You can run the file 'tests.py' to see examples of use of this module 'matrix.py'.
Testing every doctests in the module 'matrix'...
Trying:
    from matrix import *
Expecting nothing
ok
Trying:
    from matrix import Matrix as M  # shortcut
Expecting nothing
ok
Trying:
    A = M([[1, 0], [0, 1]])
Expecting nothing
ok
Trying:
    A == eye(A.n)
Expecting:
    True
ok
Trying:
    B = 2*(A**2) + 4*A + eye(A.n)
Expecting nothing
ok
Trying:
    B
Expecting:
    [[7, 0], [0, 7]]
ok
Trying:
    B == 7 * eye(A.n)
Expecting:
    True
ok
Trying:
    A[1,:] = 2; A
Expecting:
    [[1, 0], [2, 2]]
ok
Trying:
    A[0, 0] = -5; A
Expecting:
    [[-5, 0], [2, 2]]
ok
Trying:
    C = eye(2); C
Expecting:
    [[1, 0], [0, 1]]
ok
Trying:
    C + (3 * C) - C
Expecting:
    [[3, 0], [0, 3]]
ok
Trying:
    (4 * C) ** 2
Expecting:
    [[16, 0], [0, 16]]
ok
Trying:
    B = Matrix([[1, 4], [2, 5], [3, 6]])
Expecting nothing
ok
Trying:
    B.T
Expecting:
    [[1, 2, 3], [4, 5, 6]]
ok
Trying:
    B == B.T.T
Expecting:
    True
ok
Trying:
    A = Matrix([[1, 2, 3], [4, 5, 6]])
Expecting nothing
ok
Trying:
    A + A
Expecting:
    [[2, 4, 6], [8, 10, 12]]
ok
Trying:
    B = ones(A.n, A.m); B
Expecting:
    [[1, 1, 1], [1, 1, 1]]
ok
Trying:
    A + B
Expecting:
    [[2, 3, 4], [5, 6, 7]]
ok
Trying:
    B + A
Expecting:
    [[2, 3, 4], [5, 6, 7]]
ok
Trying:
    B + B + B + B + B + B + B
Expecting:
    [[7, 7, 7], [7, 7, 7]]
ok
Trying:
    B + 4  # Coefficient wise!
Expecting:
    [[5, 5, 5], [5, 5, 5]]
ok
Trying:
    B + (-2)  # Coefficient wise!
Expecting:
    [[-1, -1, -1], [-1, -1, -1]]
ok
Trying:
    B + (-1.0)  # Coefficient wise!
Expecting:
    [[0.0, 0.0, 0.0], [0.0, 0.0, 0.0]]
ok
Trying:
    4 in Matrix([[1, 2], [3, 4]])
Expecting:
    True
ok
Trying:
    4 in Matrix([[1, 2], [1, 2]])
Expecting:
    False
ok
Trying:
    O, I = zeros(7), eye(7)
Expecting nothing
ok
Trying:
    3 * I**2 + 2 * I + O ** 0
Expecting:
    [[6, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 0, 0], [0, 0, 6, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0], [0, 0, 0, 0, 6, 0, 0], [0, 0, 0, 0, 0, 6, 0], [0, 0, 0, 0, 0, 0, 6]]
ok
Trying:
    6 in (3 * I**2 + 2 * I + O ** 0)
Expecting:
    True
ok
Trying:
    B = Matrix([[1, 4], [2, 5], [3, 6]])
Expecting nothing
ok
Trying:
    B == B
Expecting:
    True
ok
Trying:
    B + B + B == 3*B == B + 2*B == 2*B + B
Expecting:
    True
ok
Trying:
    B - B + B == 1*B == -B + 2*B == 2*B - B == 2*B + (-B)
Expecting:
    True
ok
Trying:
    B != B
Expecting:
    False
ok
Trying:
    A = Matrix([[1, 2], [3, 4]])
Expecting nothing
ok
Trying:
    B = eye(A.n); C = B.map(float)
Expecting nothing
ok
Trying:
    A // C == A * C == A
Expecting:
    True
ok
Trying:
    A // B == A * B == A
Expecting:
    True
ok
Trying:
    A // 2  # Coefficient wise!
Expecting:
    [[0, 1], [1, 2]]
ok
Trying:
    A // 2.0  # Coefficient wise!
Expecting:
    [[0.0, 1.0], [1.0, 2.0]]
ok
Trying:
    A = Matrix([[1, 2, 3], [4, 5, 6]])
Expecting nothing
ok
Trying:
    A[0, 0]
Expecting:
    1
ok
Trying:
    A[0, :]
Expecting:
    [[1, 2, 3]]
ok
Trying:
    A[-1, :]
Expecting:
    [[4, 5, 6]]
ok
Trying:
    A[:, 0]
Expecting:
    [[1], [4]]
ok
Trying:
    A[1:, 1:]
Expecting:
    [[5, 6]]
ok
Trying:
    A[:, ::2]
Expecting:
    [[1, 3], [4, 6]]
ok
Trying:
    A = Matrix([[1, 2, 3], [4, 5, 6]])
Expecting nothing
ok
Trying:
    A.listrows
Expecting:
    [[1, 2, 3], [4, 5, 6]]
ok
Trying:
    A = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
Expecting nothing
ok
Trying:
    list(A)
Expecting:
    [1, 2, 3, 4, 5, 6, 7, 8, 9]
ok
Trying:
    A = Matrix([[1, 2, 3], [4, 5, 6]])
Expecting nothing
ok
Trying:
    len(A)
Expecting:
    6
ok
Trying:
    len(A) == A.n * A.m
Expecting:
    True
ok
Trying:
    B = Matrix([[1, 4], [2, 5], [3, 6]])
Expecting nothing
ok
Trying:
    B < B
Expecting:
    False
ok
Trying:
    B < B + 4
Expecting:
    True
ok
Trying:
    B > B
Expecting:
    False
ok
Trying:
    B > B - 12
Expecting:
    True
ok
Trying:
    A = Matrix([[1, 2], [3, 4]])
Expecting nothing
ok
Trying:
    A % 2
Expecting:
    [[1, 0], [1, 0]]
ok
Trying:
    (A*100) % 31
Expecting:
    [[7, 14], [21, 28]]
ok
Trying:
    (A*100) % 33 == A  # Curious property
Expecting:
    True
ok
Trying:
    (A*100) % 35
Expecting:
    [[30, 25], [20, 15]]
ok
Trying:
    A = Matrix([[1, 2], [3, 4]])
Expecting nothing
ok
Trying:
    B = Matrix([[2, 3], [2, 2]])
Expecting nothing
ok
Trying:
    A % B
Expecting:
    [[1, 2], [1, 0]]
ok
Trying:
    A = Matrix([[1, 2], [3, 4]])
Expecting nothing
ok
Trying:
    B = eye(A.n); B
Expecting:
    [[1, 0], [0, 1]]
ok
Trying:
    A * B == B * A == A
Expecting:
    True
ok
Trying:
    A * A
Expecting:
    [[7, 10], [15, 22]]
ok
Trying:
    A * (A * A) == (A * A) * A
Expecting:
    True
ok
Trying:
    A * 1 == A  # Coefficient wise!
Expecting:
    True
ok
Trying:
    A * 12.011993  # Coefficient wise!
