Mercurial > octave
view liboctave/numeric/eigs-base.cc @ 21301:40de9f8f23a6
Use '#include "config.h"' rather than <config.h>.
* mk-octave-config-h.sh, mk-opts.pl, Backend.cc, BaseControl.cc,
ButtonControl.cc, Canvas.cc, CheckBoxControl.cc, Container.cc, ContextMenu.cc,
EditControl.cc, Figure.cc, FigureWindow.cc, GLCanvas.cc, KeyMap.cc,
ListBoxControl.cc, Logger.cc, Menu.cc, MouseModeActionGroup.cc, Object.cc,
ObjectFactory.cc, ObjectProxy.cc, Panel.cc, PopupMenuControl.cc,
PushButtonControl.cc, PushTool.cc, QtHandlesUtils.cc, RadioButtonControl.cc,
SliderControl.cc, TextControl.cc, TextEdit.cc, ToggleButtonControl.cc,
ToggleTool.cc, ToolBar.cc, ToolBarButton.cc, __init_qt__.cc,
annotation-dialog.cc, gl-select.cc, module.mk, kpty.cpp, color-picker.cc,
dialog.cc, documentation-dock-widget.cc, files-dock-widget.cc,
find-files-dialog.cc, find-files-model.cc, history-dock-widget.cc,
file-editor-tab.cc, file-editor-tab.h, file-editor.cc, find-dialog.cc,
marker.cc, octave-qscintilla.cc, octave-txt-lexer.cc, main-window.cc,
octave-cmd.cc, octave-dock-widget.cc, octave-gui.cc, octave-interpreter.cc,
octave-qt-link.cc, parser.cc, webinfo.cc, resource-manager.cc,
settings-dialog.cc, shortcut-manager.cc, terminal-dock-widget.cc,
thread-manager.cc, welcome-wizard.cc, workspace-model.cc, workspace-view.cc,
build-env-features.sh, build-env.in.cc, Cell.cc, __contourc__.cc,
__dispatch__.cc, __dsearchn__.cc, __ichol__.cc, __ilu__.cc, __lin_interpn__.cc,
__pchip_deriv__.cc, __qp__.cc, balance.cc, besselj.cc, betainc.cc, bitfcns.cc,
bsxfun.cc, c-file-ptr-stream.cc, cdisplay.c, cellfun.cc, coct-hdf5-types.c,
colloc.cc, comment-list.cc, conv2.cc, daspk.cc, dasrt.cc, dassl.cc, data.cc,
debug.cc, defaults.cc, defun.cc, det.cc, dirfns.cc, display.cc, dlmread.cc,
dot.cc, dynamic-ld.cc, eig.cc, ellipj.cc, error.cc, errwarn.cc, event-queue.cc,
fft.cc, fft2.cc, fftn.cc, file-io.cc, filter.cc, find.cc, ft-text-renderer.cc,
gammainc.cc, gcd.cc, getgrent.cc, getpwent.cc, getrusage.cc, givens.cc,
gl-render.cc, gl2ps-print.cc, graphics.cc, gripes.cc, hash.cc, help.cc,
hess.cc, hex2num.cc, hook-fcn.cc, input.cc, inv.cc, jit-ir.cc, jit-typeinfo.cc,
jit-util.cc, kron.cc, load-path.cc, load-save.cc, lookup.cc,
ls-ascii-helper.cc, ls-hdf5.cc, ls-mat-ascii.cc, ls-mat4.cc, ls-mat5.cc,
ls-oct-binary.cc, ls-oct-text.cc, ls-utils.cc, lsode.cc, lu.cc, luinc.cc,
mappers.cc, matrix_type.cc, max.cc, mex.cc, mgorth.cc, nproc.cc,
oct-errno.in.cc, oct-fstrm.cc, oct-hdf5-types.cc, oct-hist.cc, oct-iostrm.cc,
oct-lvalue.cc, oct-map.cc, oct-prcstrm.cc, oct-procbuf.cc, oct-stream.cc,
oct-strstrm.cc, oct-tex-lexer.in.ll, oct-tex-parser.in.yy, octave-link.cc,
ordschur.cc, pager.cc, pinv.cc, pr-output.cc, procstream.cc, profiler.cc,
psi.cc, pt-jit.cc, quad.cc, quadcc.cc, qz.cc, rand.cc, rcond.cc, regexp.cc,
schur.cc, sighandlers.cc, siglist.c, sparse-xdiv.cc, sparse-xpow.cc, sparse.cc,
spparms.cc, sqrtm.cc, str2double.cc, strfind.cc, strfns.cc, sub2ind.cc, svd.cc,
sylvester.cc, symtab.cc, syscalls.cc, sysdep.cc, text-renderer.cc, time.cc,
toplev.cc, tril.cc, tsearch.cc, txt-eng.cc, typecast.cc, urlwrite.cc, utils.cc,
variables.cc, xdiv.cc, xgl2ps.c, xnorm.cc, xpow.cc, zfstream.cc,
__delaunayn__.cc, __eigs__.cc, __fltk_uigetfile__.cc, __glpk__.cc,
__init_fltk__.cc, __init_gnuplot__.cc, __magick_read__.cc, __osmesa_print__.cc,
__voronoi__.cc, amd.cc, audiodevinfo.cc, audioread.cc, ccolamd.cc, chol.cc,
colamd.cc, convhulln.cc, dmperm.cc, fftw.cc, qr.cc, symbfact.cc, symrcm.cc,
mkbuiltins, mkops, ov-base-diag.cc, ov-base-int.cc, ov-base-mat.cc,
ov-base-scalar.cc, ov-base-sparse.cc, ov-base.cc, ov-bool-mat.cc,
ov-bool-sparse.cc, ov-bool.cc, ov-builtin.cc, ov-cell.cc, ov-ch-mat.cc,
ov-class.cc, ov-classdef.cc, ov-colon.cc, ov-complex.cc, ov-cs-list.cc,
ov-cx-diag.cc, ov-cx-mat.cc, ov-cx-sparse.cc, ov-dld-fcn.cc, ov-fcn-handle.cc,
ov-fcn-inline.cc, ov-fcn.cc, ov-float.cc, ov-flt-complex.cc, ov-flt-cx-diag.cc,
ov-flt-cx-mat.cc, ov-flt-re-diag.cc, ov-flt-re-mat.cc, ov-int16.cc,
ov-int32.cc, ov-int64.cc, ov-int8.cc, ov-java.cc, ov-lazy-idx.cc,
ov-mex-fcn.cc, ov-null-mat.cc, ov-oncleanup.cc, ov-perm.cc, ov-range.cc,
ov-re-diag.cc, ov-re-mat.cc, ov-re-sparse.cc, ov-scalar.cc, ov-str-mat.cc,
ov-struct.cc, ov-typeinfo.cc, ov-uint16.cc, ov-uint32.cc, ov-uint64.cc,
ov-uint8.cc, ov-usr-fcn.cc, ov.cc, ovl.cc, octave.cc, op-b-b.cc, op-b-bm.cc,
op-b-sbm.cc, op-bm-b.cc, op-bm-bm.cc, op-bm-sbm.cc, op-cdm-cdm.cc, op-cell.cc,
op-chm.cc, op-class.cc, op-cm-cm.cc, op-cm-cs.cc, op-cm-m.cc, op-cm-s.cc,
op-cm-scm.cc, op-cm-sm.cc, op-cs-cm.cc, op-cs-cs.cc, op-cs-m.cc, op-cs-s.cc,
op-cs-scm.cc, op-cs-sm.cc, op-dm-dm.cc, op-dm-scm.cc, op-dm-sm.cc,
op-dm-template.cc, op-dms-template.cc, op-double-conv.cc, op-fcdm-fcdm.cc,
op-fcdm-fdm.cc, op-fcm-fcm.cc, op-fcm-fcs.cc, op-fcm-fm.cc, op-fcm-fs.cc,
op-fcn.cc, op-fcs-fcm.cc, op-fcs-fcs.cc, op-fcs-fm.cc, op-fcs-fs.cc,
op-fdm-fdm.cc, op-float-conv.cc, op-fm-fcm.cc, op-fm-fcs.cc, op-fm-fm.cc,
op-fm-fs.cc, op-fs-fcm.cc, op-fs-fcs.cc, op-fs-fm.cc, op-fs-fs.cc,
op-i16-i16.cc, op-i32-i32.cc, op-i64-i64.cc, op-i8-i8.cc, op-int-concat.cc,
op-int-conv.cc, op-m-cm.cc, op-m-cs.cc, op-m-m.cc, op-m-s.cc, op-m-scm.cc,
op-m-sm.cc, op-pm-pm.cc, op-pm-scm.cc, op-pm-sm.cc, op-pm-template.cc,
op-range.cc, op-s-cm.cc, op-s-cs.cc, op-s-m.cc, op-s-s.cc, op-s-scm.cc,
op-s-sm.cc, op-sbm-b.cc, op-sbm-bm.cc, op-sbm-sbm.cc, op-scm-cm.cc,
op-scm-cs.cc, op-scm-m.cc, op-scm-s.cc, op-scm-scm.cc, op-scm-sm.cc,
op-sm-cm.cc, op-sm-cs.cc, op-sm-m.cc, op-sm-s.cc, op-sm-scm.cc, op-sm-sm.cc,
op-str-m.cc, op-str-s.cc, op-str-str.cc, op-struct.cc, op-ui16-ui16.cc,
op-ui32-ui32.cc, op-ui64-ui64.cc, op-ui8-ui8.cc, lex.ll, oct-parse.in.yy,
pt-arg-list.cc, pt-array-list.cc, pt-assign.cc, pt-binop.cc, pt-bp.cc,
pt-cbinop.cc, pt-cell.cc, pt-check.cc, pt-classdef.cc, pt-cmd.cc, pt-colon.cc,
pt-const.cc, pt-decl.cc, pt-eval.cc, pt-except.cc, pt-exp.cc, pt-fcn-handle.cc,
pt-funcall.cc, pt-id.cc, pt-idx.cc, pt-jump.cc, pt-loop.cc, pt-mat.cc,
pt-misc.cc, pt-pr-code.cc, pt-select.cc, pt-stmt.cc, pt-unop.cc, pt.cc,
token.cc, Array-jit.cc, Array-os.cc, Array-sym.cc, Array-tc.cc, version.cc,
Array-C.cc, Array-b.cc, Array-ch.cc, Array-d.cc, Array-f.cc, Array-fC.cc,
Array-i.cc, Array-idx-vec.cc, Array-s.cc, Array-str.cc, Array-util.cc,
Array-voidp.cc, Array.cc, CColVector.cc, CDiagMatrix.cc, CMatrix.cc,
CNDArray.cc, CRowVector.cc, CSparse.cc, DiagArray2.cc, MArray-C.cc,
MArray-d.cc, MArray-f.cc, MArray-fC.cc, MArray-i.cc, MArray-s.cc, MArray.cc,
MDiagArray2.cc, MSparse-C.cc, MSparse-d.cc, MatrixType.cc, PermMatrix.cc,
Range.cc, Sparse-C.cc, Sparse-b.cc, Sparse-d.cc, Sparse.cc, boolMatrix.cc,
boolNDArray.cc, boolSparse.cc, chMatrix.cc, chNDArray.cc, dColVector.cc,
dDiagMatrix.cc, dMatrix.cc, dNDArray.cc, dRowVector.cc, dSparse.cc,
dim-vector.cc, fCColVector.cc, fCDiagMatrix.cc, fCMatrix.cc, fCNDArray.cc,
fCRowVector.cc, fColVector.cc, fDiagMatrix.cc, fMatrix.cc, fNDArray.cc,
fRowVector.cc, idx-vector.cc, int16NDArray.cc, int32NDArray.cc,
int64NDArray.cc, int8NDArray.cc, intNDArray.cc, uint16NDArray.cc,
uint32NDArray.cc, uint64NDArray.cc, uint8NDArray.cc, blaswrap.c, cquit.c,
f77-extern.cc, f77-fcn.c, lo-error.c, quit.cc, CollocWt.cc, DASPK.cc, DASRT.cc,
DASSL.cc, EIG.cc, LSODE.cc, ODES.cc, Quad.cc, aepbalance.cc, chol.cc,
eigs-base.cc, fEIG.cc, gepbalance.cc, hess.cc, lo-mappers.cc, lo-specfun.cc,
lu.cc, oct-convn.cc, oct-fftw.cc, oct-norm.cc, oct-rand.cc, oct-spparms.cc,
qr.cc, qrp.cc, randgamma.c, randmtzig.c, randpoisson.c, schur.cc,
sparse-chol.cc, sparse-dmsolve.cc, sparse-lu.cc, sparse-qr.cc, svd.cc,
mk-ops.awk, dir-ops.cc, file-ops.cc, file-stat.cc, lo-sysdep.cc, mach-info.cc,
oct-env.cc, oct-group.cc, oct-passwd.cc, oct-syscalls.cc, oct-time.cc,
oct-uname.cc, cmd-edit.cc, cmd-hist.cc, data-conv.cc, f2c-main.c,
glob-match.cc, kpse.cc, lo-array-errwarn.cc, lo-array-gripes.cc, lo-cutils.c,
lo-ieee.cc, lo-regexp.cc, lo-utils.cc, oct-base64.cc, oct-glob.cc,
oct-inttypes.cc, oct-locbuf.cc, oct-mutex.cc, oct-rl-edit.c, oct-rl-hist.c,
oct-shlib.cc, oct-sort.cc, pathsearch.cc, singleton-cleanup.cc, sparse-sort.cc,
sparse-util.cc, str-vec.cc, unwind-prot.cc, url-transfer.cc,
display-available.c, main-cli.cc, main-gui.cc, main.in.cc, mkoctfile.in.cc,
octave-config.in.cc:
Use '#include "config.h"' rather than <config.h>.
