Mercurial > octave
view libinterp/corefcn/__ichol__.cc @ 30249:bc22395f60fa
maint: merge stable to default.
author | John W. Eaton <jwe@octave.org> |
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date | Fri, 22 Oct 2021 12:05:59 -0400 |
parents | 7d6709900da7 |
children | a61e1a0f6024 |
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//////////////////////////////////////////////////////////////////////// // // Copyright (C) 2013-2021 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 "oct-locbuf.h" #include "oct-norm.h" #include "defun.h" #include "error.h" #include "builtin-defun-decls.h" OCTAVE_NAMESPACE_BEGIN // Secondary functions for complex and real case used in ichol algorithms. Complex ichol_mult_complex (Complex a, Complex b) { #if defined (HAVE_CXX_COMPLEX_SETTERS) b.imag (-b.imag ()); #elif defined (HAVE_CXX_COMPLEX_REFERENCE_ACCESSORS) b.imag () = -b.imag (); #else b = b.conj (); #endif return a * b; } double ichol_mult_real (double a, double b) { return a * b; } bool ichol_checkpivot_complex (Complex pivot) { if (pivot.imag () != 0) error ("ichol: non-real pivot encountered. The matrix must be Hermitian."); else if (pivot.real () < 0) error ("ichol: negative pivot encountered"); return true; } bool ichol_checkpivot_real (double pivot) { if (pivot < 0) error ("ichol: negative pivot encountered"); return true; } template <typename octave_matrix_t, typename T, T (*ichol_mult) (T, T), bool (*ichol_checkpivot) (T)> void ichol_0 (octave_matrix_t& sm, const std::string michol = "off") { const octave_idx_type n = sm.cols (); octave_idx_type j1, jend, j2, jrow, jjrow, j, jw, i, k, jj, r; T tl; char opt; enum {OFF, ON}; if (michol == "on") opt = ON; 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, Lfirst, n); OCTAVE_LOCAL_BUFFER (octave_idx_type, Llist, n); OCTAVE_LOCAL_BUFFER (octave_idx_type, iw, n); OCTAVE_LOCAL_BUFFER (T, dropsums, n); // Initialize working arrays for (i = 0; i < n; i++) { iw[i] = -1; Llist[i] = -1; Lfirst[i] = -1; dropsums[i] = 0; } // Loop over all columns for (k = 0; k < n; k++) { j1 = cidx[k]; j2 = cidx[k+1]; for (j = j1; j < j2; j++) iw[ridx[j]] = j; jrow = Llist[k]; // Iterate over each non-zero element in the actual row. while (jrow != -1) { jjrow = Lfirst[jrow]; jend = cidx[jrow+1]; for (jj = jjrow; jj < jend; jj++) { r = ridx[jj]; jw = iw[r]; tl = ichol_mult (data[jj], data[jjrow]); if (jw != -1) data[jw] -= tl; else // Because of the symmetry of the matrix, we know // the drops in the column r are also in the column k. if (opt == ON) { dropsums[r] -= tl; dropsums[k] -= tl; } } // Update the linked list and the first entry of the actual column. if ((jjrow + 1) < jend) { Lfirst[jrow]++; j = jrow; jrow = Llist[jrow]; Llist[j] = Llist[ridx[Lfirst[j]]]; Llist[ridx[Lfirst[j]]] = j; } else jrow = Llist[jrow]; } if (opt == ON) data[j1] += dropsums[k]; // Test for j1 == j2 must be first to avoid invalid ridx[j1] access if (j1 == j2 || ridx[j1] != k) error ("ichol: encountered a pivot equal to 0"); if (! ichol_checkpivot (data[j1])) break; data[cidx[k]] = std::sqrt (data[j1]); // Update Llist and Lfirst with the k-column information. Also, // scale the column elements by the pivot and reset the working array iw. if (k < (n - 1)) { iw[ridx[j1]] = -1; for (i = j1 + 1; i < j2; i++) { iw[ridx[i]] = -1; data[i] /= data[j1]; } Lfirst[k] = j1; if ((Lfirst[k] + 1) < j2) { Lfirst[k]++; jjrow = ridx[Lfirst[k]]; Llist[k] = Llist[jjrow]; Llist[jjrow] = k; } } } } DEFUN (__ichol0__, args, , doc: /* -*- texinfo -*- @deftypefn {} {@var{L} =} __ichol0__ (@var{A}, @var{michol}) Undocumented internal function. @end deftypefn */) { if (args.length () != 2) print_usage (); std::string michol = args(1).string_value (); // In ICHOL0 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. if (! args(0).iscomplex ()) { SparseMatrix sm = Ftril (args(0))(0).sparse_matrix_value (); ichol_0 <SparseMatrix, double, ichol_mult_real, ichol_checkpivot_real> (sm, michol); return ovl (sm); } else { SparseComplexMatrix sm = Ftril (args(0))(0).sparse_complex_matrix_value (); ichol_0 <SparseComplexMatrix, Complex, ichol_mult_complex, ichol_checkpivot_complex> (sm, michol); return ovl (sm); } } template <typename octave_matrix_t, typename T, T (*ichol_mult) (T, T), bool (*ichol_checkpivot) (T)> void ichol_t (const octave_matrix_t& sm, octave_matrix_t& L, const T* cols_norm, const T droptol, const std::string michol = "off") { const octave_idx_type n = sm.cols (); octave_idx_type j, jrow, jend, jjrow, i, k, jj, total_len, w_len, max_len, ind; char opt; enum {OFF, ON}; if (michol == "on") opt = ON; else opt = OFF; // Input matrix pointers octave_idx_type *cidx = sm.cidx (); octave_idx_type *ridx = sm.ridx (); T* data = sm.data (); // Output matrix data structures. Because the final zero pattern pattern of // the output matrix is not known due to fill-in elements, a heuristic // approach has been adopted for memory allocation. The size of ridx_out_l // and data_out_l is incremented 10% of their actual size (nnz (A) in the // beginning). If that amount is less than n, their size is just incremented // in n elements. This way the number of reallocations decreases throughout // the process, obtaining a good performance. max_len = sm.nnz (); max_len += (0.1 * max_len) > n ? 0.1 * max_len : n; 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, 1)); octave_idx_type *ridx_l = ridx_out_l.fortran_vec (); Array <T> data_out_l (dim_vector (max_len, 1)); T* data_l = data_out_l.fortran_vec (); // Working arrays OCTAVE_LOCAL_BUFFER (T, w_data, n); OCTAVE_LOCAL_BUFFER (octave_idx_type, Lfirst, n); OCTAVE_LOCAL_BUFFER (octave_idx_type, Llist, n); OCTAVE_LOCAL_BUFFER (T, col_drops, n); std::vector<octave_idx_type> vec (n, 0); std::vector<bool> mark (n, false); T zero = T (0); cidx_l[0] = cidx[0]; for (i = 0; i < n; i++) { Llist[i] = -1; Lfirst[i] = -1; w_data[i] = 0; col_drops[i] = zero; } total_len = 0; for (k = 0; k < n; k++) { ind = 0; for (j = cidx[k]; j < cidx[k+1]; j++) { w_data[ridx[j]] = data[j]; // Mark column index, intentionally outside the if-clause to ensure // that mark[k] will be set to true as well. mark[ridx[j]] = true; if (ridx[j] != k) { vec[ind] = ridx[j]; ind++; } } jrow = Llist[k]; while (jrow != -1) { jjrow = Lfirst[jrow]; jend = cidx_l[jrow+1]; for (jj = jjrow; jj < jend; jj++) { j = ridx_l[jj]; // If the element in the j position of the row is zero, // then it will become non-zero, so we add it to the // vector that tracks non-zero elements in the working row. if (! mark[j]) { mark[j] = true; vec[ind] = j; ind++; } w_data[j] -= ichol_mult (data_l[jj], data_l[jjrow]); } // Update the actual column first element and // update the linked list of the jrow row. if ((jjrow + 1) < jend) { Lfirst[jrow]++; j = jrow; jrow = Llist[jrow]; Llist[j] = Llist[ridx_l[Lfirst[j]]]; Llist[ridx_l[Lfirst[j]]] = j; } else jrow = Llist[jrow]; } // Resizing output arrays if ((max_len - total_len) < n) { max_len += (0.1 * max_len) > n ? 