HideyoshiNakazone/Otter-NumericCalculus
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This commit is contained in:
Vitor Hideyoshi
2020-05-16 15:38:24 -03:00
committed by Vitor Hideyoshi
parent bb2b938156
commit e444e2e7ed
13 changed files with 730 additions and 137 deletions
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191
Otter/Otter.py
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@@ -26,11 +26,10 @@ class Algebra:
def __init__(self, function): def __init__(self, function):
self.f = function self.f = function
def riemann(self,interval): def riemann(self,a,b,n=None):
a = interval[0] if n is None:
b = interval[1] n = 10**6
n = interval[2]
delta = (b-a)/n delta = (b-a)/n
@@ -46,15 +45,14 @@ class Algebra:
return integral return integral
def simpson(self, interval): def simpson(self,a,b,n=None):
if n is None:
n = 10**6
def x(i): def x(i):
return a + i*h return a + i*h
a = interval[0]
b = interval[1]
n = interval[2]
h = (b-a)/n h = (b-a)/n
eta = 0 eta = 0
@@ -81,15 +79,13 @@ class Algebra:
def __init__(self,function): def __init__(self,function):
self.f = function self.f = function
def riemann(self,x_interval,y_interval): def riemann(self,a,b,c,d,n=None,m=None):
if n is None:
n = 10**4
a = x_interval[0] if m is None:
b = x_interval[1] m = n
n = x_interval[2]
c = y_interval[0]
d = y_interval[1]
m = y_interval[2]
dx = (b-a)/n dx = (b-a)/n
dy = (d-c)/m dy = (d-c)/m
@@ -109,15 +105,13 @@ class Algebra:
return theta*(dx)*(dy) return theta*(dx)*(dy)
def simpson(self,x_interval,y_interval): def simpson(self,a,b,c,d,n=None,m=None):
if n is None:
n = 10**4
a = x_interval[0] if m is None:
b = x_interval[1] m = n
n = x_interval[2]
c = y_interval[0]
d = y_interval[1]
m = y_interval[2]
dx = (b-a)/n dx = (b-a)/n
dy = (d-c)/m dy = (d-c)/m
@@ -178,12 +172,10 @@ class Algebra:
if function is not None: if function is not None:
self.f = function self.f = function
def bissec(self, interval): def bissec(self,a,b,e=None):
""" invertal = [a,b,e] ; with 'a' being the first value of the interval, 'b' the last value of the interval and 'e' the precision of the procedure. """
if e is None:
a = interval[0] e = 10**(-6)
b = interval[1]
e = interval[2]
fa = self.f(a) fa = self.f(a)
@@ -208,10 +200,10 @@ class Algebra:
def d(self, x, e): def d(self, x, e):
return (self.f(x + e) - self.f(x - e))/(2*e) return (self.f(x + e) - self.f(x - e))/(2*e)
def newton(self, interval): def newton(self,a,e=None):
a = interval[0] if e is None:
e = interval[1] e = 10**(-6)
fa = self.f(a) fa = self.f(a)
da = self.d(a,e) da = self.d(a,e)
@@ -227,11 +219,10 @@ class Algebra:
return a return a
def bissec_newton(self, interval): def bissec_newton(self,a,b,e=None):
a = interval[0] if e is None:
b = interval[1] e = 10**(-6)
e = interval[2]
fa = self.f(a) fa = self.f(a)
@@ -271,12 +262,10 @@ class Algebra:
def __init__(self, function): def __init__(self, function):
self.f = function self.f = function
def euler(self, interval): def euler(self,a,y,b,n=None):
a = interval[0] if n is None:
b = interval[1] n = 10**7
y = interval[2]
n = int(interval[3])
dx = (b-a)/n dx = (b-a)/n
@@ -289,12 +278,10 @@ class Algebra:
return y return y
def runge(self, interval): def runge(self,a,y,b,n=None):
a = interval[0] if n is None:
b = interval[1] n = 10**7
y = interval[2]
n = int(interval[3])
dx = (b-a)/n dx = (b-a)/n
@@ -315,6 +302,59 @@ class Interpolation:
self.data = data self.data = data
self.polinomial = self.Polinomial(self.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: class Polinomial:
def __init__(self, data): def __init__(self, data):
@@ -437,57 +477,4 @@ class Interpolation:
y += d[i+1][0]*mult y += d[i+1][0]*mult
i += 1 i += 1
return y return y
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

4
Otter/__init__.py
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@@ -1,2 +1,2 @@
from .Otter import Algebra from .Otter import Algebra as algebra
from .Otter import Interpolation from .Otter import Interpolation as interpolation