author | Rik <rik@octave.org> |
---|---|
date | Thu, 18 Feb 2016 13:34:50 -0800 |
parents | 7e67c7f82fc1 |
children | 47c76e56a1de |
line wrap: on
line source
/* Copyright (C) 2005-2015 David Bateman 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/>. */ #ifdef HAVE_CONFIG_H # include "config.h" #endif #include <cfloat> #include <cmath> #include <vector> #include <iostream> #include "CSparse.h" #include "lu.h" #include "MatrixType.h" #include "chol.h" #include "dSparse.h" #include "eigs-base.h" #include "f77-fcn.h" #include "mx-ops.h" #include "oct-locbuf.h" #include "oct-rand.h" #include "quit.h" #include "sparse-chol.h" #include "sparse-lu.h" #ifdef HAVE_ARPACK // Arpack and blas fortran functions we call. extern "C" { F77_RET_T F77_FUNC (dsaupd, DSAUPD) (octave_idx_type&, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const double&, double*, const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type*, octave_idx_type*, double*, double*, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (dseupd, DSEUPD) (const octave_idx_type&, F77_CONST_CHAR_ARG_DECL, octave_idx_type*, double*, double*, const octave_idx_type&, const double&, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const double&, double*, const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type*, octave_idx_type*, double*, double*, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (dnaupd, DNAUPD) (octave_idx_type&, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, F77_CONST_CHAR_ARG_DECL, octave_idx_type&, const double&, double*, const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type*, octave_idx_type*, double*, double*, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (dneupd, DNEUPD) (const octave_idx_type&, F77_CONST_CHAR_ARG_DECL, octave_idx_type*, double*, double*, double*, const octave_idx_type&, const double&, const double&, double*, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, F77_CONST_CHAR_ARG_DECL, octave_idx_type&, const double&, double*, const octave_idx_type&, double*, const octave_idx_type&, octave_idx_type*, octave_idx_type*, double*, double*, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (znaupd, ZNAUPD) (octave_idx_type&, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const double&, Complex*, const octave_idx_type&, Complex*, const octave_idx_type&, octave_idx_type*, octave_idx_type*, Complex*, Complex*, const octave_idx_type&, double *, octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (zneupd, ZNEUPD) (const octave_idx_type&, F77_CONST_CHAR_ARG_DECL, octave_idx_type*, Complex*, Complex*, const octave_idx_type&, const Complex&, Complex*, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const double&, Complex*, const octave_idx_type&, Complex*, const octave_idx_type&, octave_idx_type*, octave_idx_type*, Complex*, Complex*, const octave_idx_type&, double *, octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (dgemv, DGEMV) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const double&, const double*, const octave_idx_type&, const double*, const octave_idx_type&, const double&, double*, const octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (zgemv, ZGEMV) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const Complex&, const Complex*, const octave_idx_type&, const Complex*, const octave_idx_type&, const Complex&, Complex*, const octave_idx_type& F77_CHAR_ARG_LEN_DECL); } static void warn_convergence (void) { (*current_liboctave_warning_with_id_handler) ("Octave:convergence", "eigs: 'A - sigma*B' is singular, indicating sigma is exactly " "an eigenvalue so convergence is not guaranteed"); } template <typename M, typename SM> static octave_idx_type lusolve (const SM& L, const SM& U, M& m) { octave_idx_type err = 0; double rcond; MatrixType utyp (MatrixType::Upper); // Sparse L is lower triangular, Dense L is permuted lower triangular!!! m = L.solve (m, err, rcond, 0); if (err) return err; m = U.solve (utyp, m, err, rcond, 0); return err; } template <typename SM, typename M> static M ltsolve (const SM& L, const ColumnVector& Q, const M& m) { octave_idx_type n = L.cols (); octave_idx_type b_nc = m.cols (); octave_idx_type err = 0; double rcond; MatrixType ltyp (MatrixType::Lower); M tmp = L.solve (ltyp, m, err, rcond, 0); M retval; const double* qv = Q.fortran_vec (); if (! err) { retval.resize (n, b_nc); for (octave_idx_type j = 0; j < b_nc; j++) { for (octave_idx_type i = 0; i < n; i++) retval.elem (static_cast<octave_idx_type>(qv[i]), j) = tmp.elem (i,j); } } return retval; } template <typename SM, typename M> static M utsolve (const SM& U, const ColumnVector& Q, const M& m) { octave_idx_type n = U.cols (); octave_idx_type b_nc = m.cols (); octave_idx_type err = 0; double rcond; MatrixType utyp (MatrixType::Upper); M retval (n, b_nc); const double* qv = Q.fortran_vec (); for (octave_idx_type j = 0; j < b_nc; j++) { for (octave_idx_type i = 0; i < n; i++) retval.elem (i,j) = m.elem (static_cast<octave_idx_type>(qv[i]), j); } return U.solve (utyp, retval, err, rcond, 0); } static bool vector_product (const SparseMatrix& m, const double* x, double* y) { octave_idx_type nc = m.cols (); for (octave_idx_type j = 0; j < nc; j++) y[j] = 0.; for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = m.cidx (j); i < m.cidx (j+1); i++) y[m.ridx (i)] += m.data (i) * x[j]; return true; } static bool vector_product (const Matrix& m, const double *x, double *y) { octave_idx_type nr = m.rows (); octave_idx_type nc = m.cols (); F77_XFCN (dgemv, DGEMV, (F77_CONST_CHAR_ARG2 ("N", 1), nr, nc, 1.0, m.data (), nr, x, 1, 0.0, y, 1 F77_CHAR_ARG_LEN (1))); if (f77_exception_encountered) (*current_liboctave_error_handler) ("eigs: unrecoverable error in dgemv"); return true; } static bool vector_product (const SparseComplexMatrix& m, const Complex* x, Complex* y) { octave_idx_type nc = m.cols (); for (octave_idx_type j = 0; j < nc; j++) y[j] = 0.; for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = m.cidx (j); i < m.cidx (j+1); i++) y[m.ridx (i)] += m.data (i) * x[j]; return true; } static bool vector_product (const ComplexMatrix& m, const Complex *x, Complex *y) { octave_idx_type nr = m.rows (); octave_idx_type nc = m.cols (); F77_XFCN (zgemv, ZGEMV, (F77_CONST_CHAR_ARG2 ("N", 1), nr, nc, 1.0, m.data (), nr, x, 1, 0.0, y, 1 F77_CHAR_ARG_LEN (1))); if (f77_exception_encountered) (*current_liboctave_error_handler) ("eigs: unrecoverable error in zgemv"); return true; } static bool make_cholb (Matrix& b, Matrix& bt, ColumnVector& permB) { octave_idx_type info; chol<Matrix> fact (b, info); octave_idx_type n = b.cols (); if (info != 0) return false; else { bt = fact.chol_matrix (); b = bt.transpose (); permB = ColumnVector (n); for (octave_idx_type i = 0; i < n; i++) permB(i) = i; return true; } } static bool make_cholb (SparseMatrix& b, SparseMatrix& bt, ColumnVector& permB) { octave_idx_type info; sparse_chol<SparseMatrix> fact (b, info, false); if (fact.P () != 0) return false; else { b = fact.L (); bt = b.transpose (); permB = fact.perm () - 1.0; return true; } } static bool make_cholb (ComplexMatrix& b, ComplexMatrix& bt, ColumnVector& permB) { octave_idx_type info; chol<ComplexMatrix> fact (b, info); octave_idx_type n = b.cols (); if (info != 0) return false; else { bt = fact.chol_matrix (); b = bt.hermitian (); permB = ColumnVector (n); for (octave_idx_type i = 0; i < n; i++) permB(i) = i; return true; } } static bool make_cholb (SparseComplexMatrix& b, SparseComplexMatrix& bt, ColumnVector& permB) { octave_idx_type info; sparse_chol<SparseComplexMatrix> fact (b, info, false); if (fact.P () != 0) return false; else { b = fact.L (); bt = b.hermitian (); permB = fact.perm () - 1.0; return true; } } static bool LuAminusSigmaB (const SparseMatrix &m, const SparseMatrix &b, bool cholB, const ColumnVector& permB, double sigma, SparseMatrix &L, SparseMatrix &U, octave_idx_type *P, octave_idx_type *Q) { bool have_b = ! b.is_empty (); octave_idx_type n = m.rows (); // Caclulate LU decomposition of 'A - sigma * B' SparseMatrix AminusSigmaB (m); if (have_b) { if (cholB) { if (permB.numel ()) { SparseMatrix tmp(n,n,n); for (octave_idx_type i = 0; i < n; i++) { tmp.xcidx (i) = i; tmp.xridx (i) = static_cast<octave_idx_type>(permB(i)); tmp.xdata (i) = 1; } tmp.xcidx (n) = n; AminusSigmaB -= sigma * tmp * b.transpose () * b * tmp.transpose (); } else AminusSigmaB -= sigma * b.transpose () * b; } else AminusSigmaB -= sigma * b; } else { SparseMatrix sigmat (n, n, n); // Create sigma * speye (n,n) sigmat.xcidx (0) = 0; for (octave_idx_type i = 0; i < n; i++) { sigmat.xdata (i) = sigma; sigmat.xridx (i) = i; sigmat.xcidx (i+1) = i + 1; } AminusSigmaB -= sigmat; } sparse_lu<SparseMatrix> fact (AminusSigmaB); L = fact.L (); U = fact.U (); const octave_idx_type *P2 = fact.row_perm (); const octave_idx_type *Q2 = fact.col_perm (); for (octave_idx_type j = 0; j < n; j++) { P[j] = P2[j]; Q[j] = Q2[j]; } // Test condition number of LU decomposition double minU = octave_NaN; double maxU = octave_NaN; for (octave_idx_type j = 0; j < n; j++) { double d = 0.; if (U.xcidx (j+1) > U.xcidx (j) && U.xridx (U.xcidx (j+1)-1) == j) d = std::abs (U.xdata (U.xcidx (j+1)-1)); if (xisnan (minU) || d < minU) minU = d; if (xisnan (maxU) || d > maxU) maxU = d; } double rcond = (minU / maxU); volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || xisnan (rcond)) warn_convergence (); return true; } static bool LuAminusSigmaB (const Matrix &m, const Matrix &b, bool cholB, const ColumnVector& permB, double sigma, Matrix &L, Matrix &U, octave_idx_type *P, octave_idx_type *Q) { bool have_b = ! b.is_empty (); octave_idx_type n = m.cols (); // Caclulate LU decomposition of 'A - sigma * B' Matrix AminusSigmaB (m); if (have_b) { if (cholB) { Matrix tmp = sigma * b.transpose () * b; const double *pB = permB.fortran_vec (); double *p = AminusSigmaB.fortran_vec (); if (permB.numel ()) { for (octave_idx_type j = 0; j < b.cols (); j++) for (octave_idx_type i = 0; i < b.rows (); i++) *p++ -= tmp.xelem (static_cast<octave_idx_type>(pB[i]), static_cast<octave_idx_type>(pB[j])); } else AminusSigmaB -= tmp; } else AminusSigmaB -= sigma * b; } else { double *p = AminusSigmaB.fortran_vec (); for (octave_idx_type i = 0; i < n; i++) p[i*(n+1)] -= sigma; } lu<Matrix> fact (AminusSigmaB); L = fact.P ().transpose () * fact.L (); U = fact.U (); for (octave_idx_type j = 0; j < n; j++) P[j] = Q[j] = j; // Test condition number of LU decomposition double minU = octave_NaN; double maxU = octave_NaN; for (octave_idx_type j = 0; j < n; j++) { double d = std::abs (U.xelem (j,j)); if (xisnan (minU) || d < minU) minU = d; if (xisnan (maxU) || d > maxU) maxU = d; } double rcond = (minU / maxU); volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || xisnan (rcond)) warn_convergence (); return true; } static bool LuAminusSigmaB (const SparseComplexMatrix &m, const SparseComplexMatrix &b, bool cholB, const ColumnVector& permB, Complex sigma, SparseComplexMatrix &L, SparseComplexMatrix &U, octave_idx_type *P, octave_idx_type *Q) { bool have_b = ! b.is_empty (); octave_idx_type n = m.rows (); // Caclulate