Mercurial > octave
view liboctave/array/CMatrix.cc @ 22755:3a2b891d0b33
maint: Standardize Copyright formatting.
* Makefile.am, README, build-aux/check-subst-vars.in.sh,
build-aux/find-files-with-tests.sh, build-aux/mk-builtins.sh,
build-aux/mk-default-qt-settings.in.sh, build-aux/mk-f77-def.in.sh,
build-aux/mk-hg-id.sh, build-aux/mk-mxarray-h.in.sh,
build-aux/mk-octave-config-h.sh, build-aux/mk-opts.pl,
build-aux/mk-version-h.in.sh, build-aux/subst-config-vals.in.sh,
build-aux/subst-cross-config-vals.in.sh, build-aux/subst-default-vals.in.sh,
build-aux/subst-f77-isnan-macro.in.sh, build-aux/subst-script-vals.in.sh,
configure.ac, 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/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/genpropdoc.m,
doc/interpreter/geometry.txi, doc/interpreter/geometryimages.m,
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/linalg.txi,
doc/interpreter/macros.texi, doc/interpreter/matrix.txi,
doc/interpreter/mk-doc-cache.pl, doc/interpreter/mkoctfile.1,
doc/interpreter/nonlin.txi, doc/interpreter/numbers.txi,
doc/interpreter/obsolete.txi, doc/interpreter/octave-cli.1,
doc/interpreter/octave-config.1, doc/interpreter/octave.1,
doc/interpreter/octave.css, 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/plotimages.m, 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/var.txi,
doc/interpreter/vectorize.txi, 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/refcard-a4.tex,
doc/refcard/refcard-legal.tex, doc/refcard/refcard-letter.tex,
doc/refcard/refcard.tex, etc/HACKING, etc/icons/octave.appdata.xml.in,
libgui/graphics/Backend.cc, libgui/graphics/Backend.h,
libgui/graphics/BaseControl.cc, libgui/graphics/BaseControl.h,
libgui/graphics/ButtonControl.cc, libgui/graphics/ButtonControl.h,
libgui/graphics/ButtonGroup.cc, libgui/graphics/ButtonGroup.h,
libgui/graphics/Canvas.cc, libgui/graphics/Canvas.h,
libgui/graphics/CheckBoxControl.cc, libgui/graphics/CheckBoxControl.h,
libgui/graphics/Container.cc, libgui/graphics/Container.h,
libgui/graphics/ContextMenu.cc, libgui/graphics/ContextMenu.h,
libgui/graphics/EditControl.cc, libgui/graphics/EditControl.h,
libgui/graphics/Figure.cc, libgui/graphics/Figure.h,
libgui/graphics/FigureWindow.cc, libgui/graphics/FigureWindow.h,
libgui/graphics/GLCanvas.cc, libgui/graphics/GLCanvas.h,
libgui/graphics/GenericEventNotify.h, libgui/graphics/KeyMap.cc,
libgui/graphics/KeyMap.h, libgui/graphics/ListBoxControl.cc,
libgui/graphics/ListBoxControl.h, libgui/graphics/Logger.cc,
libgui/graphics/Logger.h, libgui/graphics/Menu.cc, libgui/graphics/Menu.h,
libgui/graphics/MenuContainer.h, libgui/graphics/MouseModeActionGroup.cc,
libgui/graphics/MouseModeActionGroup.h, libgui/graphics/Object.cc,
libgui/graphics/Object.h, libgui/graphics/ObjectFactory.cc,
libgui/graphics/ObjectFactory.h, libgui/graphics/ObjectProxy.cc,
libgui/graphics/ObjectProxy.h, libgui/graphics/Panel.cc,
libgui/graphics/Panel.h, libgui/graphics/PopupMenuControl.cc,
libgui/graphics/PopupMenuControl.h, libgui/graphics/PushButtonControl.cc,
libgui/graphics/PushButtonControl.h, libgui/graphics/PushTool.cc,
libgui/graphics/PushTool.h, libgui/graphics/QtHandlesUtils.cc,
libgui/graphics/QtHandlesUtils.h, libgui/graphics/RadioButtonControl.cc,
libgui/graphics/RadioButtonControl.h, libgui/graphics/SliderControl.cc,
libgui/graphics/SliderControl.h, libgui/graphics/TextControl.cc,
libgui/graphics/TextControl.h, libgui/graphics/TextEdit.cc,
libgui/graphics/TextEdit.h, libgui/graphics/ToggleButtonControl.cc,
libgui/graphics/ToggleButtonControl.h, libgui/graphics/ToggleTool.cc,
libgui/graphics/ToggleTool.h, libgui/graphics/ToolBar.cc,
libgui/graphics/ToolBar.h, libgui/graphics/ToolBarButton.cc,
libgui/graphics/ToolBarButton.h, libgui/graphics/__init_qt__.cc,
libgui/graphics/__init_qt__.h, libgui/graphics/annotation-dialog.cc,
libgui/graphics/annotation-dialog.h, libgui/graphics/gl-select.cc,
libgui/graphics/gl-select.h, libgui/src/color-picker.cc,
libgui/src/color-picker.h, libgui/src/dialog.cc, libgui/src/dialog.h,
libgui/src/documentation-dock-widget.cc,
libgui/src/documentation-dock-widget.h, libgui/src/files-dock-widget.cc,
libgui/src/files-dock-widget.h, libgui/src/find-files-dialog.cc,
libgui/src/find-files-dialog.h, libgui/src/find-files-model.cc,
libgui/src/find-files-model.h, libgui/src/history-dock-widget.cc,
libgui/src/history-dock-widget.h, libgui/src/liboctgui-build-info.h,
libgui/src/liboctgui-build-info.in.cc,
libgui/src/m-editor/file-editor-interface.h,
libgui/src/m-editor/file-editor-tab.cc, libgui/src/m-editor/file-editor-tab.h,
libgui/src/m-editor/file-editor.cc, libgui/src/m-editor/file-editor.h,
libgui/src/m-editor/find-dialog.cc, libgui/src/m-editor/find-dialog.h,
libgui/src/m-editor/marker.cc, libgui/src/m-editor/marker.h,
libgui/src/m-editor/octave-qscintilla.cc,
libgui/src/m-editor/octave-qscintilla.h,
libgui/src/m-editor/octave-txt-lexer.cc,
libgui/src/m-editor/octave-txt-lexer.h, libgui/src/main-window.cc,
libgui/src/main-window.h, libgui/src/octave-cmd.cc, libgui/src/octave-cmd.h,
libgui/src/octave-dock-widget.cc, libgui/src/octave-dock-widget.h,
libgui/src/octave-gui.cc, libgui/src/octave-gui.h,
libgui/src/octave-interpreter.cc, libgui/src/octave-interpreter.h,
libgui/src/octave-qt-link.cc, libgui/src/octave-qt-link.h,
libgui/src/qtinfo/parser.cc, libgui/src/qtinfo/parser.h,
libgui/src/qtinfo/webinfo.cc, libgui/src/qtinfo/webinfo.h,
libgui/src/resource-manager.cc, libgui/src/resource-manager.h,
libgui/src/settings-dialog.cc, libgui/src/settings-dialog.h,
libgui/src/shortcut-manager.cc, libgui/src/shortcut-manager.h,
libgui/src/terminal-dock-widget.cc, libgui/src/terminal-dock-widget.h,
libgui/src/thread-manager.cc, libgui/src/thread-manager.h,
libgui/src/welcome-wizard.cc, libgui/src/welcome-wizard.h,
libgui/src/workspace-model.cc, libgui/src/workspace-model.h,
libgui/src/workspace-view.cc, libgui/src/workspace-view.h,
libinterp/build-env.h, libinterp/build-env.in.cc, libinterp/builtins.h,
libinterp/corefcn/Cell.cc, libinterp/corefcn/Cell.h,
libinterp/corefcn/__contourc__.cc, libinterp/corefcn/__dsearchn__.cc,
libinterp/corefcn/__ichol__.cc, libinterp/corefcn/__ilu__.cc,
libinterp/corefcn/__lin_interpn__.cc, libinterp/corefcn/__luinc__.cc,
libinterp/corefcn/__magick_read__.cc, libinterp/corefcn/__pchip_deriv__.cc,
libinterp/corefcn/__qp__.cc, libinterp/corefcn/balance.cc,
libinterp/corefcn/base-text-renderer.h, libinterp/corefcn/besselj.cc,
libinterp/corefcn/betainc.cc, libinterp/corefcn/bitfcns.cc,
libinterp/corefcn/bsxfun.cc, libinterp/corefcn/c-file-ptr-stream.cc,
libinterp/corefcn/c-file-ptr-stream.h, libinterp/corefcn/call-stack.cc,
libinterp/corefcn/call-stack.h, libinterp/corefcn/cdisplay.c,
libinterp/corefcn/cdisplay.h, libinterp/corefcn/cellfun.cc,
libinterp/corefcn/coct-hdf5-types.c, libinterp/corefcn/colloc.cc,
libinterp/corefcn/comment-list.cc, libinterp/corefcn/comment-list.h,
libinterp/corefcn/conv2.cc, libinterp/corefcn/daspk.cc,
libinterp/corefcn/dasrt.cc, libinterp/corefcn/dassl.cc,
libinterp/corefcn/data.cc, libinterp/corefcn/data.h,
libinterp/corefcn/debug.cc, libinterp/corefcn/debug.h,
libinterp/corefcn/defaults.cc, libinterp/corefcn/defaults.in.h,
libinterp/corefcn/defun-dld.h, libinterp/corefcn/defun-int.h,
libinterp/corefcn/defun.cc, libinterp/corefcn/defun.h,
libinterp/corefcn/det.cc, libinterp/corefcn/dirfns.cc,
libinterp/corefcn/dirfns.h, libinterp/corefcn/display.cc,
libinterp/corefcn/display.h, libinterp/corefcn/dlmread.cc,
libinterp/corefcn/dot.cc, libinterp/corefcn/dynamic-ld.cc,
libinterp/corefcn/dynamic-ld.h, libinterp/corefcn/eig.cc,
libinterp/corefcn/ellipj.cc, libinterp/corefcn/error.cc,
libinterp/corefcn/error.h, libinterp/corefcn/errwarn.cc,
libinterp/corefcn/errwarn.h, libinterp/corefcn/event-queue.cc,
libinterp/corefcn/event-queue.h, libinterp/corefcn/fft.cc,
libinterp/corefcn/fft2.cc, libinterp/corefcn/fftn.cc,
libinterp/corefcn/file-io.cc, libinterp/corefcn/file-io.h,
libinterp/corefcn/filter.cc, libinterp/corefcn/find.cc,
libinterp/corefcn/ft-text-renderer.cc, libinterp/corefcn/ft-text-renderer.h,
libinterp/corefcn/gammainc.cc, libinterp/corefcn/gcd.cc,
libinterp/corefcn/getgrent.cc, libinterp/corefcn/getpwent.cc,
libinterp/corefcn/getrusage.cc, libinterp/corefcn/givens.cc,
libinterp/corefcn/gl-render.cc, libinterp/corefcn/gl-render.h,
libinterp/corefcn/gl2ps-print.cc, libinterp/corefcn/gl2ps-print.h,
libinterp/corefcn/graphics.cc, libinterp/corefcn/graphics.in.h,
libinterp/corefcn/gripes.cc, libinterp/corefcn/gripes.h,
libinterp/corefcn/gsvd.cc, libinterp/corefcn/hash.cc,
libinterp/corefcn/help.cc, libinterp/corefcn/help.h, libinterp/corefcn/hess.cc,
libinterp/corefcn/hex2num.cc, libinterp/corefcn/hook-fcn.cc,
libinterp/corefcn/hook-fcn.h, libinterp/corefcn/input.cc,
libinterp/corefcn/input.h, libinterp/corefcn/interpreter.cc,
libinterp/corefcn/interpreter.h, libinterp/corefcn/inv.cc,
libinterp/corefcn/jit-ir.cc, libinterp/corefcn/jit-ir.h,
libinterp/corefcn/jit-typeinfo.cc, libinterp/corefcn/jit-typeinfo.h,
libinterp/corefcn/jit-util.cc, libinterp/corefcn/jit-util.h,
libinterp/corefcn/kron.cc, libinterp/corefcn/load-path.cc,
libinterp/corefcn/load-path.h, libinterp/corefcn/load-save.cc,
libinterp/corefcn/load-save.h, libinterp/corefcn/lookup.cc,
libinterp/corefcn/ls-ascii-helper.cc, libinterp/corefcn/ls-ascii-helper.h,
libinterp/corefcn/ls-hdf5.cc, libinterp/corefcn/ls-hdf5.h,
libinterp/corefcn/ls-mat-ascii.cc, libinterp/corefcn/ls-mat-ascii.h,
libinterp/corefcn/ls-mat4.cc, libinterp/corefcn/ls-mat4.h,
libinterp/corefcn/ls-mat5.cc, libinterp/corefcn/ls-mat5.h,
libinterp/corefcn/ls-oct-binary.cc, libinterp/corefcn/ls-oct-binary.h,
libinterp/corefcn/ls-oct-text.cc, libinterp/corefcn/ls-oct-text.h,
libinterp/corefcn/ls-utils.cc, libinterp/corefcn/ls-utils.h,
libinterp/corefcn/lsode.cc, libinterp/corefcn/lu.cc,
libinterp/corefcn/mappers.cc, libinterp/corefcn/matrix_type.cc,
libinterp/corefcn/max.cc, libinterp/corefcn/mex.cc, libinterp/corefcn/mex.h,
libinterp/corefcn/mexproto.h, libinterp/corefcn/mgorth.cc,
libinterp/corefcn/mxarray.in.h, libinterp/corefcn/nproc.cc,
libinterp/corefcn/oct-errno.h, libinterp/corefcn/oct-errno.in.cc,
libinterp/corefcn/oct-fstrm.cc, libinterp/corefcn/oct-fstrm.h,
libinterp/corefcn/oct-handle.h, libinterp/corefcn/oct-hdf5-types.cc,
libinterp/corefcn/oct-hdf5-types.h, libinterp/corefcn/oct-hdf5.h,
libinterp/corefcn/oct-hist.cc, libinterp/corefcn/oct-hist.h,
libinterp/corefcn/oct-iostrm.cc, libinterp/corefcn/oct-iostrm.h,
libinterp/corefcn/oct-lvalue.cc, libinterp/corefcn/oct-lvalue.h,
libinterp/corefcn/oct-map.cc, libinterp/corefcn/oct-map.h,
libinterp/corefcn/oct-obj.h, libinterp/corefcn/oct-opengl.h,
libinterp/corefcn/oct-prcstrm.cc, libinterp/corefcn/oct-prcstrm.h,
libinterp/corefcn/oct-procbuf.cc, libinterp/corefcn/oct-procbuf.h,
libinterp/corefcn/oct-stdstrm.h, libinterp/corefcn/oct-stream.cc,
libinterp/corefcn/oct-stream.h, libinterp/corefcn/oct-strstrm.cc,
libinterp/corefcn/oct-strstrm.h, libinterp/corefcn/oct-tex-lexer.in.ll,
libinterp/corefcn/oct-tex-parser.in.yy, libinterp/corefcn/oct.h,
libinterp/corefcn/octave-default-image.h, libinterp/corefcn/octave-link.cc,
libinterp/corefcn/octave-link.h,
libinterp/corefcn/octave-preserve-stream-state.h,
libinterp/corefcn/ordschur.cc, libinterp/corefcn/pager.cc,
libinterp/corefcn/pager.h, libinterp/corefcn/pinv.cc,
libinterp/corefcn/pr-output.cc, libinterp/corefcn/pr-output.h,
libinterp/corefcn/procstream.cc, libinterp/corefcn/procstream.h,
libinterp/corefcn/profiler.cc, libinterp/corefcn/profiler.h,
libinterp/corefcn/psi.cc, libinterp/corefcn/pt-jit.cc,
libinterp/corefcn/pt-jit.h, libinterp/corefcn/quad.cc,
libinterp/corefcn/quadcc.cc, libinterp/corefcn/qz.cc,
libinterp/corefcn/rand.cc, libinterp/corefcn/rcond.cc,
libinterp/corefcn/regexp.cc, libinterp/corefcn/schur.cc,
libinterp/corefcn/sighandlers.cc, libinterp/corefcn/sighandlers.h,
libinterp/corefcn/sparse-xdiv.cc, libinterp/corefcn/sparse-xdiv.h,
libinterp/corefcn/sparse-xpow.cc, libinterp/corefcn/sparse-xpow.h,
libinterp/corefcn/sparse.cc, libinterp/corefcn/spparms.cc,
libinterp/corefcn/sqrtm.cc, libinterp/corefcn/str2double.cc,
libinterp/corefcn/strfind.cc, libinterp/corefcn/strfns.cc,
libinterp/corefcn/sub2ind.cc, libinterp/corefcn/svd.cc,
libinterp/corefcn/sylvester.cc, libinterp/corefcn/symtab.cc,
libinterp/corefcn/symtab.h, libinterp/corefcn/syscalls.cc,
libinterp/corefcn/sysdep.cc, libinterp/corefcn/sysdep.h,
libinterp/corefcn/text-renderer.cc, libinterp/corefcn/text-renderer.h,
libinterp/corefcn/time.cc, libinterp/corefcn/toplev.cc,
