python类identity()的实例源码

def identity(cls):
        return cls()

def identity(cls):
        return cls()


###############################################################################

def identity_matrix():
    """Return 4x4 identity/unit matrix.

    >>> I = identity_matrix()
    >>> numpy.allclose(I, numpy.dot(I, I))
    True
    >>> numpy.sum(I), numpy.trace(I)
    (4.0, 4.0)
    >>> numpy.allclose(I, numpy.identity(4, dtype=numpy.float64))
    True

    """
    return numpy.identity(4, dtype=numpy.float64)

def translation_matrix(direction):
    """Return matrix to translate by direction vector.

    >>> v = numpy.random.random(3) - 0.5
    >>> numpy.allclose(v, translation_matrix(v)[:3, 3])
    True

    """
    M = numpy.identity(4)
    M[:3, 3] = direction[:3]
    return M

def reflection_matrix(point, normal):
    """Return matrix to mirror at plane defined by point and normal vector.

    >>> v0 = numpy.random.random(4) - 0.5
    >>> v0[3] = 1.0
    >>> v1 = numpy.random.random(3) - 0.5
    >>> R = reflection_matrix(v0, v1)
    >>> numpy.allclose(2., numpy.trace(R))
    True
    >>> numpy.allclose(v0, numpy.dot(R, v0))
    True
    >>> v2 = v0.copy()
    >>> v2[:3] += v1
    >>> v3 = v0.copy()
    >>> v2[:3] -= v1
    >>> numpy.allclose(v2, numpy.dot(R, v3))
    True

    """
    normal = unit_vector(normal[:3])
    M = numpy.identity(4)
    M[:3, :3] -= 2.0 * numpy.outer(normal, normal)
    M[:3, 3] = (2.0 * numpy.dot(point[:3], normal)) * normal
    return M

def scale_matrix(factor, origin=None, direction=None):
    """Return matrix to scale by factor around origin in direction.

    Use factor -1 for point symmetry.

    >>> v = (numpy.random.rand(4, 5) - 0.5) * 20.0
    >>> v[3] = 1.0
    >>> S = scale_matrix(-1.234)
    >>> numpy.allclose(numpy.dot(S, v)[:3], -1.234*v[:3])
    True
    >>> factor = random.random() * 10 - 5
    >>> origin = numpy.random.random(3) - 0.5
    >>> direct = numpy.random.random(3) - 0.5
    >>> S = scale_matrix(factor, origin)
    >>> S = scale_matrix(factor, origin, direct)

    """
    if direction is None:
        # uniform scaling
        M = numpy.array(((factor, 0.0,    0.0,    0.0),
                         (0.0,    factor, 0.0,    0.0),
                         (0.0,    0.0,    factor, 0.0),
                         (0.0,    0.0,    0.0,    1.0)), dtype=numpy.float64)
        if origin is not None:
            M[:3, 3] = origin[:3]
            M[:3, 3] *= 1.0 - factor
    else:
        # nonuniform scaling
        direction = unit_vector(direction[:3])
        factor = 1.0 - factor
        M = numpy.identity(4)
        M[:3, :3] -= factor * numpy.outer(direction, direction)
        if origin is not None:
            M[:3, 3] = (factor * numpy.dot(origin[:3], direction)) * direction
    return M

def shear_matrix(angle, direction, point, normal):
    """Return matrix to shear by angle along direction vector on shear plane.

    The shear plane is defined by a point and normal vector. The direction
    vector must be orthogonal to the plane's normal vector.

    A point P is transformed by the shear matrix into P" such that
    the vector P-P" is parallel to the direction vector and its extent is
    given by the angle of P-P'-P", where P' is the orthogonal projection
    of P onto the shear plane.

    >>> angle = (random.random() - 0.5) * 4*math.pi
    >>> direct = numpy.random.random(3) - 0.5
    >>> point = numpy.random.random(3) - 0.5
    >>> normal = numpy.cross(direct, numpy.random.random(3))
    >>> S = shear_matrix(angle, direct, point, normal)
    >>> numpy.allclose(1.0, numpy.linalg.det(S))
    True

    """
    normal = unit_vector(normal[:3])
    direction = unit_vector(direction[:3])
    if abs(numpy.dot(normal, direction)) > 1e-6:
        raise ValueError("direction and normal vectors are not orthogonal")
    angle = math.tan(angle)
    M = numpy.identity(4)
    M[:3, :3] += angle * numpy.outer(direction, normal)
    M[:3, 3] = -angle * numpy.dot(point[:3], normal) * direction
    return M

def random_rotation_matrix(rand=None):
    """Return uniform random rotation matrix.

    rnd: array like
        Three independent random variables that are uniformly distributed
        between 0 and 1 for each returned quaternion.

