10.4. Multiprocessing examples
In this example we will analyze several cases were we can use multiprocessing for accelerating our computations. Some of this cases are implemented in the modules. Other cases are implemented in specific functions.
The cases that we will se include:
Rayleigh-Sommerfed computations in XZ and XYZ modules.
Polychromatic light
Extended sources
Polychromatic and extended sources
Simultaneous simulations, as moving parts
[1]:
import time
from diffractio import degrees, mm, np, num_max_processors, plt, um
from diffractio.scalar_fields_X import (Scalar_field_X,
extended_polychromatic_source,
extended_source_multiprocessing,
polychromatic_multiprocessing)
from diffractio.scalar_masks_X import Scalar_mask_X
from diffractio.scalar_sources_X import Scalar_source_X
from diffractio.utils_multiprocessing import (_pickle_method, _unpickle_method,
execute_multiprocessing)
from multiprocessing import Pool
from diffractio.utils_optics import (gauss_spectrum, lorentz_spectrum,
uniform_spectrum)
from diffractio.scalar_fields_XZ import Scalar_field_XZ
10.4.1. Extended Source
[2]:
x = np.linspace(-500*um, 500*um, 1024 * 8)
wavelength = 0.850*um
num_fuentes = 101
S = 3000*um
z0 = -500*mm
period = 50*um
focal = 5*mm
red = Scalar_mask_X(x, wavelength)
red.ronchi_grating(x0=0*um, period=period, fill_factor=0.5)
lens = Scalar_mask_X(x, wavelength)
lens.lens(x0=0, focal=focal, radius=30*mm)
u1 = Scalar_source_X(x, wavelength)
# posiciones de la fuente
x0s = np.linspace(-S/2, S/2, num_fuentes)
intensities = Scalar_field_X(x, wavelength)
time1 = time.time()
for x0 in x0s:
u1.spherical_wave(A=1, x0=x0, z0=z0, normalize=True)
u2 = u1 * lens * red
u2.RS(z=focal, new_field=False, verbose=False)
intensities.u = intensities.u + abs(u2.u)**2
intensities.u = intensities.u / intensities.u.max()
time_proc = time.time() - time1
print("num_proc: {}, time={}".format(1, time_proc))
intensities.draw(kind='amplitude')
num_proc: 1, time=0.30816149711608887
[3]:
def __experiment_extended_source__(x0):
x = np.linspace(-500*um, 500*um, 1024)
wavelength = 0.850*um
z0 = -500*mm
period = 50*um
focal = 5*mm
red = Scalar_mask_X(x, wavelength)
red.ronchi_grating(x0=0*um, period=period, fill_factor=0.5)
lens = Scalar_mask_X(x, wavelength)
lens.lens(x0=0, focal=focal, radius=30*mm)
u1 = Scalar_source_X(x, wavelength)
u1.spherical_wave(A=1., x0=x0, z0=z0, normalize=True)
u2 = u1 * red * lens
u2.RS(z=focal, new_field=False, verbose=False)
return u2
[4]:
x0s = np.linspace(-1500*um, 1500*um, 101)
x0_central = 0*um
intensity0, u_s0, time_proc0 = extended_source_multiprocessing(
__experiment_extended_source__, x0_central, num_processors=1, verbose=True)
intensity, u_s, time_proc = extended_source_multiprocessing(
__experiment_extended_source__,
x0s,
num_processors=1,
verbose=True)
num_proc: 1, time=0.0010099411010742188
num_proc: 1, time=0.046297311782836914
[5]:
plt.figure()
plt.plot(u_s0.x, intensity0, 'k', lw=2, label='punctual source')
plt.plot(u_s[0].x, intensity, 'r', lw=2, label='extended source')
plt.legend()
plt.ylim(bottom=0)
10.4.2. Polychromatic light sources
