7.6. Polarimeter field serialization

Import Python libraries

Hide code cell content

import json
import logging
import math
import os

import attrs
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
from ampform_dpd.io import cached
from IPython.display import Markdown
from matplotlib_inline.backend_inline import set_matplotlib_formats
from scipy.interpolate import RegularGridInterpolator, griddata
from tqdm.auto import tqdm

from polarimetry import formulate_polarimetry
from polarimetry.data import (
    create_data_transformer,
    generate_meshgrid_sample,
    generate_phasespace_sample,
)
from polarimetry.io import (
    export_polarimetry_field,
    import_polarimetry_field,
    mute_jax_warnings,
)
from polarimetry.lhcb import load_model_builder, load_model_parameters
from polarimetry.lhcb.particle import load_particles
from polarimetry.plot import use_mpl_latex_fonts

mute_jax_warnings()
set_matplotlib_formats("svg")

model_choice = "Default amplitude model"
model_file = "../../data/model-definitions.yaml"
particles = load_particles("../../data/particle-definitions.yaml")
amplitude_builder = load_model_builder(model_file, particles, model_choice)
imported_parameter_values = load_model_parameters(
    model_file, amplitude_builder.decay, model_choice, particles
)
reference_subsystem = 1
model = amplitude_builder.formulate(reference_subsystem)
model = attrs.evolve(
    model,
    parameter_defaults={**model.parameter_defaults, **imported_parameter_values},
)

NO_LOG = "EXECUTE_NB" in os.environ
if NO_LOG:
    logging.disable(logging.CRITICAL)

Formulate expressions and lambdify

Hide code cell source

polarimetry_exprs = formulate_polarimetry(amplitude_builder, reference_subsystem)
unfolded_exprs = [
    cached.unfold(expr, model.amplitudes)
    for expr in tqdm([model.intensity, *polarimetry_exprs], disable=NO_LOG, leave=False)
]
actual_funcs = [
    cached.lambdify(cached.xreplace(expr, model.parameter_defaults))
    for expr in tqdm(unfolded_exprs, leave=False, desc="Lambdifying", disable=NO_LOG)
]

7.6.1. File size checks

Export do different file formats

Hide code cell source

alpha_x_func = actual_funcs[1]
alpha_x = alpha_x_func(grid_sample).real
df = pd.DataFrame(alpha_x, index=X[0], columns=Y[:, 0])
os.makedirs("export", exist_ok=True)
df.to_json("export/alpha-x-pandas.json")
df.to_json("export/alpha-x-pandas-json.zip", compression={"method": "zip"})
df.to_csv("export/alpha-x-pandas.csv")

df_dict = df.to_dict()
filtered_df_dict = {
    x: {y: v for y, v in row.items() if not math.isnan(v)} for x, row in df_dict.items()
}
with open("export/alpha-x-python.json", "w") as f:
    json.dump(filtered_df_dict, f)

json_dict = dict(
    x=X[0].tolist(),
    y=Y[:, 0].tolist(),
    z=alpha_x.tolist(),
)
with open("export/alpha-x-arrays.json", "w") as f:
    json.dump(json_dict, f, separators=(",", ":"))

File sizes for 100x100 grid:

File type	Size
export/alpha-x-arrays.json	141 kB
export/alpha-x-pandas.json	312 kB
export/alpha-x-python.json	260 kB
export/alpha-x-pandas-json.zip	51 kB
export/alpha-x-pandas.csv	129 kB

7.6.2. Export polarimetry grids

Decided to use the alpha-x-arrays.json format. It can be exported with export_polarimetry_field().

os.makedirs("export", exist_ok=True)
filename = "export/polarimetry-model-0.json"
export_polarimetry_field(
    sigma1=X[0],
    sigma2=Y[:, 0],
    intensity=actual_funcs[0](grid_sample).real,
    alpha_x=actual_funcs[1](grid_sample).real,
    alpha_y=actual_funcs[2](grid_sample).real,
    alpha_z=actual_funcs[3](grid_sample).real,
    filename=filename,
    metadata={"model description": model_choice},
)

Polarimetry grid can be downloaded here: export/polarimetry-model-0.json (540 kB).

