commit bb2b938156a9e67c62e6de32aa3165abec1d5a33 Author: Hideyoshi Date: Sat May 16 01:25:49 2020 -0300 v1.0 diff --git a/LICENSE b/LICENSE new file mode 100644 index 0000000..ecbc059 --- /dev/null +++ b/LICENSE @@ -0,0 +1,339 @@ + 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. 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If this is what you want to do, use the GNU Lesser General +Public License instead of this License. \ No newline at end of file diff --git a/Otter/Otter.py b/Otter/Otter.py new file mode 100755 index 0000000..acbb30f --- /dev/null +++ b/Otter/Otter.py @@ -0,0 +1,493 @@ +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 \ No newline at end of file diff --git a/Otter/__init__.py b/Otter/__init__.py new file mode 100644 index 0000000..80edee6 --- /dev/null +++ b/Otter/__init__.py @@ -0,0 +1,2 @@ +from .Otter import Algebra +from .Otter import Interpolation \ No newline at end of file diff --git a/README.md b/README.md new file mode 100644 index 0000000..808a0d7 --- /dev/null +++ b/README.md @@ -0,0 +1,57 @@ +# 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` \ No newline at end of file diff --git a/setup.py b/setup.py new file mode 100644 index 0000000..bedab02 --- /dev/null +++ b/setup.py @@ -0,0 +1,27 @@ +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', + ], +) \ No newline at end of file