LU decomposition of 'A - sigma * B' SparseComplexMatrix AminusSigmaB (m); if (have_b) { if (cholB) { if (permB.numel ()) { SparseMatrix tmp(n,n,n); for (octave_idx_type i = 0; i < n; i++) { tmp.xcidx (i) = i; tmp.xridx (i) = static_cast<octave_idx_type>(permB(i)); tmp.xdata (i) = 1; } tmp.xcidx (n) = n; AminusSigmaB -= tmp * b.hermitian () * b * tmp.transpose () * sigma; } else AminusSigmaB -= sigma * b.hermitian () * b; } else AminusSigmaB -= sigma * b; } else { SparseComplexMatrix sigmat (n, n, n); // Create sigma * speye (n,n) sigmat.xcidx (0) = 0; for (octave_idx_type i = 0; i < n; i++) { sigmat.xdata (i) = sigma; sigmat.xridx (i) = i; sigmat.xcidx (i+1) = i + 1; } AminusSigmaB -= sigmat; } sparse_lu<SparseComplexMatrix> fact (AminusSigmaB); L = fact.L (); U = fact.U (); const octave_idx_type *P2 = fact.row_perm (); const octave_idx_type *Q2 = fact.col_perm (); for (octave_idx_type j = 0; j < n; j++) { P[j] = P2[j]; Q[j] = Q2[j]; } // Test condition number of LU decomposition double minU = octave_NaN; double maxU = octave_NaN; for (octave_idx_type j = 0; j < n; j++) { double d = 0.; if (U.xcidx (j+1) > U.xcidx (j) && U.xridx (U.xcidx (j+1)-1) == j) d = std::abs (U.xdata (U.xcidx (j+1)-1)); if (xisnan (minU) || d < minU) minU = d; if (xisnan (maxU) || d > maxU) maxU = d; } double rcond = (minU / maxU); volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || xisnan (rcond)) warn_convergence (); return true; } static bool LuAminusSigmaB (const ComplexMatrix &m, const ComplexMatrix &b, bool cholB, const ColumnVector& permB, Complex sigma, ComplexMatrix &L, ComplexMatrix &U, octave_idx_type *P, octave_idx_type *Q) { bool have_b = ! b.is_empty (); octave_idx_type n = m.cols (); // Caclulate LU decomposition of 'A - sigma * B' ComplexMatrix AminusSigmaB (m); if (have_b) { if (cholB) { ComplexMatrix tmp = sigma * b.hermitian () * b; const double *pB = permB.fortran_vec (); Complex *p = AminusSigmaB.fortran_vec (); if (permB.numel ()) { for (octave_idx_type j = 0; j < b.cols (); j++) for (octave_idx_type i = 0; i < b.rows (); i++) *p++ -= tmp.xelem (static_cast<octave_idx_type>(pB[i]), static_cast<octave_idx_type>(pB[j])); } else AminusSigmaB -= tmp; } else AminusSigmaB -= sigma * b; } else { Complex *p = AminusSigmaB.fortran_vec (); for (octave_idx_type i = 0; i < n; i++) p[i*(n+1)] -= sigma; } lu<ComplexMatrix> fact (AminusSigmaB); L = fact.P ().transpose () * fact.L (); U = fact.U (); for (octave_idx_type j = 0; j < n; j++) P[j] = Q[j] = j; // Test condition number of LU decomposition double minU = octave_NaN; double maxU = octave_NaN; for (octave_idx_type j = 0; j < n; j++) { double d = std::abs (U.xelem (j,j)); if (xisnan (minU) || d < minU) minU = d; if (xisnan (maxU) || d > maxU) maxU = d; } double rcond = (minU / maxU); volatile double rcond_plus_one = rcond + 1.0; if (rcond_plus_one == 1.0 || xisnan (rcond)) warn_convergence (); return true; } template <typename M> octave_idx_type EigsRealSymmetricMatrix (const M& m, const std::string typ, octave_idx_type k, octave_idx_type p, octave_idx_type &info, Matrix &eig_vec, ColumnVector &eig_val, const M& _b, ColumnVector &permB, ColumnVector &resid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit) { M b(_b); octave_idx_type n = m.cols (); octave_idx_type mode = 1; bool have_b = ! b.is_empty (); bool note3 = false; char bmat = 'I'; double sigma = 0.; M bt; if (m.rows () != m.cols ()) (*current_liboctave_error_handler) ("eigs: A must be square"); if (have_b && (m.rows () != b.rows () || m.rows () != b.cols ())) (*current_liboctave_error_handler) ("eigs: B must be square and the same size as A"); if (resid.is_empty ()) { std::string rand_dist = octave_rand::distribution (); octave_rand::distribution ("uniform"); resid = ColumnVector (octave_rand::vector (n)); octave_rand::distribution (rand_dist); } if (n < 3) (*current_liboctave_error_handler) ("eigs: n must be at least 3"); if (p < 0) { p = k * 2; if (p < 20) p = 20; if (p > n - 1) p = n - 1 ; } if (k < 1 || k > n - 2) (*current_liboctave_error_handler) ("eigs: Invalid number of eigenvalues to extract (must be 0 < k < n-1-1).\n" " Use 'eig (full (A))' instead"); if (p <= k || p >= n) (*current_liboctave_error_handler) ("eigs: opts.p must be greater than k and less than n"); if (have_b && cholB && ! permB.is_empty ()) { // Check the we really have a permutation vector if (permB.numel () != n) (*current_liboctave_error_handler) ("eigs: permB vector invalid"); Array<bool> checked (dim_vector (n, 1), false); for (octave_idx_type i = 0; i < n; i++) { octave_idx_type bidx = static_cast<octave_idx_type> (permB(i)); if (checked(bidx) || bidx < 0 || bidx >= n || D_NINT (bidx) != bidx) (*current_liboctave_error_handler) ("eigs: permB vector invalid"); } } if (typ != "LM" && typ != "SM" && typ != "LA" && typ != "SA" && typ != "BE" && typ != "LR" && typ != "SR" && typ != "LI" && typ != "SI") (*current_liboctave_error_handler) ("eigs: unrecognized sigma value"); if (typ == "LI" || typ == "SI" || typ == "LR" || typ == "SR") (*current_liboctave_error_handler) ("eigs: invalid sigma value for real symmetric problem"); if (have_b) { // See Note 3 dsaupd note3 = true; if (cholB) { bt = b; b = b.transpose (); if (permB.is_empty ()) { permB = ColumnVector (n); for (octave_idx_type i = 0; i < n; i++) permB(i) = i; } } else { if (! make_cholb (b, bt, permB)) (*current_liboctave_error_handler) ("eigs: The matrix B is not positive definite"); } } Array<octave_idx_type> ip (dim_vector (11, 1)); octave_idx_type *iparam = ip.fortran_vec (); ip(0) = 1; //ishift ip(1) = 0; // ip(1) not referenced ip(2) = maxit; // mxiter, maximum number of iterations ip(3) = 1; // NB blocksize in recurrence ip(4) = 0; // nconv, number of Ritz values that satisfy convergence ip(5) = 0; //ip(5) not referenced ip(6) = mode; // mode ip(7) = 0; ip(8) = 0; ip(9) = 0; ip(10) = 0; // ip(7) to ip(10) return values Array<octave_idx_type> iptr (dim_vector (14, 1)); octave_idx_type *ipntr = iptr.fortran_vec (); octave_idx_type ido = 0; int iter = 0; octave_idx_type lwork = p * (p + 8); OCTAVE_LOCAL_BUFFER (double, v, n * p); OCTAVE_LOCAL_BUFFER (double, workl, lwork); OCTAVE_LOCAL_BUFFER (double, workd, 3 * n); double *presid = resid.fortran_vec (); do { F77_FUNC (dsaupd, DSAUPD) (ido, F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, presid, p, v, n, iparam, ipntr, workd, workl, lwork, info F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); if (f77_exception_encountered) (*current_liboctave_error_handler) ("eigs: unrecoverable exception encountered in dsaupd"); if (disp > 0 && ! xisnan (workl[iptr (5)-1])) { if (iter++) { os << "Iteration " << iter - 1 << ": a few Ritz values of the " << p << "-by-" << p << " matrix\n"; for (int i = 0 ; i < k; i++) os << " " << workl[iptr(5)+i-1] << "\n"; } // This is a kludge, as ARPACK doesn't give its // iteration pointer. But as workl[iptr(5)-1] is // an output value updated at each iteration, setting // a value in this array to NaN and testing for it // is a way of obtaining the iteration counter. if (ido != 99) workl[iptr(5)-1] = octave_NaN; } if (ido == -1 || ido == 1 || ido == 2) { if (have_b) { Matrix mtmp (n,1); for (octave_idx_type i = 0; i < n; i++) mtmp(i,0) = workd[i + iptr(0) - 1]; mtmp = utsolve (bt, permB, m * ltsolve (b, permB, mtmp)); for (octave_idx_type i = 0; i < n; i++) workd[i+iptr(1)-1] = mtmp(i,0); } else if (! vector_product (m, workd + iptr(0) - 1, workd + iptr(1) - 1)) break; } else { if (info < 0) (*current_liboctave_error_handler) ("eigs: error %d in dsaupd", info); break; } } while (1); octave_idx_type info2; // We have a problem in that the size of the C++ bool // type relative to the fortran logical type. It appears // that fortran uses 4- or 8-bytes per logical and C++ 1-byte // per bool, though this might be system dependent. As // long as the HOWMNY arg is not "S", the logical array // is just workspace for ARPACK, so use int type to // avoid problems. Array<octave_idx_type> s (dim_vector (p, 1)); octave_idx_type *sel = s.fortran_vec (); eig_vec.resize (n, k); double *z = eig_vec.fortran_vec (); eig_val.resize (k); double *d = eig_val.fortran_vec (); F77_FUNC (dseupd, DSEUPD) (rvec, F77_CONST_CHAR_ARG2 ("A", 1), sel, d, z, n, sigma, F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, presid, p, v, n, iparam, ipntr, workd, workl, lwork, info2 F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); if (f77_exception_encountered) (*current_liboctave_error_handler) ("eigs: unrecoverable exception encountered in dseupd"); if (info2 == 0) { octave_idx_type k2 = k / 2; if (typ != "SM" && typ != "BE") { for (octave_idx_type i = 0; i < k2; i++) { double dtmp = d[i]; d[i] = d[k - i - 1]; d[k - i - 1] = dtmp; } } if (rvec) { if (typ != "SM" && typ != "BE") { OCTAVE_LOCAL_BUFFER (double, dtmp, n); for (octave_idx_type i = 0; i < k2; i++) { octave_idx_type off1 = i * n; octave_idx_type off2 = (k - i - 1) * n; if (off1 == off2) continue; for (octave_idx_type j = 0; j < n; j++) dtmp[j] = z[off1 + j]; for (octave_idx_type j = 0; j < n; j++) z[off1 + j] = z[off2 + j]; for (octave_idx_type j = 0; j < n; j++) z[off2 + j] = dtmp[j]; } } if (note3) eig_vec = ltsolve (b, permB, eig_vec); } } else (*current_liboctave_error_handler) ("eigs: error %d in dseupd", info2); return ip(4); } template <typename M> octave_idx_type EigsRealSymmetricMatrixShift (const M& m, double sigma, octave_idx_type k, octave_idx_type p, octave_idx_type &info, Matrix &eig_vec, ColumnVector &eig_val, const M& _b, ColumnVector &permB, ColumnVector &resid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit) { M b(_b); octave_idx_type n = m.cols (); octave_idx_type mode = 3; bool have_b = ! b.is_empty (); std::string typ = "LM"; if (m.rows () != m.cols ()) (*current_liboctave_error_handler) ("eigs: A must be square"); if (have_b && (m.rows () != b.rows () || m.rows () != b.cols ())) (*current_liboctave_error_handler) ("eigs: B must be square and the same size as A"); // FIXME: The "SM" type for mode 1 seems unstable though faster!! //if (! std::abs (sigma)) // return EigsRealSymmetricMatrix (m, "SM", k, p, info, eig_vec, eig_val, // _b, permB, resid, os, tol, rvec, cholB, // disp, maxit); if (resid.is_empty ()) { std::string rand_dist = octave_rand::distribution (); octave_rand::distribution ("uniform"); resid = ColumnVector (octave_rand::vector (n)); octave_rand::distribution (rand_dist); } if (n < 3) (*current_liboctave_error_handler) ("eigs: n must be at least 3"); if (k <= 0 || k >= n - 1) (*current_liboctave_error_handler) ("eigs: Invalid number of eigenvalues to extract (must be 0 < k < n-1-1).