Coverage for sympy/matrices/densetools.py : 92%

""" 

Fundamental operations of dense matrices. 

The dense matrix is stored as a list of lists 

""" 

from sympy.core.compatibility import range 

def trace(matlist, K): 

    """ 

    Returns the trace of a matrix. 

    Examples 

    ======== 

    >>> from sympy.matrices.densetools import trace, eye 

    >>> from sympy import ZZ 

    >>> a = [ 

    ... [ZZ(3), ZZ(7), ZZ(4)], 

    ... [ZZ(2), ZZ(4), ZZ(5)], 

    ... [ZZ(6), ZZ(2), ZZ(3)]] 

    >>> b = eye(4, ZZ) 

    >>> trace(a, ZZ) 

    10 

    >>> trace(b, ZZ) 

    4 

    """ 

    result = K.zero 

    for i in range(len(matlist)): 

        result += matlist[i][i] 

    return result 

def transpose(matlist, K): 

    """ 

    Returns the transpose of a matrix 

    Examples 

    ======== 

    >>> from sympy.matrices.densetools import transpose 

    >>> from sympy import ZZ 

    >>> a = [ 

    ... [ZZ(3), ZZ(7), ZZ(4)], 

    ... [ZZ(2), ZZ(4), ZZ(5)], 

    ... [ZZ(6), ZZ(2), ZZ(3)]] 

    >>> transpose(a, ZZ) 

    [[3, 2, 6], [7, 4, 2], [4, 5, 3]] 

    """ 

    return [list(a) for a in (zip(*matlist))] 

def conjugate(matlist, K): 

    """ 

    Returns the conjugate of a matrix row-wise. 

    Examples 

    ======== 

    >>> from sympy.matrices.densetools import conjugate 

    >>> from sympy import ZZ 

    >>> a = [ 

    ... [ZZ(3), ZZ(2), ZZ(6)], 

    ... [ZZ(7), ZZ(4), ZZ(2)], 

    ... [ZZ(4), ZZ(5), ZZ(3)]] 

    >>> conjugate(a, ZZ) 

    [[3, 2, 6], [7, 4, 2], [4, 5, 3]] 

    See Also 

    ======== 

    conjugate_row 

    """ 

    return [conjugate_row(row, K) for row in matlist] 

def conjugate_row(row, K): 

    """ 

    Returns the conjugate of a row element-wise 

    Examples 

    ======== 

    >>> from sympy.matrices.densetools import conjugate_row 

    >>> from sympy import ZZ 

    >>> a = [ZZ(3), ZZ(2), ZZ(6)] 

    >>> conjugate_row(a, ZZ) 

    [3, 2, 6] 

    """ 

    result = [] 

    for r in row: 

        try: 

            result.append(r.conjugate()) 

        except AttributeError: 

            result.append(r) 

    return result 

def conjugate_transpose(matlist, K): 

    """ 

    Returns the conjugate-transpose of a matrix 

    Examples 

    ======== 

    >>> from sympy import ZZ 

    >>> from sympy.matrices.densetools import conjugate_transpose 

    >>> a = [ 

    ... [ZZ(3), ZZ(7), ZZ(4)], 

    ... [ZZ(2), ZZ(4), ZZ(5)], 

    ... [ZZ(6), ZZ(2), ZZ(3)]] 

    >>> conjugate_transpose(a, ZZ) 

    [[3, 2, 6], [7, 4, 2], [4, 5, 3]] 

    """ 

    return conjugate(transpose(matlist, K), K) 

def augment(matlist, column, K): 

    """ 

    Augments a matrix and a column. 

    Examples 

    ======== 

    >>> from sympy.matrices.densetools import augment 

    >>> from sympy import ZZ 

    >>> a = [ 

    ... [ZZ(3), ZZ(7), ZZ(4)], 

    ... [ZZ(2), ZZ(4), ZZ(5)], 

    ... [ZZ(6), ZZ(2), ZZ(3)]] 

    >>> b = [ 

    ... [ZZ(4)], 

    ... [ZZ(5)], 

    ... [ZZ(6)]] 

    >>> augment(a, b, ZZ) 

    [[3, 7, 4, 4], [2, 4, 5, 5], [6, 2, 3, 6]] 

    """ 

    return [row + element for row, element in zip(matlist, column)] 

def eye(n, K): 

    """ 

    Returns an identity matrix of size n. 

    Examples 

    ======== 

    >>> from sympy.matrices.densetools import eye 

    >>> from sympy import ZZ 

    >>> eye(3, ZZ) 

    [[1, 0, 0], [0, 1, 0], [0, 0, 1]] 

    """ 

    result = [] 

    for i in range(n): 

        result.append([]) 

        for j in range(n): 

            if (i == j): 

                result[i].append(K(1)) 

            else: 

                result[i].append(K.zero) 

    return result 

def row(matlist, i): 

    """ 

    Returns the ith row of a matrix 

    Examples 

    ======== 

    >>> from sympy.matrices.densetools import row 

    >>> from sympy import ZZ 

    >>> a = [ 

    ... [ZZ(3), ZZ(7), ZZ(4)], 

    ... [ZZ(2), ZZ(4), ZZ(5)], 

    ... [ZZ(6), ZZ(2), ZZ(3)]] 

    >>> row(a, 2) 

    [6, 2, 3] 

    """ 

    return matlist[i] 

def col(matlist, i): 

    """ 

    Returns the ith column of a matrix 

    Note: Currently very expensive 

    Examples 

    ======== 

    >>> from sympy.matrices.densetools import col 

    >>> from sympy import ZZ 

    >>> a = [ 

    ... [ZZ(3), ZZ(7), ZZ(4)], 

    ... [ZZ(2), ZZ(4), ZZ(5)], 

    ... [ZZ(6), ZZ(2), ZZ(3)]] 

    >>> col(a, 1) 

    [[7], [4], [2]] 

    """ 

    matcol = [list(l) for l in zip(*matlist)] 

    return [[l] for l in matcol[i]] 

def rowswap(matlist, index1, index2, K): 

    """ 

    Returns the matrix with index1 row and index2 row swapped 

    """ 

    matlist[index1], matlist[index2] = matlist[index2], matlist[index1] 

    return matlist 

def rowmul(matlist, index, k,  K): 

    """ 

    Multiplies index row with k 

    """ 

    for i in range(len(matlist[index])): 

        matlist[index][i] = k*matlist[index][i] 

    return matlist 

def rowadd(matlist, index1, index2 , k, K): 

    """ 

    Adds the index1 row with index2 row which in turn is multiplied by k 

    """ 

    result = [] 

    for i in range(len(matlist[index1])): 

        matlist[index1][i] = (matlist[index1][i] + k*matlist[index2][i]) 

    return matlist 

def isHermitian(matlist, K): 

    """ 

    Checks whether matrix is hermitian 

    Examples 

    ======== 

    >>> from sympy.matrices.densetools import isHermitian 

    >>> from sympy import QQ 

    >>> a = [ 

    ... [QQ(2,1), QQ(-1,1), QQ(-1,1)], 

    ... [QQ(0,1), QQ(4,1), QQ(-1,1)], 

    ... [QQ(0,1), QQ(0,1), QQ(3,1)]] 

    >>> isHermitian(a, QQ) 

    False 

    """ 

    return conjugate_transpose(matlist, K) == matlist