Expecting:
    [[12.011993, 24.023986], [36.035979, 48.047972]]
ok
Trying:
    A = Matrix([[1, 2, 3], [4, 5, 6]])
Expecting nothing
ok
Trying:
    -A
Expecting:
    [[-1, -2, -3], [-4, -5, -6]]
ok
Trying:
    A - A == A + (-A)
Expecting:
    True
ok
Trying:
    -(-A)  == A
Expecting:
    True
ok
Trying:
    -------A == -A  # Crazy syntax!
Expecting:
    True
ok
Trying:
    s = '-------'
Expecting nothing
ok
Trying:
    len(s) % 2 == 1  # We check that we had an od number of minus symbol
Expecting:
    True
ok
Trying:
    A = Matrix([[1, 2, 3], [4, 5, 6]])
Expecting nothing
ok
Trying:
    +A == A
Expecting:
    True
ok
Trying:
    +-+-+-+-+++----+-+-+----++++A == A  # Crazy syntax, again!
Expecting:
    True
ok
Trying:
    s = '+-+-+-+-+++----+-+-+----++++'
Expecting nothing
ok
Trying:
    s.count('-') % 2 == 0  # We check that we had an even number of minus symbol
Expecting:
    True
ok
Trying:
    A = Matrix([[1, 2], [3, 4]])
Expecting nothing
ok
Trying:
    A ** 1 == A
Expecting:
    True
ok
Trying:
    A ** 2
Expecting:
    [[7, 10], [15, 22]]
ok
Trying:
    A * A == A ** 2
Expecting:
    True
ok
Trying:
    B = eye(A.n)
Expecting nothing
ok
Trying:
    B == B ** 1 == A ** 0 == B ** 0
Expecting:
    True
ok
Trying:
    divmod(2015, 2)
Expecting:
    (1007, 1)
ok
Trying:
    2015 == 1007*2 + 1
Expecting:
    True
ok
Trying:
    A ** 2015 == ((A ** 1007) ** 2 ) * A
Expecting:
    True
ok
Trying:
    C = diag([1, 4])
Expecting nothing
ok
Trying:
    C ** 100
Expecting:
    [[1, 0], [0, 1606938044258990275541962092341162602522202993782792835301376]]
ok
Trying:
    C ** 100 == diag([1**100, 4**100])
Expecting:
    True
ok
Trying:
    A ** (-1) == A.inv()
Expecting:
    True
ok
Trying:
    C = (A ** (-1)); C
Expecting:
    [[-2.0, 1.0], [1.5, -0.5]]
ok
Trying:
    C * A == eye(A.n) == A * C
Expecting:
    True
ok
Trying:
    C.listrows  # Rounding mistakes can happen (but not here)
Expecting:
    [[-2.0, 1.0], [1.5, -0.5]]
ok
Trying:
    D = C.round(); D.listrows
Expecting:
    [[-2.0, 1.0], [1.5, -0.5]]
ok
Trying:
    D * A == eye(A.n) == A * D  # No rounding mistake!
Expecting:
    True
ok
Trying:
    (C * A).almosteq(eye(A.n))
Expecting:
    True
ok
Trying:
    (A ** (-5)) == (A ** 5).inv() == (A.inv()) ** 5
Expecting:
    False
ok
Trying:
    (A ** (-5)).round() == ((A ** 5).inv()).round() == ((A.inv()) ** 5).round()  # No rounding mistake!
Expecting:
    True
ok
Trying:
    A = Matrix([[1, 2, 3], [4, 5, 6]])
Expecting nothing
ok
Trying:
    1 + A
Expecting:
    [[2, 3, 4], [5, 6, 7]]
ok
Trying:
    B = ones(A.n, A.m)
Expecting nothing
ok
Trying:
    4 + B  # Coefficient wise!
Expecting:
    [[5, 5, 5], [5, 5, 5]]
ok
Trying:
    (-2) + B  # Coefficient wise!
Expecting:
    [[-1, -1, -1], [-1, -1, -1]]
ok
Trying:
    (-1.0) + B  # Coefficient wise!
Expecting:
    [[0.0, 0.0, 0.0], [0.0, 0.0, 0.0]]
ok
Trying:
    B = Matrix([[1, 4], [2, 5], [3, 6]])
Expecting nothing
ok
Trying:
    repr(B)
Expecting:
    '[[1, 4], [2, 5], [3, 6]]'
ok
Trying:
    A = Matrix([[1, 2], [3, 4]])
Expecting nothing
ok
Trying:
    B = eye(A.n)
Expecting nothing
ok
Trying:
    1 // B == B == B // 1
Expecting:
    True
ok
Trying:
    C = B.map(float)
Expecting nothing
ok
Trying:
    1 // B == B == B // 1
Expecting:
    True
ok
Trying:
    A.inv() == 1 // A  # special case!
Expecting:
    True
ok
Trying:
    2 // (2*A)  # XXX This is coefficient wise !
Expecting:
    [[1, 0], [0, 0]]
ok
Trying:
    A = Matrix([[1, 2], [3, 4]])
Expecting nothing
ok
Trying:
    1 * A == A  # Coefficient wise!
Expecting:
    True
ok
Trying:
    12.011993 * A  # Coefficient wise!
Expecting:
    [[12.011993, 24.023986], [36.035979, 48.047972]]
ok
Trying:
    A = Matrix([[1, 2, 3], [4, 5, 6]])
Expecting nothing
ok
Trying:
    1 - A  # Coefficient wise!
Expecting:
    [[0, -1, -2], [-3, -4, -5]]
ok
Trying:
    B = ones(A.n, A.m)
Expecting nothing
ok
Trying:
    (-1) - B  # Coefficient wise!
Expecting:
    [[-2, -2, -2], [-2, -2, -2]]
ok
Trying:
    ((-1) - B) == -(1 + B) == -(B + B)
Expecting:
    True
ok
Trying:
    A = Matrix([[1, 2], [3, 4]])
Expecting nothing
ok
Trying:
    Ainv = Matrix([[-2.0, 1.0], [1.5, -0.5]])
Expecting nothing
ok
Trying:
    B = eye(A.n)
Expecting nothing
ok
Trying:
    B == A * Ainv == Ainv * A
Expecting:
    True
ok
Trying:
    1 / B == B == B / 1
Expecting:
    True
ok
Trying:
    C = B.map(float)
Expecting nothing
ok
Trying:
    1 / B == B == B / 1
Expecting:
    True
ok
Trying:
    A.inv() == 1 / A  # special case!
