Mercurial > octave
view libinterp/corefcn/eig.cc @ 22407:34ce5be04942
maint: Style check C++ code in libinterp/.
* build-env.h, build-env.in.cc, builtins.h, Cell.cc, Cell.h, __contourc__.cc,
__dispatch__.cc, __dsearchn__.cc, __ilu__.cc, __lin_interpn__.cc, __luinc__.cc,
__magick_read__.cc, __pchip_deriv__.cc, __qp__.cc, balance.cc,
base-text-renderer.h, besselj.cc, bitfcns.cc, bsxfun.cc, c-file-ptr-stream.cc,
c-file-ptr-stream.h, call-stack.cc, call-stack.h, cdisplay.c, cdisplay.h,
cellfun.cc, coct-hdf5-types.c, comment-list.cc, comment-list.h, conv2.cc,
daspk.cc, dasrt.cc, dassl.cc, data.cc, data.h, debug.cc, debug.h, defaults.cc,
defaults.in.h, defun-dld.h, defun-int.h, defun.h, det.cc, dirfns.cc, dirfns.h,
display.cc, display.h, dlmread.cc, dynamic-ld.cc, dynamic-ld.h, eig.cc,
error.cc, error.h, errwarn.h, event-queue.cc, event-queue.h, fft.cc, fft2.cc,
fftn.cc, file-io.cc, file-io.h, filter.cc, find.cc, ft-text-renderer.cc,
ft-text-renderer.h, gammainc.cc, gcd.cc, getgrent.cc, getpwent.cc, givens.cc,
gl-render.cc, gl-render.h, gl2ps-print.cc, gl2ps-print.h, graphics.cc,
graphics.in.h, gripes.h, gsvd.cc, hash.cc, help.cc, help.h, hess.cc,
hex2num.cc, hook-fcn.cc, hook-fcn.h, input.cc, input.h, interpreter.cc,
interpreter.h, inv.cc, jit-ir.cc, jit-ir.h, jit-typeinfo.cc, jit-typeinfo.h,
jit-util.cc, jit-util.h, kron.cc, load-path.cc, load-path.h, load-save.cc,
load-save.h, lookup.cc, ls-ascii-helper.cc, ls-ascii-helper.h, ls-hdf5.cc,
ls-hdf5.h, ls-mat-ascii.cc, ls-mat-ascii.h, ls-mat4.cc, ls-mat4.h, ls-mat5.h,
ls-oct-binary.cc, ls-oct-binary.h, ls-oct-text.cc, ls-oct-text.h, ls-utils.cc,
ls-utils.h, lsode.cc, lu.cc, matrix_type.cc, max.cc, mex.cc, mex.h, mexproto.h,
mgorth.cc, mxarray.in.h, nproc.cc, oct-errno.h, oct-errno.in.cc, oct-fstrm.cc,
oct-fstrm.h, oct-handle.h, oct-hdf5-types.cc, oct-hdf5-types.h, oct-hdf5.h,
oct-hist.cc, oct-hist.h, oct-iostrm.cc, oct-iostrm.h, oct-lvalue.cc,
oct-lvalue.h, oct-map.h, oct-obj.h, oct-opengl.h, oct-prcstrm.cc,
oct-prcstrm.h, oct-procbuf.cc, oct-procbuf.h, oct-stdstrm.h, oct-stream.cc,
oct-stream.h, oct-strstrm.cc, oct-strstrm.h, oct.h, octave-default-image.h,
octave-link.h, octave-preserve-stream-state.h, ordschur.cc, pager.cc, pager.h,
pinv.cc, pr-output.cc, pr-output.h, procstream.cc, procstream.h, profiler.h,
psi.cc, pt-jit.cc, pt-jit.h, quad.cc, quadcc.cc, qz.cc, rand.cc, rcond.cc,
regexp.cc, schur.cc, sighandlers.cc, sighandlers.h, sparse-xdiv.cc,
sparse-xdiv.h, sparse-xpow.cc, sparse-xpow.h, sparse.cc, spparms.cc, sqrtm.cc,
str2double.cc, strfind.cc, strfns.cc, sub2ind.cc, svd.cc, sylvester.cc,
symtab.cc, symtab.h, syscalls.cc, sysdep.cc, sysdep.h, text-renderer.cc,
text-renderer.h, time.cc, toplev.cc, toplev.h, tril.cc, tsearch.cc, txt-eng.cc,
txt-eng.h, typecast.cc, urlwrite.cc, utils.cc, utils.h, variables.cc,
variables.h, workspace-element.h, xdiv.cc, xdiv.h, xnorm.cc, xnorm.h, xpow.cc,
xpow.h, zfstream.cc, zfstream.h, deprecated-config.h, __delaunayn__.cc,