7.6.3. Import and interpolate

The arrays in the exported JSON files can be used to create a RegularGridInterpolator for the intensity and for each components of \(\vec\alpha\).

import_polarimetry_field() returns JAX arrays, which are read-only. RegularGridInterpolator requires modifiable arrays, so we convert them to NumPy.

Also note that the values array needs to be transposed!

field_data = import_polarimetry_field("export/polarimetry-model-0.json")
imported_arrays = (
    field_data["intensity"],
    field_data["alpha_x"],
    field_data["alpha_y"],
    field_data["alpha_z"],
)
interpolated_funcs = [
    RegularGridInterpolator(
        points=(
            field_data["m^2_Kpi"],
            field_data["m^2_pK"],
        ),
        values=np.nan_to_num(z).transpose(),
        method="linear",
    )
    for z in imported_arrays
]

This is a function that can compute an interpolated value of each of these observables for a random point on the Dalitz plane.

interpolated_funcs[1]([0.8, 3.6])

array([0.18379986])

Note that RegularGridInterpolator is already in vectorized form, so there is no need to vectorize it.

n_points = 100_000
mini_sample = generate_phasespace_sample(model.decay, n_points, seed=0)
mini_sample = transformer(mini_sample)
x = mini_sample["sigma1"]
y = mini_sample["sigma2"]
z_interpolated = [func((x, y)) for func in tqdm(interpolated_funcs, disable=NO_LOG)]
z_interpolated[0]

array([2165.82154945, 5481.04128781, 6254.96174147, ..., 1369.40657535,
       4456.44114915, 7197.97782088], shape=(100000,))

Show code cell source

Hide code cell source

use_mpl_latex_fonts()
plt.rc("font", size=18)
fig, axes = plt.subplots(
    dpi=200,
    figsize=(15, 11.5),
    gridspec_kw={"width_ratios": [1, 1, 1, 1.2]},
    ncols=4,
    nrows=3,
    sharex=True,
    sharey=True,
)
fig.subplots_adjust(hspace=0.1, wspace=0.03)
fig.suptitle("Comparison interpolated and actual values", y=0.94)
fig.patch.set_facecolor("none")

points = np.transpose([x, y])
for i in tqdm(range(4), disable=NO_LOG, leave=False):
    if i == 0:
        title = "$I$"
        cmap = "viridis"
        clim = None
    else:
        title = Rf"$\alpha_{'xyz'[i - 1]}$"
        cmap = "coolwarm"
        clim = (-1, +1)
    axes[0, i].set_title(title, y=1.03)

    z_actual = actual_funcs[i](mini_sample)
    z_diff = 100 * ((z_interpolated[i] - z_actual) / z_actual).real
    Z_interpolated = griddata(points, z_interpolated[i], (X, Y))
    Z_diff = griddata(points, z_diff, (X, Y))

    mesh = (
        axes[0, i].pcolormesh(
            X, Y, actual_funcs[i](grid_sample).real, cmap=cmap, rasterized=True
        ),
        axes[1, i].pcolormesh(X, Y, Z_interpolated, cmap=cmap, rasterized=True),
        axes[2, i].pcolormesh(
            X, Y, Z_diff, clim=(-100, +100), cmap="coolwarm", rasterized=True
        ),
    )
    if i != 0:
        mesh[0].set_clim(-1, +1)
        mesh[1].set_clim(-1, +1)
    if i == 3:
        c_bar = [fig.colorbar(mesh[j], ax=axes[j, i], pad=0.015) for j in range(3)]
        c_bar[0].ax.set_ylabel("Original distribution", labelpad=3)
        c_bar[1].ax.set_ylabel("Interpolated distribution", labelpad=3)
        c_bar[2].ax.set_ylabel("Difference", labelpad=-20)
        for c in c_bar[:-1]:
            c.ax.set_yticks([-1, 0, +1])
            c.ax.set_yticklabels(["$-1$", "$0$", "$+1$"])
        c_bar[-1].ax.set_yticks([-100, 0, +100])
        c_bar[-1].ax.set_yticklabels([R"$-100\%$", R"$0\%$", R"$+100\%$"])
        axes[0, i].text(
            x=0.96,
            y=0.83,
            s=f"grid size:\n{resolution}x{resolution}",
            fontsize=16,
            horizontalalignment="right",
            transform=axes[0, i].transAxes,
        )
        axes[1, i].text(
            x=0.96,
            y=0.83,
            s=f"phsp size:\n{n_points:,}",
            fontsize=16,
            horizontalalignment="right",
            transform=axes[1, i].transAxes,
        )
plt.show()
plt.close(fig)