Expecting:
    True
ok
Trying:
    1 / A  # This is like 1 / A
Expecting:
    [[-2.0, 1.0], [1.5, -0.5]]
ok
Trying:
    2 / (2*A)  # Warning This is coefficient wise !  # doctest: +ELLIPSIS
Expecting:
    [[1.0, 0.5], [0.333333..., 0.25]]
ok
Trying:
    A = Matrix([[1, 2, 3], [4, 5, 6]])
Expecting nothing
ok
Trying:
    A[0, 0] = 4; A
Expecting:
    [[4, 2, 3], [4, 5, 6]]
ok
Trying:
    A[:, 0]
Expecting:
    [[4], [4]]
ok
Trying:
    A[-1, :] = 9; A
Expecting:
    [[4, 2, 3], [9, 9, 9]]
ok
Trying:
    A[1, 1] = 3; A
Expecting:
    [[4, 2, 3], [9, 3, 9]]
ok
Trying:
    A[0, :] = [3, 2, 1]; A
Expecting:
    [[3, 2, 1], [9, 3, 9]]
ok
Trying:
    A[1:, 1:] = -1; A
Expecting:
    [[3, 2, 1], [9, -1, -1]]
ok
Trying:
    A[1:, 1:] *= -8; A
Expecting:
    [[3, 2, 1], [9, 8, 8]]
ok
Trying:
    B = Matrix([[1, 4], [2, 5], [3, 6]])
Expecting nothing
ok
Trying:
    str(B)
Expecting:
    '[[1, 4], [2, 5], [3, 6]]'
ok
Trying:
    A = Matrix([[1, 2, 3], [4, 5, 6]])
Expecting nothing
ok
Trying:
    B = ones(A.n, A.m)
Expecting nothing
ok
Trying:
    A - B
Expecting:
    [[0, 1, 2], [3, 4, 5]]
ok
Trying:
    B - A
Expecting:
    [[0, -1, -2], [-3, -4, -5]]
ok
Trying:
    A - 1  # Coefficient wise!
Expecting:
    [[0, 1, 2], [3, 4, 5]]
ok
Trying:
    B - 2  # Coefficient wise!
Expecting:
    [[-1, -1, -1], [-1, -1, -1]]
ok
Trying:
    (A - 3.14).round()  # Coefficient wise!
Expecting:
    [[-2.14, -1.14, -0.14], [0.86, 1.86, 2.86]]
ok
Trying:
    A = Matrix([[1, 2], [3, 4]])
Expecting nothing
ok
Trying:
    B = eye(A.n)
Expecting nothing
ok
Trying:
    B.almosteq(A / A)
Expecting:
    True
ok
Trying:
    C = B.map(float)
Expecting nothing
ok
Trying:
    A / C == A * C == A
Expecting:
    True
ok
Trying:
    A / B == A * B == A
Expecting:
    True
ok
Trying:
    A / 2  # Coefficient wise!
Expecting:
    [[0.5, 1.0], [1.5, 2.0]]
ok
Trying:
    A / 2.0  # Coefficient wise!
Expecting:
    [[0.5, 1.0], [1.5, 2.0]]
ok
Trying:
    A = Matrix([[-4, 2+2j], [0, 4j]])
Expecting nothing
ok
Trying:
    abs(A)  # doctest: +ELLIPSIS
Expecting:
    [[4, 2.828427...], [0, 4.0]]
ok
Trying:
    B = -eye(2)
Expecting nothing
ok
Trying:
    B.abs()
Expecting:
    [[1, 0], [0, 1]]
ok
Trying:
    A = Matrix([[2, 0], [3, 4]])
Expecting nothing
ok
Trying:
    A.adjugate()
Expecting:
    [[4, -3], [0, 2]]
ok
Trying:
    A * A.adjugate() == A.det * eye(A.n)
Expecting:
    False
ok
Trying:
    A * A.adjugate().T == A.det * eye(A.n)
Expecting:
    True
ok
Trying:
    B = Matrix([[1, 4], [2, 5], [3, 6]])
Expecting nothing
ok
Trying:
    C = B.copy(); C[0,0] += 4*1e-6
Expecting nothing
ok
Trying:
    B == C
Expecting:
    False
ok
Trying:
    B.almosteq(C)
Expecting:
    False
ok
Trying:
    B.almosteq(C, epsilon=1e-4)
Expecting:
    True
ok
Trying:
    B.almosteq(C, epsilon=1e-5)
Expecting:
    True
ok
Trying:
    B.almosteq(C, epsilon=1e-6)
Expecting:
    False
ok
Trying:
    A = Matrix([[1, 2], [3, 4]])
Expecting nothing
ok
Trying:
    A.cofactor(0, 0)
Expecting:
    4
ok
Trying:
    A = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
Expecting nothing
ok
Trying:
    A.cofactor(0, 0)  # (-1)**0 * | 5 6  8 9 | = 5 * 9 - 6 * 8 = -3
Expecting:
    -3.000000000000007
ok
Trying:
    A.cofactor(1, 0)  # (-1)**1 * | 2 3  8 9 | = -(2 * 9 - 3 * 8) = 6
Expecting:
    6
ok
Trying:
    A = Matrix([[1, 2, 3], [4, 5, 6]])
Expecting nothing
ok
Trying:
    A.col(0)
Expecting:
    [[1], [4]]
ok
Trying:
    A.col(2)
Expecting:
    [[3], [6]]
ok
Trying:
    c = A.col(1); c *= 6
Expecting nothing
ok
Trying:
    A  # it has not been modified!
Expecting:
    [[1, 2, 3], [4, 5, 6]]
ok
Trying:
    A = Matrix([[1, 2, 3], [4, 5, 6]])
Expecting nothing
ok
Trying:
    A.m
Expecting:
    3
ok
Trying:
    A.cols == A.m
Expecting:
    True
ok
Trying:
    A = Matrix([[-1j, -2j], [-2j, -1j]])
Expecting nothing
ok
Trying:
    A.conjugate()
Expecting:
    [[1j, 2j], [2j, 1j]]
**********************************************************************
File "./matrix.py", line 1597, in __main__.Matrix.conjugate
Failed example:
    A.conjugate()
Expected:
    [[1j, 2j], [2j, 1j]]
Got:
    [[(-0+1j), (-0+2j)], [(-0+2j), (-0+1j)]]
Trying:
    A = Matrix([[1, 2, 3], [4, 5, 6]])
Expecting nothing
ok
Trying:
    B = A.copy()
Expecting nothing
ok
Trying:
    A[0, 0] = -10; A
Expecting:
    [[-10, 2, 3], [4, 5, 6]]
ok
Trying:
    B  # It has not been modified!
Expecting:
    [[1, 2, 3], [4, 5, 6]]
ok
Trying:
    Matrix([[1, 2], [3, 4]]).count(2)
Expecting:
    1
ok
Trying:
    Matrix([[1, 2], [1, 2]]).count(2)
Expecting:
    2
ok
Trying:
    zeros(7).count(2)
Expecting:
    0
ok
Trying:
    zeros(7).count(0)
Expecting:
    49
ok
Trying:
    eye(19).count(1)
Expecting:
    19
ok
Trying:
    eye(19).count(0)
Expecting:
    342
ok
Trying:
    Matrix([[1, 2], [3, 4]]).det
Expecting:
    -2
ok
Trying:
    Matrix([[1, 2], [1, 2]]).det
Expecting:
    0
ok
Trying:
    zeros(7).det
Expecting:
    0
ok
Trying:
    eye(19).det
Expecting:
    1
ok
Trying:
    A = Matrix([[1, 1], [1, -1]])
Expecting nothing
ok
Trying:
    v = [2, 3]
Expecting nothing
ok
Trying:
    A.dot(v)
Expecting:
    [[5], [-1]]
ok
Trying:
    v = Matrix([[2], [-3]])
Expecting nothing
ok
Trying:
    A.dot(v)
Expecting:
    [[-1], [5]]
ok
Trying:
    A.dot(v.T)  # v.T is not a column vector!
Expecting:
    Traceback (most recent call last):
        ...