libinterp/corefcn/toplev.h, libinterp/corefcn/tril.cc,
libinterp/corefcn/tsearch.cc, libinterp/corefcn/txt-eng.cc,
libinterp/corefcn/txt-eng.h, libinterp/corefcn/typecast.cc,
libinterp/corefcn/urlwrite.cc, libinterp/corefcn/utils.cc,
libinterp/corefcn/utils.h, libinterp/corefcn/variables.cc,
libinterp/corefcn/variables.h, libinterp/corefcn/workspace-element.h,
libinterp/corefcn/xdiv.cc, libinterp/corefcn/xdiv.h,
libinterp/corefcn/xnorm.cc, libinterp/corefcn/xnorm.h,
libinterp/corefcn/xpow.cc, libinterp/corefcn/xpow.h,
libinterp/corefcn/zfstream.cc, libinterp/corefcn/zfstream.h,
libinterp/deprecated-config.h, libinterp/dldfcn/__delaunayn__.cc,
libinterp/dldfcn/__eigs__.cc, libinterp/dldfcn/__fltk_uigetfile__.cc,
libinterp/dldfcn/__glpk__.cc, libinterp/dldfcn/__init_fltk__.cc,
libinterp/dldfcn/__init_gnuplot__.cc, libinterp/dldfcn/__osmesa_print__.cc,
libinterp/dldfcn/__voronoi__.cc, libinterp/dldfcn/amd.cc,
libinterp/dldfcn/audiodevinfo.cc, libinterp/dldfcn/audioread.cc,
libinterp/dldfcn/ccolamd.cc, libinterp/dldfcn/chol.cc,
libinterp/dldfcn/colamd.cc, libinterp/dldfcn/convhulln.cc,
libinterp/dldfcn/dmperm.cc, libinterp/dldfcn/fftw.cc, libinterp/dldfcn/gzip.cc,
libinterp/dldfcn/oct-qhull.h, libinterp/dldfcn/qr.cc,
libinterp/dldfcn/symbfact.cc, libinterp/dldfcn/symrcm.cc, libinterp/gendoc.pl,
libinterp/genprops.awk, libinterp/liboctinterp-build-info.h,
libinterp/liboctinterp-build-info.in.cc, libinterp/mk-errno-list,
libinterp/mk-pkg-add, libinterp/mkops, libinterp/octave-value/ov-base-diag.cc,
libinterp/octave-value/ov-base-diag.h, libinterp/octave-value/ov-base-int.cc,
libinterp/octave-value/ov-base-int.h, libinterp/octave-value/ov-base-mat.cc,
libinterp/octave-value/ov-base-mat.h, libinterp/octave-value/ov-base-scalar.cc,
libinterp/octave-value/ov-base-scalar.h,
libinterp/octave-value/ov-base-sparse.cc,
libinterp/octave-value/ov-base-sparse.h, libinterp/octave-value/ov-base.cc,
libinterp/octave-value/ov-base.h, libinterp/octave-value/ov-bool-mat.cc,
libinterp/octave-value/ov-bool-mat.h, libinterp/octave-value/ov-bool-sparse.cc,
libinterp/octave-value/ov-bool-sparse.h, libinterp/octave-value/ov-bool.cc,
libinterp/octave-value/ov-bool.h, libinterp/octave-value/ov-builtin.cc,
libinterp/octave-value/ov-builtin.h, libinterp/octave-value/ov-cell.cc,
libinterp/octave-value/ov-cell.h, libinterp/octave-value/ov-ch-mat.cc,
libinterp/octave-value/ov-ch-mat.h, libinterp/octave-value/ov-class.cc,
libinterp/octave-value/ov-class.h, libinterp/octave-value/ov-classdef.cc,
libinterp/octave-value/ov-classdef.h, libinterp/octave-value/ov-colon.cc,
libinterp/octave-value/ov-colon.h, libinterp/octave-value/ov-complex.cc,
libinterp/octave-value/ov-complex.h, libinterp/octave-value/ov-cs-list.cc,
libinterp/octave-value/ov-cs-list.h, libinterp/octave-value/ov-cx-diag.cc,
libinterp/octave-value/ov-cx-diag.h, libinterp/octave-value/ov-cx-mat.cc,
libinterp/octave-value/ov-cx-mat.h, libinterp/octave-value/ov-cx-sparse.cc,
libinterp/octave-value/ov-cx-sparse.h, libinterp/octave-value/ov-dld-fcn.cc,
libinterp/octave-value/ov-dld-fcn.h, libinterp/octave-value/ov-fcn-handle.cc,
libinterp/octave-value/ov-fcn-handle.h,
libinterp/octave-value/ov-fcn-inline.cc,
libinterp/octave-value/ov-fcn-inline.h, libinterp/octave-value/ov-fcn.cc,
libinterp/octave-value/ov-fcn.h, libinterp/octave-value/ov-float.cc,
libinterp/octave-value/ov-float.h, libinterp/octave-value/ov-flt-complex.cc,
libinterp/octave-value/ov-flt-complex.h,
libinterp/octave-value/ov-flt-cx-diag.cc,
libinterp/octave-value/ov-flt-cx-diag.h,
libinterp/octave-value/ov-flt-cx-mat.cc,
libinterp/octave-value/ov-flt-cx-mat.h,
libinterp/octave-value/ov-flt-re-diag.cc,
libinterp/octave-value/ov-flt-re-diag.h,
libinterp/octave-value/ov-flt-re-mat.cc,
libinterp/octave-value/ov-flt-re-mat.h, libinterp/octave-value/ov-int-traits.h,
libinterp/octave-value/ov-int16.cc, libinterp/octave-value/ov-int16.h,
libinterp/octave-value/ov-int32.cc, libinterp/octave-value/ov-int32.h,
libinterp/octave-value/ov-int64.cc, libinterp/octave-value/ov-int64.h,
libinterp/octave-value/ov-int8.cc, libinterp/octave-value/ov-int8.h,
libinterp/octave-value/ov-intx.h, libinterp/octave-value/ov-java.cc,
libinterp/octave-value/ov-java.h, libinterp/octave-value/ov-lazy-idx.cc,
libinterp/octave-value/ov-lazy-idx.h, libinterp/octave-value/ov-mex-fcn.cc,
libinterp/octave-value/ov-mex-fcn.h, libinterp/octave-value/ov-null-mat.cc,
libinterp/octave-value/ov-null-mat.h, libinterp/octave-value/ov-oncleanup.cc,
libinterp/octave-value/ov-oncleanup.h, libinterp/octave-value/ov-perm.cc,
libinterp/octave-value/ov-perm.h, libinterp/octave-value/ov-range.cc,
libinterp/octave-value/ov-range.h, libinterp/octave-value/ov-re-diag.cc,
libinterp/octave-value/ov-re-diag.h, libinterp/octave-value/ov-re-mat.cc,
libinterp/octave-value/ov-re-mat.h, libinterp/octave-value/ov-re-sparse.cc,
libinterp/octave-value/ov-re-sparse.h, libinterp/octave-value/ov-scalar.cc,
libinterp/octave-value/ov-scalar.h, libinterp/octave-value/ov-str-mat.cc,
libinterp/octave-value/ov-str-mat.h, libinterp/octave-value/ov-struct.cc,
libinterp/octave-value/ov-struct.h, libinterp/octave-value/ov-typeinfo.cc,
libinterp/octave-value/ov-typeinfo.h, libinterp/octave-value/ov-uint16.cc,
libinterp/octave-value/ov-uint16.h, libinterp/octave-value/ov-uint32.cc,
libinterp/octave-value/ov-uint32.h, libinterp/octave-value/ov-uint64.cc,
libinterp/octave-value/ov-uint64.h, libinterp/octave-value/ov-uint8.cc,
libinterp/octave-value/ov-uint8.h, libinterp/octave-value/ov-usr-fcn.cc,
libinterp/octave-value/ov-usr-fcn.h, libinterp/octave-value/ov.cc,
libinterp/octave-value/ov.h, libinterp/octave-value/ovl.cc,
libinterp/octave-value/ovl.h, libinterp/octave.cc, libinterp/octave.h,
libinterp/op-kw-docs, libinterp/operators/op-b-b.cc,
libinterp/operators/op-b-bm.cc, libinterp/operators/op-b-sbm.cc,
libinterp/operators/op-bm-b.cc, libinterp/operators/op-bm-bm.cc,
libinterp/operators/op-bm-sbm.cc, libinterp/operators/op-cdm-cdm.cc,
libinterp/operators/op-cdm-cm.cc, libinterp/operators/op-cdm-cs.cc,
libinterp/operators/op-cdm-dm.cc, libinterp/operators/op-cdm-m.cc,
libinterp/operators/op-cdm-s.cc, libinterp/operators/op-cell.cc,
libinterp/operators/op-chm.cc, libinterp/operators/op-class.cc,
libinterp/operators/op-cm-cdm.cc, libinterp/operators/op-cm-cm.cc,
libinterp/operators/op-cm-cs.cc, libinterp/operators/op-cm-dm.cc,
libinterp/operators/op-cm-m.cc, libinterp/operators/op-cm-pm.cc,
libinterp/operators/op-cm-s.cc, libinterp/operators/op-cm-scm.cc,
libinterp/operators/op-cm-sm.cc, libinterp/operators/op-cs-cm.cc,
libinterp/operators/op-cs-cs.cc, libinterp/operators/op-cs-m.cc,
libinterp/operators/op-cs-s.cc, libinterp/operators/op-cs-scm.cc,
libinterp/operators/op-cs-sm.cc, libinterp/operators/op-dm-cdm.cc,
libinterp/operators/op-dm-cm.cc, libinterp/operators/op-dm-cs.cc,
libinterp/operators/op-dm-dm.cc, libinterp/operators/op-dm-m.cc,
libinterp/operators/op-dm-s.cc, libinterp/operators/op-dm-scm.cc,
libinterp/operators/op-dm-sm.cc, libinterp/operators/op-dm-template.cc,
libinterp/operators/op-dms-template.cc, libinterp/operators/op-fcdm-fcdm.cc,
libinterp/operators/op-fcdm-fcm.cc, libinterp/operators/op-fcdm-fcs.cc,
libinterp/operators/op-fcdm-fdm.cc, libinterp/operators/op-fcdm-fm.cc,
libinterp/operators/op-fcdm-fs.cc, libinterp/operators/op-fcm-fcdm.cc,
libinterp/operators/op-fcm-fcm.cc, libinterp/operators/op-fcm-fcs.cc,
libinterp/operators/op-fcm-fdm.cc, libinterp/operators/op-fcm-fm.cc,
libinterp/operators/op-fcm-fs.cc, libinterp/operators/op-fcm-pm.cc,
libinterp/operators/op-fcn.cc, libinterp/operators/op-fcs-fcm.cc,
libinterp/operators/op-fcs-fcs.cc, libinterp/operators/op-fcs-fm.cc,
libinterp/operators/op-fcs-fs.cc, libinterp/operators/op-fdm-fcdm.cc,
libinterp/operators/op-fdm-fcm.cc, libinterp/operators/op-fdm-fcs.cc,
libinterp/operators/op-fdm-fdm.cc, libinterp/operators/op-fdm-fm.cc,
libinterp/operators/op-fdm-fs.cc, libinterp/operators/op-fm-fcdm.cc,
libinterp/operators/op-fm-fcm.cc, libinterp/operators/op-fm-fcs.cc,
libinterp/operators/op-fm-fdm.cc, libinterp/operators/op-fm-fm.cc,
libinterp/operators/op-fm-fs.cc, libinterp/operators/op-fm-pm.cc,
libinterp/operators/op-fs-fcm.cc, libinterp/operators/op-fs-fcs.cc,
libinterp/operators/op-fs-fm.cc, libinterp/operators/op-fs-fs.cc,
libinterp/operators/op-i16-i16.cc, libinterp/operators/op-i32-i32.cc,
libinterp/operators/op-i64-i64.cc, libinterp/operators/op-i8-i8.cc,
libinterp/operators/op-int-concat.cc, libinterp/operators/op-int.h,
libinterp/operators/op-m-cdm.cc, libinterp/operators/op-m-cm.cc,
libinterp/operators/op-m-cs.cc, libinterp/operators/op-m-dm.cc,
libinterp/operators/op-m-m.cc, libinterp/operators/op-m-pm.cc,
libinterp/operators/op-m-s.cc, libinterp/operators/op-m-scm.cc,
libinterp/operators/op-m-sm.cc, libinterp/operators/op-pm-cm.cc,
libinterp/operators/op-pm-fcm.cc, libinterp/operators/op-pm-fm.cc,
libinterp/operators/op-pm-m.cc, libinterp/operators/op-pm-pm.cc,
libinterp/operators/op-pm-scm.cc, libinterp/operators/op-pm-sm.cc,
libinterp/operators/op-pm-template.cc, libinterp/operators/op-range.cc,
libinterp/operators/op-s-cm.cc, libinterp/operators/op-s-cs.cc,
libinterp/operators/op-s-m.cc, libinterp/operators/op-s-s.cc,
libinterp/operators/op-s-scm.cc, libinterp/operators/op-s-sm.cc,
libinterp/operators/op-sbm-b.cc, libinterp/operators/op-sbm-bm.cc,
libinterp/operators/op-sbm-sbm.cc, libinterp/operators/op-scm-cm.cc,
libinterp/operators/op-scm-cs.cc, libinterp/operators/op-scm-m.cc,
libinterp/operators/op-scm-s.cc, libinterp/operators/op-scm-scm.cc,
libinterp/operators/op-scm-sm.cc, libinterp/operators/op-sm-cm.cc,
libinterp/operators/op-sm-cs.cc, libinterp/operators/op-sm-m.cc,
libinterp/operators/op-sm-s.cc, libinterp/operators/op-sm-scm.cc,
libinterp/operators/op-sm-sm.cc, libinterp/operators/op-str-m.cc,
libinterp/operators/op-str-s.cc, libinterp/operators/op-str-str.cc,
libinterp/operators/op-struct.cc, libinterp/operators/op-ui16-ui16.cc,
libinterp/operators/op-ui32-ui32.cc, libinterp/operators/op-ui64-ui64.cc,
libinterp/operators/op-ui8-ui8.cc, libinterp/operators/ops.h,
libinterp/options-usage.h, libinterp/parse-tree/lex.h,
libinterp/parse-tree/lex.ll, libinterp/parse-tree/oct-parse.in.yy,
libinterp/parse-tree/octave.gperf, libinterp/parse-tree/parse.h,
libinterp/parse-tree/pt-all.h, libinterp/parse-tree/pt-arg-list.cc,
libinterp/parse-tree/pt-arg-list.h, libinterp/parse-tree/pt-array-list.cc,
libinterp/parse-tree/pt-array-list.h, libinterp/parse-tree/pt-assign.cc,
libinterp/parse-tree/pt-assign.h, libinterp/parse-tree/pt-binop.cc,
libinterp/parse-tree/pt-binop.h, libinterp/parse-tree/pt-bp.cc,
libinterp/parse-tree/pt-bp.h, libinterp/parse-tree/pt-cbinop.cc,
libinterp/parse-tree/pt-cbinop.h, libinterp/parse-tree/pt-cell.cc,
libinterp/parse-tree/pt-cell.h, libinterp/parse-tree/pt-check.cc,
libinterp/parse-tree/pt-check.h, libinterp/parse-tree/pt-classdef.cc,
libinterp/parse-tree/pt-classdef.h, libinterp/parse-tree/pt-cmd.cc,
libinterp/parse-tree/pt-cmd.h, libinterp/parse-tree/pt-colon.cc,
libinterp/parse-tree/pt-colon.h, libinterp/parse-tree/pt-const.cc,
libinterp/parse-tree/pt-const.h, libinterp/parse-tree/pt-decl.cc,
libinterp/parse-tree/pt-decl.h, libinterp/parse-tree/pt-eval.cc,
libinterp/parse-tree/pt-eval.h, libinterp/parse-tree/pt-except.cc,
libinterp/parse-tree/pt-except.h, libinterp/parse-tree/pt-exp.cc,
libinterp/parse-tree/pt-exp.h, libinterp/parse-tree/pt-fcn-handle.cc,
libinterp/parse-tree/pt-fcn-handle.h, libinterp/parse-tree/pt-funcall.cc,
libinterp/parse-tree/pt-funcall.h, libinterp/parse-tree/pt-id.cc,
libinterp/parse-tree/pt-id.h, libinterp/parse-tree/pt-idx.cc,
libinterp/parse-tree/pt-idx.h, libinterp/parse-tree/pt-jump.cc,
libinterp/parse-tree/pt-jump.h, libinterp/parse-tree/pt-loop.cc,
libinterp/parse-tree/pt-loop.h, libinterp/parse-tree/pt-mat.cc,
libinterp/parse-tree/pt-mat.h, libinterp/parse-tree/pt-misc.cc,
libinterp/parse-tree/pt-misc.h, libinterp/parse-tree/pt-pr-code.cc,
libinterp/parse-tree/pt-pr-code.h, libinterp/parse-tree/pt-select.cc,
libinterp/parse-tree/pt-select.h, libinterp/parse-tree/pt-stmt.cc,
libinterp/parse-tree/pt-stmt.h, libinterp/parse-tree/pt-unop.cc,
libinterp/parse-tree/pt-unop.h, libinterp/parse-tree/pt-walk.h,
libinterp/parse-tree/pt.cc, libinterp/parse-tree/pt.h,
libinterp/parse-tree/token.cc, libinterp/parse-tree/token.h,
libinterp/template-inst/Array-jit.cc, libinterp/template-inst/Array-tc.cc,
libinterp/version.cc, libinterp/version.in.h, liboctave/array/Array-C.cc,
liboctave/array/Array-b.cc, liboctave/array/Array-ch.cc,
liboctave/array/Array-d.cc, liboctave/array/Array-f.cc,
