Python numpy.arccos方法代碼示例

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import arccos [as 別名]
def vector_angle(u, v, direction=None):
    '''
    vector_angle(u, v) yields the angle between the two vectors u and v. The optional argument 
    direction is by default None, which specifies that the smallest possible angle between the
    vectors be reported; if the vectors u and v are 2D vectors and direction parameters True and
    False specify the clockwise or counter-clockwise directions, respectively; if the vectors are
    3D vectors, then direction may be a 3D point that is not in the plane containing u, v, and the
    origin, and it specifies around which direction (u x v or v x u) the the counter-clockwise angle
    from u to v should be reported (the cross product vector that has a positive dot product with
    the direction argument is used as the rotation axis).
    '''
    if direction is None:
        return np.arccos(vector_angle_cos(u, v))
    elif direction is True:
        return np.arctan2(v[1], v[0]) - np.arctan2(u[1], u[0])
    elif direction is False:
        return np.arctan2(u[1], u[0]) - np.arctan2(v[1], v[0])
    else:
        axis1 = normalize(u)
        axis2 = normalize(np.cross(u, v))
        if np.dot(axis2, direction) < 0:
            axis2 = -axis2
        return np.arctan2(np.dot(axis2, v), np.dot(axis1, v)) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import arccos [as 別名]
def arccosine(x, null=(-np.inf, np.inf)):
    '''
    arccosine(x) is equivalent to acos(x) except that it also works on sparse arrays.

    The optional argument null (default, (-numpy.inf, numpy.inf)) may be specified to indicate what
    value(s) should be assigned when x < -1 or x > 1. If only one number is given, then it is used
    for both values; otherwise the first value corresponds to <-1 and the second to >1.  If null is
    None, then an error is raised when invalid values are encountered.
    '''
    if sps.issparse(x): x = x.toarray()
    else:               x = np.asarray(x)
    try:    (nln,nlp) = null
    except Exception: (nln,nlp) = (null,null)
    ii = None if nln is None else np.where(x < -1)
    jj = None if nlp is None else np.where(x > 1)
    if ii: x[ii] = 0
    if jj: x[jj] = 0
    x = np.arccos(x)
    if ii: x[ii] = nln
    if jj: x[jj] = nlp
    return x 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import arccos [as 別名]
def rotate_camera_to_point_at(up_from, lookat_from, up_to, lookat_to):
  inputs = [up_from, lookat_from, up_to, lookat_to]
  for i in range(4):
    inputs[i] = normalize(np.array(inputs[i]).reshape((-1,)))
  up_from, lookat_from, up_to, lookat_to = inputs
  r1 = r_between(lookat_from, lookat_to)

  new_x = np.dot(r1, np.array([1, 0, 0]).reshape((-1, 1))).reshape((-1))
  to_x = normalize(np.cross(lookat_to, up_to))
  angle = np.arccos(np.dot(new_x, to_x))
  if angle > ANGLE_EPS:
    if angle < np.pi - ANGLE_EPS:
      ax = normalize(np.cross(new_x, to_x))
      flip = np.dot(lookat_to, ax)
      if flip > 0:
        r2 = get_r_matrix(lookat_to, angle)
      elif flip < 0:
        r2 = get_r_matrix(lookat_to, -1. * angle)
    else:
      # Angle of rotation is too close to 180 degrees, direction of rotation
      # does not matter.
      r2 = get_r_matrix(lookat_to, angle)
  else:
    r2 = np.eye(3)
  return np.dot(r2, r1) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import arccos [as 別名]
def subspace_disagreement_measure(self, Ps, Pt, Pst):
        """
        Get the best value for the number of subspaces
        For more details, read section 3.4 of the paper.
        **Parameters**
          Ps: Source subspace
          Pt: Target subspace
          Pst: Source + Target subspace
        """

        def compute_angles(A, B):
            _, S, _ = np.linalg.svd(np.dot(A.T, B))
            S[np.where(np.isclose(S, 1, atol=self.eps) == True)[0]] = 1
            return np.arccos(S)