    ValueError: A.dot(v): the vector v = [[2, -3]] is not a vector: v.m = 2 != 1.
ok
Trying:
    v = Matrix([[2], [-3], [7]])
Expecting nothing
ok
Trying:
    A.dot(v)
Expecting:
    Traceback (most recent call last):
        ...
    ValueError: A.dot(v): the size of the vector v = [[2], [-3], [7]] should be compatible with the size of the matrix self = [[1, 1], [1, -1]]. Here self.m = 2 and v.n = 3, are different.
ok
Trying:
    v = [1, 2, 3, 4, 5]
Expecting nothing
ok
Trying:
    A.dot(v)
Expecting:
    Traceback (most recent call last):
        ...
    ValueError: A.dot(v): the size of the vector v = [[1], [2], [3], [4], [5]] should be compatible with the size of the matrix self = [[1, 1], [1, -1]]. Here self.m = 2 and v.n = 5, are different.
ok
Trying:
    import math
Expecting nothing
ok
Trying:
    e = math.e
Expecting nothing
ok
Trying:
    I = eye(10); I[0, :]
Expecting:
    [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
ok
Trying:
    I * e == I.exp() == diag([e] * I.n)  # Rounding mistakes!
Expecting:
    False
ok
Trying:
    (I * e).round() == I.exp().round() == diag([e] * I.n).round()  # No more rounding mistakes!
Expecting:
    True
ok
Trying:
    C = diag([1, 4])
Expecting nothing
ok
Trying:
    C.exp() == diag([e ** 1, e ** 4]) == diag([math.exp(1), math.exp(4)])  # Rounding mistakes!
Expecting:
    False
ok
Trying:
    C.exp().almosteq(diag([e ** 1, e ** 4]))  # No more rounding mistakes!
Expecting:
    True
ok
Trying:
    diag([e ** 1, e ** 4]).almosteq(diag([math.exp(1), math.exp(4)]))
Expecting:
    True
ok
Trying:
    Matrix([[1, 2], [3, 4]]).gauss()
Expecting:
    [[1, 2], [0, -2]]
ok
Trying:
    Matrix([[1, 2], [1, 2]]).gauss()
Expecting:
    [[1, 2], [0, 0]]
ok
Trying:
    Matrix([[1, 2], [-1, -0.5]]).gauss()
Expecting:
    [[1, 2], [0, 1.5]]
ok
Trying:
    Matrix([[1, 2], [3, 4]]).gauss(maxpivot=True)
Expecting:
    [[2, 1], [0, 1]]
ok
Trying:
    Matrix([[1, 2], [1, 2]]).gauss(maxpivot=True)
Expecting:
    [[2, 1], [0, 0]]
ok
Trying:
    Matrix([[1, 2], [3, 4]]).gauss(det=True)
Expecting:
    ([[1, 2], [0, -2]], -2)
ok
Trying:
    Matrix([[1, 2], [1, 2]]).gauss(det=True)
Expecting:
    ([[1, 2], [0, 0]], 0)
ok
Trying:
    A = Matrix([[-1j, -2j], [-2j, -1j]])
Expecting nothing
ok
Trying:
    A.imag
Expecting:
    [[-1.0, -2.0], [-2.0, -1.0]]
ok
Trying:
    A = Matrix([[1, 2], [3, 4]])
Expecting nothing
ok
Trying:
    A.inv()
Expecting:
    [[-2.0, 1.0], [1.5, -0.5]]
ok
Trying:
    A * A.inv() == A.inv() * A == eye(A.n)  # Rounding mistake can happen (but not here)
Expecting:
    True
ok
Trying:
    Ai = A.inv().round()  # No more rounding mistake!
Expecting nothing
ok
Trying:
    A * Ai == Ai * A == eye(A.n)
Expecting:
    True
ok
Trying:
    A.det
Expecting:
    -2
ok
Trying:
    O = Matrix([[1, 2], [0, 0]])  # O and not 0
Expecting nothing
ok
Trying:
    O.is_singular
Expecting:
    True
ok
Trying:
    O.inv()  # O is singular!
Expecting:
    Traceback (most recent call last):
        ...
    ValueError: A.inv() on a singular matrix (ie. non inversible).
ok
Trying:
    O.det
Expecting:
    0
ok
Trying:
    A = Matrix([[0, 1], [-1, 0]])
Expecting nothing
ok
Trying:
    A.is_anti_symetric
Expecting:
    True
ok
Trying:
    eye(30).is_anti_symetric
Expecting:
    False
ok
Trying:
    eye(40).is_diagonal
Expecting:
    True
ok
Trying:
    A = Matrix([[0, 1], [-1, 0]])
Expecting nothing
ok
Trying:
    A.is_diagonal
Expecting:
    False
ok
Trying:
    A = diag(range(30))
Expecting nothing
ok
Trying:
    A.is_diagonal
Expecting:
    True
ok
Trying:
    A = Matrix([[1, 2j], [-2j, 1]])
Expecting nothing
ok
Trying:
    A.is_hermitian
Expecting:
    True
ok
Trying:
    eye(30).is_hermitian
Expecting:
    True
ok
Trying:
    (1j * ones(3)).is_hermitian
Expecting:
    False
ok
Trying:
    A = Matrix([[8, 1], [0, 7]])
Expecting nothing
ok
Trying:
    A.is_lower
Expecting:
    False
ok
Trying:
    A.T.is_lower
Expecting:
    True
ok
Trying:
    A = Matrix([[2, 0], [3, 4]])
Expecting nothing
ok
Trying:
    A.is_singular
Expecting:
    False
ok
Trying:
    zeros(3).is_singular
Expecting:
    True
ok
Trying:
    (0 * A).is_singular
Expecting:
    True
ok
Trying:
    Matrix([[2, 0], [4, 0]]).is_singular
Expecting:
    True
ok
Trying:
    A = Matrix([[-4, 2+2j], [0, 4j]])
Expecting nothing
ok
Trying:
    A.is_square
Expecting:
    True
ok
Trying:
    v = Matrix([[-4], [0]])
Expecting nothing
ok
Trying:
    v.is_square
Expecting:
    False
ok
Trying:
    A = Matrix([[-4, 2+2j], [0, 4j]])
Expecting nothing
ok
Trying:
    A.is_symetric
Expecting:
    False
ok
Trying:
    eye(30).is_symetric
Expecting:
    True
ok
Trying:
    A = Matrix([[2, 0], [3, 4]])
Expecting nothing
ok
Trying:
    A.is_upper
Expecting:
    False
ok
Trying:
    A.T.is_upper
Expecting:
    True
ok
Trying:
    A = Matrix([[2, 0], [3, 4]])
Expecting nothing
ok
Trying:
    A.is_zero
Expecting:
    False
ok
Trying:
    zeros(30).is_zero
Expecting:
    True
ok
Trying:
    (0 * A).is_zero
Expecting:
    True
ok
Trying:
    O, I = zeros(2), eye(2)
Expecting nothing
ok
Trying:
    I.map(lambda x: x * 4)
Expecting:
    [[4, 0], [0, 4]]
ok
Trying:
    O.map(lambda x: x + 6)
Expecting:
    [[6, 6], [6, 6]]
ok
Trying:
    A = Matrix([[-1j, -2j], [-2j, -1j]])
Expecting nothing
ok
Trying:
    A.map(lambda z: abs(z))
Expecting:
