Mercurial > octave-nkf
view libinterp/corefcn/__qp__.cc @ 20267:a9574e3c6e9e
Deprecate Array::length() and Sparse::length() in favour of ::numel().
* liboctave/array/Array.h (Array::length): deprecate for ::numel.
* liboctave/array/Sparse.h (Sparse::length): deprecate for ::numel.
* libgui/graphics/QtHandlesUtils.cc, libgui/src/octave-qt-link.cc,
libinterp/corefcn/Cell.cc, libinterp/corefcn/__contourc__.cc,
libinterp/corefcn/__pchip_deriv__.cc, libinterp/corefcn/__qp__.cc,
libinterp/corefcn/cellfun.cc, libinterp/corefcn/daspk.cc,
libinterp/corefcn/dasrt.cc, libinterp/corefcn/dassl.cc,
libinterp/corefcn/data.cc, libinterp/corefcn/filter.cc,
libinterp/corefcn/find.cc, libinterp/corefcn/gl-render.cc,
libinterp/corefcn/gl-render.h, libinterp/corefcn/graphics.cc,
libinterp/corefcn/graphics.in.h, libinterp/corefcn/help.cc,
libinterp/corefcn/hex2num.cc, libinterp/corefcn/input.cc,
libinterp/corefcn/load-path.cc, libinterp/corefcn/load-save.cc,
libinterp/corefcn/ls-oct-ascii.h, libinterp/corefcn/lsode.cc,
libinterp/corefcn/matrix_type.cc, libinterp/corefcn/oct-hist.cc,
libinterp/corefcn/oct-map.cc, libinterp/corefcn/oct-map.h,
libinterp/corefcn/oct-obj.h, libinterp/corefcn/oct-stream.cc,
libinterp/corefcn/oct-stream.h, libinterp/corefcn/pr-output.cc,
libinterp/corefcn/quadcc.cc, libinterp/corefcn/rand.cc,
libinterp/corefcn/regexp.cc, libinterp/corefcn/strfns.cc,
libinterp/corefcn/sub2ind.cc, libinterp/corefcn/symtab.h,
libinterp/corefcn/syscalls.cc, libinterp/corefcn/tsearch.cc,
libinterp/corefcn/urlwrite.cc, libinterp/corefcn/utils.cc,
libinterp/corefcn/variables.cc, libinterp/corefcn/xdiv.cc,
libinterp/corefcn/xpow.cc, libinterp/dldfcn/__glpk__.cc,
libinterp/dldfcn/__init_fltk__.cc, libinterp/dldfcn/__magick_read__.cc,
libinterp/dldfcn/audiodevinfo.cc, libinterp/dldfcn/ccolamd.cc,
libinterp/dldfcn/colamd.cc, libinterp/octave-value/ov-cell.cc,
libinterp/octave-value/ov-class.cc, libinterp/octave-value/ov-class.h,
libinterp/octave-value/ov-fcn-inline.cc, libinterp/octave-value/ov-java.cc,
libinterp/octave-value/ov-perm.cc, libinterp/octave-value/ov-struct.cc,
libinterp/octave-value/ov-typeinfo.cc, libinterp/octave-value/ov.cc,
libinterp/operators/op-int.h, libinterp/parse-tree/pt-pr-code.cc,
liboctave/array/Array-util.cc, liboctave/array/Array.cc,
liboctave/array/CColVector.cc, liboctave/array/CDiagMatrix.cc,
liboctave/array/CMatrix.cc, liboctave/array/CRowVector.cc,
liboctave/array/DiagArray2.cc, liboctave/array/DiagArray2.h,
liboctave/array/MArray.cc, liboctave/array/PermMatrix.cc,
liboctave/array/PermMatrix.h, liboctave/array/Sparse.cc,
liboctave/array/boolMatrix.cc, liboctave/array/chMatrix.cc,
liboctave/array/chNDArray.cc, liboctave/array/dColVector.cc,
liboctave/array/dDiagMatrix.cc, liboctave/array/dMatrix.cc,
liboctave/array/dRowVector.cc, liboctave/array/fCColVector.cc,
liboctave/array/fCDiagMatrix.cc, liboctave/array/fCMatrix.cc,
liboctave/array/fCRowVector.cc, liboctave/array/fColVector.cc,
liboctave/array/fDiagMatrix.cc, liboctave/array/fMatrix.cc,
liboctave/array/fRowVector.cc, liboctave/array/idx-vector.cc,
liboctave/array/intNDArray.cc, liboctave/numeric/CmplxCHOL.cc,
liboctave/numeric/CmplxLU.cc, liboctave/numeric/CmplxQR.cc,
liboctave/numeric/DASPK.cc, liboctave/numeric/DASRT.cc,
liboctave/numeric/DASSL.cc, liboctave/numeric/LSODE.cc,
liboctave/numeric/ODES.cc, liboctave/numeric/ODES.h,
liboctave/numeric/base-dae.h, liboctave/numeric/base-lu.cc,
liboctave/numeric/dbleCHOL.cc, liboctave/numeric/dbleLU.cc,