        max_d = min(Ps.shape[1], Pt.shape[1], Pst.shape[1])
        alpha_d = compute_angles(Ps, Pst)
        beta_d = compute_angles(Pt, Pst)
        d = 0.5 * (np.sin(alpha_d) + np.sin(beta_d))
        return np.argmax(d) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import arccos [as 別名]
def inverse_method(self,N,d):
        
        t = np.linspace(1e-3,0.999,N)
        f = np.log( t / (1 - t) )
        f = f/f[0]
        
        psi= np.pi*f
        cosPsi = np.cos(psi)
        sinTheta = ( np.abs(cosPsi) + (1-np.abs(cosPsi))*np.random.rand(len(cosPsi)))
        
        theta = np.arcsin(sinTheta)
        theta = np.pi-theta + (2*theta - np.pi)*np.round(np.random.rand(len(t)))
        cosPhi = cosPsi/sinTheta
        phi = np.arccos(cosPhi)*(-1)**np.round(np.random.rand(len(t)))
        
        coords = SkyCoord(phi*u.rad,(np.pi/2-theta)*u.rad,d*np.ones(len(phi))*u.pc)

        return coords 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import arccos [as 別名]
def make12(b):
    theta1 = numpy.arccos(1/numpy.sqrt(5))
    theta2 = (numpy.pi - theta1) * .5
    r = b/2./numpy.sin(theta1/2)
    rot72 = rotmatz(numpy.pi*2/5)
    s1 = numpy.sin(theta1)
    c1 = numpy.cos(theta1)
    p1 = numpy.array(( s1*r,  0,  c1*r))
    p2 = numpy.array((-s1*r,  0, -c1*r))
    coord = [(  0,  0,    r)]
    for i in range(5):
        coord.append(p1)
        p1 = numpy.dot(p1, rot72)
    for i in range(5):
        coord.append(p2)
        p2 = numpy.dot(p2, rot72)
    coord.append((  0,  0,  -r))
    return numpy.array(coord) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import arccos [as 別名]
def get_uv(self, xyz_vec):
        # Extract lens parameters of interest.
        fov_rad = self.lens.fov_deg * pi / 180
        fov_scale = np.float32(2 * self.lens.radius_px / fov_rad)
        # Normalize the input vector and rotate to match lens reference axes.
        xyz_rot = get_rotation_matrix(self.lens.center_qq) * matrix_norm(xyz_vec)
        # Convert to polar coordinates relative to lens boresight.
        # (In lens coordinates, unit vector's X axis gives boresight angle;
        #  normalize Y/Z to get a planar unit vector for the bearing.)
        # Note: Image +Y maps to 3D +Y, and image +X maps to 3D +Z.
        theta_rad = np.arccos(xyz_rot[0,:])
        proj_vec = matrix_norm(np.concatenate((xyz_rot[2,:], xyz_rot[1,:])))
        # Fisheye lens maps 3D angle to focal-plane radius.
        # TODO: Do we need a better model for lens distortion?
        rad_px = theta_rad * fov_scale
        # Convert back to focal-plane rectangular coordinates.
        uv = np.multiply(rad_px, proj_vec) + self.lens.center_px
        return np.asarray(uv + 0.5, dtype=int)

    # Given an 2xN array of UV pixel coordinates, check if each pixel is
    # within the fisheye field of view. Returns N-element boolean mask. 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import arccos [as 別名]
def test_both_limit_angle_inactive(self, optimization_variables_avg):
        l, Q, A = optimization_variables_avg
        Q_in = 5e1 * np.eye(len(l))
        max_angle = 45
        m = 2e-3
        m1 = 4e-3
        f = .02
        x = optimization_methods.optimize_focality(l, Q, f,
                                                   max_el_current=m,
                                                   max_total_current=m1,
                                                   Qin=Q_in,
                                                   max_angle=max_angle)
        x_sp = optimize_focality(
            l, Q, f, max_el_current=m, max_total_current=m1,
            Qin=Q_in, max_angle=max_angle)