[6]:
wavelengths = np.linspace(.3*um, .9*um, 1001)
w_central = wavelengths.mean()
spectrum_gauss = gauss_spectrum(wavelengths=wavelengths,
w_central=w_central,
Dw=0.4,
normalize=True)
[7]:
def __function_polychromatic__(wavelength):
x0 = np.linspace(-75*um, 75*um, 1024 * 8)
t1 = Scalar_mask_X(x0, wavelength)
t1.slit(x0=0, size=100*um)
f1 = Scalar_source_X(x0, wavelength)
f1.gauss_beam(x0=0*um, w0=200*um, z0=0*um, A=1, theta=0*degrees)
u1 = f1 * t1
u1.RS(z=10*um, new_field=False, verbose=False)
return u1
[8]:
time1 = time.time()
intensity_0, u_s0, time_monochromatic_proc_0 = polychromatic_multiprocessing(
__function_polychromatic__, w_central, 1, num_processors=1, verbose=True)
time_proc_0 = time.time() - time1
print("Monochromatic: time={:2.5f}".format(time_proc_0))
Monochromatic: time=0.00492
[9]:
time1 = time.time()
intensity_1, u_s1, time_proc_1 = polychromatic_multiprocessing(
__function_polychromatic__,
wavelengths,
spectrum_gauss,
num_processors=1,
verbose=True)
time_proc1 = time.time() - time1
print("Polychromatic - num_proc: 1, time={}".format(time_proc_1))
num_proc: 1, time=3.5671141147613525
1001
Polychromatic - num_proc: 1, time=3.5671141147613525
[10]:
intensity_n, u_s, time_proc_n = polychromatic_multiprocessing(
__function_polychromatic__,
wavelengths,
spectrum_gauss,
num_processors=1,
verbose=True)
num_proc: 1, time=3.4867842197418213
1001
[11]:
plt.figure()
plt.plot(u_s0.x, intensity_0, 'k', lw=2, label='monochromatic')
plt.plot(u_s0.x, intensity_1, 'b', lw=2, label='polychromatic - 1 proc.')
plt.plot(u_s[0].x,
intensity_n,
'r',
lw=2,
label='polychromatic - {} proc.'.format(num_max_processors))
plt.legend()
plt.text(
0, 0.5, 't0 = {:2.4f} s\nt1 = {:2.4f} s\ntn = {:2.4f} s'.format(
time_proc_0, time_proc_1, time_proc_n))
10.4.3. Simultaneous experiments: moving a grating in a double grating experiment
[12]:
def __experiment_grating_movement__(dict_params):
delta_x = dict_params['delta_x']
period = dict_params['period']
t1 = dict_params['t1']
t2 = dict_params['t2']
t2.ronchi_grating(x0=delta_x, period=period, fill_factor=0.5)
u2 = t1 * t2
return u2
[13]:
def creation_dictionary(deltas_x, period, t1, t2):
# create Parameters: for multiprocessing
dict_Parameters = []
for i, delta_x in enumerate(deltas_x):
dict_Parameters.append(
dict(delta_x=delta_x, period=period, t1=t1, t2=t2))
return dict_Parameters
[14]:
x0 = np.linspace(-400*um, 400*um, 1024 * 2)
wavelength = 0.85*um
period = 50*um
z_talbot = 2 * period**2 / wavelength
z0 = z_talbot/2
delay = 0.001
t1 = Scalar_mask_X(x0, wavelength, info="__experiment_grating_movement__")
t1.ronchi_grating(x0=0*um, period=period, fill_factor=0.5)
t1.RS(z=z0, new_field=False)
t2 = Scalar_mask_X(x0, wavelength, info="__experiment_grating_movement__")
t2.ronchi_grating(x0=0*um, period=period, fill_factor=0.5)
deltas_x = np.linspace(-60*um, 60*um, 128) # 512
num_processors = 1
dict_Parameters = creation_dictionary(deltas_x=deltas_x,
period=period,
t1=t1,
t2=t2)
u_s, time_proc = execute_multiprocessing(__experiment_grating_movement__,
dict_Parameters,
num_processors,
verbose=True)
