# O-Matrix 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. # # To start the test: menu File -> Run Program... select "c://OMatrix2.oms" clear # By default O-Matrix multi-threads the various windows within the # application. This allows editing, graphics etc. to continue # while a calculation is running. This reduces performance # about 10-15% so we are turning it off here interrupt(0) clc begin runs = 3 # Number of times the tests are executed times = zeros(5, 3) print " O-Matrix Benchmark 2" print " ====================" print "Number of times each test is run__________________________: ", runs print " " print " I. Matrix calculation" print " ---------------------" # (1) cumulate = 0; a = 0; b = 0 for i = 1 to runs begin tic a = abs(snormal(1500, 1500)/10) b = a' dim b(750, 3000) a = b'; timing = toc cumulate = cumulate + timing end timing = cumulate/runs times(1, 1) = timing print "Creation, transp., deformation of a 1500x1500 matrix (sec): ", timing # (2) cumulate = 0; b = 0 for i = 1 to runs begin a = abs(snormal(800, 800)/2); tic b = a^1000; timing = toc cumulate = cumulate + timing end timing = cumulate/runs times(2, 1) = timing print "800x800 normal distributed random matrix ^1000______ (sec): ", timing # (3) cumulate = 0; b = 0 for i = 1 to runs begin a = snormal(2000000, 1) tic b = sort(a) timing = toc cumulate = cumulate + timing end timing = cumulate/runs times(3, 1) = timing print "Sorting of 2,000,000 random values__________________ (sec): ", timing # (4) cumulate = 0; b = 0 for i = 1 to runs begin a = snormal(700, 700) tic b = a'*a timing = toc cumulate = cumulate + timing end timing = cumulate/runs times(4, 1) = timing print "700x700 cross-product matrix (b = a' * a)___________ (sec): ", timing # (5) cumulate = 0; c = 0 for i = 1 to runs begin a = snormal(600, 600) b = 1::600 tic c = a\b timing = toc cumulate = cumulate + timing end timing = cumulate/runs times(5, 1) = timing print "Linear regression over a 600x600 matrix (c = a \ b') (sec): ", timing times(1::5,1) = sort(times(1::5,1)) print " ----------------------------------------------------" print " Trimmed geom. mean (2 extremes eliminated): ", exp(colmean(log(double(times(2::4,1))))) print " " print " II. Matrix functions" print " --------------------" # (1) cumulate = 0; b = 0 for i = 1 to runs begin a = snormal(800000, 1) tic b = fft(a) timing = toc cumulate = cumulate + timing end timing = cumulate/runs times(1, 2) = timing print "FFT over 800,000 random values______________________ (sec): ", timing # (2) cumulate = 0; b = 0 for i = 1 to runs begin a = snormal(320, 320) tic b = eigen(a) timing = toc cumulate = cumulate + timing end timing = cumulate/runs times(2, 2) = timing print "Eigenvalues of a 320x320 random matrix______________ (sec): ", timing # (3) cumulate = 0; b = 0 for i = 1 to runs begin a = snormal(650, 650) tic b = det(a) timing = toc cumulate = cumulate + timing end timing = cumulate/runs times(3, 2) = timing print "Determinant of a 650x650 random matrix______________ (sec): ", timing # (4) cumulate = 0; b = 0 for i = 1 to runs begin a = snormal(900, 900) a = a'*a tic b = cholesky(a) timing = toc cumulate = cumulate + timing end timing = cumulate/runs times(4, 2) = timing print "Cholesky decomposition of a 900x900 matrix__________ (sec): ", timing # (5) cumulate = 0; b = 0 for i = 1 to runs begin a = snormal(400, 400) tic b = inv(a) timing = toc cumulate = cumulate + timing end timing = cumulate/runs times(5, 2) = timing print "Inverse of a 400x400 random matrix__________________ (sec): ", timing times(1::5,2) = sort(times(1::5, 2)) print " ----------------------------------------------------" print " Trimmed geom. mean (2 extremes eliminated): ", exp(colmean(log(double(times(2::4,2))))) print " " print " III. Programmation" print " ------------------" # (1) cumulate = 0; a = 0; b = 0; phi = 1.6180339887498949 for i = 1 to runs begin 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 print "750,000 Fibonacci numbers calculation (vector calc)_ (sec): ", timing # (2) cumulate = 0; a = 2250; b = 0 for i = 1 to runs begin tic b = ones(a, a)/double((1::a) * ones(1, a) + ones(a, 1) * (0::(a-1))') timing = toc cumulate = cumulate + timing end timing = cumulate/runs times(2, 3) = timing print "Creation of a 2250x2250 Hilbert matrix (matrix calc) (sec): ", timing # (3) cumulate = 0; c = 0 local function gcd2(a, b) begin if sum(b > 1.0E-4) == 0 then return a b([find(b == 0)]) = a([find(b == 0)]) return gcd2(b, rem(a, b)) end for i = 1 to runs begin a = ceil(1000 * rand(1, 70000)) b = ceil(1000 * rand(1, 70000)) tic c = gcd2(a, b) # gcd2 is a recursive function timing = toc cumulate = cumulate + timing end timing = cumulate/runs times(3, 3) = timing print "Grand common divisors of 70,000 pairs (recursion)___ (sec): ", timing # (4) cumulate = 0; b = 0 for i = 1 to runs begin b = zeros(220, 220) tic for j = 1 to 220 begin for k = 1 to 220 begin b(k,j) = abs(j - k) + 1 end end timing = toc cumulate = cumulate + timing end timing = cumulate/runs times(4, 3) = timing print "Creation of a 220x220 Toeplitz matrix (loops)_______ (sec): ", timing # (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 to runs begin x = abs(snormal(37, 37)) tic # Calculation of Escoufier's equivalent vectors p = size(x, 2) vt = [1::p] # Variables to test vr = zeros(p, 1) # Result: ordered variables RV = [1::p] # Result: correlations for j = 1 to p begin # loop on the variable number Rvmax = 0 for k = 1 to (p-j+1) begin # loop on the variables if (j == 1) then x2 = [x, x(:, vt(k))] else x2 = [x, x(:, nonzeros(vr)), x(:, vt(k))] # New table to test R = colcor(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*Ryy)*trace(Rxx*Rxx))^0.5); # RV calculation if rvt > Rvmax then begin Rvmax = rvt # test of RV vrt = vt(k) # temporary held variable end end vr(j) = vrt # 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 timing = cumulate/runs times(5, 3) = timing print "Escoufier's method on a 37x37 matrix (mixed)________ (sec): ", timing times(1::5,3) = sort(times(1::5,3)) print " ----------------------------------------------------" print " Trimmed geom. mean (2 extremes eliminated): ", exp(colmean(log(double(times(2::4,3))))) print " " print " " print "Total time for all 15 tests_________________________ (sec): ", sum(sum(double(times))) print "Overall mean (sum of I, II and III trimmed means/3)_ (sec): ", exp(sum(colmean(log(double(times(2::4, 1::3)))))/3) print " --- End of test ---" end clear