78
README.md
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@@ -1,50 +1,68 @@
# Numeric Calculus # Otter - Numeric Calculus
This is a Repository of Python Packages for Numeric Calculus. It contains two packages: Seals and Otter. This python package is made for applied Numeric Calculus of Algebra Functions. It is made with the following objectives in mind:
## Seals * Receive one variable function from user input
* Receive two variable function from user input
The package Seals is made for Linear Algebra. It's able to: * Performe derivatives with one variable functions
* Scan *csv* files to make a numpy matrix. * Performe integral with received functions
* Write a matrix into a *csv* file
* Insert user input into a matrix or a vector.
* Use methods to proccess the matrices. * Use methods to proccess the matrices.
* Identity Matrix
* Gauss Elimination
* Inverse Matrix
* Cholesky Decomposition
* LU Decomposition
* Cramer
### Syntax * Find root of functions throw method of bissection and method of newton
The function *scan* has the following syntax `scan(path)`, where `path` is the path to your directory. * Solve Diferential Equations throw method of euler and runge
The function *solution* has the following syntax `write(array,path)`, where `array` is the matrix that you desire to output and `path` is the path to your directory. * Performe Minimus Interpolation and Polinomial Interpolation
The python class *Insert* has a method for *matrix* and another for *vector*, and it has the following syntax `Insert.method(array)`, where `Insert` is the *Python Class* and `method` is either a `matrix` or a `vector` and `array` is either a *matrix* or a *vector*. ## Syntax
### Processes 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*.
The python class *process* has all the methods described in the first session. 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`.
To call the method use a syntax like `sl = Seals.process()`, where `sl` is an instance and to use a method you have to append the method in front of the instance like: `sl.identity(array)`. ### Algebra
* The method *identity* returns a *numpy* identity matrix of the order of the matrix passed into to it, and it has the following syntax `sl.identity(array)`, which `array` is a square matrix. Algebra is a Python Class where some of the features described previously are defined as Classes as well, like: `Integral`, `Roots`, `EDO` (diferential equations).
* The method *gauss* returns a *numpy* vector containing the vector of variables from the augmented matrix. `sl.gauss(matrix)`, which `matrix` is the augmented matrix. #### Integral
* The method *inverse* returns a *numpy* inverse matrix of the matrix passed into to it, and it has the following syntax `sl.inverse(matrix)`, which `matrix` is a square matrix. 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.
* The method *cholesky* returns a *numpy* vector containing the vector of variables from the coefficient matrix and the constants vector, and it has the following syntax `sl.cholesky(A,b)`, which `A` is the coefficient matrix and `b` is the constants vector. 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 method *decomposition* returns a *numpy* vector containing the vector of variables from the coefficient matrix and the constants vector, and it has the following syntax `sl.cholesky(A,b)`, which `A` is the coefficient matrix and `b` is the constants vector.
* The method *cramer* returns a *numpy* vector containing the vector of variables from the coefficient matrix and the constants vector, and it has the following syntax `sl.cholesky(A,b)`, which `A` is the coefficient matrix and `b` is the constants vector. 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 ## Installation
@@ -54,4 +72,4 @@ To install the package from source `cd` into the directory and run:
or run or run
`pip install Numeric-Calculus_HideyoshiNakazone` `pip install yoshi-otter`

480
build/lib/Otter/Otter.py Normal file
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@@ -0,0 +1,480 @@
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

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build/lib/Otter/__init__.py Normal file
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from .Otter import Algebra as algebra
from .Otter import Interpolation as interpolation

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setup.py
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@@ -4,11 +4,11 @@ with open("README.md", "r") as fh:
long_description = fh.read() long_description = fh.read()
setuptools.setup( setuptools.setup(
name="Otter", # Replace with your own username name="yoshi-otter", # Replace with your own username
version="1.0", version="1.1",
author="Vitor Hideyoshi", author="Vitor Hideyoshi",
author_email="vitor.h.n.batista@gmail.com", author_email="vitor.h.n.batista@gmail.com",
description="Algebra Functions Python Module for Numeric Calculus", 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", long_description_content_type="text/markdown",
url="https://github.com/HideyoshiNakazone/Otter-NumericCalculus.git", url="https://github.com/HideyoshiNakazone/Otter-NumericCalculus.git",
@@ -23,5 +23,6 @@ setuptools.setup(
install_requires=[ install_requires=[
'numpy', 'numpy',
'pandas', 'pandas',
'yoshi-seals'
], ],
) )

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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

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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