diff --git a/linear_algebra_python/README.md b/linear_algebra_python/README.md index ebfcdab7b..1e34d0bd7 100644 --- a/linear_algebra_python/README.md +++ b/linear_algebra_python/README.md @@ -13,9 +13,9 @@ This module contains some useful classes and functions for dealing with linear a - constructor(components : list) : init the vector - set(components : list) : changes the vector components. - - __str__() : toString method + - \_\_str\_\_() : toString method - component(i : int): gets the i-th component (start by 0) - - size() : gets the size of the vector (number of components) + - \_\_len\_\_() : gets the size / length of the vector (number of components) - euclidLength() : returns the eulidean length of the vector. - operator + : vector addition - operator - : vector subtraction @@ -31,12 +31,13 @@ This module contains some useful classes and functions for dealing with linear a - computes the axpy operation - function randomVector(N,a,b) - returns a random vector of size N, with random integer components between 'a' and 'b'. + - class Matrix - This class represents a matrix of arbitrary size and operations on it. **Overview about the methods:** - - __str__() : returns a string representation + - \_\_str\_\_() : returns a string representation - operator * : implements the matrix vector multiplication implements the matrix-scalar multiplication. - changeComponent(x,y,value) : changes the specified component. @@ -45,6 +46,7 @@ This module contains some useful classes and functions for dealing with linear a - 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 - function randomMatrix(W,H,a,b) diff --git a/linear_algebra_python/src/lib.py b/linear_algebra_python/src/lib.py index 66f27ff89..281991a93 100644 --- a/linear_algebra_python/src/lib.py +++ b/linear_algebra_python/src/lib.py @@ -36,7 +36,7 @@ class Vector(object): 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) + __len__() : gets the size of the vector (number of components) euclidLength() : returns the eulidean length of the vector. operator + : vector addition operator - : vector subtraction @@ -45,12 +45,12 @@ class Vector(object): changeComponent(pos,value) : changes the specified component. TODO: compare-operator """ - def __init__(self,components): + def __init__(self,components=[]): """ input: components or nothing simple constructor for init the vector """ - self.__components = components + self.__components = list(components) def set(self,components): """ input: new components @@ -58,33 +58,24 @@ class Vector(object): replace the components with newer one. """ if len(components) > 0: - self.__components = components + self.__components = list(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 + return "(" + ",".join(map(str, self.__components)) + ")" 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: + if type(i) is int and -len(self.__components) <= i < len(self.__components) : return self.__components[i] else: raise Exception("index out of range") - def size(self): + def __len__(self): """ returns the size of the vector """ @@ -103,52 +94,45 @@ class Vector(object): 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)) + size = len(self) + if size == len(other): + result = [self.__components[i] + other.component(i) for i in range(size)] + return Vector(result) 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)) + size = len(self) + if size == len(other): + result = [self.__components[i] - other.component(i) for i in range(size)] + return result 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() + ans = [c*other for c in self.__components] + return ans + elif (isinstance(other,Vector) and (len(self) == len(other))): + size = len(self) 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) + return Vector(self.__components) def changeComponent(self,pos,value): """ input: an index (pos) and a value @@ -156,7 +140,7 @@ class Vector(object): 'value' """ #precondition - assert (pos >= 0 and pos < len(self.__components)) + assert (-len(self.__components) <= pos < len(self.__components)) self.