Mercurial > octave
view libinterp/corefcn/sparse-xpow.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 | b542b88ad3b6 |
children | aac27ad79be6 |
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//////////////////////////////////////////////////////////////////////// // // Copyright (C) 1998-2022 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 <cassert> #include <limits> #include "Array-util.h" #include "oct-cmplx.h" #include "quit.h" #include "error.h" #include "ovl.h" #include "utils.h" #include "dSparse.h" #include "CSparse.h" #include "ov-re-sparse.h" #include "ov-cx-sparse.h" #include "sparse-xpow.h" OCTAVE_BEGIN_NAMESPACE(octave) static inline bool xisint (double x) { return (octave::math::x_nint (x) == x && ((x >= 0 && x < std::numeric_limits<int>::max ()) || (x <= 0 && x > std::numeric_limits<int>::min ()))); } // Safer pow functions. Only two make sense for sparse matrices, the // others should all promote to full matrices. octave_value xpow (const SparseMatrix& a, double b) { octave_value retval; octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); if (nr == 0 || nc == 0) return SparseMatrix (); // If we are here, A is not empty ==> A needs to be square. if (nr != nc) error ("for A^b, A must be a square matrix. Use .^ for elementwise power."); if (! xisint (b)) error ("use full(a) ^ full(b)"); int btmp = static_cast<int> (b); if (btmp == 0) { SparseMatrix tmp = SparseMatrix (nr, nr, nr); for (octave_idx_type i = 0; i < nr; i++) { tmp.data (i) = 1.0; tmp.ridx (i) = i; } for (octave_idx_type i = 0; i < nr + 1; i++) tmp.cidx (i) = i; retval = tmp; } else { SparseMatrix atmp; if (btmp < 0) { btmp = -btmp; octave_idx_type info; double rcond = 0.0; MatrixType mattyp (a); // FIXME: This causes an error if the input sparse matrix is all-zeros. // That behavior is inconsistent with A ^ b when A is a full all-zeros // matrix, which just returns Inf of the same size with a warning. atmp = a.inverse (mattyp, info, rcond, 1); if (info == -1) warning ("inverse: matrix singular to machine precision, rcond = %g", rcond); } else atmp = a; if (atmp.nnz () == 0) // Fast return for all-zeros matrix return atmp; SparseMatrix result (atmp); btmp--; // There are two approaches to the actual exponentiation. // Exponentiation by squaring uses only a logarithmic number // of multiplications but the matrices it multiplies tend to be dense // towards the end. // Linear multiplication uses a linear number of multiplications // but one of the matrices it uses will be as sparse as the original // matrix. // // The time to multiply fixed-size matrices is strongly affected by their // sparsity. Denser matrices take much longer to multiply together. // See this URL for a worked-through example: // https://octave.discourse.group/t/3216/4 // // The tradeoff is between many fast multiplications or a few slow ones. // // Large exponents favor the squaring technique, and sparse matrices // favor linear multiplication. // // We calculate a threshold based on the sparsity of the input // and use squaring for exponents larger than that. // // FIXME: Improve this threshold calculation. uint64_t sparsity = atmp.numel () / atmp.nnz (); // reciprocal of density int threshold = (sparsity >= 1000) ? 40 : (sparsity >= 100) ? 20 : 3; if (btmp > threshold) // use squaring technique { while (btmp > 0) { if (btmp & 1) result = result * atmp; btmp >>= 1; if (btmp > 0) atmp = atmp * atmp; } } else // use linear multiplication { for (int i = 0; i < btmp; i++) result = result * atmp; } retval = result; } return retval; } octave_value xpow (const SparseComplexMatrix& a, double b) { octave_value retval; octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); if (nr == 0 || nc == 0) return SparseMatrix (); // If we are here, A is not empty ==> A needs to be square. if (nr != nc) error ("for A^b, A must be a square matrix. Use .