Merge pull request #260 from christianbender/added_linearAlgebra

Added a linear algebra library

linear-algebra-python/README.md

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+# Linear algebra library for Python  
+
+This module contains some useful classes and functions for dealing with linear algebra in python 2.  
+
+---
+
+## Overview  
+
+- class Vector  
+    - This class represents a vector of arbitray size and operations on it.  
+
+    **Overview about the methods:**    
+        
+    - constructor(components : list) : init the vector  
+    - set(components : list) : changes the vector components.  
+    - __str__() : toString method  
+    - component(i : int): gets the i-th component (start by 0)  
+    - size() : gets the size of the vector (number of components)  
+    - euclidLength() : returns the eulidean length of the vector.  
+    - operator + : vector addition  
+    - operator - : vector subtraction  
+    - operator * : scalar multiplication and dot product  
+    - copy() : copies this vector and returns it.  
+    - changeComponent(pos,value) : changes the specified component.  
+
+- function zeroVector(dimension)  
+    - returns a zero vector of 'dimension'  
+- function unitBasisVector(dimension,pos)  
+    - returns a unit basis vector with a One at index 'pos' (indexing at 0)  
+- function axpy(scalar,vector1,vector2)  
+    - computes the axpy operation  
+- class Matrix
+    - This class represents a matrix of arbitrary size and operations on it.
+
+    **Overview about the methods:**  
+    
+    -  __str__() : returns a string representation  
+    - operator * : implements the matrix vector multiplication  
+                   implements the matrix-scalar multiplication.  
+    - changeComponent(x,y,value) : changes the specified component.  
+    - component(x,y) : returns the specified component.  
+    - width() : returns the width of the matrix  
+    - height() : returns the height of the matrix  
+    - operator + : implements the matrix-addition.  
+    - operator - _ implements the matrix-subtraction  
+- function squareZeroMatrix(N)  
+    - returns a square zero-matrix of dimension NxN  
+---
+
+## Documentation  
+
+The module is well documented. You can use the python in-built ```help(...)``` function.  
+For instance: ```help(Vector)``` gives you all information about the Vector-class.  
+Or ```help(unitBasisVector)``` gives you all information you needed about the  
+global function ```unitBasisVector(...)```. If you need informations about a certain  
+method you type ```help(CLASSNAME.METHODNAME)```.  
+
+---
+
+## Usage  
+
+You will find the module in the **src** directory its called ```lib.py```. You need to  
+import this module in your project. Alternative you can also use the file ```lib.pyc``` in python-bytecode.   
+
+---
+
+## Tests  
+
+In the **src** directory you also find the test-suite, its called ```tests.py```.  
+The test-suite uses the built-in python-test-framework **unittest**.  

