Mercurial > octave
view libinterp/corefcn/xpow.cc @ 31771:21f9b34eb893
maint: Eliminate "(void)" in C++ function prototypes/declarations.
* mk-opts.pl, external.txi, embedded.cc, make_int.cc, standalone.cc,
standalonebuiltin.cc, BaseControl.cc, BaseControl.h, ButtonControl.cc,
ButtonControl.h, ButtonGroup.cc, ButtonGroup.h, Canvas.cc, Canvas.h,
CheckBoxControl.cc, CheckBoxControl.h, Container.cc, Container.h,
ContextMenu.cc, ContextMenu.h, EditControl.cc, EditControl.h, Figure.cc,
Figure.h, FigureWindow.cc, FigureWindow.h, GLCanvas.cc, GLCanvas.h,
GenericEventNotify.h, KeyMap.cc, ListBoxControl.cc, ListBoxControl.h,
Logger.cc, Logger.h, Menu.cc, Menu.h, MenuContainer.h, Object.cc, Object.h,
ObjectProxy.cc, ObjectProxy.h, Panel.cc, Panel.h, PopupMenuControl.cc,
PopupMenuControl.h, PushButtonControl.cc, PushButtonControl.h, PushTool.cc,
PushTool.h, RadioButtonControl.cc, RadioButtonControl.h, SliderControl.cc,
SliderControl.h, Table.cc, Table.h, TextControl.cc, TextControl.h, TextEdit.h,
ToggleButtonControl.cc, ToggleButtonControl.h, ToggleTool.cc, ToggleTool.h,
ToolBar.cc, ToolBar.h, ToolBarButton.cc, ToolBarButton.h, gl-select.cc,
gl-select.h, qopengl-functions.h, qt-graphics-toolkit.h, qdialog.cpp,
qfontdialog.cpp, qprintdialog_win.cpp, liboctgui-build-info.h,
liboctgui-build-info.in.cc, color-picker.cc, color-picker.h, command-widget.cc,
command-widget.h, community-news.cc, community-news.h, dialog.cc, dialog.h,
documentation-bookmarks.cc, documentation-bookmarks.h,
documentation-dock-widget.cc, documentation-dock-widget.h, documentation.cc,
documentation.h, dw-main-window.cc, dw-main-window.h,
external-editor-interface.cc, external-editor-interface.h,
files-dock-widget.cc, files-dock-widget.h, find-files-dialog.cc,
find-files-dialog.h, find-files-model.cc, find-files-model.h,
gui-preferences.cc, gui-preferences.h, gui-settings.cc, gui-settings.h,
history-dock-widget.cc, history-dock-widget.h, interpreter-qobject.cc,
interpreter-qobject.h, file-editor-interface.h, file-editor-tab.cc,
file-editor-tab.h, file-editor.cc, file-editor.h, find-dialog.cc,
find-dialog.h, marker.cc, marker.h, octave-qscintilla.cc, octave-qscintilla.h,
octave-txt-lexer.cc, octave-txt-lexer.h, main-window.cc, main-window.h,
news-reader.cc, news-reader.h, octave-dock-widget.cc, octave-dock-widget.h,
octave-qobject.cc, octave-qobject.h, qt-application.cc, qt-application.h,
qt-interpreter-events.cc, qt-interpreter-events.h, release-notes.cc,
release-notes.h, set-path-dialog.cc, set-path-dialog.h, set-path-model.cc,
set-path-model.h, settings-dialog.cc, settings-dialog.h,
shortcuts-tree-widget.cc, shortcuts-tree-widget.h, tab-bar.cc, tab-bar.h,
terminal-dock-widget.cc, terminal-dock-widget.h, variable-editor-model.cc,
variable-editor-model.h, variable-editor.cc, variable-editor.h,
welcome-wizard.cc, welcome-wizard.h, workspace-model.cc, workspace-model.h,
workspace-view.cc, workspace-view.h, build-env.h, Cell.cc, Cell.h,
__contourc__.cc, __magick_read__.cc, auto-shlib.cc, auto-shlib.h,
base-text-renderer.h, bsxfun.cc, c-file-ptr-stream.cc, c-file-ptr-stream.h,
call-stack.cc, call-stack.h, debug.cc, defaults.cc, defaults.h, defun.cc,
display.cc, display.h, dynamic-ld.cc, dynamic-ld.h, environment.cc,
environment.h, error.cc, error.h, errwarn.cc, errwarn.h, event-manager.cc,
event-manager.h, event-queue.cc, event-queue.h, fcn-info.cc, fcn-info.h,
ft-text-renderer.cc, ft-text-renderer.h, genprops.awk, gh-manager.cc,
gh-manager.h, gl-render.cc, gl-render.h, gl2ps-print.cc, graphics-toolkit.h,
graphics.cc, graphics.in.h, gtk-manager.cc, gtk-manager.h, help.cc, help.h,
hook-fcn.h, input.cc, input.h, interpreter-private.cc, interpreter-private.h,
interpreter.cc, interpreter.h, jsondecode.cc, latex-text-renderer.cc,
latex-text-renderer.h, load-path.cc, load-path.h, load-save.cc, load-save.h,
ls-hdf5.cc, ls-hdf5.h, mxarray.h, oct-errno.h, oct-errno.in.cc, oct-fstrm.cc,
oct-fstrm.h, oct-handle.h, oct-hist.cc, oct-hist.h, oct-iostrm.cc,
oct-iostrm.h, oct-map.cc, oct-map.h, oct-opengl.h, oct-prcstrm.cc,
oct-prcstrm.h, oct-procbuf.cc, oct-procbuf.h, oct-process.h, oct-stdstrm.h,
oct-stream.cc, oct-stream.h, oct-strstrm.cc, oct-strstrm.h,
oct-tex-lexer.in.ll, pager.cc, pager.h, pr-flt-fmt.cc, pr-flt-fmt.h,
pr-output.cc, pr-output.h, procstream.cc, procstream.h, settings.cc,
settings.h, sighandlers.cc, sighandlers.h, stack-frame.cc, stack-frame.h,
svd.cc, syminfo.cc, syminfo.h, symrec.cc, symrec.h, symscope.cc, symscope.h,
symtab.cc, symtab.h, sysdep.cc, sysdep.h, text-engine.cc, text-engine.h,
text-renderer.cc, text-renderer.h, toplev.cc, url-handle-manager.cc,