W0706 22:30:32.923474    7756 pjrt_executable.cc:642] Assume version compatibility. PjRt-IFRT does not track XLA executable versions.
E0706 22:30:32.926856    7807 cpu_aot_loader.cc:220] Loading XLA:CPU AOT result. Target machine feature +prefer-no-gather is not  supported on the host machine. Machine type used for XLA:CPU compilation doesn't match the machine type for execution. Compile machine features: [+64bit,+adx,+aes,+avx,+avx2,+avx512bf16,+avx512bitalg,+avx512bw,+avx512cd,+avx512dq,+avx512f,+avx512ifma,+avx512vbmi,+avx512vbmi2,+avx512vl,+avx512vnni,+avx512vpopcntdq,+bmi,+bmi2,+clflushopt,+clwb,+clzero,+cmov,+crc32,+cx16,+cx8,+f16c,+fma,+fsgsbase,+fxsr,+gfni,+invpcid,+lzcnt,+mmx,+movbe,+pclmul,+popcnt,+prefer-no-gather,+prefer-no-scatter,+prfchw,+rdpid,+rdpru,+rdrnd,+rdseed,+sahf,+sha,+shstk,+sse,+sse2,+sse3,+sse4.1,+sse4.2,+sse4a,+ssse3,+vaes,+vpclmulqdq,+xsave,+xsavec,+xsaveopt,+xsaves,-amx-avx512,-amx-bf16,-amx-complex,-amx-fp16,-amx-fp8,-amx-int8,-amx-movrs,-amx-tf32,-amx-tile,-avx10.1,-avx10.2,-avx512fp16,-avx512vp2intersect,-avxifma,-avxneconvert,-avxvnni,-avxvnniint16,-avxvnniint8,-ccmp,-cf,-cldemote,-cmpccxadd,-egpr,-enqcmd,-fma4,-hreset,-kl,-lwp,-movdir64b,-movdiri,-movrs,-mwaitx,-ndd,-nf,-pconfig,-pku,-ppx,-prefetchi,-ptwrite,-push2pop2,-raoint,-rtm,-serialize,-sgx,-sha512,-sm3,-sm4,-tbm,-tsxldtrk,-uintr,-usermsr,-waitpkg,-wbnoinvd,-widekl,-xop,-zu] vs host machine features: [prfchw,avx,aes,sahf,pclmul,crc32,xsaves,sse4.1,avx512ifma,xsave,sse4.2,invpcid,64bit,xsavec,avx512vpopcntdq,cmov,avx512cd,movbe,adx,avx2,vpclmulqdq,avx512vl,clflushopt,bmi,sse,gfni,xsaveopt,rdrnd,avx512f,avx512bf16,avx512vnni,cx8,avx512bw,sse3,fsgsbase,clzero,lzcnt,sha,ssse3,cx16,bmi2,fma,popcnt,f16c,avx512bitalg,rdpru,clwb,mmx,sse2,rdseed,avx512vbmi2,rdpid,avx512vbmi,shstk,vaes,fxsr,avx512dq,sse4a]. This could lead to execution errors such as SIGILL.