^ for elementwise power."); if (! xisint (b)) error ("use full(a) ^ full(b)"); int btmp = static_cast<int> (b); if (btmp == 0) { SparseMatrix tmp = SparseMatrix (nr, nr, nr); for (octave_idx_type i = 0; i < nr; i++) { tmp.data (i) = 1.0; tmp.ridx (i) = i; } for (octave_idx_type i = 0; i < nr + 1; i++) tmp.cidx (i) = i; retval = tmp; } else { SparseComplexMatrix atmp; if (btmp < 0) { btmp = -btmp; octave_idx_type info; double rcond = 0.0; MatrixType mattyp (a); atmp = a.inverse (mattyp, info, rcond, 1); if (info == -1) warning ("inverse: matrix singular to machine precision, rcond = %g", rcond); } else atmp = a; if (atmp.nnz () == 0) // Fast return for all-zeros matrix return atmp; SparseComplexMatrix result (atmp); btmp--; // Select multiplication sequence based on sparsity of atmp. // See the long comment in xpow (const SparseMatrix& a, double b) // for more details. // // FIXME: Improve this threshold calculation. uint64_t sparsity = atmp.numel () / atmp.nnz (); // reciprocal of density int threshold = (sparsity >= 1000) ? 40 : (sparsity >= 100) ? 20 : 3; if (btmp > threshold) // use squaring technique { while (btmp > 0) { if (btmp & 1) result = result * atmp; btmp >>= 1; if (btmp > 0) atmp = atmp * atmp; } } else // use linear multiplication { for (int i = 0; i < btmp; i++) result = result * atmp; } retval = result; } return retval; } // Safer pow functions that work elementwise for matrices. // // op2 \ op1: s m cs cm // +-- +---+---+----+----+ // scalar | | * | 3 | * | 9 | // +---+---+----+----+ // matrix | 1 | 4 | 7 | 10 | // +---+---+----+----+ // complex_scalar | * | 5 | * | 11 | // +---+---+----+----+ // complex_matrix | 2 | 6 | 8 | 12 | // +---+---+----+----+ // // * -> not needed. // FIXME: these functions need to be fixed so that things // like // // a = -1; b = [ 0, 0.5, 1 ]; r = a .^ b // // and // // a = -1; b = [ 0, 0.5, 1 ]; for i = 1:3, r(i) = a .^ b(i), end // // produce identical results. Also, it would be nice if -1^0.5 // produced a pure imaginary result instead of a complex number with a // small real part. But perhaps that's really a problem with the math // library... // Handle special case of scalar-sparse-matrix .^ sparse-matrix. // Forwarding to the scalar elem_xpow function and then converting the // result back to a sparse matrix is a bit wasteful but it does not // seem worth the effort to optimize -- how often does this case come up // in practice? template <typename S, typename SM> inline octave_value scalar_xpow (const S& a, const SM& b) { octave_value val = elem_xpow (a, b); if (val.iscomplex ()) return SparseComplexMatrix (val.complex_matrix_value ()); else return SparseMatrix (val.matrix_value ()); } /* %!assert (sparse (2) .^ [3, 4], sparse ([8, 16])) %!assert <47775> (sparse (2i) .^ [3, 4], sparse ([-0-8i, 16])) %!test <*63080> %! Z = sparse ([]); %! A = sparse (zeros (0, 2)); %! B = sparse (zeros (2, 0)); %! assert (Z ^ 1, Z); %! assert (Z ^ 0, Z); %! assert (Z ^ -1, Z); %! assert (A ^ 1, Z); %! assert (A ^ 0, Z); %! assert (A ^ -1, Z); %! assert (B ^ 1, Z); %! assert (B ^ 0, Z); %! assert (B ^ -1, Z); %!test <*63080> %! A = sparse (zeros (2, 2)); %! assert (A ^ 1, A); %! assert (A ^ 0, sparse (eye (2, 2))); %!test <63080> %! A = sparse (zeros (2, 2)); %! assert (A ^ -1, sparse (inf (2, 2))); */ // -*- 1 -*- octave_value elem_xpow (double a, const SparseMatrix& b) { octave_value retval; octave_idx_type nr = b.rows (); octave_idx_type nc = b.cols (); double d1, d2; if (a < 0.0 && ! b.all_integers (d1, d2)) { Complex atmp (a); ComplexMatrix result (nr, nc); for (octave_idx_type j = 0; j < nc; j++) { for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); result(i, j) = std::pow (atmp, b(i, j)); } } retval = result; } else { Matrix result (nr, nc); for (octave_idx_type j = 0; j < nc; j++) { for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); result(i, j) = std::pow (a, b(i, j)); } } retval = result; } return retval; } // -*- 2 -*- octave_value elem_xpow (double a, const SparseComplexMatrix& b) { octave_idx_type nr = b.rows (); octave_idx_type nc = b.cols (); Complex atmp (a); ComplexMatrix result (nr, nc); for (octave_idx_type j = 0; j < nc; j++) { for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); result(i, j) = std::pow (atmp, b(i, j)); } } return result; } // -*- 3 -*- octave_value elem_xpow (const SparseMatrix& a, double b) { // FIXME: What should a .