Mercurial > octave-nkf
annotate liboctave/cruft/daspk/dspigm.f @ 19627:446c46af4b42 stable
strip trailing whitespace from most source files
* Makefile.am, NEWS, build-aux/common.mk, configure.ac,
doc/Makefile.am, doc/doxyhtml/Makefile.am,
doc/interpreter/Makefile.am, doc/interpreter/arith.txi,
doc/interpreter/audio.txi, doc/interpreter/basics.txi,
doc/interpreter/bugs.txi, doc/interpreter/container.txi,
doc/interpreter/cp-idx.txi, doc/interpreter/data.txi,
doc/interpreter/debug.txi, doc/interpreter/diagperm.txi,
doc/interpreter/diffeq.txi, doc/interpreter/doccheck/README,
doc/interpreter/doccheck/spellcheck, doc/interpreter/emacs.txi,
doc/interpreter/errors.txi, doc/interpreter/eval.txi,
doc/interpreter/expr.txi, doc/interpreter/external.txi,
doc/interpreter/fn-idx.txi, doc/interpreter/func.txi,
doc/interpreter/geometry.txi, doc/interpreter/geometryimages.m,
doc/interpreter/gpl.txi, doc/interpreter/grammar.txi,
doc/interpreter/gui.txi, doc/interpreter/image.txi,
doc/interpreter/install.txi, doc/interpreter/interp.txi,
doc/interpreter/interpimages.m, doc/interpreter/intro.txi,
doc/interpreter/io.txi, doc/interpreter/java.txi,
doc/interpreter/linalg.txi, doc/interpreter/macros.texi,
doc/interpreter/matrix.txi, doc/interpreter/munge-texi.pl,
doc/interpreter/nonlin.txi, doc/interpreter/numbers.txi,
doc/interpreter/obsolete.txi, doc/interpreter/octave-config.1,
doc/interpreter/octave.texi, doc/interpreter/oop.txi,
doc/interpreter/op-idx.txi, doc/interpreter/optim.txi,
doc/interpreter/package.txi, doc/interpreter/plot.txi,
doc/interpreter/poly.txi, doc/interpreter/preface.txi,
doc/interpreter/quad.txi, doc/interpreter/set.txi,
doc/interpreter/signal.txi, doc/interpreter/sparse.txi,
doc/interpreter/sparseimages.m, doc/interpreter/splineimages.m,
doc/interpreter/stats.txi, doc/interpreter/stmt.txi,
doc/interpreter/strings.txi, doc/interpreter/system.txi,
doc/interpreter/testfun.txi, doc/interpreter/tips.txi,
doc/interpreter/var.txi, doc/interpreter/vectorize.txi,
doc/liboctave/Makefile.am, doc/liboctave/array.texi,
doc/liboctave/bugs.texi, doc/liboctave/cp-idx.texi,
doc/liboctave/dae.texi, doc/liboctave/diffeq.texi,
doc/liboctave/error.texi, doc/liboctave/factor.texi,
doc/liboctave/fn-idx.texi, doc/liboctave/gpl.texi,
doc/liboctave/install.texi, doc/liboctave/intro.texi,
doc/liboctave/liboctave.texi, doc/liboctave/matvec.texi,
doc/liboctave/nleqn.texi, doc/liboctave/nlfunc.texi,
doc/liboctave/ode.texi, doc/liboctave/optim.texi,
doc/liboctave/preface.texi, doc/liboctave/quad.texi,
doc/liboctave/range.texi, doc/refcard/Makefile.am,
doc/refcard/refcard.tex, etc/HACKING, etc/NEWS.1, etc/NEWS.2,
etc/NEWS.3, etc/OLD-ChangeLogs/ChangeLog,
etc/OLD-ChangeLogs/doc-ChangeLog,
etc/OLD-ChangeLogs/scripts-ChangeLog,
etc/OLD-ChangeLogs/src-ChangeLog, etc/OLD-ChangeLogs/test-ChangeLog,
etc/PROJECTS, etc/README.Cygwin, etc/README.MacOS, etc/README.MinGW,
etc/README.gnuplot, etc/gdbinit, etc/icons/Makefile.am,
examples/@polynomial/end.m, examples/@polynomial/subsasgn.m,
examples/Makefile.am, examples/standalonebuiltin.cc,
libgui/Makefile.am, libgui/qterminal/libqterminal/README,
libgui/qterminal/libqterminal/unix/BlockArray.cpp,
libgui/qterminal/libqterminal/unix/BlockArray.h,
libgui/qterminal/libqterminal/unix/Character.h,
libgui/qterminal/libqterminal/unix/CharacterColor.h,
libgui/qterminal/libqterminal/unix/Emulation.cpp,
libgui/qterminal/libqterminal/unix/Emulation.h,
libgui/qterminal/libqterminal/unix/Filter.cpp,
libgui/qterminal/libqterminal/unix/Filter.h,
libgui/qterminal/libqterminal/unix/History.cpp,
libgui/qterminal/libqterminal/unix/History.h,
libgui/qterminal/libqterminal/unix/KeyboardTranslator.cpp,
libgui/qterminal/libqterminal/unix/KeyboardTranslator.h,