    [[1.0, 2.0], [2.0, 1.0]]
ok
Trying:
    A.map(lambda z: int(abs(z)))
Expecting:
    [[1, 2], [2, 1]]
ok
Trying:
    A.map(lambda z: z + 1j)
Expecting:
    [[0j, -1j], [-1j, 0j]]
ok
Trying:
    A.map(lambda z: '"%s"' % str(z))
Expecting:
    [["-1j", "-2j"], ["-2j", "-1j"]]
**********************************************************************
File "./matrix.py", line 1466, in __main__.Matrix.map
Failed example:
    A.map(lambda z: '"%s"' % str(z))
Expected:
    [["-1j", "-2j"], ["-2j", "-1j"]]
Got:
    [["(-0-1j)", "(-0-2j)"], ["(-0-2j)", "(-0-1j)"]]
Trying:
    A.map(lambda z: "Look: %s" % str(z))
Expecting:
    [[Look: -1j, Look: -2j], [Look: -2j, Look: -1j]]
**********************************************************************
File "./matrix.py", line 1468, in __main__.Matrix.map
Failed example:
    A.map(lambda z: "Look: %s" % str(z))
Expected:
    [[Look: -1j, Look: -2j], [Look: -2j, Look: -1j]]
Got:
    [[Look: (-0-1j), Look: (-0-2j)], [Look: (-0-2j), Look: (-0-1j)]]
Trying:
    def f(x, n, offset=0):
        return (x ** n) + offset
Expecting nothing
ok
Trying:
    A = Matrix([[1, 2], [2, 1]])
Expecting nothing
ok
Trying:
    A.map(f, 2)
Expecting:
    [[1, 4], [4, 1]]
ok
Trying:
    A.map(f, 2, offset=4)
Expecting:
    [[5, 8], [8, 5]]
ok
Trying:
    A = Matrix([[1, 2], [3, 4]])
Expecting nothing
ok
Trying:
    A.minor(0, 0)
Expecting:
    4
ok
Trying:
    A = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
Expecting nothing
ok
Trying:
    A.minor(0, 0)  # | 5 6  8 9 | = 5 * 9 - 6 * 8 = -3
Expecting:
    -3.000000000000007
ok
Trying:
    A.minor(1, 0)  # | 2 3  8 9 | = 2 * 9 - 3 * 8 = -6
Expecting:
    -6
ok
Trying:
    A = Matrix([[1, 2], [3, 4]])
Expecting nothing
ok
Trying:
    B = eye(A.n)
Expecting nothing
ok
Trying:
    A.multiply_elementwise(B)
Expecting:
    [[1, 0], [0, 4]]
ok
Trying:
    A.multiply_elementwise(A)  # A .^ 2 in Matlab?
Expecting:
    [[1, 4], [9, 16]]
ok
Trying:
    A = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
Expecting nothing
ok
Trying:
    for x in A:
        print(x)
Expecting:
    1
    2
    3
    4
    5
    6
    7
    8
    9
ok
Trying:
    for i, x in enumerate(A):
        print(i, "th value of A is", x)
Expecting:
    0 th value of A is 1
    1 th value of A is 2
    2 th value of A is 3
    3 th value of A is 4
    4 th value of A is 5
    5 th value of A is 6
    6 th value of A is 7
    7 th value of A is 8
    8 th value of A is 9
ok
Trying:
    A = Matrix([[1, 2], [-3, -1]])
Expecting nothing
ok
Trying:
    A.norm()  # (1)**2 + (2)**2 + (-3)**2 + (-1)**2
Expecting:
    3.872983346207417
ok
Trying:
    15**0.5
Expecting:
    3.872983346207417
ok
Trying:
    A.norm('inf')
Expecting:
    3
ok
Trying:
    A.norm(1) == 7  # (1) + (2) + (3) + (1)
Expecting:
    True
ok
Trying:
    A.norm(3)
Expecting:
    3.332221851645953
ok
Trying:
    A = Matrix([[1, 2], [-3, -1]])
Expecting nothing
ok
Trying:
    A.normalized(p='inf')  # doctest: +ELLIPSIS
Expecting:
    [[0.333333..., 1.0], [-1.0, -0.5]]
ok
Trying:
    eye(5).normalized(p='inf').map(int)  # normalize then round to an int
Expecting:
    [[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]]
ok
Trying:
    B = -eye(5)
Expecting nothing
ok
Trying:
    (2*B).normalized()  # each vector is divided by its norm = 2
Expecting:
    [[-1.0, 0.0, 0.0, 0.0, 0.0], [0.0, -1.0, 0.0, 0.0, 0.0], [0.0, 0.0, -1.0, 0.0, 0.0], [0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, -1.0]]
ok
Trying:
    B.normalized(p='inf')
Expecting:
    [[-1.0, 0.0, 0.0, 0.0, 0.0], [0.0, -1.0, 0.0, 0.0, 0.0], [0.0, 0.0, -1.0, 0.0, 0.0], [0.0, 0.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 0.0, -1.0]]
ok
Trying:
    v = Matrix([[1], [-2], [3]])
Expecting nothing
ok
Trying:
    v.normalized()  # doctest: +ELLIPSIS
Expecting:
    [[0.267261...], [-0.534522...], [0.801783...]]
ok
Trying:
    v.normalized(p=2)  # doctest: +ELLIPSIS
Expecting:
    [[0.267261...], [-0.534522...], [0.801783...]]
ok
Trying:
    v.normalized() * (14**0.5)
Expecting:
    [[1.0], [-2.0], [3.0]]
ok
Trying:
    v.normalized(p=1)  # doctest: +ELLIPSIS
Expecting:
    [[0.166666...], [-0.333333...], [0.5]]
ok
Trying:
    v.normalized(p=1) * 6
Expecting:
    [[1.0], [-2.0], [3.0]]
ok
Trying:
    6 * v.normalized(p=1)
Expecting:
    [[1.0], [-2.0], [3.0]]
ok
Trying:
    Matrix([[1, 2], [3, 4]]).rank
Expecting:
    2
ok
Trying:
    Matrix([[1, 2], [1, 2]]).rank
Expecting:
    1
ok
Trying:
    zeros(7).rank
Expecting:
    0
ok
Trying:
    eye(19).rank
Expecting:
    19
ok
Trying:
    A = Matrix([[1j, 2j], [2j, 1j]])
Expecting nothing
ok
Trying:
    A.real
Expecting:
    [[0.0, 0.0], [0.0, 0.0]]
ok
Trying:
    A = Matrix([[1+6j, 2], [-1+2j, 1+9j]])
Expecting nothing
ok
Trying:
    A.real
Expecting:
    [[1.0, 2], [-1.0, 1.0]]
ok
Trying:
    A = (1. / 3.) * eye(2) + 4
Expecting nothing
ok
Trying:
    A.round(0)
Expecting:
    [[4.0, 4.0], [4.0, 4.0]]
ok
Trying:
    A.round(2)
Expecting:
    [[4.33, 4.0], [4.0, 4.33]]
ok
Trying:
    A.round(7)
Expecting:
    [[4.3333333, 4.0], [4.0, 4.3333333]]
ok
Trying:
    A = Matrix([[1, 2, 3], [4, 5, 6]])
Expecting nothing
ok
Trying:
    A.row(0)
Expecting:
    [[1, 2, 3]]
ok
Trying:
    A.row(1)
Expecting:
    [[4, 5, 6]]
ok
Trying:
    r = A.row(0); r *= 3
Expecting nothing
ok
Trying:
    A  # it has not been modified!
