Mercurial > octave
view libinterp/corefcn/__ilu__.cc @ 21724:aba2e6293dd8
use "#if ..." consistently instead of "#ifdef" and "#ifndef"
* configure.ac, Doxyfile.in, make_int.cc, 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, __init_qt__.cc,
annotation-dialog.cc, gl-select.cc, module.mk, 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,
liboctgui-build-info.in.cc, file-editor-tab.cc, file-editor.cc,
find-dialog.cc, marker.cc, marker.h, 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.in.cc, Cell.cc, __contourc__.cc,
__dispatch__.cc, __dsearchn__.cc, __ichol__.cc, __ilu__.cc,
__lin_interpn__.cc, __luinc__.cc, __magick_read__.cc,
__pchip_deriv__.cc, __qp__.cc, balance.cc, besselj.cc, betainc.cc,
bitfcns.cc, bsxfun.cc, c-file-ptr-stream.cc, c-file-ptr-stream.h,
cdisplay.c, cdisplay.h, 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, defaults.in.h, 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, input.cc, 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-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-oct-text.h, ls-utils.cc,
lsode.cc, lu.cc, mappers.cc, matrix_type.cc, max.cc, mex.cc, mex.h,
mexproto.h, mgorth.cc, nproc.cc, oct-errno.in.cc, oct-fstrm.cc,
oct-hdf5-types.cc, oct-hdf5-types.h, oct-hist.cc, oct-iostrm.cc,
oct-lvalue.cc, oct-map.cc, oct-prcstrm.cc, oct-procbuf.cc,
oct-stdstrm.h, 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, pt-jit.h, quad.cc, quadcc.cc, qz.cc, rand.cc, rcond.cc,
regexp.cc, schur.cc, sighandlers.cc, sighandlers.h, siglist.c,
siglist.h, 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, zfstream.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, qr.cc, symbfact.cc, symrcm.cc,
liboctinterp-build-info.in.cc, mkbuiltins, mkops, 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-usr-fcn.h, ov.cc, ovl.cc, 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-cdm-cm.cc, op-cdm-dm.cc,
op-cdm-m.cc, op-cell.cc, op-chm.cc, op-class.cc, op-cm-cdm.cc,
op-cm-cm.cc, op-cm-cs.cc, op-cm-dm.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-cdm.cc, op-dm-cm.cc,
op-dm-dm.cc, op-dm-m.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-fcm.cc, op-fcdm-fdm.cc, op-fcdm-fm.cc,
op-fcm-fcdm.cc, op-fcm-fcm.cc, op-fcm-fcs.cc, op-fcm-fdm.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-fcdm.cc, op-fdm-fcm.cc,
op-fdm-fdm.cc, op-fdm-fm.cc, op-float-conv.cc, op-fm-fcdm.cc,
op-fm-fcm.cc, op-fm-fcs.cc, op-fm-fdm.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-cdm.cc, op-m-cm.cc, op-m-cs.cc, op-m-dm.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-loop.h, 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-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, MArray-C.cc, MArray-d.cc, MArray-f.cc,
MArray-fC.cc, MArray-i.cc, MArray-s.cc, MSparse-C.cc, MSparse-d.cc,
MatrixType.cc, PermMatrix.cc, Range.cc, Sparse-C.cc, Sparse-b.cc,
Sparse-d.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,
dim-vector.h, 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,
uint16NDArray.cc, uint32NDArray.cc, uint64NDArray.cc,
uint8NDArray.cc, Faddeeva.cc, blaswrap.c, cquit.c, f77-extern.cc,
f77-fcn.c, f77-fcn.h, lo-error.c, lo-error.h, quit.cc, quit.h,
liboctave-build-info.in.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,
randmtzig.cc, randpoisson.cc, schur.cc, sparse-chol.cc,
sparse-dmsolve.cc, sparse-lu.cc, sparse-qr.cc, svd.cc, mk-ops.awk,
mx-defs.h, 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, pathlen.h, syswait.h,
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-cutils.h, lo-ieee.cc, lo-ieee.h, lo-regexp.cc, lo-utils.cc,
oct-base64.cc, oct-glob.cc, oct-inttypes.cc, oct-inttypes.h,
oct-locbuf.cc, oct-mutex.cc, oct-rl-edit.c, oct-rl-edit.h,
oct-rl-hist.c, oct-rl-hist.h, oct-shlib.cc, oct-sort.cc,
pathsearch.cc, singleton-cleanup.cc, sparse-sort.cc, sparse-util.cc,
statdefs.h, str-vec.cc, unwind-prot.cc, url-transfer.cc,
acinclude.m4, display-available.c, display-available.h, main-cli.cc,
main-gui.cc, main.in.cc, mkoctfile.in.cc, octave-build-info.in.cc,
octave-config.in.cc, shared-fcns.h:
Use "#if ..." consistently instead of "#ifdef" and "#ifndef".