url-handle-manager.h, variables.cc, xpow.cc, __init_fltk__.cc,
__init_gnuplot__.cc, __ode15__.cc, audiodevinfo.cc, gzip.cc,
liboctinterp-build-info.h, liboctinterp-build-info.in.cc,
mk-build-env-features.sh, mk-builtins.pl, cdef-class.cc, cdef-class.h,
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-diag.cc, ov-base-diag.h, ov-base-int.cc,
ov-base-int.h, ov-base-mat.cc, ov-base-mat.h, ov-base-scalar.cc,
ov-base-scalar.h, ov-base-sparse.cc, ov-base-sparse.h, ov-base.cc, ov-base.h,
ov-bool-mat.cc, ov-bool-mat.h, ov-bool-sparse.cc, ov-bool-sparse.h, ov-bool.cc,
ov-bool.h, ov-builtin.cc, ov-builtin.h, ov-cell.cc, ov-cell.h, ov-ch-mat.cc,
ov-ch-mat.h, ov-class.cc, ov-class.h, ov-classdef.cc, ov-classdef.h,
ov-colon.h, ov-complex.cc, ov-complex.h, ov-cs-list.h, ov-cx-diag.cc,
ov-cx-diag.h, ov-cx-mat.cc, ov-cx-mat.h, ov-cx-sparse.cc, ov-cx-sparse.h,
ov-dld-fcn.cc, ov-dld-fcn.h, ov-fcn-handle.cc, ov-fcn-handle.h, ov-fcn.cc,
ov-fcn.h, ov-float.cc, ov-float.h, ov-flt-complex.cc, ov-flt-complex.h,
ov-flt-cx-diag.cc, ov-flt-cx-diag.h, ov-flt-cx-mat.cc, ov-flt-cx-mat.h,
ov-flt-re-diag.cc, ov-flt-re-diag.h, ov-flt-re-mat.cc, ov-flt-re-mat.h,
ov-intx.h, ov-java.cc, ov-java.h, ov-lazy-idx.cc, ov-lazy-idx.h,
ov-legacy-range.cc, ov-legacy-range.h, ov-magic-int.cc, ov-magic-int.h,
ov-mex-fcn.cc, ov-mex-fcn.h, ov-null-mat.cc, ov-null-mat.h, ov-oncleanup.cc,
ov-oncleanup.h, ov-perm.cc, ov-perm.h, ov-range.cc, ov-range.h, ov-re-diag.cc,
ov-re-diag.h, ov-re-mat.cc, ov-re-mat.h, ov-re-sparse.cc, ov-re-sparse.h,
ov-scalar.cc, ov-scalar.h, ov-str-mat.cc, ov-str-mat.h, ov-struct.cc,
ov-struct.h, ov-typeinfo.cc, ov-typeinfo.h, ov-usr-fcn.cc, ov-usr-fcn.h, ov.cc,
ov.h, ovl.cc, ovl.h, octave.cc, octave.h, 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.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.h, pt-cbinop.h, pt-cell.h, pt-check.h,
pt-classdef.cc, pt-classdef.h, pt-cmd.h, pt-colon.h, 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.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-walk.h, pt.cc, pt.h, token.cc, token.h, usage.h, Array-base.cc, Array.h,
CColVector.cc, CColVector.h, CDiagMatrix.cc, CDiagMatrix.h, CMatrix.cc,
CMatrix.h, CNDArray.cc, CNDArray.h, CRowVector.cc, CRowVector.h, CSparse.cc,
CSparse.h, DiagArray2.cc, DiagArray2.h, MArray.cc, MArray.h, MDiagArray2.h,
MSparse.h, MatrixType.cc, MatrixType.h, PermMatrix.cc, PermMatrix.h, Range.cc,
Range.h, Sparse-b.cc, Sparse.cc, Sparse.h, boolMatrix.cc, boolMatrix.h,
boolNDArray.cc, boolNDArray.h, boolSparse.cc, boolSparse.h, chMatrix.h,
chNDArray.h, dColVector.cc, dColVector.h, dDiagMatrix.cc, dDiagMatrix.h,
dMatrix.cc, dMatrix.h, dNDArray.cc, dNDArray.h, dRowVector.cc, dRowVector.h,
dSparse.cc, dSparse.h, dim-vector.cc, dim-vector.h, fCColVector.cc,
fCColVector.h, fCDiagMatrix.cc, fCDiagMatrix.h, fCMatrix.cc, fCMatrix.h,
fCNDArray.cc, fCNDArray.h, fCRowVector.cc, fCRowVector.h, fColVector.cc,
fColVector.h, fDiagMatrix.cc, fDiagMatrix.h, fMatrix.cc, fMatrix.h,
fNDArray.cc, fNDArray.h, fRowVector.cc, fRowVector.h, idx-vector.cc,
idx-vector.h, intNDArray.cc, intNDArray.h, liboctave-build-info.h,
liboctave-build-info.in.cc, CollocWt.cc, CollocWt.h, DAE.h, DAEFunc.h, DAERT.h,
DAERTFunc.h, DASPK.cc, DASPK.h, DASRT.cc, DASRT.h, DASSL.cc, DASSL.h, DET.h,
EIG.h, LSODE.cc, LSODE.h, ODE.h, ODEFunc.h, ODES.h, ODESFunc.h, Quad.h,
aepbalance.cc, aepbalance.h, base-dae.h, base-de.h, chol.cc, chol.h,
eigs-base.cc, fEIG.h, gepbalance.h, gsvd.cc, gsvd.h, hess.h, lu.cc, lu.h,
oct-fftw.cc, oct-fftw.h, oct-rand.cc, oct-rand.h, oct-spparms.cc,
oct-spparms.h, qr.cc, qr.h, qrp.cc, qrp.h, randmtzig.cc, randmtzig.h, 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.h, base-list.h, caseless-str.h, cmd-edit.cc, cmd-edit.h,
cmd-hist.cc, cmd-hist.h, data-conv.cc, file-info.h, glob-match.cc,
glob-match.h, kpse.cc, kpse.h, lo-array-errwarn.cc, lo-array-errwarn.h,
lo-hash.cc, lo-hash.h, lo-ieee.cc, lo-ieee.h, lo-regexp.cc, lo-regexp.h,
oct-inttypes.cc, oct-inttypes.h, oct-mutex.cc, oct-mutex.h, oct-refcount.h,
oct-shlib.cc, oct-shlib.h, oct-sort.cc, oct-sort.h, oct-sparse.cc,
octave-preserve-stream-state.h, pathsearch.cc, pathsearch.h, quit.cc,
singleton-cleanup.cc, singleton-cleanup.h, str-vec.cc, str-vec.h,
unwind-prot.cc, unwind-prot.h, url-transfer.cc, url-transfer.h, version.cc,
version.in.h, cxx-signal-helpers.cc, acinclude.m4, main-cli.cc, main-gui.cc,
main.in.cc, mkoctfile.in.cc, octave-build-info.h, octave-build-info.in.cc,
octave-config.in.cc, octave-svgconvert.cc, shared-fcns.h:
maint: Eliminate "(void)" in C++ function prototypes/declarations.
