Mercurial > octave
view libinterp/corefcn/__qp__.cc @ 31605:e88a07dec498 stable
maint: Use macros to begin/end C++ namespaces.
* oct-conf-post-public.in.h: Define two macros (OCTAVE_BEGIN_NAMESPACE,
OCTAVE_END_NAMESPACE) that can be used to start/end a namespace.
* mk-opts.pl, build-env.h, build-env.in.cc, __betainc__.cc, __contourc__.cc,
__dsearchn__.cc, __eigs__.cc, __expint__.cc, __ftp__.cc, __gammainc__.cc,
__ichol__.cc, __ilu__.cc, __isprimelarge__.cc, __lin_interpn__.cc,
__magick_read__.cc, __pchip_deriv__.cc, __qp__.cc, amd.cc, auto-shlib.cc,
auto-shlib.h, balance.cc, base-text-renderer.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, ccolamd.cc, cellfun.cc, chol.cc, colamd.cc,
colloc.cc, conv2.cc, daspk.cc, dasrt.cc, dassl.cc, data.cc, data.h, debug.cc,
defaults.cc, defaults.h, defun-int.h, defun.cc, det.cc, dirfns.cc, display.cc,
display.h, dlmread.cc, dmperm.cc, dot.cc, dynamic-ld.cc, dynamic-ld.h, eig.cc,
ellipj.cc, environment.cc, environment.h, error.cc, error.h, errwarn.h,
event-manager.cc, event-manager.h, event-queue.cc, event-queue.h, fcn-info.cc,
fcn-info.h, fft.cc, fft2.cc, fftn.cc, file-io.cc, filter.cc, find.cc,
ft-text-renderer.cc, ft-text-renderer.h, gcd.cc, getgrent.cc, getpwent.cc,
getrusage.cc, givens.cc, gl-render.cc, gl-render.h, gl2ps-print.cc,
gl2ps-print.h, graphics-toolkit.cc, graphics-toolkit.h, graphics.cc,
graphics.in.h, gsvd.cc, gtk-manager.cc, gtk-manager.h, hash.cc, help.cc,
help.h, hess.cc, hex2num.cc, hook-fcn.cc, hook-fcn.h, input.cc, input.h,
interpreter-private.cc, interpreter-private.h, interpreter.cc, interpreter.h,
inv.cc, jsondecode.cc, jsonencode.cc, kron.cc, latex-text-renderer.cc,
latex-text-renderer.h, load-path.cc, load-path.h, load-save.cc, load-save.h,
lookup.cc, ls-ascii-helper.cc, ls-ascii-helper.h, ls-oct-text.cc, ls-utils.cc,
ls-utils.h, lsode.cc, lu.cc, mappers.cc, matrix_type.cc, max.cc, mex-private.h,
mex.cc, mgorth.cc, nproc.cc, oct-fstrm.cc, oct-fstrm.h, oct-hdf5-types.cc,
oct-hdf5-types.h, oct-hist.cc, oct-hist.h, oct-iostrm.cc, oct-iostrm.h,
oct-opengl.h, oct-prcstrm.cc, oct-prcstrm.h, oct-procbuf.cc, oct-procbuf.h,
oct-process.cc, oct-process.h, oct-stdstrm.h, oct-stream.cc, oct-stream.h,
oct-strstrm.cc, oct-strstrm.h, oct-tex-lexer.in.ll, oct-tex-parser.yy,
ordqz.cc, ordschur.cc, pager.cc, pager.h, pinv.cc, pow2.cc, pr-flt-fmt.cc,
pr-output.cc, procstream.cc, procstream.h, psi.cc, qr.cc, quad.cc, quadcc.cc,
qz.cc, rand.cc, rcond.cc, regexp.cc, schur.cc, settings.cc, settings.h,
sighandlers.cc, sighandlers.h, sparse-xdiv.cc, sparse-xdiv.h, sparse-xpow.cc,
sparse-xpow.h, sparse.cc, spparms.cc, sqrtm.cc, stack-frame.cc, stack-frame.h,
stream-euler.cc, strfind.cc, strfns.cc, sub2ind.cc, svd.cc, sylvester.cc,
symbfact.cc, syminfo.cc, syminfo.h, symrcm.cc, symrec.cc, symrec.h,
symscope.cc, symscope.h, symtab.cc, symtab.h, syscalls.cc, sysdep.cc, sysdep.h,
text-engine.cc, text-engine.h, text-renderer.cc, text-renderer.h, time.cc,
toplev.cc, tril.cc, tsearch.cc, typecast.cc, url-handle-manager.cc,
url-handle-manager.h, urlwrite.cc, utils.cc, utils.h, variables.cc,
variables.h, xdiv.cc, xdiv.h, xnorm.cc, xnorm.h, xpow.cc, xpow.h,