liboctave/array/Array-fC.cc, liboctave/array/Array-i.cc,
liboctave/array/Array-idx-vec.cc, liboctave/array/Array-s.cc,
liboctave/array/Array-str.cc, liboctave/array/Array-util.cc,
liboctave/array/Array-util.h, liboctave/array/Array-voidp.cc,
liboctave/array/Array.cc, liboctave/array/Array.h,
liboctave/array/CColVector.cc, liboctave/array/CColVector.h,
liboctave/array/CDiagMatrix.cc, liboctave/array/CDiagMatrix.h,
liboctave/array/CMatrix.cc, liboctave/array/CMatrix.h,
liboctave/array/CNDArray.cc, liboctave/array/CNDArray.h,
liboctave/array/CRowVector.cc, liboctave/array/CRowVector.h,
liboctave/array/CSparse.cc, liboctave/array/CSparse.h,
liboctave/array/DiagArray2.cc, liboctave/array/DiagArray2.h,
liboctave/array/MArray-C.cc, liboctave/array/MArray-d.cc,
liboctave/array/MArray-f.cc, liboctave/array/MArray-fC.cc,
liboctave/array/MArray-i.cc, liboctave/array/MArray-s.cc,
liboctave/array/MArray.cc, liboctave/array/MArray.h,
liboctave/array/MDiagArray2.cc, liboctave/array/MDiagArray2.h,
liboctave/array/MSparse-C.cc, liboctave/array/MSparse-d.cc,
liboctave/array/MSparse.cc, liboctave/array/MSparse.h,
liboctave/array/Matrix.h, liboctave/array/MatrixType.cc,
liboctave/array/MatrixType.h, liboctave/array/PermMatrix.cc,
liboctave/array/PermMatrix.h, liboctave/array/Range.cc,
liboctave/array/Range.h, liboctave/array/Sparse-C.cc,
liboctave/array/Sparse-b.cc, liboctave/array/Sparse-d.cc,
liboctave/array/Sparse.cc, liboctave/array/Sparse.h,
liboctave/array/boolMatrix.cc, liboctave/array/boolMatrix.h,
liboctave/array/boolNDArray.cc, liboctave/array/boolNDArray.h,
liboctave/array/boolSparse.cc, liboctave/array/boolSparse.h,
liboctave/array/chMatrix.cc, liboctave/array/chMatrix.h,
liboctave/array/chNDArray.cc, liboctave/array/chNDArray.h,
liboctave/array/dColVector.cc, liboctave/array/dColVector.h,
liboctave/array/dDiagMatrix.cc, liboctave/array/dDiagMatrix.h,
liboctave/array/dMatrix.cc, liboctave/array/dMatrix.h,
liboctave/array/dNDArray.cc, liboctave/array/dNDArray.h,
liboctave/array/dRowVector.cc, liboctave/array/dRowVector.h,
liboctave/array/dSparse.cc, liboctave/array/dSparse.h,
liboctave/array/dim-vector.cc, liboctave/array/dim-vector.h,
liboctave/array/fCColVector.cc, liboctave/array/fCColVector.h,
liboctave/array/fCDiagMatrix.cc, liboctave/array/fCDiagMatrix.h,
liboctave/array/fCMatrix.cc, liboctave/array/fCMatrix.h,
liboctave/array/fCNDArray.cc, liboctave/array/fCNDArray.h,
liboctave/array/fCRowVector.cc, liboctave/array/fCRowVector.h,
liboctave/array/fColVector.cc, liboctave/array/fColVector.h,
liboctave/array/fDiagMatrix.cc, liboctave/array/fDiagMatrix.h,
liboctave/array/fMatrix.cc, liboctave/array/fMatrix.h,
liboctave/array/fNDArray.cc, liboctave/array/fNDArray.h,
liboctave/array/fRowVector.cc, liboctave/array/fRowVector.h,
liboctave/array/idx-vector.cc, liboctave/array/idx-vector.h,
liboctave/array/int16NDArray.cc, liboctave/array/int16NDArray.h,
liboctave/array/int32NDArray.cc, liboctave/array/int32NDArray.h,
liboctave/array/int64NDArray.cc, liboctave/array/int64NDArray.h,
liboctave/array/int8NDArray.cc, liboctave/array/int8NDArray.h,
liboctave/array/intNDArray.cc, liboctave/array/intNDArray.h,
liboctave/array/uint16NDArray.cc, liboctave/array/uint16NDArray.h,
liboctave/array/uint32NDArray.cc, liboctave/array/uint32NDArray.h,
liboctave/array/uint64NDArray.cc, liboctave/array/uint64NDArray.h,
liboctave/array/uint8NDArray.cc, liboctave/array/uint8NDArray.h,
liboctave/cruft/misc/blaswrap.c, liboctave/cruft/misc/cquit.c,
liboctave/cruft/misc/f77-extern.cc, liboctave/cruft/misc/f77-fcn.c,
liboctave/cruft/misc/f77-fcn.h, liboctave/cruft/misc/lo-error.c,
liboctave/cruft/misc/lo-error.h, liboctave/cruft/misc/quit.cc,
liboctave/cruft/misc/quit.h, liboctave/liboctave-build-info.h,
liboctave/liboctave-build-info.in.cc, liboctave/numeric/CollocWt.cc,
liboctave/numeric/CollocWt.h, liboctave/numeric/DAE.h,
liboctave/numeric/DAEFunc.h, liboctave/numeric/DAERT.h,
liboctave/numeric/DAERTFunc.h, liboctave/numeric/DASPK-opts.in,
liboctave/numeric/DASPK.cc, liboctave/numeric/DASPK.h,
liboctave/numeric/DASRT-opts.in, liboctave/numeric/DASRT.cc,
liboctave/numeric/DASRT.h, liboctave/numeric/DASSL-opts.in,
liboctave/numeric/DASSL.cc, liboctave/numeric/DASSL.h, liboctave/numeric/DET.h,
liboctave/numeric/EIG.cc, liboctave/numeric/EIG.h,
liboctave/numeric/LSODE-opts.in, liboctave/numeric/LSODE.cc,
liboctave/numeric/LSODE.h, liboctave/numeric/ODE.h,
liboctave/numeric/ODEFunc.h, liboctave/numeric/ODES.cc,
liboctave/numeric/ODES.h, liboctave/numeric/ODESFunc.h,
liboctave/numeric/Quad-opts.in, liboctave/numeric/Quad.cc,
liboctave/numeric/Quad.h, liboctave/numeric/aepbalance.cc,
liboctave/numeric/aepbalance.h, liboctave/numeric/base-dae.h,
liboctave/numeric/base-de.h, liboctave/numeric/base-min.h,
liboctave/numeric/bsxfun-decl.h, liboctave/numeric/bsxfun-defs.cc,
liboctave/numeric/bsxfun.h, liboctave/numeric/chol.cc,
liboctave/numeric/chol.h, liboctave/numeric/eigs-base.cc,
liboctave/numeric/eigs-base.h, liboctave/numeric/fEIG.cc,
liboctave/numeric/fEIG.h, liboctave/numeric/gepbalance.cc,
liboctave/numeric/gepbalance.h, liboctave/numeric/gsvd.cc,
liboctave/numeric/gsvd.h, liboctave/numeric/hess.cc, liboctave/numeric/hess.h,
liboctave/numeric/lo-amos-proto.h, liboctave/numeric/lo-arpack-proto.h,
liboctave/numeric/lo-blas-proto.h, liboctave/numeric/lo-fftpack-proto.h,
liboctave/numeric/lo-lapack-proto.h, liboctave/numeric/lo-mappers.cc,
liboctave/numeric/lo-mappers.h, liboctave/numeric/lo-qrupdate-proto.h,
liboctave/numeric/lo-ranlib-proto.h, liboctave/numeric/lo-slatec-proto.h,
liboctave/numeric/lo-specfun.cc, liboctave/numeric/lo-specfun.h,
liboctave/numeric/lu.cc, liboctave/numeric/lu.h,
liboctave/numeric/oct-convn.cc, liboctave/numeric/oct-convn.h,
liboctave/numeric/oct-fftw.cc, liboctave/numeric/oct-fftw.h,
liboctave/numeric/oct-norm.cc, liboctave/numeric/oct-norm.h,
liboctave/numeric/oct-rand.cc, liboctave/numeric/oct-rand.h,
liboctave/numeric/oct-spparms.cc, liboctave/numeric/oct-spparms.h,
liboctave/numeric/qr.cc, liboctave/numeric/qr.h, liboctave/numeric/qrp.cc,
liboctave/numeric/qrp.h, liboctave/numeric/randgamma.cc,
liboctave/numeric/randgamma.h, liboctave/numeric/randmtzig.cc,
liboctave/numeric/randmtzig.h, liboctave/numeric/randpoisson.cc,
liboctave/numeric/randpoisson.h, liboctave/numeric/schur.cc,
liboctave/numeric/schur.h, liboctave/numeric/sparse-chol.cc,
liboctave/numeric/sparse-chol.h, liboctave/numeric/sparse-dmsolve.cc,
liboctave/numeric/sparse-dmsolve.h, liboctave/numeric/sparse-lu.cc,
liboctave/numeric/sparse-lu.h, liboctave/numeric/sparse-qr.cc,
liboctave/numeric/sparse-qr.h, liboctave/numeric/svd.cc,
liboctave/numeric/svd.h, liboctave/operators/Sparse-diag-op-defs.h,
liboctave/operators/Sparse-op-decls.h, liboctave/operators/Sparse-op-defs.h,
liboctave/operators/Sparse-perm-op-defs.h, liboctave/operators/mk-ops.awk,
liboctave/operators/mx-base.h, liboctave/operators/mx-defs.h,
liboctave/operators/mx-ext.h, liboctave/operators/mx-inlines.cc,
liboctave/operators/mx-op-decl.h, liboctave/operators/mx-op-defs.h,
liboctave/operators/mx-ops, liboctave/operators/smx-ops,
liboctave/operators/vx-ops, liboctave/system/child-list.cc,
liboctave/system/child-list.h, liboctave/system/dir-ops.cc,
liboctave/system/dir-ops.h, liboctave/system/file-ops.cc,
liboctave/system/file-ops.h, liboctave/system/file-stat.cc,
liboctave/system/file-stat.h, liboctave/system/lo-sysdep.cc,
liboctave/system/lo-sysdep.h, liboctave/system/mach-info.cc,
liboctave/system/mach-info.h, liboctave/system/oct-env.cc,
liboctave/system/oct-env.h, liboctave/system/oct-group.cc,
liboctave/system/oct-group.h, liboctave/system/oct-passwd.cc,
liboctave/system/oct-passwd.h, liboctave/system/oct-syscalls.cc,
liboctave/system/oct-syscalls.h, liboctave/system/oct-time.cc,
liboctave/system/oct-time.h, liboctave/system/oct-uname.cc,
liboctave/system/oct-uname.h, liboctave/util/action-container.h,
liboctave/util/base-list.h, liboctave/util/byte-swap.h,
liboctave/util/caseless-str.h, liboctave/util/cmd-edit.cc,
liboctave/util/cmd-edit.h, liboctave/util/cmd-hist.cc,
liboctave/util/cmd-hist.h, liboctave/util/data-conv.cc,
liboctave/util/data-conv.h, liboctave/util/f2c-main.c,
liboctave/util/functor.h, liboctave/util/glob-match.cc,
liboctave/util/glob-match.h, liboctave/util/kpse.cc, liboctave/util/kpse.h,
liboctave/util/lo-array-errwarn.cc, liboctave/util/lo-array-errwarn.h,
liboctave/util/lo-array-gripes.cc, liboctave/util/lo-array-gripes.h,
liboctave/util/lo-cutils.c, liboctave/util/lo-cutils.h,
liboctave/util/lo-hash.cc, liboctave/util/lo-hash.h, liboctave/util/lo-ieee.cc,
liboctave/util/lo-ieee.h, liboctave/util/lo-macros.h, liboctave/util/lo-math.h,
liboctave/util/lo-regexp.cc, liboctave/util/lo-regexp.h,
liboctave/util/lo-traits.h, liboctave/util/lo-utils.cc,
liboctave/util/lo-utils.h, liboctave/util/oct-alloc.h,
liboctave/util/oct-base64.cc, liboctave/util/oct-base64.h,
liboctave/util/oct-binmap.h, liboctave/util/oct-cmplx.h,
liboctave/util/oct-glob.cc, liboctave/util/oct-glob.h,
liboctave/util/oct-inttypes-fwd.h, liboctave/util/oct-inttypes.cc,
liboctave/util/oct-inttypes.h, liboctave/util/oct-locbuf.cc,
liboctave/util/oct-locbuf.h, liboctave/util/oct-mutex.cc,
liboctave/util/oct-mutex.h, liboctave/util/oct-refcount.h,
liboctave/util/oct-rl-edit.c, liboctave/util/oct-rl-edit.h,
liboctave/util/oct-rl-hist.c, liboctave/util/oct-rl-hist.h,
liboctave/util/oct-shlib.cc, liboctave/util/oct-shlib.h,
liboctave/util/oct-sort.cc, liboctave/util/oct-sort.h,
liboctave/util/oct-sparse.h, liboctave/util/oct-string.cc,
liboctave/util/oct-string.h, liboctave/util/pathsearch.cc,
liboctave/util/pathsearch.h, liboctave/util/singleton-cleanup.cc,
liboctave/util/sparse-sort.cc, liboctave/util/sparse-sort.h,
liboctave/util/sparse-util.cc, liboctave/util/sparse-util.h,
liboctave/util/str-vec.cc, liboctave/util/str-vec.h,
liboctave/util/sun-utils.h, liboctave/util/unwind-prot.cc,
liboctave/util/unwind-prot.h, liboctave/util/url-transfer.cc,
liboctave/util/url-transfer.h, liboctave/wrappers/areadlink-wrapper.c,
liboctave/wrappers/areadlink-wrapper.h,
liboctave/wrappers/async-system-wrapper.c,
liboctave/wrappers/async-system-wrapper.h,
liboctave/wrappers/base64-wrappers.c, liboctave/wrappers/base64-wrappers.h,
liboctave/wrappers/canonicalize-file-name-wrapper.c,
liboctave/wrappers/canonicalize-file-name-wrapper.h,
liboctave/wrappers/dirent-wrappers.c, liboctave/wrappers/dirent-wrappers.h,
liboctave/wrappers/fcntl-wrappers.c, liboctave/wrappers/fcntl-wrappers.h,
liboctave/wrappers/filepos-wrappers.c, liboctave/wrappers/filepos-wrappers.h,
liboctave/wrappers/fpucw-wrappers.c, liboctave/wrappers/fpucw-wrappers.h,
liboctave/wrappers/gen-tempname-wrapper.c,
liboctave/wrappers/gen-tempname-wrapper.h, liboctave/wrappers/getopt-wrapper.c,
liboctave/wrappers/getopt-wrapper.h, liboctave/wrappers/glob-wrappers.c,
liboctave/wrappers/glob-wrappers.h, liboctave/wrappers/hash-wrappers.c,
liboctave/wrappers/hash-wrappers.h, liboctave/wrappers/math-wrappers.c,
liboctave/wrappers/math-wrappers.h, liboctave/wrappers/mkostemp-wrapper.c,
liboctave/wrappers/mkostemp-wrapper.h, liboctave/wrappers/nanosleep-wrapper.c,
liboctave/wrappers/nanosleep-wrapper.h, liboctave/wrappers/nproc-wrapper.c,
liboctave/wrappers/nproc-wrapper.h, liboctave/wrappers/octave-popen2.c,
liboctave/wrappers/octave-popen2.h, liboctave/wrappers/putenv-wrapper.c,
liboctave/wrappers/putenv-wrapper.h,
liboctave/wrappers/set-program-name-wrapper.c,
liboctave/wrappers/set-program-name-wrapper.h,
liboctave/wrappers/signal-wrappers.c, liboctave/wrappers/signal-wrappers.h,
liboctave/wrappers/stat-wrappers.c, liboctave/wrappers/stat-wrappers.h,
liboctave/wrappers/strdup-wrapper.c, liboctave/wrappers/strdup-wrapper.h,
liboctave/wrappers/strftime-wrapper.c, liboctave/wrappers/strftime-wrapper.h,
liboctave/wrappers/strmode-wrapper.c, liboctave/wrappers/strmode-wrapper.h,
liboctave/wrappers/strptime-wrapper.c, liboctave/wrappers/strptime-wrapper.h,
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liboctave/wrappers/tmpfile-wrapper.c, liboctave/wrappers/tmpfile-wrapper.h,
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liboctave/wrappers/unistd-wrappers.c, liboctave/wrappers/unistd-wrappers.h,
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liboctave/wrappers/vasprintf-wrapper.c, liboctave/wrappers/vasprintf-wrapper.h,
liboctave/wrappers/wait-for-input.c, liboctave/wrappers/wait-for-input.h,
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Use the same Copyright formatting throughout Octave.