x = u_s[0].x
Good result: factor 8.01
num_proc: 1, time=0.004861593246459961
[15]:
%matplotlib qt5
[16]:
fig = plt.figure()
ax1 = fig.add_subplot(211)
ax2 = fig.add_subplot(212)
perfil = np.zeros_like(deltas_x)
h1, = ax1.plot(x, np.zeros_like(x), 'k', lw=2)
ax1.set_xlim(x[0], x[-1])
ax1.set_ylim(0, 2)
ax1.set_xlabel(r'$x (\mu m)$')
h2, = ax2.plot(deltas_x, perfil, 'k', lw=2)
ax2.set_xlim(deltas_x[0], deltas_x[-1])
ax2.set_ylim(0, .5)
ax2.set_xlabel(r'$\Delta x (\mu m)$')
incr_frames = 1
for i in range(0, len(deltas_x), incr_frames):
intensidad = abs(u_s[i].u)**2 # sacar fuera
perfil[i] = intensidad.mean()
plt.suptitle(r"$\delta x={:6.2f}\,\mu m$".format(deltas_x[i]), fontsize=18)
h1.set_ydata(intensidad)
h2.set_ydata(perfil)
plt.draw()
plt.pause(0.005)
[17]:
%matplotlib inline
10.4.4. Drawing at several distances
[18]:
def __experiment_double_slit_dictionary__(dict_params):
x0 = dict_params['x0']
wavelength = dict_params['wavelength']
z = dict_params['z']
slit_size = dict_params['slit_size']
separation = dict_params['separation']
t1 = Scalar_mask_X(x0, wavelength)
t1.slit(x0=0, size=20*um)
t1.double_slit(x0=0, size=slit_size, separation=separation)
f1 = Scalar_source_X(x0, wavelength)
f1.gauss_beam(x0=0*um, w0=200*um, z0=0*um, A=1, theta=0*degrees)
u1 = f1 * t1
u1.RS(z, new_field=False, verbose=False)
return u1
[19]:
def creation_dictionary(wavelengths, x0, z, slit_size, separation):
# create Parameters: for multiprocessing
dict_Parameters = []
for i, wavelength in enumerate(wavelengths):
dict_Parameters.append(
dict(x0=x0,
wavelength=wavelength,
z=z,
slit_size=slit_size,
separation=separation))
return dict_Parameters
x0 = np.linspace(-100*um, 100*um, 1024 * 16)
wavelengths = np.linspace(0.3*um, 0.8*um, 101)
spectrum_gauss = gauss_spectrum(wavelengths=wavelengths,
w_central=0.6,
Dw=0.1,
normalize=True)
num_processors = 1
dict_Parameters0 = dict(x0=x0,
wavelength=0.6*um,
z=.05*mm,
slit_size=50*um,
separation=75*um)
dict_Parameters = creation_dictionary(wavelengths=wavelengths,
x0=x0,
z=.05*mm,
slit_size=50*um,
separation=75*um)
[20]:
t1 = time.time()
I0 = __experiment_double_slit_dictionary__(dict_Parameters0)
t2 = time.time()
print("num_proc= 1, time={:2.2}s".format(t2 - t1))
num_proc= 1, time=0.011s
[21]:
I_wavelengths, time_proc = execute_multiprocessing(
__experiment_double_slit_dictionary__,
dict_Parameters,
num_processors,
verbose=False)
print("num_proc= {}, time={:2.2f}s".format(num_processors, time_proc))
num_proc= 1, time=0.65s
[22]:
intensity = np.zeros_like(I_wavelengths[0].x)
for i in range(len(wavelengths)):
intensity = intensity + spectrum_gauss[i] * abs(I_wavelengths[i].u)**2
plt.figure()
plt.plot(x0, abs(I0.u)**2, 'k', lw=2, label='monochromatic')
plt.plot(x0, intensity, 'r', lw=2, label='polychromatic')
plt.title('polychromatic')
plt.legend()
10.4.5. Several independent experiments
[36]:
def __experiment_double_slit_array__(slit_size):
x0 = np.linspace(-75*um, 75*um, 1024 * 32)
wavelength = 0.6328*um
separation = 50*um
z = 100*um
t1 = Scalar_mask_X(x0, wavelength)
t1.slit(x0=0, size=20*um)