__eigs__.cc, __fltk_uigetfile__.cc, __glpk__.cc, __init_fltk__.cc,
__init_gnuplot__.cc, __osmesa_print__.cc, __voronoi__.cc, amd.cc,
audiodevinfo.cc, audioread.cc, ccolamd.cc, chol.cc, colamd.cc, convhulln.cc,
dmperm.cc, fftw.cc, gzip.cc, oct-qhull.h, qr.cc, symbfact.cc, symrcm.cc,
liboctinterp-build-info.h, liboctinterp-build-info.in.cc, ov-base-diag.h,
ov-base-int.cc, ov-base-int.h, ov-base-mat.cc, ov-base-mat.h, ov-base-scalar.h,
ov-base-sparse.cc, ov-base-sparse.h, ov-base.cc, ov-base.h, ov-bool-mat.cc,
ov-bool-mat.h, ov-bool-sparse.cc, ov-bool-sparse.h, ov-bool.cc, ov-bool.h,
ov-builtin.cc, ov-builtin.h, ov-cell.cc, ov-cell.h, ov-ch-mat.cc, ov-ch-mat.h,
ov-class.cc, ov-class.h, ov-classdef.cc, ov-classdef.h, ov-colon.cc,
ov-colon.h, ov-complex.cc, ov-complex.h, ov-cs-list.h, ov-cx-diag.cc,
ov-cx-diag.h, ov-cx-mat.cc, ov-cx-mat.h, ov-cx-sparse.cc, ov-cx-sparse.h,
ov-dld-fcn.cc, ov-dld-fcn.h, ov-fcn-handle.cc, ov-fcn-handle.h,
ov-fcn-inline.cc, ov-fcn-inline.h, ov-fcn.cc, ov-fcn.h, ov-float.cc,
ov-float.h, ov-flt-complex.cc, ov-flt-complex.h, ov-flt-cx-diag.cc,
ov-flt-cx-diag.h, ov-flt-cx-mat.cc, ov-flt-cx-mat.h, ov-flt-re-diag.cc,
ov-flt-re-diag.h, ov-flt-re-mat.cc, ov-flt-re-mat.h, ov-int-traits.h,
ov-int16.cc, ov-int16.h, ov-int32.cc, ov-int32.h, ov-int64.cc, ov-int64.h,
ov-int8.cc, ov-int8.h, ov-intx.h, ov-java.cc, ov-java.h, ov-lazy-idx.cc,
ov-lazy-idx.h, ov-mex-fcn.cc, ov-mex-fcn.h, ov-null-mat.cc, ov-null-mat.h,
ov-oncleanup.cc, ov-oncleanup.h, ov-perm.cc, ov-perm.h, ov-range.cc,
ov-range.h, ov-re-diag.cc, ov-re-diag.h, ov-re-mat.cc, ov-re-mat.h,
ov-re-sparse.cc, ov-re-sparse.h, ov-scalar.cc, ov-scalar.h, ov-str-mat.cc,
ov-str-mat.h, ov-struct.cc, ov-struct.h, ov-typeinfo.cc, ov-typeinfo.h,
ov-uint16.cc, ov-uint16.h, ov-uint32.cc, ov-uint32.h, ov-uint64.cc,
ov-uint64.h, ov-uint8.cc, ov-uint8.h, ov-usr-fcn.cc, ov-usr-fcn.h, ov.h,
ovl.cc, ovl.h, octave.cc, octave.h, 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-pm.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-fcdm-fcdm.cc, op-fcm-fcm.cc,
op-fcm-fcs.cc, op-fcm-fm.cc, op-fcm-fs.cc, op-fcm-pm.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-fm-fcm.cc, op-fm-fcs.cc, op-fm-fm.cc, op-fm-fs.cc, op-fm-pm.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.h,
op-m-cm.cc, op-m-cs.cc, op-m-m.cc, op-m-pm.cc, op-m-s.cc, op-m-scm.cc,
op-m-sm.cc, op-pm-cm.cc, op-pm-fcm.cc, op-pm-fm.cc, op-pm-m.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,
ops.h, options-usage.h, lex.h, parse.h, pt-all.h, pt-arg-list.cc,
pt-arg-list.h, pt-array-list.h, pt-assign.cc, pt-assign.h, pt-binop.cc,
pt-binop.h, pt-bp.cc, pt-bp.h, pt-cbinop.cc, pt-cbinop.h, pt-cell.cc,
pt-cell.h, pt-check.cc, pt-check.h, pt-classdef.cc, pt-classdef.h, pt-cmd.cc,
pt-cmd.h, pt-colon.cc, pt-colon.h, pt-const.cc, pt-const.h, pt-decl.cc,
pt-decl.h, pt-eval.cc, pt-eval.h, pt-except.cc, pt-except.h, pt-exp.cc,
pt-exp.h, pt-fcn-handle.cc, pt-fcn-handle.h, pt-funcall.cc, pt-funcall.h,
pt-id.cc, pt-id.h, pt-idx.cc, pt-idx.h, pt-jump.cc, pt-jump.h, pt-loop.cc,
pt-loop.h, pt-mat.cc, pt-mat.h, pt-misc.cc, pt-misc.h, pt-pr-code.cc,
