% Octave Benchmark 2 (8 March 2003) % version 2, scaled to get 1 +/- 0.1 sec with R 1.6.2 % using the standard ATLAS library (Rblas.dll) % on a Pentium IV 1.6 Ghz with 1 Gb Ram on Win XP pro % Author : Philippe Grosjean % eMail : phgrosjean@sciviews.org % Web : http://www.sciviews.org % License: GPL 2 or above at your convenience (see: http://www.gnu.org) % % Several tests are adapted from: %*************************************************************************** %* Matlab Benchmark program version 2.0 * %* Author : Stefan Steinhaus * %* EMAIL : stst@informatik.uni-frankfurt.de * %* This program is public domain. Feel free to copy it freely. * %*************************************************************************** % Escoufier's equivalents vectors (III.5) is adapted from Planque & Fromentin, 1996 % Ref: Escoufier Y., 1970. Echantillonnage dans une population de variables % aleatoires réelles. Publ. Inst. Statis. Univ. Paris 19 Fasc 4, 1-47. % % From the Matlab Benchmark... only cosmetic changes % % Type "cd('/')" and then "source('Octave2.m')" to start the test clc runs = 3; % Number of times the tests are executed times = zeros(5, 3); disp(' Octave Benchmark 2') disp(' ==================') disp(['Number of times each test is run__________________________: ' num2str(runs)]) disp(' ') disp(' I. Matrix calculation') disp(' ---------------------') % (1) cumulate = 0; a = 0; b = 0; for i = 1:runs tic; a = abs(randn(1500, 1500)/10); b = a'; a = reshape(b, 750, 3000); b = a'; timing = toc; cumulate = cumulate + timing; end; timing = cumulate/runs; times(1, 1) = timing; disp(['Creation, transp., deformation of a 1500x1500 matrix (sec): ' num2str(timing)]) clear a; clear b; % (2) cumulate = 0; b = 0; for i = 1:runs a = abs(randn(800, 800)/2); tic; b = a.^1000; timing = toc; cumulate = cumulate + timing; end timing = cumulate/runs; times(2, 1) = timing; disp(['800x800 normal distributed random matrix ^1000_______ (sec): ' num2str(timing)]) clear a; clear b; % (3) cumulate = 0; b = 0; for i = 1:runs a = randn(2000000, 1); tic; b = sort(a); timing = toc; cumulate = cumulate + timing; end timing = cumulate/runs; times(3, 1) = timing; disp(['Sorting of 2,000,000 random values___________________ (sec): ' num2str(timing)]) clear a; clear b; % (4) cumulate = 0; b = 0; for i = 1:runs a = randn(700, 700); tic; b = a'*a; timing = toc; cumulate = cumulate + timing; end timing = cumulate/runs; times(4, 1) = timing; disp(['700x700 cross-product matrix (b = a'' * a)___________ (sec): ' num2str(timing)]) clear a; clear b; % (5) cumulate = 0; c = 0; for i = 1:runs a = randn(600, 600); b = 1:600; tic; c = a\b'; timing = toc; cumulate = cumulate + timing; end timing = cumulate/runs; times(5, 1) = timing; disp(['Linear regression over a 600x600 matrix (c = a \\ b'') (sec): ' num2str(timing)]) clear a; clear b; clear c; times = sort(times); disp(' ------------------------------------------------------') disp([' Trimmed geom. mean (2 extremes eliminated): ' num2str(exp(mean(log(times(2:4,1)))))]) disp(' ') disp(' II. Matrix functions') disp(' --------------------') % (1) cumulate = 0; b = 0; for i = 1:runs a = randn(800000, 1); tic; b = fft(a); timing = toc; cumulate = cumulate + timing; end timing = cumulate/runs; times(1, 2) = timing; disp(['FFT over 800,000 random values_______________________ (sec): ' num2str(timing)]) clear a; clear b; % (2) cumulate = 0; b = 0; for i = 1:runs a = randn(320, 320); tic; b = eig(a); timing = toc; cumulate = cumulate + timing; end timing = cumulate/runs; times(2, 2) = timing; disp(['Eigenvalues of a 320x320 random matrix_______________ (sec): ' num2str(timing)]) clear a; clear b; % (3) cumulate = 0; b = 0; for i = 1:runs a = randn(650, 650); tic; b = det(a); timing = toc; cumulate = cumulate + timing; end timing = cumulate/runs; times(3, 2) = timing; disp(['Determinant of a 650x650 random matrix_______________ (sec): ' num2str(timing)]) clear a; clear b; % (4) cumulate = 0; b = 0; for i = 1:runs a = randn(900, 900); a = a'*a; tic; b = chol(a); timing = toc; cumulate = cumulate + timing; end timing = cumulate/runs; times(4, 2) = timing; disp(['Cholesky decomposition of a 900x900 