def propagate_1D_fresnel_radius(wavefront, propagation_distance, eta):
"""
1D Fresnel propagator using convolution via Fourier transform
:param wavefront:
:param propagation_distance: propagation distance
:return: a new 1D wavefront object with propagated wavefront
"""
fft_scale = numpy.fft.fftfreq(wavefront.size()) / wavefront.delta()
fft = numpy.fft.fft(wavefront.get_complex_amplitude())
fft *= numpy.exp(1.0j * numpy.pi * wavefront.get_wavelength() *
propagation_distance *
(-fft_scale**2 + eta * fft_scale**2))
H = numpy.fft.ifft(fft)
H *= -1.0j * eta * propagation_distance / wavefront.get_wavelength(
) * numpy.exp(1.0j * numpy.pi / eta / propagation_distance /
wavefront.get_wavelength() * wavefront.get_abscissas()**2)
ifft = numpy.fft.fft(H)
ifft *= numpy.exp(1.0j * numpy.pi / eta / propagation_distance /
wavefront.get_wavelength() *
wavefront.get_abscissas()**2)
return Wavefront1D(
wavefront.get_wavelength(),
ScaledArray.initialize_from_steps(ifft, wavefront.offset(),
wavefront.delta()))
def propagate_1D_integral(wavefront, propagation_distance, detector_abscissas=[None]):
"""
1D Fresnel-Kirchhoff propagator via simplified integral
:param wavefront:
:param propagation_distance: propagation distance
:param detector_abscissas: a numpy array with the anscissas at the image position. If undefined ([None])
it uses the same abscissas present in input wavefront.
:return: a new 1D wavefront object with propagated wavefront
"""
if detector_abscissas[0] == None:
detector_abscissas = wavefront.get_abscissas()
# calculate via outer product, it spreads over a lot of memory, but it is OK for 1D
x1 = numpy.outer(wavefront.get_abscissas(),numpy.ones(detector_abscissas.size))
x2 = numpy.outer(numpy.ones(wavefront.size()),detector_abscissas)
r = numpy.sqrt( numpy.power(x1-x2,2) + numpy.power(propagation_distance,2) )
wavenumber = numpy.pi*2/wavefront.get_wavelength()
distances_matrix = numpy.exp(1.j * wavenumber * r)
fieldComplexAmplitude = numpy.dot(wavefront.get_complex_amplitude(),distances_matrix)
return Wavefront1D(wavefront.get_wavelength(), ScaledArray.initialize_from_steps(fieldComplexAmplitude, \
detector_abscissas[0], detector_abscissas[1]-detector_abscissas[0] ))
def propagator1d_fourier_rescaling(wavefront, propagation_distance, m=1):
wf = wavefront.duplicate() # todo: cambiato da giovanni, controllare
shape = wf.size()
delta = wf.delta()
wavenumber = wf.get_wavenumber()
wavelength = wf.get_wavelength()
fft_scale = numpy.fft.fftfreq(shape, d=delta)
x = wf.get_abscissas()
x_rescaling = wf.get_abscissas() * m
r1sq = x**2 * (1 - m)
r2sq = x_rescaling**2 * ((m - 1) / m)
fsq = (fft_scale**2 / m)
Q1 = wavenumber / 2 / propagation_distance * r1sq
Q2 = numpy.exp(-1.0j * numpy.pi * wavelength * propagation_distance * fsq)
Q3 = numpy.exp(1.0j * wavenumber / 2 / propagation_distance * r2sq)
wf.add_phase_shift(Q1)
fft = numpy.fft.fft(wf.get_complex_amplitude())
ifft = numpy.fft.ifft(fft * Q2) * Q3 / numpy.sqrt(m)
return Wavefront1D(
wf.get_wavelength(),
ScaledArray.initialize_from_steps(ifft, m * wf.offset(),
m * wf.delta()))
def propagate_wavefront(cls,
wavefront,
propagation_distance,
magnification_x=1.0,
magnification_N=1.0):
method = 0
wavenumber = numpy.pi * 2 / wavefront.get_wavelength()
x = wavefront.get_abscissas()
if magnification_N != 1.0:
npoints_exit = int(magnification_N * x.size)
else:
npoints_exit = x.size