author | Rik <rik@octave.org> |
---|---|
date | Tue, 24 Jan 2023 17:19:44 -0800 |
parents | 597f3ee61a48 |
children | 1de97b475564 |
line wrap: on
line source
//////////////////////////////////////////////////////////////////////// // // Copyright (C) 1993-2023 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 "CColVector.h" #include "CDiagMatrix.h" #include "fCDiagMatrix.h" #include "fCMatrix.h" #include "CMatrix.h" #include "EIG.h" #include "fEIG.h" #include "dDiagMatrix.h" #include "fDiagMatrix.h" #include "dMatrix.h" #include "PermMatrix.h" #include "mx-cm-cdm.h" #include "mx-fcm-fcdm.h" #include "oct-cmplx.h" #include "Range.h" #include "quit.h" #include "error.h" #include "ovl.h" #include "utils.h" #include "xpow.h" #include "bsxfun.h" OCTAVE_BEGIN_NAMESPACE(octave) static void err_failed_diagonalization () { error ("Failed to diagonalize matrix while calculating matrix exponential"); } static void err_nonsquare_matrix () { error ("for x^y, only square matrix arguments are permitted and one " \ "argument must be scalar. Use .^ for elementwise power."); } template <typename T> static inline bool xisint (T x) { return (octave::math::x_nint (x) == x && x <= std::numeric_limits<int>::max () && x >= std::numeric_limits<int>::min ()); } static inline bool xisint (float x) { static const float out_of_range_top = static_cast<float>(std::numeric_limits<int>::max ()) + 1.; return (octave::math::x_nint (x) == x && x < out_of_range_top && x >= std::numeric_limits<int>::min ()); } // Safer pow functions. // // op2 \ op1: s m cs cm // +-- +---+---+----+----+ // scalar | | 1 | 5 | 7 | 11 | // +---+---+----+----+ // matrix | 2 | * | 8 | * | // +---+---+----+----+ // complex_scalar | 3 | 6 | 9 | 12 | // +---+---+----+----+ // complex_matrix | 4 | * | 10 | * | // +---+---+----+----+ // -*- 1 -*- octave_value xpow (double a, double b) { double retval; if (a < 0.0 && ! xisint (b)) { Complex acplx (a); return std::pow (acplx, b); } else retval = std::pow (a, b); return retval; } // -*- 2 -*- octave_value xpow (double a, const Matrix& b) { octave_value retval; octave_idx_type nr = b.rows (); octave_idx_type nc = b.cols (); if (nr == 0 || nc == 0) return Matrix (); if (nr != nc) err_nonsquare_matrix (); EIG b_eig (b); try { ComplexColumnVector lambda (b_eig.eigenvalues ()); ComplexMatrix Q (b_eig.right_eigenvectors ()); for (octave_idx_type i = 0; i < nr; i++) lambda(i) = std::pow (a, lambda(i)); ComplexDiagMatrix D (lambda); ComplexMatrix C = Q * D * Q.inverse (); if (a > 0) retval = real (C); else retval = C; } catch (const octave::execution_exception&) { err_failed_diagonalization (); } return retval; } // -*- 3 -*- octave_value xpow (double a, const Complex& b) { Complex result = std::pow (a, b); return result; } // -*- 4 -*- octave_value xpow (double a, const ComplexMatrix& b) { octave_value retval; octave_idx_type nr = b.rows (); octave_idx_type nc = b.cols (); if (nr == 0 || nc == 0) return Matrix (); if (nr != nc) err_nonsquare_matrix (); EIG b_eig (b); try { ComplexColumnVector lambda (b_eig.eigenvalues ()); ComplexMatrix Q (b_eig.right_eigenvectors ()); for (octave_idx_type i = 0; i < nr; i++) lambda(i) = std::pow (a, lambda(i)); ComplexDiagMatrix D (lambda); retval = ComplexMatrix (Q * D * Q.inverse ()); } catch (const octave::execution_exception&) { err_failed_diagonalization (); } return retval; } // -*- 5 -*- octave_value xpow (const Matrix& a, double b) { octave_value retval; octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); if (nr == 0 || nc == 0) return Matrix (); if (nr != nc) err_nonsquare_matrix (); if (xisint (b)) { int bint = static_cast<int> (b); if (bint == 0) { retval = DiagMatrix (nr, nr, 1.0); } else { // Too much copying? // FIXME: we shouldn't do this if the exponent is large... Matrix atmp; if (bint < 0) { bint = -bint; octave_idx_type info; double rcond = 0.0; MatrixType mattype (a); atmp = a.inverse (mattype, info, rcond, 1); if (info == -1) warning ("inverse: matrix singular to machine precision, rcond = %g", rcond); } else atmp = a; Matrix result (atmp); bint--; while (bint > 0) { if (bint & 1) // Use atmp * result instead of result * atmp // for ML compatibility (bug #52706). result = atmp * result; bint >>= 1; if (bint > 0) atmp = atmp * atmp; } retval = result; } } else { EIG a_eig (a); try { ComplexColumnVector lambda (a_eig.eigenvalues ()); ComplexMatrix Q (a_eig.right_eigenvectors ()); for (octave_idx_type i = 0; i < nr; i++) lambda(i) = std::pow (lambda(i), b); ComplexDiagMatrix D (lambda); retval = ComplexMatrix (Q * D * Q.inverse ()); } catch (const octave::execution_exception&) { err_failed_diagonalization (); } } return retval; } // -*- 5d -*- octave_value xpow (const DiagMatrix& a, double b) { octave_value retval; octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); if (nr == 0 || nc == 0) return Matrix (); if (nr != nc) err_nonsquare_matrix (); if (xisint (b)) { int bint = static_cast<int> (b); DiagMatrix r (nr, nc); for (octave_idx_type i = 0; i < nc; i++) r.dgxelem (i) = std::pow (a.dgxelem (i), bint); retval = r; } else { ComplexDiagMatrix r (nr, nc); for (octave_idx_type i = 0; i < nc; i++) r.dgxelem (i) = std::pow (static_cast<Complex> (a.dgxelem (i)), b); retval = r; } return retval; } // -*- 5p -*- octave_value xpow (const PermMatrix& a, double b) { if (xisint (b)) return a.power (static_cast<int> (b)); else return xpow (Matrix (a), b); } // -*- 6 -*- octave_value xpow (const Matrix& a, const Complex& b) { octave_value retval; octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); if (nr == 0 || nc == 0) return Matrix (); if (nr != nc) err_nonsquare_matrix (); EIG a_eig (a); try { ComplexColumnVector lambda (a_eig.eigenvalues ()); ComplexMatrix Q (a_eig.right_eigenvectors ()); for (octave_idx_type i = 0; i < nr; i++) lambda(i) = std::pow (lambda(i), b); ComplexDiagMatrix D (lambda); retval = ComplexMatrix (Q * D * Q.inverse ()); } catch (const octave::execution_exception&) { err_failed_diagonalization (); } return retval; } // -*- 7 -*- octave_value xpow (const Complex& a, double b) { Complex result; if (xisint (b)) result = std::pow (a, static_cast<int> (b)); else result = std::pow (a, b); return result; } // -*- 8 -*- octave_value xpow (const Complex& a, const Matrix& b) { octave_value retval; octave_idx_type nr = b.rows (); octave_idx_type nc = b.cols (); if (nr == 0 || nc == 0) return Matrix (); if (nr != nc) err_nonsquare_matrix (); EIG b_eig (b); try { ComplexColumnVector lambda (b_eig.eigenvalues ()); ComplexMatrix Q (b_eig.right_eigenvectors ()); for (octave_idx_type i = 0; i < nr; i++) lambda(i) = std::pow (a, lambda(i)); ComplexDiagMatrix D (lambda); retval = ComplexMatrix (Q * D * Q.inverse ()); } catch (const octave::execution_exception&) { err_failed_diagonalization (); } return retval; } // -*- 9 -*- octave_value xpow (const Complex& a, const Complex& b) { Complex result; result = std::pow (a, b); return result; } // -*- 10 -*- octave_value xpow (const Complex& a, const ComplexMatrix& b) { octave_value retval; octave_idx_type nr = b.rows (); octave_idx_type nc = b.cols (); if (nr == 0 || nc == 0) return Matrix (); if (nr != nc) err_nonsquare_matrix (); EIG b_eig (b); try { ComplexColumnVector lambda (b_eig.eigenvalues ()); ComplexMatrix Q (b_eig.right_eigenvectors ()); for (octave_idx_type i = 0; i < nr; i++) lambda(i) = std::pow (a, lambda(i)); ComplexDiagMatrix D (lambda); retval = ComplexMatrix (Q * D * Q.inverse ()); } catch (const octave::execution_exception&) { err_failed_diagonalization (); } return retval; } // -*- 11 -*- octave_value xpow (const ComplexMatrix& a, double b) { octave_value retval; octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); if (nr == 0 || nc == 0) return Matrix (); if (nr != nc) err_nonsquare_matrix (); if (xisint (b)) { int bint = static_cast<int> (b); if (bint == 0) { retval = DiagMatrix (nr, nr, 1.0); } else { // Too much copying? // FIXME: we shouldn't do this if the exponent is large... ComplexMatrix atmp; if (bint < 0) { bint = -bint; octave_idx_type info; double rcond = 0.0; MatrixType mattype (a); atmp = a.inverse (mattype, info, rcond, 1); if (info == -1) warning ("inverse: matrix singular to machine precision, rcond = %g", rcond); } else atmp = a; ComplexMatrix result (atmp); bint--; while (bint > 0) { if (bint & 1) // Use atmp * result instead of result * atmp // for ML compatibility (bug #52706). result = atmp * result; bint >>= 1; if (bint > 0) atmp = atmp * atmp; } retval = result; } } else { EIG a_eig (a); try { ComplexColumnVector lambda (a_eig.eigenvalues ()); ComplexMatrix Q (a_eig.right_eigenvectors ()); for (octave_idx_type i = 0; i < nr; i++) lambda(i) = std::pow (lambda(i), b); ComplexDiagMatrix D (lambda); retval = ComplexMatrix (Q * D * Q.inverse ()); } catch (const octave::execution_exception&) { err_failed_diagonalization (); } } return retval; } // -*- 12 -*- octave_value xpow (const ComplexMatrix& a, const Complex& b) { octave_value retval; octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); if (nr == 0 || nc == 0) return Matrix (); if (nr != nc) err_nonsquare_matrix (); EIG a_eig (a); try { ComplexColumnVector lambda (a_eig.eigenvalues ()); ComplexMatrix Q (a_eig.right_eigenvectors ()); for (octave_idx_type i = 0; i < nr; i++) lambda(i) = std::pow (lambda(i), b); ComplexDiagMatrix D (lambda); retval = ComplexMatrix (Q * D * Q.inverse ()); } catch (const octave::execution_exception&) { err_failed_diagonalization (); } return retval; } // -*- 12d -*- octave_value xpow (const ComplexDiagMatrix& a, const Complex& b) { octave_value retval; octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); if (nr == 0 || nc == 0) return Matrix (); if (nr != nc) err_nonsquare_matrix (); ComplexDiagMatrix r (nr, nc); for (octave_idx_type i = 0; i < nc; i++) r.dgxelem (i) = std::pow (a.dgxelem (i), b); retval = r; return retval; } // mixed octave_value xpow (const ComplexDiagMatrix& a, double b) { return xpow (a, static_cast<Complex> (b)); } octave_value xpow (const DiagMatrix& a, const Complex& b) { return xpow (ComplexDiagMatrix (a), b); } // 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... // -*- 