libgui/qterminal/libqterminal/unix/LineFont.h,
libgui/qterminal/libqterminal/unix/QUnixTerminalImpl.cpp,
libgui/qterminal/libqterminal/unix/QUnixTerminalImpl.h,
libgui/qterminal/libqterminal/unix/Screen.cpp,
libgui/qterminal/libqterminal/unix/Screen.h,
libgui/qterminal/libqterminal/unix/ScreenWindow.cpp,
libgui/qterminal/libqterminal/unix/ScreenWindow.h,
libgui/qterminal/libqterminal/unix/TerminalCharacterDecoder.cpp,
libgui/qterminal/libqterminal/unix/TerminalCharacterDecoder.h,
libgui/qterminal/libqterminal/unix/Vt102Emulation.h,
libgui/qterminal/libqterminal/win32/QWinTerminalImpl.cpp,
libgui/qterminal/qterminal/main.cpp,
libgui/src/m-editor/file-editor-tab.cc, libgui/src/octave-gui.cc,
libgui/src/octave-qt-link.cc, libinterp/corefcn/data.cc,
libinterp/corefcn/defun-int.h, libinterp/corefcn/det.cc,
libinterp/corefcn/gl2ps-renderer.cc, libinterp/corefcn/graphics.cc,
libinterp/corefcn/graphics.in.h, libinterp/corefcn/ls-mat5.cc,
libinterp/corefcn/lu.cc, libinterp/corefcn/oct-tex-parser.yy,
libinterp/corefcn/oct-tex-symbols.in, libinterp/corefcn/quadcc.cc,
libinterp/corefcn/zfstream.cc, libinterp/dldfcn/__eigs__.cc,
libinterp/dldfcn/__voronoi__.cc, libinterp/gendoc.pl,
libinterp/genprops.awk, libinterp/mk-errno-list, libinterp/mk-pkg-add,
libinterp/mkbuiltins, libinterp/mkdefs, libinterp/mkdocs,
libinterp/mkops, libinterp/octave-value/ov-java.cc,
libinterp/parse-tree/lex.ll, libinterp/parse-tree/oct-parse.in.yy,
libinterp/parse-tree/octave.gperf, liboctave/Makefile.am,
liboctave/array/Array.cc, liboctave/array/module.mk,
liboctave/cruft/daspk/datv.f, liboctave/cruft/daspk/dcnst0.f,
liboctave/cruft/daspk/dcnstr.f, liboctave/cruft/daspk/ddasic.f,
liboctave/cruft/daspk/ddasid.f, liboctave/cruft/daspk/ddasik.f,
liboctave/cruft/daspk/ddaspk.f, liboctave/cruft/daspk/ddstp.f,
liboctave/cruft/daspk/ddwnrm.f, liboctave/cruft/daspk/dfnrmd.f,
liboctave/cruft/daspk/dfnrmk.f, liboctave/cruft/daspk/dhels.f,
liboctave/cruft/daspk/dheqr.f, liboctave/cruft/daspk/dinvwt.f,
liboctave/cruft/daspk/dlinsd.f, liboctave/cruft/daspk/dlinsk.f,
liboctave/cruft/daspk/dmatd.f, liboctave/cruft/daspk/dnedd.f,
liboctave/cruft/daspk/dnedk.f, liboctave/cruft/daspk/dnsd.f,
liboctave/cruft/daspk/dnsid.f, liboctave/cruft/daspk/dnsik.f,
liboctave/cruft/daspk/dnsk.f, liboctave/cruft/daspk/dorth.f,
liboctave/cruft/daspk/dslvd.f, liboctave/cruft/daspk/dslvk.f,
liboctave/cruft/daspk/dspigm.f, liboctave/cruft/daspk/dyypnw.f,
liboctave/cruft/dasrt/ddasrt.f, liboctave/cruft/dasrt/drchek.f,
liboctave/cruft/dassl/ddaslv.f, liboctave/cruft/dassl/ddassl.f,
liboctave/cruft/misc/blaswrap.c, liboctave/cruft/misc/module.mk,
liboctave/cruft/odepack/cfode.f, liboctave/cruft/odepack/dlsode.f,
liboctave/cruft/odepack/ewset.f, liboctave/cruft/odepack/intdy.f,
liboctave/cruft/odepack/prepj.f, liboctave/cruft/odepack/sintdy.f,
liboctave/cruft/odepack/slsode.f, liboctave/cruft/odepack/solsy.f,
liboctave/cruft/odepack/ssolsy.f, liboctave/cruft/odepack/stode.f,
liboctave/cruft/odepack/vnorm.f, liboctave/cruft/ranlib/Basegen.doc,
liboctave/cruft/ranlib/README, liboctave/cruft/ranlib/genbet.f,
liboctave/cruft/ranlib/genexp.f, liboctave/cruft/ranlib/gennch.f,
liboctave/cruft/ranlib/gennf.f, liboctave/cruft/ranlib/gennor.f,
liboctave/cruft/ranlib/getsd.f, liboctave/cruft/ranlib/initgn.f,
liboctave/cruft/ranlib/phrtsd.f, liboctave/cruft/ranlib/randlib.fdoc,
liboctave/cruft/ranlib/setsd.f, liboctave/cruft/ranlib/tstgmn.for,
liboctave/cruft/ranlib/tstmid.for, liboctave/cruft/slatec-fn/atanh.f,
liboctave/cruft/slatec-fn/datanh.f,
liboctave/cruft/slatec-fn/xgmainc.f,
liboctave/cruft/slatec-fn/xsgmainc.f, liboctave/numeric/module.mk,
liboctave/operators/mk-ops.awk, liboctave/operators/mx-ops,
liboctave/operators/sparse-mk-ops.awk,