author | John W. Eaton <jwe@octave.org> |
---|---|
date | Tue, 17 May 2016 12:09:30 -0400 |
parents | d7a268e68e69 |
children | 43f613cca3ab |
line wrap: on
line source
/* Copyright (C) 2014-2015 Eduardo Ramos Fernández <eduradical951@gmail.com> Copyright (C) 2013-2015 Kai T. Ohlhus <k.ohlhus@gmail.com> 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 "oct-locbuf.h" #include "defun.h" #include "error.h" #include "parse.h" // This function implements the IKJ and JKI variants of Gaussian elimination to // perform the ILUTP decomposition. The behavior is controlled by milu // parameter. If milu = ['off'|'col'] the JKI version is performed taking // advantage of CCS format of the input matrix. If milu = 'row' the input // matrix has to be transposed to obtain the equivalent CRS structure so we can // work efficiently with rows. In this case IKJ version is used. template <typename octave_matrix_t, typename T> void ilu_0 (octave_matrix_t& sm, const std::string milu = "off") { const octave_idx_type n = sm.cols (); octave_idx_type j1, j2, jrow, jw, i, j, k, jj; T tl, r; enum {OFF, ROW, COL}; char opt; if (milu == "row") { opt = ROW; sm = sm.transpose (); } else if (milu == "col") opt = COL; else opt = OFF; // Input matrix pointers octave_idx_type* cidx = sm.cidx (); octave_idx_type* ridx = sm.ridx (); T* data = sm.data (); // Working arrays OCTAVE_LOCAL_BUFFER (octave_idx_type, iw, n); OCTAVE_LOCAL_BUFFER (octave_idx_type, uptr, n); // Initialize working arrays for (i = 0; i < n; i++) iw[i] = -1; // Loop over all columns for (k = 0; k < n; k++) { j1 = cidx[k]; j2 = cidx[k+1]; if (j1 == j2) error ("ilu: A has a zero on the diagonal"); for (j = j1; j < j2; j++) iw[ridx[j]] = j; r = 0; j = j1; jrow = ridx[j1]; while ((jrow < k) && (j < j2)) { if (opt == ROW) { tl = data[j] / data[uptr[jrow]]; data[j] = tl; } for (jj = uptr[jrow] + 1; jj < cidx[jrow+1]; jj++) { jw = iw[ridx[jj]]; if (jw != -1) if (opt == ROW) data[jw] -= tl * data[jj]; else data[jw] -= data[j] * data[jj]; else // That is for the milu='row' if (opt == ROW) r += tl * data[jj]; else if (opt == COL) r += data[j] * data[jj]; } j++; jrow = ridx[j]; } uptr[k] = j; if (opt != OFF) data[uptr[k]] -= r; if (opt != ROW) for (jj = uptr[k] + 1; jj < cidx[k+1]; jj++) data[jj] /= data[uptr[k]]; if (k != jrow) error ("ilu: A has a zero on the diagonal"); if (data[j] == T(0)) error ("ilu: encountered a pivot equal to 0"); for (i = j1; i < j2; i++) iw[ridx[i]] = -1; } if (opt == ROW) sm = sm.transpose (); } DEFUN (__ilu0__, args, , "-*- texinfo -*-\n\ @deftypefn {} {[@var{L}, @var{U}] =} __ilu0__ (@var{A})\n\ @deftypefnx {} {[@var{L}, @var{U}] =} __ilu0__ (@var{A}, @var{milu})\n\ @deftypefnx {} {[@var{L}, @var{U}, @var{P}] =} __ilu0__ (@var{A}, @dots{})\n\ Undocumented internal function.\n\ @end deftypefn") { int nargin = args.length (); if (nargin < 1 || nargin > 2) print_usage (); octave_value_list retval (2); std::string milu; // In ILU0 algorithm the zero-pattern of the input matrix is preserved so // its structure does not change during the algorithm. The same input // matrix is used to build the output matrix due to that fact. octave_value_list arg_list; if (! args(0).is_complex_type ()) { SparseMatrix sm = args(0).sparse_matrix_value (); ilu_0 <SparseMatrix, double> (sm, milu); arg_list.append (sm); retval(1) = feval ("triu", arg_list)(0).sparse_matrix_value (); SparseMatrix eye = feval ("speye", ovl (sm.cols ()))(0).sparse_matrix_value (); arg_list.append (-1); retval(0) = eye + feval ("tril", arg_list)(0).sparse_matrix_value (); } else { SparseComplexMatrix sm = args(0).sparse_complex_matrix_value (); ilu_0 <SparseComplexMatrix, Complex> (sm, milu); arg_list.append (sm); retval(1) = feval ("triu", arg_list)(0).sparse_complex_matrix_value (); SparseComplexMatrix eye = feval ("speye", ovl (sm.cols ()))(0).sparse_complex_matrix_value (); arg_list.append (-1); retval(0) = eye + feval ("tril", arg_list)(0).sparse_complex_matrix_value (); } return retval; } template <typename octave_matrix_t, typename T> void ilu_crout (octave_matrix_t& sm_l, octave_matrix_t& sm_u, octave_matrix_t& L, octave_matrix_t& U, T* cols_norm, T* rows_norm, const T droptol = 0, const std::string milu = "off") { // Map the strings into chars for faster comparing inside loops char opt; enum {OFF, ROW, COL}; if (milu == "row") opt = ROW; else if (milu == "col") opt = COL; else opt = OFF; octave_idx_type jrow, i, j, k, jj, total_len_l, total_len_u, max_len_u, max_len_l, w_len_u, w_len_l, cols_list_len, rows_list_len; const octave_idx_type n = sm_u.cols (); sm_u = sm_u.transpose (); max_len_u = sm_u.nnz (); max_len_u += (0.1 * max_len_u) > n ? 0.1 * max_len_u : n; max_len_l = sm_l.nnz (); max_len_l += (0.1 * max_len_l) > n ? 0.1 * max_len_l : n; // Extract pointers to the arrays for faster access inside loops octave_idx_type* cidx_in_u = sm_u.cidx (); octave_idx_type* ridx_in_u = sm_u.ridx (); T* data_in_u = sm_u.data (); octave_idx_type* cidx_in_l = sm_l.cidx (); octave_idx_type* ridx_in_l = sm_l.ridx (); T* data_in_l = sm_l.data (); // L output arrays Array <octave_idx_type> ridx_out_l (dim_vector (max_len_l, 1)); octave_idx_type* ridx_l = ridx_out_l.fortran_vec (); Array <T> data_out_l (dim_vector (max_len_l, 1)); T* data_l = data_out_l.fortran_vec (); // U output arrays Array <octave_idx_type> ridx_out_u (dim_vector (max_len_u, 1)); octave_idx_type* ridx_u = ridx_out_u.fortran_vec (); Array <T> data_out_u (dim_vector (max_len_u, 1)); T* data_u = data_out_u.fortran_vec (); // Working arrays OCTAVE_LOCAL_BUFFER (octave_idx_type, cidx_l, n + 1); OCTAVE_LOCAL_BUFFER (octave_idx_type, cidx_u, n + 1); OCTAVE_LOCAL_BUFFER (octave_idx_type, cols_list, n); OCTAVE_LOCAL_BUFFER (octave_idx_type, rows_list, n); OCTAVE_LOCAL_BUFFER (T, w_data_l, n); OCTAVE_LOCAL_BUFFER (T, w_data_u, n); OCTAVE_LOCAL_BUFFER (octave_idx_type, Ufirst, n); OCTAVE_LOCAL_BUFFER (octave_idx_type, Lfirst, n); OCTAVE_LOCAL_BUFFER (T, cr_sum, n); T zero = T (0); // Initialize working arrays cidx_u[0] = cidx_in_u[0]; cidx_l[0] = cidx_in_l[0]; for (i = 0; i < n; i++) { w_data_u[i] = zero; w_data_l[i] = zero; cr_sum[i] = zero; } total_len_u = 0; total_len_l = 0; cols_list_len = 0; rows_list_len = 0; // Loop over all columns for (k = 0; k < n; k++) { // Load the working column and working row for (i = cidx_in_l[k]; i < cidx_in_l[k+1]; i++) w_data_l[ridx_in_l[i]] = data_in_l[i]; for (i = cidx_in_u[k]; i < cidx_in_u[k+1]; i++) w_data_u[ridx_in_u[i]] = data_in_u[i]; // Update U working row for (j = 0; j < rows_list_len; j++) { if ((Ufirst[rows_list[j]] != -1)) for (jj = Ufirst[rows_list[j]]; jj < cidx_u[rows_list[j]+1]; jj++) { jrow = ridx_u[jj]; w_data_u[jrow] -= data_u[jj] * data_l[Lfirst[rows_list[j]]]; } } // Update L working column for (j = 0; j < cols_list_len; j++) { if (Lfirst[cols_list[j]] != -1) for (jj = Lfirst[cols_list[j]]; jj < cidx_l[cols_list[j]+1]; jj++) { jrow = ridx_l[jj]; w_data_l[jrow] -= data_l[jj] * data_u[Ufirst[cols_list[j]]]; } } if ((max_len_u - total_len_u) < n) { max_len_u += (0.1 * max_len_u) > n ? 0.1 * max_len_u : n; data_out_u.resize (dim_vector (max_len_u, 1)); data_u = data_out_u.fortran_vec (); ridx_out_u.resize (dim_vector (max_len_u, 1)); ridx_u = ridx_out_u.fortran_vec (); } if ((max_len_l - total_len_l) < n) { max_len_l += (0.1 * max_len_l) > n ? 