1 -*- octave_value elem_xpow (double a, const Matrix& 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 acplx (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 (acplx, 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 ComplexMatrix& b) { octave_idx_type nr = b.rows (); octave_idx_type nc = b.cols (); ComplexMatrix result (nr, nc); Complex acplx (a); 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 (acplx, b(i, j)); } return result; } static inline bool same_sign (double a, double b) { return (a >= 0 && b >= 0) || (a <= 0 && b <= 0); } octave_value elem_xpow (double a, const octave::range<double>& r) { octave_value retval; // Only optimize powers with ranges that are integer and monotonic in // magnitude. if (r.numel () > 1 && r.all_elements_are_ints () && same_sign (r.base (), r.limit ())) { octave_idx_type n = r.numel (); Matrix result (1, n); if (same_sign (r.base (), r.increment ())) { double base = std::pow (a, r.base ()); double inc = std::pow (a, r.increment ()); result(0) = base; for (octave_idx_type i = 1; i < n; i++) result(i) = (base *= inc); } else { double limit = std::pow (a, r.final_value ()); double inc = std::pow (a, -r.increment ()); result(n-1) = limit; for (octave_idx_type i = n-2; i >= 0; i--) result(i) = (limit *= inc); } retval = result; } else { Matrix tmp = r.array_value (); retval = elem_xpow (a, tmp); } return retval; } // -*- 3 -*- octave_value elem_xpow (const Matrix& a, double b) { octave_value retval; octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); if (! xisint (b) && a.any_element_is_negative ()) { ComplexMatrix result (nr, nc); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); Complex acplx (a(i, j)); result(i, j) = std::pow (acplx, b); } 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(i, j), b); } retval = result; } return retval; } // -*- 4 -*- octave_value elem_xpow (const Matrix& a, const Matrix& 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 (nr != b_nr || nc != b_nc) octave::err_nonconformant ("operator .^", nr, nc, b_nr, b_nc); bool convert_to_complex = false; for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); double atmp = a(i, j); double btmp = b(i, j); if (atmp < 0.0 && ! xisint (btmp)) { convert_to_complex = true; goto done; } } done: if (convert_to_complex) { ComplexMatrix complex_result (nr, nc); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); Complex acplx (a(i, j)); Complex bcplx (b(i, j)); complex_result(i, j) = std::pow (acplx, bcplx); } retval = complex_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(i, j), b(i, j)); } retval = result; } return retval; } // -*- 5 -*- octave_value elem_xpow (const Matrix& a, const Complex& b) { octave_idx_type nr = a.rows (); octave_idx_type nc = a.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 (Complex (a(i, j)), b); } return result; } // -*- 6 -*- octave_value elem_xpow (const Matrix& a, const ComplexMatrix& 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 (nr != b_nr || nc != b_nc) octave::err_nonconformant ("operator .^", nr, nc, b_nr, b_nc); 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 (Complex (a(i, j)), b(i, j)); } return result; } // -*- 7 -*- octave_value elem_xpow (const Complex& a, const Matrix& 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 ComplexMatrix& 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; } octave_value elem_xpow (const Complex& a, const octave::range<double>& r) { octave_value retval; // Only optimize powers with ranges that are integer and monotonic in // magnitude. if (r.numel () > 1 && r.all_elements_are_ints () && same_sign (r.base (), r.limit ())) { octave_idx_type n = r.numel (); ComplexMatrix result (1, n); if (same_sign (r.base (), r.increment ())) { Complex base = std::pow (a, r.base ()); Complex inc = std::pow (a, r.increment ()); result(0) = base; for (octave_idx_type i = 1; i < n; i++) result(i) = (base *= inc); } else { Complex limit = std::pow (a, r.final_value ()); Complex inc = std::pow (a, -r.increment ()); result(n-1) = limit; for (octave_idx_type i = n-2; i >= 0; i--) result(i) = (limit *= inc); } retval = result; } else { Matrix tmp = r.array_value (); retval = elem_xpow (a, tmp); } return retval; } // -*- 9 -*- octave_value elem_xpow (const ComplexMatrix& a, double b) { octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); ComplexMatrix result (nr, nc); if (xisint (b)) { int bint = static_cast<int> (b); 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(i, j), bint); } } else { 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(i, j), b); } } return result; } // -*- 10 -*- octave_value elem_xpow (const ComplexMatrix& a, const Matrix& 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 (nr != b_nr || nc != b_nc) octave::err_nonconformant ("operator .^", nr, nc, b_nr, b_nc); 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(i, j), static_cast<int> (btmp)); else result(i, j) = std::pow (a(i, j), btmp); } return result; } // -*- 11 -*- octave_value elem_xpow (const ComplexMatrix& a, const Complex& b) { octave_idx_type nr = a.rows (); octave_idx_type nc = a.