    >>> R = random_rotation_matrix()
    >>> numpy.allclose(numpy.dot(R.T, R), numpy.identity(4))
    True

    """
    return quaternion_matrix(random_quaternion(rand))

def concatenate_matrices(*matrices):
    """Return concatenation of series of transformation matrices.

    >>> M = numpy.random.rand(16).reshape((4, 4)) - 0.5
    >>> numpy.allclose(M, concatenate_matrices(M))
    True
    >>> numpy.allclose(numpy.dot(M, M.T), concatenate_matrices(M, M.T))
    True

    """
    M = numpy.identity(4)
    for i in matrices:
        M = numpy.dot(M, i)
    return M

def is_same_transform(matrix0, matrix1):
    """Return True if two matrices perform same transformation.

    >>> is_same_transform(numpy.identity(4), numpy.identity(4))
    True
    >>> is_same_transform(numpy.identity(4), random_rotation_matrix())
    False

    """
    matrix0 = numpy.array(matrix0, dtype=numpy.float64, copy=True)
    matrix0 /= matrix0[3, 3]
    matrix1 = numpy.array(matrix1, dtype=numpy.float64, copy=True)
    matrix1 /= matrix1[3, 3]
    return numpy.allclose(matrix0, matrix1)

def _init_action_model(self, rand_init=True):
        '''
        Summary:
            Initializes model parameters
        '''
        self.model = {'act': {}, 'act_inv': {}, 'theta': {}, 'b': {}}
        for action_id in xrange(len(self.actions)):
            self.model['act'][action_id] = np.identity(self.context_size)
            self.model['act_inv'][action_id] = np.identity(self.context_size)
            if rand_init:
                self.model['theta'][action_id] = np.random.random((self.context_size, 1))
            else:
                self.model['theta'][action_id] = np.zeros((self.context_size, 1))
            self.model['b'][action_id] = np.zeros((self.context_size,1))

def img_affine_aug_pipeline_2d(img, op_str='rts', rotate_angle_range=5, translate_range=3, shear_range=3, random_mode=True, probability=0.5):
    if random_mode:
        if random.random() < 0.5:
            return img

    mat = np.identity(3)
    for op in op_str:
        if op == 'r':
            rad = math.radian(((random.random() * 2) - 1) * rotate_angle_range)
            cos = math.cos(rad)
            sin = math.sin(rad)
            rot_mat = np.identity(3)
            rot_mat[0][0] = cos
            rot_mat[0][1] = sin
            rot_mat[1][0] = -sin
            rot_mat[1][1] = cos
            mat = np.dot(mat, rot_mat)
        elif op == 't':
            dx = ((random.random() * 2) - 1) * translate_range
            dy = ((random.random() * 2) - 1) * translate_range
            shift_mat = np.identity(3)
            shift_mat[0][2] = dx
            shift_mat[1][2] = dy
            mat = np.dot(mat, shift_mat)
        elif op == 's':
            dx = ((random.random() * 2) - 1) * shear_range
            dy = ((random.random() * 2) - 1) * shear_range
            shear_mat = np.identity(3)
            shear_mat[0][1] = dx
            shear_mat[1][0] = dy
            mat = np.dot(mat, shear_mat)
        else:
            continue

    affine_mat = np.array([mat[0], mat[1]])
    return apply_affine(img, affine_mat), affine_mat

def __init__(self, nn, xs, ys, alpha, beta, gamma, width, bc):
        """xs: x-coordinates
           ys: y-coordinates"""

        # load the vertices
        self.vertices = []
        for v in zip(xs, ys):
            self.vertices.append(array(v))
        self.vertices = array(self.vertices)
        self.length = self.vertices.shape[0]
        # boundary condition
        assert bc == 'PBC' or bc == 'OBC'
        self._bc = bc
        # width of snake (determining the sensing region)
        self.widths = np.ones((self.length, 1)) * width
        # for neighbour calculations
        id_ = np.arange(self.length)
        self.less1 = np.roll(id_, +1)
        self.less2 = np.roll(id_, +2)
        self.more1 = np.roll(id_, -1)
        self.more2 = np.roll(id_, -2)
        # implicit time-evolution matrix as in Kass
        self._A = alpha * self._alpha_term() + beta * self._beta_term()
        self._gamma = gamma
        self._inv = np.linalg.inv(self._A + self._gamma * np.identity(self.length))
        # the NN for this snake
        self.nn = nn

def identity_matrix():
    """Return 4x4 identity/unit matrix.

    >>> I = identity_matrix()
    >>> numpy.allclose(I, numpy.dot(I, I))
    True
    >>> numpy.sum(I), numpy.trace(I)
    (4.0, 4.0)
    >>> numpy.allclose(I, numpy.identity(4))
    True

    """
    return numpy.identity(4)

def translation_matrix(direction):
    """Return matrix to translate by direction vector.