0.1 * max_len_l : n; data_out_l.resize (dim_vector (max_len_l, 1)); data_l = data_out_l.fortran_vec (); ridx_out_l.resize (dim_vector (max_len_l, 1)); ridx_l = ridx_out_l.fortran_vec (); } // Expand the working row into the U output data structures w_len_l = 0; data_u[total_len_u] = w_data_u[k]; ridx_u[total_len_u] = k; w_len_u = 1; for (i = k + 1; i < n; i++) { if (w_data_u[i] != zero) { if (std::abs (w_data_u[i]) < (droptol * rows_norm[k])) { if (opt == ROW) cr_sum[k] += w_data_u[i]; else if (opt == COL) cr_sum[i] += w_data_u[i]; } else { data_u[total_len_u + w_len_u] = w_data_u[i]; ridx_u[total_len_u + w_len_u] = i; w_len_u++; } } // Expand the working column into the L output data structures if (w_data_l[i] != zero) { if (std::abs (w_data_l[i]) < (droptol * cols_norm[k])) { if (opt == COL) cr_sum[k] += w_data_l[i]; else if (opt == ROW) cr_sum[i] += w_data_l[i]; } else { data_l[total_len_l + w_len_l] = w_data_l[i]; ridx_l[total_len_l + w_len_l] = i; w_len_l++; } } w_data_u[i] = zero; w_data_l[i] = zero; } // Compensate row and column sums --> milu option if (opt == COL || opt == ROW) data_u[total_len_u] += cr_sum[k]; // Check if the pivot is zero if (data_u[total_len_u] == zero) error ("ilu: encountered a pivot equal to 0"); // Scale the elements in L by the pivot for (i = total_len_l ; i < (total_len_l + w_len_l); i++) data_l[i] /= data_u[total_len_u]; total_len_u += w_len_u; total_len_l += w_len_l; // Check if there are too many elements to be indexed with // octave_idx_type type due to fill-in during the process. if (total_len_l < 0 || total_len_u < 0) error ("ilu: integer overflow. Too many fill-in elements in L or U"); cidx_u[k+1] = cidx_u[k] - cidx_u[0] + w_len_u; cidx_l[k+1] = cidx_l[k] - cidx_l[0] + w_len_l; // The tricky part of the algorithm. The arrays pointing to the first // working element of each column in the next iteration (Lfirst) or // the first working element of each row (Ufirst) are updated. Also the // arrays working as lists cols_list and rows_list are filled with // indices pointing to Ufirst and Lfirst respectively. // FIXME: Maybe the -1 indicating in Ufirst and Lfirst, that no elements // have to be considered in a certain column or row in next iteration, // can be removed. It feels safer to me using such an indicator. if (k < (n - 1)) { if (w_len_u > 0) Ufirst[k] = cidx_u[k]; else Ufirst[k] = -1; if (w_len_l > 0) Lfirst[k] = cidx_l[k]; else Lfirst[k] = -1; cols_list_len = 0; rows_list_len = 0; for (i = 0; i <= k; i++) { if (Ufirst[i] != -1) { jj = ridx_u[Ufirst[i]]; if (jj < (k + 1)) { if (Ufirst[i] < (cidx_u[i+1])) { Ufirst[i]++; if (Ufirst[i] == cidx_u[i+1]) Ufirst[i] = -1; else jj = ridx_u[Ufirst[i]]; } } if (jj == (k + 1)) { cols_list[cols_list_len] = i; cols_list_len++; } } if (Lfirst[i] != -1) { jj = ridx_l[Lfirst[i]]; if (jj < (k + 1)) if (Lfirst[i] < (cidx_l[i+1])) { Lfirst[i]++; if (Lfirst[i] == cidx_l[i+1]) Lfirst[i] = -1; else jj = ridx_l[Lfirst[i]]; } if (jj == (k + 1)) { rows_list[rows_list_len] = i; rows_list_len++; } } } } } // Build the output matrices L = octave_matrix_t (n, n, total_len_l); U = octave_matrix_t (n, n, total_len_u); // FIXME: Can these loops be replaced by std::copy? for (i = 0; i <= n; i++) L.cidx (i) = cidx_l[i]; for (i = 0; i < total_len_l; i++) { L.ridx (i) = ridx_l[i]; L.data (i) = data_l[i]; } for (i = 0; i <= n; i++) U.cidx (i) = cidx_u[i]; for (i = 0; i < total_len_u; i++) { U.ridx (i) = ridx_u[i]; U.data (i) = data_u[i]; } U = U.transpose (); } DEFUN (__iluc__, args, , "-*- texinfo -*-\n\ @deftypefn {} {[@var{L}, @var{U}] =} __iluc__ (@var{A})\n\ @deftypefnx {} {[@var{L}, @var{U}] =} __iluc__ (@var{A}, @var{droptol})\n\ @deftypefnx {} {[@var{L}, @var{U}] =} __iluc__ (@var{A}, @var{droptol}, @var{milu})\n\ Undocumented internal function.