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(i, j), b); } return result; } // -*- 12 -*- octave_value elem_xpow (const ComplexMatrix& a, const ComplexMatrix& 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 (nr != b_nr || nc != b_nc) octave::err_nonconformant ("operator .^", nr, nc, b_nr, b_nc); 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(i, j), b(i, j)); } return result; } // Safer pow functions that work elementwise for N-D arrays. // // op2 \ op1: s nd cs cnd // +-- +---+---+----+----+ // scalar | | * | 3 | * | 9 | // +---+---+----+----+ // N_d | 1 | 4 | 7 | 10 | // +---+---+----+----+ // complex_scalar | * | 5 | * | 11 | // +---+---+----+----+ // complex_N_d | 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... // -*- 1 -*- octave_value elem_xpow (double a, const NDArray& b) { octave_value retval; if (a < 0.0 && ! b.all_integers ()) { Complex acplx (a); ComplexNDArray result (b.dims ()); for (octave_idx_type i = 0; i < b.numel (); i++) { octave_quit (); result(i) = std::pow (acplx, b(i)); } retval = result; } else { NDArray result (b.dims ()); for (octave_idx_type i = 0; i < b.numel (); i++) { octave_quit (); result(i) = std::pow (a, b(i)); } retval = result; } return retval; } // -*- 2 -*- octave_value elem_xpow (double a, const ComplexNDArray& b) { ComplexNDArray result (b.dims ()); for (octave_idx_type i = 0; i < b.numel (); i++) { octave_quit (); result(i) = std::pow (a, b(i)); } return result; } // -*- 3 -*- octave_value elem_xpow (const NDArray& a, double b) { octave_value retval; if (xisint (b)) { NDArray result (a.dims ()); int bint = static_cast<int> (b); if (bint == 2) { for (octave_idx_type i = 0; i < a.numel (); i++) result.xelem (i) = a(i) * a(i); } else if (bint == 3) { for (octave_idx_type i = 0; i < a.numel (); i++) result.xelem (i) = a(i) * a(i) * a(i); } else if (bint == -1) { for (octave_idx_type i = 0; i < a.numel (); i++) result.xelem (i) = 1.0 / a(i); } else { for (octave_idx_type i = 0; i < a.numel (); i++) { octave_quit (); result.xelem (i) = std::pow (a(i), bint); } } retval = result; } else { if (a.any_element_is_negative ()) { ComplexNDArray result (a.dims ()); for (octave_idx_type i = 0; i < a.numel (); i++) { octave_quit (); Complex acplx (a(i)); result(i) = std::pow (acplx, b); } retval = result; } else { NDArray result (a.dims ()); for (octave_idx_type i = 0; i < a.numel (); i++) { octave_quit (); result(i) = std::pow (a(i), b); } retval = result; } } return retval; } // -*- 4 -*- octave_value elem_xpow (const NDArray& a, const NDArray& b) { octave_value retval; dim_vector a_dims = a.dims (); dim_vector b_dims = b.dims (); if (a_dims != b_dims) { if (! is_valid_bsxfun ("operator .^", a_dims, b_dims)) octave::err_nonconformant ("operator .^", a_dims, b_dims); // Potentially complex results NDArray xa = octave_value_extract<NDArray> (a); NDArray xb = octave_value_extract<NDArray> (b); if (! xb.all_integers () && xa.any_element_is_negative ()) return octave_value (bsxfun_pow (ComplexNDArray (xa), xb)); else return octave_value (bsxfun_pow (xa, xb)); } int len = a.numel (); bool convert_to_complex = false; for (octave_idx_type i = 0; i < len; i++) { octave_quit (); double atmp = a(i); double btmp = b(i); if (atmp < 0.0 && ! xisint (btmp)) { convert_to_complex = true; goto done; } } done: if (convert_to_complex) { ComplexNDArray complex_result (a_dims); for (octave_idx_type i = 0; i < len; i++) { octave_quit (); Complex acplx (a(i)); complex_result(i) = std::pow (acplx, b(i)); } retval = complex_result; } else { NDArray result (a_dims); for (octave_idx_type i = 0; i < len; i++) { octave_quit (); result(i) = std::pow (a(i), b(i)); } retval = result; } return retval; } // -*- 5 -*- octave_value elem_xpow (const NDArray& a, const Complex& b) { ComplexNDArray result (a.dims ()); for (octave_idx_type i = 0; i < a.numel (); i++) { octave_quit (); result(i) = std::pow (a(i), b); } return result; } // -*- 6 -*- octave_value elem_xpow (const NDArray& a, const ComplexNDArray& b) { dim_vector a_dims = a.dims (); dim_vector b_dims = b.dims (); if (a_dims != b_dims) { if (! is_valid_bsxfun ("operator .^", a_dims, b_dims)) octave::err_nonconformant ("operator .^", a_dims, b_dims); return bsxfun_pow (a, b); } ComplexNDArray result (a_dims); for (octave_idx_type i = 0; i < a.numel (); i++) { octave_quit (); result(i) = std::pow (a(i), b(i)); } return result; } // -*- 7 -*- octave_value elem_xpow (const Complex& a, const NDArray& b) { ComplexNDArray result (b.dims ()); for (octave_idx_type i = 0; i < b.numel (); i++) { octave_quit (); double btmp = b(i); if (xisint (btmp)) result(i) = std::pow (a, static_cast<int> (btmp)); else result(i) = std::pow (a, btmp); } return result; } // -*- 8 -*- octave_value elem_xpow (const Complex& a, const ComplexNDArray& b) { ComplexNDArray result (b.dims ()); for (octave_idx_type i = 0; i < b.numel (); i++) { octave_quit (); result(i) = std::pow (a, b(i)); } return result; } // -*- 9 -*- octave_value elem_xpow (const ComplexNDArray& a, double b) { ComplexNDArray result (a.dims ()); if (xisint (b)) { int bint = static_cast<int> (b); if (bint == -1) { for (octave_idx_type i = 0; i < a.numel (); i++) result.xelem (i) = 1.0 / a(i); } else { for (octave_idx_type i = 0; i < a.numel (); i++) { octave_quit (); result(i) = std::pow (a(i), bint); } } } else { for (octave_idx_type i = 0; i < a.numel (); i++) { octave_quit (); result(i) = std::pow (a(i), b); } } return result; } // -*- 10 -*- octave_value elem_xpow (const ComplexNDArray& a, const NDArray& b) { dim_vector a_dims = a.dims (); dim_vector b_dims = b.dims (); if (a_dims != b_dims) { if (! is_valid_bsxfun ("operator .