E0706 22:30:32.926874    7807 cpu_aot_loader.cc:220] Loading XLA:CPU AOT result. Target machine feature +prefer-no-scatter is not  supported on the host machine. Machine type used for XLA:CPU compilation doesn't match the machine type for execution. Compile machine features: [+64bit,+adx,+aes,+avx,+avx2,+avx512bf16,+avx512bitalg,+avx512bw,+avx512cd,+avx512dq,+avx512f,+avx512ifma,+avx512vbmi,+avx512vbmi2,+avx512vl,+avx512vnni,+avx512vpopcntdq,+bmi,+bmi2,+clflushopt,+clwb,+clzero,+cmov,+crc32,+cx16,+cx8,+f16c,+fma,+fsgsbase,+fxsr,+gfni,+invpcid,+lzcnt,+mmx,+movbe,+pclmul,+popcnt,+prefer-no-gather,+prefer-no-scatter,+prfchw,+rdpid,+rdpru,+rdrnd,+rdseed,+sahf,+sha,+shstk,+sse,+sse2,+sse3,+sse4.1,+sse4.2,+sse4a,+ssse3,+vaes,+vpclmulqdq,+xsave,+xsavec,+xsaveopt,+xsaves,-amx-avx512,-amx-bf16,-amx-complex,-amx-fp16,-amx-fp8,-amx-int8,-amx-movrs,-amx-tf32,-amx-tile,-avx10.1,-avx10.2,-avx512fp16,-avx512vp2intersect,-avxifma,-avxneconvert,-avxvnni,-avxvnniint16,-avxvnniint8,-ccmp,-cf,-cldemote,-cmpccxadd,-egpr,-enqcmd,-fma4,-hreset,-kl,-lwp,-movdir64b,-movdiri,-movrs,-mwaitx,-ndd,-nf,-pconfig,-pku,-ppx,-prefetchi,-ptwrite,-push2pop2,-raoint,-rtm,-serialize,-sgx,-sha512,-sm3,-sm4,-tbm,-tsxldtrk,-uintr,-usermsr,-waitpkg,-wbnoinvd,-widekl,-xop,-zu] vs host machine features: [prfchw,avx,aes,sahf,pclmul,crc32,xsaves,sse4.1,avx512ifma,xsave,sse4.2,invpcid,64bit,xsavec,avx512vpopcntdq,cmov,avx512cd,movbe,adx,avx2,vpclmulqdq,avx512vl,clflushopt,bmi,sse,gfni,xsaveopt,rdrnd,avx512f,avx512bf16,avx512vnni,cx8,avx512bw,sse3,fsgsbase,clzero,lzcnt,sha,ssse3,cx16,bmi2,fma,popcnt,f16c,avx512bitalg,rdpru,clwb,mmx,sse2,rdseed,avx512vbmi2,rdpid,avx512vbmi,shstk,vaes,fxsr,avx512dq,sse4a]. This could lead to execution errors such as SIGILL.