\n\ @end deftypefn") { int nargin = args.length (); if (nargin < 1 || nargin > 3) print_usage (); std::string milu = "off"; double droptol = 0; // Don't repeat input validation of arguments done in ilu.m if (nargin >= 2) droptol = args(1).double_value (); if (nargin == 3) milu = args(2).string_value (); octave_value_list arg_list; if (! args(0).is_complex_type ()) { Array<double> cols_norm, rows_norm; arg_list.append (args(0).sparse_matrix_value ()); SparseMatrix sm_u = feval ("triu", arg_list)(0).sparse_matrix_value (); arg_list.append (-1); SparseMatrix sm_l = feval ("tril", arg_list)(0).sparse_matrix_value (); arg_list(1) = "rows"; rows_norm = feval ("norm", arg_list)(0).vector_value (); arg_list(1) = "cols"; cols_norm = feval ("norm", arg_list)(0).vector_value (); arg_list.clear (); SparseMatrix U, L; ilu_crout <SparseMatrix, double> (sm_l, sm_u, L, U, cols_norm.fortran_vec (), rows_norm.fortran_vec (), droptol, milu); arg_list.append (octave_value (L.cols ())); SparseMatrix eye = feval ("speye", arg_list)(0).sparse_matrix_value (); return ovl (L + eye, U); } else { Array<Complex> cols_norm, rows_norm; arg_list.append (args(0).sparse_complex_matrix_value ()); SparseComplexMatrix sm_u = feval ("triu", arg_list)(0).sparse_complex_matrix_value (); arg_list.append (-1); SparseComplexMatrix sm_l = feval ("tril", arg_list)(0).sparse_complex_matrix_value (); arg_list(1) = "rows"; rows_norm = feval ("norm", arg_list)(0).complex_vector_value (); arg_list(1) = "cols"; cols_norm = feval ("norm", arg_list)(0).complex_vector_value (); arg_list.clear (); SparseComplexMatrix U, L; ilu_crout < SparseComplexMatrix, Complex > (sm_l, sm_u, L, U, cols_norm.fortran_vec () , rows_norm.fortran_vec (), Complex (droptol), milu); arg_list.append (octave_value (L.cols ())); SparseComplexMatrix eye = feval ("speye", arg_list)(0).sparse_complex_matrix_value (); return ovl (L + eye, U); } } // This function implements the IKJ and JKI variants of gaussian elimination // to perform the ILUTP decomposition. The behavior is controlled by milu // parameter. If milu = ['off'|'col'] the JKI version is performed taking // advantage of CCS format of the input matrix. Row pivoting is performed. // If milu = 'row' the input matrix has to be transposed to obtain the // equivalent CRS structure so we can work efficiently with rows. In that // case IKJ version is used and column pivoting is performed. template <typename octave_matrix_t, typename T> void ilu_tp (octave_matrix_t& sm, octave_matrix_t& L, octave_matrix_t& U, octave_idx_type nnz_u, octave_idx_type nnz_l, T* cols_norm, Array <octave_idx_type>& perm_vec, const T droptol = T(0), const T thresh = T(0), const std::string milu = "off", const double udiag = 0) { char opt; enum {OFF, ROW, COL}; if (milu == "row") opt = ROW; else if (milu == "col") opt = COL; else opt = OFF; const octave_idx_type n = sm.cols (); // This is necessary for the JKI (milu = "row") variant. if (opt == ROW) sm = sm.transpose (); // Extract pointers to the arrays for faster access inside loops octave_idx_type* cidx_in = sm.cidx (); octave_idx_type* ridx_in = sm.ridx (); T* data_in = sm.data (); octave_idx_type jrow, i, j, k, jj, c, total_len_l, total_len_u, p_perm, max_ind, max_len_l, max_len_u; T zero = T(0); T tl = zero, aux, maximum; max_len_u = nnz_u; max_len_u += (0.1 * max_len_u) > n ? 0.1 * max_len_u : n; max_len_l = nnz_l; max_len_l += (0.1 * max_len_l) > n ? 