\n" " Use 'eig (full (A))' instead"); if (p < 0) { p = k * 2; if (p < 20) p = 20; if (p > n - 1) p = n - 1 ; } if (p <= k || p >= n) (*current_liboctave_error_handler) ("eigs: opts.p must be greater than k and less than n"); if (have_b && cholB && ! permB.is_empty ()) { // Check the we really have a permutation vector if (permB.numel () != n) (*current_liboctave_error_handler) ("eigs: permB vector invalid"); Array<bool> checked (dim_vector (n, 1), false); for (octave_idx_type i = 0; i < n; i++) { octave_idx_type bidx = static_cast<octave_idx_type> (permB(i)); if (checked(bidx) || bidx < 0 || bidx >= n || D_NINT (bidx) != bidx) (*current_liboctave_error_handler) ("eigs: permB vector invalid"); } } char bmat = 'I'; if (have_b) bmat = 'G'; Array<octave_idx_type> ip (dim_vector (11, 1)); octave_idx_type *iparam = ip.fortran_vec (); ip(0) = 1; //ishift ip(1) = 0; // ip(1) not referenced ip(2) = maxit; // mxiter, maximum number of iterations ip(3) = 1; // NB blocksize in recurrence ip(4) = 0; // nconv, number of Ritz values that satisfy convergence ip(5) = 0; //ip(5) not referenced ip(6) = mode; // mode ip(7) = 0; ip(8) = 0; ip(9) = 0; ip(10) = 0; // ip(7) to ip(10) return values Array<octave_idx_type> iptr (dim_vector (14, 1)); octave_idx_type *ipntr = iptr.fortran_vec (); octave_idx_type ido = 0; int iter = 0; M L, U; OCTAVE_LOCAL_BUFFER (octave_idx_type, P, (have_b ? b.rows () : m.rows ())); OCTAVE_LOCAL_BUFFER (octave_idx_type, Q, (have_b ? b.cols () : m.cols ())); if (! LuAminusSigmaB (m, b, cholB, permB, sigma, L, U, P, Q)) return -1; octave_idx_type lwork = p * (p + 8); OCTAVE_LOCAL_BUFFER (double, v, n * p); OCTAVE_LOCAL_BUFFER (double, workl, lwork); OCTAVE_LOCAL_BUFFER (double, workd, 3 * n); double *presid = resid.fortran_vec (); do { F77_FUNC (dsaupd, DSAUPD) (ido, F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, presid, p, v, n, iparam, ipntr, workd, workl, lwork, info F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); if (f77_exception_encountered) (*current_liboctave_error_handler) ("eigs: unrecoverable exception encountered in dsaupd"); if (disp > 0 && ! xisnan (workl[iptr (5)-1])) { if (iter++) { os << "Iteration " << iter - 1 << ": a few Ritz values of the " << p << "-by-" << p << " matrix\n"; for (int i = 0 ; i < k; i++) os << " " << workl[iptr(5)+i-1] << "\n"; } // This is a kludge, as ARPACK doesn't give its // iteration pointer. But as workl[iptr(5)-1] is // an output value updated at each iteration, setting // a value in this array to NaN and testing for it // is a way of obtaining the iteration counter. if (ido != 99) workl[iptr(5)-1] = octave_NaN; } if (ido == -1 || ido == 1 || ido == 2) { if (have_b) { if (ido == -1) { OCTAVE_LOCAL_BUFFER (double, dtmp, n); vector_product (m, workd+iptr(0)-1, dtmp); Matrix tmp(n, 1); for (octave_idx_type i = 0; i < n; i++) tmp(i,0) = dtmp[P[i]]; lusolve (L, U, tmp); double *ip2 = workd+iptr(1)-1; for (octave_idx_type i = 0; i < n; i++) ip2[Q[i]] = tmp(i,0); } else if (ido == 2) vector_product (b, workd+iptr(0)-1, workd+iptr(1)-1); else { double *ip2 = workd+iptr(2)-1; Matrix tmp(n, 1); for (octave_idx_type i = 0; i < n; i++) tmp(i,0) = ip2[P[i]]; lusolve (L, U, tmp); ip2 = workd+iptr(1)-1; for (octave_idx_type i = 0; i < n; i++) ip2[Q[i]] = tmp(i,0); } } else { if (ido == 2) { for (octave_idx_type i = 0; i < n; i++) workd[iptr(0) + i - 1] = workd[iptr(1) + i - 1]; } else { double *ip2 = workd+iptr(0)-1; Matrix tmp(n, 1); for (octave_idx_type i = 0; i < n; i++) tmp(i,0) = ip2[P[i]]; lusolve (L, U, tmp); ip2 = workd+iptr(1)-1; for (octave_idx_type i = 0; i < n; i++) ip2[Q[i]] = tmp(i,0); } } } else { if (info < 0) (*current_liboctave_error_handler) ("eigs: error %d in dsaupd", info); break; } } while (1); octave_idx_type info2; // We have a problem in that the size of the C++ bool // type relative to the fortran logical type. It appears // that fortran uses 4- or 8-bytes per logical and C++ 1-byte // per bool, though this might be system dependent. As // long as the HOWMNY arg is not "S", the logical array // is just workspace for ARPACK, so use int type to // avoid problems. Array<octave_idx_type> s (dim_vector (p, 1)); octave_idx_type *sel = s.fortran_vec (); eig_vec.resize (n, k); double *z = eig_vec.fortran_vec (); eig_val.resize (k); double *d = eig_val.fortran_vec (); F77_FUNC (dseupd, DSEUPD) (rvec, F77_CONST_CHAR_ARG2 ("A", 1), sel, d, z, n, sigma, F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, presid, p, v, n, iparam, ipntr, workd, workl, lwork, info2 F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); if (f77_exception_encountered) (*current_liboctave_error_handler) ("eigs: unrecoverable exception encountered in dseupd"); if (info2 == 0) { octave_idx_type k2 = k / 2; for (octave_idx_type i = 0; i < k2; i++) { double dtmp = d[i]; d[i] = d[k - i - 1]; d[k - i - 1] = dtmp; } if (rvec) { OCTAVE_LOCAL_BUFFER (double, dtmp, n); for (octave_idx_type i = 0; i < k2; i++) { octave_idx_type off1 = i * n; octave_idx_type off2 = (k - i - 1) * n; if (off1 == off2) continue; for (octave_idx_type j = 0; j < n; j++) dtmp[j] = z[off1 + j]; for (octave_idx_type j = 0; j < n; j++) z[off1 + j] = z[off2 + j]; for (octave_idx_type j = 0; j < n; j++) z[off2 + j] = dtmp[j]; } } } else (*current_liboctave_error_handler) ("eigs: error %d in dseupd", info2); return ip(4); } octave_idx_type EigsRealSymmetricFunc (EigsFunc fun, octave_idx_type n, const std::string &_typ, double sigma, octave_idx_type k, octave_idx_type p, octave_idx_type &info, Matrix &eig_vec, ColumnVector &eig_val, ColumnVector &resid, std::ostream& os, double tol, bool rvec, bool /* cholB */, int disp, int maxit) { std::string typ (_typ); bool have_sigma = (sigma ? true : false); char bmat = 'I'; octave_idx_type mode = 1; int err = 0; if (resid.is_empty ()) { std::string rand_dist = octave_rand::distribution (); octave_rand::distribution ("uniform"); resid = ColumnVector (octave_rand::vector (n)); octave_rand::distribution (rand_dist); } if (n < 3) (*current_liboctave_error_handler) ("eigs: n must be at least 3"); if (p < 0) { p = k * 2; if (p < 20) p = 20; if (p > n - 1) p = n - 1 ; } if (k <= 0 || k >= n - 1) (*current_liboctave_error_handler) ("eigs: Invalid number of eigenvalues to extract (must be 0 < k < n-1).\n" " Use 'eig (full (A))' instead"); if (p <= k || p >= n) (*current_liboctave_error_handler) ("eigs: opts.p must be greater than k and less than n"); if (! have_sigma) { if (typ != "LM" && typ != "SM" && typ != "LA" && typ != "SA" && typ != "BE" && typ != "LR" && typ != "SR" && typ != "LI" && typ != "SI") (*current_liboctave_error_handler) ("eigs: unrecognized sigma value"); if (typ == "LI" || typ == "SI" || typ == "LR" || typ == "SR") (*current_liboctave_error_handler) ("eigs: invalid sigma value for real symmetric problem"); if (typ == "SM") { typ = "LM"; sigma = 0.; mode = 3; } } else if (! std::abs (sigma)) typ = "SM"; else { typ = "LM"; mode = 3; } Array<octave_idx_type> ip (dim_vector (11, 1)); octave_idx_type *iparam = ip.fortran_vec (); ip(0) = 1; //ishift ip(1) = 0; // ip(1) not referenced ip(2) = maxit; // mxiter, maximum number of iterations ip(3) = 1; // NB blocksize in recurrence ip(4) = 0; // nconv, number of Ritz values that satisfy convergence ip(5) = 0; //ip(5) not referenced ip(6) = mode; // mode ip(7) = 0; ip(8) = 0; ip(9) = 0; ip(10) = 0; // ip(7) to ip(10) return values Array<octave_idx_type> iptr (dim_vector (14, 1)); octave_idx_type *ipntr = iptr.fortran_vec (); octave_idx_type ido = 0; int iter = 0; octave_idx_type lwork = p * (p + 8); OCTAVE_LOCAL_BUFFER (double, v, n * p); OCTAVE_LOCAL_BUFFER (double, workl, lwork); OCTAVE_LOCAL_BUFFER (double, workd, 3 * n); double *presid = resid.fortran_vec (); do { F77_FUNC (dsaupd, DSAUPD) (ido, F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, presid, p, v, n, iparam, ipntr, workd, workl, lwork, info F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); if (f77_exception_encountered) (*current_liboctave_error_handler) ("eigs: unrecoverable exception encountered in dsaupd"); if (disp > 0 && ! xisnan (workl[iptr (5)-1])) { if (iter++) { os << "Iteration " << iter - 1 << ": a few Ritz values of the " << p << "-by-" << p << " matrix\n"; for (int i = 0 ; i < k; i++) os << " " << workl[iptr(5)+i-1] << "\n"; } // This is a kludge, as ARPACK doesn't give its // iteration pointer. But as workl[iptr(5)-1] is // an output value updated at each iteration, setting // a value in this array to NaN and testing for it // is a way of obtaining the iteration counter. if (ido != 99) workl[iptr(5)-1] = octave_NaN; } if (ido == -1 || ido == 1 || ido == 2) { double *ip2 = workd + iptr(0) - 1; ColumnVector x(n); for (octave_idx_type i = 0; i < n; i++) x(i) = *ip2++; ColumnVector y = fun (x, err); if (err) return false; ip2 = workd + iptr(1) - 1; for (octave_idx_type i = 0; i < n; i++) *ip2++ = y(i); } else { if (info < 0) (*current_liboctave_error_handler) ("eigs: error %d in dsaupd", info); break; } } while (1); octave_idx_type info2; // We have a problem in that the size of the C++ bool // type relative to the fortran logical type. It appears // that fortran uses 4- or 8-bytes per logical and C++ 1-byte // per bool, though this might be system dependent. As // long as the HOWMNY arg is not "S", the logical array // is just workspace for ARPACK, so use int type to // avoid problems. Array<octave_idx_type> s (dim_vector (p, 1)); octave_idx_type *sel = s.fortran_vec (); eig_vec.resize (n, k); double *z = eig_vec.fortran_vec (); eig_val.resize (k); double *d = eig_val.fortran_vec (); F77_FUNC (dseupd, DSEUPD) (rvec, F77_CONST_CHAR_ARG2 ("A", 1), sel, d, z, n, sigma, F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, presid, p, v, n, iparam, ipntr, workd, workl, lwork, info2 F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); if (f77_exception_encountered) (*current_liboctave_error_handler) ("eigs: unrecoverable exception encountered in dseupd"); if (info2 == 0) { octave_idx_type k2 = k / 2; if (typ != "SM" && typ != "BE") { for (octave_idx_type i = 0; i < k2; i++) { double dtmp = d[i]; d[i] = d[k - i - 1]; d[k - i - 1] = dtmp; } } if (rvec) { if (typ != "SM" && typ != "BE") { OCTAVE_LOCAL_BUFFER (double, dtmp, n); for (octave_idx_type i = 0; i < k2; i++) { octave_idx_type off1 = i * n; octave_idx_type off2 = (k - i - 1) * n; if (off1 == off2) continue; for (octave_idx_type j = 0; j < n; j++) dtmp[j] = z[off1 + j]; for (octave_idx_type j = 0; j < n; j++) z[off1 + j] = z[off2 + j]; for (octave_idx_type j = 0; j < n; j++) z[off2 + j] = dtmp[j]; } } } } else (*current_liboctave_error_handler) ("eigs: error %d in dseupd", info2); return ip(4); } template <typename M> octave_idx_type EigsRealNonSymmetricMatrix (const M& m, const std::string typ, octave_idx_type k, octave_idx_type p, octave_idx_type &info, ComplexMatrix &eig_vec, ComplexColumnVector &eig_val, const M& _b, ColumnVector &permB, ColumnVector &resid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit) { M b(_b); octave_idx_type n = m.cols (); octave_idx_type mode = 1; bool have_b = ! b.is_empty (); bool note3 = false; char bmat = 'I'; double sigmar = 0.; double sigmai = 0.; M bt; if (m.rows () != m.cols ()) (*current_liboctave_error_handler) ("eigs: A must be square"); if (have_b && (m.rows () != b.rows () || m.rows () != b.cols ())) (*current_liboctave_error_handler) ("eigs: B must be square and the same size as A"); if (resid.is_empty ()) { std::string rand_dist = octave_rand::distribution (); octave_rand::distribution ("uniform"); resid = ColumnVector (octave_rand::vector (n)); octave_rand::distribution (rand_dist); } if (n < 3) (*current_liboctave_error_handler) ("eigs: n must be at least 3"); if (p < 0) { p = k * 2 + 1; if (p < 20) p = 20; if (p > n - 1) p = n - 1 ; } if (k <= 0 || k >= n - 1) (*current_liboctave_error_handler) ("eigs: Invalid number of eigenvalues to extract (must be 0 < k < n-1).