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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,interval):
a = interval[0]
b = interval[1]
n = interval[2]
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, interval):
def x(i):
return a + i*h
a = interval[0]
b = interval[1]
n = interval[2]
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,x_interval,y_interval):
a = x_interval[0]
b = x_interval[1]
n = x_interval[2]
c = y_interval[0]
d = y_interval[1]
m = y_interval[2]
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,x_interval,y_interval):
a = x_interval[0]
b = x_interval[1]
n = x_interval[2]
c = y_interval[0]
d = y_interval[1]
m = y_interval[2]
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, interval):
""" 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. """
a = interval[0]
b = interval[1]
e = interval[2]
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, interval):
a = interval[0]
e = interval[1]
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, interval):
a = interval[0]
b = interval[1]
e = interval[2]
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, interval):
a = interval[0]
b = interval[1]
y = interval[2]
n = int(interval[3])
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, interval):
a = interval[0]
b = interval[1]
y = interval[2]
n = int(interval[3])
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)
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
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

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from .Otter import Algebra
from .Otter import Interpolation

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README.md Normal file
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# Numeric Calculus
This is a Repository of Python Packages for Numeric Calculus. It contains two packages: Seals and Otter.
## Seals
The package Seals is made for Linear Algebra. It's able to:
* Scan *csv* files to make a numpy matrix.
* Write a matrix into a *csv* file
* Insert user input into a matrix or a vector.
* Use methods to proccess the matrices.
* Identity Matrix
* Gauss Elimination
* Inverse Matrix
* Cholesky Decomposition
* LU Decomposition
* Cramer
### Syntax
The function *scan* has the following syntax `scan(path)`, where `path` is the path to your directory.
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.
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*.
### Processes
The python class *process* has all the methods described in the first session.
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)`.
* 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.
* 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.
* 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.
* 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.
* 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.
## Installation
To install the package from source `cd` into the directory and run:
`pip install .`
or run
`pip install Numeric-Calculus_HideyoshiNakazone`

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setup.py Normal file
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import setuptools
with open("README.md", "r") as fh:
long_description = fh.read()
setuptools.setup(
name="Otter", # Replace with your own username
version="1.0",
author="Vitor Hideyoshi",
author_email="vitor.h.n.batista@gmail.com",
description="Algebra Functions Python Module for Numeric Calculus",
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',
],
)