Python numpy.identity() 使用实例

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Example 1

def quaternion_matrix(quaternion):
    """Return homogeneous rotation matrix from quaternion.

    >>> R = quaternion_matrix([0.06146124, 0, 0, 0.99810947])
    >>> numpy.allclose(R, rotation_matrix(0.123, (1, 0, 0)))
    True

    """
    q = numpy.array(quaternion[:4], dtype=numpy.float64, copy=True)
    nq = numpy.dot(q, q)
    if nq < _EPS:
        return numpy.identity(4)
    q *= math.sqrt(2.0 / nq)
    q = numpy.outer(q, q)
    return numpy.array((
        (1.0-q[1, 1]-q[2, 2],     q[0, 1]-q[2, 3],     q[0, 2]+q[1, 3], 0.0),
        (    q[0, 1]+q[2, 3], 1.0-q[0, 0]-q[2, 2],     q[1, 2]-q[0, 3], 0.0),
        (    q[0, 2]-q[1, 3],     q[1, 2]+q[0, 3], 1.0-q[0, 0]-q[1, 1], 0.0),
        (                0.0,                 0.0,                 0.0, 1.0)
        ), dtype=numpy.float64) 

Example 2

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.
    >>> 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 

Example 3

def quaternion_matrix(quaternion):
    """Return homogeneous rotation matrix from quaternion.

    >>> M = quaternion_matrix([0.99810947, 0.06146124, 0, 0])
    >>> numpy.allclose(M, rotation_matrix(0.123, [1, 0, 0]))
    True
    >>> M = quaternion_matrix([1, 0, 0, 0])
    >>> numpy.allclose(M, numpy.identity(4))
    True
    >>> M = quaternion_matrix([0, 1, 0, 0])
    >>> numpy.allclose(M, numpy.diag([1, -1, -1, 1]))
    True

    """
    q = numpy.array(quaternion, dtype=numpy.float64, copy=True)
    n = numpy.dot(q, q)
    if n < _EPS:
        return numpy.identity(4)
    q *= math.sqrt(2.0 / n)
    q = numpy.outer(q, q)
    return numpy.array([
        [1.0-q[2, 2]-q[3, 3],     q[1, 2]-q[3, 0],     q[1, 3]+q[2, 0], 0.0],
        [    q[1, 2]+q[3, 0], 1.0-q[1, 1]-q[3, 3],     q[2, 3]-q[1, 0], 0.0],
        [    q[1, 3]-q[2, 0],     q[2, 3]+q[1, 0], 1.0-q[1, 1]-q[2, 2], 0.0],
        [                0.0,                 0.0,                 0.0, 1.0]]) 

Example 4

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 

Example 5

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.
    >>> 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 

Example 6

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]]) 

Example 7

def quaternion_matrix(quaternion):
    """Return homogeneous rotation matrix from quaternion.

    >>> M = quaternion_matrix([0.99810947, 0.06146124, 0, 0])
    >>> numpy.allclose(M, rotation_matrix(0.123, [1, 0, 0]))
    True
    >>> M = quaternion_matrix([1, 0, 0, 0])
    >>> numpy.allclose(M, numpy.identity(4))
    True
    >>> M = quaternion_matrix([0, 1, 0, 0])
    >>> numpy.allclose(M, numpy.diag([1, -1, -1, 1]))
    True

    """
    q = numpy.array(quaternion, dtype=numpy.float64, copy=True)
    n = numpy.dot(q, q)
    if n < _EPS:
        return numpy.identity(4)
    q *= math.sqrt(2.0 / n)
    q = numpy.outer(q, q)
    return numpy.array([
        [1.0-q[2, 2]-q[3, 3],     q[1, 2]-q[3, 0],     q[1, 3]+q[2, 0], 0.0],
        [    q[1, 2]+q[3, 0], 1.0-q[1, 1]-q[3, 3],     q[2, 3]-q[1, 0], 0.0],
        [    q[1, 3]-q[2, 0],     q[2, 3]+q[1, 0], 1.0-q[1, 1]-q[2, 2], 0.0],
        [                0.0,                 0.0,                 0.0, 1.0]]) 

Example 8

def test_basic(self):
        import numpy.linalg as linalg

        A = np.array([[1., 2.], [3., 4.]])
        mA = matrix(A)