detector_abscissas = numpy.linspace(magnification_x * x[0],
magnification_x * x[-1],
npoints_exit)
if method == 0:
# calculate via loop pver detector coordinates
x1 = wavefront.get_abscissas()
x2 = detector_abscissas
fieldComplexAmplitude = numpy.zeros_like(x2, dtype=complex)
for ix, x in enumerate(x2):
r = numpy.sqrt(
numpy.power(x1 - x, 2) +
numpy.power(propagation_distance, 2))
distances_array = numpy.exp(1.j * wavenumber * r)
fieldComplexAmplitude[ix] = (
wavefront.get_complex_amplitude() * distances_array).sum()
elif method == 1:
# calculate via outer product, it spreads over a lot of memory, but it is OK for 1D
x1 = numpy.outer(wavefront.get_abscissas(),
numpy.ones(detector_abscissas.size))
x2 = numpy.outer(numpy.ones(wavefront.size()), detector_abscissas)
r = numpy.sqrt(
numpy.power(x1 - x2, 2) + numpy.power(propagation_distance, 2))
distances_matrix = numpy.exp(1.j * wavenumber * r)
fieldComplexAmplitude = numpy.dot(
wavefront.get_complex_amplitude(), distances_matrix)
wavefront_out = GenericWavefront1D(
wavefront.get_wavelength(),
ScaledArray.initialize_from_steps(
fieldComplexAmplitude, detector_abscissas[0],
detector_abscissas[1] - detector_abscissas[0]))
# added [email protected] 2018-03-23 to conserve energy - TODO: review method!
# wavefront_out.rescale_amplitude( numpy.sqrt(wavefront.get_intensity().sum() /
# wavefront_out.get_intensity().sum()
# / magnification_x))
wavefront_out.rescale_amplitude( (1/numpy.sqrt(1j*wavefront.get_wavelength()*propagation_distance))*(x1[1]-x1[0]) * \
numpy.exp(1j * wavenumber * propagation_distance))
return wavefront_out
def initialize_wavefront_from_steps(cls, x_start=0.0, x_step=0.0, number_of_points=1000, wavelength=1e-10):
return Wavefront1D(
wavelength,
ScaledArray.initialize_from_steps(
np_array=numpy.full(number_of_points, (1.0 + 0.0j), dtype=complex),
initial_scale_value=x_start,
scale_step=x_step,
),
)
def initialize_wavefront_from_arrays(cls, x_array, y_array, wavelength=1e-10):
if x_array.size != y_array.size:
raise Exception("Unmatched shapes for x and y")
return Wavefront1D(
wavelength,
ScaledArray.initialize_from_steps(
np_array=y_array, initial_scale_value=x_array[0], scale_step=numpy.abs(x_array[1] - x_array[0])
),
)
def initialize_wavefront_from_steps(cls,
x_start=0.0,
x_step=0.0,
number_of_points=1000,
wavelength=1e-10):
return Wavefront1D(
wavelength,
ScaledArray.initialize_from_steps(np_array=numpy.full(
number_of_points, (1.0 + 0.0j), dtype=complex),
initial_scale_value=x_start,
scale_step=x_step))
def propagate_1D_integral(wavefront,
propagation_distance,
detector_abscissas=[None],
method=0,
magnification=1.0,
npoints_exit=None):
"""
1D Fresnel-Kirchhoff propagator via integral implemented as sum
:param wavefront:
:param propagation_distance: propagation distance
:param detector_abscissas: a numpy array with the abscissas at the image position. If undefined ([None])
it uses the same abscissas present in input wavefront.
:param method: 0 (default_ makes a loop over detector coordinates, 1: makes matrices (outer products) so
it is more memory hungry.
:param magnification: if detector_abscissas is [None], the detector abscissas range is the input
wavefront range times this magnification factor. Default =1
:param npoints_exit: if detector_abscissas is [None], the number of points of detector abscissas.
Default=None meaning that the same number of points than wavefront are used.
