d(c,e)
|
||||
h = c - fc/dc # 'h' é uma variável de controle
|
||||
|
||||
while abs(c-h) > e:
|
||||
|
||||
h = c
|
||||
c -= (fc/dc)
|
||||
fc = self.f(c)
|
||||
dc = self.d(c,e)
|
||||
|
||||
return (c)
|
||||
|
||||
|
||||
class Edo:
|
||||
|
||||
def __init__(self, function):
|
||||
self.F = function
|
||||
|
||||
def euler(self,a,y,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
dx = (b-a)/n
|
||||
|
||||
def x(i):
|
||||
return a + i*dx
|
||||
|
||||
for i in range(n):
|
||||
|
||||
y = y + (self.F(x(i),y))*dx
|
||||
|
||||
return y
|
||||
|
||||
def runge(self,a,y,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
dx = (b-a)/n
|
||||
|
||||
def x(i):
|
||||
return (a + i*dx)
|
||||
|
||||
for i in range(n):
|
||||
|
||||
y = y + (dx/2)*(self.F(x(i),y)+self.F(x(i+1),(y+(dx*self.F(x(i),y)))))
|
||||
|
||||
return y
|
||||
|
||||
def adams(self,a,y,b,n=None):
|
||||
|
||||
if n is None:
|
||||
n = 10**6
|
||||
|
||||
dx = (b-a)/n
|
||||
|
||||
def x(i):
|
||||
return (a + i*dx)
|
||||
|
||||
for i in range(n):
|
||||
|
||||
f0 = self.F(x(i),y)
|
||||
f1 = self.F(x(i+1),y + dx*self.F(x(i)+(dx/2),y+(dx/2)*self.F(x(i),y)))
|
||||
f2 = self.F(x(i+2),y + (dx/2)*(3*f1-f0))
|
||||
|
||||
y += (dx/12)*(5*f2 + 8*f1 - f0)
|
||||
|
||||
return y
|
||||
|
||||
class Interpolation:
|
||||
""" Data should be organized in two columns: X and Y"""
|
||||
|
||||
def __init__(self, data):
|
||||
|
||||
self.data = data
|
||||
self.polinomial = self.Polinomial(self.data)
|
||||
|
||||
def minimus(self,x):
|
||||
|
||||
theta = 0
|
||||
# somatorio de x
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
theta += self.data.x[i]
|
||||
|
||||
eta = 0
|
||||
#somatorio de y
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
eta += self.data.y[i]
|
||||
|
||||
sigma = 0
|
||||
#somatorio de xy
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
sigma += self.data.x[i]*self.data.y[i]
|
||||
|
||||
omega = 0
|
||||
#somatorio de x^2self.dself.dself.d
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
omega += self.data.x[i]**2
|
||||
|
||||
|
||||
self.a = (self.data.shape[0]*sigma - theta*eta)/(self.data.shape[0]*omega - (theta**2))
|
||||
|
||||
self.b = (theta*sigma - eta*omega)/((theta**2) - self.data.shape[0]*omega)
|
||||
|
||||
ym = 0
|
||||
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
ym += self.data.y[i]/self.data.shape[0]
|
||||
|
||||
sqreq = 0
|
||||
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
sqreq += ((self.a*self.data.x[i] + self.b) - ym)**2
|
||||
|
||||
sqtot = 0
|
||||
|
||||
for i in range(self.data.shape[0]):
|
||||
|
||||
sqtot += (self.data.y[i] - ym)**2
|
||||
|
||||
self.r2 = sqreq/sqtot
|
||||
|
||||
return self.a*x + self.b
|
||||
|
||||
class Polinomial:
|
||||
|
||||
def __init__(self, data):
|
||||
self.data = data
|
||||
|
||||
def vandermonde(self, x):
|
||||
|
||||
matrix = np.zeros((self.data.shape[0],self.data.shape[0]))
|
||||
|
||||
for k in range(0, self.data.shape[0]):
|
||||
|
||||
matrix[:,k] = self.data.x[:]**k
|
||||
|
||||
self.A = sl.gauss(np.c_[matrix,self.data[:,1]])
|
||||
|
||||
y = 0
|
||||
|
||||
for i in range(0,self.A.shape[0]):
|
||||
|
||||
y += self.A[i]*(x**i)
|
||||
|
||||