Expecting:
    [[1, 2, 3], [4, 5, 6]]
ok
Trying:
    A = Matrix([[1, 2, 3], [4, 5, 6]])
Expecting nothing
ok
Trying:
    A.n
Expecting:
    2
ok
Trying:
    A.rows == A.n
Expecting:
    True
ok
Trying:
    A = Matrix([[1, 2, 3], [4, 5, 6]])
Expecting nothing
ok
Trying:
    A.shape
Expecting:
    (2, 3)
ok
Trying:
    A = Matrix([[2, 0], [3, 4]]); A
Expecting:
    [[2, 0], [3, 4]]
ok
Trying:
    A.swap_cols(0, 1); A
Expecting:
    [[0, 2], [4, 3]]
ok
Trying:
    A = Matrix([[2, 0], [3, 4]]); A
Expecting:
    [[2, 0], [3, 4]]
ok
Trying:
    A.swap_rows(0, 1); A
Expecting:
    [[3, 4], [2, 0]]
ok
Trying:
    A = Matrix([[-4, 2+2j], [0, 4j]])
Expecting nothing
ok
Trying:
    A.trace()
Expecting:
    (-4+4j)
ok
Trying:
    eye(19).trace()
Expecting:
    19
ok
Trying:
    zeros(20).trace()
Expecting:
    0
ok
Trying:
    ones(100).trace()
Expecting:
    100
ok
Trying:
    A = Matrix([[1, 2, 3], [4, 5, 6]])
Expecting nothing
ok
Trying:
    A.transpose()
Expecting:
    [[1, 4], [2, 5], [3, 6]]
ok
Trying:
    A.transpose().transpose() == A
Expecting:
    True
ok
Trying:
    det(eye(2))
Expecting:
    1
ok
Trying:
    det((-1) * eye(4))
Expecting:
    1
ok
Trying:
    det((-1) * eye(5))
Expecting:
    -1
ok
Trying:
    D = diag(range(1,6))
Expecting nothing
ok
Trying:
    D[2, :]
Expecting:
    [[0, 0, 3, 0, 0]]
ok
Trying:
    D.trace()
Expecting:
    15
ok
Trying:
    D.trace() == sum(range(1,6))
Expecting:
    True
ok
Trying:
    D.det
Expecting:
    120
ok
Trying:
    from math import factorial
Expecting nothing
ok
Trying:
    D.det == factorial(5)
Expecting:
    True
ok
Trying:
    diag([-1, 1])
Expecting:
    [[-1, 0], [0, 1]]
ok
Trying:
    diag([-4, 1]) + 3
Expecting:
    [[-1, 3], [3, 4]]
ok
Trying:
    diag(3.14, 3)
Expecting:
    [[3.14, 0, 0], [0, 3.14, 0], [0, 0, 3.14]]
ok
Trying:
    diag([3.14]*3)  # Same !
Expecting:
    [[3.14, 0, 0], [0, 3.14, 0], [0, 0, 3.14]]
ok
Trying:
    import math
Expecting nothing
ok
Trying:
    e = math.exp(1.0)
Expecting nothing
ok
Trying:
    C = diag([1, 4])
Expecting nothing
ok
Trying:
    exp(C) == diag([e ** 1, e ** 4]) == diag([math.exp(1), math.exp(4)])  # Rounding mistakes!
Expecting:
    False
ok
Trying:
    exp(C).almosteq(diag([e ** 1, e ** 4]))  # No more rounding mistakes!
Expecting:
    True
ok
Trying:
    diag([e ** 1, e ** 4]).almosteq(diag([math.exp(1), math.exp(4)]))
Expecting:
    True
ok
Trying:
    eye(2)
Expecting:
    [[1, 0], [0, 1]]
ok
Trying:
    zeros(18) == eye(18) * 0
Expecting:
    True
ok
Trying:
    eye(60).is_diagonal
Expecting:
    True
ok
Trying:
    eye(40).is_square
Expecting:
    True
ok
Trying:
    eye(20).is_singular
Expecting:
    False
ok
Trying:
    eye(5).det
Expecting:
    1
ok
Trying:
    eye(7).trace()
Expecting:
    7
ok
Trying:
    V = Matrix([[1, 2, 3], [-1, 0, 4]])
Expecting nothing
ok
Trying:
    gram_schmidt(V)
Expecting:
    [[1, 2, 3], [-1, 0, 4]]
ok
Trying:
    vx = [1, 2, 3]; vy = [-1, 0, 4]
Expecting nothing
ok
Trying:
    innerproduct(vx, vy)
Expecting:
    11
ok
Trying:
    vx = [1j, 2j, 3j]; vy = [-1, 0, 4]
Expecting nothing
ok
Trying:
    (-1j) * (-1) + (-2j) * (0) + (-3j) * (4)
Expecting:
    -11j
ok
Trying:
    innerproduct(vx, vy)
Expecting:
    -11j
ok
Trying:
    inv(eye(2)) == eye(2)
Expecting:
    True
ok
Trying:
    mat_from_f(lambda i, j: 1 if i == j else 0, 3) == eye(3)
Expecting:
    True
ok
Trying:
    mat_from_f(lambda i, j: 1, 3) == ones(3)
Expecting:
    True
ok
Trying:
    mat_from_f(lambda i, j: i+j, 3)
Expecting:
    [[0, 1, 2], [1, 2, 3], [2, 3, 4]]
ok
Trying:
    mat_from_f(lambda i, j: i*j, 3)
Expecting:
    [[0, 0, 0], [0, 1, 2], [0, 2, 4]]
ok
Trying:
    def f(i, j, e, offset=0):
        return (i * e) + offset
Expecting nothing
ok
Trying:
    mat_from_f(f, 2, 2, 4)  # n = 2, m = 2, e = 4
Expecting:
    [[0, 0], [4, 4]]
ok
Trying:
    mat_from_f(f, 2, 2, 4, offset=10)  # n = 2, m = 2, e = 4, offset = 10
Expecting:
    [[10, 10], [14, 14]]
ok
Trying:
    u = [1, 2, 3]
Expecting nothing
ok
Trying:
    norm2(u)
Expecting:
    3.7416573867739413
ok
Trying:
    u = [1j, -2j, 3j]
Expecting nothing
ok
Trying:
    norm2(u)
Expecting:
    3.7416573867739413
ok
Trying:
    u = [1+1j, 2-2j, 3+3j]
Expecting nothing
ok
Trying:
    norm2(u)
Expecting:
    5.291502622129181
ok
Trying:
    u = [1, 2, 3]
Expecting nothing
ok
Trying:
    norm_square(u)
Expecting:
    14
ok
Trying:
    u = [1j, -2j, 3j]
Expecting nothing
ok
Trying:
    norm_square(u)
Expecting:
    14.0
ok
Trying:
    u = [1+1j, 2-2j, 3+3j]
Expecting nothing
ok
Trying:
    norm_square(u)
Expecting:
    28.0
ok
Trying:
    ones(3, 2)
Expecting:
    [[1, 1], [1, 1], [1, 1]]
ok
Trying:
    ones(2, 3)
Expecting:
    [[1, 1, 1], [1, 1, 1]]
ok
Trying:
    ones(2)
Expecting:
    [[1, 1], [1, 1]]
ok
Trying:
    ones((2, 3))
Expecting:
    [[1, 1, 1], [1, 1, 1]]
ok
Trying:
    u = [1, 2, 3]; v = [-1, 0, 4]
Expecting nothing
ok
Trying:
    proj(u, v)  # 11/14 * u
Expecting:
    [0.7857142857142857, 1.5714285714285714, 2.357142857142857]
ok
Trying:
    proj(u, v) == [(11/14) * x for x in u]
Expecting:
    True
ok
Trying:
    from random import seed
Expecting nothing
ok
Trying:
    seed(0)  # We want the examples to always be the same
Expecting nothing
ok
Trying:
    rand_matrix(2, 3)
Expecting:
    [[7, 5, -2], [-5, 0, -2]]
**********************************************************************
File "./matrix.py", line 2318, in __main__.rand_matrix
Failed example:
    rand_matrix(2, 3)
Expected:
    [[7, 5, -2], [-5, 0, -2]]
Got:
    [[2, 3, -9], [-2, 6, 5]]
Trying:
    rand_matrix(3, 2, 40)
Expecting:
    [[23, -16], [-2, 7], [33, 0]]