^", a_dims, b_dims)) octave::err_nonconformant ("operator .^", a_dims, b_dims); return bsxfun_pow (a, b); } ComplexNDArray result (a_dims); for (octave_idx_type i = 0; i < a.numel (); i++) { octave_quit (); double btmp = b(i); if (xisint (btmp)) result(i) = std::pow (a(i), static_cast<int> (btmp)); else result(i) = std::pow (a(i), btmp); } return result; } // -*- 11 -*- octave_value elem_xpow (const ComplexNDArray& a, const Complex& b) { ComplexNDArray result (a.dims ()); for (octave_idx_type i = 0; i < a.numel (); i++) { octave_quit (); result(i) = std::pow (a(i), b); } return result; } // -*- 12 -*- octave_value elem_xpow (const ComplexNDArray& a, const ComplexNDArray& b) { dim_vector a_dims = a.dims (); dim_vector b_dims = b.dims (); if (a_dims != b_dims) { if (! is_valid_bsxfun ("operator .^", a_dims, b_dims)) octave::err_nonconformant ("operator .^", a_dims, b_dims); return bsxfun_pow (a, b); } ComplexNDArray result (a_dims); for (octave_idx_type i = 0; i < a.numel (); i++) { octave_quit (); result(i) = std::pow (a(i), b(i)); } return result; } // Safer pow functions. // // op2 \ op1: s m cs cm // +-- +---+---+----+----+ // scalar | | 1 | 5 | 7 | 11 | // +---+---+----+----+ // matrix | 2 | * | 8 | * | // +---+---+----+----+ // complex_scalar | 3 | 6 | 9 | 12 | // +---+---+----+----+ // complex_matrix | 4 | * | 10 | * | // +---+---+----+----+ // -*- 1 -*- octave_value xpow (float a, float b) { float retval; if (a < 0.0 && ! xisint (b)) { FloatComplex acplx (a); return std::pow (acplx, b); } else retval = std::pow (a, b); return retval; } // -*- 2 -*- octave_value xpow (float a, const FloatMatrix& b) { octave_value retval; octave_idx_type nr = b.rows (); octave_idx_type nc = b.cols (); if (nr == 0 || nc == 0) return FloatMatrix (); if (nr != nc) err_nonsquare_matrix (); FloatEIG b_eig (b); try { FloatComplexColumnVector lambda (b_eig.eigenvalues ()); FloatComplexMatrix Q (b_eig.right_eigenvectors ()); for (octave_idx_type i = 0; i < nr; i++) lambda(i) = std::pow (a, lambda(i)); FloatComplexDiagMatrix D (lambda); FloatComplexMatrix C = Q * D * Q.inverse (); if (a > 0) retval = real (C); else retval = C; } catch (const octave::execution_exception&) { err_failed_diagonalization (); } return retval; } // -*- 3 -*- octave_value xpow (float a, const FloatComplex& b) { FloatComplex result = std::pow (a, b); return result; } // -*- 4 -*- octave_value xpow (float a, const FloatComplexMatrix& b) { octave_value retval; octave_idx_type nr = b.rows (); octave_idx_type nc = b.cols (); if (nr == 0 || nc == 0) return FloatMatrix (); if (nr != nc) err_nonsquare_matrix (); FloatEIG b_eig (b); try { FloatComplexColumnVector lambda (b_eig.eigenvalues ()); FloatComplexMatrix Q (b_eig.right_eigenvectors ()); for (octave_idx_type i = 0; i < nr; i++) lambda(i) = std::pow (a, lambda(i)); FloatComplexDiagMatrix D (lambda); retval = FloatComplexMatrix (Q * D * Q.inverse ()); } catch (const octave::execution_exception&) { err_failed_diagonalization (); } return retval; } // -*- 5 -*- octave_value xpow (const FloatMatrix& a, float b) { octave_value retval; octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); if (nr == 0 || nc == 0) return FloatMatrix (); if (nr != nc) err_nonsquare_matrix (); if (xisint (b)) { int bint = static_cast<int> (b); if (bint == 0) { retval = FloatDiagMatrix (nr, nr, 1.0f); } else { // Too much copying? // FIXME: we shouldn't do this if the exponent is large... FloatMatrix atmp; if (bint < 0) { bint = -bint; octave_idx_type info; float rcond = 0.0; MatrixType mattype (a); atmp = a.inverse (mattype, info, rcond, 1); if (info == -1) warning ("inverse: matrix singular to machine precision, rcond = %g", rcond); } else atmp = a; FloatMatrix result (atmp); bint--; while (bint > 0) { if (bint & 1) // Use atmp * result instead of result * atmp // for ML compatibility (bug #52706). result = atmp * result; bint >>= 1; if (bint > 0) atmp = atmp * atmp; } retval = result; } } else { FloatEIG a_eig (a); try { FloatComplexColumnVector lambda (a_eig.eigenvalues ()); FloatComplexMatrix Q (a_eig.right_eigenvectors ()); for (octave_idx_type i = 0; i < nr; i++) lambda(i) = std::pow (lambda(i), b); FloatComplexDiagMatrix D (lambda); retval = FloatComplexMatrix (Q * D * Q.inverse ()); } catch (const octave::execution_exception&) { err_failed_diagonalization (); } } return retval; } // -*- 5d -*- octave_value xpow (const