linear-algebra-python/src/lib.py

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+# -*- coding: utf-8 -*-
+"""
+Created on Mon Feb 26 14:29:11 2018
+
+@author: Christian Bender
+@license: MIT-license
+
+This module contains some useful classes and functions for dealing
+with linear algebra in python.
+
+Overview:
+
+- class Vector
+- function zeroVector(dimension)
+- function unitBasisVector(dimension,pos)
+- function axpy(scalar,vector1,vector2)
+- class Matrix
+- squareZeroMatrix(N)
+"""
+
+
+import math
+
+
+class Vector(object):
+    """
+        This class represents a vector of arbitray size.
+        You need to give the vector components. 
+        
+        Overview about the methods:
+        
+        constructor(components : list) : init the vector
+        set(components : list) : changes the vector components.
+        __str__() : toString method
+        component(i : int): gets the i-th component (start by 0)
+        size() : gets the size of the vector (number of components)
+        euclidLength() : returns the eulidean length of the vector.
+        operator + : vector addition
+        operator - : vector subtraction
+        operator * : scalar multiplication and dot product
+        copy() : copies this vector and returns it.
+        changeComponent(pos,value) : changes the specified component.
+        TODO: compare-operator
+    """
+    def __init__(self,components):
+        """
+            input: components or nothing
+            simple constructor for init the vector
+        """
+        self.__components = components
+    def set(self,components):
+        """
+            input: new components
+            changes the components of the vector.
+            replace the components with newer one.
+        """
+        if len(components) > 0:
+            self.__components = components
+        else:
+            raise Exception("please give any vector")
+    def __str__(self):
+        """
+            returns a string representation of the vector
+        """
+        ans = "("
+        length = len(self.__components)
+        for i in range(length):
+            if i != length-1:
+                ans += str(self.__components[i]) + ","
+            else:
+                ans += str(self.__components[i]) + ")"
+        if len(ans) == 1:
+            ans += ")"
+        return ans
+    def component(self,i):
+        """
+            input: index (start at 0)
+            output: the i-th component of the vector.
+        """
+        if i < len(self.__components) and i >= 0:
+            return self.__components[i]
+        else:
+            raise Exception("index out of range")
+    def size(self):
+        """
+            returns the size of the vector
+        """
+        return len(self.__components)
+    def eulidLength(self):
+        """
+            returns the eulidean length of the vector
+        """
+        summe = 0
+        for c in self.__components:
+            summe += c**2
+        return math.sqrt(summe)
+    def __add__(self,other):
+        """
+            input: other vector
+            assumes: other vector has the same size
+            returns a new vector that represents the sum.
+        """
+        size = self.size()
+        result = []
+        if size == other.size():
+            for i in range(size):
+                result.append(self.__components[i] + other.component(i))
+        else:
+            raise Exception("must have the same size")
+        return Vector(result)
+    def __sub__(self,other):
+        """
+            input: other vector
+            assumes: other vector has the same size
+            returns a new vector that represents the differenz.
+        """
+        size = self.size()
+        result = []
+        if size == other.size():
+            for i in range(size):
+                result.append(self.__components[i] - other.component(i))
+        else: # error case
+            raise Exception("must have the same size")
+        return Vector(result)
+    def __mul__(self,other):
+        """
+            mul implements the scalar multiplication 
+            and the dot-product
+        """
+        ans = []
+        if isinstance(other,float) or isinstance(other,int):
+            for c in self.__components:
+                ans.append(c*other)
+        elif (isinstance(other,Vector) and (self.size() == other.size())):
+            size = self.size()
+            summe = 0
+            for i in range(size):
+                summe += self.__components[i] * other.component(i)
+            return summe
+        else: # error case
+            raise Exception("invalide operand!")
+        return Vector(ans)
+    def copy(self):
+        """
+            copies this vector and returns it.
+        """
+        components = [x for x in self.__components]
+        return Vector(components)
+    def changeComponent(self,pos,value):
+        """
+            input: an index (pos) and a value
+            changes the specified component (pos) with the
+            'value'
+        """
+        #precondition
+        assert (pos >= 0 and pos < len(self.__components))
+        self.__components[pos] = value
+    
+def zeroVector(dimension):
+    """
+        returns a zero-vector of size 'dimension'
+    """        
+    #precondition
+    assert(isinstance(dimension,int))
+    ans = []
+    for i in range(dimension):
+        ans.append(0)
+    return Vector(ans)
+
+
+def unitBasisVector(dimension,pos):
+    """
+        returns a unit basis vector with a One 