        B = np.identity(2)
        for i in range(6):
            assert_(np.allclose((mA ** i).A, B))
            B = np.dot(B, A)

        Ainv = linalg.inv(A)
        B = np.identity(2)
        for i in range(6):
            assert_(np.allclose((mA ** -i).A, B))
            B = np.dot(B, Ainv)

        assert_(np.allclose((mA * mA).A, np.dot(A, A)))
        assert_(np.allclose((mA + mA).A, (A + A)))
        assert_(np.allclose((3*mA).A, (3*A)))

        mA2 = matrix(A)
        mA2 *= 3
        assert_(np.allclose(mA2.A, 3*A)) 

Example 9

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.
    >>> 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 

Example 10

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]]) 

Example 11

def quaternion_matrix(quaternion):
    """Return homogeneous rotation matrix from quaternion.

    >>> M = quaternion_matrix([0.99810947, 0.06146124, 0, 0])
    >>> numpy.allclose(M, rotation_matrix(0.123, [1, 0, 0]))
    True
    >>> M = quaternion_matrix([1, 0, 0, 0])
    >>> numpy.allclose(M, numpy.identity(4))
    True
    >>> M = quaternion_matrix([0, 1, 0, 0])
    >>> numpy.allclose(M, numpy.diag([1, -1, -1, 1]))
    True

    """
    q = numpy.array(quaternion, dtype=numpy.float64, copy=True)
    n = numpy.dot(q, q)
    if n < _EPS:
        return numpy.identity(4)
    q *= math.sqrt(2.0 / n)
    q = numpy.outer(q, q)
    return numpy.array([
        [1.0-q[2, 2]-q[3, 3],     q[1, 2]-q[3, 0],     q[1, 3]+q[2, 0], 0.0],
        [    q[1, 2]+q[3, 0], 1.0-q[1, 1]-q[3, 3],     q[2, 3]-q[1, 0], 0.0],
        [    q[1, 3]-q[2, 0],     q[2, 3]+q[1, 0], 1.0-q[1, 1]-q[2, 2], 0.0],
        [                0.0,                 0.0,                 0.0, 1.0]]) 

Example 12

def svm(x, y):
    """
    classification SVM

    Minimize
    1/2 * w^T w
    subject to
    y_n (w^T x_n + b) >= 1
    """
    weights_total = len(x[0])
    I_n = np.identity(weights_total-1)
    P_int =  np.vstack(([np.zeros(weights_total-1)], I_n))
    zeros = np.array([np.zeros(weights_total)]).T
    P = np.hstack((zeros, P_int))
    q = np.zeros(weights_total)
    G = -1 * vec_to_dia(y).dot(x)
    h = -1 * np.ones(len(y))
    matrix_arg = [ matrix(x) for x in [P,q,G,h] ]
    sol = solvers.qp(*matrix_arg)
    return np.array(sol['x']).flatten() 

Example 13

def lookat(eye, center, up):
    f = normalize(center - eye)
    s = normalize(cross(f, up))
    u = cross(s, f)

    res = identity()
    res[0][0] = s[0]
    res[1][0] = s[1]
    res[2][0] = s[2]
    res[0][1] = u[0]
    res[1][1] = u[1]
    res[2][1] = u[2]
    res[0][2] = -f[0]
    res[1][2] = -f[1]
    res[2][2] = -f[2]
    res[3][0] = -dot(s, eye)
    res[3][1] = -dot(u, eye)
    res[3][2] = -dot(f, eye)
    return res.T 

Example 14

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.
    >>> 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 

Example 15

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]]) 

Example 16

def quaternion_matrix(quaternion):
    """Return homogeneous rotation matrix from quaternion.

    >>> M = quaternion_matrix([0.99810947, 0.06146124, 0, 0])
    >>> numpy.allclose(M, rotation_matrix(0.123, [1, 0, 0]))
    True
    >>> M = quaternion_matrix([1, 0, 0, 0])
    >>> numpy.allclose(M, numpy.identity(4))
    True
    >>> M = quaternion_matrix([0, 1, 0, 0])
    >>> numpy.allclose(M, numpy.diag([1, -1, -1, 1]))
    True