__delaunayn__.cc, __fltk_uigetfile__.cc, __glpk__.cc, __init_fltk__.cc,
__init_gnuplot__.cc, __ode15__.cc, __voronoi__.cc, audiodevinfo.cc,
audioread.cc, convhulln.cc, fftw.cc, gzip.cc, mk-build-env-features.sh,
mk-builtins.pl, cdef-class.cc, cdef-class.h, cdef-fwd.h, cdef-manager.cc,
cdef-manager.h, cdef-method.cc, cdef-method.h, cdef-object.cc, cdef-object.h,
cdef-package.cc, cdef-package.h, cdef-property.cc, cdef-property.h,
cdef-utils.cc, cdef-utils.h, ov-base.cc, ov-base.h, ov-bool-mat.cc,
ov-builtin.h, ov-cell.cc, ov-class.cc, ov-class.h, ov-classdef.cc,
ov-classdef.h, ov-complex.cc, ov-fcn-handle.cc, ov-fcn-handle.h, ov-fcn.h,
ov-java.cc, ov-java.h, ov-mex-fcn.h, ov-null-mat.cc, ov-oncleanup.cc,
ov-struct.cc, ov-typeinfo.cc, ov-typeinfo.h, ov-usr-fcn.cc, ov-usr-fcn.h,
ov.cc, ov.h, octave.cc, octave.h, mk-ops.sh, 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-fcdm-fcdm.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-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-m-cm.cc, op-m-cs.cc, op-m-m.cc, op-m-s.cc,
op-m-scm.cc, op-m-sm.cc, op-mi.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,
anon-fcn-validator.cc, anon-fcn-validator.h, bp-table.cc, bp-table.h,
comment-list.cc, comment-list.h, filepos.h, lex.h, lex.ll, oct-lvalue.cc,
oct-lvalue.h, oct-parse.yy, parse.h, profiler.cc, profiler.h,
pt-anon-scopes.cc, pt-anon-scopes.h, pt-arg-list.cc, pt-arg-list.h,
pt-args-block.cc, pt-args-block.h, pt-array-list.cc, 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.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-id.cc,
pt-id.h, pt-idx.cc, pt-idx.h, 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-spmd.cc, pt-spmd.h, pt-stmt.cc, pt-stmt.h, pt-tm-const.cc,
pt-tm-const.h, pt-unop.cc, pt-unop.h, pt-vm-eval.cc, pt-walk.cc, pt-walk.h,
pt.cc, pt.h, token.cc, token.h, Range.cc, Range.h, idx-vector.cc, idx-vector.h,
range-fwd.h, CollocWt.cc, CollocWt.h, aepbalance.cc, aepbalance.h, chol.cc,
chol.h, gepbalance.cc, gepbalance.h, gsvd.cc, gsvd.h, hess.cc, hess.h,
lo-mappers.cc, lo-mappers.h, lo-specfun.cc, lo-specfun.h, lu.cc, lu.h,
oct-convn.cc, oct-convn.h, oct-fftw.cc, oct-fftw.h, oct-norm.cc, oct-norm.h,
oct-rand.cc, oct-rand.h, oct-spparms.cc, oct-spparms.h, qr.cc, qr.h, qrp.cc,
qrp.h, randgamma.cc, randgamma.h, randmtzig.cc, randmtzig.h, randpoisson.cc,
randpoisson.h, schur.cc, schur.h, sparse-chol.cc, sparse-chol.h, sparse-lu.cc,
sparse-lu.h, sparse-qr.cc, sparse-qr.h, svd.cc, svd.h, child-list.cc,
child-list.h, dir-ops.cc, dir-ops.h, file-ops.cc, file-ops.h, file-stat.cc,
file-stat.h, lo-sysdep.cc, lo-sysdep.h, lo-sysinfo.cc, lo-sysinfo.h,
mach-info.cc, mach-info.h, oct-env.cc, oct-env.h, oct-group.cc, oct-group.h,
oct-password.cc, oct-password.h, oct-syscalls.cc, oct-syscalls.h, oct-time.cc,
oct-time.h, oct-uname.cc, oct-uname.h, action-container.cc, action-container.h,
base-list.h, cmd-edit.cc, cmd-edit.h, cmd-hist.cc, cmd-hist.h, f77-fcn.h,
file-info.cc, file-info.h, lo-array-errwarn.cc, lo-array-errwarn.h, lo-hash.cc,
lo-hash.h, lo-ieee.h, lo-regexp.cc, lo-regexp.h, lo-utils.cc, lo-utils.h,
oct-base64.cc, oct-base64.h, oct-glob.cc, oct-glob.h, oct-inttypes.h,
oct-mutex.cc, oct-mutex.h, oct-refcount.h, oct-shlib.cc, oct-shlib.h,
oct-sparse.cc, oct-sparse.h, oct-string.h, octave-preserve-stream-state.h,