liboctave/numeric/dbleQR.cc, liboctave/numeric/eigs-base.cc,
liboctave/numeric/fCmplxCHOL.cc, liboctave/numeric/fCmplxLU.cc,
liboctave/numeric/fCmplxQR.cc, liboctave/numeric/floatCHOL.cc,
liboctave/numeric/floatLU.cc, liboctave/numeric/floatQR.cc,
liboctave/numeric/lo-specfun.cc, liboctave/numeric/oct-rand.cc,
liboctave/numeric/oct-spparms.cc, liboctave/numeric/sparse-base-chol.cc,
liboctave/operators/mx-inlines.cc, liboctave/system/file-ops.cc,
liboctave/util/glob-match.h, liboctave/util/kpse.cc,
liboctave/util/lo-regexp.cc, liboctave/util/oct-glob.cc,
liboctave/util/pathsearch.cc, liboctave/util/str-vec.cc,
liboctave/util/str-vec.h, liboctave/util/url-transfer.cc: replace all usage
of Array::length() and Sparse::length() with ::numel().
author | Carnë Draug <carandraug@octave.org> |
---|---|
date | Sat, 30 May 2015 03:14:07 +0100 |
parents | 4197fc428c7d |
children |
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/* Copyright (C) 2000-2015 Gabriele Pannocchia 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 "dbleCHOL.h" #include "dbleSVD.h" #include "mx-m-dm.h" #include "EIG.h" #include "defun.h" #include "error.h" #include "gripes.h" #include "oct-obj.h" #include "pr-output.h" #include "utils.h" static Matrix null (const Matrix& A, octave_idx_type& rank) { Matrix retval; rank = 0; if (! A.is_empty ()) { SVD 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, ColumnVector& x, ColumnVector& lambda, int& iter) { int info = 0; iter = 0; double rtol = sqrt (std::numeric_limits<double>::epsilon ()); // 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 (H); if (error_state) { error ("qp: failed to compute eigenvalues of H"); return -1; } ColumnVector eigenvalH = real (eigH.eigenvalues ()); Matrix eigenvecH = real (eigH.eigenvectors ()); double minReal = eigenvalH.min (); octave_idx_type indminR = 0; for (octave_idx_type i = 0; i < n; i++) { if (minReal == eigenvalH(i)) { indminR = i; break; } } 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. if (minReal > 0.0) { // Inverting the Hessian. Using the Cholesky // factorization since the Hessian is positive // definite. CHOL cholH (H); R = cholH.chol_matrix (); Matrix Hinv = 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). CHOL 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 = 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 (rH); if (error_state) { error ("qp: failed to compute eigenvalues of rH"); return -1; } ColumnVector eigenvalrH = real (eigrH.eigenvalues ()); Matrix eigenvecrH = real (eigrH.eigenvectors ()); double mRrH = eigenvalrH.min (); indminR = 0; for (octave_idx_type i = 0; i < n; i++) { if (mRrH == eigenvalH(i)) { indminR = i; break; } } 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, , "-*- texinfo -*-\n\ @deftypefn {Built-in Function} {[@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})\n\ Undocumented internal function.\n\ @end deftypefn") { octave_value_list retval; if (args.length () == 8) { 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 ()); if (! error_state) { int iter = 0; // Copying the initial guess in the working variable ColumnVector x = x0; // Reordering the Lagrange multipliers ColumnVector lambda; int info = qp (H, q, Aeq, beq, Ain, bin, maxit, x, lambda, iter); if (! error_state) { retval(3) = iter; retval(2) = info; retval(1) = lambda; retval(0) = x; } else error ("qp: internal error"); } else error ("__qp__: invalid arguments"); } else print_usage (); return retval; } /* ## No test needed for internal helper function. %!assert (1) */