Source code for numdifftools.run_benchmark

from __future__ import print_function
import numpy as np
import timeit

import numdifftools as nd
import numdifftools.nd_algopy as nda
from algopy import dot

from collections import OrderedDict
from numdifftools.core import MinStepGenerator, MaxStepGenerator
import matplotlib.pyplot as plt


[docs]class BenchmarkFunction(object): """Return 0.5 * np.dot(x**2, np.dot(A,x))""" def __init__(self, n): A = np.arange(n * n, dtype=float).reshape((n, n)) self.A = np.dot(A.T, A) def __call__(self, xi): x = np.array(xi) return 0.5 * dot(x * x, dot(self.A, x))
def _plot(plot, problem_sizes, objects, symbols, ylabel='', loc=2, logx=False): for title, funcs, results in objects: plt.figure() plt.title(title) for i, method in enumerate(funcs): plot(problem_sizes, results[i], symbols[i], markerfacecolor='None', label=method) plt.ylabel(ylabel) plt.xlabel('problem size $N$') if logx: plt.xlim(loglimits(problem_sizes)) plt.ylim(loglimits(results)) plt.grid() leg = plt.legend(loc=loc) frame = leg.get_frame() frame.set_alpha(0.4) plt.savefig(title.lower().replace(' ', '_') + '.png', format='png')
[docs]def plot_errors(error_objects, problem_sizes, symbols): _plot(plt.semilogy, problem_sizes, error_objects, symbols, ylabel=r'Absolute error $\|g_{ref} - g\|$', loc=7, logx=False)
[docs]def plot_runtimes(run_time_objects, problem_sizes, symbols): _plot(plt.loglog, problem_sizes, run_time_objects, symbols, ylabel='time $t$', loc=2, logx=True)
[docs]def loglimits(data, border=0.05): low, high = np.min(data), np.max(data) scale = (high/low)**border return low/scale, high*scale
fixed_step = MinStepGenerator(num_steps=1, use_exact_steps=True, offset=0) epsilon = MaxStepGenerator(num_steps=14, use_exact_steps=True, step_ratio=1.6, offset=0) adaptiv_txt = '_adaptive_{0:d}_{1!s}_{2:d}'.format(epsilon.num_steps, str(epsilon.step_ratio), epsilon.offset) gradient_funs = OrderedDict() nda_method = 'forward' nda_txt = 'algopy_' + nda_method gradient_funs[nda_txt] = nda.Jacobian(1, method=nda_method) hessian_fun = 'Hessdiag' ndc_hessian = getattr(nd, hessian_fun) hessian_funs = OrderedDict() hessian_funs[nda_txt] = getattr(nda, hessian_fun)(1, method=nda_method) order = 2 for method in ['forward', 'central', 'complex']: method2 = method + adaptiv_txt options = dict(method=method, order=order) gradient_funs[method] = nd.Jacobian(1, step=fixed_step, **options) gradient_funs[method2] = nd.Jacobian(1, step=epsilon, **options) hessian_funs[method] = ndc_hessian(1, step=fixed_step, **options) hessian_funs[method2] = ndc_hessian(1, step=epsilon, **options) def _compute_benchmark(functions, problem_sizes): result_list = [] for n in problem_sizes: print('n=', n) num_methods = len(functions) results = np.zeros((num_methods, 3)) ref_g = None f = BenchmarkFunction(n) for i, (_key, function) in enumerate(functions.items()): t = timeit.default_timer() function.f = f preproc_time = timeit.default_timer() - t t = timeit.default_timer() x = 3 * np.ones(n) val = function(x) run_time = timeit.default_timer() - t if ref_g is None: ref_g = val err = 0 norm_ref_g = np.linalg.norm(ref_g) else: err = np.linalg.norm(val - ref_g) / norm_ref_g results[i] = run_time, err, preproc_time result_list.append(results) return np.array(result_list) + 1e-16
[docs]def compute_gradients(gradient_funs, problem_sizes): print('starting gradient computation ') results_gradients = _compute_benchmark(gradient_funs, problem_sizes) print('results_gradients=\n', results_gradients) return results_gradients
[docs]def compute_hessians(hessian_funs, problem_sizes): print('starting hessian computation ') results_hessians = _compute_benchmark(hessian_funs, problem_sizes) print(problem_sizes) print('results_hessians=\n', results_hessians) return results_hessians
[docs]def main(): problem_sizes = (4, 8, 16, 32, 64, 96) symbols = ('-kx', ':k>', ':k<', '--k^', '--kv', '-kp', '-ks', 'b', '--b', '-k+') results_gradients = compute_gradients(gradient_funs, problem_sizes) results_hessians = compute_hessians(hessian_funs, problem_sizes) print(results_gradients.shape) for i, txt in enumerate(['run times', 'errors']): objects = [('Jacobian ' + txt, gradient_funs, results_gradients[..., i].T), ('Hessian ' + txt, hessian_funs, results_hessians[..., i].T)] if i == 0: plot_runtimes(objects, problem_sizes, symbols) else: plot_errors(objects, problem_sizes, symbols)
if __name__ == '__main__': main()