Time measurements for the different MTF solvers

This routine measures the time taken for solving the problem presented in e1.laplace_transmission_mtf.ipynb with the routines mtf_laplace_n_spheres_point_source_direct_solver and mtf_laplace_n_spheres_point_source_indirect_solver.

Setup of the parameters and environment

The following block is to control some environment variables. Specifically the threads allowed to use for some underlying libraries.

import os
number = "1"
os.environ["OMP_NUM_THREADS"] = number
os.environ["OPENBLAS_NUM_THREADS"] = number
os.environ["MKL_NUM_THREADS"] = number
os.environ["VECLIB_MAXIMUM_THREADS"] = number
os.environ["NUMEXPR_NUM_THREADS"] = number

import numpy as np
import biosspheres.miscella.spherearrangements as pos
import biosspheres.formulations.mtf.solvertemplates as solver
import biosspheres.formulations.mtf.solvertemplates as solver
import time

n = 8
big_l = 15
big_l_c = 55

r = 0.875
radii = np.ones(n) * r

d = 1.15
center_positions = pos.cube_vertex_positions(int(n**(1/3)), r, d)

sigma_e = 1.75
sigma_i = 0.75
sigmas = np.ones(n+1) * sigma_i
sigmas[0] = sigma_e

p0 = np.ones(3)*-5.
p0

tolerance = 10**(-10)

/opt/hostedtoolcache/Python/3.12.15/x64/lib/python3.12/site-packages/tqdm/auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html
  from .autonotebook import tqdm as notebook_tqdm

Time measurements

We are going to measure (approximately) the time taken to solve a certain number of times using both methods

number_of_times = 10
times_taken_direct = np.empty(number_of_times)
t0 = 0.
for i in np.arange(0, number_of_times):
    print(i)
    t0 = time.time()
    traces = solver.mtf_laplace_n_spheres_point_source_direct_solver(n, big_l, big_l_c, radii, center_positions, sigmas, p0)
    times_taken_direct[i] = time.time()-t0

times_taken_indirect = np.empty(number_of_times)
for i in np.arange(0, number_of_times):
    print(i)
    t0 = time.time()
    traces = solver.mtf_laplace_n_spheres_point_source_indirect_solver(n, big_l, big_l_c, radii, center_positions, sigmas, p0, tolerance)
    times_taken_indirect[i] = time.time()-t0

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Results

Averages:

print("Direct method average:   ", np.mean(times_taken_direct))
print("Indirect method average: ", np.mean(times_taken_indirect))

Direct method average:    10.637980508804322
Indirect method average:  1.0162214279174804

Standart deviations:

print("Direct method std:   ", np.std(times_taken_direct))
print("Indirect method sdt: ", np.std(times_taken_indirect))

Direct method std:    0.48223268985757184
Indirect method sdt:  0.020951528330944554

Minimum and maximum values:

print("Direct method min:   ", np.min(times_taken_direct))
print("Indirect method min: ", np.min(times_taken_indirect))
print("Direct method max:   ", np.max(times_taken_direct))
print("Indirect method max: ", np.max(times_taken_indirect))

Direct method min:    9.575477838516235
Indirect method min:  0.9794068336486816
Direct method max:    11.478553533554077
Indirect method max:  1.0550894737243652