        assert np.linalg.norm(x, 1) <= 2 * m1 + 1e-4
        assert np.all(np.abs(x) <= m + 1e-4)
        assert np.isclose(np.sum(x), 0)
        assert np.isclose(l.dot(x), f)
        assert np.arccos(l.dot(x) / np.sqrt(x.dot(Q_in).dot(x))) <= np.deg2rad(max_angle)
        assert np.allclose(x.dot(Q.dot(x)), x_sp.dot(Q.dot(x_sp)), rtol=1e-4, atol=1e-5) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import arccos [as 別名]
def test_both_limit_angle_limit(self, optimization_variables_avg):
        l, Q, A = optimization_variables_avg
        Q_in = 5e1 * np.eye(len(l))
        max_angle = 25
        m = 2e-3
        m1 = 4e-3
        f = .02
        x = optimization_methods.optimize_focality(l, Q, f,
                                                   max_el_current=m,
                                                   max_total_current=m1,
                                                   Qin=Q_in,
                                                   max_angle=max_angle)
        x_sp = optimize_focality(
            l, Q, f, max_el_current=m, max_total_current=m1,
            Qin=Q_in, max_angle=max_angle)
        assert np.linalg.norm(x, 1) <= 2 * m1 + 1e-4
        assert np.all(np.abs(x) <= m + 1e-4)
        assert np.isclose(np.sum(x), 0)
        assert np.isclose(l.dot(x), f)
        assert np.arccos(l.dot(x) / np.sqrt(x.dot(Q_in).dot(x))) <= np.deg2rad(max_angle)
        assert np.allclose(x.dot(Q.dot(x)), x_sp.dot(Q.dot(x_sp)), rtol=1e-4, atol=1e-5) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import arccos [as 別名]
def test_both_limit_angle_Q_iteration(self, optimization_variables_avg_QCQP):
        l, Q, A, Q_in = optimization_variables_avg_QCQP
        # l, Q, A = optimization_variables_avg
        # Q_in = 6 * np.eye(len(l)) + np.outer(l, l)
        max_angle = 20
        m = 2e-3
        m1 = 4e-3
        f = .01
        x = optimization_methods.optimize_focality(l, Q, f,
                                                   max_el_current=m,
                                                   max_total_current=m1,
                                                   Qin=Q_in,
                                                   max_angle=max_angle)
        x_sp = optimize_focality(
            l, Q, f, max_el_current=m, max_total_current=m1,
            Qin=Q_in, max_angle=max_angle)
        assert np.linalg.norm(x, 1) <= 2 * m1 + 1e-4
        assert np.all(np.abs(x) <= m + 1e-4)
        assert np.isclose(np.sum(x), 0)
        assert np.isclose(l.dot(x), f)
        assert np.arccos(l.dot(x) / np.sqrt(x.dot(Q_in).dot(x))) <= np.deg2rad(max_angle)
        assert np.allclose(x.dot(Q.dot(x)), x_sp.dot(Q.dot(x_sp)), rtol=1e-4, atol=1e-5) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import arccos [as 別名]
def test_both_limit_angle_infeasible_field(self, optimization_variables_avg_QCQP):
        l, Q, A, Q_in = optimization_variables_avg_QCQP
        max_angle = 15
        m = 2e-3
        m1 = 4e-3
        f = 2
        x = optimization_methods.optimize_focality(l, Q, f,
                                                   max_el_current=m,
                                                   max_total_current=m1,
                                                   Qin=Q_in,
                                                   max_angle=max_angle)

        assert np.linalg.norm(x, 1) <= 2 * m1 + 1e-4
        assert np.all(np.abs(x) <= m + 1e-4)
        assert np.isclose(np.sum(x), 0)
        assert np.arccos(l.dot(x) / np.sqrt(x.dot(Q_in).dot(x))) <= np.deg2rad(max_angle) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import arccos [as 別名]
def test_limit_nr_angle(seld, optimization_variables_avg_QCQP):
        l, Q, A, Q_in = optimization_variables_avg_QCQP
        max_angle = 15
        m = 2e-3
        m1 = 4e-3
        f = 2
        n = 4
        x = optimization_methods.optimize_focality(l, Q, f,
                                                   max_el_current=m,
                                                   max_total_current=m1,
                                                   Qin=Q_in,
                                                   max_angle=max_angle,
                                                   max_active_electrodes=n)