^ 0 give? Matlab gives a // sparse matrix with same structure as a, which is strictly // incorrect. Keep compatibility. octave_value retval; octave_idx_type nz = a.nnz (); if (b <= 0.0) { octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); if (! xisint (b) && a.any_element_is_negative ()) { ComplexMatrix result (nr, nc, Complex (std::pow (0.0, b))); // FIXME: avoid apparent GNU libm bug by // converting A and B to complex instead of just A. Complex btmp (b); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = a.cidx (j); i < a.cidx (j+1); i++) { octave_quit (); Complex atmp (a.data (i)); result(a.ridx (i), j) = std::pow (atmp, btmp); } retval = octave_value (result); } else { Matrix result (nr, nc, (std::pow (0.0, b))); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = a.cidx (j); i < a.cidx (j+1); i++) { octave_quit (); result(a.ridx (i), j) = std::pow (a.data (i), b); } retval = octave_value (result); } } else if (! xisint (b) && a.any_element_is_negative ()) { SparseComplexMatrix result (a); for (octave_idx_type i = 0; i < nz; i++) { octave_quit (); // FIXME: avoid apparent GNU libm bug by // converting A and B to complex instead of just A. Complex atmp (a.data (i)); Complex btmp (b); result.data (i) = std::pow (atmp, btmp); } result.maybe_compress (true); retval = result; } else { SparseMatrix result (a); for (octave_idx_type i = 0; i < nz; i++) { octave_quit (); result.data (i) = std::pow (a.data (i), b); } result.maybe_compress (true); retval = result; } return retval; } // -*- 4 -*- octave_value elem_xpow (const SparseMatrix& a, const SparseMatrix& b) { octave_value retval; octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); octave_idx_type b_nr = b.rows (); octave_idx_type b_nc = b.cols (); if (a.numel () == 1 && b.numel () > 1) return scalar_xpow (a(0), b); if (nr != b_nr || nc != b_nc) octave::err_nonconformant ("operator .^", nr, nc, b_nr, b_nc); int convert_to_complex = 0; for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = a.cidx (j); i < a.cidx (j+1); i++) { if (a.data(i) < 0.0) { double btmp = b (a.ridx (i), j); if (! xisint (btmp)) { convert_to_complex = 1; goto done; } } } done: // This is a dumb operator for sparse matrices anyway, and there is // no sensible way to handle the 0.^0 versus the 0.^x cases. Therefore // allocate a full matrix filled for the 0.^0 case and shrink it later // as needed. if (convert_to_complex) { SparseComplexMatrix complex_result (nr, nc, Complex (1.0, 0.0)); for (octave_idx_type j = 0; j < nc; j++) { for (octave_idx_type i = a.cidx (j); i < a.cidx (j+1); i++) { octave_quit (); complex_result.xelem (a.ridx (i), j) = std::pow (Complex (a.data (i)), Complex (b(a.ridx (i), j))); } } complex_result.maybe_compress (true); retval = complex_result; } else { SparseMatrix result (nr, nc, 1.0); for (octave_idx_type j = 0; j < nc; j++) { for (octave_idx_type i = a.cidx (j); i < a.cidx (j+1); i++) { octave_quit (); result.xelem (a.ridx (i), j) = std::pow (a.data (i), b(a.ridx (i), j)); } } result.maybe_compress (true); retval = result; } return retval; } // -*- 5 -*- octave_value elem_xpow (const SparseMatrix& a, const Complex& b) { octave_value retval; if (b == 0.0) // Can this case ever happen, due to automatic retyping with maybe_mutate? retval = octave_value (NDArray (a.dims (), 1)); else { octave_idx_type nz = a.nnz (); SparseComplexMatrix result (a); for (octave_idx_type i = 0; i < nz; i++) { octave_quit (); result.data (i) = std::pow (Complex (a.data (i)), b); } result.maybe_compress (true); retval = result; } return retval; } // -*- 6 -*- octave_value elem_xpow (const SparseMatrix& a, const SparseComplexMatrix& b) { octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); octave_idx_type b_nr = b.rows (); octave_idx_type b_nc = b.cols (); if (a.numel () == 1 && b.numel () > 1) return scalar_xpow (a(0), b); if (nr != b_nr || nc != b_nc) octave::err_nonconformant ("operator .