return float(y)
|
||||
|
||||
def lagrange(self, x):
|
||||
|
||||
def L(k,x):
|
||||
|
||||
up = down = 1
|
||||
|
||||
for i in [x for x in range(self.data.x.shape[0]) if x != k]:
|
||||
up = up*(x - self.data.x[i])
|
||||
|
||||
for i in [x for x in range(self.data.x.shape[0]) if x != k]:
|
||||
down = down*(self.data.x[k] - self.data.x[i])
|
||||
|
||||
return up/down
|
||||
|
||||
y = 0
|
||||
|
||||
for i in range(self.data.x.shape[0]):
|
||||
|
||||
y += self.data.y[i]*L(i,x)
|
||||
|
||||
return y
|
||||
|
||||
def newton(self,x):
|
||||
|
||||
d = np.array(np.zeros((self.data.shape[0],self.data.shape[0])))
|
||||
|
||||
d[0] = self.data.y
|
||||
|
||||
i = j = 0
|
||||
|
||||
while (i < self.data.shape[0]):
|
||||
|
||||
while (j < (self.data.shape[0]-(i+1))):
|
||||
|
||||
d[i+1][j] = (d[i][j+1] - d[i][j])/(self.data.x[(i+1)+j]-self.data.x[j])
|
||||
j += 1
|
||||
|
||||
i += 1
|
||||
j = 0
|
||||
|
||||
def f(x):
|
||||
|
||||
y = d[0][0]
|
||||
i = 0
|
||||
|
||||
while ((i+1) < self.data.shape[0]):
|
||||
|
||||
mult = 1
|
||||
k = 0
|
||||
while (k <= i):
|
||||
mult = mult*(x - self.data.x[k])
|
||||
k += 1
|
||||
|
||||
y += d[i+1][0]*mult
|
||||
i += 1
|
||||
|
||||
return y
|
||||
|
||||
self.f = f
|
||||
|
||||
return f(x)
|
||||
|
||||
def gregory(self,x):
|
||||
|
||||
h = self.data.x[0] - self.data.x[1]
|
||||
|
||||
d = np.array(np.zeros((self.data.shape[0],self.data.shape[0])))
|
||||
|
||||
d[0] = self.data.y
|
||||
|
||||
i = j = 0
|
||||
|
||||
while (i < self.data.shape[0]):
|
||||
|
||||
while (j < (self.data.shape[0]-(i+1))):
|
||||
|
||||
d[i+1][j] = (d[i][j+1] - d[i][j])/((i+1)*h)
|
||||
j += 1
|
||||
|
||||
i += 1
|
||||
j = 0
|
||||
|
||||
y = d[0][0]
|
||||
i = 0
|
||||
|
||||
while ((i+1) < self.data.shape[0]):
|
||||
|
||||
mult = 1
|
||||
k = 0
|
||||
while (k <= i):
|
||||
mult = mult*(x - self.data.x[k])
|
||||
k += 1
|
||||
|
||||
y += d[i+1][0]*mult
|
||||
i += 1
|
||||
|
||||
return y
|
||||
@@ -1,21 +0,0 @@
|
||||
# Otter - Program made for educational intent, can be freely distributed
|
||||
# and can be used for economical intent. I will not take legal actions
|
||||
# unless my intelectual propperty, the code, is stolen or change without permission.
|
||||
|
||||
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
|
||||
|
||||
# This program is free software; you can redistribute it and/or modify
|
||||
# it under the terms of the GNU General Public License version 2 as published by
|
||||
# the Free Software Foundation.
|
||||
|
||||
# This program is distributed in the hope that it will be useful,
|
||||
# but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
# GNU General Public License for more details.
|
||||
|
||||
# You should have received a copy of the GNU General Public License along
|
||||
# with this program; if not, write to the Free Software Foundation, Inc.,
|
||||
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
|
||||
|
||||
from .Otter import Algebra as algebra
|
||||
from .Otter import Interpolation as interpolation
|
||||
BIN
yoshi-otter1.3.3/dist/yoshi-otter-1.3.3.tar.gz
vendored
BIN
yoshi-otter1.3.3/dist/yoshi-otter-1.3.3.tar.gz
vendored
Binary file not shown.
Binary file not shown.