:return: a new 1D wavefront object with propagated wavefront
"""
if detector_abscissas[0] == None:
x = wavefront.get_abscissas()
if npoints_exit is None:
npoints_exit = x.size
detector_abscissas = numpy.linspace(magnification * x[0],
magnification * x[-1],
npoints_exit)
wavenumber = numpy.pi * 2 / wavefront.get_wavelength()
if method == 0:
x1 = wavefront.get_abscissas()
x2 = detector_abscissas
fieldComplexAmplitude = numpy.zeros_like(x2, dtype=complex)
for ix, x in enumerate(x2):
r = numpy.sqrt(
numpy.power(x1 - x, 2) + numpy.power(propagation_distance, 2))
distances_array = numpy.exp(1.j * wavenumber * r)
fieldComplexAmplitude[ix] = (wavefront.get_complex_amplitude() *
distances_array).sum()
elif method == 1:
# calculate via outer product, it spreads over a lot of memory, but it is OK for 1D
x1 = numpy.outer(wavefront.get_abscissas(),
numpy.ones(detector_abscissas.size))
x2 = numpy.outer(numpy.ones(wavefront.size()), detector_abscissas)
r = numpy.sqrt(
numpy.power(x1 - x2, 2) + numpy.power(propagation_distance, 2))
distances_matrix = numpy.exp(1.j * wavenumber * r)
fieldComplexAmplitude = numpy.dot(wavefront.get_complex_amplitude(),
distances_matrix)
return Wavefront1D(wavefront.get_wavelength(), ScaledArray.initialize_from_steps(fieldComplexAmplitude, \
detector_abscissas[0], detector_abscissas[1]-detector_abscissas[0] ))
def propagate_wavefront(cls, wavefront, propagation_distance):
fft_scale = numpy.fft.fftfreq(wavefront.size()) / wavefront.delta()
fft = numpy.fft.fft(wavefront.get_complex_amplitude())
fft *= numpy.exp((-1.0j) * numpy.pi * wavefront.get_wavelength() *
propagation_distance * fft_scale**2)
ifft = numpy.fft.ifft(fft)
return GenericWavefront1D(
wavefront.get_wavelength(),
ScaledArray.initialize_from_steps(ifft, wavefront.offset(),
wavefront.delta()))
def initialize_wavefront_from_steps(cls,
x_start=-1.0,
x_step=0.002,
number_of_points=1000,
wavelength=1e-10,
polarization=Polarization.SIGMA):
sA = ScaledArray.initialize_from_steps(np_array=numpy.full(
number_of_points, (1.0 + 0.0j), dtype=complex),
initial_scale_value=x_start,
scale_step=x_step)
if ((polarization == Polarization.PI)
or (polarization == Polarization.TOTAL)):
sA_pi = ScaledArray.initialize_from_steps(
np_array=numpy.full(number_of_points, (0.0 + 0.0j),
dtype=complex),
initial_scale_value=x_start,
scale_step=x_step)
else:
sA_pi = None
return GenericWavefront1D(wavelength, sA, sA_pi)
def initialize_wavefront_from_arrays(cls,
x_array,
y_array,
y_array_pi=None,
wavelength=1e-10):
if x_array.size != y_array.size:
raise Exception("Unmatched shapes for x and y")
sA = ScaledArray.initialize_from_steps(
np_array=y_array,
initial_scale_value=x_array[0],
scale_step=numpy.abs(x_array[1] - x_array[0]))
if y_array_pi is not None:
sA_pi = ScaledArray.initialize_from_steps(
np_array=y_array_pi,
initial_scale_value=x_array[0],
scale_step=numpy.abs(x_array[1] - x_array[0]))
else:
sA_pi = None
return GenericWavefront1D(wavelength, sA, sA_pi)
def propagate_1D_fresnel(wavefront, propagation_distance):
"""
1D Fresnel propagator using convolution via Fourier transform
:param wavefront:
:param propagation_distance: propagation distance
:return: a new 1D wavefront object with propagated wavefront
"""
fft_scale = numpy.fft.fftfreq(wavefront.size())/wavefront.delta()
fft = numpy.fft.fft(wavefront.get_complex_amplitude())
fft *= numpy.exp((-1.0j) * numpy.pi * wavefront.get_wavelength() * propagation_distance * fft_scale**2)
ifft = numpy.fft.ifft(fft)
return Wavefront1D(wavefront.get_wavelength(), ScaledArray.initialize_from_steps(ifft, wavefront.offset(), wavefront.delta()))