^", nr, nc, b_nr, b_nc); SparseComplexMatrix result (nr, nc, Complex (1.0, 0.0)); for (octave_idx_type j = 0; j < nc; j++) { for (octave_idx_type i = a.cidx (j); i < a.cidx (j+1); i++) { octave_quit (); result.xelem (a.ridx(i), j) = std::pow (a.data (i), b(a.ridx (i), j)); } } result.maybe_compress (true); return result; } // -*- 7 -*- octave_value elem_xpow (const Complex& a, const SparseMatrix& b) { octave_idx_type nr = b.rows (); octave_idx_type nc = b.cols (); ComplexMatrix result (nr, nc); for (octave_idx_type j = 0; j < nc; j++) { for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); double btmp = b (i, j); if (xisint (btmp)) result (i, j) = std::pow (a, static_cast<int> (btmp)); else result (i, j) = std::pow (a, btmp); } } return result; } // -*- 8 -*- octave_value elem_xpow (const Complex& a, const SparseComplexMatrix& b) { octave_idx_type nr = b.rows (); octave_idx_type nc = b.cols (); ComplexMatrix result (nr, nc); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); result (i, j) = std::pow (a, b (i, j)); } return result; } // -*- 9 -*- octave_value elem_xpow (const SparseComplexMatrix& a, double b) { octave_value retval; if (b <= 0) { octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); ComplexMatrix result (nr, nc, Complex (std::pow (0.0, b))); if (xisint (b)) { for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = a.cidx (j); i < a.cidx (j+1); i++) { octave_quit (); result (a.ridx (i), j) = std::pow (a.data (i), static_cast<int> (b)); } } else { for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = a.cidx (j); i < a.cidx (j+1); i++) { octave_quit (); result (a.ridx (i), j) = std::pow (a.data (i), b); } } retval = result; } else { octave_idx_type nz = a.nnz (); SparseComplexMatrix result (a); if (xisint (b)) { for (octave_idx_type i = 0; i < nz; i++) { octave_quit (); result.data (i) = std::pow (a.data (i), static_cast<int> (b)); } } else { for (octave_idx_type i = 0; i < nz; i++) { octave_quit (); result.data (i) = std::pow (a.data (i), b); } } result.maybe_compress (true); retval = result; } return retval; } // -*- 10 -*- octave_value elem_xpow (const SparseComplexMatrix& a, const SparseMatrix& b) { octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); octave_idx_type b_nr = b.rows (); octave_idx_type b_nc = b.cols (); if (a.numel () == 1 && b.numel () > 1) return scalar_xpow (a(0), b); if (nr != b_nr || nc != b_nc) octave::err_nonconformant ("operator .^", nr, nc, b_nr, b_nc); SparseComplexMatrix result (nr, nc, Complex (1.0, 0.0)); for (octave_idx_type j = 0; j < nc; j++) { for (octave_idx_type i = a.cidx (j); i < a.cidx (j+1); i++) { octave_quit (); double btmp = b(a.ridx (i), j); if (xisint (btmp)) result.xelem (a.ridx (i), j) = std::pow (a.data (i), static_cast<int> (btmp)); else result.xelem (a.ridx (i), j) = std::pow (a.data (i), btmp); } } result.maybe_compress (true); return result; } // -*- 11 -*- octave_value elem_xpow (const SparseComplexMatrix& a, const Complex& b) { octave_value retval; if (b == 0.0) // Can this case ever happen, due to automatic retyping with maybe_mutate? retval = octave_value (NDArray (a.dims (), 1)); else { octave_idx_type nz = a.nnz (); SparseComplexMatrix result (a); for (octave_idx_type i = 0; i < nz; i++) { octave_quit (); result.data (i) = std::pow (a.data (i), b); } result.maybe_compress (true); retval = result; } return retval; } // -*- 12 -*- octave_value elem_xpow (const SparseComplexMatrix& a, const SparseComplexMatrix& b) { octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); octave_idx_type b_nr = b.rows (); octave_idx_type b_nc = b.cols (); if (a.numel () == 1 && b.numel () > 1) return scalar_xpow (a(0), b); if (nr != b_nr || nc != b_nc) octave::err_nonconformant ("operator .^", nr, nc, b_nr, b_nc); SparseComplexMatrix result (nr, nc, Complex (1.0, 0.0)); for (octave_idx_type j = 0; j < nc; j++) { for (octave_idx_type i = a.cidx (j); i < a.cidx (j+1); i++) { octave_quit (); result.xelem (a.ridx (i), j) = std::pow (a.data (i), b(a.ridx (i), j)); } } result.maybe_compress (true); return result; } OCTAVE_END_NAMESPACE(octave)