0.1 * max_len_l : n; // Extract pointers to the arrays for faster access inside loops Array <octave_idx_type> cidx_out_l (dim_vector (n + 1, 1)); octave_idx_type* cidx_l = cidx_out_l.fortran_vec (); Array <octave_idx_type> ridx_out_l (dim_vector (max_len_l, 1)); octave_idx_type* ridx_l = ridx_out_l.fortran_vec (); Array <T> data_out_l (dim_vector (max_len_l ,1)); T* data_l = data_out_l.fortran_vec (); // Data for U Array <octave_idx_type> cidx_out_u (dim_vector (n + 1, 1)); octave_idx_type* cidx_u = cidx_out_u.fortran_vec (); Array <octave_idx_type> ridx_out_u (dim_vector (max_len_u, 1)); octave_idx_type* ridx_u = ridx_out_u.fortran_vec (); Array <T> data_out_u (dim_vector (max_len_u, 1)); T* data_u = data_out_u.fortran_vec (); // Working arrays and permutation arrays octave_idx_type w_len_u, w_len_l; T total_sum, partial_col_sum = zero, partial_row_sum = zero; std::set <octave_idx_type> iw_l; std::set <octave_idx_type> iw_u; std::set <octave_idx_type>::iterator it, it2; OCTAVE_LOCAL_BUFFER (T, w_data, n); OCTAVE_LOCAL_BUFFER (octave_idx_type, iperm, n); octave_idx_type* perm = perm_vec.fortran_vec (); OCTAVE_LOCAL_BUFFER (octave_idx_type, uptr, n); // Initialize working and permutation arrays cidx_l[0] = cidx_in[0]; cidx_u[0] = cidx_in[0]; for (i = 0; i < n; i++) { w_data[i] = 0; perm[i] = i; iperm[i] = i; } total_len_u = 0; total_len_l = 0; // Loop over all columns for (k = 0; k < n; k++) { for (j = cidx_in[k]; j < cidx_in[k+1]; j++) { p_perm = iperm[ridx_in[j]]; w_data[iperm[ridx_in[j]]] = data_in[j]; if (p_perm > k) iw_l.insert (ridx_in[j]); else iw_u.insert (p_perm); } it = iw_u.begin (); jrow = *it; total_sum = zero; while ((jrow < k) && (it != iw_u.end ())) { if (opt == COL) partial_col_sum = w_data[jrow]; if (w_data[jrow] != zero) { if (opt == ROW) { partial_row_sum = w_data[jrow]; tl = w_data[jrow] / data_u[uptr[jrow]]; } for (jj = cidx_l[jrow]; jj < cidx_l[jrow+1]; jj++) { p_perm = iperm[ridx_l[jj]]; aux = w_data[p_perm]; if (opt == ROW) { w_data[p_perm] -= tl * data_l[jj]; partial_row_sum += tl * data_l[jj]; } else { tl = data_l[jj] * w_data[jrow]; w_data[p_perm] -= tl; if (opt == COL) partial_col_sum += tl; } if ((aux == zero) && (w_data[p_perm] != zero)) { if (p_perm > k) iw_l.insert (ridx_l[jj]); else iw_u.insert (p_perm); } } // Drop element from the U part in IKJ // and L part in JKI variant (milu = [col|off]) if ((std::abs (w_data[jrow]) < (droptol * cols_norm[k])) && (w_data[jrow] != zero)) { if (opt == COL) total_sum += partial_col_sum; else if (opt == ROW) total_sum += partial_row_sum; w_data[jrow] = zero; it2 = it; it++; iw_u.erase (it2); jrow = *it; continue; } else // This is the element scaled by the pivot // in the actual iteration if (opt == ROW) w_data[jrow] = tl; } jrow = *(++it); } // Search for the pivot and update iw_l and iw_u if the pivot is not the // diagonal element if ((thresh > zero) && (k < (n - 1))) { maximum = std::abs (w_data[k]) / thresh; max_ind = perm[k]; for (it = iw_l.begin (); it != iw_l.end (); ++it) { p_perm = iperm[*it]; if (std::abs (w_data[p_perm]) > maximum) { maximum = std::abs (w_data[p_perm]); max_ind = *it; it2 = it; } } // If the pivot is not the diagonal element update all p_perm = iperm[max_ind]; if (max_ind != perm[k]) { iw_l.erase (it2); if (w_data[k] != zero) iw_l.insert (perm[k]); else iw_u.insert (k); // Swap data and update permutation vectors aux = w_data[k]; iperm[perm[p_perm]] = k; iperm[perm[k]] = p_perm; c = perm[k]; perm[k] = perm[p_perm]; perm[p_perm] = c; w_data[k] = w_data[p_perm]; w_data[p_perm] = aux; } } // Drop elements in the L part in the IKJ version, // and from the U part in the JKI version. it = iw_l.begin (); while (it != iw_l.end ()) { p_perm = iperm[*it]; if (droptol > zero) if (std::abs (w_data[p_perm]) < (droptol * cols_norm[k])) { if (opt != OFF) total_sum += w_data[p_perm]; w_data[p_perm] = zero; it2 = it; it++; iw_l.erase (it2); continue; } it++; } // If milu == [row|col] summation is preserved. // Compensate diagonal element. if (opt != OFF) { if ((total_sum > zero) && (w_data[k] == zero)) iw_u.insert (k); w_data[k] += total_sum; } // Check if the pivot is zero and if udiag is active. // NOTE: If the pivot == 0 and udiag is active, then if milu = [col|row] // will not preserve the row sum for that column/row. if (w_data[k] == zero) { if (udiag != 1) error ("ilu: encountered a pivot equal to 0"); w_data[k] = droptol; iw_u.insert (k); } // Scale the elements on the L part for IKJ version (milu = [col|off]) if (opt != ROW) for (it = iw_l.begin (); it != iw_l.end (); ++it) { p_perm = iperm[*it]; w_data[p_perm] = w_data[p_perm] / w_data[k]; } if ((max_len_u - total_len_u) < n) { max_len_u += (0.1 * max_len_u) > n ? 0.1 * max_len_u : n; data_out_u.resize (dim_vector (max_len_u, 1)); data_u = data_out_u.fortran_vec (); ridx_out_u.resize (dim_vector (max_len_u, 1)); ridx_u = ridx_out_u.fortran_vec (); } if ((max_len_l - total_len_l) < n) { max_len_l += (0.1 * max_len_l) > n ? 0.1 * max_len_l : n; data_out_l.resize (dim_vector (max_len_l, 1)); data_l = data_out_l.fortran_vec (); ridx_out_l.resize (dim_vector (max_len_l, 1)); ridx_l = ridx_out_l.fortran_vec (); } // Expand working vector into U. w_len_u = 0; for (it = iw_u.begin (); it != iw_u.end (); ++it) { if (w_data[*it] != zero) { data_u[total_len_u + w_len_u] = w_data[*it]; ridx_u[total_len_u + w_len_u] = *it; w_len_u++; } w_data[*it] = 0; } // Expand working vector into L. w_len_l = 0; for (it = iw_l.begin (); it != iw_l.end (); ++it) { p_perm = iperm[*it]; if (w_data[p_perm] != zero) { data_l[total_len_l + w_len_l] = w_data[p_perm]; ridx_l[total_len_l + w_len_l] = *it; w_len_l++; } w_data[p_perm] = 0; } total_len_u += w_len_u; total_len_l += w_len_l; // Check if there are too many elements to be indexed with // octave_idx_type type due to fill-in during the process. if (total_len_l < 0 || total_len_u < 0) error ("ilu: Integer overflow. Too many fill-in elements in L or U"); if (opt == ROW) uptr[k] = total_len_u - 1; cidx_u[k+1] = cidx_u[k] - cidx_u[0] + w_len_u; cidx_l[k+1] = cidx_l[k] - cidx_l[0] + w_len_l; iw_l.clear (); iw_u.clear (); } octave_matrix_t *L_ptr; octave_matrix_t *U_ptr; octave_matrix_t diag (n, n, n); // L and U are interchanged if milu = 'row'. It is a matter // of nomenclature to re-use code with both IKJ and JKI // versions of the algorithm. if (opt == ROW) { L_ptr = &U; U_ptr = &L; L = octave_matrix_t (n, n, total_len_u - n); U = octave_matrix_t (n, n, total_len_l); } else { L_ptr = &L; U_ptr = &U; L = octave_matrix_t (n, n, total_len_l); U = octave_matrix_t (n, n, total_len_u); } for (i = 0; i <= n; i++) { L_ptr->cidx (i) = cidx_l[i]; U_ptr->cidx (i) = cidx_u[i]; if (opt == ROW) U_ptr->cidx (i) -= i; } for (i = 0; i < n; i++) { if (opt == ROW) diag.elem (i,i) = data_u[uptr[i]]; j = cidx_l[i]; while (j < cidx_l[i+1]) { L_ptr->ridx (j) = ridx_l[j]; L_ptr->data (j) = data_l[j]; j++; } j = cidx_u[i]; while (j < cidx_u[i+1]) { c = j; if (opt == ROW) { // The diagonal is removed from L if milu = 'row'. // That is because is convenient to have it inside // the L part to carry out the process. if (ridx_u[j] == i) { j++; continue; } else c -= i; } U_ptr->data (c) = data_u[j]; U_ptr->ridx (c) = ridx_u[j]; j++; } } if (opt == ROW) { U = U.transpose (); // The diagonal, conveniently permuted is added to U U += diag.index (idx_vector::colon, perm_vec); L = L.transpose (); } } DEFUN (__ilutp__, args, nargout, "-*- texinfo -*-\n\ @deftypefn {} {[@var{L}, @var{U}] =} __ilutp__ (@var{A})\n\ @deftypefnx {} {[@var{L}, @var{U}] =} __ilutp__ (@var{A}, @var{droptol})\n\ @deftypefnx {} {[@var{L}, @var{U}] =} __ilutp__ (@var{A}, @var{droptol}, @var{thresh})\n\ @deftypefnx {} {[@var{L}, @var{U}] =} __ilutp__ (@var{A}, @var{droptol}, @var{thresh}, @var{milu})\n\ @deftypefnx {} {[@var{L}, @var{U}] =} __ilutp__ (@var{A}, @var{droptol}, @var{thresh}, @var{milu}, @var{udiag})\n\ @deftypefnx {} {[@var{L}, @var{U}, @var{P}] =} __ilutp__ (@var{A}, @dots{})\n\ Undocumented internal function.\n\ @end deftypefn") { int nargin = args.length (); if (nargin < 1 || nargin > 5) print_usage (); octave_value_list retval; std::string milu = ""; double droptol = 0; double thresh = 1; double udiag = 0; // Don't repeat input validation of arguments done in ilu.m if (nargin >= 2) droptol = args(1).double_value (); if (nargin >= 3) thresh = args(2).double_value (); if (nargin >= 4) milu = args(3).string_value (); if (nargin == 5) udiag = args(4).double_value (); octave_value_list arg_list; octave_idx_type nnz_u, nnz_l; if (! args(0).is_complex_type ()) { Array <double> rc_norm; SparseMatrix sm = args(0).sparse_matrix_value (); arg_list.append (sm); nnz_u = (feval ("triu", arg_list)(0).sparse_matrix_value ()).nnz (); arg_list.append (-1); nnz_l = (feval ("tril", arg_list)(0).sparse_matrix_value ()).nnz (); if (milu == "row") arg_list (1) = "rows"; else arg_list (1) = "cols"; rc_norm = feval ("norm", arg_list)(0).vector_value (); arg_list.clear (); Array <octave_idx_type> perm (dim_vector (sm.cols (), 1)); SparseMatrix U, L; ilu_tp <SparseMatrix, double> (sm, L, U, nnz_u, nnz_l, rc_norm.fortran_vec (), perm, droptol, thresh, milu, udiag); arg_list.append (octave_value (L.cols ())); SparseMatrix eye = feval ("speye", arg_list)(0).sparse_matrix_value (); if (milu == "row") { if (nargout == 3) { retval(2) = eye.index (idx_vector::colon, perm); retval(1) = U.index (idx_vector::colon, perm); } else if (nargout == 2) retval(1) = U; retval(0) = L + eye; } else { if (nargout == 3) { retval(2) = eye.index (perm, idx_vector::colon); retval(1) = U; retval(0) = L.index (perm, idx_vector::colon) + eye; } else { retval(1) = U; retval(0) = L + eye.index (perm, idx_vector::colon); } } } else { Array <Complex> rc_norm; SparseComplexMatrix sm = args(0).sparse_complex_matrix_value (); arg_list.append (sm); nnz_u = feval ("triu", arg_list)(0).sparse_complex_matrix_value ().nnz (); arg_list.append (-1); nnz_l = feval ("tril", arg_list)(0).sparse_complex_matrix_value ().nnz (); if (milu == "row") arg_list(1) = "rows"; else arg_list(1) = "cols"; rc_norm = feval ("norm", arg_list)(0).complex_vector_value (); arg_list.clear (); Array <octave_idx_type> perm (dim_vector (sm.cols (), 1)); SparseComplexMatrix U, L; ilu_tp < SparseComplexMatrix, Complex> (sm, L, U, nnz_u, nnz_l, rc_norm.fortran_vec (), perm, Complex (droptol), Complex (thresh), milu, udiag); arg_list.append (octave_value (L.cols ())); SparseComplexMatrix eye = feval ("speye", arg_list)(0).sparse_complex_matrix_value (); if (milu == "row") { if (nargout == 3) { retval(2) = eye.index (idx_vector::colon, perm); retval(1) = U.index (idx_vector::colon, perm); } else if (nargout == 2) retval(1) = U; retval(0) = L + eye; } else { if (nargout == 3) { retval(2) = eye.index (perm, idx_vector::colon); retval(1) = U; retval(0) = L.index (perm, idx_vector::colon) + eye; } else { retval(1) = U; retval(0) = L + eye.index (perm, idx_vector::colon); } } } return retval; } /* ## No test needed for internal helper function. %!assert (1) */