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# 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

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# 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

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# 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`

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# 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

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# 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

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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'
],
)

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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

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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

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numpy
pandas
yoshi-seals

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Otter