__components[pos] = value def zeroVector(dimension): @@ -165,10 +149,7 @@ def zeroVector(dimension): """ #precondition assert(isinstance(dimension,int)) - ans = [] - for i in range(dimension): - ans.append(0) - return Vector(ans) + return Vector([0]*dimension) def unitBasisVector(dimension,pos): @@ -178,12 +159,8 @@ def unitBasisVector(dimension,pos): """ #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) + ans = [0]*dimension + ans[pos] = 1 return Vector(ans) @@ -206,11 +183,9 @@ def randomVector(N,a,b): output: returns a random vector of size N, with random integer components between 'a' and 'b'. """ - ans = zeroVector(N) random.seed(None) - for i in range(N): - ans.changeComponent(i,random.randint(a,b)) - return ans + ans = [random.randint(a,b) for i in range(N)] + return Vector(ans) class Matrix(object): @@ -220,7 +195,7 @@ class Matrix(object): Overview about the methods: - __str__() : returns a string representation + __str__() : returns a string representation operator * : implements the matrix vector multiplication implements the matrix-scalar multiplication. changeComponent(x,y,value) : changes the specified component. @@ -284,7 +259,7 @@ class Matrix(object): implements the matrix-scalar multiplication """ if isinstance(other, Vector): # vector-matrix - if (other.size() == self.__width): + if (len(other) == self.__width): ans = zeroVector(self.__height) for i in range(self.__height): summe = 0 @@ -294,15 +269,9 @@ class Matrix(object): summe = 0 return ans else: - raise Exception("vector must have the same size as the " - + "number of columns of the matrix!") + 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) + matrix = [[self.__matrix[i][j] * other for j in range(self.__width)] for i in range(self.__height)] return Matrix(matrix,self.__width,self.__height) def __add__(self,other): """ @@ -338,12 +307,7 @@ 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) + ans = [[0]*N for i in range(N)] return Matrix(ans,N,N) @@ -352,13 +316,8 @@ def randomMatrix(W,H,a,b): returns a random matrix WxH with integer components between 'a' and 'b' """ - matrix = [] random.seed(None) - for i in range(H): - row = [] - for j in range(W): - row.append(random.randint(a,b)) - matrix.append(row) + matrix = [[random.randint(a,b) for j in range(W)] for i in range(H)] return Matrix(matrix,W,H) - \ No newline at end of file + diff --git a/linear_algebra_python/src/tests.py b/linear_algebra_python/src/tests.py index b84612b4c..a26eb9265 100644 --- a/linear_algebra_python/src/tests.py +++ b/linear_algebra_python/src/tests.py @@ -29,13 +29,13 @@ class Test(unittest.TestCase): test for toString() method """ x = Vector([0,0,0,0,0,1]) - self.assertEqual(x.__str__(),"(0,0,0,0,0,1)") + self.assertEqual(str(x),"(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) + self.assertEqual(len(x),4) def test_euclidLength(self): """ test for the eulidean length @@ -67,32 +67,32 @@ class Test(unittest.TestCase): 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(str(x*3.0),"(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) + self.assertTrue(str(zeroVector(10)).count("0") == 10) def test_unitBasisVector(self): """ test for the global function unitBasisVector(...) """ - self.assertEqual(unitBasisVector(3,1).__str__(),"(0,1,0)") + self.assertEqual(str(unitBasisVector(3,1)),"(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)") + self.assertEqual(str(axpy(2,x,y)),"(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__()) + self.assertEqual(str(x),str(y)) def test_changeComponent(self): """ test for the changeComponent(...)-method @@ -100,34 +100,34 @@ class Test(unittest.TestCase): x = Vector([1,0,0]) x.changeComponent(0,0) x.changeComponent(1,1) - self.assertEqual(x.__str__(),"(0,1,0)") + self.assertEqual(str(x),"(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__()) + self.assertEqual("|1,2,3|\n|2,4,5|\n|6,7,8|\n",str(A)) 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__()) + self.assertEqual("(14,32,50)",str(A*x)) + self.assertEqual("|2,4,6|\n|8,10,12|\n|14,16,18|\n",str(A*2)) 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__()) + self.assertEqual("|1,2,5|\n|2,4,5|\n|6,7,8|\n",str(A)) 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__()) + self.assertEqual("|2,4,10|\n|4,8,10|\n|12,14,18|\n",str(A+B)) 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__()) + self.assertEqual("|0,0,-4|\n|0,0,0|\n|0,0,-2|\n",str(A-B)) 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__()) + +'\n|0,0,0,0,0|\n',str(squareZeroMatrix(5))) if __name__ == "__main__": - unittest.main() \ No newline at end of file + unittest.main()