+        at index 'pos' (indexing at 0)
+    """
+    #precondition
+    assert(isinstance(dimension,int) and (isinstance(pos,int)))
+    ans = []
+    for i in range(dimension):
+        if i != pos:
+            ans.append(0)
+        else:
+            ans.append(1)
+    return Vector(ans)
+        
+
+def axpy(scalar,x,y):
+    """
+        input: a 'scalar' and two vectors 'x' and 'y'
+        output: a vector
+        computes the axpy operation
+    """
+    # precondition
+    assert(isinstance(x,Vector) and (isinstance(y,Vector)) \
+    and (isinstance(scalar,int) or isinstance(scalar,float)))
+    return (x*scalar + y)
+    
+
+class Matrix(object):
+    """
+    class: Matrix
+    This class represents a arbitrary matrix.
+    
+    Overview about the methods:
+    
+         __str__() : returns a string representation 
+           operator * : implements the matrix vector multiplication
+                        implements the matrix-scalar multiplication.
+           changeComponent(x,y,value) : changes the specified component.
+           component(x,y) : returns the specified component.
+           width() : returns the width of the matrix
+           height() : returns the height of the matrix
+           operator + : implements the matrix-addition.
+           operator - _ implements the matrix-subtraction
+    """
+    def __init__(self,matrix,w,h):
+        """
+            simple constructor for initialzes 
+            the matrix with components.
+        """
+        self.__matrix = matrix
+        self.__width = w
+        self.__height = h
+    def __str__(self):
+        """
+            returns a string representation of this
+            matrix.
+        """
+        ans = ""
+        for i in range(self.__height):
+            ans += "|"
+            for j in range(self.__width):
+                if j < self.__width -1:
+                    ans += str(self.__matrix[i][j]) + ","
+                else:
+                    ans += str(self.__matrix[i][j]) + "|\n"
+        return ans
+    def changeComponent(self,x,y, value):
+        """
+            changes the x-y component of this matrix
+        """
+        if x >= 0 and x < self.__height and y >= 0 and y < self.__width:
+            self.__matrix[x][y] = value
+        else:
+            raise Exception ("changeComponent: indices out of bounds")
+    def component(self,x,y):
+        """
+            returns the specified (x,y) component
+        """
+        if x >= 0 and x < self.__height and y >= 0 and y < self.__width:
+            return self.__matrix[x][y]
+        else:
+            raise Exception ("changeComponent: indices out of bounds")
+    def width(self):
+        """
+            getter for the width
+        """
+        return self.__width
+    def height(self):
+        """
+            getter for the height
+        """
+        return self.__height
+    def __mul__(self,other):
+        """
+            implements the matrix-vector multiplication.
+            implements the matrix-scalar multiplication
+        """
+        if isinstance(other, Vector): # vector-matrix 
+            if (other.size() == self.__width):
+                ans = zeroVector(self.__height)
+                for i in range(self.__height):
+                    summe = 0
+                    for j in range(self.__width):
+                        summe += other.component(j) * self.__matrix[i][j]
+                    ans.changeComponent(i,summe)
+                    summe = 0
+                return ans
+            else:
+                raise Exception("vector must have the same size as the "
+                + "number of columns of the matrix!")
+        elif isinstance(other,int) or isinstance(other,float): # matrix-scalar
+            matrix = []
+            for i in range(self.__height):
+                row = []
+                for j in range(self.__width):
+                    row.append(self.__matrix[i][j] * other)
+                matrix.append(row)
+            return Matrix(matrix,self.__width,self.__height)
+    def __add__(self,other):
+        """
+            implements the matrix-addition.
+        """
+        if (self.__width == other.width() and self.__height == other.height()):
+            matrix = []
+            for i in range(self.__height):
+                row = []
+                for j in range(self.__width):
+                    row.append(self.__matrix[i][j] + other.component(i,j))
+                matrix.append(row)
+            return Matrix(matrix,self.__width,self.__height)
+        else:
+            raise Exception("matrix must have the same dimension!")
+    def __sub__(self,other):
+        """
+            implements the matrix-subtraction.
+        """
+        if (self.__width == other.width() and self.__height == other.height()):
+            matrix = []
+            for i in range(self.__height):
+                row = []
+                for j in range(self.__width):
+                    row.append(self.__matrix[i][j] - other.component(i,j))
+                matrix.append(row)
+            return Matrix(matrix,self.__width,self.__height)
+        else:
+            raise Exception("matrix must have the same dimension!")
+    
+
+def squareZeroMatrix(N):
+    """
+        returns a square zero-matrix of dimension NxN
+    """
+    ans = []
+    for i in range(N):
+        row = []
+        for j in range(N):
+            row.append(0)
+        ans.append(row)
+    return Matrix(ans,N,N)
+            
+        