    >>> v = numpy.random.random(3) - 0.5
    >>> numpy.allclose(v, translation_matrix(v)[:3, 3])
    True

    """
    M = numpy.identity(4)
    M[:3, 3] = direction[:3]
    return M

def scale_matrix(factor, origin=None, direction=None):
    """Return matrix to scale by factor around origin in direction.

    Use factor -1 for point symmetry.

    >>> v = (numpy.random.rand(4, 5) - 0.5) * 20
    >>> v[3] = 1
    >>> S = scale_matrix(-1.234)
    >>> numpy.allclose(numpy.dot(S, v)[:3], -1.234*v[:3])
    True
    >>> factor = random.random() * 10 - 5
    >>> origin = numpy.random.random(3) - 0.5
    >>> direct = numpy.random.random(3) - 0.5
    >>> S = scale_matrix(factor, origin)
    >>> S = scale_matrix(factor, origin, direct)

    """
    if direction is None:
        # uniform scaling
        M = numpy.diag([factor, factor, factor, 1.0])
        if origin is not None:
            M[:3, 3] = origin[:3]
            M[:3, 3] *= 1.0 - factor
    else:
        # nonuniform scaling
        direction = unit_vector(direction[:3])
        factor = 1.0 - factor
        M = numpy.identity(4)
        M[:3, :3] -= factor * numpy.outer(direction, direction)
        if origin is not None:
            M[:3, 3] = (factor * numpy.dot(origin[:3], direction)) * direction
    return M

def shear_matrix(angle, direction, point, normal):
    """Return matrix to shear by angle along direction vector on shear plane.

    The shear plane is defined by a point and normal vector. The direction
    vector must be orthogonal to the plane's normal vector.

    A point P is transformed by the shear matrix into P" such that
    the vector P-P" is parallel to the direction vector and its extent is
    given by the angle of P-P'-P", where P' is the orthogonal projection
    of P onto the shear plane.

    >>> angle = (random.random() - 0.5) * 4*math.pi
    >>> direct = numpy.random.random(3) - 0.5
    >>> point = numpy.random.random(3) - 0.5
    >>> normal = numpy.cross(direct, numpy.random.random(3))
    >>> S = shear_matrix(angle, direct, point, normal)
    >>> numpy.allclose(1, numpy.linalg.det(S))
    True

    """
    normal = unit_vector(normal[:3])
    direction = unit_vector(direction[:3])
    if abs(numpy.dot(normal, direction)) > 1e-6:
        raise ValueError("direction and normal vectors are not orthogonal")
    angle = math.tan(angle)
    M = numpy.identity(4)
    M[:3, :3] += angle * numpy.outer(direction, normal)
    M[:3, 3] = -angle * numpy.dot(point[:3], normal) * direction
    return M

def orthogonalization_matrix(lengths, angles):
    """Return orthogonalization matrix for crystallographic cell coordinates.

    Angles are expected in degrees.

    The de-orthogonalization matrix is the inverse.

    >>> O = orthogonalization_matrix([10, 10, 10], [90, 90, 90])
    >>> numpy.allclose(O[:3, :3], numpy.identity(3, float) * 10)
    True
    >>> O = orthogonalization_matrix([9.8, 12.0, 15.5], [87.2, 80.7, 69.7])
    >>> numpy.allclose(numpy.sum(O), 43.063229)
    True

    """
    a, b, c = lengths
    angles = numpy.radians(angles)
    sina, sinb, _ = numpy.sin(angles)
    cosa, cosb, cosg = numpy.cos(angles)
    co = (cosa * cosb - cosg) / (sina * sinb)
    return numpy.array([
        [ a*sinb*math.sqrt(1.0-co*co),  0.0,    0.0, 0.0],
        [-a*sinb*co,                    b*sina, 0.0, 0.0],
        [ a*cosb,                       b*cosa, c,   0.0],
        [ 0.0,                          0.0,    0.0, 1.0]])

def random_rotation_matrix(rand=None):
    """Return uniform random rotation matrix.

    rand: array like
        Three independent random variables that are uniformly distributed
        between 0 and 1 for each returned quaternion.

    >>> R = random_rotation_matrix()
    >>> numpy.allclose(numpy.dot(R.T, R), numpy.identity(4))
    True

    """
    return quaternion_matrix(random_quaternion(rand))

def concatenate_matrices(*matrices):
    """Return concatenation of series of transformation matrices.

    >>> M = numpy.random.rand(16).reshape((4, 4)) - 0.5
    >>> numpy.allclose(M, concatenate_matrices(M))
    True
    >>> numpy.allclose(numpy.dot(M, M.T), concatenate_matrices(M, M.T))
    True

    """
    M = numpy.identity(4)
    for i in matrices:
        M = numpy.dot(M, i)
    return M