Mercurial > octave-antonio
diff scripts/sparse/pcr.m @ 17336:b81b9d079515
Use '##' for comments which stand alone on a line.
* libinterp/corefcn/besselj.cc, libinterp/corefcn/conv2.cc,
libinterp/corefcn/pinv.cc, libinterp/corefcn/rand.cc,
libinterp/corefcn/regexp.cc, libinterp/corefcn/sqrtm.cc,
libinterp/dldfcn/qr.cc, libinterp/parse-tree/pt-eval.cc,
scripts/general/cplxpair.m, scripts/general/repmat.m, scripts/help/doc.m,
scripts/help/doc_cache_create.m, scripts/image/colorcube.m,
scripts/image/hsv2rgb.m, scripts/image/image.m, scripts/io/strread.m,
scripts/io/textscan.m, scripts/miscellaneous/bzip2.m,
scripts/miscellaneous/edit.m, scripts/miscellaneous/gzip.m,
scripts/optimization/__all_opts__.m, scripts/optimization/fminbnd.m,
scripts/optimization/sqp.m, scripts/pkg/private/get_forge_pkg.m,
scripts/plot/area.m, scripts/plot/stemleaf.m, scripts/plot/surfc.m,
scripts/plot/uiresume.m, scripts/plot/zlabel.m, scripts/polynomial/mkpp.m,
scripts/polynomial/ppval.m, scripts/set/intersect.m, scripts/signal/freqz.m,
scripts/sparse/pcg.m, scripts/sparse/pcr.m, scripts/sparse/svds.m,
scripts/sparse/treelayout.m, scripts/specfun/ellipke.m,
scripts/special-matrix/toeplitz.m, scripts/strings/dec2base.m,
scripts/strings/strsplit.m, scripts/testfun/test.m, test/build-sparse-tests.sh,
test/index.tst, test/system.tst:
Use '##' for comments which stand alone on a line.
| author | Rik <rik@octave.org> |
|---|---|
| date | Wed, 28 Aug 2013 08:27:38 -0700 |
| parents | 5d3a684236b0 |
| children | d63878346099 |
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line diff
--- a/scripts/sparse/pcr.m Wed Aug 28 08:41:55 2013 +0100 +++ b/scripts/sparse/pcr.m Wed Aug 28 08:27:38 2013 -0700 @@ -303,7 +303,7 @@ %!demo -%! # Simplest usage of PCR (see also 'help pcr') +%! ## Simplest usage of PCR (see also 'help pcr') %! %! N = 20; %! A = diag (linspace (-3.1,3,N)); b = rand (N,1); @@ -311,13 +311,13 @@ %! x = pcr (A,b); %! printf ("The solution relative error is %g\n", norm (x-y) / norm (y)); %! -%! # You shouldn't be afraid if PCR issues some warning messages in this -%! # example: watch out in the second example, why it takes N iterations -%! # of PCR to converge to (a very accurate, by the way) solution +%! ## You shouldn't be afraid if PCR issues some warning messages in this +%! ## example: watch out in the second example, why it takes N iterations +%! ## of PCR to converge to (a very accurate, by the way) solution. %!demo -%! # Full output from PCR -%! # We use this output to plot the convergence history +%! ## Full output from PCR +%! ## We use this output to plot the convergence history %! %! N = 20; %! A = diag (linspace (-3.1,30,N)); b = rand (N,1); @@ -330,11 +330,11 @@ %! semilogy ([0:iter], resvec/resvec(1), "o-g;relative residual;"); %!demo -%! # Full output from PCR -%! # We use indefinite matrix based on the Hilbert matrix, with one -%! # strongly negative eigenvalue -%! # Hilbert matrix is extremely ill conditioned, so is ours, -%! # and that's why PCR WILL have problems +%! ## Full output from PCR +%! ## We use indefinite matrix based on the Hilbert matrix, with one +%! ## strongly negative eigenvalue +%! ## Hilbert matrix is extremely ill conditioned, so is ours, +%! ## and that's why PCR WILL have problems %! %! N = 10; %! A = hilb (N); A(1,1) = -A(1,1); b = rand (N,1); @@ -350,14 +350,14 @@ %! semilogy ([0:iter], resvec, "o-g;absolute residual;"); %!demo -%! # Full output from PCR -%! # We use an indefinite matrix based on the 1-D Laplacian matrix for A, -%! # and here we have cond(A) = O(N^2) -%! # That's the reason we need some preconditioner; here we take -%! # a very simple and not powerful Jacobi preconditioner, -%! # which is the diagonal of A +%! ## Full output from PCR +%! ## We use an indefinite matrix based on the 1-D Laplacian matrix for A, +%! ## and here we have cond(A) = O(N^2) +%! ## That's the reason we need some preconditioner; here we take +%! ## a very simple and not powerful Jacobi preconditioner, +%! ## which is the diagonal of A. %! -%! # Note that we use here indefinite preconditioners! +%! ## Note that we use here indefinite preconditioners! %! %! N = 100; %! A = zeros (N,N); @@ -369,7 +369,7 @@ %! X = A \ b; # X is the true solution %! maxit = 80; %! printf ("System condition number is %g\n", cond (A)); -%! # No preconditioner: the convergence is very slow! +%! ## No preconditioner: the convergence is very slow! %! %! [x, flag, relres, iter, resvec] = pcr (A,b,[],maxit); %! clf; @@ -378,7 +378,7 @@ %! semilogy ([0:iter], resvec, "o-g;NO preconditioning: absolute residual;"); %! %! pause (1); -%! # Test Jacobi preconditioner: it will not help much!!! +%! ## Test Jacobi preconditioner: it will not help much!!! %! %! M = diag (diag (A)); # Jacobi preconditioner %! [x, flag, relres, iter, resvec] = pcr (A,b,[],maxit,M); @@ -386,8 +386,8 @@ %! semilogy ([0:iter],resvec,"o-r;JACOBI preconditioner: absolute residual;"); %! %! pause (1); -%! # Test nonoverlapping block Jacobi preconditioner: this one should give -%! # some convergence speedup! +%! ## Test nonoverlapping block Jacobi preconditioner: this one should give +%! ## some convergence speedup! %! %! M = zeros (N,N); k = 4; %! for i=1:k:N # get k x k diagonal blocks of A @@ -399,7 +399,7 @@ %! hold off; %!test -%! # solve small indefinite diagonal system +%! ## solve small indefinite diagonal system %! %! N = 10; %! A = diag (linspace (-10.1,10,N)); b = ones (N,1); @@ -409,8 +409,8 @@ %! assert (flag, 0); %!test -%! # solve tridiagonal system, do not converge in default 20 iterations -%! # should perform max allowable default number of iterations +%! ## solve tridiagonal system, do not converge in default 20 iterations +%! ## should perform max allowable default number of iterations %! %! N = 100; %! A = zeros (N,N); @@ -425,8 +425,8 @@ %! assert (iter, 20); %!test -%! # solve tridiagonal system with "perfect" preconditioner -%! # converges in one iteration +%! ## solve tridiagonal system with "perfect" preconditioner +%! ## converges in one iteration %! %! N = 100; %! A = zeros (N,N);