pt-pr-code.h, pt-select.cc, pt-select.h, pt-stmt.cc, pt-stmt.h, pt-unop.cc,
pt-unop.h, pt-walk.h, pt.cc, pt.h, token.cc, token.h, Array-jit.cc,
Array-tc.cc, version.cc, version.in.h:
Style check C++ code in libinterp/
author | Rik <rik@octave.org> |
---|---|
date | Tue, 30 Aug 2016 21:46:47 -0700 |
parents | bac0d6f07a3e |
children | 3a2b891d0b33 e9a0469dedd9 |
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/* Copyright (C) 1996-2016 John W. Eaton Copyright (C) 2016 Barbara Lócsi 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 "defun.h" #include "error.h" #include "errwarn.h" #include "ovl.h" #include "EIG.h" #include "fEIG.h" #include "oct-string.h" DEFUN (eig, args, nargout, doc: /* -*- texinfo -*- @deftypefn {} {@var{lambda} =} eig (@var{A}) @deftypefnx {} {@var{lambda} =} eig (@var{A}, @var{B}) @deftypefnx {} {[@var{V}, @var{lambda}] =} eig (@var{A}) @deftypefnx {} {[@var{V}, @var{lambda}] =} eig (@var{A}, @var{B}) @deftypefnx {} {[@var{V}, @var{lambda}, @var{W}] =} eig (@var{A}) @deftypefnx {} {[@var{V}, @var{lambda}, @var{W}] =} eig (@var{A}, @var{B}) @deftypefnx {} {[@dots{}] =} eig (@var{A}, @var{balanceOption}) @deftypefnx {} {[@dots{}] =} eig (@var{A}, @var{B}, @var{algorithm}) @deftypefnx {} {[@dots{}] =} eig (@dots{}, @var{eigvalOption}) Compute the right eigenvalues(V) and optionally the eigenvectors(lambda) and the left eigenvalues(W) of a matrix or a pair of matrices. The flag @var{balanceOption} can be one of: @table @asis @item @qcode{"balance"} Preliminary balancing is on. (default) @item @qcode{"nobalance"} Disables preliminary balancing. @end table The flag @var{eigvalOption} can be one of: @table @asis @item @qcode{"matrix"} Return the eigenvalues in a diagonal matrix. (default if 2 or 3 outputs are specified) @item @qcode{"vector"} Return the eigenvalues in a column vector. (default if 1 output is specified, e.g. @var{lambda} = eig (@var{A})) @end table The flag @var{algorithm} can be one of: @table @asis @item @qcode{"chol"} Uses the Cholesky factorization of B. (default if A is symmetric (Hermitian) and B is symmetric (Hermitian) positive definite) @item @qcode{"qz"} Uses the QZ algorithm. (When A or B are not symmetric always the QZ algorithm will be used) @end table @multitable @columnfractions .31 .23 .23 .23 @headitem @tab no flag @tab chol @tab qz @item both are symmetric @tab @qcode{"chol"} @tab @qcode{"chol"} @tab @qcode{"qz"} @item at least one is not symmetric @tab @qcode{"qz"} @tab @qcode{"qz"} @tab @qcode{"qz"} @end multitable The eigenvalues returned by @code{eig} are not ordered. @seealso{eigs, svd} @end deftypefn */) { int nargin = args.length (); if (nargin > 4 || nargin == 0) print_usage (); octave_value_list retval; octave_value arg_a, arg_b; arg_a = args(0); if (arg_a.is_empty ()) return octave_value_list (2, Matrix ()); if (! arg_a.is_float_type ()) err_wrong_type_arg ("eig", arg_a); if (arg_a.rows () != arg_a.columns ()) err_square_matrix_required ("eig", "A"); // determine if it's AEP or GEP bool AEPcase = nargin == 1 || args(1).is_string (); if (! AEPcase) { arg_b = args(1); if (arg_b.is_empty ()) return octave_value_list (2, Matrix ()); if (! arg_b.is_float_type ()) err_wrong_type_arg ("eig", arg_b); if (arg_b.rows () != arg_b.columns ()) err_square_matrix_required ("eig", "B"); } bool qz_flag = false; bool chol_flag = false; bool balance_flag = false; bool no_balance_flag = false; bool matrix_flag = false; bool vector_flag = false; for (int i = (AEPcase ? 1 : 2); i < args.length (); ++i) { if (! args(i).is_string ()) err_wrong_type_arg ("eig", args(i)); std::string arg_i = args(i).string_value (); if (octave::string::strcmpi (arg_i, "qz")) qz_flag = true; else if (octave::string::strcmpi (arg_i, "chol")) chol_flag = true; else if (octave::string::strcmpi (arg_i, "balance")) balance_flag = true; else if (octave::string::strcmpi (arg_i, "nobalance")) no_balance_flag = true; else if (octave::string::strcmpi (arg_i, "matrix")) matrix_flag = true; else if (octave::string::strcmpi (arg_i, "vector")) vector_flag = true; else error ("eig: invalid option \"%s\"", arg_i.c_str ()); } if (balance_flag && no_balance_flag) error ("eig: \"balance\" and \"nobalance\" options are mutually exclusive"); if (vector_flag && matrix_flag) error ("eig: \"vector\" and \"matrix\" options are mutually exclusive"); if (qz_flag && chol_flag) error ("eig: \"qz\" and \"chol\" options are mutually exclusive"); if (AEPcase) { if (qz_flag) error ("eig: invalid \"qz\" option for algebraic eigenvalue problem"); if (chol_flag) error ("eig: invalid \"chol\" option for algebraic eigenvalue problem"); } else { if (balance_flag) error ("eig: invalid \"balance\" option for generalized eigenvalue problem"); if (no_balance_flag) error ("eig: invalid \"nobalance\" option for generalized eigenvalue problem"); } // Default is to balance const bool balance = no_balance_flag ? false : true; const bool force_qz = qz_flag; Matrix tmp_a, tmp_b; ComplexMatrix ctmp_a, ctmp_b; FloatMatrix ftmp_a, ftmp_b; FloatComplexMatrix fctmp_a, fctmp_b; if (arg_a.is_single_type ()) { FloatEIG result; if (AEPcase) { if (arg_a.is_real_type ()) { ftmp_a = arg_a.float_matrix_value (); result = FloatEIG (ftmp_a, nargout > 1, nargout > 2, balance); } else { fctmp_a = arg_a.float_complex_matrix_value (); result = FloatEIG (fctmp_a, nargout > 1, nargout > 2, balance); } } else { if (arg_a.is_real_type () && arg_b.is_real_type ()) { ftmp_a = arg_a.float_matrix_value (); ftmp_b = arg_b.float_matrix_value (); result = FloatEIG (ftmp_a, ftmp_b, nargout > 1, nargout > 2, force_qz); } else { fctmp_a = arg_a.float_complex_matrix_value (); fctmp_b = arg_b.float_complex_matrix_value (); result = FloatEIG (fctmp_a, fctmp_b, nargout > 1, nargout > 2, force_qz); } } if (nargout == 0 || nargout == 1) { if (matrix_flag) retval = ovl (FloatComplexDiagMatrix (result.eigenvalues ())); else retval = ovl (result.eigenvalues ()); } else if (nargout == 2) { if (vector_flag) retval = ovl (result.right_eigenvectors (), result.eigenvalues ()); else retval = ovl (result.right_eigenvectors (), FloatComplexDiagMatrix (result.eigenvalues ())); } else { if (vector_flag) retval = ovl (result.right_eigenvectors (), result.eigenvalues (), result.left_eigenvectors ()); else retval = ovl (result.right_eigenvectors (), FloatComplexDiagMatrix (result.eigenvalues ()), result.left_eigenvectors ()); } } else { EIG result; if (AEPcase) { if (arg_a.is_real_type ()) { tmp_a = arg_a.matrix_value (); result = EIG (tmp_a, nargout > 1, nargout > 2, balance); } else { ctmp_a = arg_a.complex_matrix_value (); result = EIG (ctmp_a, nargout > 1, nargout > 2, balance); } } else { if (arg_a.is_real_type () && arg_b.is_real_type ()) { tmp_a = arg_a.matrix_value (); tmp_b = arg_b.matrix_value (); result = EIG (tmp_a, tmp_b, nargout > 1, nargout > 2, force_qz); } else { ctmp_a = arg_a.complex_matrix_value (); ctmp_b = arg_b.complex_matrix_value (); result = EIG (ctmp_a, ctmp_b, nargout > 1, nargout > 2, force_qz); } } if (nargout == 0 || nargout == 1) { if (matrix_flag) retval = ovl (ComplexDiagMatrix (result.eigenvalues ())); else retval = ovl (result.eigenvalues ()); } else if (nargout == 2) { if (vector_flag) retval = ovl (result.right_eigenvectors (), result.eigenvalues ()); else retval = ovl (result.right_eigenvectors (), ComplexDiagMatrix (result.eigenvalues ())); } else { if (vector_flag) retval = ovl (result.right_eigenvectors (), result.eigenvalues (), result.left_eigenvectors ()); else retval = ovl (result.right_eigenvectors (), ComplexDiagMatrix (result.eigenvalues ()), result.left_eigenvectors ()); } } return retval; } /* %!assert (eig ([1, 2; 2, 1]), [-1; 3], sqrt (eps)) %!test %! [v, d] = eig ([1, 2; 2, 1]); %! x = 1 / sqrt (2); %! assert (d, [-1, 0; 0, 3], sqrt (eps)) %! assert (v, [-x, x; x, x], sqrt (eps)) %!test %! [v, d, w] = eig ([1, 2; 2, 1]); %! x = 1 / sqrt (2); %! assert (w, [-x, x; x, x], sqrt (eps)) %!test %! [v, d] = eig ([1, 2; 2, 1], "balance"); %! x = 1 / sqrt (2); %! assert (d, [-1, 0; 0, 3], sqrt (eps)) %! assert (v, [-x, x; x, x], sqrt (eps)) %!test %! [v, d, w] = eig ([1, 2; 2, 1], "balance"); %! x = 1 / sqrt (2); %! assert (w, [-x, x; x, x], sqrt (eps)); %!assert (eig (single ([1, 2; 2, 1])), single ([-1; 3]), sqrt (eps ("single"))) %!assert (eig (single ([1, 2; 2, 1]), "balance"), %! single ([-1; 3]), sqrt (eps ("single"))) %!test %! [v, d] = eig (single ([1, 2; 2, 1])); %! x = single (1 / sqrt (2)); %! assert (d, single ([-1, 0; 0, 3]), sqrt (eps ("single"))) %! assert (v, [-x, x; x, x], sqrt (eps ("single"))) %!test %! [v, d, w] = eig (single ([1, 2; 2, 1])); %! x = single (1 / sqrt (2)); %! assert (w, [-x, x; x, x], sqrt (eps ("single"))) %!test %! [v, d] = eig (single ([1, 2; 2, 1]), "balance"); %! x = single (1 / sqrt (2)); %! assert (d, single ([-1, 0; 0, 3]), sqrt (eps ("single"))); %! assert (v, [-x, x; x, x], sqrt (eps ("single"))) %!test %! [v, d, w] = eig (single ([1, 2; 2, 1]), "balance"); %! x = single (1 / sqrt (2)); %! assert (w, [-x, x; x, x], sqrt (eps ("single"))) ## If (at least one of) the matrices are non-symmetric, ## regardless