liboctave/operators/sparse-mx-ops, liboctave/operators/vx-ops,
liboctave/util/module.mk, run-octave.in, scripts/@ftp/ftp.m,
scripts/audio/wavread.m, scripts/deprecated/java_convert_matrix.m,
scripts/deprecated/java_debug.m, scripts/deprecated/java_invoke.m,
scripts/deprecated/java_new.m,
scripts/deprecated/java_unsigned_conversion.m,
scripts/deprecated/javafields.m, scripts/deprecated/javamethods.m,
scripts/deprecated/shell_cmd.m, scripts/general/accumarray.m,
scripts/general/display.m, scripts/general/fieldnames.m,
scripts/general/interp1.m, scripts/general/interp2.m,
scripts/general/interp3.m, scripts/general/isa.m,
scripts/general/methods.m, scripts/general/sortrows.m,
scripts/geometry/convhull.m, scripts/geometry/delaunay.m,
scripts/geometry/delaunay3.m, scripts/geometry/delaunayn.m,
scripts/geometry/griddata.m, scripts/geometry/griddatan.m,
scripts/geometry/voronoi.m, scripts/geometry/voronoin.m,
scripts/gui/guihandles.m, scripts/gui/inputdlg.m,
scripts/gui/listdlg.m, scripts/gui/msgbox.m, scripts/gui/questdlg.m,
scripts/gui/uigetfile.m, scripts/gui/waitbar.m, scripts/gui/warndlg.m,
scripts/help/doc.m, scripts/help/help.m, scripts/help/type.m,
scripts/image/bone.m, scripts/image/cmpermute.m,
scripts/image/cmunique.m, scripts/image/colorcube.m,
scripts/image/colormap.m, scripts/image/contrast.m,
scripts/image/gray2ind.m, scripts/image/image.m,
scripts/image/imshow.m, scripts/image/ind2gray.m, scripts/image/jet.m,
scripts/image/rgb2ntsc.m, scripts/image/spinmap.m,
scripts/io/importdata.m, scripts/io/strread.m, scripts/io/textread.m,
scripts/io/textscan.m, scripts/java/java_get.m,
scripts/java/java_set.m, scripts/java/javaaddpath.m,
scripts/java/javaclasspath.m, scripts/java/javamem.m,
scripts/linear-algebra/linsolve.m, scripts/linear-algebra/qzhess.m,
scripts/miscellaneous/debug.m, scripts/miscellaneous/desktop.m,
scripts/miscellaneous/dir.m, scripts/miscellaneous/dos.m,
scripts/miscellaneous/edit.m, scripts/miscellaneous/fact.m,
scripts/miscellaneous/getappdata.m, scripts/miscellaneous/inputname.m,
scripts/miscellaneous/license.m, scripts/miscellaneous/ls_command.m,
scripts/miscellaneous/run.m, scripts/miscellaneous/setfield.m,
scripts/miscellaneous/unix.m, scripts/miscellaneous/ver.m,
scripts/mk-pkg-add, scripts/mkdoc.pl,
scripts/optimization/fminsearch.m, scripts/optimization/optimset.m,
scripts/optimization/sqp.m, scripts/pkg/pkg.m,
scripts/pkg/private/create_pkgadddel.m,
scripts/pkg/private/fix_depends.m, scripts/pkg/private/install.m,
scripts/plot/appearance/axis.m, scripts/plot/appearance/box.m,
scripts/plot/appearance/clabel.m, scripts/plot/appearance/daspect.m,
scripts/plot/appearance/datetick.m, scripts/plot/appearance/grid.m,
scripts/plot/appearance/legend.m, scripts/plot/appearance/orient.m,
scripts/plot/appearance/shading.m, scripts/plot/appearance/text.m,
scripts/plot/appearance/title.m, scripts/plot/appearance/xlabel.m,
scripts/plot/appearance/ylabel.m, scripts/plot/appearance/zlabel.m,
scripts/plot/draw/area.m, scripts/plot/draw/bar.m,
scripts/plot/draw/barh.m, scripts/plot/draw/colorbar.m,
scripts/plot/draw/contour.m, scripts/plot/draw/contour3.m,
scripts/plot/draw/contourf.m, scripts/plot/draw/ellipsoid.m,
scripts/plot/draw/errorbar.m, scripts/plot/draw/ezcontour.m,
scripts/plot/draw/ezcontourf.m, scripts/plot/draw/ezmesh.m,
scripts/plot/draw/ezpolar.m, scripts/plot/draw/fill.m,
scripts/plot/draw/fplot.m, scripts/plot/draw/hist.m,
scripts/plot/draw/meshc.m, scripts/plot/draw/meshz.m,
scripts/plot/draw/pareto.m, scripts/plot/draw/patch.m,
scripts/plot/draw/peaks.m, scripts/plot/draw/pie.m,
scripts/plot/draw/pie3.m, scripts/plot/draw/plot.m,
scripts/plot/draw/plotyy.m, scripts/plot/draw/private/__bar__.m,
scripts/plot/draw/private/__contour__.m,
scripts/plot/draw/private/__errplot__.m,