0.1 * max_len : n; data_out_l.resize (dim_vector (max_len, 1)); data_l = data_out_l.fortran_vec (); ridx_out_l.resize (dim_vector (max_len, 1)); ridx_l = ridx_out_l.fortran_vec (); } // The sorting of the non-zero elements of the working column can be // handled in a couple of ways. The most efficient two I found, are // keeping the elements in an ordered binary search tree dynamically or // keep them unsorted in a vector and at the end of the outer iteration // order them. The last approach exhibits lower execution times. std::sort (vec.begin (), vec.begin () + ind); data_l[total_len] = w_data[k]; ridx_l[total_len] = k; w_len = 1; // Extract the non-zero elements of working column and // drop the elements that are lower than droptol * cols_norm[k]. for (i = 0; i < ind ; i++) { jrow = vec[i]; if (w_data[jrow] != zero) { if (std::abs (w_data[jrow]) < (droptol * cols_norm[k])) { if (opt == ON) { col_drops[k] += w_data[jrow]; col_drops[jrow] += w_data[jrow]; } } else { data_l[total_len + w_len] = w_data[jrow]; ridx_l[total_len + w_len] = jrow; w_len++; } } // Clear mark, vec, and w_data. However, mark[k] is not set to zero. mark[jrow] = false; vec[i] = 0; w_data[jrow] = zero; } // Compensate column sums --> michol option if (opt == ON) data_l[total_len] += col_drops[k]; if (data_l[total_len] == zero) error ("ichol: encountered a pivot equal to 0"); if (! ichol_checkpivot (data_l[total_len])) break; // Once elements are dropped and compensation of column sums are done, // scale the elements by the pivot. data_l[total_len] = std::sqrt (data_l[total_len]); for (jj = total_len + 1; jj < (total_len + w_len); jj++) data_l[jj] /= data_l[total_len]; total_len += w_len; // 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 < 0) error ("ichol: integer overflow. Too many fill-in elements in L"); cidx_l[k+1] = cidx_l[k] - cidx_l[0] + w_len; // Update Llist and Lfirst with the k-column information. if (k < (n - 1)) { Lfirst[k] = cidx_l[k]; if ((Lfirst[k] + 1) < cidx_l[k+1]) { Lfirst[k]++; jjrow = ridx_l[Lfirst[k]]; Llist[k] = Llist[jjrow]; Llist[jjrow] = k; } } } // Build the output matrices L = octave_matrix_t (n, n, total_len); for (i = 0; i <= n; i++) L.cidx (i) = cidx_l[i]; for (i = 0; i < total_len; i++) { L.ridx (i) = ridx_l[i]; L.data (i) = data_l[i]; } } DEFUN (__icholt__, args, , doc: /* -*- texinfo -*- @deftypefn {} {@var{L} =} __icholt__ (@var{A}, @var{droptol}, @var{michol}) Undocumented internal function. @end deftypefn */) { if (args.length () != 3) print_usage (); double droptol = args(1).double_value (); std::string michol = args(2).string_value (); if (! args(0).iscomplex ()) { SparseMatrix L; SparseMatrix sm_l = Ftril (args(0))(0).sparse_matrix_value (); ichol_t <SparseMatrix, double, ichol_mult_real, ichol_checkpivot_real> (sm_l, L, xcolnorms (sm_l, 1).fortran_vec (), droptol, michol); return ovl (L); } else { SparseComplexMatrix L; SparseComplexMatrix sm_l = Ftril (args(0))(0).sparse_complex_matrix_value (); Array <Complex> cols_norm = xcolnorms (sm_l, 1); ichol_t <SparseComplexMatrix, Complex, ichol_mult_complex, ichol_checkpivot_complex> (sm_l, L, cols_norm.fortran_vec (), Complex (droptol), michol); return ovl (L); } } /* %!test <*51736> %! k = 4; %! n = 2^k; %! Afull = diag (ones (n,1)) / ... %! 2+triu ([zeros(n,2), [n.^-[1;1;2]*ones(1,n-2);zeros(n-3,n-2)]], 1); %! A = sparse (Afull + Afull.'); %! opts.type = "ict"; %! opts.droptol = 0; %! L = ichol (A, opts); %! assert (norm (A - L*L.'), 0, 2*eps); */ OCTAVE_NAMESPACE_END