W0706 22:30:35.176795    7756 pjrt_executable.cc:642] Assume version compatibility. PjRt-IFRT does not track XLA executable versions.
E0706 22:30:35.181781    7807 cpu_aot_loader.cc:220] Loading XLA:CPU AOT result. Target machine feature +prefer-no-gather is not  supported on the host machine. Machine type used for XLA:CPU compilation doesn't match the machine type for execution. Compile machine features: [+64bit,+adx,+aes,+avx,+avx2,+avx512bf16,+avx512bitalg,+avx512bw,+avx512cd,+avx512dq,+avx512f,+avx512ifma,+avx512vbmi,+avx512vbmi2,+avx512vl,+avx512vnni,+avx512vpopcntdq,+bmi,+bmi2,+clflushopt,+clwb,+clzero,+cmov,+crc32,+cx16,+cx8,+f16c,+fma,+fsgsbase,+fxsr,+gfni,+invpcid,+lzcnt,+mmx,+movbe,+pclmul,+popcnt,+prefer-no-gather,+prefer-no-scatter,+prfchw,+rdpid,+rdpru,+rdrnd,+rdseed,+sahf,+sha,+shstk,+sse,+sse2,+sse3,+sse4.1,+sse4.2,+sse4a,+ssse3,+vaes,+vpclmulqdq,+xsave,+xsavec,+xsaveopt,+xsaves,-amx-avx512,-amx-bf16,-amx-complex,-amx-fp16,-amx-fp8,-amx-int8,-amx-movrs,-amx-tf32,-amx-tile,-avx10.1,-avx10.2,-avx512fp16,-avx512vp2intersect,-avxifma,-avxneconvert,-avxvnni,-avxvnniint16,-avxvnniint8,-ccmp,-cf,-cldemote,-cmpccxadd,-egpr,-enqcmd,-fma4,-hreset,-kl,-lwp,-movdir64b,-movdiri,-movrs,-mwaitx,-ndd,-nf,-pconfig,-pku,-ppx,-prefetchi,-ptwrite,-push2pop2,-raoint,-rtm,-serialize,-sgx,-sha512,-sm3,-sm4,-tbm,-tsxldtrk,-uintr,-usermsr,-waitpkg,-wbnoinvd,-widekl,-xop,-zu] vs host machine features: [prfchw,avx,aes,sahf,pclmul,crc32,xsaves,sse4.1,avx512ifma,xsave,sse4.2,invpcid,64bit,xsavec,avx512vpopcntdq,cmov,avx512cd,movbe,adx,avx2,vpclmulqdq,avx512vl,clflushopt,bmi,sse,gfni,xsaveopt,rdrnd,avx512f,avx512bf16,avx512vnni,cx8,avx512bw,sse3,fsgsbase,clzero,lzcnt,sha,ssse3,cx16,bmi2,fma,popcnt,f16c,avx512bitalg,rdpru,clwb,mmx,sse2,rdseed,avx512vbmi2,rdpid,avx512vbmi,shstk,vaes,fxsr,avx512dq,sse4a]. This could lead to execution errors such as SIGILL.
E0706 22:30:35.181810    7807 cpu_aot_loader.cc:220] Loading XLA:CPU AOT result. Target machine feature +prefer-no-scatter is not  supported on the host machine. Machine type used for XLA:CPU compilation doesn't match the machine type for execution. Compile machine features: [+64bit,+adx,+aes,+avx,+avx2,+avx512bf16,+avx512bitalg,+avx512bw,+avx512cd,+avx512dq,+avx512f,+avx512ifma,+avx512vbmi,+avx512vbmi2,+avx512vl,+avx512vnni,+avx512vpopcntdq,+bmi,+bmi2,+clflushopt,+clwb,+clzero,+cmov,+crc32,+cx16,+cx8,+f16c,+fma,+fsgsbase,+fxsr,+gfni,+invpcid,+lzcnt,+mmx,+movbe,+pclmul,+popcnt,+prefer-no-gather,+prefer-no-scatter,+prfchw,+rdpid,+rdpru,+rdrnd,+rdseed,+sahf,+sha,+shstk,+sse,+sse2,+sse3,+sse4.1,+sse4.2,+sse4a,+ssse3,+vaes,+vpclmulqdq,+xsave,+xsavec,+xsaveopt,+xsaves,-amx-avx512,-amx-bf16,-amx-complex,-amx-fp16,-amx-fp8,-amx-int8,-amx-movrs,-amx-tf32,-amx-tile,-avx10.1,-avx10.2,-avx512fp16,-avx512vp2intersect,-avxifma,-avxneconvert,-avxvnni,-avxvnniint16,-avxvnniint8,-ccmp,-cf,-cldemote,-cmpccxadd,-egpr,-enqcmd,-fma4,-hreset,-kl,-lwp,-movdir64b,-movdiri,-movrs,-mwaitx,-ndd,-nf,-pconfig,-pku,-ppx,-prefetchi,-ptwrite,-push2pop2,-raoint,-rtm,-serialize,-sgx,-sha512,-sm3,-sm4,-tbm,-tsxldtrk,-uintr,-usermsr,-waitpkg,-wbnoinvd,-widekl,-xop,-zu] vs host machine features: [prfchw,avx,aes,sahf,pclmul,crc32,xsaves,sse4.1,avx512ifma,xsave,sse4.2,invpcid,64bit,xsavec,avx512vpopcntdq,cmov,avx512cd,movbe,adx,avx2,vpclmulqdq,avx512vl,clflushopt,bmi,sse,gfni,xsaveopt,rdrnd,avx512f,avx512bf16,avx512vnni,cx8,avx512bw,sse3,fsgsbase,clzero,lzcnt,sha,ssse3,cx16,bmi2,fma,popcnt,f16c,avx512bitalg,rdpru,clwb,mmx,sse2,rdseed,avx512vbmi2,rdpid,avx512vbmi,shstk,vaes,fxsr,avx512dq,sse4a]. This could lead to execution errors such as SIGILL.