scripts/plot/draw/private/__ezplot__.m,
scripts/plot/draw/private/__patch__.m,
scripts/plot/draw/private/__stem__.m, scripts/plot/draw/rectangle.m,
scripts/plot/draw/ribbon.m, scripts/plot/draw/rose.m,
scripts/plot/draw/scatter.m, scripts/plot/draw/scatter3.m,
scripts/plot/draw/semilogx.m, scripts/plot/draw/shrinkfaces.m,
scripts/plot/draw/sombrero.m, scripts/plot/draw/sphere.m,
scripts/plot/draw/stairs.m, scripts/plot/draw/stem.m,
scripts/plot/draw/stemleaf.m, scripts/plot/draw/surf.m,
scripts/plot/draw/surface.m, scripts/plot/draw/surfc.m,
scripts/plot/draw/surfl.m, scripts/plot/draw/surfnorm.m,
scripts/plot/draw/tetramesh.m, scripts/plot/draw/trimesh.m,
scripts/plot/draw/triplot.m, scripts/plot/draw/trisurf.m,
scripts/plot/util/__gnuplot_drawnow__.m,
scripts/plot/util/__plt_get_axis_arg__.m, scripts/plot/util/axes.m,
scripts/plot/util/clf.m, scripts/plot/util/copyobj.m,
scripts/plot/util/figure.m, scripts/plot/util/gcbo.m,
scripts/plot/util/graphics_toolkit.m, scripts/plot/util/hggroup.m,
scripts/plot/util/meshgrid.m, scripts/plot/util/newplot.m,
scripts/plot/util/print.m,
scripts/plot/util/private/__add_default_menu__.m,
scripts/plot/util/private/__fltk_print__.m,
scripts/plot/util/private/__gnuplot_print__.m,
scripts/plot/util/private/__print_parse_opts__.m,
scripts/plot/util/refreshdata.m, scripts/plot/util/subplot.m,
scripts/polynomial/conv.m, scripts/polynomial/poly.m,
scripts/polynomial/polyeig.m, scripts/polynomial/polyfit.m,
scripts/polynomial/polyval.m,
scripts/polynomial/private/__splinefit__.m,
scripts/polynomial/spline.m, scripts/prefs/prefdir.m,
scripts/prefs/preferences.m, scripts/prefs/private/prefsfile.m,
scripts/prefs/rmpref.m, scripts/signal/freqz.m,
scripts/signal/module.mk, scripts/sparse/eigs.m, scripts/sparse/pcg.m,
scripts/sparse/private/__sprand_impl__.m, scripts/sparse/sprand.m,
scripts/sparse/sprandn.m, scripts/sparse/spy.m, scripts/sparse/svds.m,
scripts/specfun/expint.m, scripts/specfun/factor.m,
scripts/special-matrix/gallery.m, scripts/special-matrix/hankel.m,
scripts/special-matrix/toeplitz.m, scripts/startup/inputrc,
scripts/statistics/base/kurtosis.m, scripts/statistics/base/moment.m,
scripts/statistics/base/qqplot.m, scripts/statistics/base/var.m,
scripts/statistics/distributions/betarnd.m,
scripts/statistics/distributions/binoinv.m,
scripts/statistics/distributions/binopdf.m,
scripts/statistics/distributions/binornd.m,
scripts/statistics/distributions/cauchy_rnd.m,
scripts/statistics/distributions/chi2rnd.m,
scripts/statistics/distributions/discrete_pdf.m,
scripts/statistics/distributions/discrete_rnd.m,
scripts/statistics/distributions/empirical_rnd.m,
scripts/statistics/distributions/exprnd.m,
scripts/statistics/distributions/frnd.m,
scripts/statistics/distributions/gamrnd.m,
scripts/statistics/distributions/geornd.m,
scripts/statistics/distributions/hygernd.m,
scripts/statistics/distributions/kolmogorov_smirnov_cdf.m,
scripts/statistics/distributions/laplace_cdf.m,
scripts/statistics/distributions/laplace_pdf.m,
scripts/statistics/distributions/logistic_cdf.m,
scripts/statistics/distributions/logistic_pdf.m,
scripts/statistics/distributions/lognrnd.m,
scripts/statistics/distributions/nbincdf.m,
scripts/statistics/distributions/nbininv.m,
scripts/statistics/distributions/nbinpdf.m,
scripts/statistics/distributions/nbinrnd.m,
scripts/statistics/distributions/normrnd.m,
scripts/statistics/distributions/poissinv.m,
scripts/statistics/distributions/poissrnd.m,
scripts/statistics/distributions/tinv.m,
scripts/statistics/distributions/trnd.m,
scripts/statistics/distributions/unidcdf.m,
scripts/statistics/distributions/unidpdf.m,
scripts/statistics/distributions/unidrnd.m,
scripts/statistics/distributions/unifrnd.m,