**********************************************************************
File "./matrix.py", line 2320, in __main__.rand_matrix
Failed example:
    rand_matrix(3, 2, 40)
Expected:
    [[23, -16], [-2, 7], [33, 0]]
Got:
    [[11, -2], [21, 5], [34, -13]]
Trying:
    rand_matrix(4, 4, 100)
Expecting:
    [[-44, 51, 24, -50], [82, 97, 62, 81], [-38, 46, 80, 37], [-6, -80, -13, 22]]
**********************************************************************
File "./matrix.py", line 2322, in __main__.rand_matrix
Failed example:
    rand_matrix(4, 4, 100)
Expected:
    [[-44, 51, 24, -50], [82, 97, 62, 81], [-38, 46, 80, 37], [-6, -80, -13, 22]]
Got:
    [[29, -65, -28, -65], [93, -76, 58, -36], [36, 80, 54, -63], [-21, -75, 86, -82]]
Trying:
    from random import seed
Expecting nothing
ok
Trying:
    seed(0)  # We want the examples to always be the same
Expecting nothing
ok
Trying:
    rand_matrix_float(2, 3)
Expecting:
    [[6.8884370305, 5.15908805881, -1.58856838338], [-4.82166499414, 0.225494427372, -1.90131725099]]
**********************************************************************
File "./matrix.py", line 2334, in __main__.rand_matrix_float
Failed example:
    rand_matrix_float(2, 3)
Expected:
    [[6.8884370305, 5.15908805881, -1.58856838338], [-4.82166499414, 0.225494427372, -1.90131725099]]
Got:
    [[6.888437030500963, 5.159088058806049, -1.5885683833831], [-4.821664994140733, 0.22549442737217085, -1.9013172509917133]]
Trying:
    rand_matrix_float(3, 2, 1)
Expecting:
    [[0.56759717807, -0.393374547842], [-0.0468060916953, 0.16676407891], [0.816225770391, 0.00937371163478]]
**********************************************************************
File "./matrix.py", line 2336, in __main__.rand_matrix_float
Failed example:
    rand_matrix_float(3, 2, 1)
Expected:
    [[0.56759717807, -0.393374547842], [-0.0468060916953, 0.16676407891], [0.816225770391, 0.00937371163478]]
Got:
    [[0.5675971780695452, -0.3933745478421451], [-0.04680609169528838, 0.1667640789100624], [0.8162257703906703, 0.009373711634780513]]
Trying:
    rand_matrix_float(4, 4, 20)
Expecting:
    [[-8.72648622401, 10.2321681663, 4.73475986701, -9.9797463455], [16.3898502387, 19.3114190415, 12.4086894399, 16.0866380176], [-7.59409722723, 9.19326993041, 15.9535315187, 7.35935727662], [-1.11429138189, -15.9719516773, -2.63312658185, 4.43547893775]]
**********************************************************************
File "./matrix.py", line 2338, in __main__.rand_matrix_float
Failed example:
    rand_matrix_float(4, 4, 20)
Expected:
    [[-8.72648622401, 10.2321681663, 4.73475986701, -9.9797463455], [16.3898502387, 19.3114190415, 12.4086894399, 16.0866380176], [-7.59409722723, 9.19326993041, 15.9535315187, 7.35935727662], [-1.11429138189, -15.9719516773, -2.63312658185, 4.43547893775]]
Got:
    [[-8.726486224011847, 10.232168166288957, 4.734759867013267, -9.979746345502377], [16.389850238729608, 19.311419041506127, 12.40868943986358, 16.08663801758331], [-7.594097227226694, 9.193269930405144, 15.953531518719743, 7.359357276617651], [-1.1142913818914657, -15.971951677265368, -2.6331265818486536, 4.435478937752066]]
Trying:
    rank(eye(2))
Expecting:
    2
ok
Trying:
    vx = [1, 2, 3]; vy = [-1, 0, 4]
Expecting nothing
ok
Trying:
    vect_const_multi(vx, 2)
Expecting:
    [2, 4, 6]
ok
Trying:
    vect_const_multi(vy, -4)
Expecting:
    [4, 0, -16]
ok
Trying:
    zeros(3, 2)
Expecting:
    [[0, 0], [0, 0], [0, 0]]
ok
Trying:
    zeros(2, 3)
Expecting:
    [[0, 0, 0], [0, 0, 0]]
ok
Trying:
    ones(2, 3) == zeros(2, 3) + 1
Expecting:
    True
ok
Trying:
    zeros(2, 3) == ones(2, 3) * 0
Expecting:
    True
ok
Trying:
    zeros(2)
Expecting:
    [[0, 0], [0, 0]]
ok
Trying:
    zeros((2, 3))
Expecting:
    [[0, 0, 0], [0, 0, 0]]
ok
20 items had no tests:
    __main__.Decimal
    __main__.Decimal.__str__
    __main__.Fraction
    __main__.Fraction.__str__
    __main__.Matrix
    __main__.Matrix.__next__
    __main__.Matrix.gauss_jordan
    __main__.Matrix.type
    __main__.PLUdecomposition
    __main__._argmax
    __main__._ifnone
    __main__._prod
    __main__._slice_to_range
    __main__.adjugate
    __main__.cofactor
    __main__.gauss
    __main__.gauss_jordan
    __main__.minor
    __main__.norm
    __main__.trace
79 items passed all tests:
  12 tests in __main__
   3 tests in __main__.Matrix.T
   9 tests in __main__.Matrix.__add__
   5 tests in __main__.Matrix.__contains__
   5 tests in __main__.Matrix.__eq__
   6 tests in __main__.Matrix.__floordiv__
   7 tests in __main__.Matrix.__getitem__
   2 tests in __main__.Matrix.__init__
   2 tests in __main__.Matrix.__iter__
   3 tests in __main__.Matrix.__len__
   5 tests in __main__.Matrix.__lt__
   8 tests in __main__.Matrix.__mod__
   7 tests in __main__.Matrix.__mul__
   7 tests in __main__.Matrix.__neg__
   5 tests in __main__.Matrix.__pos__
  21 tests in __main__.Matrix.__pow__
   6 tests in __main__.Matrix.__radd__
   2 tests in __main__.Matrix.__repr__
   7 tests in __main__.Matrix.__rfloordiv__
   3 tests in __main__.Matrix.__rmul__
   5 tests in __main__.Matrix.__rsub__
  10 tests in __main__.Matrix.__rtruediv__
   8 tests in __main__.Matrix.__setitem__
   2 tests in __main__.Matrix.__str__
   7 tests in __main__.Matrix.__sub__
   8 tests in __main__.Matrix.__truediv__
   4 tests in __main__.Matrix.abs
   4 tests in __main__.Matrix.adjugate
   7 tests in __main__.Matrix.almosteq
   5 tests in __main__.Matrix.cofactor
   5 tests in __main__.Matrix.col
   3 tests in __main__.Matrix.cols
   4 tests in __main__.Matrix.copy
   6 tests in __main__.Matrix.count
   4 tests in __main__.Matrix.det