W0706 22:30:36.972680    7756 pjrt_executable.cc:642] Assume version compatibility. PjRt-IFRT does not track XLA executable versions.
E0706 22:30:36.976986    7807 cpu_aot_loader.cc:220] Loading XLA:CPU AOT result. Target machine feature +prefer-no-gather is not  supported on the host machine. Machine type used for XLA:CPU compilation doesn't match the machine type for execution. Compile machine features: [+64bit,+adx,+aes,+avx,+avx2,+avx512bf16,+avx512bitalg,+avx512bw,+avx512cd,+avx512dq,+avx512f,+avx512ifma,+avx512vbmi,+avx512vbmi2,+avx512vl,+avx512vnni,+avx512vpopcntdq,+bmi,+bmi2,+clflushopt,+clwb,+clzero,+cmov,+crc32,+cx16,+cx8,+f16c,+fma,+fsgsbase,+fxsr,+gfni,+invpcid,+lzcnt,+mmx,+movbe,+pclmul,+popcnt,+prefer-no-gather,+prefer-no-scatter,+prfchw,+rdpid,+rdpru,+rdrnd,+rdseed,+sahf,+sha,+shstk,+sse,+sse2,+sse3,+sse4.1,+sse4.2,+sse4a,+ssse3,+vaes,+vpclmulqdq,+xsave,+xsavec,+xsaveopt,+xsaves,-amx-avx512,-amx-bf16,-amx-complex,-amx-fp16,-amx-fp8,-amx-int8,-amx-movrs,-amx-tf32,-amx-tile,-avx10.1,-avx10.2,-avx512fp16,-avx512vp2intersect,-avxifma,-avxneconvert,-avxvnni,-avxvnniint16,-avxvnniint8,-ccmp,-cf,-cldemote,-cmpccxadd,-egpr,-enqcmd,-fma4,-hreset,-kl,-lwp,-movdir64b,-movdiri,-movrs,-mwaitx,-ndd,-nf,-pconfig,-pku,-ppx,-prefetchi,-ptwrite,-push2pop2,-raoint,-rtm,-serialize,-sgx,-sha512,-sm3,-sm4,-tbm,-tsxldtrk,-uintr,-usermsr,-waitpkg,-wbnoinvd,-widekl,-xop,-zu] vs host machine features: [prfchw,avx,aes,sahf,pclmul,crc32,xsaves,sse4.1,avx512ifma,xsave,sse4.2,invpcid,64bit,xsavec,avx512vpopcntdq,cmov,avx512cd,movbe,adx,avx2,vpclmulqdq,avx512vl,clflushopt,bmi,sse,gfni,xsaveopt,rdrnd,avx512f,avx512bf16,avx512vnni,cx8,avx512bw,sse3,fsgsbase,clzero,lzcnt,sha,ssse3,cx16,bmi2,fma,popcnt,f16c,avx512bitalg,rdpru,clwb,mmx,sse2,rdseed,avx512vbmi2,rdpid,avx512vbmi,shstk,vaes,fxsr,avx512dq,sse4a]. This could lead to execution errors such as SIGILL.
E0706 22:30:36.977002    7807 cpu_aot_loader.cc:220] Loading XLA:CPU AOT result. Target machine feature +prefer-no-scatter is not  supported on the host machine. Machine type used for XLA:CPU compilation doesn't match the machine type for execution. Compile machine features: [+64bit,+adx,+aes,+avx,+avx2,+avx512bf16,+avx512bitalg,+avx512bw,+avx512cd,+avx512dq,+avx512f,+avx512ifma,+avx512vbmi,+avx512vbmi2,+avx512vl,+avx512vnni,+avx512vpopcntdq,+bmi,+bmi2,+clflushopt,+clwb,+clzero,+cmov,+crc32,+cx16,+cx8,+f16c,+fma,+fsgsbase,+fxsr,+gfni,+invpcid,+lzcnt,+mmx,+movbe,+pclmul,+popcnt,+prefer-no-gather,+prefer-no-scatter,+prfchw,+rdpid,+rdpru,+rdrnd,+rdseed,+sahf,+sha,+shstk,+sse,+sse2,+sse3,+sse4.1,+sse4.2,+sse4a,+ssse3,+vaes,+vpclmulqdq,+xsave,+xsavec,+xsaveopt,+xsaves,-amx-avx512,-amx-bf16,-amx-complex,-amx-fp16,-amx-fp8,-amx-int8,-amx-movrs,-amx-tf32,-amx-tile,-avx10.1,-avx10.2,-avx512fp16,-avx512vp2intersect,-avxifma,-avxneconvert,-avxvnni,-avxvnniint16,-avxvnniint8,-ccmp,-cf,-cldemote,-cmpccxadd,-egpr,-enqcmd,-fma4,-hreset,-kl,-lwp,-movdir64b,-movdiri,-movrs,-mwaitx,-ndd,-nf,-pconfig,-pku,-ppx,-prefetchi,-ptwrite,-push2pop2,-raoint,-rtm,-serialize,-sgx,-sha512,-sm3,-sm4,-tbm,-tsxldtrk,-uintr,-usermsr,-waitpkg,-wbnoinvd,-widekl,-xop,-zu] vs host machine features: [prfchw,avx,aes,sahf,pclmul,crc32,xsaves,sse4.1,avx512ifma,xsave,sse4.2,invpcid,64bit,xsavec,avx512vpopcntdq,cmov,avx512cd,movbe,adx,avx2,vpclmulqdq,avx512vl,clflushopt,bmi,sse,gfni,xsaveopt,rdrnd,avx512f,avx512bf16,avx512vnni,cx8,avx512bw,sse3,fsgsbase,clzero,lzcnt,sha,ssse3,cx16,bmi2,fma,popcnt,f16c,avx512bitalg,rdpru,clwb,mmx,sse2,rdseed,avx512vbmi2,rdpid,avx512vbmi,shstk,vaes,fxsr,avx512dq,sse4a]. This could lead to execution errors such as SIGILL.