    """
    q = numpy.array(quaternion, dtype=numpy.float64, copy=True)
    n = numpy.dot(q, q)
    if n < _EPS:
        return numpy.identity(4)
    q *= math.sqrt(2.0 / n)
    q = numpy.outer(q, q)
    return numpy.array([
        [1.0-q[2, 2]-q[3, 3],     q[1, 2]-q[3, 0],     q[1, 3]+q[2, 0], 0.0],
        [    q[1, 2]+q[3, 0], 1.0-q[1, 1]-q[3, 3],     q[2, 3]-q[1, 0], 0.0],
        [    q[1, 3]-q[2, 0],     q[2, 3]+q[1, 0], 1.0-q[1, 1]-q[2, 2], 0.0],
        [                0.0,                 0.0,                 0.0, 1.0]]) 

Example 17

def calc_rotation_matrix(q1, q2, ref_q1, ref_q2):
  ref_nv = np.cross(ref_q1, ref_q2) 
  q_nv = np.cross(q1, q2)
  if min(norm(ref_nv), norm(q_nv)) == 0.:  # avoid 0 degree including angle
    return np.identity(3)
  axis = np.cross(ref_nv, q_nv)
  angle = rad2deg(acos(ref_nv.dot(q_nv) / (norm(ref_nv) * norm(q_nv))))
  R1 = axis_angle_to_rotation_matrix(axis, angle)
  rot_ref_q1, rot_ref_q2 = R1.dot(ref_q1), R1.dot(ref_q2)  # rotate ref_q1,2 plane to q1,2 plane

  cos1 = max(min(q1.dot(rot_ref_q1) / (norm(rot_ref_q1) * norm(q1)), 1.), -1.)  # avoid math domain error
  cos2 = max(min(q2.dot(rot_ref_q2) / (norm(rot_ref_q2) * norm(q2)), 1.), -1.)
  angle1 = rad2deg(acos(cos1))
  angle2 = rad2deg(acos(cos2))
  angle = (angle1 + angle2) / 2.
  axis = np.cross(rot_ref_q1, q1)
  R2 = axis_angle_to_rotation_matrix(axis, angle)

  R = R2.dot(R1)
  return R 

Example 18

def __init__(self, posterior, scale, nsims, initials, 
        cov_matrix=None, thinning=2, warm_up_period=True, model_object=None, quiet_progress=False):
        self.posterior = posterior
        self.scale = scale
        self.nsims = (1+warm_up_period)*nsims*thinning
        self.initials = initials
        self.param_no = self.initials.shape[0]
        self.phi = np.zeros([self.nsims, self.param_no])
        self.phi[0] = self.initials # point from which to start the Metropolis-Hasting algorithm
        self.quiet_progress = quiet_progress

        if cov_matrix is None:
            self.cov_matrix = np.identity(self.param_no) * np.abs(self.initials)
        else:
            self.cov_matrix = cov_matrix

        self.thinning = thinning
        self.warm_up_period = warm_up_period

        if model_object is not None:
            self.model = model_object 

Example 19

def _ss_matrices(self, beta):
        """ Creates the state space matrices required

        Parameters
        ----------
        beta : np.array
            Contains untransformed starting values for latent variables

        Returns
        ----------
        T, Z, R, Q, H : np.array
            State space matrices used in KFS algorithm
        """     

        T = np.identity(self.z_no-1)
        H = np.identity(1)*self.latent_variables.z_list[0].prior.transform(beta[0])       
        Z = self.X
        R = np.identity(self.z_no-1)
        
        Q = np.identity(self.z_no-1)
        for i in range(0,self.z_no-1):
            Q[i][i] = self.latent_variables.z_list[i+1].prior.transform(beta[i+1])

        return T, Z, R, Q, H 

Example 20

def _ss_matrices(self,beta):
        """ Creates the state space matrices required

        Parameters
        ----------
        beta : np.array
            Contains untransformed starting values for latent variables

        Returns
        ----------
        T, Z, R, Q, H : np.array
            State space matrices used in KFS algorithm
        """     

        T = np.identity(self.z_no-1)
        H = np.identity(1)*self.latent_variables.z_list[0].prior.transform(beta[0])       
        Z = self.X
        R = np.identity(self.z_no-1)
        
        Q = np.identity(self.z_no-1)
        for i in range(0,self.z_no-1):
            Q[i][i] = self.latent_variables.z_list[i+1].prior.transform(beta[i+1])

        return T, Z, R, Q, H 

Example 21

def _ss_matrices(self,beta):
        """ Creates the state space matrices required

