def decompose_matrix(matrix):
    """Return sequence of transformations from transformation matrix.

    matrix : array_like
        Non-degenerative homogeneous transformation matrix

    Return tuple of:
        scale : vector of 3 scaling factors
        shear : list of shear factors for x-y, x-z, y-z axes
        angles : list of Euler angles about static x, y, z axes
        translate : translation vector along x, y, z axes
        perspective : perspective partition of matrix

    Raise ValueError if matrix is of wrong type or degenerative.

    >>> T0 = translation_matrix([1, 2, 3])
    >>> scale, shear, angles, trans, persp = decompose_matrix(T0)
    >>> T1 = translation_matrix(trans)
    >>> numpy.allclose(T0, T1)
    True
    >>> S = scale_matrix(0.123)
    >>> scale, shear, angles, trans, persp = decompose_matrix(S)
    >>> scale[0]
    0.123
    >>> R0 = euler_matrix(1, 2, 3)
    >>> scale, shear, angles, trans, persp = decompose_matrix(R0)
    >>> R1 = euler_matrix(*angles)
    >>> numpy.allclose(R0, R1)
    True

    """
    M = numpy.array(matrix, dtype=numpy.float64, copy=True).T
    if abs(M[3, 3]) < _EPS:
        raise ValueError("M[3, 3] is zero")
    M /= M[3, 3]
    P = M.copy()
    P[:, 3] = 0.0, 0.0, 0.0, 1.0
    if not numpy.linalg.det(P):
        raise ValueError("matrix is singular")

    scale = numpy.zeros((3,))
    shear = [0.0, 0.0, 0.0]
    angles = [0.0, 0.0, 0.0]

    if any(abs(M[:3, 3]) > _EPS):
        perspective = numpy.dot(M[:, 3], numpy.linalg.inv(P.T))
        M[:, 3] = 0.0, 0.0, 0.0, 1.0
    else:
        perspective = numpy.array([0.0, 0.0, 0.0, 1.0])

    translate = M[3, :3].copy()
    M[3, :3] = 0.0

    row = M[:3, :3].copy()
    scale[0] = vector_norm(row[0])
    row[0] /= scale[0]
    shear[0] = numpy.dot(row[0], row[1])
    row[1] -= row[0] * shear[0]
    scale[1] = vector_norm(row[1])
    row[1] /= scale[1]
    shear[0] /= scale[1]
    shear[1] = numpy.dot(row[0], row[2])
    row[2] -= row[0] * shear[1]
    shear[2] = numpy.dot(row[1], row[2])
    row[2] -= row[1] * shear[2]
    scale[2] = vector_norm(row[2])
    row[2] /= scale[2]
    shear[1:] /= scale[2]

    if numpy.dot(row[0], numpy.cross(row[1], row[2])) < 0:
        numpy.negative(scale, scale)
        numpy.negative(row, row)

    angles[1] = math.asin(-row[0, 2])
    if math.cos(angles[1]):
        angles[0] = math.atan2(row[1, 2], row[2, 2])
        angles[2] = math.atan2(row[0, 1], row[0, 0])
    else:
        #angles[0] = math.atan2(row[1, 0], row[1, 1])
        angles[0] = math.atan2(-row[2, 1], row[1, 1])
        angles[2] = 0.0

    return scale, shear, angles, translate, perspective
Return sequence of transformations from transformation matrix.

    matrix : array_like
        Non-degenerative homogeneous transformation matrix

    Return tuple of:
        scale : vector of 3 scaling factors
        shear : list of shear factors for x-y, x-z, y-z axes
        angles : list of Euler angles about static x, y, z axes
        translate : translation vector along x, y, z axes
        perspective : perspective partition of matrix

    Raise ValueError if matrix is of wrong type or degenerative.

    >>> T0 = translation_matrix([1, 2, 3])
    >>> scale, shear, angles, trans, persp = decompose_matrix(T0)
    >>> T1 = translation_matrix(trans)
    >>> numpy.allclose(T0, T1)
    True
    >>> S = scale_matrix(0.123)
    >>> scale, shear, angles, trans, persp = decompose_matrix(S)
    >>> scale[0]
    0.123
    >>> R0 = euler_matrix(1, 2, 3)
    >>> scale, shear, angles, trans, persp = decompose_matrix(R0)
    >>> R1 = euler_matrix(*angles)
    >>> numpy.allclose(R0, R1)
    True

    
deploy/helpers/transformations.py