@@ -1,28 +0,0 @@
|
||||
import setuptools
|
||||
|
||||
with open("README.md", "r") as fh:
|
||||
long_description = fh.read()
|
||||
|
||||
setuptools.setup(
|
||||
name="yoshi-otter", # Replace with your own username
|
||||
version="1.3.3",
|
||||
author="Vitor Hideyoshi",
|
||||
author_email="vitor.h.n.batista@gmail.com",
|
||||
description="Numeric Calculus python module in the topic of Algebra Functions",
|
||||
long_description=long_description,
|
||||
long_description_content_type="text/markdown",
|
||||
url="https://github.com/HideyoshiNakazone/Otter-NumericCalculus.git",
|
||||
packages=setuptools.find_packages(),
|
||||
classifiers=[
|
||||
"Programming Language :: Python :: 3",
|
||||
"License :: OSI Approved :: GNU General Public License v2 (GPLv2)",
|
||||
"Operating System :: OS Independent",
|
||||
"Development Status :: 2 - Pre-Alpha",
|
||||
],
|
||||
python_requires='>=3.6',
|
||||
install_requires=[
|
||||
'numpy',
|
||||
'pandas',
|
||||
'yoshi-seals'
|
||||
],
|
||||
)
|
||||
@@ -1,91 +0,0 @@
|
||||
Metadata-Version: 2.1
|
||||
Name: yoshi-otter
|
||||
Version: 1.3.3
|
||||
Summary: Numeric Calculus python module in the topic of Algebra Functions
|
||||
Home-page: https://github.com/HideyoshiNakazone/Otter-NumericCalculus.git
|
||||
Author: Vitor Hideyoshi
|
||||
Author-email: vitor.h.n.batista@gmail.com
|
||||
License: UNKNOWN
|
||||
Description: # Otter - Numeric Calculus
|
||||
|
||||
This python package is made for applied Numeric Calculus of Algebra Functions. It is made with the following objectives in mind:
|
||||
|
||||
* Receive one variable function from user input
|
||||
|
||||
* Receive two variable function from user input
|
||||
|
||||
* Performe derivatives with one variable functions
|
||||
|
||||
* Performe integral with received functions
|
||||
|
||||
* Use methods to proccess the matrices.
|
||||
|
||||
* Find root of functions throw method of bissection and method of newton
|
||||
|
||||
* Solve Diferential Equations throw method of euler and runge
|
||||
|
||||
* Performe Minimus Interpolation and Polinomial Interpolation
|
||||
|
||||
## Syntax
|
||||
|
||||
To initialize a Otter instance linked to functions use the following syntax `otr = Otter.algebra(f)`, where `otr` will be a arbitrary name for the instance and `f` is a function of *one variable*.
|
||||
|
||||
To initialize a Otter instance linked to data and interpolation use the following syntax `otr = Otter.interpolation(data)`, where `otr` will be a arbitrary name for the instance and data will be a *numpy* matrix where the first columns has to contain the values for `x` and the second column contains the values for `y`.
|
||||
|
||||
### Algebra
|
||||
|
||||
Algebra is a Python Class where some of the features described previously are defined as Classes as well, like: `Integral`, `Roots`, `EDO` (diferential equations).
|
||||
|
||||
#### Integral
|
||||
|
||||
To call the class *Integral* append the sufix with lower case in front of the instance like: `otr.integral`. The Integral class has two other class defined inside, `Simple` and `Double`, to call them append the sufix with lower case in front as `otr.integral.simple` or `otr.integral.double`. Then pick between Riemann's Method or Simpson's Method by appending the sufix `riemann` or `simpson` as well.
|
||||
|
||||
After that the syntax will be something like `otr.integral.double.riemann(a,b,c,d,n,m)`, where `a` and `c` will be the first value of the interval of integration respectively in x and y, `b` and `d` will be the last, `n` and `m` will be the number of partitions.
|
||||
|
||||
The syntax for one variable integrations will be `otr.integral.simple.riemann(a,b,n)`.
|
||||
|
||||
If `n` is not defined the standart value in 10^6 partitions for one variable and 10^4 for double. And if `m` is not defined the standart value will be equal to `n`.
|
||||
|
||||
#### Roots
|
||||
|
||||
To call the class *Root* append the sufix with lower case in front of the instance like: `otr.roots`. The Roots class has three methods defined inside, `bissec`, `newton` and `bissec_newton`, to call them append the sufix with lower case in front as `otr.roots.bissec` or `otr.roots.newton` or even `otr.roots.bissecnewton`.
|
||||
|
||||
The syntax for the bissection method and bissec_newton is equal to `otr.roots.bissec(a,b,e)` and `otr.roots.bissec_newton(a,b,e)`, where `a` is the first element of the interval containing the root and `b` is the last, `e` being the precision.