        Parameters
        ----------
        beta : np.array
            Contains untransformed starting values for latent_variables

        Returns
        ----------
        T, Z, R, Q, H : np.array
            State space matrices used in KFS algorithm
        """     

        T = np.identity(1)
        R = np.identity(1)
        Z = np.identity(1)
        H = np.identity(1)*self.latent_variables.z_list[0].prior.transform(beta[0])
        Q = np.identity(1)*self.latent_variables.z_list[1].prior.transform(beta[1])

        return T, Z, R, Q, H 

Example 22

def _ss_matrices(self, beta):
        """ Creates the state space matrices required

        Parameters
        ----------
        beta : np.array
            Contains untransformed starting values for latent variables

        Returns
        ----------
        T, Z, R, Q : np.array
            State space matrices used in KFS algorithm
        """     

        T = np.identity(1)
        R = np.identity(1)
        Z = np.identity(1)
        Q = np.identity(1)*self.latent_variables.z_list[0].prior.transform(beta[0])

        return T, Z, R, Q 

Example 23

def _ss_matrices(self,beta):
        """ Creates the state space matrices required

        Parameters
        ----------
        beta : np.array
            Contains untransformed starting values for latent variables

        Returns
        ----------
        T, Z, R, Q : np.array
            State space matrices used in KFS algorithm
        """     


        T = np.identity(self.state_no)
        Z = self.X
        R = np.identity(self.state_no)
        
        Q = np.identity(self.state_no)
        for i in range(0,self.state_no):
            Q[i][i] = self.latent_variables.z_list[i].prior.transform(beta[i])

        return T, Z, R, Q 

Example 24

def setup_awg_channels(physicalChannels):
    translators = {}
    for chan in physicalChannels:
        translators[chan.instrument] = import_module('QGL.drivers.' + chan.translator)

    data = {awg: translator.get_empty_channel_set()
            for awg, translator in translators.items()}
    for name, awg in data.items():
        for chan in awg.keys():
            awg[chan] = {
                'linkList': [],
                'wfLib': {},
                'correctionT': np.identity(2)
            }
        data[name]['translator'] = translators[name]
        data[name]['seqFileExt'] = translators[name].get_seq_file_extension()
    return data 

Example 25

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 

Example 26

def dexp(v):
	x = np.linalg.norm(v)
	a = trig.sinox(x)
	b = trig.cosox2(x)
	c = trig.sinox3(x)
	I = np.identity(3)
	S = skew(v)
	W = v * v.transpose()
	return a*I + b*S + c*W 

Example 27

def dlog(v):
	x = np.linalg.norm(v)
	y = trig.specialFun4(x)
	z = trig.specialFun2(x)
	I = np.identity(3)
	S = skew(v)
	W = v * v.transpose()
	return y*I - 0.5*S + z*W 

Example 28

def mt(v):
	r = v[0:3]
	t = v[3:6]
	x = np.linalg.norm(r)
	b = trig.cosox2(x)
	c = trig.sinox3(x)
	g = trig.specialFun1(x)
	h = trig.specialFun3(x)
	I = np.identity(3)
	return b*quat.skew(t) + c*(r*t.transpose() + t*r.transpose()) + v3.dot(r,t)*((c - b) * I + g*quat.skew(r) + h*r*r.transpose()) 

Example 29

def get_embeddings(self, *args):
        return np.identity(self.output_size, np.float32) 

Example 30

def fit(self, paths):
        featmat = np.concatenate([self._features(path) for path in paths])
        returns = np.concatenate([path["returns"] for path in paths])
        n_col = featmat.shape[1]
        lamb = 2.0
        self.coeffs = np.linalg.lstsq(featmat.T.dot(featmat) + lamb * np.identity(n_col), featmat.T.dot(returns))[0] 

Example 31

def identity(cls):
        return cls() 

Example 32

def identity(cls):
        return cls()

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

Example 33

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) 

Example 34

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 

Example 35

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 

Example 36

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 

Example 37

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 

Example 38

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)) 

Example 39

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 

Example 40

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) 

Example 41

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)) 

Example 42

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 

Example 43

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 

Example 44

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) 

Example 45

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 

Example 46

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 

Example 47

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 

Example 48

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]]) 

Example 49

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)) 

Example 50

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 
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