author | Rik <rik@octave.org> |
---|---|
date | Sun, 13 Nov 2016 20:33:47 -0800 |
parents | dd80fb1ef949 |
children | 4a31bd79d7e8 |
line wrap: on
line source
// Matrix manipulations. /* Copyright (C) 1994-2016 John W. Eaton Copyright (C) 2008-2009 Jaroslav Hajek Copyright (C) 2009 VZLU Prague, a.s. This file is part of Octave. Octave is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version. Octave is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with Octave; see the file COPYING. If not, see <http://www.gnu.org/licenses/>. */ #if defined (HAVE_CONFIG_H) # include "config.h" #endif #include <cfloat> #include <iostream> #include <vector> // FIXME #include <sys/types.h> #include "Array-util.h" #include "boolMatrix.h" #include "chMatrix.h" #include "chol.h" #include "dMatrix.h" #include "CMatrix.h" #include "CNDArray.h" #include "CRowVector.h" #include "dRowVector.h" #include "CDiagMatrix.h" #include "dDiagMatrix.h" #include "schur.h" #include "svd.h" #include "DET.h" #include "functor.h" #include "lo-blas-proto.h" #include "lo-error.h" #include "lo-ieee.h" #include "lo-lapack-proto.h" #include "lo-mappers.h" #include "lo-utils.h" #include "mx-cm-dm.h" #include "mx-cm-s.h" #include "mx-dm-cm.h" #include "mx-inlines.cc" #include "mx-op-defs.h" #include "oct-cmplx.h" #include "oct-fftw.h" #include "oct-locbuf.h" #include "oct-norm.h" static const Complex Complex_NaN_result (octave::numeric_limits<double>::NaN (), octave::numeric_limits<double>::NaN ()); // Complex Matrix class ComplexMatrix::ComplexMatrix (const Matrix& a) : ComplexNDArray (a) { } ComplexMatrix::ComplexMatrix (const RowVector& rv) : ComplexNDArray (rv) { } ComplexMatrix::ComplexMatrix (const ColumnVector& cv) : ComplexNDArray (cv) { } ComplexMatrix::ComplexMatrix (const DiagMatrix& a) : ComplexNDArray (a.dims (), 0.0) { for (octave_idx_type i = 0; i < a.length (); i++) elem (i, i) = a.elem (i, i); } ComplexMatrix::ComplexMatrix (const MDiagArray2<double>& a) : ComplexNDArray (a.dims (), 0.0) { for (octave_idx_type i = 0; i < a.length (); i++) elem (i, i) = a.elem (i, i); } ComplexMatrix::ComplexMatrix (const DiagArray2<double>& a) : ComplexNDArray (a.dims (), 0.0) { for (octave_idx_type i = 0; i < a.length (); i++) elem (i, i) = a.elem (i, i); } ComplexMatrix::ComplexMatrix (const ComplexRowVector& rv) : ComplexNDArray (rv) { } ComplexMatrix::ComplexMatrix (const ComplexColumnVector& cv) : ComplexNDArray (cv) { } ComplexMatrix::ComplexMatrix (const ComplexDiagMatrix& a) : ComplexNDArray (a.dims (), 0.0) { for (octave_idx_type i = 0; i < a.length (); i++) elem (i, i) = a.elem (i, i); } ComplexMatrix::ComplexMatrix (const MDiagArray2<Complex>& a) : ComplexNDArray (a.dims (), 0.0) { for (octave_idx_type i = 0; i < a.length (); i++) elem (i, i) = a.elem (i, i); } ComplexMatrix::ComplexMatrix (const DiagArray2<Complex>& a) : ComplexNDArray (a.dims (), 0.0) { for (octave_idx_type i = 0; i < a.length (); i++) elem (i, i) = a.elem (i, i); } // FIXME: could we use a templated mixed-type copy function here? ComplexMatrix::ComplexMatrix (const boolMatrix& a) : ComplexNDArray (a) { } ComplexMatrix::ComplexMatrix (const charMatrix& a) : ComplexNDArray (a.dims (), 0.0) { for (octave_idx_type i = 0; i < a.rows (); i++) for (octave_idx_type j = 0; j < a.cols (); j++) elem (i, j) = static_cast<unsigned char> (a.elem (i, j)); } ComplexMatrix::ComplexMatrix (const Matrix& re, const Matrix& im) : ComplexNDArray (re.dims ()) { if (im.rows () != rows () || im.cols () != cols ()) (*current_liboctave_error_handler) ("complex: internal error"); octave_idx_type nel = numel (); for (octave_idx_type i = 0; i < nel; i++) xelem (i) = Complex (re(i), im(i)); } bool ComplexMatrix::operator == (const ComplexMatrix& a) const { if (rows () != a.rows () || cols () != a.cols ()) return false; return mx_inline_equal (numel (), data (), a.data ()); } bool ComplexMatrix::operator != (const ComplexMatrix& a) const { return !(*this == a); } bool ComplexMatrix::is_hermitian (void) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (is_square () && nr > 0) { for (octave_idx_type i = 0; i < nr; i++) for (octave_idx_type j = i; j < nc; j++) if (elem (i, j) != conj (elem (j, i))) return false; return true; } return false; } // destructive insert/delete/reorder operations ComplexMatrix& ComplexMatrix::insert (const Matrix& a, octave_idx_type r, octave_idx_type c) { octave_idx_type a_nr = a.rows (); octave_idx_type a_nc = a.cols (); if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) (*current_liboctave_error_handler) ("range error for insert"); if (a_nr >0 && a_nc > 0) { make_unique (); for (octave_idx_type j = 0; j < a_nc; j++) for (octave_idx_type i = 0; i < a_nr; i++) xelem (r+i, c+j) = a.elem (i, j); } return *this; } ComplexMatrix& ComplexMatrix::insert (const RowVector& a, octave_idx_type r, octave_idx_type c) { octave_idx_type a_len = a.numel (); if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) (*current_liboctave_error_handler) ("range error for insert"); if (a_len > 0) { make_unique (); for (octave_idx_type i = 0; i < a_len; i++) xelem (r, c+i) = a.elem (i); } return *this; } ComplexMatrix& ComplexMatrix::insert (const ColumnVector& a, octave_idx_type r, octave_idx_type c) { octave_idx_type a_len = a.numel (); if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) (*current_liboctave_error_handler) ("range error for insert"); if (a_len > 0) { make_unique (); for (octave_idx_type i = 0; i < a_len; i++) xelem (r+i, c) = a.elem (i); } return *this; } ComplexMatrix& ComplexMatrix::insert (const DiagMatrix& a, octave_idx_type r, octave_idx_type c) { octave_idx_type a_nr = a.rows (); octave_idx_type a_nc = a.cols (); if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) (*current_liboctave_error_handler) ("range error for insert"); fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); octave_idx_type a_len = a.length (); if (a_len > 0) { make_unique (); for (octave_idx_type i = 0; i < a_len; i++) xelem (r+i, c+i) = a.elem (i, i); } return *this; } ComplexMatrix& ComplexMatrix::insert (const ComplexMatrix& a, octave_idx_type r, octave_idx_type c) { ComplexNDArray::insert (a, r, c); return *this; } ComplexMatrix& ComplexMatrix::insert (const ComplexRowVector& a, octave_idx_type r, octave_idx_type c) { octave_idx_type a_len = a.numel (); if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) (*current_liboctave_error_handler) ("range error for insert"); for (octave_idx_type i = 0; i < a_len; i++) elem (r, c+i) = a.elem (i); return *this; } ComplexMatrix& ComplexMatrix::insert (const ComplexColumnVector& a, octave_idx_type r, octave_idx_type c) { octave_idx_type a_len = a.numel (); if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) (*current_liboctave_error_handler) ("range error for insert"); if (a_len > 0) { make_unique (); for (octave_idx_type i = 0; i < a_len; i++) xelem (r+i, c) = a.elem (i); } return *this; } ComplexMatrix& ComplexMatrix::insert (const ComplexDiagMatrix& a, octave_idx_type r, octave_idx_type c) { octave_idx_type a_nr = a.rows (); octave_idx_type a_nc = a.cols (); if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) (*current_liboctave_error_handler) ("range error for insert"); fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); octave_idx_type a_len = a.length (); if (a_len > 0) { make_unique (); for (octave_idx_type i = 0; i < a_len; i++) xelem (r+i, c+i) = a.elem (i, i); } return *this; } ComplexMatrix& ComplexMatrix::fill (double val) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr > 0 && nc > 0) { make_unique (); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = 0; i < nr; i++) xelem (i, j) = val; } return *this; } ComplexMatrix& ComplexMatrix::fill (const Complex& val) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr > 0 && nc > 0) { make_unique (); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = 0; i < nr; i++) xelem (i, j) = val; } return *this; } ComplexMatrix& ComplexMatrix::fill (double val, octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) (*current_liboctave_error_handler) ("range error for fill"); if (r1 > r2) { std::swap (r1, r2); } if (c1 > c2) { std::swap (c1, c2); } if (r2 >= r1 && c2 >= c1) { make_unique (); for (octave_idx_type j = c1; j <= c2; j++) for (octave_idx_type i = r1; i <= r2; i++) xelem (i, j) = val; } return *this; } ComplexMatrix& ComplexMatrix::fill (const Complex& val, octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) (*current_liboctave_error_handler) ("range error for fill"); if (r1 > r2) { std::swap (r1, r2); } if (c1 > c2) { std::swap (c1, c2); } if (r2 >= r1 && c2 >=c1) { make_unique (); for (octave_idx_type j = c1; j <= c2; j++) for (octave_idx_type i = r1; i <= r2; i++) xelem (i, j) = val; } return *this; } ComplexMatrix ComplexMatrix::append (const Matrix& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != a.rows ()) (*current_liboctave_error_handler) ("row dimension mismatch for append"); octave_idx_type nc_insert = nc; ComplexMatrix retval (nr, nc + a.cols ()); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } ComplexMatrix ComplexMatrix::append (const RowVector& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != 1) (*current_liboctave_error_handler) ("row dimension mismatch for append"); octave_idx_type nc_insert = nc; ComplexMatrix retval (nr, nc + a.numel ()); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } ComplexMatrix ComplexMatrix::append (const ColumnVector& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != a.numel ()) (*current_liboctave_error_handler) ("row dimension mismatch for append"); octave_idx_type nc_insert = nc; ComplexMatrix retval (nr, nc + 1); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } ComplexMatrix ComplexMatrix::append (const DiagMatrix& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != a.rows ()) (*current_liboctave_error_handler) ("row dimension mismatch for append"); octave_idx_type nc_insert = nc; ComplexMatrix retval (nr, nc + a.cols ()); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } ComplexMatrix ComplexMatrix::append (const ComplexMatrix& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != a.rows ()) (*current_liboctave_error_handler) ("row dimension mismatch for append"); octave_idx_type nc_insert = nc; ComplexMatrix retval (nr, nc + a.cols ()); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } ComplexMatrix ComplexMatrix::append (const ComplexRowVector& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != 1) (*current_liboctave_error_handler) ("row dimension mismatch for append"); octave_idx_type nc_insert = nc; ComplexMatrix retval (nr, nc + a.numel ()); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } ComplexMatrix ComplexMatrix::append (const ComplexColumnVector& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != a.numel ()) (*current_liboctave_error_handler) ("row dimension mismatch for append"); octave_idx_type nc_insert = nc; ComplexMatrix retval (nr, nc + 1); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } ComplexMatrix ComplexMatrix::append (const ComplexDiagMatrix& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != a.rows ()) (*current_liboctave_error_handler) ("row dimension mismatch for append"); octave_idx_type nc_insert = nc; ComplexMatrix retval (nr, nc + a.cols ()); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } ComplexMatrix ComplexMatrix::stack (const Matrix& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nc != a.cols ()) (*current_liboctave_error_handler) ("column dimension mismatch for stack"); octave_idx_type nr_insert = nr; ComplexMatrix retval (nr + a.rows (), nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } ComplexMatrix ComplexMatrix::stack (const RowVector& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nc != a.numel ()) (*current_liboctave_error_handler) ("column dimension mismatch for stack"); octave_idx_type nr_insert = nr; ComplexMatrix retval (nr + 1, nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } ComplexMatrix ComplexMatrix::stack (const ColumnVector& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nc != 1) (*current_liboctave_error_handler) ("column dimension mismatch for stack"); octave_idx_type nr_insert = nr; ComplexMatrix retval (nr + a.numel (), nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } ComplexMatrix ComplexMatrix::stack (const DiagMatrix& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nc != a.cols ()) (*current_liboctave_error_handler) ("column dimension mismatch for stack"); octave_idx_type nr_insert = nr; ComplexMatrix retval (nr + a.rows (), nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } ComplexMatrix ComplexMatrix::stack (const ComplexMatrix& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nc != a.cols ()) (*current_liboctave_error_handler) ("column dimension mismatch for stack"); octave_idx_type nr_insert = nr; ComplexMatrix retval (nr + a.rows (), nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } ComplexMatrix ComplexMatrix::stack (const ComplexRowVector& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nc != a.numel ()) (*current_liboctave_error_handler) ("column dimension mismatch for stack"); octave_idx_type nr_insert = nr; ComplexMatrix retval (nr + 1, nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } ComplexMatrix ComplexMatrix::stack (const ComplexColumnVector& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nc != 1) (*current_liboctave_error_handler) ("column dimension mismatch for stack"); octave_idx_type nr_insert = nr; ComplexMatrix retval (nr + a.numel (), nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } ComplexMatrix ComplexMatrix::stack (const ComplexDiagMatrix& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nc != a.cols ()) (*current_liboctave_error_handler) ("column dimension mismatch for stack"); octave_idx_type nr_insert = nr; ComplexMatrix retval (nr + a.rows (), nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } ComplexMatrix conj (const ComplexMatrix& a) { return do_mx_unary_map<Complex, Complex, std::conj<double> > (a); } // resize is the destructive equivalent for this one ComplexMatrix ComplexMatrix::extract (octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) const { if (r1 > r2) { std::swap (r1, r2); } if (c1 > c2) { std::swap (c1, c2); } return index (idx_vector (r1, r2+1), idx_vector (c1, c2+1)); } ComplexMatrix ComplexMatrix::extract_n (octave_idx_type r1, octave_idx_type c1, octave_idx_type nr, octave_idx_type nc) const { return index (idx_vector (r1, r1 + nr), idx_vector (c1, c1 + nc)); } // extract row or column i. ComplexRowVector ComplexMatrix::row (octave_idx_type i) const { return index (idx_vector (i), idx_vector::colon); } ComplexColumnVector ComplexMatrix::column (octave_idx_type i) const { return index (idx_vector::colon, idx_vector (i)); } ComplexMatrix ComplexMatrix::inverse (void) const { octave_idx_type info; double rcon; MatrixType mattype (*this); return inverse (mattype, info, rcon, 0, 0); } ComplexMatrix ComplexMatrix::inverse (octave_idx_type& info) const { double rcon; MatrixType mattype (*this); return inverse (mattype, info, rcon, 0, 0); } ComplexMatrix ComplexMatrix::inverse (octave_idx_type& info, double& rcon, bool force, bool calc_cond) const { MatrixType mattype (*this); return inverse (mattype, info, rcon, force, calc_cond); } ComplexMatrix ComplexMatrix::inverse (MatrixType &mattype) const { octave_idx_type info; double rcon; return inverse (mattype, info, rcon, 0, 0); } ComplexMatrix ComplexMatrix::inverse (MatrixType &mattype, octave_idx_type& info) const { double rcon; return inverse (mattype, info, rcon, 0, 0); } ComplexMatrix ComplexMatrix::tinverse (MatrixType &mattype, octave_idx_type& info, double& rcon, bool force, bool calc_cond) const { ComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != nc || nr == 0 || nc == 0) (*current_liboctave_error_handler) ("inverse requires square matrix"); int typ = mattype.type (); char uplo = (typ == MatrixType::Lower ? 'L' : 'U'); char udiag = 'N'; retval = *this; Complex *tmp_data = retval.fortran_vec (); F77_XFCN (ztrtri, ZTRTRI,(F77_CONST_CHAR_ARG2 (&uplo, 1), F77_CONST_CHAR_ARG2 (&udiag, 1), nr, F77_DBLE_CMPLX_ARG (tmp_data), nr, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); // Throw-away extra info LAPACK gives so as to not change output. rcon = 0.0; if (info != 0) info = -1; else if (calc_cond) { octave_idx_type ztrcon_info = 0; char job = '1'; OCTAVE_LOCAL_BUFFER (Complex, cwork, 2*nr); OCTAVE_LOCAL_BUFFER (double, rwork, nr); F77_XFCN (ztrcon, ZTRCON, (F77_CONST_CHAR_ARG2 (&job, 1), F77_CONST_CHAR_ARG2 (&uplo, 1), F77_CONST_CHAR_ARG2 (&udiag, 1), nr, F77_DBLE_CMPLX_ARG (tmp_data), nr, rcon, F77_DBLE_CMPLX_ARG (cwork), rwork, ztrcon_info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); if (ztrcon_info != 0) info = -1; } if (info == -1 && ! force) retval = *this; // Restore matrix contents. return retval; } ComplexMatrix ComplexMatrix::finverse (MatrixType &mattype, octave_idx_type& info, double& rcon, bool force, bool calc_cond) const { ComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != nc) (*current_liboctave_error_handler) ("inverse requires square matrix"); Array<octave_idx_type> ipvt (dim_vector (nr, 1)); octave_idx_type *pipvt = ipvt.fortran_vec (); retval = *this; Complex *tmp_data = retval.fortran_vec (); Array<Complex> z (dim_vector (1, 1)); octave_idx_type lwork = -1; // Query the optimum work array size. F77_XFCN (zgetri, ZGETRI, (nc, F77_DBLE_CMPLX_ARG (tmp_data), nr, pipvt, F77_DBLE_CMPLX_ARG (z.fortran_vec ()), lwork, info)); lwork = static_cast<octave_idx_type> (octave::math::real (z(0))); lwork = (lwork < 2 *nc ? 2*nc : lwork); z.resize (dim_vector (lwork, 1)); Complex *pz = z.fortran_vec (); info = 0; // Calculate (always, see bug #45577) the norm of the matrix, for later use. double anorm = retval.abs ().sum ().row (static_cast<octave_idx_type>(0)).max (); // Work around bug #45577, LAPACK crashes Octave if norm is NaN // and bug #46330, segfault with matrices containing Inf & NaN if (octave::math::isnan (anorm) || octave::math::isinf (anorm)) info = -1; else F77_XFCN (zgetrf, ZGETRF, (nc, nc, F77_DBLE_CMPLX_ARG (tmp_data), nr, pipvt, info)); // Throw-away extra info LAPACK gives so as to not change output. rcon = 0.0; if (info != 0) info = -1; else if (calc_cond) { // Now calculate the condition number for non-singular matrix. octave_idx_type zgecon_info = 0; char job = '1'; Array<double> rz (dim_vector (2 * nc, 1)); double *prz = rz.fortran_vec (); F77_XFCN (zgecon, ZGECON, (F77_CONST_CHAR_ARG2 (&job, 1), nc, F77_DBLE_CMPLX_ARG (tmp_data), nr, anorm, rcon, F77_DBLE_CMPLX_ARG (pz), prz, zgecon_info F77_CHAR_ARG_LEN (1))); if (zgecon_info != 0) info = -1; } if ((info == -1 && ! force) || octave::math::isinf (anorm)) retval = *this; // Restore contents. else { octave_idx_type zgetri_info = 0; F77_XFCN (zgetri, ZGETRI, (nc, F77_DBLE_CMPLX_ARG (tmp_data), nr, pipvt, F77_DBLE_CMPLX_ARG (pz), lwork, zgetri_info)); if (zgetri_info != 0) info = -1; } if (info != 0) mattype.mark_as_rectangular (); return retval; } ComplexMatrix ComplexMatrix::inverse (MatrixType &mattype, octave_idx_type& info, double& rcon, bool force, bool calc_cond) const { int typ = mattype.type (false); ComplexMatrix ret; if (typ == MatrixType::Unknown) typ = mattype.type (*this); if (typ == MatrixType::Upper || typ == MatrixType::Lower) ret = tinverse (mattype, info, rcon, force, calc_cond); else { if (mattype.is_hermitian ()) { octave::math::chol<ComplexMatrix> chol (*this, info, true, calc_cond); if (info == 0) { if (calc_cond) rcon = chol.rcond (); else rcon = 1.0; ret = chol.inverse (); } else mattype.mark_as_unsymmetric (); } if (! mattype.is_hermitian ()) ret = finverse (mattype, info, rcon, force, calc_cond); if ((mattype.is_hermitian () || calc_cond) && rcon == 0.) ret = ComplexMatrix (rows (), columns (), Complex (octave::numeric_limits<double>::Inf (), 0.)); } return ret; } ComplexMatrix ComplexMatrix::pseudo_inverse (double tol) const { ComplexMatrix retval; octave::math::svd<ComplexMatrix> result (*this, octave::math::svd<ComplexMatrix>::Type::economy); DiagMatrix S = result.singular_values (); ComplexMatrix U = result.left_singular_matrix (); ComplexMatrix V = result.right_singular_matrix (); ColumnVector sigma = S.extract_diag (); octave_idx_type r = sigma.numel () - 1; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (tol <= 0.0) { if (nr > nc) tol = nr * sigma.elem (0) * std::numeric_limits<double>::epsilon (); else tol = nc * sigma.elem (0) * std::numeric_limits<double>::epsilon (); } while (r >= 0 && sigma.elem (r) < tol) r--; if (r < 0) retval = ComplexMatrix (nc, nr, 0.0); else { ComplexMatrix Ur = U.extract (0, 0, nr-1, r); DiagMatrix D = DiagMatrix (sigma.extract (0, r)).inverse (); ComplexMatrix Vr = V.extract (0, 0, nc-1, r); retval = Vr * D * Ur.hermitian (); } return retval; } #if defined (HAVE_FFTW) ComplexMatrix ComplexMatrix::fourier (void) const { size_t nr = rows (); size_t nc = cols (); ComplexMatrix retval (nr, nc); size_t npts, nsamples; if (nr == 1 || nc == 1) { npts = nr > nc ? nr : nc; nsamples = 1; } else { npts = nr; nsamples = nc; } const Complex *in (data ()); Complex *out (retval.fortran_vec ()); octave_fftw::fft (in, out, npts, nsamples); return retval; } ComplexMatrix ComplexMatrix::ifourier (void) const { size_t nr = rows (); size_t nc = cols (); ComplexMatrix retval (nr, nc); size_t npts, nsamples; if (nr == 1 || nc == 1) { npts = nr > nc ? nr : nc; nsamples = 1; } else { npts = nr; nsamples = nc; } const Complex *in (data ()); Complex *out (retval.fortran_vec ()); octave_fftw::ifft (in, out, npts, nsamples); return retval; } ComplexMatrix ComplexMatrix::fourier2d (void) const { dim_vector dv (rows (), cols ()); ComplexMatrix retval (rows (), cols ()); const Complex *in (data ()); Complex *out (retval.fortran_vec ()); octave_fftw::fftNd (in, out, 2, dv); return retval; } ComplexMatrix ComplexMatrix::ifourier2d (void) const { dim_vector dv (rows (), cols ()); ComplexMatrix retval (rows (), cols ()); const Complex *in (data ()); Complex *out (retval.fortran_vec ()); octave_fftw::ifftNd (in, out, 2, dv); return retval; } #else #include "lo-fftpack-proto.h" ComplexMatrix ComplexMatrix::fourier (void) const { ComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type npts, nsamples; if (nr == 1 || nc == 1) { npts = nr > nc ? nr : nc; nsamples = 1; } else { npts = nr; nsamples = nc; } octave_idx_type nn = 4*npts+15; Array<Complex> wsave (dim_vector (nn, 1)); Complex *pwsave = wsave.fortran_vec (); retval = *this; Complex *tmp_data = retval.fortran_vec (); F77_FUNC (zffti, ZFFTI) (npts, F77_DBLE_CMPLX_ARG (pwsave)); for (octave_idx_type j = 0; j < nsamples; j++) { octave_quit (); F77_FUNC (zfftf, ZFFTF) (npts, F77_DBLE_CMPLX_ARG (&tmp_data[npts*j]), F77_DBLE_CMPLX_ARG (pwsave)); } return retval; } ComplexMatrix ComplexMatrix::ifourier (void) const { ComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type npts, nsamples; if (nr == 1 || nc == 1) { npts = nr > nc ? nr : nc; nsamples = 1; } else { npts = nr; nsamples = nc; } octave_idx_type nn = 4*npts+15; Array<Complex> wsave (dim_vector (nn, 1)); Complex *pwsave = wsave.fortran_vec (); retval = *this; Complex *tmp_data = retval.fortran_vec (); F77_FUNC (zffti, ZFFTI) (npts, F77_DBLE_CMPLX_ARG (pwsave)); for (octave_idx_type j = 0; j < nsamples; j++) { octave_quit (); F77_FUNC (zfftb, ZFFTB) (npts, F77_DBLE_CMPLX_ARG (&tmp_data[npts*j]), F77_DBLE_CMPLX_ARG (pwsave)); } for (octave_idx_type j = 0; j < npts*nsamples; j++) tmp_data[j] = tmp_data[j] / static_cast<double> (npts); return retval; } ComplexMatrix ComplexMatrix::fourier2d (void) const { ComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type npts, nsamples; if (nr == 1 || nc == 1) { npts = nr > nc ? nr : nc; nsamples = 1; } else { npts = nr; nsamples = nc; } octave_idx_type nn = 4*npts+15; Array<Complex> wsave (dim_vector (nn, 1)); Complex *pwsave = wsave.fortran_vec (); retval = *this; Complex *tmp_data = retval.fortran_vec (); F77_FUNC (zffti, ZFFTI) (npts, F77_DBLE_CMPLX_ARG (pwsave)); for (octave_idx_type j = 0; j < nsamples; j++) { octave_quit (); F77_FUNC (zfftf, ZFFTF) (npts, F77_DBLE_CMPLX_ARG (&tmp_data[npts*j]), F77_DBLE_CMPLX_ARG (pwsave)); } npts = nc; nsamples = nr; nn = 4*npts+15; wsave.resize (dim_vector (nn, 1)); pwsave = wsave.fortran_vec (); Array<Complex> tmp (dim_vector (npts, 1)); Complex *prow = tmp.fortran_vec (); F77_FUNC (zffti, ZFFTI) (npts, F77_DBLE_CMPLX_ARG (pwsave)); for (octave_idx_type j = 0; j < nsamples; j++) { octave_quit (); for (octave_idx_type i = 0; i < npts; i++) prow[i] = tmp_data[i*nr + j]; F77_FUNC (zfftf, ZFFTF) (npts, F77_DBLE_CMPLX_ARG (prow), F77_DBLE_CMPLX_ARG (pwsave)); for (octave_idx_type i = 0; i < npts; i++) tmp_data[i*nr + j] = prow[i]; } return retval; } ComplexMatrix ComplexMatrix::ifourier2d (void) const { ComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type npts, nsamples; if (nr == 1 || nc == 1) { npts = nr > nc ? nr : nc; nsamples = 1; } else { npts = nr; nsamples = nc; } octave_idx_type nn = 4*npts+15; Array<Complex> wsave (dim_vector (nn, 1)); Complex *pwsave = wsave.fortran_vec (); retval = *this; Complex *tmp_data = retval.fortran_vec (); F77_FUNC (zffti, ZFFTI) (npts, F77_DBLE_CMPLX_ARG (pwsave)); for (octave_idx_type j = 0; j < nsamples; j++) { octave_quit (); F77_FUNC (zfftb, ZFFTB) (npts, F77_DBLE_CMPLX_ARG (&tmp_data[npts*j]), F77_DBLE_CMPLX_ARG (pwsave)); } for (octave_idx_type j = 0; j < npts*nsamples; j++) tmp_data[j] = tmp_data[j] / static_cast<double> (npts); npts = nc; nsamples = nr; nn = 4*npts+15; wsave.resize (dim_vector (nn, 1)); pwsave = wsave.fortran_vec (); Array<Complex> tmp (dim_vector (npts, 1)); Complex *prow = tmp.fortran_vec (); F77_FUNC (zffti, ZFFTI) (npts, F77_DBLE_CMPLX_ARG (pwsave)); for (octave_idx_type j = 0; j < nsamples; j++) { octave_quit (); for (octave_idx_type i = 0; i < npts; i++) prow[i] = tmp_data[i*nr + j]; F77_FUNC (zfftb, ZFFTB) (npts, F77_DBLE_CMPLX_ARG (prow), F77_DBLE_CMPLX_ARG (pwsave)); for (octave_idx_type i = 0; i < npts; i++) tmp_data[i*nr + j] = prow[i] / static_cast<double> (npts); } return retval; } #endif ComplexDET ComplexMatrix::determinant (void) const { octave_idx_type info; double rcon; return determinant (info, rcon, 0); } ComplexDET ComplexMatrix::determinant (octave_idx_type& info) const { double rcon; return determinant (info, rcon, 0); } ComplexDET ComplexMatrix::determinant (octave_idx_type& info, double& rcon, bool calc_cond) const { MatrixType mattype (*this); return determinant (mattype, info, rcon, calc_cond); } ComplexDET ComplexMatrix::determinant (MatrixType& mattype, octave_idx_type& info, double& rcon, bool calc_cond) const { ComplexDET retval (1.0); info = 0; rcon = 0.0; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != nc) (*current_liboctave_error_handler) ("matrix must be square"); volatile int typ = mattype.type (); // Even though the matrix is marked as singular (Rectangular), we may // still get a useful number from the LU factorization, because it always // completes. if (typ == MatrixType::Unknown) typ = mattype.type (*this); else if (typ == MatrixType::Rectangular) typ = MatrixType::Full; if (typ == MatrixType::Lower || typ == MatrixType::Upper) { for (octave_idx_type i = 0; i < nc; i++) retval *= elem (i,i); } else if (typ == MatrixType::Hermitian) { ComplexMatrix atmp = *this; Complex *tmp_data = atmp.fortran_vec (); double anorm = 0; if (calc_cond) anorm = xnorm (*this, 1); char job = 'L'; F77_XFCN (zpotrf, ZPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, F77_DBLE_CMPLX_ARG (tmp_data), nr, info F77_CHAR_ARG_LEN (1))); if (info != 0) { rcon = 0.0; mattype.mark_as_unsymmetric (); typ = MatrixType::Full; } else { Array<Complex> z (dim_vector (2 * nc, 1)); Complex *pz = z.fortran_vec (); Array<double> rz (dim_vector (nc, 1)); double *prz = rz.fortran_vec (); F77_XFCN (zpocon, ZPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), nr, F77_DBLE_CMPLX_ARG (tmp_data), nr, anorm, rcon, F77_DBLE_CMPLX_ARG (pz), prz, info F77_CHAR_ARG_LEN (1))); if (info != 0) rcon = 0.0; for (octave_idx_type i = 0; i < nc; i++) retval *= atmp (i,i); retval = retval.square (); } } else if (typ != MatrixType::Full) (*current_liboctave_error_handler) ("det: invalid dense matrix type"); if (typ == MatrixType::Full) { Array<octave_idx_type> ipvt (dim_vector (nr, 1)); octave_idx_type *pipvt = ipvt.fortran_vec (); ComplexMatrix atmp = *this; Complex *tmp_data = atmp.fortran_vec (); info = 0; // Calculate (always, see bug #45577) the norm of the matrix, for later use. double anorm = xnorm (*this, 1); // Work around bug #45577, LAPACK crashes Octave if norm is NaN if (octave::math::isnan (anorm)) info = -1; else F77_XFCN (zgetrf, ZGETRF, (nr, nr, F77_DBLE_CMPLX_ARG (tmp_data), nr, pipvt, info)); // Throw-away extra info LAPACK gives so as to not change output. rcon = 0.0; if (info != 0) { info = -1; retval = ComplexDET (); } else { if (calc_cond) { // Now calc the condition number for non-singular matrix. char job = '1'; Array<Complex> z (dim_vector (2 * nc, 1)); Complex *pz = z.fortran_vec (); Array<double> rz (dim_vector (2 * nc, 1)); double *prz = rz.fortran_vec (); F77_XFCN (zgecon, ZGECON, (F77_CONST_CHAR_ARG2 (&job, 1), nc, F77_DBLE_CMPLX_ARG (tmp_data), nr, anorm, rcon, F77_DBLE_CMPLX_ARG (pz), prz, info F77_CHAR_ARG_LEN (1))); } if (info != 0) { info = -1; retval = ComplexDET (); } else { for (octave_idx_type i = 0; i < nc; i++) { Complex c = atmp(i,i); retval *= (ipvt(i) != (i+1)) ? -c : c; } } } } return retval; } double ComplexMatrix::rcond (void) const { MatrixType mattype (*this); return rcond (mattype); } double ComplexMatrix::rcond (MatrixType &mattype) const { double rcon = octave::numeric_limits<double>::NaN (); octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != nc) (*current_liboctave_error_handler) ("matrix must be square"); if (nr == 0 || nc == 0) rcon = octave::numeric_limits<double>::Inf (); else { volatile int typ = mattype.type (); if (typ == MatrixType::Unknown) typ = mattype.type (*this); // Only calculate the condition number for LU/Cholesky if (typ == MatrixType::Upper) { const Complex *tmp_data = fortran_vec (); octave_idx_type info = 0; char norm = '1'; char uplo = 'U'; char dia = 'N'; Array<Complex> z (dim_vector (2 * nc, 1)); Complex *pz = z.fortran_vec (); Array<double> rz (dim_vector (nc, 1)); double *prz = rz.fortran_vec (); F77_XFCN (ztrcon, ZTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), F77_CONST_CHAR_ARG2 (&uplo, 1), F77_CONST_CHAR_ARG2 (&dia, 1), nr, F77_CONST_DBLE_CMPLX_ARG (tmp_data), nr, rcon, F77_DBLE_CMPLX_ARG (pz), prz, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); if (info != 0) rcon = 0; } else if (typ == MatrixType::Permuted_Upper) (*current_liboctave_error_handler) ("permuted triangular matrix not implemented"); else if (typ == MatrixType::Lower) { const Complex *tmp_data = fortran_vec (); octave_idx_type info = 0; char norm = '1'; char uplo = 'L'; char dia = 'N'; Array<Complex> z (dim_vector (2 * nc, 1)); Complex *pz = z.fortran_vec (); Array<double> rz (dim_vector (nc, 1)); double *prz = rz.fortran_vec (); F77_XFCN (ztrcon, ZTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), F77_CONST_CHAR_ARG2 (&uplo, 1), F77_CONST_CHAR_ARG2 (&dia, 1), nr, F77_CONST_DBLE_CMPLX_ARG (tmp_data), nr, rcon, F77_DBLE_CMPLX_ARG (pz), prz, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); if (info != 0) rcon = 0.0; } else if (typ == MatrixType::Permuted_Lower) (*current_liboctave_error_handler) ("permuted triangular matrix not implemented"); else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) { double anorm = -1.0; if (typ == MatrixType::Hermitian) { octave_idx_type info = 0; char job = 'L'; ComplexMatrix atmp = *this; Complex *tmp_data = atmp.fortran_vec (); anorm = atmp.abs().sum(). row(static_cast<octave_idx_type>(0)).max(); F77_XFCN (zpotrf, ZPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, F77_DBLE_CMPLX_ARG (tmp_data), nr, info F77_CHAR_ARG_LEN (1))); if (info != 0) { rcon = 0.0; mattype.mark_as_unsymmetric (); typ = MatrixType::Full; } else { Array<Complex> z (dim_vector (2 * nc, 1)); Complex *pz = z.fortran_vec (); Array<double> rz (dim_vector (nc, 1)); double *prz = rz.fortran_vec (); F77_XFCN (zpocon, ZPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), nr, F77_DBLE_CMPLX_ARG (tmp_data), nr, anorm, rcon, F77_DBLE_CMPLX_ARG (pz), prz, info F77_CHAR_ARG_LEN (1))); if (info != 0) rcon = 0.0; } } if (typ == MatrixType::Full) { octave_idx_type info = 0; ComplexMatrix atmp = *this; Complex *tmp_data = atmp.fortran_vec (); Array<octave_idx_type> ipvt (dim_vector (nr, 1)); octave_idx_type *pipvt = ipvt.fortran_vec (); if (anorm < 0.) anorm = atmp.abs ().sum (). row(static_cast<octave_idx_type>(0)).max (); Array<Complex> z (dim_vector (2 * nc, 1)); Complex *pz = z.fortran_vec (); Array<double> rz (dim_vector (2 * nc, 1)); double *prz = rz.fortran_vec (); // Work around bug #45577, LAPACK crashes Octave if norm is NaN if (octave::math::isnan (anorm)) info = -1; else F77_XFCN (zgetrf, ZGETRF, (nr, nr, F77_DBLE_CMPLX_ARG (tmp_data), nr, pipvt, info)); if (info != 0) { rcon = 0.0; mattype.mark_as_rectangular (); } else { char job = '1'; F77_XFCN (zgecon, ZGECON, (F77_CONST_CHAR_ARG2 (&job, 1), nc, F77_DBLE_CMPLX_ARG (tmp_data), nr, anorm, rcon, F77_DBLE_CMPLX_ARG (pz), prz, info F77_CHAR_ARG_LEN (1))); if (info != 0) rcon = 0.0; } } } else rcon = 0.0; } return rcon; } ComplexMatrix ComplexMatrix::utsolve (MatrixType &mattype, const ComplexMatrix& b, octave_idx_type& info, double& rcon, solve_singularity_handler sing_handler, bool calc_cond, blas_trans_type transt) const { ComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (nr == 0 || nc == 0 || b.cols () == 0) retval = ComplexMatrix (nc, b.cols (), Complex (0.0, 0.0)); else { volatile int typ = mattype.type (); if (typ != MatrixType::Permuted_Upper && typ != MatrixType::Upper) (*current_liboctave_error_handler) ("incorrect matrix type"); octave_idx_type b_nc = b.cols (); rcon = 1.; info = 0; if (typ == MatrixType::Permuted_Upper) (*current_liboctave_error_handler) ("permuted triangular matrix not implemented"); const Complex *tmp_data = fortran_vec (); retval = b; Complex *result = retval.fortran_vec (); char uplo = 'U'; char trans = get_blas_char (transt); char dia = 'N'; F77_XFCN (ztrtrs, ZTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), F77_CONST_CHAR_ARG2 (&trans, 1), F77_CONST_CHAR_ARG2 (&dia, 1), nr, b_nc, F77_CONST_DBLE_CMPLX_ARG (tmp_data), nr, F77_DBLE_CMPLX_ARG (result), nr, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); if (calc_cond) { char norm = '1'; uplo = 'U'; dia = 'N'; Array<Complex> z (dim_vector (2 * nc, 1)); Complex *pz = z.fortran_vec (); Array<double> rz (dim_vector (nc, 1)); double *prz = rz.fortran_vec (); F77_XFCN (ztrcon, ZTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), F77_CONST_CHAR_ARG2 (&uplo, 1), F77_CONST_CHAR_ARG2 (&dia, 1), nr, F77_CONST_DBLE_CMPLX_ARG (tmp_data), nr, rcon, F77_DBLE_CMPLX_ARG (pz), prz, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); if (info != 0) info = -2; volatile double rcond_plus_one = rcon + 1.0; if (rcond_plus_one == 1.0 || octave::math::isnan (rcon)) { info = -2; if (sing_handler) sing_handler (rcon); else octave::warn_singular_matrix (rcon); } } } return retval; } ComplexMatrix ComplexMatrix::ltsolve (MatrixType &mattype, const ComplexMatrix& b, octave_idx_type& info, double& rcon, solve_singularity_handler sing_handler, bool calc_cond, blas_trans_type transt) const { ComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (nr == 0 || nc == 0 || b.cols () == 0) retval = ComplexMatrix (nc, b.cols (), Complex (0.0, 0.0)); else { volatile int typ = mattype.type (); if (typ != MatrixType::Permuted_Lower && typ != MatrixType::Lower) (*current_liboctave_error_handler) ("incorrect matrix type"); octave_idx_type b_nc = b.cols (); rcon = 1.; info = 0; if (typ == MatrixType::Permuted_Lower) (*current_liboctave_error_handler) ("permuted triangular matrix not implemented"); const Complex *tmp_data = fortran_vec (); retval = b; Complex *result = retval.fortran_vec (); char uplo = 'L'; char trans = get_blas_char (transt); char dia = 'N'; F77_XFCN (ztrtrs, ZTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), F77_CONST_CHAR_ARG2 (&trans, 1), F77_CONST_CHAR_ARG2 (&dia, 1), nr, b_nc, F77_CONST_DBLE_CMPLX_ARG (tmp_data), nr, F77_DBLE_CMPLX_ARG (result), nr, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); if (calc_cond) { char norm = '1'; uplo = 'L'; dia = 'N'; Array<Complex> z (dim_vector (2 * nc, 1)); Complex *pz = z.fortran_vec (); Array<double> rz (dim_vector (nc, 1)); double *prz = rz.fortran_vec (); F77_XFCN (ztrcon, ZTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), F77_CONST_CHAR_ARG2 (&uplo, 1), F77_CONST_CHAR_ARG2 (&dia, 1), nr, F77_CONST_DBLE_CMPLX_ARG (tmp_data), nr, rcon, F77_DBLE_CMPLX_ARG (pz), prz, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); if (info != 0) info = -2; volatile double rcond_plus_one = rcon + 1.0; if (rcond_plus_one == 1.0 || octave::math::isnan (rcon)) { info = -2; if (sing_handler) sing_handler (rcon); else octave::warn_singular_matrix (rcon); } } } return retval; } ComplexMatrix ComplexMatrix::fsolve (MatrixType &mattype, const ComplexMatrix& b, octave_idx_type& info, double& rcon, solve_singularity_handler sing_handler, bool calc_cond) const { ComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (nr == 0 || b.cols () == 0) retval = ComplexMatrix (nc, b.cols (), Complex (0.0, 0.0)); else { volatile int typ = mattype.type (); // Calculate the norm of the matrix, for later use. double anorm = -1.; if (typ == MatrixType::Hermitian) { info = 0; char job = 'L'; ComplexMatrix atmp = *this; Complex *tmp_data = atmp.fortran_vec (); anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); F77_XFCN (zpotrf, ZPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, F77_DBLE_CMPLX_ARG (tmp_data), nr, info F77_CHAR_ARG_LEN (1))); // Throw-away extra info LAPACK gives so as to not change output. rcon = 0.0; if (info != 0) { info = -2; mattype.mark_as_unsymmetric (); typ = MatrixType::Full; } else { if (calc_cond) { Array<Complex> z (dim_vector (2 * nc, 1)); Complex *pz = z.fortran_vec (); Array<double> rz (dim_vector (nc, 1)); double *prz = rz.fortran_vec (); F77_XFCN (zpocon, ZPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), nr, F77_DBLE_CMPLX_ARG (tmp_data), nr, anorm, rcon, F77_DBLE_CMPLX_ARG (pz), prz, info F77_CHAR_ARG_LEN (1))); if (info != 0) info = -2; volatile double rcond_plus_one = rcon + 1.0; if (rcond_plus_one == 1.0 || octave::math::isnan (rcon)) { info = -2; if (sing_handler) sing_handler (rcon); else octave::warn_singular_matrix (rcon); } } if (info == 0) { retval = b; Complex *result = retval.fortran_vec (); octave_idx_type b_nc = b.cols (); F77_XFCN (zpotrs, ZPOTRS, (F77_CONST_CHAR_ARG2 (&job, 1), nr, b_nc, F77_DBLE_CMPLX_ARG (tmp_data), nr, F77_DBLE_CMPLX_ARG (result), b.rows (), info F77_CHAR_ARG_LEN (1))); } else { mattype.mark_as_unsymmetric (); typ = MatrixType::Full; } } } if (typ == MatrixType::Full) { info = 0; Array<octave_idx_type> ipvt (dim_vector (nr, 1)); octave_idx_type *pipvt = ipvt.fortran_vec (); ComplexMatrix atmp = *this; Complex *tmp_data = atmp.fortran_vec (); Array<Complex> z (dim_vector (2 * nc, 1)); Complex *pz = z.fortran_vec (); Array<double> rz (dim_vector (2 * nc, 1)); double *prz = rz.fortran_vec (); // Calculate the norm of the matrix, for later use. if (anorm < 0.) anorm = atmp.abs ().sum ().row (static_cast<octave_idx_type>(0)) .max (); // Work around bug #45577, LAPACK crashes Octave if norm is NaN // and bug #46330, segfault with matrices containing Inf & NaN if (octave::math::isnan (anorm) || octave::math::isinf (anorm)) info = -2; else F77_XFCN (zgetrf, ZGETRF, (nr, nr, F77_DBLE_CMPLX_ARG (tmp_data), nr, pipvt, info)); // Throw-away extra info LAPACK gives so as to not change output. rcon = 0.0; if (info != 0) { info = -2; if (sing_handler) sing_handler (rcon); else octave::warn_singular_matrix (); mattype.mark_as_rectangular (); } else { if (calc_cond) { // Now calculate the condition number for // non-singular matrix. char job = '1'; F77_XFCN (zgecon, ZGECON, (F77_CONST_CHAR_ARG2 (&job, 1), nc, F77_DBLE_CMPLX_ARG (tmp_data), nr, anorm, rcon, F77_DBLE_CMPLX_ARG (pz), prz, info F77_CHAR_ARG_LEN (1))); if (info != 0) info = -2; volatile double rcond_plus_one = rcon + 1.0; if (rcond_plus_one == 1.0 || octave::math::isnan (rcon)) { info = -2; if (sing_handler) sing_handler (rcon); else octave::warn_singular_matrix (rcon); } } if (info == 0) { retval = b; Complex *result = retval.fortran_vec (); octave_idx_type b_nc = b.cols (); char job = 'N'; F77_XFCN (zgetrs, ZGETRS, (F77_CONST_CHAR_ARG2 (&job, 1), nr, b_nc, F77_DBLE_CMPLX_ARG (tmp_data), nr, pipvt, F77_DBLE_CMPLX_ARG (result), b.rows (), info F77_CHAR_ARG_LEN (1))); } else mattype.mark_as_rectangular (); } } if (octave::math::isinf (anorm)) { retval = ComplexMatrix (b.rows (), b.cols (), Complex (0, 0)); mattype.mark_as_full (); } } return retval; } ComplexMatrix ComplexMatrix::solve (MatrixType &typ, const Matrix& b) const { octave_idx_type info; double rcon; return solve (typ, b, info, rcon, 0); } ComplexMatrix ComplexMatrix::solve (MatrixType &typ, const Matrix& b, octave_idx_type& info) const { double rcon; return solve (typ, b, info, rcon, 0); } ComplexMatrix ComplexMatrix::solve (MatrixType &typ, const Matrix& b, octave_idx_type& info, double& rcon) const { return solve (typ, b, info, rcon, 0); } ComplexMatrix ComplexMatrix::solve (MatrixType &typ, const Matrix& b, octave_idx_type& info, double& rcon, solve_singularity_handler sing_handler, bool singular_fallback, blas_trans_type transt) const { ComplexMatrix tmp (b); return solve (typ, tmp, info, rcon, sing_handler, singular_fallback, transt); } ComplexMatrix ComplexMatrix::solve (MatrixType &typ, const ComplexMatrix& b) const { octave_idx_type info; double rcon; return solve (typ, b, info, rcon, 0); } ComplexMatrix ComplexMatrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info) const { double rcon; return solve (typ, b, info, rcon, 0); } ComplexMatrix ComplexMatrix::solve (MatrixType &typ, const ComplexMatrix& b, octave_idx_type& info, double& rcon) const { return solve (typ, b, info, rcon, 0); } ComplexMatrix ComplexMatrix::solve (MatrixType &mattype, const ComplexMatrix& b, octave_idx_type& info, double& rcon, solve_singularity_handler sing_handler, bool singular_fallback, blas_trans_type transt) const { ComplexMatrix retval; int typ = mattype.type (); if (typ == MatrixType::Unknown) typ = mattype.type (*this); // Only calculate the condition number for LU/Cholesky if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper) retval = utsolve (mattype, b, info, rcon, sing_handler, true, transt); else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) retval = ltsolve (mattype, b, info, rcon, sing_handler, true, transt); else if (transt == blas_trans) return transpose ().solve (mattype, b, info, rcon, sing_handler, singular_fallback); else if (transt == blas_conj_trans) retval = hermitian ().solve (mattype, b, info, rcon, sing_handler, singular_fallback); else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) retval = fsolve (mattype, b, info, rcon, sing_handler, true); else if (typ != MatrixType::Rectangular) (*current_liboctave_error_handler) ("unknown matrix type"); // Rectangular or one of the above solvers flags a singular matrix if (singular_fallback && mattype.type () == MatrixType::Rectangular) { octave_idx_type rank; retval = lssolve (b, info, rank, rcon); } return retval; } ComplexColumnVector ComplexMatrix::solve (MatrixType &typ, const ColumnVector& b) const { octave_idx_type info; double rcon; return solve (typ, ComplexColumnVector (b), info, rcon, 0); } ComplexColumnVector ComplexMatrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info) const { double rcon; return solve (typ, ComplexColumnVector (b), info, rcon, 0); } ComplexColumnVector ComplexMatrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, double& rcon) const { return solve (typ, ComplexColumnVector (b), info, rcon, 0); } ComplexColumnVector ComplexMatrix::solve (MatrixType &typ, const ColumnVector& b, octave_idx_type& info, double& rcon, solve_singularity_handler sing_handler, blas_trans_type transt) const { return solve (typ, ComplexColumnVector (b), info, rcon, sing_handler, transt); } ComplexColumnVector ComplexMatrix::solve (MatrixType &typ, const ComplexColumnVector& b) const { octave_idx_type info; double rcon; return solve (typ, b, info, rcon, 0); } ComplexColumnVector ComplexMatrix::solve (MatrixType &typ, const ComplexColumnVector& b, octave_idx_type& info) const { double rcon; return solve (typ, b, info, rcon, 0); } ComplexColumnVector ComplexMatrix::solve (MatrixType &typ, const ComplexColumnVector& b, octave_idx_type& info, double& rcon) const { return solve (typ, b, info, rcon, 0); } ComplexColumnVector ComplexMatrix::solve (MatrixType &typ, const ComplexColumnVector& b, octave_idx_type& info, double& rcon, solve_singularity_handler sing_handler, blas_trans_type transt) const { ComplexMatrix tmp (b); tmp = solve (typ, tmp, info, rcon, sing_handler, true, transt); return tmp.column (static_cast<octave_idx_type> (0)); } ComplexMatrix ComplexMatrix::solve (const Matrix& b) const { octave_idx_type info; double rcon; return solve (b, info, rcon, 0); } ComplexMatrix ComplexMatrix::solve (const Matrix& b, octave_idx_type& info) const { double rcon; return solve (b, info, rcon, 0); } ComplexMatrix ComplexMatrix::solve (const Matrix& b, octave_idx_type& info, double& rcon) const { return solve (b, info, rcon, 0); } ComplexMatrix ComplexMatrix::solve (const Matrix& b, octave_idx_type& info, double& rcon, solve_singularity_handler sing_handler, blas_trans_type transt) const { ComplexMatrix tmp (b); return solve (tmp, info, rcon, sing_handler, transt); } ComplexMatrix ComplexMatrix::solve (const ComplexMatrix& b) const { octave_idx_type info; double rcon; return solve (b, info, rcon, 0); } ComplexMatrix ComplexMatrix::solve (const ComplexMatrix& b, octave_idx_type& info) const { double rcon; return solve (b, info, rcon, 0); } ComplexMatrix ComplexMatrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcon) const { return solve (b, info, rcon, 0); } ComplexMatrix ComplexMatrix::solve (const ComplexMatrix& b, octave_idx_type& info, double& rcon, solve_singularity_handler