|
||||
|
||||
The syntax for the newton method is equal to `otr.roots.newton(a,e)`, where `a` is the element closest to the root and `e` is the precision.
|
||||
|
||||
If `e` is not defined the standart value is 10^(-6).
|
||||
|
||||
#### Diferential Equations
|
||||
|
||||
To call the class *EDO* (*E*quações *D*iferenciais *O*rdinárias) append the sufix with lower case in front of the instance like: `otr.edo`. The *EDO* class has two methods defined inside: `euler` and `runge`, to call them append the sufix with lower case in front as `otr.edo.euler` or `otr.edo.runge`.
|
||||
|
||||
The syntax for the diferential equations method is equal to `otr.edo.euler(a,y,b,n)` or `otr.edo.runge(a,y,b,n)`, where `a` and `y` will be the inintial point and `b` is the value in *x* which you want to know the corresponding value in *y* and `n` is the number of operations.
|
||||
|
||||
If `n` is not defined the standart value is 10^7.
|
||||
|
||||
### Interpolation
|
||||
|
||||
The python class *Interpolation* is divided in one method, minimus interpolation, and one class, polinomial interpolation.
|
||||
|
||||
To call the method *minimus* use a syntax like `otr = Otter.interpolation(data)`, where `data` is a data frame containing values for *x* and *y*, `otr` is an instance and append the method in front of the instance like: `otr.minimus(x)`, where *x* is value of *f(x)* you want to estimate.
|
||||
|
||||
To call the class *Polinomial* append the sufix with lower case in front of the instance like: `otr.polinomial`. The *Polinomial* class has four methods defined inside: `vandermonde`, `lagrange`, `newton` and `gregory`, to call them append the sufix with lower case in front like `otr.edo.gregory(x)` where *x* is value of *f(x)* you want to estimate.
|
||||
|
||||
## Installation
|
||||
|
||||
To install the package from source `cd` into the directory and run:
|
||||
|
||||
`pip install .`
|
||||
|
||||
or run
|
||||
|
||||
`pip install yoshi-otter`
|
||||
|
||||
Platform: UNKNOWN
|
||||
Classifier: Programming Language :: Python :: 3
|
||||
Classifier: License :: OSI Approved :: GNU General Public License v2 (GPLv2)