  10 tests in __main__.Matrix.dot
   9 tests in __main__.Matrix.exp
   7 tests in __main__.Matrix.gauss
   2 tests in __main__.Matrix.imag
  10 tests in __main__.Matrix.inv
   3 tests in __main__.Matrix.is_anti_symetric
   5 tests in __main__.Matrix.is_diagonal
   4 tests in __main__.Matrix.is_hermitian
   3 tests in __main__.Matrix.is_lower
   5 tests in __main__.Matrix.is_singular
   4 tests in __main__.Matrix.is_square
   3 tests in __main__.Matrix.is_symetric
   3 tests in __main__.Matrix.is_upper
   4 tests in __main__.Matrix.is_zero
   5 tests in __main__.Matrix.minor
   4 tests in __main__.Matrix.multiply_elementwise
   3 tests in __main__.Matrix.next
   6 tests in __main__.Matrix.norm
  13 tests in __main__.Matrix.normalized
   4 tests in __main__.Matrix.rank
   4 tests in __main__.Matrix.real
   4 tests in __main__.Matrix.round
   5 tests in __main__.Matrix.row
   3 tests in __main__.Matrix.rows
   2 tests in __main__.Matrix.shape
   2 tests in __main__.Matrix.swap_cols
   2 tests in __main__.Matrix.swap_rows
   5 tests in __main__.Matrix.trace
   3 tests in __main__.Matrix.transpose
   3 tests in __main__.det
  11 tests in __main__.diag
   6 tests in __main__.exp
   7 tests in __main__.eye
   2 tests in __main__.gram_schmidt
   5 tests in __main__.innerproduct
   1 tests in __main__.inv
   7 tests in __main__.mat_from_f
   6 tests in __main__.norm2
   6 tests in __main__.norm_square
   4 tests in __main__.ones
   3 tests in __main__.proj
   1 tests in __main__.rank
   3 tests in __main__.vect_const_multi
   6 tests in __main__.zeros
**********************************************************************
4 items had failures:
   1 of   2 in __main__.Matrix.conjugate
   2 of  13 in __main__.Matrix.map
   3 of   5 in __main__.rand_matrix
   3 of   5 in __main__.rand_matrix_float
440 tests in 103 items.
431 passed and 9 failed.
***Test Failed*** 9 failures.
**********************************************************************
File "./matrix.py", line 1597, in __main__.Matrix.conjugate
Failed example:
    A.conjugate()
Expected:
    [[1j, 2j], [2j, 1j]]
Got:
    [[(-0+1j), (-0+2j)], [(-0+2j), (-0+1j)]]
**********************************************************************
File "./matrix.py", line 1466, in __main__.Matrix.map
Failed example:
    A.map(lambda z: '"%s"' % str(z))
Expected:
    [["-1j", "-2j"], ["-2j", "-1j"]]
Got:
    [["(-0-1j)", "(-0-2j)"], ["(-0-2j)", "(-0-1j)"]]
**********************************************************************
File "./matrix.py", line 1468, in __main__.Matrix.map
Failed example:
    A.map(lambda z: "Look: %s" % str(z))
Expected:
    [[Look: -1j, Look: -2j], [Look: -2j, Look: -1j]]
Got:
    [[Look: (-0-1j), Look: (-0-2j)], [Look: (-0-2j), Look: (-0-1j)]]
**********************************************************************
File "./matrix.py", line 2318, in __main__.rand_matrix
Failed example:
    rand_matrix(2, 3)
Expected:
    [[7, 5, -2], [-5, 0, -2]]
Got:
    [[2, 3, -9], [-2, 6, 5]]
**********************************************************************
File "./matrix.py", line 2320, in __main__.rand_matrix
Failed example:
    rand_matrix(3, 2, 40)
Expected:
    [[23, -16], [-2, 7], [33, 0]]
Got:
    [[11, -2], [21, 5], [34, -13]]
**********************************************************************
File "./matrix.py", line 2322, in __main__.rand_matrix
Failed example:
    rand_matrix(4, 4, 100)
Expected:
    [[-44, 51, 24, -50], [82, 97, 62, 81], [-38, 46, 80, 37], [-6, -80, -13, 22]]
Got:
    [[29, -65, -28, -65], [93, -76, 58, -36], [36, 80, 54, -63], [-21, -75, 86, -82]]
**********************************************************************
File "./matrix.py", line 2334, in __main__.rand_matrix_float
Failed example:
    rand_matrix_float(2, 3)
Expected:
    [[6.8884370305, 5.15908805881, -1.58856838338], [-4.82166499414, 0.225494427372, -1.90131725099]]
Got:
    [[6.888437030500963, 5.159088058806049, -1.5885683833831], [-4.821664994140733, 0.22549442737217085, -1.9013172509917133]]
**********************************************************************
File "./matrix.py", line 2336, in __main__.rand_matrix_float
Failed example:
    rand_matrix_float(3, 2, 1)
Expected:
    [[0.56759717807, -0.393374547842], [-0.0468060916953, 0.16676407891], [0.816225770391, 0.00937371163478]]
Got:
    [[0.5675971780695452, -0.3933745478421451], [-0.04680609169528838, 0.1667640789100624], [0.8162257703906703, 0.009373711634780513]]
**********************************************************************
File "./matrix.py", line 2338, in __main__.rand_matrix_float
Failed example:
    rand_matrix_float(4, 4, 20)
Expected:
    [[-8.72648622401, 10.2321681663, 4.73475986701, -9.9797463455], [16.3898502387, 19.3114190415, 12.4086894399, 16.0866380176], [-7.59409722723, 9.19326993041, 15.9535315187, 7.35935727662], [-1.11429138189, -15.9719516773, -2.63312658185, 4.43547893775]]
Got:
    [[-8.726486224011847, 10.232168166288957, 4.734759867013267, -9.979746345502377], [16.389850238729608, 19.311419041506127, 12.40868943986358, 16.08663801758331], [-7.594097227226694, 9.193269930405144, 15.953531518719743, 7.359357276617651], [-1.1142913818914657, -15.971951677265368, -2.6331265818486536, 4.435478937752066]]
**********************************************************************
4 items had failures:
   1 of   2 in __main__.Matrix.conjugate
   2 of  13 in __main__.Matrix.map
   3 of   5 in __main__.rand_matrix
   3 of   5 in __main__.rand_matrix_float
***Test Failed*** 9 failures.

More details about doctest can be found on the Python documentation: 
https://docs.python.org/2/library/doctest.html