import os
os.environ["SAS_OPENCL"] = "cuda"   # use CUDA GPU backend for sasmodels

import escape as esc
import numpy as np
esc.require("0.9.8")

Loading material database from C:\dev\escape-core\python\src\escape\scattering\..\data\mdb\materials.db

SAXS. Form-factors. Sphere (SasView-aligned)

Uniform sphere with contrast $\Delta\rho$ and radius R. Matches sphere — SasView 6.1.3.

Reference: https://www.sasview.org/docs/user/models/sphere.html

Parameters (SasView defaults)

Parameter	Variable	Value
Scale	scale	1
Background (cm⁻¹)	background	0.001
Contrast Δρ (10⁻⁶ Å⁻²)	contrast	3 (= sld 4 − sld_solvent 1)
Radius (Å)	radius	60

Form-factor

$$I(q) = \frac{\mathrm{scale}}{V}\left[\Delta\rho\,V\,\frac{3(\sin(qR)-qR\cos(qR))}{(qR)^3}\right]^2 + \mathrm{background}, \quad V = \frac{4\pi}{3}R^3$$

The model is isotropic: 2D uses $q = \sqrt{q_x^2+q_y^2}$.

# ── Variables ──────────────────────────────────────────────────────────────
q = esc.var("Q")

# ── Parameters ─────────────────────────────────────────────────────────────
scale      = esc.par("Scale",      1.0,  scale=1e8, fixed=True)
radius     = esc.par("Radius",    60.0,  units=esc.angstr)
contrast   = esc.par("Contrast",   3.0,  scale=1e-6, units=f"{esc.angstr}^-2")
background = esc.par("Background", 0.001, userlim=[0.0, 0.03])

# ── Geometry ───────────────────────────────────────────────────────────────
volume = 4.0 / 3.0 * np.pi * esc.pow(radius, 3)
QR     = q * radius

kern = esc.conditional(
    esc.abs(QR) < 1e-10,
    1.0 / 3.0,
    (esc.sin(QR) - QR * esc.cos(QR)) / esc.pow(QR, 3),
)
F   = 3.0 * volume * contrast * kern
i1d = scale / volume * esc.pow(F, 2) + background

i1d.device = "gpu"

qs = np.linspace(0.001, 0.5, 300)
i1d.show(coordinates=qs).config(
    title="Sphere — 1D",
    xlog=True, ylog=True,
    xlabel=f"Q [{esc.angstr}^-1]", ylabel="I(q) [cm^-1]")

2D isotropic scattering (qx, qy)

The model is isotropic. The 2D intensity is the same as 1D with $q = \sqrt{q_x^2+q_y^2}$.

qx = esc.var("qx")
qy = esc.var("qy")
q2d = esc.sqrt(esc.pow(qx, 2) + esc.pow(qy, 2))

QR2   = q2d * radius
kern2 = esc.conditional(
    esc.abs(QR2) < 1e-10,
    1.0 / 3.0,
    (esc.sin(QR2) - QR2 * esc.cos(QR2)) / esc.pow(QR2, 3),
)
F2  = 3.0 * volume * contrast * kern2
i2d = scale / volume * esc.pow(F2, 2) + background

i2d.device = "gpu"

xs = np.linspace(-0.5, 0.5, 300); ys = np.linspace(-0.5, 0.5, 300)
xv, yv = np.meshgrid(xs, ys)
coords_2d = np.column_stack([xv.flatten(), yv.flatten()]).flatten()

i2d.show(coordinates=coords_2d).config(
    title="Sphere — isotropic 2D (qx, qy)",
    xlabel=f"qx [{esc.angstr}^-1]", ylabel=f"qy [{esc.angstr}^-1]",
    cblog=True, colorscale="jet")

SasView reference model & comparison

ESCAPE parameter	SasView parameter	Notes
contrast * 1e-6	sld - sld_solvent	contrast in Å⁻²
radius	radius	sphere radius (Å)

import time
import matplotlib.pyplot as plt
from sasmodels.core import load_model
from sasmodels.data import empty_data1D
from sasmodels.direct_model import DirectModel

qs = np.linspace(0.001, 0.5, 300).copy()

kernel = load_model("sphere")
f_sas  = DirectModel(empty_data1D(qs), kernel)
sas_pars = dict(scale=1.0, background=0.001, sld=4.0, sld_solvent=1.0, radius=60.0)

f_sas(**sas_pars)
i1d.device = "gpu"; i1d(qs[:5])

def timeit(fn, n=5):
    t0 = time.perf_counter()
    for _ in range(n): result = fn()
    return (time.perf_counter() - t0) / n * 1e3, result

t_sas, Iq_sas = timeit(lambda: f_sas(**sas_pars))

i1d.device = "gpu"
t_gpu, Iq_gpu = timeit(lambda: i1d(qs), n=3)
i1d.device = "cpu"
t_cpu, Iq_cpu = timeit(lambda: i1d(qs))
i1d.device = "gpu"

print(f"SASView GPU : {t_sas:.0f} ms")
print(f"ESCAPE GPU  : {t_gpu:.0f} ms")
print(f"ESCAPE CPU  : {t_cpu:.0f} ms  ({len(qs)} q-pts)")
rel = np.max(np.abs((Iq_gpu - Iq_sas) / Iq_sas)) * 100
print(f"Max relative diff vs SasView: {rel:.2f}%")

esc.overlay(Iq_sas, Iq_gpu, Iq_cpu, coordinates=qs).config(
    xlabel="Q (1/A)", ylabel="I(q) (1/cm)",
    xlog=True, ylog=True,
    fig_title=f"Sphere I(q) — {len(qs)} pts",
    labels=["SASView", "ESCAPE GPU", "ESCAPE CPU"],
    line_styles=["solid", "dash", "dot"],
    line_widths=[2, 3, 3]
)

SASView GPU : 9 ms
ESCAPE GPU  : 0 ms
ESCAPE CPU  : 2 ms  (300 q-pts)
Max relative diff vs SasView: 0.24%

C:\Users\User\AppData\Local\Temp\ipykernel_44940\978670999.py:14: UserWarning:

Input array does not own its data (e.g. it is a view or slice); data will be copied