Re: [Gretl-devel] fdjac: a better example

On Tue, 29 Dec 2015, Allin Cottrell wrote: > In current git I've modified fdjac2 to use a step size as in your script > (when Richardson is selected). We need to do more testing on this in case > it goes nasty under some conditions It would seem that the results are somewhat sensitive to the amount of nonlinearity of the problem: I ran an old script I had which uses matrix inversion (notoriously differentiable almost everywhere but highly nonlinear --- especially in the nieighbourhood of singularity). <hansl> set echo off set messages off function matrix vec22inv(matrix x) n = round(sqrt(rows(x))) A = mshape(x,n,n) return vec(inv(A))' end function function matrix grad(matrix x) n = round(sqrt(rows(x))) iA = inv(mshape(x,n,n)) return -iA' ** iA end function n = 12 k = 1.0e4 a = vec(ones(n,n) - I(n)/k) ia = vec22inv(a) ag = grad(a) printf "\n" loop i=0..2 --quiet set fdjac_quality $i set stopwatch ng$i = fdjac(a, "vec22inv(a)") tt = $stopwatch scalar aae = meanc(abs(vec(ag - ng$i))) scalar mae = maxc(abs(vec(ag - ng$i))) scalar are = meanc(abs(1 - vec(ag ./ ng$i))) scalar mre = maxc(abs(1 - vec(ag ./ ng$i))) printf "quality = $i\n" printf "\tAverage and max absolute error = %g, %g\n", aae, mae printf "\tAverage and max relative error = %g, %g\n", are, mre printf "\t(cpu time = %g)\n", tt endloop </hansl> This is what I get before and after the patch: <before> quality = 0 Average and max absolute error = 53.1382, 11477.9 Average and max relative error = 2.27644e-05, 0.00013658 (cpu time = 0.02) quality = 1 Average and max absolute error = 0.0163915, 6.19778 Average and max relative error = 7.58353e-09, 1.68055e-07 (cpu time = 0.04) quality = 2 Average and max absolute error = 0.00128204, 0.149397 Average and max relative error = 1.11463e-09, 2.15128e-07 (cpu time = 0.09) </before> <after> quality = 0 Average and max absolute error = 53.1382, 11477.9 Average and max relative error = 2.27644e-05, 0.00013658 (cpu time = 0.02) quality = 1 Average and max absolute error = 0.0163915, 6.19778 Average and max relative error = 7.58353e-09, 1.68055e-07 (cpu time = 0.08) quality = 2 Average and max absolute error = 298.462, 128846 Average and max relative error = 0.000128065, 0.00153573 (cpu time = 0.07) </after>