def initialize_wavefront_from_arrays(
cls,
x_array,
y_array,
wavelength=1e-10,
):
if x_array.size != y_array.size:
raise Exception("Unmatched shapes for x and y")
return Wavefront1D(
wavelength,
ScaledArray.initialize_from_steps(
np_array=y_array,
initial_scale_value=x_array[0],
scale_step=numpy.abs(x_array[1] - x_array[0])))
def propagate_1D_fresnel_convolution(wavefront, propagation_distance):
"""
1D Fresnel propagator using direct convolution
:param wavefront:
:param propagation_distance:
:return:
"""
# instead of numpy.convolve, this can be used:
# from scipy.signal import fftconvolve
kernel = numpy.exp(1j*2*numpy.pi/wavefront.get_wavelength() * wavefront.get_abscissas()**2 / 2 / propagation_distance)
kernel *= numpy.exp(1j*2*numpy.pi/wavefront.get_wavelength() * propagation_distance)
kernel /= 1j * wavefront.get_wavelength() * propagation_distance
tmp = numpy.convolve(wavefront.get_complex_amplitude(),kernel,mode='same')
return Wavefront1D(wavefront.get_wavelength(), ScaledArray.initialize_from_steps(tmp, wavefront.offset(), wavefront.delta()))
def propagate_wavefront(cls, wavefront, propagation_distance):
kernel = numpy.exp(1j * 2 * numpy.pi / wavefront.get_wavelength() *
wavefront.get_abscissas()**2 / 2 /
propagation_distance)
kernel *= numpy.exp(1j * 2 * numpy.pi / wavefront.get_wavelength() *
propagation_distance)
kernel /= 1j * wavefront.get_wavelength() * propagation_distance
tmp = numpy.convolve(wavefront.get_complex_amplitude(),
kernel,
mode='same')
wavefront_out = GenericWavefront1D(
wavefront.get_wavelength(),
ScaledArray.initialize_from_steps(tmp, wavefront.offset(),
wavefront.delta()))
# added [email protected] 2018-03-23 to conserve energy - TODO: review method!
wavefront_out.rescale_amplitude(
numpy.sqrt(wavefront.get_intensity().sum() /
wavefront_out.get_intensity().sum()))
return wavefront_out
def propagate_1D_fresnel_convolution(wavefront, propagation_distance):
"""
1D Fresnel propagator using direct convolution
:param wavefront:
:param propagation_distance:
:return:
"""
# instead of numpy.convolve, this can be used:
# from scipy.signal import fftconvolve
kernel = numpy.exp(1j * 2 * numpy.pi / wavefront.get_wavelength() *
wavefront.get_abscissas()**2 / 2 / propagation_distance)
kernel *= numpy.exp(1j * 2 * numpy.pi / wavefront.get_wavelength() *
propagation_distance)
kernel /= 1j * wavefront.get_wavelength() * propagation_distance
tmp = numpy.convolve(wavefront.get_complex_amplitude(),
kernel,
mode='same')
return Wavefront1D(
wavefront.get_wavelength(),
ScaledArray.initialize_from_steps(tmp, wavefront.offset(),
wavefront.delta()))
def propagate_2D(calculation_parameters, input_parameters):
shadow_oe = calculation_parameters.shadow_oe_end
if calculation_parameters.do_ff_z and calculation_parameters.do_ff_x:
global_phase_shift_profile = None
if shadow_oe._oe.F_MOVE == 1 and shadow_oe._oe.X_ROT != 0.0:
if input_parameters.ghy_calcType == 3 or input_parameters.ghy_calcType == 4:
global_phase_shift_profile = calculation_parameters.w_mirr_2D_values
elif input_parameters.ghy_calcType == 2:
global_phase_shift_profile = ScaledMatrix.initialize_from_range(numpy.zeros((3, 3)),
shadow_oe._oe.RWIDX2, shadow_oe._oe.RWIDX1,
shadow_oe._oe.RLEN2, shadow_oe._oe.RLEN1)
for x_index in range(global_phase_shift_profile.size_x()):
global_phase_shift_profile.z_values[x_index, :] += global_phase_shift_profile.get_y_values()*numpy.sin(numpy.radians(-shadow_oe._oe.X_ROT))
elif input_parameters.ghy_calcType == 3 or input_parameters.ghy_calcType == 4:
global_phase_shift_profile = calculation_parameters.w_mirr_2D_values