sing_handler, blas_trans_type transt) const { MatrixType mattype (*this); return solve (mattype, b, info, rcon, sing_handler, true, transt); } ComplexColumnVector ComplexMatrix::solve (const ColumnVector& b) const { octave_idx_type info; double rcon; return solve (ComplexColumnVector (b), info, rcon, 0); } ComplexColumnVector ComplexMatrix::solve (const ColumnVector& b, octave_idx_type& info) const { double rcon; return solve (ComplexColumnVector (b), info, rcon, 0); } ComplexColumnVector ComplexMatrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcon) const { return solve (ComplexColumnVector (b), info, rcon, 0); } ComplexColumnVector ComplexMatrix::solve (const ColumnVector& b, octave_idx_type& info, double& rcon, solve_singularity_handler sing_handler, blas_trans_type transt) const { return solve (ComplexColumnVector (b), info, rcon, sing_handler, transt); } ComplexColumnVector ComplexMatrix::solve (const ComplexColumnVector& b) const { octave_idx_type info; double rcon; return solve (b, info, rcon, 0); } ComplexColumnVector ComplexMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info) const { double rcon; return solve (b, info, rcon, 0); } ComplexColumnVector ComplexMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcon) const { return solve (b, info, rcon, 0); } ComplexColumnVector ComplexMatrix::solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcon, solve_singularity_handler sing_handler, blas_trans_type transt) const { MatrixType mattype (*this); return solve (mattype, b, info, rcon, sing_handler, transt); } ComplexMatrix ComplexMatrix::lssolve (const Matrix& b) const { octave_idx_type info; octave_idx_type rank; double rcon; return lssolve (ComplexMatrix (b), info, rank, rcon); } ComplexMatrix ComplexMatrix::lssolve (const Matrix& b, octave_idx_type& info) const { octave_idx_type rank; double rcon; return lssolve (ComplexMatrix (b), info, rank, rcon); } ComplexMatrix ComplexMatrix::lssolve (const Matrix& b, octave_idx_type& info, octave_idx_type& rank) const { double rcon; return lssolve (ComplexMatrix (b), info, rank, rcon); } ComplexMatrix ComplexMatrix::lssolve (const Matrix& b, octave_idx_type& info, octave_idx_type& rank, double& rcon) const { return lssolve (ComplexMatrix (b), info, rank, rcon); } ComplexMatrix ComplexMatrix::lssolve (const ComplexMatrix& b) const { octave_idx_type info; octave_idx_type rank; double rcon; return lssolve (b, info, rank, rcon); } ComplexMatrix ComplexMatrix::lssolve (const ComplexMatrix& b, octave_idx_type& info) const { octave_idx_type rank; double rcon; return lssolve (b, info, rank, rcon); } ComplexMatrix ComplexMatrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, octave_idx_type& rank) const { double rcon; return lssolve (b, info, rank, rcon); } ComplexMatrix ComplexMatrix::lssolve (const ComplexMatrix& b, octave_idx_type& info, octave_idx_type& rank, double& rcon) const { ComplexMatrix retval; octave_idx_type nrhs = b.cols (); octave_idx_type m = rows (); octave_idx_type n = cols (); if (m != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (m == 0 || n == 0 || b.cols () == 0) retval = ComplexMatrix (n, b.cols (), Complex (0.0, 0.0)); else { volatile octave_idx_type minmn = (m < n ? m : n); octave_idx_type maxmn = m > n ? m : n; rcon = -1.0; if (m != n) { retval = ComplexMatrix (maxmn, nrhs); for (octave_idx_type j = 0; j < nrhs; j++) for (octave_idx_type i = 0; i < m; i++) retval.elem (i, j) = b.elem (i, j); } else retval = b; ComplexMatrix atmp = *this; Complex *tmp_data = atmp.fortran_vec (); Complex *pretval = retval.fortran_vec (); Array<double> s (dim_vector (minmn, 1)); double *ps = s.fortran_vec (); // Ask ZGELSD what the dimension of WORK should be. octave_idx_type lwork = -1; Array<Complex> work (dim_vector (1, 1)); octave_idx_type smlsiz; F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("ZGELSD", 6), F77_CONST_CHAR_ARG2 (" ", 1), 0, 0, 0, 0, smlsiz F77_CHAR_ARG_LEN (6) F77_CHAR_ARG_LEN (1)); octave_idx_type mnthr; F77_FUNC (xilaenv, XILAENV) (6, F77_CONST_CHAR_ARG2 ("ZGELSD", 6), F77_CONST_CHAR_ARG2 (" ", 1), m, n, nrhs, -1, mnthr F77_CHAR_ARG_LEN (6) F77_CHAR_ARG_LEN (1)); // We compute the size of rwork and iwork because ZGELSD in // older versions of LAPACK does not return them on a query // call. double dminmn = static_cast<double> (minmn); double dsmlsizp1 = static_cast<double> (smlsiz+1); double tmp = octave::math::log2 (dminmn / dsmlsizp1); double anorm = 0.0; octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; if (nlvl < 0) nlvl = 0; octave_idx_type lrwork = minmn*(10 + 2*smlsiz + 8*nlvl) + 3*smlsiz*nrhs + std::max ((smlsiz+1)*(smlsiz+1), n*(1+nrhs) + 2*nrhs); if (lrwork < 1) lrwork = 1; Array<double> rwork (dim_vector (lrwork, 1)); double *prwork = rwork.fortran_vec (); octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; if (liwork < 1) liwork = 1; Array<octave_idx_type> iwork (dim_vector (liwork, 1)); octave_idx_type* piwork = iwork.fortran_vec (); F77_XFCN (zgelsd, ZGELSD, (m, n, nrhs, F77_DBLE_CMPLX_ARG (tmp_data), m, F77_DBLE_CMPLX_ARG (pretval), maxmn, ps, rcon, rank, F77_DBLE_CMPLX_ARG (work.fortran_vec ()), lwork, prwork, piwork, info)); // The workspace query is broken in at least LAPACK 3.0.0 // through 3.1.1 when n >= mnthr. The obtuse formula below // should provide sufficient workspace for ZGELSD to operate // efficiently. if (n > m && n >= mnthr) { octave_idx_type addend = m; if (2*m-4 > addend) addend = 2*m-4; if (nrhs > addend) addend = nrhs; if (n-3*m > addend) addend = n-3*m; const octave_idx_type lworkaround = 4*m + m*m + addend; if (octave::math::real (work(0)) < lworkaround) work(0) = lworkaround; } else if (m >= n) { octave_idx_type lworkaround = 2*m + m*nrhs; if (octave::math::real (work(0)) < lworkaround) work(0) = lworkaround; } lwork = static_cast<octave_idx_type> (octave::math::real (work(0))); work.resize (dim_vector (lwork, 1)); anorm = xnorm (*this, 1); if (octave::math::isinf (anorm) || octave::math::isnan (anorm)) { rcon = 0.0; octave::warn_singular_matrix (); retval = Matrix (n, m, 0.0); } else { F77_XFCN (zgelsd, ZGELSD, (m, n, nrhs, F77_DBLE_CMPLX_ARG (tmp_data), m, F77_DBLE_CMPLX_ARG (pretval), maxmn, ps, rcon, rank, F77_DBLE_CMPLX_ARG (work.fortran_vec ()), lwork, prwork, piwork, info)); if (s.elem (0) == 0.0) rcon = 0.0; else rcon = s.elem (minmn - 1) / s.elem (0); retval.resize (n, nrhs); } } return retval; } ComplexColumnVector ComplexMatrix::lssolve (const ColumnVector& b) const { octave_idx_type info; octave_idx_type rank; double rcon; return lssolve (ComplexColumnVector (b), info, rank, rcon); } ComplexColumnVector ComplexMatrix::lssolve (const ColumnVector& b, octave_idx_type& info) const { octave_idx_type rank; double rcon; return lssolve (ComplexColumnVector (b), info, rank, rcon); } ComplexColumnVector ComplexMatrix::lssolve (const ColumnVector& b, octave_idx_type& info, octave_idx_type& rank) const { double rcon; return lssolve (ComplexColumnVector (b), info, rank, rcon); } ComplexColumnVector ComplexMatrix::lssolve (const ColumnVector& b, octave_idx_type& info, octave_idx_type& rank, double& rcon) const { return lssolve (ComplexColumnVector (b), info, rank, rcon); } ComplexColumnVector ComplexMatrix::lssolve (const ComplexColumnVector& b) const { octave_idx_type info; octave_idx_type rank; double rcon; return lssolve (b, info, rank, rcon); } ComplexColumnVector ComplexMatrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info) const { octave_idx_type rank; double rcon; return lssolve (b, info, rank, rcon); } ComplexColumnVector ComplexMatrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, octave_idx_type& rank) const { double rcon; return lssolve (b, info, rank, rcon); } ComplexColumnVector ComplexMatrix::lssolve (const ComplexColumnVector& b, octave_idx_type& info, octave_idx_type& rank, double& rcon) const { ComplexColumnVector retval; octave_idx_type nrhs = 1; octave_idx_type m = rows (); octave_idx_type n = cols (); if (m != b.numel ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (m == 0 || n == 0 || b.cols () == 0) retval = ComplexColumnVector (n, Complex (0.0, 0.0)); else { volatile octave_idx_type minmn = (m < n ? m : n); octave_idx_type maxmn = m > n ? m : n; rcon = -1.0; if (m != n) { retval = ComplexColumnVector (maxmn); for (octave_idx_type i = 0; i < m; i++) retval.elem (i) = b.elem (i); } else retval = b; ComplexMatrix atmp = *this; Complex *tmp_data = atmp.fortran_vec (); Complex *pretval = retval.fortran_vec (); Array<double> s (dim_vector (minmn, 1)); double *ps = s.fortran_vec (); // Ask ZGELSD what the dimension of WORK should be. octave_idx_type lwork = -1; Array<Complex> work (dim_vector (1, 1)); octave_idx_type smlsiz; F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("ZGELSD", 6), F77_CONST_CHAR_ARG2 (" ", 1), 0, 0, 0, 0, smlsiz F77_CHAR_ARG_LEN (6) F77_CHAR_ARG_LEN (1)); // We compute the size of rwork and iwork because ZGELSD in // older versions of LAPACK does not return them on a query // call. double dminmn = static_cast<double> (minmn); double dsmlsizp1 = static_cast<double> (smlsiz+1); double tmp = octave::math::log2 (dminmn / dsmlsizp1); octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; if (nlvl < 0) nlvl = 0; octave_idx_type lrwork = minmn*(10 + 2*smlsiz + 8*nlvl) + 3*smlsiz*nrhs + (smlsiz+1)*(smlsiz+1); if (lrwork < 1) lrwork = 1; Array<double> rwork (dim_vector (lrwork, 1)); double *prwork = rwork.fortran_vec (); octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; if (liwork < 1) liwork = 1; Array<octave_idx_type> iwork (dim_vector (liwork, 1)); octave_idx_type* piwork = iwork.fortran_vec (); F77_XFCN (zgelsd, ZGELSD, (m, n, nrhs, F77_DBLE_CMPLX_ARG (tmp_data), m, F77_DBLE_CMPLX_ARG (pretval), maxmn, ps, rcon, rank, F77_DBLE_CMPLX_ARG (work.fortran_vec ()), lwork, prwork, piwork, info)); lwork = static_cast<octave_idx_type> (octave::math::real (work(0))); work.resize (dim_vector (lwork, 1)); rwork.resize (dim_vector (static_cast<octave_idx_type> (rwork(0)), 1)); iwork.resize (dim_vector (iwork(0), 1)); F77_XFCN (zgelsd, ZGELSD, (m, n, nrhs, F77_DBLE_CMPLX_ARG (tmp_data), m, F77_DBLE_CMPLX_ARG (pretval), maxmn, ps, rcon, rank, F77_DBLE_CMPLX_ARG (work.fortran_vec ()), lwork, prwork, piwork, info)); if (rank < minmn) { if (s.elem (0) == 0.0) rcon = 0.0; else rcon = s.elem (minmn - 1) / s.elem (0); retval.resize (n, nrhs); } } return retval; } // column vector by row vector -> matrix operations ComplexMatrix operator * (const ColumnVector& v, const ComplexRowVector& a) { ComplexColumnVector tmp (v); return tmp * a; } ComplexMatrix operator * (const ComplexColumnVector& a, const RowVector& b) { ComplexRowVector tmp (b); return a * tmp; } ComplexMatrix operator * (const ComplexColumnVector& v, const ComplexRowVector& a) { ComplexMatrix retval; octave_idx_type len = v.numel (); if (len != 0) { octave_idx_type a_len = a.numel (); retval = ComplexMatrix (len, a_len); Complex *c = retval.fortran_vec (); F77_XFCN (zgemm, ZGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), F77_CONST_CHAR_ARG2 ("N", 1), len, a_len, 1, 1.0, F77_CONST_DBLE_CMPLX_ARG (v.data ()), len, F77_CONST_DBLE_CMPLX_ARG (a.data ()), 1, 0.0, F77_DBLE_CMPLX_ARG (c), len F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); } return retval; } // matrix by diagonal matrix -> matrix operations ComplexMatrix& ComplexMatrix::operator += (const DiagMatrix& a) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type a_nr = rows (); octave_idx_type a_nc = cols (); if (nr != a_nr || nc != a_nc) octave::err_nonconformant ("operator +=", nr, nc, a_nr, a_nc); for (octave_idx_type i = 0; i < a.length (); i++) elem (i, i) += a.elem (i, i); return *this; } ComplexMatrix& ComplexMatrix::operator -= (const DiagMatrix& a) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type a_nr = rows (); octave_idx_type a_nc = cols (); if (nr != a_nr || nc != a_nc) octave::err_nonconformant ("operator -=", nr, nc, a_nr, a_nc); for (octave_idx_type i = 0; i < a.length (); i++) elem (i, i) -= a.elem (i, i); return *this; } ComplexMatrix& ComplexMatrix::operator += (const ComplexDiagMatrix& a) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type a_nr = rows (); octave_idx_type a_nc = cols (); if (nr != a_nr || nc != a_nc) octave::err_nonconformant ("operator +=", nr, nc, a_nr, a_nc); for (octave_idx_type i = 0; i < a.length (); i++) elem (i, i) += a.elem (i, i); return *this; } ComplexMatrix& ComplexMatrix::operator -= (const ComplexDiagMatrix& a) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type a_nr = rows (); octave_idx_type a_nc = cols (); if (nr != a_nr || nc != a_nc) octave::err_nonconformant ("operator -=", nr, nc, a_nr, a_nc); for (octave_idx_type i = 0; i < a.length (); i++) elem (i, i) -= a.elem (i, i); return *this; } // matrix by matrix -> matrix operations ComplexMatrix& ComplexMatrix::operator += (const Matrix& a) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type a_nr = a.rows (); octave_idx_type a_nc = a.cols (); if (nr != a_nr || nc != a_nc) octave::err_nonconformant ("operator +=", nr, nc, a_nr, a_nc); if (nr == 0 || nc == 0) return *this; Complex *d = fortran_vec (); // Ensures only one reference to my privates! mx_inline_add2 (numel (), d, a.data ()); return *this; } ComplexMatrix& ComplexMatrix::operator -= (const Matrix& a) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type a_nr = a.rows (); octave_idx_type a_nc = a.cols (); if (nr != a_nr || nc != a_nc) octave::err_nonconformant ("operator -=", nr, nc, a_nr, a_nc); if (nr == 0 || nc == 0) return *this; Complex *d = fortran_vec (); // Ensures only one reference to my privates! mx_inline_sub2 (numel (), d, a.data ()); return *this; } // other operations boolMatrix ComplexMatrix::all (int dim) const { return ComplexNDArray::all (dim); } boolMatrix ComplexMatrix::any (int dim) const { return ComplexNDArray::any (dim); } ComplexMatrix ComplexMatrix::cumprod (int dim) const { return ComplexNDArray::cumprod (dim); } ComplexMatrix ComplexMatrix::cumsum (int dim) const { return ComplexNDArray::cumsum (dim); } ComplexMatrix ComplexMatrix::prod (int dim) const { return ComplexNDArray::prod (dim); } ComplexMatrix ComplexMatrix::sum (int dim) const { return ComplexNDArray::sum (dim); } ComplexMatrix ComplexMatrix::sumsq (int dim) const { return ComplexNDArray::sumsq (dim); } Matrix ComplexMatrix::abs (void) const { return ComplexNDArray::abs (); } ComplexMatrix ComplexMatrix::diag (octave_idx_type k) const { return ComplexNDArray::diag (k); } ComplexDiagMatrix ComplexMatrix::diag (octave_idx_type m, octave_idx_type n) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != 1 && nc != 1) (*current_liboctave_error_handler) ("diag: expecting vector argument"); return ComplexDiagMatrix (*this, m, n); } bool ComplexMatrix::row_is_real_only (octave_idx_type i) const { bool retval = true; octave_idx_type nc = columns (); for (octave_idx_type j = 0; j < nc; j++) { if (octave::math::imag (elem (i, j)) != 0.0) { retval = false; break; } } return retval; } bool ComplexMatrix::column_is_real_only (octave_idx_type j) const { bool retval = true; octave_idx_type nr = rows (); for (octave_idx_type i = 0; i < nr; i++) { if (octave::math::imag (elem (i, j)) != 0.0) { retval = false; break; } } return retval; } ComplexColumnVector ComplexMatrix::row_min (void) const { Array<octave_idx_type> dummy_idx; return row_min (dummy_idx); } ComplexColumnVector ComplexMatrix::row_min (Array<octave_idx_type>& idx_arg) const { ComplexColumnVector result; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr > 0 && nc > 0) { result.resize (nr); idx_arg.resize (dim_vector (nr, 1)); for (octave_idx_type i = 0; i < nr; i++) { bool real_only = row_is_real_only (i); octave_idx_type idx_j; Complex tmp_min; double abs_min = octave::numeric_limits<double>::NaN (); for (idx_j = 0; idx_j < nc; idx_j++) { tmp_min = elem (i, idx_j); if (! octave::math::isnan (tmp_min)) { abs_min = real_only ? tmp_min.real () : std::abs (tmp_min); break; } } for (octave_idx_type j = idx_j+1; j < nc; j++) { Complex tmp = elem (i, j); if (octave::math::isnan (tmp)) continue; double abs_tmp = real_only ? tmp.real () : std::abs (tmp); if (abs_tmp < abs_min) { idx_j = j; tmp_min = tmp; abs_min = abs_tmp; } } if (octave::math::isnan (tmp_min)) { result.elem (i) = Complex_NaN_result; idx_arg.elem (i) = 0; } else { result.elem (i) = tmp_min; idx_arg.elem (i) = idx_j; } } } return result; } ComplexColumnVector ComplexMatrix::row_max (void) const { Array<octave_idx_type> dummy_idx; return row_max (dummy_idx); } ComplexColumnVector ComplexMatrix::row_max (Array<octave_idx_type>& idx_arg) const { ComplexColumnVector result; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr > 0 && nc > 0) { result.resize (nr); idx_arg.resize (dim_vector (nr, 1)); for (octave_idx_type i = 0; i < nr; i++) { bool real_only = row_is_real_only (i); octave_idx_type idx_j; Complex tmp_max; double abs_max = octave::numeric_limits<double>::NaN (); for (idx_j = 0; idx_j < nc; idx_j++) { tmp_max = elem (i, idx_j); if (! octave::math::isnan (tmp_max)) { abs_max = real_only ? tmp_max.real () : std::abs (tmp_max); break; } } for (octave_idx_type j = idx_j+1; j < nc; j++) { Complex tmp = elem (i, j); if (octave::math::isnan (tmp)) continue; double abs_tmp = real_only ? tmp.real () : std::abs (tmp); if (abs_tmp > abs_max) { idx_j = j; tmp_max = tmp; abs_max = abs_tmp; } } if (octave::math::isnan (tmp_max)) { result.elem (i) = Complex_NaN_result; idx_arg.elem (i) = 0; } else { result.elem (i) = tmp_max; idx_arg.elem (i) = idx_j; } } } return result; } ComplexRowVector ComplexMatrix::column_min (void) const { Array<octave_idx_type> dummy_idx; return column_min (dummy_idx); } ComplexRowVector ComplexMatrix::column_min (Array<octave_idx_type>& idx_arg) const { ComplexRowVector result; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr > 0 && nc > 0) { result.resize (nc); idx_arg.resize (dim_vector (1, nc)); for (octave_idx_type j = 0; j < nc; j++) { bool real_only = column_is_real_only (j); octave_idx_type idx_i; Complex tmp_min; double abs_min = octave::numeric_limits<double>::NaN (); for (idx_i = 0; idx_i < nr; idx_i++) { tmp_min = elem (idx_i, j); if (! octave::math::isnan (tmp_min)) { abs_min = real_only ? tmp_min.real () : std::abs (tmp_min); break; } } for (octave_idx_type i = idx_i+1; i < nr; i++) { Complex tmp = elem (i, j); if (octave::math::isnan (tmp)) continue; double abs_tmp = real_only ? tmp.real () : std::abs (tmp); if (abs_tmp < abs_min) { idx_i = i; tmp_min = tmp; abs_min = abs_tmp; } } if (octave::math::isnan (tmp_min)) { result.elem (j) = Complex_NaN_result; idx_arg.elem (j) = 0; } else { result.elem (j) = tmp_min; idx_arg.elem (j) = idx_i; } } } return result; } ComplexRowVector ComplexMatrix::column_max (void) const { Array<octave_idx_type> dummy_idx; return column_max (dummy_idx); } ComplexRowVector ComplexMatrix::column_max (Array<octave_idx_type>& idx_arg) const { ComplexRowVector result; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr > 0 && nc > 0) { result.resize (nc); idx_arg.resize (dim_vector (1, nc)); for (octave_idx_type j = 0; j < nc; j++) { bool real_only = column_is_real_only (j); octave_idx_type idx_i; Complex tmp_max; double abs_max = octave::numeric_limits<double>::NaN (); for (idx_i = 0; idx_i < nr; idx_i++) { tmp_max = elem (idx_i, j); if (! octave::math::isnan (tmp_max)) { abs_max = real_only ? tmp_max.real () : std::abs (tmp_max); break; } } for (octave_idx_type i = idx_i+1; i < nr; i++) { Complex tmp = elem (i, j); if (octave::math::isnan (tmp)) continue; double abs_tmp = real_only ? tmp.real () : std::abs (tmp); if (abs_tmp > abs_max) { idx_i = i; tmp_max = tmp; abs_max = abs_tmp; } } if (octave::math::isnan (tmp_max)) { result.elem (j) = Complex_NaN_result; idx_arg.elem (j) = 0; } else { result.elem (j) = tmp_max; idx_arg.elem (j) = idx_i; } } } return result; } // i/o std::ostream& operator << (std::ostream& os, const ComplexMatrix& a) { for (octave_idx_type i = 0; i < a.rows (); i++) { for (octave_idx_type j = 0; j < a.cols (); j++) { os << " "; octave_write_complex (os, a.elem (i, j)); } os << "\n"; } return os; } std::istream& operator >> (std::istream& is, ComplexMatrix& a) { octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); if (nr > 0 && nc > 0) { Complex tmp; for (octave_idx_type i = 0; i < nr; i++) for (octave_idx_type j = 0; j < nc; j++) { tmp = octave_read_value<Complex> (is); if (is) a.elem (i, j) = tmp; else return is; } } return is; } ComplexMatrix Givens (const Complex& x, const Complex& y) { double cc; Complex cs, temp_r; F77_FUNC (zlartg, ZLARTG) (F77_CONST_DBLE_CMPLX_ARG (&x), F77_CONST_DBLE_CMPLX_ARG (&y), cc, F77_DBLE_CMPLX_ARG (&cs), F77_DBLE_CMPLX_ARG (&temp_r)); ComplexMatrix g (2, 2); g.elem (0, 0) = cc; g.elem (1, 1) = cc; g.elem (0, 1) = cs; g.elem (1, 0) = -conj (cs); return g; } ComplexMatrix Sylvester (const ComplexMatrix& a, const ComplexMatrix& b, const ComplexMatrix& c) { ComplexMatrix retval; // FIXME: need to check that a, b, and c are all the same size. // Compute Schur decompositions octave::math::schur<ComplexMatrix> as (a, "U"); octave::math::schur<ComplexMatrix> bs (b, "U"); // Transform c to new coordinates. ComplexMatrix ua = as.unitary_matrix (); ComplexMatrix sch_a = as.schur_matrix (); ComplexMatrix ub = bs.unitary_matrix (); ComplexMatrix sch_b = bs.schur_matrix (); ComplexMatrix cx = ua.hermitian () * c * ub; // Solve the sylvester equation, back-transform, and return the solution. octave_idx_type a_nr = a.rows (); octave_idx_type b_nr = b.rows (); double scale; octave_idx_type info; Complex *pa = sch_a.fortran_vec (); Complex *pb = sch_b.fortran_vec (); Complex *px = cx.fortran_vec (); F77_XFCN (ztrsyl, ZTRSYL, (F77_CONST_CHAR_ARG2 ("N", 1), F77_CONST_CHAR_ARG2 ("N", 1), 1, a_nr, b_nr, F77_DBLE_CMPLX_ARG (pa), a_nr, F77_DBLE_CMPLX_ARG (pb), b_nr, F77_DBLE_CMPLX_ARG (px), a_nr, scale, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); // FIXME: check info? retval = ua * cx * ub.hermitian (); return retval; } ComplexMatrix operator * (const ComplexMatrix& m, const Matrix& a) { if (m.columns () > std::min (m.rows (), a.columns ()) / 10) return ComplexMatrix (real (m) * a, imag (m) * a); else return m * ComplexMatrix (a); } ComplexMatrix operator * (const Matrix& m, const ComplexMatrix& a) { if (a.rows () > std::min (m.rows (), a.columns ()) / 10) return ComplexMatrix (m * real (a), m * imag (a)); else return ComplexMatrix (m) * a; } /* ## Simple Dot Product, Matrix-Vector, and Matrix-Matrix Unit tests %!assert ([1+i 2+i 3+i] * [ 4+i ; 5+i ; 6+i], 29+21i, 1e-14) %!assert ([1+i 2+i ; 3+i 4+i ] * [5+i ; 6+i], [15 + 14i ; 37 + 18i], 1e-14) %!assert ([1+i 2+i ; 3+i 4+i ] * [5+i 6+i ; 7+i 8+i], [17 + 15i 20 + 17i; 41 + 19i 48 + 21i], 1e-14) %!assert ([1 i]*[i 0]', -i) ## Test some simple identities %!shared M, cv, rv %! M = randn (10,10) + i*rand (10,10); %! cv = randn (10,1) + i*rand (10,1); %! rv = randn (1,10) + i*rand (1,10); %!assert ([M*cv,M*cv], M*[cv,cv], 1e-14) %!assert ([M.'*cv,M.'*cv], M.'*[cv,cv], 1e-14) %!assert ([M'*cv,M'*cv], M'*[cv,cv], 1e-14) %!assert ([rv*M;rv*M], [rv;rv]*M, 1e-14) %!assert ([rv*M.';rv*M.'], [rv;rv]*M.', 1e-14) %!assert ([rv*M';rv*M'], [rv;rv]*M', 1e-14) %!assert (2*rv*cv, [rv,rv]*[cv;cv], 1e-14) */ static inline char get_blas_trans_arg (bool trans, bool conj) { return trans ? (conj ? 'C' : 'T') : 'N'; } // the general GEMM operation ComplexMatrix xgemm (const ComplexMatrix& a, const ComplexMatrix& b, blas_trans_type transa, blas_trans_type transb) { ComplexMatrix retval; bool tra = transa != blas_no_trans; bool trb = transb != blas_no_trans; bool cja = transa == blas_conj_trans; bool cjb = transb == blas_conj_trans; octave_idx_type a_nr = tra ? a.cols () : a.rows (); octave_idx_type a_nc = tra ? a.rows () : a.cols (); octave_idx_type b_nr = trb ? b.cols () : b.rows (); octave_idx_type b_nc = trb ? b.rows () : b.cols (); if (a_nc != b_nr) octave::err_nonconformant ("operator *", a_nr, a_nc, b_nr, b_nc); if (a_nr == 0 || a_nc == 0 || b_nc == 0) retval = ComplexMatrix (a_nr, b_nc, 0.0); else if (a.data () == b.data () && a_nr == b_nc && tra != trb) { octave_idx_type lda = a.rows (); // FIXME: looking at the reference BLAS, it appears that it // should not be necessary to initialize the output matrix if // BETA is 0 in the call to ZHERK, but ATLAS appears to // use the result matrix before zeroing the elements. retval = ComplexMatrix (a_nr, b_nc, 0.0); Complex *c = retval.fortran_vec (); const char ctra = get_blas_trans_arg (tra, cja); if (cja || cjb) { F77_XFCN (zherk, ZHERK, (F77_CONST_CHAR_ARG2 ("U", 1), F77_CONST_CHAR_ARG2 (&ctra, 1), a_nr, a_nc, 1.0, F77_CONST_DBLE_CMPLX_ARG (a.data ()), lda, 0.0, F77_DBLE_CMPLX_ARG (c), a_nr F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); for (octave_idx_type j = 0; j < a_nr; j++) for (octave_idx_type i = 0; i < j; i++) retval.xelem (j,i) = octave::math::conj (retval.xelem (i,j)); } else { F77_XFCN (zsyrk, ZSYRK, (F77_CONST_CHAR_ARG2 ("U", 1), F77_CONST_CHAR_ARG2 (&ctra, 1), a_nr, a_nc, 1.0, F77_CONST_DBLE_CMPLX_ARG (a.data ()), lda, 0.0, F77_DBLE_CMPLX_ARG (c), a_nr F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); for (octave_idx_type j = 0; j < a_nr; j++) for (octave_idx_type i = 0; i < j; i++) retval.xelem (j,i) = retval.xelem (i,j); } } else { octave_idx_type lda = a.rows (); octave_idx_type tda = a.cols (); octave_idx_type ldb = b.rows (); octave_idx_type tdb = b.cols (); retval = ComplexMatrix (a_nr, b_nc, 0.0); Complex *c = retval.fortran_vec (); if (b_nc == 1 && a_nr == 1) { if (cja == cjb) { F77_FUNC (xzdotu, XZDOTU) (a_nc, F77_CONST_DBLE_CMPLX_ARG (a.data ()), 1, F77_CONST_DBLE_CMPLX_ARG (b.data ()), 1, F77_DBLE_CMPLX_ARG (c)); if (cja) *c = octave::math::conj (*c); } else if (cja) F77_FUNC (xzdotc, XZDOTC) (a_nc, F77_CONST_DBLE_CMPLX_ARG (a.data ()), 1, F77_CONST_DBLE_CMPLX_ARG (b.data ()), 1, F77_DBLE_CMPLX_ARG (c)); else F77_FUNC (xzdotc, XZDOTC) (a_nc, F77_CONST_DBLE_CMPLX_ARG (b.data ()), 1, F77_CONST_DBLE_CMPLX_ARG (a.data ()), 1, F77_DBLE_CMPLX_ARG (c)); } else if (b_nc == 1 && ! cjb) { const char ctra = get_blas_trans_arg (tra, cja); F77_XFCN (zgemv, ZGEMV, (F77_CONST_CHAR_ARG2 (&ctra, 1), lda, tda, 1.0, F77_CONST_DBLE_CMPLX_ARG (a.data ()), lda, F77_CONST_DBLE_CMPLX_ARG (b.data ()), 1, 0.0, F77_DBLE_CMPLX_ARG (c), 1 F77_CHAR_ARG_LEN (1))); } else if (a_nr == 1 && ! cja && ! cjb) { const char crevtrb = get_blas_trans_arg (! trb, cjb); F77_XFCN (zgemv, ZGEMV, (F77_CONST_CHAR_ARG2 (&crevtrb, 1), ldb, tdb, 1.0, F77_CONST_DBLE_CMPLX_ARG (b.data ()), ldb, F77_CONST_DBLE_CMPLX_ARG (a.data ()), 1, 0.0, F77_DBLE_CMPLX_ARG (c), 1 F77_CHAR_ARG_LEN (1))); } else { const char ctra = get_blas_trans_arg (tra, cja); const char ctrb = get_blas_trans_arg (trb, cjb); F77_XFCN (zgemm, ZGEMM, (F77_CONST_CHAR_ARG2 (&ctra, 1), F77_CONST_CHAR_ARG2 (&ctrb, 1), a_nr, b_nc, a_nc, 1.0, F77_CONST_DBLE_CMPLX_ARG (a.data ()), lda, F77_CONST_DBLE_CMPLX_ARG (b.data ()), ldb, 0.0, F77_DBLE_CMPLX_ARG (c), a_nr F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); } } return retval; } ComplexMatrix operator * (const ComplexMatrix& a, const ComplexMatrix& b) { return xgemm (a, b); } // FIXME: it would be nice to share code among the min/max functions below. #define EMPTY_RETURN_CHECK(T) \ if (nr == 0 || nc == 0) \ return T (nr, nc); ComplexMatrix min (const Complex& c, const ComplexMatrix& m) { octave_idx_type nr = m.rows (); octave_idx_type nc = m.columns (); EMPTY_RETURN_CHECK (ComplexMatrix); ComplexMatrix result (nr, nc); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); result(i, j) = octave::math::min (c, m(i, j)); } return result; } ComplexMatrix min (const ComplexMatrix& m, const Complex& c) { return min (c, m); } ComplexMatrix min (const ComplexMatrix& a, const ComplexMatrix& b) { octave_idx_type nr = a.rows (); octave_idx_type nc = a.columns (); if (nr != b.rows () || nc != b.columns ()) (*current_liboctave_error_handler) ("two-arg min requires same size arguments"); EMPTY_RETURN_CHECK (ComplexMatrix); ComplexMatrix result (nr, nc); for (octave_idx_type j = 0; j < nc; j++) { bool columns_are_real_only = true; for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); if (octave::math::imag (a(i, j)) != 0.0 || octave::math::imag (b(i, j)) != 0.0) { columns_are_real_only = false; break; } } if (columns_are_real_only) { for (octave_idx_type i = 0; i < nr; i++) result(i, j) = octave::math::min (octave::math::real (a(i, j)), octave::math::real (b(i, j))); } else { for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); result(i, j) = octave::math::min (a(i, j), b(i, j)); } } } return result; } ComplexMatrix max (const Complex& c, const ComplexMatrix& m) { octave_idx_type nr = m.rows (); octave_idx_type nc = m.columns (); EMPTY_RETURN_CHECK (ComplexMatrix); ComplexMatrix result (nr, nc); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); result(i, j) = octave::math::max (c, m(i, j)); } return result; } ComplexMatrix max (const ComplexMatrix& m, const Complex& c) { return max (c, m); } ComplexMatrix max (const ComplexMatrix& a, const ComplexMatrix& b) { octave_idx_type nr = a.rows (); octave_idx_type nc = a.columns (); if (nr != b.rows () || nc != b.columns ()) (*current_liboctave_error_handler) ("two-arg max requires same size arguments"); EMPTY_RETURN_CHECK (ComplexMatrix); ComplexMatrix result (nr, nc); for (octave_idx_type j = 0; j < nc; j++) { bool columns_are_real_only = true; for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); if (octave::math::imag (a(i, j)) != 0.0 || octave::math::imag (b(i, j)) != 0.0) { columns_are_real_only = false; break; } } // FIXME: is it so much faster? if (columns_are_real_only) { for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); result(i, j) = octave::math::max (octave::math::real (a(i, j)), octave::math::real (b(i, j))); } } else { for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); result(i, j) = octave::math::max (a(i, j), b(i, j)); } } } return result; } ComplexMatrix linspace (const ComplexColumnVector& x1, const ComplexColumnVector& x2, octave_idx_type n) { octave_idx_type m = x1.numel (); if (x2.numel () != m) (*current_liboctave_error_handler) ("linspace: vectors must be of equal length"); NoAlias<ComplexMatrix> retval; if (n < 1) { retval.clear (m, 0); return retval; } retval.clear (m, n); for (octave_idx_type i = 0; i < m; i++) retval(i, 0) = x1(i); // The last column is unused so temporarily store delta there Complex *delta = &retval(0, n-1); for (octave_idx_type i = 0; i < m; i++) delta[i] = (x2(i) - x1(i)) / (n - 1.0); for (octave_idx_type j = 1; j < n-1; j++) for (octave_idx_type i = 0; i < m; i++) retval(i, j) = x1(i) + static_cast<double> (j)*delta[i]; for (octave_idx_type i = 0; i < m; i++) retval(i, n-1) = x2(i); return retval; } MS_CMP_OPS (ComplexMatrix, Complex) MS_BOOL_OPS (ComplexMatrix, Complex) SM_CMP_OPS (Complex, ComplexMatrix) SM_BOOL_OPS (Complex, ComplexMatrix) MM_CMP_OPS (ComplexMatrix, ComplexMatrix) MM_BOOL_OPS (ComplexMatrix, ComplexMatrix)