\n" " Use 'eig (full (A))' instead"); if (p <= k || p >= n) (*current_liboctave_error_handler) ("eigs: opts.p must be greater than k and less than n"); if (have_b && cholB && ! permB.is_empty ()) { // Check the we really have a permutation vector if (permB.numel () != n) (*current_liboctave_error_handler) ("eigs: permB vector invalid"); Array<bool> checked (dim_vector (n, 1), false); for (octave_idx_type i = 0; i < n; i++) { octave_idx_type bidx = static_cast<octave_idx_type> (permB(i)); if (checked(bidx) || bidx < 0 || bidx >= n || D_NINT (bidx) != bidx) (*current_liboctave_error_handler) ("eigs: permB vector invalid"); } } if (typ != "LM" && typ != "SM" && typ != "LA" && typ != "SA" && typ != "BE" && typ != "LR" && typ != "SR" && typ != "LI" && typ != "SI") (*current_liboctave_error_handler) ("eigs: unrecognized sigma value"); if (typ == "LA" || typ == "SA" || typ == "BE") (*current_liboctave_error_handler) ("eigs: invalid sigma value for unsymmetric problem"); if (have_b) { // See Note 3 dsaupd note3 = true; if (cholB) { bt = b; b = b.transpose (); if (permB.is_empty ()) { permB = ColumnVector (n); for (octave_idx_type i = 0; i < n; i++) permB(i) = i; } } else { if (! make_cholb (b, bt, permB)) (*current_liboctave_error_handler) ("eigs: The matrix B is not positive definite"); } } Array<octave_idx_type> ip (dim_vector (11, 1)); octave_idx_type *iparam = ip.fortran_vec (); ip(0) = 1; //ishift ip(1) = 0; // ip(1) not referenced ip(2) = maxit; // mxiter, maximum number of iterations ip(3) = 1; // NB blocksize in recurrence ip(4) = 0; // nconv, number of Ritz values that satisfy convergence ip(5) = 0; //ip(5) not referenced ip(6) = mode; // mode ip(7) = 0; ip(8) = 0; ip(9) = 0; ip(10) = 0; // ip(7) to ip(10) return values Array<octave_idx_type> iptr (dim_vector (14, 1)); octave_idx_type *ipntr = iptr.fortran_vec (); octave_idx_type ido = 0; int iter = 0; octave_idx_type lwork = 3 * p * (p + 2); OCTAVE_LOCAL_BUFFER (double, v, n * (p + 1)); OCTAVE_LOCAL_BUFFER (double, workl, lwork + 1); OCTAVE_LOCAL_BUFFER (double, workd, 3 * n + 1); double *presid = resid.fortran_vec (); do { F77_FUNC (dnaupd, DNAUPD) (ido, F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, presid, p, v, n, iparam, ipntr, workd, workl, lwork, info F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); if (f77_exception_encountered) (*current_liboctave_error_handler) ("eigs: unrecoverable exception encountered in dnaupd"); if (disp > 0 && ! xisnan(workl[iptr(5)-1])) { if (iter++) { os << "Iteration " << iter - 1 << ": a few Ritz values of the " << p << "-by-" << p << " matrix\n"; for (int i = 0 ; i < k; i++) os << " " << workl[iptr(5)+i-1] << "\n"; } // This is a kludge, as ARPACK doesn't give its // iteration pointer. But as workl[iptr(5)-1] is // an output value updated at each iteration, setting // a value in this array to NaN and testing for it // is a way of obtaining the iteration counter. if (ido != 99) workl[iptr(5)-1] = octave_NaN; } if (ido == -1 || ido == 1 || ido == 2) { if (have_b) { Matrix mtmp (n,1); for (octave_idx_type i = 0; i < n; i++) mtmp(i,0) = workd[i + iptr(0) - 1]; mtmp = utsolve (bt, permB, m * ltsolve (b, permB, mtmp)); for (octave_idx_type i = 0; i < n; i++) workd[i+iptr(1)-1] = mtmp(i,0); } else if (! vector_product (m, workd + iptr(0) - 1, workd + iptr(1) - 1)) break; } else { if (info < 0) (*current_liboctave_error_handler) ("eigs: error %d in dnaupd", info); break; } } while (1); octave_idx_type info2; // We have a problem in that the size of the C++ bool // type relative to the fortran logical type. It appears // that fortran uses 4- or 8-bytes per logical and C++ 1-byte // per bool, though this might be system dependent. As // long as the HOWMNY arg is not "S", the logical array // is just workspace for ARPACK, so use int type to // avoid problems. Array<octave_idx_type> s (dim_vector (p, 1)); octave_idx_type *sel = s.fortran_vec (); // FIXME: initialize eig_vec2 to zero; apparently dneupd can skip // the assignment to elements of Z that represent imaginary parts. // Found with valgrind and // // A = [1,0,0,-1;0,1,0,0;0,0,1,0;0,0,2,1]; // [vecs, vals, f] = eigs (A, 1) Matrix eig_vec2 (n, k + 1, 0.0); double *z = eig_vec2.fortran_vec (); OCTAVE_LOCAL_BUFFER (double, dr, k + 1); OCTAVE_LOCAL_BUFFER (double, di, k + 1); OCTAVE_LOCAL_BUFFER (double, workev, 3 * p); for (octave_idx_type i = 0; i < k+1; i++) dr[i] = di[i] = 0.; F77_FUNC (dneupd, DNEUPD) (rvec, F77_CONST_CHAR_ARG2 ("A", 1), sel, dr, di, z, n, sigmar, sigmai, workev, F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, presid, p, v, n, iparam, ipntr, workd, workl, lwork, info2 F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); if (f77_exception_encountered) (*current_liboctave_error_handler) ("eigs: unrecoverable exception encountered in dneupd"); eig_val.resize (k+1); Complex *d = eig_val.fortran_vec (); if (info2 == 0) { octave_idx_type jj = 0; for (octave_idx_type i = 0; i < k+1; i++) { if (dr[i] == 0.0 && di[i] == 0.0 && jj == 0) jj++; else d[i-jj] = Complex (dr[i], di[i]); } if (jj == 0 && ! rvec) for (octave_idx_type i = 0; i < k; i++) d[i] = d[i+1]; octave_idx_type k2 = k / 2; for (octave_idx_type i = 0; i < k2; i++) { Complex dtmp = d[i]; d[i] = d[k - i - 1]; d[k - i - 1] = dtmp; } eig_val.resize (k); if (rvec) { OCTAVE_LOCAL_BUFFER (double, dtmp, n); for (octave_idx_type i = 0; i < k2; i++) { octave_idx_type off1 = i * n; octave_idx_type off2 = (k - i - 1) * n; if (off1 == off2) continue; for (octave_idx_type j = 0; j < n; j++) dtmp[j] = z[off1 + j]; for (octave_idx_type j = 0; j < n; j++) z[off1 + j] = z[off2 + j]; for (octave_idx_type j = 0; j < n; j++) z[off2 + j] = dtmp[j]; } eig_vec.resize (n, k); octave_idx_type i = 0; while (i < k) { octave_idx_type off1 = i * n; octave_idx_type off2 = (i+1) * n; if (std::imag (eig_val(i)) == 0) { for (octave_idx_type j = 0; j < n; j++) eig_vec(j,i) = Complex (z[j+off1],0.); i++; } else { for (octave_idx_type j = 0; j < n; j++) { eig_vec(j,i) = Complex (z[j+off1],z[j+off2]); if (i < k - 1) eig_vec(j,i+1) = Complex (z[j+off1],-z[j+off2]); } i+=2; } } if (note3) eig_vec = ltsolve (M(b), permB, eig_vec); } } else (*current_liboctave_error_handler) ("eigs: error %d in dneupd", info2); return ip(4); } template <typename M> octave_idx_type EigsRealNonSymmetricMatrixShift (const M& m, double sigmar, octave_idx_type k, octave_idx_type p, octave_idx_type &info, ComplexMatrix &eig_vec, ComplexColumnVector &eig_val, const M& _b, ColumnVector &permB, ColumnVector &resid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit) { M b(_b); octave_idx_type n = m.cols (); octave_idx_type mode = 3; bool have_b = ! b.is_empty (); std::string typ = "LM"; double sigmai = 0.; if (m.rows () != m.cols ()) (*current_liboctave_error_handler) ("eigs: A must be square"); if (have_b && (m.rows () != b.rows () || m.rows () != b.cols ())) (*current_liboctave_error_handler) ("eigs: B must be square and the same size as A"); // FIXME: The "SM" type for mode 1 seems unstable though faster!! //if (! std::abs (sigmar)) // return EigsRealNonSymmetricMatrix (m, "SM", k, p, info, eig_vec, eig_val, // _b, permB, resid, os, tol, rvec, cholB, // disp, maxit); if (resid.is_empty ()) { std::string rand_dist = octave_rand::distribution (); octave_rand::distribution ("uniform"); resid = ColumnVector (octave_rand::vector (n)); octave_rand::distribution (rand_dist); } if (n < 3) (*current_liboctave_error_handler) ("eigs: n must be at least 3"); if (p < 0) { p = k * 2 + 1; if (p < 20) p = 20; if (p > n - 1) p = n - 1 ; } if (k <= 0 || k >= n - 1) (*current_liboctave_error_handler) ("eigs: Invalid number of eigenvalues to extract (must be 0 < k < n-1).\n" " Use 'eig (full (A))' instead"); if (p <= k || p >= n) (*current_liboctave_error_handler) ("eigs: opts.p must be greater than k and less than n"); if (have_b && cholB && ! permB.is_empty ()) { // Check that we really have a permutation vector if (permB.numel () != n) (*current_liboctave_error_handler) ("eigs: permB vector invalid"); Array<bool> checked (dim_vector (n, 1), false); for (octave_idx_type i = 0; i < n; i++) { octave_idx_type bidx = static_cast<octave_idx_type> (permB(i)); if (checked(bidx) || bidx < 0 || bidx >= n || D_NINT (bidx) != bidx) (*current_liboctave_error_handler) ("eigs: permB vector invalid"); } } char bmat = 'I'; if (have_b) bmat = 'G'; Array<octave_idx_type> ip (dim_vector (11, 1)); octave_idx_type *iparam = ip.fortran_vec (); ip(0) = 1; //ishift ip(1) = 0; // ip(1) not referenced ip(2) = maxit; // mxiter, maximum number of iterations ip(3) = 1; // NB blocksize in recurrence ip(4) = 0; // nconv, number of Ritz values that satisfy convergence ip(5) = 0; //ip(5) not referenced ip(6) = mode; // mode ip(7) = 0; ip(8) = 0; ip(9) = 0; ip(10) = 0; // ip(7) to ip(10) return values Array<octave_idx_type> iptr (dim_vector (14, 1)); octave_idx_type *ipntr = iptr.fortran_vec (); octave_idx_type ido = 0; int iter = 0; M L, U; OCTAVE_LOCAL_BUFFER (octave_idx_type, P, (have_b ? b.rows () : m.rows ())); OCTAVE_LOCAL_BUFFER (octave_idx_type, Q, (have_b ? b.cols () : m.cols ())); if (! LuAminusSigmaB (m, b, cholB, permB, sigmar, L, U, P, Q)) return -1; octave_idx_type lwork = 3 * p * (p + 2); OCTAVE_LOCAL_BUFFER (double, v, n * (p + 1)); OCTAVE_LOCAL_BUFFER (double, workl, lwork + 1); OCTAVE_LOCAL_BUFFER (double, workd, 3 * n + 1); double *presid = resid.fortran_vec (); do { F77_FUNC (dnaupd, DNAUPD) (ido, F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, presid, p, v, n, iparam, ipntr, workd, workl, lwork, info F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); if (f77_exception_encountered) (*current_liboctave_error_handler) ("eigs: unrecoverable exception encountered in dsaupd"); if (disp > 0 && ! xisnan (workl[iptr (5)-1])) { if (iter++) { os << "Iteration " << iter - 1 << ": a few Ritz values of the " << p << "-by-" << p << " matrix\n"; for (int i = 0 ; i < k; i++) os << " " << workl[iptr(5)+i-1] << "\n"; } // This is a kludge, as ARPACK doesn't give its // iteration pointer. But as workl[iptr(5)-1] is // an output value updated at each iteration, setting // a value in this array to NaN and testing for it // is a way of obtaining the iteration counter. if (ido != 99) workl[iptr(5)-1] = octave_NaN; } if (ido == -1 || ido == 1 || ido == 2) { if (have_b) { if (ido == -1) { OCTAVE_LOCAL_BUFFER (double, dtmp, n); vector_product (m, workd+iptr(0)-1, dtmp); Matrix tmp(n, 1); for (octave_idx_type i = 0; i < n; i++) tmp(i,0) = dtmp[P[i]]; lusolve (L, U, tmp); double *ip2 = workd+iptr(1)-1; for (octave_idx_type i = 0; i < n; i++) ip2[Q[i]] = tmp(i,0); } else if (ido == 2) vector_product (b, workd+iptr(0)-1, workd+iptr(1)-1); else { double *ip2 = workd+iptr(2)-1; Matrix tmp(n, 1); for (octave_idx_type i = 0; i < n; i++) tmp(i,0) = ip2[P[i]]; lusolve (L, U, tmp); ip2 = workd+iptr(1)-1; for (octave_idx_type i = 0; i < n; i++) ip2[Q[i]] = tmp(i,0); } } else { if (ido == 2) { for (octave_idx_type i = 0; i < n; i++) workd[iptr(0) + i - 1] = workd[iptr(1) + i - 1]; } else { double *ip2 = workd+iptr(0)-1; Matrix tmp(n, 1); for (octave_idx_type i = 0; i < n; i++) tmp(i,0) = ip2[P[i]]; lusolve (L, U, tmp); ip2 = workd+iptr(1)-1; for (octave_idx_type i = 0; i < n; i++) ip2[Q[i]] = tmp(i,0); } } } else { if (info < 0) (*current_liboctave_error_handler) ("eigs: error %d in dsaupd", info); break; } } while (1); octave_idx_type info2; // We have a problem in that the size of the C++ bool // type relative to the fortran logical type. It appears // that fortran uses 4- or 8-bytes per logical and C++ 1-byte // per bool, though this might be system dependent. As // long as the HOWMNY arg is not "S", the logical array // is just workspace for ARPACK, so use int type to // avoid problems. Array<octave_idx_type> s (dim_vector (p, 1)); octave_idx_type *sel = s.fortran_vec (); // FIXME: initialize eig_vec2 to zero; apparently dneupd can skip // the assignment to elements of Z that represent imaginary parts. // Found with valgrind and // // A = [1,0,0,-1;0,1,0,0;0,0,1,0;0,0,2,1]; // [vecs, vals, f] = eigs (A, 1) Matrix eig_vec2 (n, k + 1, 0.0); double *z = eig_vec2.fortran_vec (); OCTAVE_LOCAL_BUFFER (double, dr, k + 1); OCTAVE_LOCAL_BUFFER (double, di, k + 1); OCTAVE_LOCAL_BUFFER (double, workev, 3 * p); for (octave_idx_type i = 0; i < k+1; i++) dr[i] = di[i] = 0.; F77_FUNC (dneupd, DNEUPD) (rvec, F77_CONST_CHAR_ARG2 ("A", 1), sel, dr, di, z, n, sigmar, sigmai, workev, F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, presid, p, v, n, iparam, ipntr, workd, workl, lwork, info2 F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); if (f77_exception_encountered) (*current_liboctave_error_handler) ("eigs: unrecoverable exception encountered in dneupd"); eig_val.resize (k+1); Complex *d = eig_val.fortran_vec (); if (info2 == 0) { octave_idx_type jj = 0; for (octave_idx_type i = 0; i < k+1; i++) { if (dr[i] == 0.0 && di[i] == 0.0 && jj == 0) jj++; else d[i-jj] = Complex (dr[i], di[i]); } if (jj == 0 && ! rvec) for (octave_idx_type i = 0; i < k; i++) d[i] = d[i+1]; octave_idx_type k2 = k / 2; for (octave_idx_type i = 0; i < k2; i++) { Complex dtmp = d[i]; d[i] = d[k - i - 1]; d[k - i - 1] = dtmp; } eig_val.resize (k); if (rvec) { OCTAVE_LOCAL_BUFFER (double, dtmp, n); for (octave_idx_type i = 0; i < k2; i++) { octave_idx_type off1 = i * n; octave_idx_type off2 = (k - i - 1) * n; if (off1 == off2) continue; for (octave_idx_type j = 0; j < n; j++) dtmp[j] = z[off1 + j]; for (octave_idx_type j = 0; j < n; j++) z[off1 + j] = z[off2 + j]; for (octave_idx_type j = 0; j < n; j++) z[off2 + j] = dtmp[j]; } eig_vec.resize (n, k); octave_idx_type i = 0; while (i < k) { octave_idx_type off1 = i * n; octave_idx_type off2 = (i+1) * n; if (std::imag (eig_val(i)) == 0) { for (octave_idx_type j = 0; j < n; j++) eig_vec(j,i) = Complex (z[j+off1],0.); i++; } else { for (octave_idx_type j = 0; j < n; j++) { eig_vec(j,i) = Complex (z[j+off1],z[j+off2]); if (i < k - 1) eig_vec(j,i+1) = Complex (z[j+off1],-z[j+off2]); } i+=2; } } } } else (*current_liboctave_error_handler) ("eigs: error %d in dneupd", info2); return ip(4); } octave_idx_type EigsRealNonSymmetricFunc (EigsFunc fun, octave_idx_type n, const std::string &_typ, double sigmar, octave_idx_type k, octave_idx_type p, octave_idx_type &info, ComplexMatrix &eig_vec, ComplexColumnVector &eig_val, ColumnVector &resid, std::ostream& os, double tol, bool rvec, bool /* cholB */, int disp, int maxit) { std::string typ (_typ); bool have_sigma = (sigmar ? true : false); char bmat = 'I'; double sigmai = 0.; octave_idx_type mode = 1; int err = 0; if (resid.is_empty ()) { std::string rand_dist = octave_rand::distribution (); octave_rand::distribution ("uniform"); resid = ColumnVector (octave_rand::vector (n)); octave_rand::distribution (rand_dist); } if (n < 3) (*current_liboctave_error_handler) ("eigs: n must be at least 3"); if (p < 0) { p = k * 2 + 1; if (p < 20) p = 20; if (p > n - 1) p = n - 1 ; } if (k <= 0 || k >= n - 1) (*current_liboctave_error_handler) ("eigs: Invalid number of eigenvalues to extract (must be 0 < k < n-1).\n" " Use 'eig (full (A))' instead"); if (p <= k || p >= n) (*current_liboctave_error_handler) ("eigs: opts.p must be greater than k and less than n"); if (! have_sigma) { if (typ != "LM" && typ != "SM" && typ != "LA" && typ != "SA" && typ != "BE" && typ != "LR" && typ != "SR" && typ != "LI" && typ != "SI") (*current_liboctave_error_handler) ("eigs: unrecognized sigma value"); if (typ == "LA" || typ == "SA" || typ == "BE") (*current_liboctave_error_handler) ("eigs: invalid sigma value for unsymmetric problem"); if (typ == "SM") { typ = "LM"; sigmar = 0.; mode = 3; } } else if (! std::abs (sigmar)) typ = "SM"; else { typ = "LM"; mode = 3; } Array<octave_idx_type> ip (dim_vector (11, 1)); octave_idx_type *iparam = ip.fortran_vec (); ip(0) = 1; //ishift ip(1) = 0; // ip(1) not referenced ip(2) = maxit; // mxiter, maximum number of iterations ip(3) = 1; // NB blocksize in recurrence ip(4) = 0; // nconv, number of Ritz values that satisfy convergence ip(5) = 0; //ip(5) not referenced ip(6) = mode; // mode ip(7) = 0; ip(8) = 0; ip(9) = 0; ip(10) = 0; // ip(7) to ip(10) return values Array<octave_idx_type> iptr (dim_vector (14, 1)); octave_idx_type *ipntr = iptr.fortran_vec (); octave_idx_type ido = 0; int iter = 0; octave_idx_type lwork = 3 * p * (p + 2); OCTAVE_LOCAL_BUFFER (double, v, n * (p + 1)); OCTAVE_LOCAL_BUFFER (double, workl, lwork + 1); OCTAVE_LOCAL_BUFFER (double, workd, 3 * n + 1); double *presid = resid.fortran_vec (); do { F77_FUNC (dnaupd, DNAUPD) (ido, F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, presid, p, v, n, iparam, ipntr, workd, workl, lwork, info F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); if (f77_exception_encountered) (*current_liboctave_error_handler) ("eigs: unrecoverable exception encountered in dnaupd"); if (disp > 0 && ! xisnan(workl[iptr(5)-1])) { if (iter++) { os << "Iteration " << iter - 1 << ": a few Ritz values of the " << p << "-by-" << p << " matrix\n"; for (int i = 0 ; i < k; i++) os << " " << workl[iptr(5)+i-1] << "\n"; } // This is a kludge, as ARPACK doesn't give its // iteration pointer. But as workl[iptr(5)-1] is // an output value updated at each iteration, setting // a value in this array to NaN and testing for it // is a way of obtaining the iteration counter. if (ido != 99) workl[iptr(5)-1] = octave_NaN; } if (ido == -1 || ido == 1 || ido == 2) { double *ip2 = workd + iptr(0) - 1; ColumnVector x(n); for (octave_idx_type i = 0; i < n; i++) x(i) = *ip2++; ColumnVector y = fun (x, err); if (err) return false; ip2 = workd + iptr(1) - 1; for (octave_idx_type i = 0; i < n; i++) *ip2++ = y(i); } else { if (info < 0) (*current_liboctave_error_handler) ("eigs: error %d in dsaupd", info); break; } } while (1); octave_idx_type info2; // We have a problem in that the size of the C++ bool // type relative to the fortran logical type. It appears // that fortran uses 4- or 8-bytes per logical and C++ 1-byte // per bool, though this might be system dependent. As // long as the HOWMNY arg is not "S", the logical array // is just workspace for ARPACK, so use int type to // avoid problems. Array<octave_idx_type> s (dim_vector (p, 1)); octave_idx_type *sel = s.fortran_vec (); // FIXME: initialize eig_vec2 to zero; apparently dneupd can skip // the assignment to elements of Z that represent imaginary parts. // Found with valgrind and // // A = [1,0,0,-1;0,1,0,0;0,0,1,0;0,0,2,1]; // [vecs, vals, f] = eigs (A, 1) Matrix eig_vec2 (n, k + 1, 0.0); double *z = eig_vec2.fortran_vec (); OCTAVE_LOCAL_BUFFER (double, dr, k + 1); OCTAVE_LOCAL_BUFFER (double, di, k + 1); OCTAVE_LOCAL_BUFFER (double, workev, 3 * p); for (octave_idx_type i = 0; i < k+1; i++) dr[i] = di[i] = 0.; F77_FUNC (dneupd, DNEUPD) (rvec, F77_CONST_CHAR_ARG2 ("A", 1), sel, dr, di, z, n, sigmar, sigmai, workev, F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, presid, p, v, n, iparam, ipntr, workd, workl, lwork, info2 F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); if (f77_exception_encountered) (*current_liboctave_error_handler) ("eigs: unrecoverable exception encountered in dneupd"); eig_val.resize (k+1); Complex *d = eig_val.fortran_vec (); if (info2 == 0) { octave_idx_type jj = 0; for (octave_idx_type i = 0; i < k+1; i++) { if (dr[i] == 0.0 && di[i] == 0.0 && jj == 0) jj++; else d[i-jj] = Complex (dr[i], di[i]); } if (jj == 0 && ! rvec) for (octave_idx_type i = 0; i < k; i++) d[i] = d[i+1]; octave_idx_type k2 = k / 2; for (octave_idx_type i = 0; i < k2; i++) { Complex dtmp = d[i]; d[i] = d[k - i - 1]; d[k - i - 1] = dtmp; } eig_val.resize (k); if (rvec) { OCTAVE_LOCAL_BUFFER (double, dtmp, n); for (octave_idx_type i = 0; i < k2; i++) { octave_idx_type off1 = i * n; octave_idx_type off2 = (k - i - 1) * n; if (off1 == off2) continue; for (octave_idx_type j = 0; j < n; j++) dtmp[j] = z[off1 + j]; for (octave_idx_type j = 0; j < n; j++) z[off1 + j] = z[off2 + j]; for (octave_idx_type j = 0; j < n; j++) z[off2 + j] = dtmp[j]; } eig_vec.resize (n, k); octave_idx_type i = 0; while (i < k) { octave_idx_type off1 = i * n; octave_idx_type off2 = (i+1) * n; if (std::imag (eig_val(i)) == 0) { for (octave_idx_type j = 0; j < n; j++) eig_vec(j,i) = Complex (z[j+off1],0.); i++; } else { for (octave_idx_type j = 0; j < n; j++) { eig_vec(j,i) = Complex (z[j+off1],z[j+off2]); if (i < k - 1) eig_vec(j,i+1) = Complex (z[j+off1],-z[j+off2]); } i+=2; } } } } else (*current_liboctave_error_handler) ("eigs: error %d in dneupd", info2); return ip(4); } template <typename M> octave_idx_type EigsComplexNonSymmetricMatrix (const M& m, const std::string typ, octave_idx_type k, octave_idx_type p, octave_idx_type &info, ComplexMatrix &eig_vec, ComplexColumnVector &eig_val, const M& _b, ColumnVector &permB, ComplexColumnVector &cresid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit) { M b(_b); octave_idx_type n = m.cols (); octave_idx_type mode = 1; bool have_b = ! b.is_empty (); bool note3 = false; char bmat = 'I'; Complex sigma = 0.; M bt; if (m.rows () != m.cols ()) (*current_liboctave_error_handler) ("eigs: A must be square"); if (have_b && (m.rows () != b.rows () || m.rows () != b.cols ())) (*current_liboctave_error_handler) ("eigs: B must be square and the same size as A"); if (cresid.is_empty ()) { std::string rand_dist = octave_rand::distribution (); octave_rand::distribution ("uniform"); Array<double> rr (octave_rand::vector (n)); Array<double> ri (octave_rand::vector (n)); cresid = ComplexColumnVector (n); for (octave_idx_type i = 0; i < n; i++) cresid(i) = Complex (rr(i),ri(i)); octave_rand::distribution (rand_dist); } if (n < 3) (*current_liboctave_error_handler) ("eigs: n must be at least 3"); if (p < 0) { p = k * 2 + 1; if (p < 20) p = 20; if (p > n - 1) p = n - 1 ; } if (k <= 0 || k >= n - 1) (*current_liboctave_error_handler) ("eigs: Invalid number of eigenvalues to extract (must be 0 < k < n-1).