scripts/statistics/distributions/wblrnd.m,
scripts/statistics/models/module.mk,
scripts/statistics/tests/kruskal_wallis_test.m,
scripts/strings/base2dec.m, scripts/strings/deblank.m,
scripts/strings/dec2base.m, scripts/strings/dec2bin.m,
scripts/strings/dec2hex.m, scripts/strings/mat2str.m,
scripts/strings/ostrsplit.m, scripts/strings/regexptranslate.m,
scripts/strings/str2num.m, scripts/strings/strcat.m,
scripts/strings/strjoin.m, scripts/strings/strsplit.m,
scripts/strings/strtok.m, scripts/strings/strtrim.m,
scripts/strings/strtrunc.m, scripts/strings/substr.m,
scripts/testfun/__run_test_suite__.m, scripts/testfun/speed.m,
scripts/testfun/test.m, scripts/time/asctime.m,
scripts/time/datenum.m, scripts/time/datevec.m,
scripts/time/weekday.m, src/Makefile.am, test/Makefile.am,
test/build-bc-overload-tests.sh, test/build-sparse-tests.sh,
test/jit.tst, test/line-continue.tst: Strip trailing whitespace.
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Tue, 20 Jan 2015 08:26:57 -0500 |
| parents | 648dabbb4c6b |
| children |
| rev | line source |
|---|---|
| 3911 | 1 C Work performed under the auspices of the U.S. Department of Energy |
|
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changeset
|
2 C by Lawrence Livermore National Laboratory under contract number |
| 3911 | 3 C W-7405-Eng-48. |
| 4 C | |
| 5 SUBROUTINE DSPIGM (NEQ, TN, Y, YPRIME, SAVR, R, WGHT, MAXL, | |
| 6 * MAXLP1, KMP, EPLIN, CJ, RES, IRES, NRE, PSOL, NPSL, Z, V, | |
| 7 * HES, Q, LGMR, WP, IWP, WK, DL, RHOK, IFLAG, IRST, NRSTS, | |
| 8 * RPAR, IPAR) | |
| 9 C | |
| 10 C***BEGIN PROLOGUE DSPIGM | |
| 11 C***DATE WRITTEN 890101 (YYMMDD) | |
| 12 C***REVISION DATE 900926 (YYMMDD) | |
| 13 C***REVISION DATE 940927 Removed MNEWT and added RHOK in call list. | |
| 14 C | |
| 15 C | |
| 16 C----------------------------------------------------------------------- | |
| 17 C***DESCRIPTION | |
| 18 C | |
| 19 C This routine solves the linear system A * Z = R using a scaled | |
| 20 C preconditioned version of the generalized minimum residual method. | |
| 21 C An initial guess of Z = 0 is assumed. | |
| 22 C | |
| 23 C On entry | |
| 24 C | |
| 25 C NEQ = Problem size, passed to PSOL. | |
| 26 C | |
| 27 C TN = Current Value of T. | |
| 28 C | |
| 29 C Y = Array Containing current dependent variable vector. | |
| 30 C | |
| 31 C YPRIME = Array Containing current first derivative of Y. | |
| 32 C | |
| 33 C SAVR = Array containing current value of G(T,Y,YPRIME). | |
| 34 C | |
| 35 C R = The right hand side of the system A*Z = R. | |
| 36 C R is also used as work space when computing | |
| 37 C the final approximation and will therefore be | |
| 38 C destroyed. | |
| 39 C (R is the same as V(*,MAXL+1) in the call to DSPIGM.) | |
| 40 C | |
| 41 C WGHT = The vector of length NEQ containing the nonzero | |
| 42 C elements of the diagonal scaling matrix. | |
| 43 C | |
| 44 C MAXL = The maximum allowable order of the matrix H. | |
| 45 C | |
| 46 C MAXLP1 = MAXL + 1, used for dynamic dimensioning of HES. | |
| 47 C | |
| 48 C KMP = The number of previous vectors the new vector, VNEW, | |
| 49 C must be made orthogonal to. (KMP .LE. MAXL.) | |
| 50 C | |
| 51 C EPLIN = Tolerance on residuals R-A*Z in weighted rms norm. | |
| 52 C | |
|
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John W. Eaton <jwe@octave.org>
parents:
15271
diff
changeset
|
53 C CJ = Scalar proportional to current value of |
| 3911 | 54 C 1/(step size H). |
| 55 C | |
| 56 C WK = Real work array used by routine DATV and PSOL. | |
| 57 C | |
| 58 C DL = Real work array used for calculation of the residual | |
| 59 C norm RHO when the method is incomplete (KMP.LT.MAXL) | |
| 60 C and/or when using restarting. | |
| 61 C | |