W0706 22:30:38.675056    7756 pjrt_executable.cc:642] Assume version compatibility. PjRt-IFRT does not track XLA executable versions.
E0706 22:30:38.678999    7807 cpu_aot_loader.cc:220] Loading XLA:CPU AOT result. Target machine feature +prefer-no-gather is not  supported on the host machine. Machine type used for XLA:CPU compilation doesn't match the machine type for execution. Compile machine features: [+64bit,+adx,+aes,+avx,+avx2,+avx512bf16,+avx512bitalg,+avx512bw,+avx512cd,+avx512dq,+avx512f,+avx512ifma,+avx512vbmi,+avx512vbmi2,+avx512vl,+avx512vnni,+avx512vpopcntdq,+bmi,+bmi2,+clflushopt,+clwb,+clzero,+cmov,+crc32,+cx16,+cx8,+f16c,+fma,+fsgsbase,+fxsr,+gfni,+invpcid,+lzcnt,+mmx,+movbe,+pclmul,+popcnt,+prefer-no-gather,+prefer-no-scatter,+prfchw,+rdpid,+rdpru,+rdrnd,+rdseed,+sahf,+sha,+shstk,+sse,+sse2,+sse3,+sse4.1,+sse4.2,+sse4a,+ssse3,+vaes,+vpclmulqdq,+xsave,+xsavec,+xsaveopt,+xsaves,-amx-avx512,-amx-bf16,-amx-complex,-amx-fp16,-amx-fp8,-amx-int8,-amx-movrs,-amx-tf32,-amx-tile,-avx10.1,-avx10.2,-avx512fp16,-avx512vp2intersect,-avxifma,-avxneconvert,-avxvnni,-avxvnniint16,-avxvnniint8,-ccmp,-cf,-cldemote,-cmpccxadd,-egpr,-enqcmd,-fma4,-hreset,-kl,-lwp,-movdir64b,-movdiri,-movrs,-mwaitx,-ndd,-nf,-pconfig,-pku,-ppx,-prefetchi,-ptwrite,-push2pop2,-raoint,-rtm,-serialize,-sgx,-sha512,-sm3,-sm4,-tbm,-tsxldtrk,-uintr,-usermsr,-waitpkg,-wbnoinvd,-widekl,-xop,-zu] vs host machine features: [prfchw,avx,aes,sahf,pclmul,crc32,xsaves,sse4.1,avx512ifma,xsave,sse4.2,invpcid,64bit,xsavec,avx512vpopcntdq,cmov,avx512cd,movbe,adx,avx2,vpclmulqdq,avx512vl,clflushopt,bmi,sse,gfni,xsaveopt,rdrnd,avx512f,avx512bf16,avx512vnni,cx8,avx512bw,sse3,fsgsbase,clzero,lzcnt,sha,ssse3,cx16,bmi2,fma,popcnt,f16c,avx512bitalg,rdpru,clwb,mmx,sse2,rdseed,avx512vbmi2,rdpid,avx512vbmi,shstk,vaes,fxsr,avx512dq,sse4a]. This could lead to execution errors such as SIGILL.