matrix___________ (sec): ' num2str(timing)]) clear a; clear b; % (5) cumulate = 0; b = 0; for i = 1:runs a = randn(400, 400); tic; b = inv(a); timing = toc; cumulate = cumulate + timing; end timing = cumulate/runs; times(5, 2) = timing; disp(['Inverse of a 400x400 random matrix___________________ (sec): ' num2str(timing)]) clear a; clear b; times = sort(times); disp(' ------------------------------------------------------') disp([' Trimmed geom. mean (2 extremes eliminated): ' num2str(exp(mean(log(times(2:4,2)))))]) disp(' ') disp(' III. Programmation') disp(' ------------------') % (1) cumulate = 0; a = 0; b = 0; phi = 1.6180339887498949; for i = 1:runs a = floor(1000 * rand(750000, 1)); tic; b = (phi.^a - (-phi).^(-a)) / sqrt(5); timing = toc; cumulate = cumulate + timing; end timing = cumulate/runs; times(1, 3) = timing; disp(['750,000 Fibonacci numbers calculation (vector calc)__ (sec): ' num2str(timing)]) clear a; clear b; clear phi; % (1) cumulate = 0; a = 2250; b = 0; for i = 1:runs tic; b = ones(a, a)./((1:a)' * ones(1, a) + ones(a, 1) * (0:(a-1))); timing = toc; cumulate = cumulate + timing; end timing = cumulate/runs; times(2, 3) = timing; disp(['Creation of a 2250x2250 Hilbert matrix (matrix calc)_ (sec): ' num2str(timing)]) clear a; clear b; % (3) cumulate = 0; c = 0; for i = 1:runs a = ceil(1000 * rand(70000, 1)); b = ceil(1000 * rand(70000, 1)); tic; c = gcd2(a, b); % gcd2 is a recursive function timing = toc; cumulate = cumulate + timing; end timing = cumulate/runs; times(3, 3) = timing; disp(['Grand common divisors of 70,000 pairs (recursion)____ (sec): ' num2str(timing)]) clear a; clear b; clear c; % (4) cumulate = 0; b = 0; for i = 1:runs b = zeros(220, 220); tic; for j = 1:220 for k = 1:220 b(k,j) = abs(j - k) + 1; end end timing = toc; cumulate = cumulate + timing; end timing = cumulate/runs; times(4, 3) = timing; disp(['Creation of a 220x220 Toeplitz matrix (loops)________ (sec): ' num2str(timing)]) clear b; clear j; clear k; % (5) cumulate = 0; p = 0; vt = 0; vr = 0; vrt = 0; rvt = 0; RV = 0; j = 0; k = 0; x2 = 0; R = 0; Rxx = 0; Ryy = 0; Rxy = 0; Ryx = 0; Rvmax = 0; f = 0; for i = 1:runs x = abs(randn(37, 37)); tic; % Calculation of Escoufier's equivalent vectors p = size(x, 2); vt = [1:p]; % Variables to test vr = []; % Result: ordered variables RV = [1:p]; % Result: correlations for j = 1:p % loop on the variable number Rvmax = 0; for k = 1:(p-j+1) % loop on the variables if j == 1 x2 = [x, x(:, vt(k))]; else x2 = [x, x(:, vr), x(:, vt(k))]; % New table to test end # R = corrcoef(x2); % Correlations table R = corr(x2); % Correlations table Ryy = R(1:p, 1:p); Rxx = R(p+1:p+j, p+1:p+j); Rxy = R(p+1:p+j, 1:p); Ryx = Rxy'; rvt = trace(Ryx*Rxy)/((trace(Ryy^2)*trace(Rxx^2))^0.5); % RV calculation if rvt > Rvmax Rvmax = rvt; % test of RV vrt(j) = vt(k); % temporary held variable end end vr(j) = vrt(j); % Result: variable RV(j) = Rvmax; % Result: correlation f = find(vt~=vr(j)); % identify the held variable vt = vt(f); % reidentify variables to test end timing = toc; cumulate = cumulate + timing; end times(5, 3) = timing; disp(['Escoufier''s method on a 37x37 matrix (mixed)________ (sec): ' num2str(timing)]) clear x; clear p; clear vt; clear vr; clear vrt; clear rvt; clear RV; clear j; clear k; clear x2; clear R; clear Rxx; clear Ryy; clear Rxy; clear Ryx; clear Rvmax; clear f; times = sort(times); disp(' ------------------------------------------------------') disp([' Trimmed geom. mean (2 extremes eliminated): ' num2str(exp(mean(log(times(2:4,3)))))]) disp(' ') disp(' ') disp(['Total time for all 15 tests_________________________ (sec): ' num2str(sum(sum(times)))]) disp(['Overall mean (sum of I, II and III trimmed means/3)_ (sec): ' num2str(exp(mean(mean(log(times(2:4,:))))))]) clear cumulate; clear timing; clear times; clear runs; clear i; disp(' --- End of test ---') function c = gcd2(a, b) % Greatest common divisor by a recursive algorithm % This function is used for the Matlab benchmark % Use gcd(a, b) instead for other uses % % by Ph. Grosjean, 2001 (phgrosjean@sciviews.org) if b <= 1.0E-4 c = a; else b(b == 0) = a(b == 0); c = gcd2(b, rem(a, b)); end endfunction