# only tangential slopes
if input_parameters.ghy_calcType == 3 or input_parameters.ghy_calcType == 4:
rms_slope = hy_findrmsslopefromheight(ScaledArray(np_array=global_phase_shift_profile.z_values[int(global_phase_shift_profile.size_x()/2), :],
scale=global_phase_shift_profile.get_y_values()))
print("Using RMS slope = " + str(rms_slope))
# ------------------------------------------
# far field calculation
# ------------------------------------------
focallength_ff = calculate_focal_length_ff_2D(calculation_parameters.ghy_x_min,
calculation_parameters.ghy_x_max,
calculation_parameters.ghy_z_min,
calculation_parameters.ghy_z_max,
input_parameters.ghy_npeak,
calculation_parameters.gwavelength)
if (input_parameters.ghy_calcType == 3 or input_parameters.ghy_calcType == 4) and rms_slope != 0:
focallength_ff = min(focallength_ff,(calculation_parameters.ghy_z_max-calculation_parameters.ghy_z_min) / 16 / rms_slope ) #xshi changed
elif input_parameters.ghy_calcType == 2 and not global_phase_shift_profile is None:
focallength_ff = min(focallength_ff, input_parameters.ghy_distance*4) #TODO: PATCH to be found with a formula
print("FF: calculated focal length: " + str(focallength_ff))
fftsize_x = int(calculate_fft_size(calculation_parameters.ghy_x_min,
calculation_parameters.ghy_x_max,
calculation_parameters.gwavelength,
focallength_ff,
input_parameters.ghy_fftnpts,
factor=20))
fftsize_z = int(calculate_fft_size(calculation_parameters.ghy_z_min,
calculation_parameters.ghy_z_max,
calculation_parameters.gwavelength,
focallength_ff,
input_parameters.ghy_fftnpts,
factor=20))
print("FF: creating plane wave begin, fftsize_x = " + str(fftsize_x) + ", fftsize_z = " + str(fftsize_z))
wavefront = Wavefront2D.initialize_wavefront_from_range(wavelength=calculation_parameters.gwavelength,
number_of_points=(fftsize_x, fftsize_z),
x_min=calculation_parameters.ghy_x_min,
x_max=calculation_parameters.ghy_x_max,
y_min=calculation_parameters.ghy_z_min,
y_max=calculation_parameters.ghy_z_max)
try:
for i in range(0, len(wavefront.electric_field_array.x_coord)):
for j in range(0, len(wavefront.electric_field_array.y_coord)):
interpolated = calculation_parameters.wIray_2d.interpolate_value(wavefront.electric_field_array.x_coord[i],
wavefront.electric_field_array.y_coord[j])
wavefront.electric_field_array.set_z_value(i, j, numpy.sqrt(0.0 if interpolated < 0 else interpolated))
except IndexError:
raise Exception("Unexpected Error during interpolation: try reduce Number of bins for I(Tangential) histogram")
wavefront.apply_ideal_lens(focallength_ff, focallength_ff)
shadow_oe = calculation_parameters.shadow_oe_end
if input_parameters.ghy_calcType == 3 or \
(input_parameters.ghy_calcType == 2 and not global_phase_shift_profile is None):
print("FF: calculating phase shift due to Height Error Profile")
phase_shifts = numpy.zeros(wavefront.size())
for index in range(0, phase_shifts.shape[0]):
np_array = numpy.zeros(global_phase_shift_profile.shape()[1])
for j in range(0, len(np_array)):
np_array[j] = global_phase_shift_profile.interpolate_value(wavefront.get_coordinate_x()[index], calculation_parameters.w_mirr_2D_values.get_y_value(j))
global_phase_shift_profile_z = ScaledArray.initialize_from_steps(np_array,
global_phase_shift_profile.y_coord[0],
global_phase_shift_profile.y_coord[1] - global_phase_shift_profile.y_coord[0])
phase_shifts[index, :] = get_mirror_phase_shift(wavefront.get_coordinate_y(),
calculation_parameters.gwavelength,
calculation_parameters.wangle_z,
calculation_parameters.wl_z,
global_phase_shift_profile_z)