| 62 C WP = Real work array used by preconditioner PSOL. | |
| 63 C | |
| 64 C IWP = Integer work array used by preconditioner PSOL. | |
| 65 C | |
| 66 C IRST = Method flag indicating if restarting is being | |
| 67 C performed. IRST .GT. 0 means restarting is active, | |
| 68 C while IRST = 0 means restarting is not being used. | |
| 69 C | |
| 70 C NRSTS = Counter for the number of restarts on the current | |
| 71 C call to DSPIGM. If NRSTS .GT. 0, then the residual | |
| 72 C R is already scaled, and so scaling of R is not | |
| 73 C necessary. | |
| 74 C | |
| 75 C | |
| 76 C On Return | |
| 77 C | |
| 78 C Z = The final computed approximation to the solution | |
| 79 C of the system A*Z = R. | |
| 80 C | |
| 81 C LGMR = The number of iterations performed and | |
| 82 C the current order of the upper Hessenberg | |
| 83 C matrix HES. | |
| 84 C | |
| 85 C NRE = The number of calls to RES (i.e. DATV) | |
| 86 C | |
| 87 C NPSL = The number of calls to PSOL. | |
| 88 C | |
| 89 C V = The neq by (LGMR+1) array containing the LGMR | |
| 90 C orthogonal vectors V(*,1) to V(*,LGMR). | |
| 91 C | |
| 92 C HES = The upper triangular factor of the QR decomposition | |
| 93 C of the (LGMR+1) by LGMR upper Hessenberg matrix whose | |
| 94 C entries are the scaled inner-products of A*V(*,I) | |
| 95 C and V(*,K). | |
| 96 C | |
| 97 C Q = Real array of length 2*MAXL containing the components | |
| 98 C of the givens rotations used in the QR decomposition | |
| 99 C of HES. It is loaded in DHEQR and used in DHELS. | |
| 100 C | |
| 101 C IRES = Error flag from RES. | |
| 102 C | |
|
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103 C DL = Scaled preconditioned residual, |
| 3911 | 104 C (D-inverse)*(P-inverse)*(R-A*Z). Only loaded when |
| 105 C performing restarts of the Krylov iteration. | |
| 106 C | |
| 107 C RHOK = Weighted norm of final preconditioned residual. | |
| 108 C | |
| 109 C IFLAG = Integer error flag.. | |
| 110 C 0 Means convergence in LGMR iterations, LGMR.LE.MAXL. | |
| 111 C 1 Means the convergence test did not pass in MAXL | |
| 112 C iterations, but the new residual norm (RHO) is | |
| 113 C .LT. the old residual norm (RNRM), and so Z is | |
| 114 C computed. | |
| 115 C 2 Means the convergence test did not pass in MAXL | |
| 116 C iterations, new residual norm (RHO) .GE. old residual | |
| 117 C norm (RNRM), and the initial guess, Z = 0, is | |
| 118 C returned. | |
| 119 C 3 Means there was a recoverable error in PSOL | |
| 120 C caused by the preconditioner being out of date. | |
| 121 C -1 Means there was an unrecoverable error in PSOL. | |
| 122 C | |
| 123 C----------------------------------------------------------------------- | |
| 124 C***ROUTINES CALLED | |
| 125 C PSOL, DNRM2, DSCAL, DATV, DORTH, DHEQR, DCOPY, DHELS, DAXPY | |
| 126 C | |
| 127 C***END PROLOGUE DSPIGM | |
| 128 C | |
| 129 INTEGER NEQ,MAXL,MAXLP1,KMP,IRES,NRE,NPSL,LGMR,IWP, | |
| 130 1 IFLAG,IRST,NRSTS,IPAR | |
| 131 DOUBLE PRECISION TN,Y,YPRIME,SAVR,R,WGHT,EPLIN,CJ,Z,V,HES,Q,WP,WK, | |
| 132 1 DL,RHOK,RPAR | |
| 133 DIMENSION Y(*), YPRIME(*), SAVR(*), R(*), WGHT(*), Z(*), | |
| 134 1 V(NEQ,*), HES(MAXLP1,*), Q(*), WP(*), IWP(*), WK(*), DL(*), | |
| 135 2 RPAR(*), IPAR(*) | |
| 136 INTEGER I, IER, INFO, IP1, I2, J, K, LL, LLP1 | |
| 137 DOUBLE PRECISION RNRM,C,DLNRM,PROD,RHO,S,SNORMW,DNRM2,TEM | |
| 138 EXTERNAL RES, PSOL | |
| 139 C | |
| 140 IER = 0 | |
| 141 IFLAG = 0 | |
| 142 LGMR = 0 | |
| 143 NPSL = 0 | |
| 144 NRE = 0 | |
| 145 C----------------------------------------------------------------------- | |
| 146 C The initial guess for Z is 0. The initial residual is therefore | |
| 147 C the vector R. Initialize Z to 0. | |