pathsearch.cc, pathsearch.h, quit.cc, quit.h, unwind-prot.cc, unwind-prot.h,
url-transfer.cc, url-transfer.h : Use new macros to begin/end C++ namespaces.
author | Rik <rik@octave.org> |
---|---|
date | Thu, 01 Dec 2022 14:23:45 -0800 |
parents | 796f54d4ddbf |
children | 597f3ee61a48 |
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//////////////////////////////////////////////////////////////////////// // // Copyright (C) 2000-2022 The Octave Project Developers // // See the file COPYRIGHT.md in the top-level directory of this // distribution or <https://octave.org/copyright/>. // // 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 // <https://www.gnu.org/licenses/>. // //////////////////////////////////////////////////////////////////////// #if defined (HAVE_CONFIG_H) # include "config.h" #endif #include <cmath> #include <limits> #include "chol.h" #include "svd.h" #include "mx-m-dm.h" #include "EIG.h" #include "defun.h" #include "error.h" #include "errwarn.h" #include "ovl.h" #include "pr-output.h" #include "utils.h" OCTAVE_BEGIN_NAMESPACE(octave) static octave_idx_type min_index (const ColumnVector& x) { double min_val = x.min (); for (octave_idx_type i = 0; i < x.numel (); i++) if (min_val == x.xelem (i)) return i; return 0; } static Matrix null (const Matrix& A, octave_idx_type& rank) { Matrix retval; rank = 0; if (! A.isempty ()) { math::svd<Matrix> A_svd (A); DiagMatrix S = A_svd.singular_values (); ColumnVector s = S.extract_diag (); Matrix V = A_svd.right_singular_matrix (); octave_idx_type A_nr = A.rows (); octave_idx_type A_nc = A.cols (); octave_idx_type tmp = (A_nr > A_nc ? A_nr : A_nc); double tol = tmp * s(0) * std::numeric_limits<double>::epsilon (); octave_idx_type n = s.numel (); for (octave_idx_type i = 0; i < n; i++) { if (s(i) > tol) rank++; } if (rank < A_nc) retval = V.extract (0, rank, A_nc-1, A_nc-1); else retval.resize (A_nc, 0); for (octave_idx_type i = 0; i < retval.numel (); i++) if (std::abs (retval(i)) < std::numeric_limits<double>::epsilon ()) retval(i) = 0; } return retval; } static int qp (const Matrix& H, const ColumnVector& q, const Matrix& Aeq, const ColumnVector& beq, const Matrix& Ain, const ColumnVector& bin, int maxit, double rtol, ColumnVector& x, ColumnVector& lambda, int& iter) { int info = 0; iter = 0; // Problem dimension. octave_idx_type n = x.numel (); // Dimension of constraints. octave_idx_type n_eq = beq.numel (); octave_idx_type n_in = bin.numel (); // Filling the current active set. octave_idx_type n_act = n_eq; octave_idx_type n_tot = n_eq + n_in; // Equality constraints come first. We won't check the sign of the // Lagrange multiplier for those. Matrix Aact = Aeq; ColumnVector bact = beq; ColumnVector Wact; if (n_in > 0) { ColumnVector res = Ain*x - bin; for (octave_idx_type i = 0; i < n_in; i++) { res(i) /= (1.0 + std::abs (bin(i))); if (res(i) < rtol) { n_act++; Aact = Aact.stack (Ain.row (i)); bact.resize (n_act, bin(i)); Wact.resize (n_act-n_eq, i); } } } // Computing the ??? EIG eigH; try { eigH = EIG (H); } catch (execution_exception& ee) { error (ee, "qp: failed to compute eigenvalues of H"); } ColumnVector eigenvalH = real (eigH.eigenvalues ()); Matrix eigenvecH = real (eigH.right_eigenvectors ()); octave_idx_type indminR = min_index (eigenvalH); bool done = false; double alpha = 0.0; Matrix R; Matrix Y (n, 0, 0.0); ColumnVector g (n, 0.0); ColumnVector p (n, 0.0); ColumnVector lambda_tmp (n_in, 0.0); while (! done) { iter++; // Current Gradient // g = q + H * x; g = q + H * x; if (n_act == 0) { // There are no active constraints. double minReal = eigenvalH.xelem (indminR); if (minReal > 0.0) { // Inverting the Hessian. Using the Cholesky // factorization since the Hessian is positive // definite. math::chol<Matrix> cholH (H); R = cholH.chol_matrix (); Matrix Hinv = math::chol2inv (R); // Computing the unconstrained step. // p = -Hinv * g; p = -Hinv * g; info = 0; } else { // Finding the negative curvature of H. p = eigenvecH.column (indminR); // Following the negative curvature of H. if (p.transpose () * g > std::numeric_limits<double>::epsilon ()) p = -p; info = 1; } // Multipliers are zero. lambda_tmp.fill (0.0); } else { // There are active constraints. // Computing the null space. octave_idx_type rank; Matrix Z = null (Aact, rank); octave_idx_type dimZ = n - rank; // FIXME: still remain to handle the case of // non-full rank active set matrix. // Computing the Y matrix (orthogonal to Z) Y = Aact.pseudo_inverse (); // Reduced Hessian Matrix Zt = Z.transpose (); Matrix rH = Zt * H * Z; octave_idx_type pR = 0; if (dimZ > 0) { // Computing the Cholesky factorization (pR = 0 means // that the reduced Hessian was positive definite). math::chol<Matrix> cholrH (rH, pR); Matrix tR = cholrH.chol_matrix (); if (pR == 0) R = tR; } if (pR == 0) { info = 0; // Computing the step pz. if (dimZ > 0) { // Using the Cholesky factorization to invert rH Matrix rHinv = math::chol2inv (R); ColumnVector pz = -rHinv * Zt * g; // Global step. p = Z * pz; } else { // Global step. p.fill (0.0); } } else { info = 1; // Searching for the most negative curvature. EIG eigrH; try { eigrH = EIG (rH); } catch (execution_exception& ee) { error (ee, "qp: failed to compute eigenvalues of rH"); } ColumnVector eigenvalrH = real (eigrH.eigenvalues ()); Matrix eigenvecrH = real (eigrH.right_eigenvectors ()); indminR = min_index (eigenvalrH); ColumnVector eVrH = eigenvecrH.column (indminR); // Computing the step pz. p = Z * eVrH; if (p.transpose () * g > std::numeric_limits<double>::epsilon ()) p = -p; } } // Checking the step-size. ColumnVector abs_p (n); for (octave_idx_type i = 0; i < n; i++) abs_p(i) = std::abs (p(i)); double max_p = abs_p.max (); if (max_p < rtol) { // The step is null. Checking constraints. if (n_act - n_eq == 0) // Solution is found because no inequality // constraints are active. done = true; else { // Computing the multipliers only for the inequality // constraints that are active. We do NOT compute // multipliers for the equality constraints. Matrix Yt = Y.transpose (); Yt = Yt.extract_n (n_eq, 0, n_act-n_eq, n); lambda_tmp = Yt * (g + H * p); // Checking the multipliers. We remove the most // negative from the set (if any). double min_lambda = lambda_tmp.min (); if (min_lambda >= 0) { // Solution is found. done = true; } else { octave_idx_type which_eig = 0; for (octave_idx_type i = 0; i < n_act; i++) { if (lambda_tmp(i) == min_lambda) { which_eig = i; break; } } // At least one multiplier is negative, we // remove it from the set. n_act--; for (octave_idx_type i = which_eig; i < n_act - n_eq; i++) { Wact(i) = Wact(i+1); for (octave_idx_type j = 0; j < n; j++) Aact(n_eq+i, j) = Aact(n_eq+i+1, j); bact(n_eq+i) = bact(n_eq+i+1); } // Resizing the active set. Wact.resize (n_act-n_eq); bact.resize (n_act); Aact.resize (n_act, n); } } } else { // The step is not null. if (n_act - n_eq == n_in) { // All inequality constraints were active. We can // add the whole step. x += p; } else { // Some constraints were not active. Checking if // there is a blocking constraint. alpha = 1.0; octave_idx_type is_block = -1; for (octave_idx_type i = 0; i < n_in; i++) { bool found = false; for (octave_idx_type j = 0; j < n_act-n_eq; j++) { if (Wact(j) == i) { found = true; break; } } if (! found) { // The i-th constraint was not in the set. Is it a // blocking constraint? RowVector tmp_row = Ain.row (i); double tmp = tmp_row * p; double res = tmp_row * x; if (tmp < 0.0) { double alpha_tmp = (bin(i) - res) / tmp; if (alpha_tmp < alpha) { alpha = alpha_tmp; is_block = i; } } } } // In is_block there is the index of the blocking // constraint (if any). if (is_block >= 0) { // There is a blocking constraint (index in // is_block) which is added to the active set. n_act++; Aact = Aact.stack (Ain.row (is_block)); bact.resize (n_act, bin(is_block)); Wact.resize (n_act-n_eq, is_block); // Adding the reduced step x += alpha * p; } else { // There are no blocking constraints. Adding the // whole step. x += alpha * p; } } } if (iter == maxit) { done = true; // warning ("qp_main: maximum number of iteration reached"); info = 3; } } lambda_tmp = Y.transpose () * (g + H * p); // Reordering the Lagrange multipliers. lambda.resize (n_tot); lambda.fill (0.0); for (octave_idx_type i = 0; i < n_eq; i++) lambda(i) = lambda_tmp(i); for (octave_idx_type i = n_eq; i < n_tot; i++) { for (octave_idx_type j = 0; j < n_act-n_eq; j++) { if (Wact(j) == i - n_eq) { lambda(i) = lambda_tmp(n_eq+j); break; } } } return info; } DEFUN (__qp__, args, , doc: /* -*- texinfo -*- @deftypefn {} {[@var{x}, @var{lambda}, @var{info}, @var{iter}] =} __qp__ (@var{x0}, @var{H}, @var{q}, @var{Aeq}, @var{beq}, @var{Ain}, @var{bin}, @var{maxit}, @var{rtol}) Undocumented internal function. @end deftypefn */) { if (args.length () != 9) print_usage (); const ColumnVector x0 (args(0).vector_value ()); const Matrix H (args(1).matrix_value ()); const ColumnVector q (args(2).vector_value ()); const Matrix Aeq (args(3).matrix_value ()); const ColumnVector beq (args(4).vector_value ()); const Matrix Ain (args(5).matrix_value ()); const ColumnVector bin (args(6).vector_value ()); const int maxit (args(7).int_value ()); const double rtol (args(8).double_value()); int iter = 0; // Copy the initial guess into the working variable ColumnVector x = x0; // Reordering the Lagrange multipliers ColumnVector lambda; int info = qp (H, q, Aeq, beq, Ain, bin, maxit, rtol, x, lambda, iter); return ovl (x, lambda, info, iter); } /* ## No test needed for internal helper function. %!assert (1) */ OCTAVE_END_NAMESPACE(octave)