the algorithm flag the qz algorithm should be used. ## So the results without algorithm flag, with "qz" and with "chol" ## should be the same. %!function nonsym_chol_2_output (A, B, res = sqrt (eps)) %! [v, d] = eig (A, B); %! [v2, d2] = eig (A, B, "qz"); %! [v3, d3] = eig (A, B, "chol"); %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), res) %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), res) %! assert (v, v2) %! assert (v, v3) %! assert (d, d2) %! assert (d, d3) %!endfunction %!test nonsym_chol_2_output ([1, 2; -1, 1], [3, 3; 1, 2]) %!test nonsym_chol_2_output ([1+3i, 2+3i; 3-8i, 8+3i], [8+i, 3+i; 4-9i, 3+i]) %!test nonsym_chol_2_output ([1, 2; 3, 8], [8, 3; 4, 3]) %!test nonsym_chol_2_output (single ([1, 2; -1, 1]), %! single ([3, 3; 1, 2]), sqrt (eps ("single"))) %!test nonsym_chol_2_output (single ([1+3i, 2+3i; 3-8i, 8+3i]), %! single ([8+i, 3+i; 4-9i, 3+i]), %! sqrt (eps ("single"))) %!function nonsym_chol_3_output (A, B, res = sqrt (eps)) %! [v, d, w] = eig (A, B); %! [v2, d2, w2] = eig (A, B, "qz"); %! [v3, d3, w3] = eig (A, B, "chol"); %! wt = w'; %! assert (wt(1, :)* A, d(1, 1) * wt(1, :) * B, res) %! assert (wt(2, :)* A, d(2, 2) * wt(2, :) * B, res) %! assert (v, v2) %! assert (v, v3) %! assert (d, d2) %! assert (d, d3) %! assert (w, w2) %! assert (w, w3) %!endfunction %!test nonsym_chol_3_output ([1, 2; -1, 1], [3, 3; 1, 2]) %!test nonsym_chol_3_output ([1+3i, 2+3i; 3-8i, 8+3i], [8+i, 3+i; 4-9i, 3+i]) %!test nonsym_chol_3_output ([1, 2; 3, 8], [8, 3; 4, 3]) %!test nonsym_chol_3_output (single ([1, 2; -1, 1]), %! single ([3, 3; 1, 2]), sqrt (eps ("single"))) %!test nonsym_chol_3_output (single ([1+3i, 2+3i; 3-8i, 8+3i]), %! single ([8+i, 3+i; 4-9i, 3+i]), %! sqrt (eps ("single"))) ## If the matrices are symmetric, ## then the chol method is default. ## So the results without algorithm flag and with "chol" should be the same. %!function sym_chol_2_input (A, B, res = sqrt (eps)) %! [v, d] = eig (A, B); %! [v2, d2] = eig (A, B, "chol"); %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), res) %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), res) %! assert (v, v2) %! assert (d, d2) %!endfunction %!test sym_chol_2_input ([1, 2; 2, 1], [3, -2; -2, 3]) %!test sym_chol_2_input ([1+3i, 2+i; 2-i, 1+3i], [5+9i, 2+i; 2-i, 5+9i]) %!test sym_chol_2_input ([1, 1+i; 1-i, 1], [2, 0; 0, 2]) %!test sym_chol_2_input (single ([1, 2; 2, 1]), single ([3, -2; -2, 3]), %! sqrt (eps ("single"))) %!test sym_chol_2_input (single ([1+3i, 2+i; 2-i, 1+3i]), %! single ([5+9i, 2+i; 2-i, 5+9i]), sqrt (eps ("single"))) %!test sym_chol_2_input (single ([1, 1+i; 1-i, 1]), single ([2, 0; 0, 2]), %! sqrt (eps ("single"))) %!function sym_chol_3_input (A, B, res = sqrt (eps)) %! [v, d, w] = eig (A, B); %! [v2, d2, w2] = eig (A, B, "chol"); %! wt = w'; %! assert (wt(1, :)* A, d(1, 1) * wt(1, :) * B, res) %! assert (wt(2, :)* A, d(2, 2) * wt(2, :) * B, res) %! assert (v, v2) %! assert (d, d2) %! assert (w, w2) %!endfunction %!test sym_chol_3_input ([1, 2; 2, 