| 148 C----------------------------------------------------------------------- | |
| 149 DO 10 I = 1,NEQ | |
| 150 10 Z(I) = 0.0D0 | |
| 151 C----------------------------------------------------------------------- | |
| 152 C Apply inverse of left preconditioner to vector R if NRSTS .EQ. 0. | |
| 153 C Form V(*,1), the scaled preconditioned right hand side. | |
| 154 C----------------------------------------------------------------------- | |
| 155 IF (NRSTS .EQ. 0) THEN | |
| 156 CALL PSOL (NEQ, TN, Y, YPRIME, SAVR, WK, CJ, WGHT, WP, IWP, | |
| 157 1 R, EPLIN, IER, RPAR, IPAR) | |
| 158 NPSL = 1 | |
| 159 IF (IER .NE. 0) GO TO 300 | |
| 160 DO 30 I = 1,NEQ | |
| 161 30 V(I,1) = R(I)*WGHT(I) | |
| 162 ELSE | |
| 163 DO 35 I = 1,NEQ | |
| 164 35 V(I,1) = R(I) | |
| 165 ENDIF | |
| 166 C----------------------------------------------------------------------- | |
| 167 C Calculate norm of scaled vector V(*,1) and normalize it | |
| 168 C If, however, the norm of V(*,1) (i.e. the norm of the preconditioned | |
| 169 C residual) is .le. EPLIN, then return with Z=0. | |
| 170 C----------------------------------------------------------------------- | |
| 171 RNRM = DNRM2 (NEQ, V, 1) | |
| 172 IF (RNRM .LE. EPLIN) THEN | |
| 173 RHOK = RNRM | |
| 174 RETURN | |
| 175 ENDIF | |
| 176 TEM = 1.0D0/RNRM | |
| 177 CALL DSCAL (NEQ, TEM, V(1,1), 1) | |
| 178 C----------------------------------------------------------------------- | |
| 179 C Zero out the HES array. | |
| 180 C----------------------------------------------------------------------- | |
| 181 DO 65 J = 1,MAXL | |
| 182 DO 60 I = 1,MAXLP1 | |
| 183 60 HES(I,J) = 0.0D0 | |
| 184 65 CONTINUE | |
| 185 C----------------------------------------------------------------------- | |
| 186 C Main loop to compute the vectors V(*,2) to V(*,MAXL). | |
| 187 C The running product PROD is needed for the convergence test. | |
| 188 C----------------------------------------------------------------------- | |
| 189 PROD = 1.0D0 | |
| 190 DO 90 LL = 1,MAXL | |
| 191 LGMR = LL | |
| 192 C----------------------------------------------------------------------- | |
| 193 C Call routine DATV to compute VNEW = ABAR*V(LL), where ABAR is | |
| 194 C the matrix A with scaling and inverse preconditioner factors applied. | |
| 195 C Call routine DORTH to orthogonalize the new vector VNEW = V(*,LL+1). | |
| 196 C call routine DHEQR to update the factors of HES. | |
| 197 C----------------------------------------------------------------------- | |
| 198 CALL DATV (NEQ, Y, TN, YPRIME, SAVR, V(1,LL), WGHT, Z, | |
| 199 1 RES, IRES, PSOL, V(1,LL+1), WK, WP, IWP, CJ, EPLIN, | |
| 200 1 IER, NRE, NPSL, RPAR, IPAR) | |
| 201 IF (IRES .LT. 0) RETURN | |
| 202 IF (IER .NE. 0) GO TO 300 | |
| 203 CALL DORTH (V(1,LL+1), V, HES, NEQ, LL, MAXLP1, KMP, SNORMW) | |
| 204 HES(LL+1,LL) = SNORMW | |
| 205 CALL DHEQR (HES, MAXLP1, LL, Q, INFO, LL) | |
| 206 IF (INFO .EQ. LL) GO TO 120 | |
| 207 C----------------------------------------------------------------------- | |
| 208 C Update RHO, the estimate of the norm of the residual R - A*ZL. | |
| 209 C If KMP .LT. MAXL, then the vectors V(*,1),...,V(*,LL+1) are not | |
| 210 C necessarily orthogonal for LL .GT. KMP. The vector DL must then | |
| 211 C be computed, and its norm used in the calculation of RHO. | |
| 212 C----------------------------------------------------------------------- | |
| 213 PROD = PROD*Q(2*LL) | |
| 214 RHO = ABS(PROD*RNRM) | |
| 215 IF ((LL.GT.KMP) .AND. (KMP.LT.MAXL)) THEN | |
| 216 IF (LL .EQ. KMP+1) THEN | |
| 217 CALL DCOPY (NEQ, V(1,1), 1, DL, 1) | |
| 218 DO 75 I = 1,KMP | |
| 219 IP1 = I + 1 | |
| 220 I2 = I*2 | |
| 221 S = Q(I2) | |
| 222 C = Q(I2-1) | |
| 223 DO 70 K = 1,NEQ | |
| 224 70 DL(K) = S*DL(K) + C*V(K,IP1) | |