wavefront.add_phase_shifts(phase_shifts)
elif input_parameters.ghy_calcType == 4:
print("FF: calculating phase shift due to Height Error Profile")
phase_shifts = numpy.zeros(wavefront.size())
for index in range(0, phase_shifts.shape[0]):
global_phase_shift_profile_z = ScaledArray.initialize_from_steps(global_phase_shift_profile.z_values[index, :],
global_phase_shift_profile.y_coord[0],
global_phase_shift_profile.y_coord[1] - global_phase_shift_profile.y_coord[0])
phase_shifts[index, :] = get_grating_phase_shift(wavefront.get_coordinate_y(),
calculation_parameters.gwavelength,
calculation_parameters.wangle_z,
calculation_parameters.wangle_ref_z,
calculation_parameters.wl_z,
global_phase_shift_profile_z)
wavefront.add_phase_shifts(phase_shifts)
elif input_parameters.ghy_calcType == 6:
for w_mirr_2D_values in calculation_parameters.w_mirr_2D_values:
phase_shift = get_crl_phase_shift(w_mirr_2D_values,
input_parameters,
calculation_parameters,
[wavefront.get_coordinate_x(), wavefront.get_coordinate_y()])
wavefront.add_phase_shift(phase_shift)
print("calculated plane wave: begin FF propagation (distance = " + str(focallength_ff) + ")")
propagated_wavefront = propagator2D.propagate_2D_fresnel(wavefront, focallength_ff)
print("dif_zp: begin calculation")
imagesize_x = min(abs(calculation_parameters.ghy_x_max), abs(calculation_parameters.ghy_x_min)) * 2
imagesize_x = min(imagesize_x,
input_parameters.ghy_npeak*2*0.88*calculation_parameters.gwavelength*focallength_ff/abs(calculation_parameters.ghy_x_max-calculation_parameters.ghy_x_min))
# TODO: this is a patch: to be rewritten
if shadow_oe._oe.F_MOVE==1 and not shadow_oe._oe.Y_ROT==0:
imagesize_x = max(imagesize_x, 8*(focallength_ff*numpy.tan(numpy.radians(numpy.abs(shadow_oe._oe.Y_ROT))) + numpy.abs(shadow_oe._oe.OFFX)))
delta_x = propagated_wavefront.delta()[0]
imagenpts_x = int(round(imagesize_x/delta_x/2) * 2 + 1)
imagesize_z = min(abs(calculation_parameters.ghy_z_max), abs(calculation_parameters.ghy_z_min)) * 2
imagesize_z = min(imagesize_z,
input_parameters.ghy_npeak*2*0.88*calculation_parameters.gwavelength*focallength_ff/abs(calculation_parameters.ghy_z_max-calculation_parameters.ghy_z_min))
# TODO: this is a patch: to be rewritten
if shadow_oe._oe.F_MOVE==1 and not shadow_oe._oe.X_ROT==0:
imagesize_z = max(imagesize_z, 8*(focallength_ff*numpy.tan(numpy.radians(numpy.abs(shadow_oe._oe.X_ROT))) + numpy.abs(shadow_oe._oe.OFFZ)))
delta_z = propagated_wavefront.delta()[1]
imagenpts_z = int(round(imagesize_z/delta_z/2) * 2 + 1)
dif_xpzp = ScaledMatrix.initialize_from_range(numpy.ones((imagenpts_x, imagenpts_z)),
min_scale_value_x = -(imagenpts_x - 1) / 2 * delta_x,
max_scale_value_x =(imagenpts_x - 1) / 2 * delta_x,
min_scale_value_y = -(imagenpts_z - 1) / 2 * delta_z,
max_scale_value_y =(imagenpts_z - 1) / 2 * delta_z)
for i in range(0, dif_xpzp.shape()[0]):
for j in range(0, dif_xpzp.shape()[1]):
dif_xpzp.set_z_value(i, j, numpy.absolute(propagated_wavefront.get_interpolated_complex_amplitude(
dif_xpzp.x_coord[i],
dif_xpzp.y_coord[j]))**2
)
dif_xpzp.set_scale_from_range(0,
-(imagenpts_x - 1) / 2 * delta_x / focallength_ff,
(imagenpts_x - 1) / 2 * delta_x / focallength_ff)
dif_xpzp.set_scale_from_range(1,
-(imagenpts_z - 1) / 2 * delta_z / focallength_ff,
(imagenpts_z - 1) / 2 * delta_z / focallength_ff)
calculation_parameters.dif_xpzp = dif_xpzp
def test_ScaledArray(self,do_plot=do_plot):
#
# ScaledArray.initialize + set_scale_from_steps
#
test_array = numpy.arange(15.0, 18.8, 0.2)
print("\nTesting ScaledArray.initialize + set_scale_from_steps...")