        assert np.linalg.norm(x, 1) <= 2 * m1 + 1e-4
        assert np.all(np.abs(x) <= m + 1e-4)
        assert np.isclose(np.sum(x), 0)
        assert np.linalg.norm(x, 0) <= n
        assert np.arccos(l.dot(x) / np.sqrt(x.dot(Q_in).dot(x))) <= np.deg2rad(max_angle) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import arccos [as 別名]
def test_limit_nr_angle_change_Q(seld, optimization_variables_avg_QCQP):
        l, Q, A, Q_in = optimization_variables_avg_QCQP
        max_angle = 15
        m = 2e-3
        m1 = 4e-3
        f = .01
        n = 4
        x = optimization_methods.optimize_focality(l, Q, f,
                                                   max_el_current=m,
                                                   max_total_current=m1,
                                                   Qin=Q_in,
                                                   max_angle=max_angle,
                                                   max_active_electrodes=n)

        assert np.linalg.norm(x, 1) <= 2 * m1 + 1e-4
        assert np.all(np.abs(x) <= m + 1e-4)
        assert np.isclose(np.sum(x), 0)
        assert np.linalg.norm(x, 0) <= n
        assert np.arccos(l.dot(x) / np.sqrt(x.dot(Q_in).dot(x))) <= np.deg2rad(max_angle) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import arccos [as 別名]
def model_model_angles_btwn_axes(A, B, mxBasis):  # Note: default 'gm' basis
    """ Angle between the rotation axes of A and B (1-qubit gates)"""
    decomp = _tools.decompose_gate_matrix(A)
    decomp2 = _tools.decompose_gate_matrix(B)
    axisOfRotn = decomp.get('axis of rotation', None)
    rotnAngle = decomp.get('pi rotations', 'X')
    axisOfRotn2 = decomp2.get('axis of rotation', None)
    rotnAngle2 = decomp2.get('pi rotations', 'X')

    if rotnAngle == 'X' or abs(rotnAngle) < 1e-4 or \
       rotnAngle2 == 'X' or abs(rotnAngle2) < 1e-4:
        return _np.nan

    if axisOfRotn is None or axisOfRotn2 is None:
        return _np.nan

    real_dot = _np.clip(_np.real(_np.dot(axisOfRotn, axisOfRotn2)), -1.0, 1.0)
    return _np.arccos(abs(real_dot)) / _np.pi
    #Note: abs() allows axis to be off by 180 degrees -- if showing *angle* as
    #      well, must flip sign of angle of rotation if you allow axis to
    #      "reverse" by 180 degrees. 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import arccos [as 別名]
def axisangle_from_rotm(R):
  # logarithm of rotation matrix
  # R = R.reshape(-1,3,3)
  # tr = np.trace(R, axis1=1, axis2=2)
  # phi = np.arccos(np.clip((tr - 1) / 2, -1, 1))
  # scale = np.zeros_like(phi)
  # div = 2 * np.sin(phi)
  # np.divide(phi, div, out=scale, where=np.abs(div) > 1e-6)
  # A = (R - R.transpose(0,2,1)) * scale.reshape(-1,1,1)
  # aa = np.stack((A[:,2,1], A[:,0,2], A[:,1,0]), axis=1)
  # return aa.squeeze()
  R = R.reshape(-1,3,3)
  omega = np.empty((R.shape[0], 3), dtype=R.dtype)
  omega[:,0] = R[:,2,1] - R[:,1,2]
  omega[:,1] = R[:,0,2] - R[:,2,0]
  omega[:,2] = R[:,1,0] - R[:,0,1]
  r = np.linalg.norm(omega, axis=1).reshape(-1,1)
  t = np.trace(R, axis1=1, axis2=2).reshape(-1,1)
  omega = np.arctan2(r, t-1) * omega
  aa = np.zeros_like(omega)
  np.divide(omega, r, out=aa, where=r != 0)
  return aa.squeeze()