| 225 75 CONTINUE | |
| 226 ENDIF | |
| 227 S = Q(2*LL) | |
| 228 C = Q(2*LL-1)/SNORMW | |
| 229 LLP1 = LL + 1 | |
| 230 DO 80 K = 1,NEQ | |
| 231 80 DL(K) = S*DL(K) + C*V(K,LLP1) | |
| 232 DLNRM = DNRM2 (NEQ, DL, 1) | |
| 233 RHO = RHO*DLNRM | |
| 234 ENDIF | |
| 235 C----------------------------------------------------------------------- | |
| 236 C Test for convergence. If passed, compute approximation ZL. | |
| 237 C If failed and LL .LT. MAXL, then continue iterating. | |
| 238 C----------------------------------------------------------------------- | |
| 239 IF (RHO .LE. EPLIN) GO TO 200 | |
| 240 IF (LL .EQ. MAXL) GO TO 100 | |
| 241 C----------------------------------------------------------------------- | |
| 242 C Rescale so that the norm of V(1,LL+1) is one. | |
| 243 C----------------------------------------------------------------------- | |
| 244 TEM = 1.0D0/SNORMW | |
| 245 CALL DSCAL (NEQ, TEM, V(1,LL+1), 1) | |
| 246 90 CONTINUE | |
| 247 100 CONTINUE | |
| 248 IF (RHO .LT. RNRM) GO TO 150 | |
| 249 120 CONTINUE | |
| 250 IFLAG = 2 | |
| 251 DO 130 I = 1,NEQ | |
| 252 130 Z(I) = 0.D0 | |
| 253 RETURN | |
| 254 150 IFLAG = 1 | |
| 255 C----------------------------------------------------------------------- | |
| 256 C The tolerance was not met, but the residual norm was reduced. | |
| 257 C If performing restarting (IRST .gt. 0) calculate the residual vector | |
|
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258 C RL and store it in the DL array. If the incomplete version is |
| 3911 | 259 C being used (KMP .lt. MAXL) then DL has already been calculated. |
| 260 C----------------------------------------------------------------------- | |
| 261 IF (IRST .GT. 0) THEN | |
| 262 IF (KMP .EQ. MAXL) THEN | |
| 263 C | |
| 264 C Calculate DL from the V(I)'s. | |
| 265 C | |
| 266 CALL DCOPY (NEQ, V(1,1), 1, DL, 1) | |
| 267 MAXLM1 = MAXL - 1 | |
| 268 DO 175 I = 1,MAXLM1 | |
| 269 IP1 = I + 1 | |
| 270 I2 = I*2 | |
| 271 S = Q(I2) | |
| 272 C = Q(I2-1) | |
| 273 DO 170 K = 1,NEQ | |
| 274 170 DL(K) = S*DL(K) + C*V(K,IP1) | |
| 275 175 CONTINUE | |
| 276 S = Q(2*MAXL) | |
| 277 C = Q(2*MAXL-1)/SNORMW | |
| 278 DO 180 K = 1,NEQ | |
| 279 180 DL(K) = S*DL(K) + C*V(K,MAXLP1) | |
| 280 ENDIF | |
| 281 C | |
| 282 C Scale DL by RNRM*PROD to obtain the residual RL. | |
| 283 C | |
| 284 TEM = RNRM*PROD | |
| 285 CALL DSCAL(NEQ, TEM, DL, 1) | |
| 286 ENDIF | |
| 287 C----------------------------------------------------------------------- | |
| 288 C Compute the approximation ZL to the solution. | |
| 289 C Since the vector Z was used as work space, and the initial guess | |
| 290 C of the Newton correction is zero, Z must be reset to zero. | |
| 291 C----------------------------------------------------------------------- | |
| 292 200 CONTINUE | |
| 293 LL = LGMR | |
| 294 LLP1 = LL + 1 | |
| 295 DO 210 K = 1,LLP1 | |
| 296 210 R(K) = 0.0D0 | |
| 297 R(1) = RNRM | |
| 298 CALL DHELS (HES, MAXLP1, LL, Q, R) | |
| 299 DO 220 K = 1,NEQ | |
| 300 220 Z(K) = 0.0D0 | |
| 301 DO 230 I = 1,LL | |
| 302 CALL DAXPY (NEQ, R(I), V(1,I), 1, Z, 1) | |
| 303 230 CONTINUE | |
| 304 DO 240 I = 1,NEQ | |
| 305 240 Z(I) = Z(I)/WGHT(I) | |
| 306 C Load RHO into RHOK. | |
| 307 RHOK = RHO | |
| 308 RETURN | |
| 309 C----------------------------------------------------------------------- | |
| 310 C This block handles error returns forced by routine PSOL. | |
| 311 C----------------------------------------------------------------------- | |
| 312 300 CONTINUE | |
| 313 IF (IER .LT. 0) IFLAG = -1 | |
| 314 IF (IER .GT. 0) IFLAG = 3 | |
| 315 C | |
| 316 RETURN | |
| 317 C | |
| 318 C------END OF SUBROUTINE DSPIGM----------------------------------------- | |
| 319 END |