t1.double_slit(x0=0, size=slit_size, separation=separation)
f1 = Scalar_source_X(x0, wavelength)
f1.gauss_beam(x0=0*um, w0=200*um, z0=0*um, A=1, theta=0*degrees)
u1 = f1 * t1
u1.RS(z, new_field=False, verbose=False)
return u1
[ ]:
slit_sizes = np.linspace(5*um, 50*um, 20)
num_processors = 1
u_s, time_proc = execute_multiprocessing(__experiment_double_slit_array__,
slit_sizes,
num_processors,
verbose=True)
num_proc: 1, time=0.3028137683868408
[ ]:
slit_sizes = np.linspace(5*um, 50*um, 20)
num_processors = num_max_processors
u_s, time_proc = execute_multiprocessing(__experiment_double_slit_array__,
slit_sizes,
num_processors,
verbose=True)
num_proc: 24, time=0.267017126083374
[26]:
plt.figure()
ax = plt.subplot(111)
for i, slit_size in enumerate(slit_sizes):
ax.plot(u_s[i].x,
abs(u_s[i].u)**2 + 2 * i,
lw=2,
label=r"${:2.2f}\,\mu m$".format(slit_size))
box = ax.get_position()
ax.set_position([box.x0, box.y0, box.width * 0.8, box.height])
# Put a legend to the right of the current axis
ax.legend(fontsize=8,
frameon=False,
loc='center left',
bbox_to_anchor=(1, 0.5))
10.4.6. def test_extended_polychromatic_source(self):
[27]:
x0s = np.linspace(-50*um, 50*um, 21)
wavelengths = np.linspace(.55*um, .65*um, 11)
w_central = wavelengths.mean()
spectrum_gauss = gauss_spectrum(wavelengths=wavelengths,
w_central=w_central,
Dw=0.01,
normalize=True)
[28]:
def __experiment_extended_polychromatic_source__(dict_params):
wavelength = dict_params['wavelength']
x0 = dict_params['x0']
x = np.linspace(-1250*um, 1250*um, 1024 * 8)
periodo = 100*um
z = 5 * periodo**2 / (0.6*um)
z0 = -50*mm
t1 = Scalar_mask_X(x, wavelength)
t1.ronchi_grating(x0=0*um, period=periodo, fill_factor=0.5)
f1 = Scalar_source_X(x, wavelength)
f1.spherical_wave(A=1, x0=x0, z0=z0, normalize=True)
u1 = f1 * t1
u1.RS(z, new_field=False, verbose=False)
return u1
[29]:
u0 = __experiment_extended_polychromatic_source__(
dict(x0=0, wavelength=w_central))
intensity, u_s, time_proc = extended_polychromatic_source(
__experiment_extended_polychromatic_source__,
x0s,
wavelengths,
spectrum_gauss,
num_processors=1,
verbose=True)
num_proc: 1, time=0.6768193244934082
[30]:
plt.figure()
plt.plot(u_s[0].x, abs(u0.u)**2, 'k', lw=1, label='mono')
plt.plot(u_s[0].x, intensity, 'r', lw=2, label='LED')
plt.legend()
10.4.7. Multiprocessing implemented in XZ module
[31]:
x = np.linspace(-350*um, 350*um, 1024 * 8)
z = np.linspace(1*mm, 10*mm, 1024)
wavelength = 0.6238*um
period = 40*um
z_talbot = 2 * period**2 / wavelength
[32]:
u0 = Scalar_source_X(x, wavelength)
u0.plane_wave(A=1)
t = Scalar_mask_X(x, wavelength)
t.ronchi_grating(x0=0*um, period=40*um, fill_factor=0.5)
talbot_effect = Scalar_field_XZ(x, z, wavelength)
talbot_effect.incident_field(u0 * t)
[33]:
t0 = time.time()
talbot_effect.RS(num_processors=1)
t1 = time.time()
t_proc1 = t1 - t0
print(t_proc1, t_proc1 / len(z))
2.8463592529296875 0.002779647707939148
[34]:
t0 = time.time()
talbot_effect.RS(num_processors = 1)
t1 = time.time()
t_procn = t1 - t0
print(t_procn, t_procn / len(z))
2.7334649562835693 0.002669399371370673
[35]:
talbot_effect.draw()
plt.ylim(-250*um, 250*um)