linear-algebra-python/src/tests.py

@@ -0,0 +1,133 @@
+# -*- coding: utf-8 -*-
+"""
+Created on Mon Feb 26 15:40:07 2018
+
+@author: Christian Bender
+@license: MIT-license
+
+This file contains the test-suite for the linear algebra library.
+"""
+
+import unittest
+from lib import *
+
+class Test(unittest.TestCase):
+    def test_component(self):
+        """
+            test for method component
+        """
+        x = Vector([1,2,3])
+        self.assertEqual(x.component(0),1)
+        self.assertEqual(x.component(2),3)
+        try:
+            y = Vector()
+            self.assertTrue(False)
+        except:
+            self.assertTrue(True)
+    def test_str(self):
+        """
+            test for toString() method
+        """
+        x = Vector([0,0,0,0,0,1])
+        self.assertEqual(x.__str__(),"(0,0,0,0,0,1)")
+    def test_size(self):
+        """
+            test for size()-method
+        """
+        x = Vector([1,2,3,4])
+        self.assertEqual(x.size(),4)
+    def test_euclidLength(self):
+        """
+            test for the eulidean length
+        """
+        x = Vector([1,2])
+        self.assertAlmostEqual(x.eulidLength(),2.236,3)
+    def test_add(self):
+        """
+            test for + operator
+        """
+        x = Vector([1,2,3])
+        y = Vector([1,1,1])
+        self.assertEqual((x+y).component(0),2)
+        self.assertEqual((x+y).component(1),3)
+        self.assertEqual((x+y).component(2),4)
+    def test_sub(self):
+        """
+            test for - operator
+        """
+        x = Vector([1,2,3])
+        y = Vector([1,1,1])
+        self.assertEqual((x-y).component(0),0)
+        self.assertEqual((x-y).component(1),1)
+        self.assertEqual((x-y).component(2),2)
+    def test_mul(self):
+        """
+            test for * operator
+        """
+        x = Vector([1,2,3])
+        a = Vector([2,-1,4]) # for test of dot-product
+        b = Vector([1,-2,-1])
+        self.assertEqual((x*3.0).__str__(),"(3.0,6.0,9.0)")
+        self.assertEqual((a*b),0)
+    def test_zeroVector(self):
+        """
+            test for the global function zeroVector(...)
+        """
+        self.assertTrue(zeroVector(10).__str__().count("0") == 10)
+    def test_unitBasisVector(self):
+        """
+            test for the global function unitBasisVector(...)
+        """
+        self.assertEqual(unitBasisVector(3,1).__str__(),"(0,1,0)")
+    def test_axpy(self):
+        """
+            test for the global function axpy(...) (operation)
+        """
+        x = Vector([1,2,3])
+        y = Vector([1,0,1])
+        self.assertEqual(axpy(2,x,y).__str__(),"(3,4,7)")
+    def test_copy(self):
+        """
+            test for the copy()-method
+        """
+        x = Vector([1,0,0,0,0,0])
+        y = x.copy()
+        self.assertEqual(x.__str__(),y.__str__())
+    def test_changeComponent(self):
+        """
+            test for the changeComponent(...)-method
+        """
+        x = Vector([1,0,0])
+        x.changeComponent(0,0)
+        x.changeComponent(1,1)
+        self.assertEqual(x.__str__(),"(0,1,0)")
+    def test_str_matrix(self):
+        A = Matrix([[1,2,3],[2,4,5],[6,7,8]],3,3)
+        self.assertEqual("|1,2,3|\n|2,4,5|\n|6,7,8|\n",A.__str__())
+    def test__mul__matrix(self):
+        A = Matrix([[1,2,3],[4,5,6],[7,8,9]],3,3)
+        x = Vector([1,2,3])
+        self.assertEqual("(14,32,50)",(A*x).__str__())
+        self.assertEqual("|2,4,6|\n|8,10,12|\n|14,16,18|\n",(A*2).__str__())
+    def test_changeComponent_matrix(self):
+        A = Matrix([[1,2,3],[2,4,5],[6,7,8]],3,3)
+        A.changeComponent(0,2,5)
+        self.assertEqual("|1,2,5|\n|2,4,5|\n|6,7,8|\n",A.__str__())
+    def test_component_matrix(self):
+        A = Matrix([[1,2,3],[2,4,5],[6,7,8]],3,3)
+        self.assertEqual(7,A.component(2,1),0.01)
+    def test__add__matrix(self):
+        A = Matrix([[1,2,3],[2,4,5],[6,7,8]],3,3)
+        B = Matrix([[1,2,7],[2,4,5],[6,7,10]],3,3)
+        self.assertEqual("|2,4,10|\n|4,8,10|\n|12,14,18|\n",(A+B).__str__())
+    def test__sub__matrix(self):
+        A = Matrix([[1,2,3],[2,4,5],[6,7,8]],3,3)
+        B = Matrix([[1,2,7],[2,4,5],[6,7,10]],3,3)
+        self.assertEqual("|0,0,-4|\n|0,0,0|\n|0,0,-2|\n",(A-B).__str__())
+    def test_squareZeroMatrix(self):
+        self.assertEqual('|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|' 
+        +'\n|0,0,0,0,0|\n',squareZeroMatrix(5).__str__())
+        
+
+if __name__ == "__main__":
+    unittest.main()