E0706 22:30:38.679014    7807 cpu_aot_loader.cc:220] Loading XLA:CPU AOT result. Target machine feature +prefer-no-scatter is not  supported on the host machine. Machine type used for XLA:CPU compilation doesn't match the machine type for execution. Compile machine features: [+64bit,+adx,+aes,+avx,+avx2,+avx512bf16,+avx512bitalg,+avx512bw,+avx512cd,+avx512dq,+avx512f,+avx512ifma,+avx512vbmi,+avx512vbmi2,+avx512vl,+avx512vnni,+avx512vpopcntdq,+bmi,+bmi2,+clflushopt,+clwb,+clzero,+cmov,+crc32,+cx16,+cx8,+f16c,+fma,+fsgsbase,+fxsr,+gfni,+invpcid,+lzcnt,+mmx,+movbe,+pclmul,+popcnt,+prefer-no-gather,+prefer-no-scatter,+prfchw,+rdpid,+rdpru,+rdrnd,+rdseed,+sahf,+sha,+shstk,+sse,+sse2,+sse3,+sse4.1,+sse4.2,+sse4a,+ssse3,+vaes,+vpclmulqdq,+xsave,+xsavec,+xsaveopt,+xsaves,-amx-avx512,-amx-bf16,-amx-complex,-amx-fp16,-amx-fp8,-amx-int8,-amx-movrs,-amx-tf32,-amx-tile,-avx10.1,-avx10.2,-avx512fp16,-avx512vp2intersect,-avxifma,-avxneconvert,-avxvnni,-avxvnniint16,-avxvnniint8,-ccmp,-cf,-cldemote,-cmpccxadd,-egpr,-enqcmd,-fma4,-hreset,-kl,-lwp,-movdir64b,-movdiri,-movrs,-mwaitx,-ndd,-nf,-pconfig,-pku,-ppx,-prefetchi,-ptwrite,-push2pop2,-raoint,-rtm,-serialize,-sgx,-sha512,-sm3,-sm4,-tbm,-tsxldtrk,-uintr,-usermsr,-waitpkg,-wbnoinvd,-widekl,-xop,-zu] vs host machine features: [prfchw,avx,aes,sahf,pclmul,crc32,xsaves,sse4.1,avx512ifma,xsave,sse4.2,invpcid,64bit,xsavec,avx512vpopcntdq,cmov,avx512cd,movbe,adx,avx2,vpclmulqdq,avx512vl,clflushopt,bmi,sse,gfni,xsaveopt,rdrnd,avx512f,avx512bf16,avx512vnni,cx8,avx512bw,sse3,fsgsbase,clzero,lzcnt,sha,ssse3,cx16,bmi2,fma,popcnt,f16c,avx512bitalg,rdpru,clwb,mmx,sse2,rdseed,avx512vbmi2,rdpid,avx512vbmi,shstk,vaes,fxsr,avx512dq,sse4a]. This could lead to execution errors such as SIGILL.

Note

The interpolated values over this phase space sample have been visualized by interpolating again over a meshgrid with scipy.interpolate.griddata.

Tip

Determination of polarization shows how this interpolation method can be used to determine the polarization \(\vec{P}\) from a given intensity distribution.