1], [3, -2; -2, 3]) %!test sym_chol_3_input ([1+3i, 2+i; 2-i, 1+3i], [5+9i, 2+i; 2-i, 5+9i]) %!test sym_chol_3_input ([1, 1+i; 1-i, 1], [2, 0; 0, 2]) %!test sym_chol_3_input (single ([1, 2; 2, 1]), single ([3, -2; -2, 3]), %! sqrt (eps ("single"))) %!test sym_chol_3_input (single ([1+3i, 2+i; 2-i, 1+3i]), %! single ([5+9i, 2+i; 2-i, 5+9i]), sqrt (eps ("single"))) %!test sym_chol_3_input (single ([1, 1+i; 1-i, 1]), single ([2, 0; 0, 2]), %! sqrt (eps ("single"))) ## "balance" is always default ## so the results with and without "balance" should be the same ## while in this case "nobalance" should produce different result %!test %! A = [3 -2 -0.9 0; -2 4 1 -0; -0 0 -1 0; -0.5 -0.5 0.1 1]; %! [V1, D1] = eig (A); %! [V2, D2] = eig (A, "balance"); %! [V3, D3] = eig (A, "nobalance"); %! assert (V1, V2) %! assert (D1, D2) %! assert (isequal (V2, V3), false) ## Testing the flags in all combination. ## If 2 flags are on, than the result should be the same regardless ## of the flags order. ## option1 represents the first order while option2 represents the other order. ## d and d2 should be a diagonal matrix if "matrix" flag is on while ## these should be column vectors if the "vector" flag is on. %!function test_eig_args (args, options1, options2, testd = @() true) %! [v, d, w] = eig (args{:}, options1{:}); %! [v2, d2, w2] = eig (args{:}, options2{:}); %! assert (testd (d)) %! assert (testd (d2)) %! assert (v, v2) %! assert (d, d2) %! assert (w, w2) %!endfunction %!function qz_chol_with_shapes (A, B) %! for shapes = struct ("name", {"vector", "matrix"}, %! "test", {@isvector, @isdiag}) %! test_eig_args ({A, B}, {"qz", shapes.name}, %! {shapes.name, "qz"}, shapes.test); %! test_eig_args ({A, B}, {"chol", shapes.name}, %! {shapes.name, "chol"}, shapes.test); %! endfor %!endfunction %!function balance_nobalance_with_shapes (A) %! for shapes = struct ("name", {"vector", "matrix"}, %! "test", {@isvector, @isdiag}) %! test_eig_args ({A}, {"balance", shapes.name}, %! {shapes.name, "balance"}, shapes.test); %! test_eig_args ({A}, {"nobalance", shapes.name}, %! {shapes.name, "nobalance"}, shapes.test); %! endfor %!endfunction ## Default return format: ## diagonal matrix if 2 or 3 outputs are specified ## column vector if 1 output is specified %!function test_shapes (args) %! d = eig (args{:}); %! assert (isvector(d)) %! d2 = eig (args{:}, "vector"); %! assert (isvector(d2)) %! [v, d3] = eig (args{:}); %! assert (isdiag(d3)) %! d4 = eig (args{:}, "matrix"); %! assert (isdiag(d4)) %! [v, d5, w] = eig (args{:}); %! assert (isdiag(d5)) %! d6 = eig (args{:}, "matrix"); %! assert (isdiag(d6)) %! assert (d, d2) %! assert (d3, d4) %! assert (d5, d6) %! assert (d, diag(d3)) %! assert (d, diag(d5)) %!endfunction %!function shapes_AEP (A) %! test_shapes({A}); %!endfunction %!function shapes_GEP (A, B) %! test_shapes({A, B}); %!endfunction %!test balance_nobalance_with_shapes ([1, 2; 2, 1]); %!test balance_nobalance_with_shapes (single ([1, 2; 2, 1])); %!test shapes_AEP ([1, 2; 2, 1]); %!test shapes_AEP (single ([1, 2; 2, 1])); %!test qz_chol_with_shapes ([1, 1+i; 1-i, 1], [2, 0; 0, 2]); %!test qz_chol_with_shapes ([1, 2; 3, 8], [8, 3; 4, 3]); %!test qz_chol_with_shapes ([1, 2; -1, 1], [3, 3; 1, 2]); %!test qz_chol_with_shapes (single ([1, 1+i; 1-i, 1]), single ([2, 0; 0, 2])); %!test qz_chol_with_shapes (single ([1, 2; 3, 8]), single ([8, 3; 4, 3])); %!test qz_chol_with_shapes (single ([1, 2; -1, 1]), single ([3, 3; 1, 2])); %!test shapes_GEP ([1, 1+i; 1-i, 1], [2, 0; 0, 2]); %!test shapes_GEP ([1, 2; 3, 8], [8, 3; 4, 3]); %!test shapes_GEP ([1, 2; -1, 1], [3, 3; 1, 2]); %!test shapes_GEP (single ([1, 1+i; 1-i, 1]), single ([2, 0; 0, 2])); %!test shapes_GEP (single ([1, 2; 3, 8]), single ([8, 3; 4, 3])); %!test shapes_GEP (single ([1, 2; -1, 1]), single ([3, 3; 1, 2])); %!function chol_qz_accuracy (A, B, is_qz_accurate, is_chol_accurate) %! [V1,D1] = eig (A,B, 'qz'); %! [V2,D2] = eig (A,B); #default is chol %! assert (isequal (A*V1,A*V1*D1), is_qz_accurate) %! assert (isequal (A*V2, A*V2*D2), is_chol_accurate) %!endfunction %!test %! minij_100 = gallery('minij',100); %! chol_qz_accuracy (minij_100, minij_100, false, true); %!test %! moler_100 = gallery('moler',100); %! chol_qz_accuracy (moler_100, moler_100, false, true); %!test %! A = diag([10^-16, 10^-15]); %! chol_qz_accuracy (A, A, true, false); %!error eig () %!error eig (false) %!error eig ([1, 2; 3, 4], [4, 3; 2, 1], 1) %!error <EIG requires same size matrices> %! eig ([1, 2; 3, 4], 2) %!error <must be a square matrix> %! eig ([1, 2; 3, 4; 5, 6]) %!error <wrong type argument> %! eig ("abcd") %!error <invalid option "abcd"> %! eig ([1 2 ; 2 3], "abcd") %!error <invalid "chol" option for algebraic eigenvalue problem> %! eig ([1 2 ; 2 3], "chol") %!error <invalid "qz" option for algebraic eigenvalue problem> %! eig ([1 2 ; 2 3], "qz") %!error <wrong type argument> %! eig (false, [1 2 ; 2 3]) %!error <invalid option "abcd"> %! eig ([1 2 ; 2 3], [1 2 ; 2 3], "abcd") %!error <invalid "qz" option for algebraic eigenvalue problem> %! eig ([1 2 ; 2 3], "balance", "qz") %!error <invalid option "abcd"> %! eig ([1 2 ; 2 3], [1 2 ; 2 3], "vector", "abcd") %!error <invalid option "abcd"> %! eig ([1 2 ; 2 3], "balance", "matrix", "abcd") %!error <"balance" and "nobalance" options are mutually exclusive> %! eig ([1 2 ; 2 3], "balance", "nobalance") %!error <"balance" and "nobalance" options are mutually exclusive> %! eig ([1 2 ; 2 3], "nobalance", "balance") %!error <"vector" and "matrix" options are mutually exclusive> %! eig ([1 2 ; 2 3], "matrix", "vector") %!error <"vector" and "matrix" options are mutually exclusive> %! eig ([1 2 ; 2 3], "vector", "matrix") %!error <"vector" and "matrix" options are mutually exclusive> %! eig ([1 2 ; 2 3], [1 2 ; 2 3], "matrix", "vector") %!error <"vector" and "matrix" options are mutually exclusive> %! eig ([1 2 ; 2 3], [1 2 ; 2 3], "vector", "matrix") %!error <wrong type argument> %! eig ([1 2 ; 2 3], [1 2 ; 2 3], false) %!error <wrong type argument> %! eig ([1 2 ; 2 3], [1 2 ; 2 3], [1 2 ; 2 3]) */