\n" " Use 'eig (full (A))' instead"); if (p <= k || p >= n) (*current_liboctave_error_handler) ("eigs: opts.p must be greater than k and less than n"); if (have_b && cholB && ! permB.is_empty ()) { // Check the we really have a permutation vector if (permB.numel () != n) (*current_liboctave_error_handler) ("eigs: permB vector invalid"); Array<bool> checked (dim_vector (n, 1), false); for (octave_idx_type i = 0; i < n; i++) { octave_idx_type bidx = static_cast<octave_idx_type> (permB(i)); if (checked(bidx) || bidx < 0 || bidx >= n || D_NINT (bidx) != bidx) (*current_liboctave_error_handler) ("eigs: permB vector invalid"); } } if (typ != "LM" && typ != "SM" && typ != "LA" && typ != "SA" && typ != "BE" && typ != "LR" && typ != "SR" && typ != "LI" && typ != "SI") (*current_liboctave_error_handler) ("eigs: unrecognized sigma value"); if (typ == "LA" || typ == "SA" || typ == "BE") (*current_liboctave_error_handler) ("eigs: invalid sigma value for complex problem"); if (have_b) { // See Note 3 dsaupd note3 = true; if (cholB) { bt = b; b = b.hermitian (); if (permB.is_empty ()) { permB = ColumnVector (n); for (octave_idx_type i = 0; i < n; i++) permB(i) = i; } } else { if (! make_cholb (b, bt, permB)) (*current_liboctave_error_handler) ("eigs: The matrix B is not positive definite"); } } Array<octave_idx_type> ip (dim_vector (11, 1)); octave_idx_type *iparam = ip.fortran_vec (); ip(0) = 1; //ishift ip(1) = 0; // ip(1) not referenced ip(2) = maxit; // mxiter, maximum number of iterations ip(3) = 1; // NB blocksize in recurrence ip(4) = 0; // nconv, number of Ritz values that satisfy convergence ip(5) = 0; //ip(5) not referenced ip(6) = mode; // mode ip(7) = 0; ip(8) = 0; ip(9) = 0; ip(10) = 0; // ip(7) to ip(10) return values Array<octave_idx_type> iptr (dim_vector (14, 1)); octave_idx_type *ipntr = iptr.fortran_vec (); octave_idx_type ido = 0; int iter = 0; octave_idx_type lwork = p * (3 * p + 5); OCTAVE_LOCAL_BUFFER (Complex, v, n * p); OCTAVE_LOCAL_BUFFER (Complex, workl, lwork); OCTAVE_LOCAL_BUFFER (Complex, workd, 3 * n); OCTAVE_LOCAL_BUFFER (double, rwork, p); Complex *presid = cresid.fortran_vec (); do { F77_FUNC (znaupd, ZNAUPD) (ido, F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, presid, p, v, n, iparam, ipntr, workd, workl, lwork, rwork, info F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); if (f77_exception_encountered) (*current_liboctave_error_handler) ("eigs: unrecoverable exception encountered in znaupd"); if (disp > 0 && ! xisnan (workl[iptr (5)-1])) { if (iter++) { os << "Iteration " << iter - 1 << ": a few Ritz values of the " << p << "-by-" << p << " matrix\n"; for (int i = 0 ; i < k; i++) os << " " << workl[iptr(5)+i-1] << "\n"; } // This is a kludge, as ARPACK doesn't give its // iteration pointer. But as workl[iptr(5)-1] is // an output value updated at each iteration, setting // a value in this array to NaN and testing for it // is a way of obtaining the iteration counter. if (ido != 99) workl[iptr(5)-1] = octave_NaN; } if (ido == -1 || ido == 1 || ido == 2) { if (have_b) { ComplexMatrix mtmp (n,1); for (octave_idx_type i = 0; i < n; i++) mtmp(i,0) = workd[i + iptr(0) - 1]; mtmp = utsolve (bt, permB, m * ltsolve (b, permB, mtmp)); for (octave_idx_type i = 0; i < n; i++) workd[i+iptr(1)-1] = mtmp(i,0); } else if (! vector_product (m, workd + iptr(0) - 1, workd + iptr(1) - 1)) break; } else { if (info < 0) (*current_liboctave_error_handler) ("eigs: error %d in znaupd", info); break; } } while (1); octave_idx_type info2; // We have a problem in that the size of the C++ bool // type relative to the fortran logical type. It appears // that fortran uses 4- or 8-bytes per logical and C++ 1-byte // per bool, though this might be system dependent. As // long as the HOWMNY arg is not "S", the logical array // is just workspace for ARPACK, so use int type to // avoid problems. Array<octave_idx_type> s (dim_vector (p, 1)); octave_idx_type *sel = s.fortran_vec (); eig_vec.resize (n, k); Complex *z = eig_vec.fortran_vec (); eig_val.resize (k+1); Complex *d = eig_val.fortran_vec (); OCTAVE_LOCAL_BUFFER (Complex, workev, 2 * p); F77_FUNC (zneupd, ZNEUPD) (rvec, F77_CONST_CHAR_ARG2 ("A", 1), sel, d, z, n, sigma, workev, F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, presid, p, v, n, iparam, ipntr, workd, workl, lwork, rwork, info2 F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); if (f77_exception_encountered) (*current_liboctave_error_handler) ("eigs: unrecoverable exception encountered in zneupd"); if (info2 == 0) { octave_idx_type k2 = k / 2; for (octave_idx_type i = 0; i < k2; i++) { Complex ctmp = d[i]; d[i] = d[k - i - 1]; d[k - i - 1] = ctmp; } eig_val.resize (k); if (rvec) { OCTAVE_LOCAL_BUFFER (Complex, ctmp, n); for (octave_idx_type i = 0; i < k2; i++) { octave_idx_type off1 = i * n; octave_idx_type off2 = (k - i - 1) * n; if (off1 == off2) continue; for (octave_idx_type j = 0; j < n; j++) ctmp[j] = z[off1 + j]; for (octave_idx_type j = 0; j < n; j++) z[off1 + j] = z[off2 + j]; for (octave_idx_type j = 0; j < n; j++) z[off2 + j] = ctmp[j]; } if (note3) eig_vec = ltsolve (b, permB, eig_vec); } } else (*current_liboctave_error_handler) ("eigs: error %d in zneupd", info2); return ip(4); } template <typename M> octave_idx_type EigsComplexNonSymmetricMatrixShift (const M& m, Complex sigma, octave_idx_type k, octave_idx_type p, octave_idx_type &info, ComplexMatrix &eig_vec, ComplexColumnVector &eig_val, const M& _b, ColumnVector &permB, ComplexColumnVector &cresid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit) { M b(_b); octave_idx_type n = m.cols (); octave_idx_type mode = 3; bool have_b = ! b.is_empty (); std::string typ = "LM"; if (m.rows () != m.cols ()) (*current_liboctave_error_handler) ("eigs: A must be square"); if (have_b && (m.rows () != b.rows () || m.rows () != b.cols ())) (*current_liboctave_error_handler) ("eigs: B must be square and the same size as A"); // FIXME: The "SM" type for mode 1 seems unstable though faster!! //if (! std::abs (sigma)) // return EigsComplexNonSymmetricMatrix (m, "SM", k, p, info, eig_vec, // eig_val, _b, permB, cresid, os, tol, // rvec, cholB, disp, maxit); if (cresid.is_empty ()) { std::string rand_dist = octave_rand::distribution (); octave_rand::distribution ("uniform"); Array<double> rr (octave_rand::vector (n)); Array<double> ri (octave_rand::vector (n)); cresid = ComplexColumnVector (n); for (octave_idx_type i = 0; i < n; i++) cresid(i) = Complex (rr(i),ri(i)); octave_rand::distribution (rand_dist); } if (n < 3) (*current_liboctave_error_handler) ("eigs: n must be at least 3"); if (p < 0) { p = k * 2 + 1; if (p < 20) p = 20; if (p > n - 1) p = n - 1 ; } if (k <= 0 || k >= n - 1) (*current_liboctave_error_handler) ("eigs: Invalid number of eigenvalues to extract (must be 0 < k < n-1).\n" " Use 'eig (full (A))' instead"); if (p <= k || p >= n) (*current_liboctave_error_handler) ("eigs: opts.p must be greater than k and less than n"); if (have_b && cholB && ! permB.is_empty ()) { // Check that we really have a permutation vector if (permB.numel () != n) (*current_liboctave_error_handler) ("eigs: permB vector invalid"); Array<bool> checked (dim_vector (n, 1), false); for (octave_idx_type i = 0; i < n; i++) { octave_idx_type bidx = static_cast<octave_idx_type> (permB(i)); if (checked(bidx) || bidx < 0 || bidx >= n || D_NINT (bidx) != bidx) (*current_liboctave_error_handler) ("eigs: permB vector invalid"); } } char bmat = 'I'; if (have_b) bmat = 'G'; Array<octave_idx_type> ip (dim_vector (11, 1)); octave_idx_type *iparam = ip.fortran_vec (); ip(0) = 1; //ishift ip(1) = 0; // ip(1) not referenced ip(2) = maxit; // mxiter, maximum number of iterations ip(3) = 1; // NB blocksize in recurrence ip(4) = 0; // nconv, number of Ritz values that satisfy convergence ip(5) = 0; //ip(5) not referenced ip(6) = mode; // mode ip(7) = 0; ip(8) = 0; ip(9) = 0; ip(10) = 0; // ip(7) to ip(10) return values Array<octave_idx_type> iptr (dim_vector (14, 1)); octave_idx_type *ipntr = iptr.fortran_vec (); octave_idx_type ido = 0; int iter = 0; M L, U; OCTAVE_LOCAL_BUFFER (octave_idx_type, P, (have_b ? b.rows () : m.rows ())); OCTAVE_LOCAL_BUFFER (octave_idx_type, Q, (have_b ? b.cols () : m.cols ())); if (! LuAminusSigmaB (m, b, cholB, permB, sigma, L, U, P, Q)) return -1; octave_idx_type lwork = p * (3 * p + 5); OCTAVE_LOCAL_BUFFER (Complex, v, n * p); OCTAVE_LOCAL_BUFFER (Complex, workl, lwork); OCTAVE_LOCAL_BUFFER (Complex, workd, 3 * n); OCTAVE_LOCAL_BUFFER (double, rwork, p); Complex *presid = cresid.fortran_vec (); do { F77_FUNC (znaupd, ZNAUPD) (ido, F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, presid, p, v, n, iparam, ipntr, workd, workl, lwork, rwork, info F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); if (f77_exception_encountered) (*current_liboctave_error_handler) ("eigs: unrecoverable exception encountered in znaupd"); if (disp > 0 && ! xisnan(workl[iptr(5)-1])) { if (iter++) { os << "Iteration " << iter - 1 << ": a few Ritz values of the " << p << "-by-" << p << " matrix\n"; for (int i = 0 ; i < k; i++) os << " " << workl[iptr(5)+i-1] << "\n"; } // This is a kludge, as ARPACK doesn't give its // iteration pointer. But as workl[iptr(5)-1] is // an output value updated at each iteration, setting // a value in this array to NaN and testing for it // is a way of obtaining the iteration counter. if (ido != 99) workl[iptr(5)-1] = octave_NaN; } if (ido == -1 || ido == 1 || ido == 2) { if (have_b) { if (ido == -1) { OCTAVE_LOCAL_BUFFER (Complex, ctmp, n); vector_product (m, workd+iptr(0)-1, ctmp); ComplexMatrix tmp(n, 1); for (octave_idx_type i = 0; i < n; i++) tmp(i,0) = ctmp[P[i]]; lusolve (L, U, tmp); Complex *ip2 = workd+iptr(1)-1; for (octave_idx_type i = 0; i < n; i++) ip2[Q[i]] = tmp(i,0); } else if (ido == 2) vector_product (b, workd + iptr(0) - 1, workd + iptr(1) - 1); else { Complex *ip2 = workd+iptr(2)-1; ComplexMatrix tmp(n, 1); for (octave_idx_type i = 0; i < n; i++) tmp(i,0) = ip2[P[i]]; lusolve (L, U, tmp); ip2 = workd+iptr(1)-1; for (octave_idx_type i = 0; i < n; i++) ip2[Q[i]] = tmp(i,0); } } else { if (ido == 2) { for (octave_idx_type i = 0; i < n; i++) workd[iptr(0) + i - 1] = workd[iptr(1) + i - 1]; } else { Complex *ip2 = workd+iptr(0)-1; ComplexMatrix tmp(n, 1); for (octave_idx_type i = 0; i < n; i++) tmp(i,0) = ip2[P[i]]; lusolve (L, U, tmp); ip2 = workd+iptr(1)-1; for (octave_idx_type i = 0; i < n; i++) ip2[Q[i]] = tmp(i,0); } } } else { if (info < 0) (*current_liboctave_error_handler) ("eigs: error %d in dsaupd", info); break; } } while (1); octave_idx_type info2; // We have a problem in that the size of the C++ bool // type relative to the fortran logical type. It appears // that fortran uses 4- or 8-bytes per logical and C++ 1-byte // per bool, though this might be system dependent. As // long as the HOWMNY arg is not "S", the logical array // is just workspace for ARPACK, so use int type to // avoid problems. Array<octave_idx_type> s (dim_vector (p, 1)); octave_idx_type *sel = s.fortran_vec (); eig_vec.resize (n, k); Complex *z = eig_vec.fortran_vec (); eig_val.resize (k+1); Complex *d = eig_val.fortran_vec (); OCTAVE_LOCAL_BUFFER (Complex, workev, 2 * p); F77_FUNC (zneupd, ZNEUPD) (rvec, F77_CONST_CHAR_ARG2 ("A", 1), sel, d, z, n, sigma, workev, F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, presid, p, v, n, iparam, ipntr, workd, workl, lwork, rwork, info2 F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); if (f77_exception_encountered) (*current_liboctave_error_handler) ("eigs: unrecoverable exception encountered in zneupd"); if (info2 == 0) { octave_idx_type k2 = k / 2; for (octave_idx_type i = 0; i < k2; i++) { Complex ctmp = d[i]; d[i] = d[k - i - 1]; d[k - i - 1] = ctmp; } eig_val.resize (k); if (rvec) { OCTAVE_LOCAL_BUFFER (Complex, ctmp, n); for (octave_idx_type i = 0; i < k2; i++) { octave_idx_type off1 = i * n; octave_idx_type off2 = (k - i - 1) * n; if (off1 == off2) continue; for (octave_idx_type j = 0; j < n; j++) ctmp[j] = z[off1 + j]; for (octave_idx_type j = 0; j < n; j++) z[off1 + j] = z[off2 + j]; for (octave_idx_type j = 0; j < n; j++) z[off2 + j] = ctmp[j]; } } } else (*current_liboctave_error_handler) ("eigs: error %d in zneupd", info2); return ip(4); } octave_idx_type EigsComplexNonSymmetricFunc (EigsComplexFunc fun, octave_idx_type n, const std::string &_typ, Complex sigma, octave_idx_type k, octave_idx_type p, octave_idx_type &info, ComplexMatrix &eig_vec, ComplexColumnVector &eig_val, ComplexColumnVector &cresid, std::ostream& os, double tol, bool rvec, bool /* cholB */, int disp, int maxit) { std::string typ (_typ); bool have_sigma = (std::abs (sigma) ? true : false); char bmat = 'I'; octave_idx_type mode = 1; int err = 0; if (cresid.is_empty ()) { std::string rand_dist = octave_rand::distribution (); octave_rand::distribution ("uniform"); Array<double> rr (octave_rand::vector (n)); Array<double> ri (octave_rand::vector (n)); cresid = ComplexColumnVector (n); for (octave_idx_type i = 0; i < n; i++) cresid(i) = Complex (rr(i),ri(i)); octave_rand::distribution (rand_dist); } if (n < 3) (*current_liboctave_error_handler) ("eigs: n must be at least 3"); if (p < 0) { p = k * 2 + 1; if (p < 20) p = 20; if (p > n - 1) p = n - 1 ; } if (k <= 0 || k >= n - 1) (*current_liboctave_error_handler) ("eigs: Invalid number of eigenvalues to extract (must be 0 < k < n-1).\n" " Use 'eig (full (A))' instead"); if (p <= k || p >= n) (*current_liboctave_error_handler) ("eigs: opts.p must be greater than k and less than n"); if (! have_sigma) { if (typ != "LM" && typ != "SM" && typ != "LA" && typ != "SA" && typ != "BE" && typ != "LR" && typ != "SR" && typ != "LI" && typ != "SI") (*current_liboctave_error_handler) ("eigs: unrecognized sigma value"); if (typ == "LA" || typ == "SA" || typ == "BE") (*current_liboctave_error_handler) ("eigs: invalid sigma value for complex problem"); if (typ == "SM") { typ = "LM"; sigma = 0.; mode = 3; } } else if (! std::abs (sigma)) typ = "SM"; else { typ = "LM"; mode = 3; } Array<octave_idx_type> ip (dim_vector (11, 1)); octave_idx_type *iparam = ip.fortran_vec (); ip(0) = 1; //ishift ip(1) = 0; // ip(1) not referenced ip(2) = maxit; // mxiter, maximum number of iterations ip(3) = 1; // NB blocksize in recurrence ip(4) = 0; // nconv, number of Ritz values that satisfy convergence ip(5) = 0; //ip(5) not referenced ip(6) = mode; // mode ip(7) = 0; ip(8) = 0; ip(9) = 0; ip(10) = 0; // ip(7) to ip(10) return values Array<octave_idx_type> iptr (dim_vector (14, 1)); octave_idx_type *ipntr = iptr.fortran_vec (); octave_idx_type ido = 0; int iter = 0; octave_idx_type lwork = p * (3 * p + 5); OCTAVE_LOCAL_BUFFER (Complex, v, n * p); OCTAVE_LOCAL_BUFFER (Complex, workl, lwork); OCTAVE_LOCAL_BUFFER (Complex, workd, 3 * n); OCTAVE_LOCAL_BUFFER (double, rwork, p); Complex *presid = cresid.fortran_vec (); do { F77_FUNC (znaupd, ZNAUPD) (ido, F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, presid, p, v, n, iparam, ipntr, workd, workl, lwork, rwork, info F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); if (f77_exception_encountered) (*current_liboctave_error_handler) ("eigs: unrecoverable exception encountered in znaupd"); if (disp > 0 && ! xisnan(workl[iptr(5)-1])) { if (iter++) { os << "Iteration " << iter - 1 << ": a few Ritz values of the " << p << "-by-" << p << " matrix\n"; for (int i = 0 ; i < k; i++) os << " " << workl[iptr(5)+i-1] << "\n"; } // This is a kludge, as ARPACK doesn't give its // iteration pointer. But as workl[iptr(5)-1] is // an output value updated at each iteration, setting // a value in this array to NaN and testing for it // is a way of obtaining the iteration counter. if (ido != 99) workl[iptr(5)-1] = octave_NaN; } if (ido == -1 || ido == 1 || ido == 2) { Complex *ip2 = workd + iptr(0) - 1; ComplexColumnVector x(n); for (octave_idx_type i = 0; i < n; i++) x(i) = *ip2++; ComplexColumnVector y = fun (x, err); if (err) return false; ip2 = workd + iptr(1) - 1; for (octave_idx_type i = 0; i < n; i++) *ip2++ = y(i); } else { if (info < 0) (*current_liboctave_error_handler) ("eigs: error %d in dsaupd", info); break; } } while (1); octave_idx_type info2; // We have a problem in that the size of the C++ bool // type relative to the fortran logical type. It appears // that fortran uses 4- or 8-bytes per logical and C++ 1-byte // per bool, though this might be system dependent. As // long as the HOWMNY arg is not "S", the logical array // is just workspace for ARPACK, so use int type to // avoid problems. Array<octave_idx_type> s (dim_vector (p, 1)); octave_idx_type *sel = s.fortran_vec (); eig_vec.resize (n, k); Complex *z = eig_vec.fortran_vec (); eig_val.resize (k+1); Complex *d = eig_val.fortran_vec (); OCTAVE_LOCAL_BUFFER (Complex, workev, 2 * p); F77_FUNC (zneupd, ZNEUPD) (rvec, F77_CONST_CHAR_ARG2 ("A", 1), sel, d, z, n, sigma, workev, F77_CONST_CHAR_ARG2 (&bmat, 1), n, F77_CONST_CHAR_ARG2 ((typ.c_str ()), 2), k, tol, presid, p, v, n, iparam, ipntr, workd, workl, lwork, rwork, info2 F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(1) F77_CHAR_ARG_LEN(2)); if (f77_exception_encountered) (*current_liboctave_error_handler) ("eigs: unrecoverable exception encountered in zneupd"); if (info2 == 0) { octave_idx_type k2 = k / 2; for (octave_idx_type i = 0; i < k2; i++) { Complex ctmp = d[i]; d[i] = d[k - i - 1]; d[k - i - 1] = ctmp; } eig_val.resize (k); if (rvec) { OCTAVE_LOCAL_BUFFER (Complex, ctmp, n); for (octave_idx_type i = 0; i < k2; i++) { octave_idx_type off1 = i * n; octave_idx_type off2 = (k - i - 1) * n; if (off1 == off2) continue; for (octave_idx_type j = 0; j < n; j++) ctmp[j] = z[off1 + j]; for (octave_idx_type j = 0; j < n; j++) z[off1 + j] = z[off2 + j]; for (octave_idx_type j = 0; j < n; j++) z[off2 + j] = ctmp[j]; } } } else (*current_liboctave_error_handler) ("eigs: error %d in zneupd", info2); return ip(4); } // Instantiations for the types we need. // Matrix template octave_idx_type EigsRealSymmetricMatrix<Matrix> (const Matrix& m, const std::string typ, octave_idx_type k, octave_idx_type p, octave_idx_type& info, Matrix& eig_vec, ColumnVector& eig_val, const Matrix& _b, ColumnVector& permB, ColumnVector& resid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit); template octave_idx_type EigsRealSymmetricMatrixShift<Matrix> (const Matrix& m, double sigma, octave_idx_type k, octave_idx_type p, octave_idx_type& info, Matrix& eig_vec, ColumnVector& eig_val, const Matrix& _b, ColumnVector& permB, ColumnVector& resid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit); template octave_idx_type EigsRealNonSymmetricMatrix<Matrix> (const Matrix& m, const std::string typ, octave_idx_type k, octave_idx_type p, octave_idx_type& info, ComplexMatrix& eig_vec, ComplexColumnVector& eig_val, const Matrix& _b, ColumnVector& permB, ColumnVector& resid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit); template octave_idx_type EigsRealNonSymmetricMatrixShift<Matrix> (const Matrix& m, double sigmar, octave_idx_type k, octave_idx_type p, octave_idx_type& info, ComplexMatrix& eig_vec, ComplexColumnVector& eig_val, const Matrix& _b, ColumnVector& permB, ColumnVector& resid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit); // SparseMatrix template octave_idx_type EigsRealSymmetricMatrix<SparseMatrix> (const SparseMatrix& m, const std::string typ, octave_idx_type k, octave_idx_type p, octave_idx_type& info, Matrix& eig_vec, ColumnVector& eig_val, const SparseMatrix& _b, ColumnVector& permB, ColumnVector& resid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit); template octave_idx_type EigsRealSymmetricMatrixShift<SparseMatrix> (const SparseMatrix& m, double sigma, octave_idx_type k, octave_idx_type p, octave_idx_type& info, Matrix& eig_vec, ColumnVector& eig_val, const SparseMatrix& _b, ColumnVector& permB, ColumnVector& resid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit); template octave_idx_type EigsRealNonSymmetricMatrix<SparseMatrix> (const SparseMatrix& m, const std::string typ, octave_idx_type k, octave_idx_type p, octave_idx_type& info, ComplexMatrix& eig_vec, ComplexColumnVector& eig_val, const SparseMatrix& _b, ColumnVector& permB, ColumnVector& resid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit); template octave_idx_type EigsRealNonSymmetricMatrixShift<SparseMatrix> (const SparseMatrix& m, double sigmar, octave_idx_type k, octave_idx_type p, octave_idx_type& info, ComplexMatrix& eig_vec, ComplexColumnVector& eig_val, const SparseMatrix& _b, ColumnVector& permB, ColumnVector& resid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit); // ComplexMatrix template octave_idx_type EigsComplexNonSymmetricMatrix<ComplexMatrix> (const ComplexMatrix& m, const std::string typ, octave_idx_type k, octave_idx_type p, octave_idx_type& info, ComplexMatrix& eig_vec, ComplexColumnVector& eig_val, const ComplexMatrix& _b, ColumnVector& permB, ComplexColumnVector& cresid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit); template octave_idx_type EigsComplexNonSymmetricMatrixShift<ComplexMatrix> (const ComplexMatrix& m, Complex sigma, octave_idx_type k, octave_idx_type p, octave_idx_type& info, ComplexMatrix& eig_vec, ComplexColumnVector& eig_val, const ComplexMatrix& _b, ColumnVector& permB, ComplexColumnVector& cresid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit); // SparseComplexMatrix template octave_idx_type EigsComplexNonSymmetricMatrix<SparseComplexMatrix> (const SparseComplexMatrix& m, const std::string typ, octave_idx_type k, octave_idx_type p, octave_idx_type& info, ComplexMatrix& eig_vec, ComplexColumnVector& eig_val, const SparseComplexMatrix& _b, ColumnVector& permB, ComplexColumnVector& cresid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit); template octave_idx_type EigsComplexNonSymmetricMatrixShift<SparseComplexMatrix> (const SparseComplexMatrix& m, Complex sigma, octave_idx_type k, octave_idx_type p, octave_idx_type& info, ComplexMatrix& eig_vec, ComplexColumnVector& eig_val, const SparseComplexMatrix& _b, ColumnVector& permB, ComplexColumnVector& cresid, std::ostream& os, double tol, bool rvec, bool cholB, int disp, int maxit); #endif