scaled_array = ScaledArray.initialize(test_array)
scaled_array.set_scale_from_steps(test_array[0],0.2)
print("Using array: ",test_array)
print("Stored array: ",scaled_array.get_values())
print("Using array: ",test_array)
print("Stored abscissas: ",scaled_array.get_abscissas())
numpy.testing.assert_almost_equal(test_array,scaled_array.get_values(),11)
numpy.testing.assert_almost_equal(test_array,scaled_array.get_abscissas(),11)
self.assertAlmostEqual(0.2,scaled_array.delta(),11)
self.assertAlmostEqual(15.0,scaled_array.offset(),11)
x_in = (18.80,16.22,22.35)
x_good = (18.80,16.22,18.8)
for i,x in enumerate(x_in):
print("interpolated at %3.2f is: %3.2f (must give %3.2f)"%( x,scaled_array.interpolate_value(x), x_good[i] ))
self.assertAlmostEqual(scaled_array.interpolate_value(x), x_good[i], 2)
#
# ScaledArray.initialize + set_scale_from_range ; interpolate vectorized
#
print("\nTesting ScaledArray.initialize + set_scale_from_range ; interpolate vectorized...")
scaled_array = ScaledArray.initialize(test_array)
scaled_array.set_scale_from_range(test_array[0],test_array[-1])
x_in = (18.80,16.22,22.35)
x_good = (18.80,16.22,18.8)
for i,x in enumerate(x_in):
print("interpolated at %3.2f is: %3.2f (must give %3.2f)"%( x,scaled_array.interpolate_value(x), x_good[i] ))
self.assertAlmostEqual(scaled_array.interpolate_value(x), x_good[i], 2)
#
# ScaledArray.initialize_from_steps
#
print("\nTesting ScaledArray.initialize_from_steps...")
scaled_array = ScaledArray.initialize_from_steps(test_array, test_array[0], 0.2)
x_in = (18.80,16.22,22.35)
x_good = (18.80,16.22,18.8)
for i,x in enumerate(x_in):
print("interpolated at %3.2f is: %3.2f (must give %3.2f)"%( x,scaled_array.interpolate_value(x), x_good[i] ))
self.assertAlmostEqual(scaled_array.interpolate_value(x), x_good[i], 2)
#
# ScaledArray.initialize_from_steps
#
print("\nTesting ScaledArray.initialize_from_range...")
scaled_array = ScaledArray.initialize_from_range(test_array,test_array[0], test_array[-1])
x_in = (18.80,16.22,22.35)
x_good = (18.80,16.22,18.8)
for i,x in enumerate(x_in):
print("interpolated at %3.2f is: %3.2f (must give %3.2f)"%( x,scaled_array.interpolate_value(x), x_good[i] ))
self.assertAlmostEqual(scaled_array.interpolate_value(x), x_good[i], 2)
#
# interpolator
#
print("\nTesting interpolator...")
x = numpy.arange(-5.0, 18.8, 3)
y = x**2
scaled_array = ScaledArray.initialize_from_range(y,x[0],x[-1])
print("for interpolation; x=",x)
print("for interpolation; offset, delta:=",scaled_array.offset(),scaled_array.delta())
print("for interpolation; abscissas:=",scaled_array.get_abscissas())
x1 = numpy.concatenate( ( numpy.arange(-6, -4, 0.1) , [0], numpy.arange(11, 20.0, 0.1) ) )
y1 = scaled_array.interpolate_values(x1)
if do_plot:
from srxraylib.plot.gol import plot
plot(x,y,x1,y1,legend=["Data",'Interpolated'],legend_position=[0.4,0.8],
marker=['','o'],linestyle=['-',''],xrange=[-6,21],yrange=[-5,375])
for i in range(len(x1)):
y2 = x1[i]**2
if x1[i] <= x[0]:
y2 = y[0]
if x1[i] >= x[-1]:
y2 = y[-1]
print(" interpolated at x=%g is: %g (expected: %g)"%(x1[i],y1[i],y2))
self.assertAlmostEqual(1e-3*y1[i], 1e-3*y2, 2)
# interpolate on same grid
print("\nTesting interpolation on the same grid...")
y1 = scaled_array.interpolate_values(scaled_array.get_abscissas())
if do_plot:
from srxraylib.plot.gol import plot
plot(scaled_array.get_abscissas(),scaled_array.get_values(),
scaled_array.get_abscissas(),y1,legend=["Data",'Interpolated on same grid'],legend_position=[0.4,0.8],
marker=['','o'],linestyle=['-',''])
numpy.testing.assert_almost_equal(scaled_array.get_values(),y1,5)