def find_elem_m66(elem, orbit=None, **kwargs):
"""
Numerically find the 6x6 transfer matrix of a single element
INPUT
elem AT element
KEYWORDS
orbit=None closed orbit at the entrance of the element,
default: 0.0
XYStep=6.055e-6 transverse step for numerical computation
DPStep=6.055e-6 longitudinal step for numerical computation
OUTPUT
m66 (6, 6) transfer matrix
"""
xy_step = kwargs.pop('XYStep', XYDEFSTEP)
dp_step = kwargs.pop('DPStep', DPSTEP)
if orbit is None:
orbit = numpy.zeros((6, ))
# Construct matrix of plus and minus deltas
scaling = numpy.array(
[xy_step, xy_step, xy_step, xy_step, dp_step, dp_step])
dg = numpy.asfortranarray(0.5 * numpy.diag(scaling))
dmat = numpy.concatenate((dg, -dg), axis=1)
in_mat = orbit.reshape(6, 1) + dmat
element_pass(elem, in_mat)
m66 = (in_mat[:, :6] - in_mat[:, 6:]) / scaling.reshape((1, 6))
return m66
def find_elem_m66(elem, orbit=None, **kwargs):
"""
Numerically find the 6x6 transfer matrix of a single element
INPUT
elem AT element
KEYWORDS
orbit=None closed orbit at the entrance of the element,
default: 0.0
XYStep=1.e-8 transverse step for numerical computation
OUTPUT
m66 (6, 6) transfer matrix
"""
xy_step = kwargs.pop('XYStep', DConstant.XYStep)
if orbit is None:
orbit = numpy.zeros((6,))
# Construct matrix of plus and minus deltas
# scaling = 2*xy_step*numpy.array([1.0, 0.1, 1.0, 0.1, 1.0, 1.0])
scaling = xy_step * numpy.array([1.0, 1.0, 1.0, 1.0, 1.0, 1.0])
dg = numpy.asfortranarray(0.5 * numpy.diag(scaling))
dmat = numpy.concatenate((dg, -dg), axis=1)
in_mat = orbit.reshape(6, 1) + dmat
element_pass(elem, in_mat)
m66 = (in_mat[:, :6] - in_mat[:, 6:]) / scaling
return m66
def test_exact_hamiltonian_pass_with_dls_dipole(rin):
bend = elements.Multipole('rb', 0.15, [0, 0, 0, 0],
[-0.0116333, 3.786786, 0, 0])
bend.Type = 1
bend.PassMethod = 'ExactHamiltonianPass'
bend.BendingAngle = -0.001745
bend.Energy = 3.5e9
bend.MaxOrder = 3
element_pass(bend, rin)
# Results from Matlab
expected = numpy.array([9.23965e-9, 1.22319e-5, 0, 0, 0,
-4.8100e-10]).reshape(6, 1)
numpy.testing.assert_allclose(rin, expected, rtol=1e-5, atol=1e-6)
def test_pydrift():
pydrift = elements.Drift('drift', 1.0, PassMethod='pyDriftPass')
cdrift = elements.Drift('drift', 1.0, PassMethod='DriftPass')
pyout = element_pass(pydrift, numpy.zeros(6) + 1.0e-6)
cout = element_pass(cdrift, numpy.zeros(6) + 1.0e-6)
numpy.testing.assert_equal(pyout, cout)
shift_elem(pydrift, 1.0e-3, 1.0e-3)
shift_elem(cdrift, 1.0e-3, 1.0e-3)
pyout = element_pass(pydrift, numpy.zeros(6) + 1.0e-6)
cout = element_pass(cdrift, numpy.zeros(6) + 1.0e-6)
numpy.testing.assert_equal(pyout, cout)
tilt_elem(pydrift, 1.0e-3, 1.0e-3)
tilt_elem(cdrift, 1.0e-3, 1.0e-3)
pyout = element_pass(pydrift, numpy.zeros(6) + 1.0e-6)
cout = element_pass(cdrift, numpy.zeros(6) + 1.0e-6)
numpy.testing.assert_equal(pyout, cout)
# Multiple particles
pyout = element_pass(pydrift, numpy.zeros((6, 2)) + 1.0e-6)
cout = element_pass(cdrift, numpy.zeros((6, 2)) + 1.0e-6)
numpy.testing.assert_equal(pyout, cout)
def test_bndstrmpole_symplectic_4_pass(rin):
bend = elements.Dipole('b', 1.0)
bend.PassMethod = 'BndStrMPoleSymplectic4Pass'
element_pass(bend, rin)
def test_gwig_symplectic_pass(rin, passmethod):
# Parameters copied from one of the Diamond wigglers.
wiggler = elements.Wiggler('w', 1.15, 0.05, 0.8, 3e9)
wiggler.PassMethod = passmethod
element_pass(wiggler, rin)
def test_exact_hamiltonian_pass(rin):
drift = elements.Multipole('m1', 1, [0, 0, 0, 0], [0, 0, 0, 0])
drift.Type = 0
drift.PassMethod = 'ExactHamiltonianPass'
drift.BendingAngle = 0
element_pass(drift, rin)