|
||||
Classifier: Operating System :: OS Independent
|
||||
Classifier: Development Status :: 2 - Pre-Alpha
|
||||
Requires-Python: >=3.6
|
||||
Description-Content-Type: text/markdown
|
||||
@@ -1,9 +0,0 @@
|
||||
README.md
|
||||
setup.py
|
||||
Otter/Otter.py
|
||||
Otter/__init__.py
|
||||
yoshi_otter.egg-info/PKG-INFO
|
||||
yoshi_otter.egg-info/SOURCES.txt
|
||||
yoshi_otter.egg-info/dependency_links.txt
|
||||
yoshi_otter.egg-info/requires.txt
|
||||
yoshi_otter.egg-info/top_level.txt
|
||||
@@ -1 +0,0 @@
|
||||
|
||||
@@ -1,3 +0,0 @@
|
||||
numpy
|
||||
pandas
|
||||
yoshi-seals
|
||||
@@ -1 +0,0 @@
|
||||
Otter
|
||||
@@ -17,5 +17,5 @@
|
||||
# with this program; if not, write to the Free Software Foundation, Inc.,
|
||||
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
|
||||
|
||||
from .Otter import Algebra as algebra
|
||||
from .Otter import Interpolation as interpolation
|
||||
from yoshi_otter.algebra import Algebra
|
||||
from yoshi_otter.interpolation import Interpolation
|
||||
52
yoshi_otter/algebra/__algebra.py
Normal file
52
yoshi_otter/algebra/__algebra.py
Normal file
@@ -0,0 +1,52 @@
|
||||
# Otter - Program made for educational intent, can be freely distributed
|
||||
# and can be used for economical intent. I will not take legal actions
|
||||
# unless my intelectual propperty, the code, is stolen or change without permission.
|
||||
#
|
||||
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
|
||||
#
|
||||
# This program is free software; you can redistribute it and/or modify
|
||||
# it under the terms of the GNU General Public License version 2 as published by
|
||||
# the Free Software Foundation.
|
||||
#
|
||||
# This program is distributed in the hope that it will be useful,
|
||||
# but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
# GNU General Public License for more details.
|
||||
#
|
||||
# You should have received a copy of the GNU General Public License along
|
||||
# with this program; if not, write to the Free Software Foundation, Inc.,
|
||||
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
|
||||
|
||||
from yoshi_otter.algebra.integral.double import Double
|
||||
from yoshi_otter.algebra.integral.simple import Simple
|
||||
from yoshi_otter.algebra.roots import Roots
|
||||
from yoshi_otter.algebra.edo import Edo
|
||||
|
||||
from typing import Callable, Union
|
||||
from inspect import signature
|
||||
|
||||
from yoshi_otter.shared import InvalidFunctionSignature
|
||||
|
||||
|
||||
class Algebra:
|
||||
|
||||
def __init__(self, function: Callable[[float], float] | Callable[[float, float], float]) -> None:
|
||||
self.f = function
|
||||
|
||||
self.integral = self.__Integral(self.f)
|
||||
self.roots = Roots(self.f)
|
||||
self.edo = Edo(self.f)
|
||||
|
||||
def d(self, x: float, e: float = 10 ** -4) -> float:
|
||||
if len(signature(self.f).parameters) == 1:
|
||||
return (self.f(x + e) - self.f(x - e)) / (2 * e)
|
||||
else:
|
||||
raise InvalidFunctionSignature("This method is only valid for one dimensional functions.")
|
||||
|
||||
class __Integral:
|
||||
|
||||
def __init__(self, function: Union[Callable[[float], float], Callable[[float, float], float]]) -> None:
|
||||
self.f = function
|
||||
|
||||
self.simple = Simple(self.f)
|
||||
self.double = Double(self.f)
|
||||
1
yoshi_otter/algebra/__init__.py
Normal file
1
yoshi_otter/algebra/__init__.py
Normal file
@@ -0,0 +1 @@
|
||||
from .__algebra import Algebra
|
||||
51
yoshi_otter/algebra/edo/__edo.py
Normal file
51
yoshi_otter/algebra/edo/__edo.py
Normal file
@@ -0,0 +1,51 @@
|
||||
from typing import Callable
|
||||
|
||||
|
||||
class Edo:
|
||||
|
||||
def __init__(self, function: Callable[[float], float]) -> None:
|
||||
self.F = function
|
||||
|
||||
def euler(self, a: float, y: float, b: float, n: int = 10**6) -> float:
|
||||
|
||||
dx = (b - a) / n
|
||||
|
||||
def x(i):
|
||||
return a + i * dx
|
||||
|
||||
for i in range(n):
|
||||
y = y + (self.F(x(i), y)) * dx
|
||||
|
||||
return y
|
||||
|
||||
def runge(self, a: float, y: float, b: float, n: int = 10**6) -> float:
|
||||
|
||||
dx = (b - a) / n
|
||||
|
||||
def x(i):
|
||||
return a + i * dx
|
||||
|
||||
for i in range(n):
|
||||
y = y + (dx / 2) * (self.F(x(i), y) + self.F(x(i + 1), (y + (dx * self.F(x(i), y)))))
|
||||
|
||||
return y
|
||||
|
||||
def adams(self, a: float, y: float, b: float, n: int = None
|
||||
) -> float:
|
||||
|
||||
if n is None:
|
||||
n = 10 ** 6
|
||||
|
||||
dx = (b - a) / n
|
||||
|
||||
def x(i):
|
||||
return a + i * dx
|
||||
|
||||
for i in range(n):
|
||||
f0 = self.F(x(i), y)
|
||||
f1 = self.F(x(i + 1), y + dx * self.F(x(i) + (dx / 2), y + (dx / 2) * self.F(x(i), y)))
|
||||
f2 = self.F(x(i + 2), y + (dx / 2) * (3 * f1 - f0))
|
||||
|
||||
y += (dx / 12) * (5 * f2 + 8 * f1 - f0)
|
||||
|
||||
return y
|
||||
1
yoshi_otter/algebra/edo/__init__.py
Normal file
1
yoshi_otter/algebra/edo/__init__.py
Normal file
@@ -0,0 +1 @@
|
||||
from .__edo import Edo
|
||||
0
yoshi_otter/algebra/integral/__init__.py
Normal file
0
yoshi_otter/algebra/integral/__init__.py
Normal file
Some files were not shown because too many files have changed in this diff Show More
Reference in New Issue
Block a user