FloatDiagMatrix& a, float b) { octave_value retval; octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); if (nr == 0 || nc == 0) return FloatMatrix (); if (nr != nc) err_nonsquare_matrix (); if (xisint (b)) { int bint = static_cast<int> (b); FloatDiagMatrix r (nr, nc); for (octave_idx_type i = 0; i < nc; i++) r.dgxelem (i) = std::pow (a.dgxelem (i), bint); retval = r; } else { FloatComplexDiagMatrix r (nr, nc); for (octave_idx_type i = 0; i < nc; i++) r.dgxelem (i) = std::pow (static_cast<FloatComplex> (a.dgxelem (i)), b); retval = r; } return retval; } // -*- 6 -*- octave_value xpow (const FloatMatrix& a, const FloatComplex& b) { octave_value retval; octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); if (nr == 0 || nc == 0) return FloatMatrix (); if (nr != nc) err_nonsquare_matrix (); FloatEIG a_eig (a); try { FloatComplexColumnVector lambda (a_eig.eigenvalues ()); FloatComplexMatrix Q (a_eig.right_eigenvectors ()); for (octave_idx_type i = 0; i < nr; i++) lambda(i) = std::pow (lambda(i), b); FloatComplexDiagMatrix D (lambda); retval = FloatComplexMatrix (Q * D * Q.inverse ()); } catch (const octave::execution_exception&) { err_failed_diagonalization (); } return retval; } // -*- 7 -*- octave_value xpow (const FloatComplex& a, float b) { FloatComplex result; if (xisint (b)) result = std::pow (a, static_cast<int> (b)); else result = std::pow (a, b); return result; } // -*- 8 -*- octave_value xpow (const FloatComplex& a, const FloatMatrix& b) { octave_value retval; octave_idx_type nr = b.rows (); octave_idx_type nc = b.cols (); if (nr == 0 || nc == 0) return FloatMatrix (); if (nr != nc) err_nonsquare_matrix (); FloatEIG b_eig (b); try { FloatComplexColumnVector lambda (b_eig.eigenvalues ()); FloatComplexMatrix Q (b_eig.right_eigenvectors ()); for (octave_idx_type i = 0; i < nr; i++) lambda(i) = std::pow (a, lambda(i)); FloatComplexDiagMatrix D (lambda); retval = FloatComplexMatrix (Q * D * Q.inverse ()); } catch (const octave::execution_exception&) { err_failed_diagonalization (); } return retval; } // -*- 9 -*- octave_value xpow (const FloatComplex& a, const FloatComplex& b) { FloatComplex result; result = std::pow (a, b); return result; } // -*- 10 -*- octave_value xpow (const FloatComplex& a, const FloatComplexMatrix& b) { octave_value retval; octave_idx_type nr = b.rows (); octave_idx_type nc = b.cols (); if (nr == 0 || nc == 0) return FloatMatrix (); if (nr != nc) err_nonsquare_matrix (); FloatEIG b_eig (b); try { FloatComplexColumnVector lambda (b_eig.eigenvalues ()); FloatComplexMatrix Q (b_eig.right_eigenvectors ()); for (octave_idx_type i = 0; i < nr; i++) lambda(i) = std::pow (a, lambda(i)); FloatComplexDiagMatrix D (lambda); retval = FloatComplexMatrix (Q * D * Q.inverse ()); } catch (const octave::execution_exception&) { err_failed_diagonalization (); } return retval; } // -*- 11 -*- octave_value xpow (const FloatComplexMatrix& a, float b) { octave_value retval; octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); if (nr == 0 || nc == 0) return FloatMatrix (); if (nr != nc) err_nonsquare_matrix (); if (xisint (b)) { int bint = static_cast<int> (b); if (bint == 0) { retval = FloatDiagMatrix (nr, nr, 1.0); } else { // Too much copying? // FIXME: we shouldn't do this if the exponent is large... FloatComplexMatrix atmp; if (bint < 0) { bint = -bint; octave_idx_type info; float rcond = 0.0; MatrixType mattype (a); atmp = a.inverse (mattype, info, rcond, 1); if (info == -1) warning ("inverse: matrix singular to machine precision, rcond = %g", rcond); } else atmp = a; FloatComplexMatrix result (atmp); bint--; while (bint > 0) { if (bint & 1) // Use atmp * result instead of result * atmp // for ML compatibility (bug #52706). result = atmp * result; bint >>= 1; if (bint > 0) atmp = atmp * atmp; } retval = result; } } else { FloatEIG a_eig (a); try { FloatComplexColumnVector lambda (a_eig.eigenvalues ()); FloatComplexMatrix Q (a_eig.right_eigenvectors ()); for (octave_idx_type i = 0; i < nr; i++) lambda(i) = std::pow (lambda(i), b); FloatComplexDiagMatrix D (lambda); retval = FloatComplexMatrix (Q * D * Q.inverse ()); } catch (const octave::execution_exception&) { err_failed_diagonalization (); } } return retval; } // -*- 12 -*- octave_value xpow (const FloatComplexMatrix& a, const FloatComplex& b) { octave_value retval; octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); if (nr == 0 || nc == 0) return FloatMatrix (); if (nr != nc) err_nonsquare_matrix (); FloatEIG a_eig (a); try { FloatComplexColumnVector lambda (a_eig.eigenvalues ()); FloatComplexMatrix Q (a_eig.right_eigenvectors ()); for (octave_idx_type i = 0; i < nr; i++) lambda(i) = std::pow (lambda(i), b); FloatComplexDiagMatrix D (lambda); retval = FloatComplexMatrix (Q * D * Q.inverse ()); } catch (const octave::execution_exception&) { err_failed_diagonalization (); } return retval; } // -*- 12d -*- octave_value xpow (const FloatComplexDiagMatrix& a, const FloatComplex& b) { octave_value retval; octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); if (nr == 0 || nc == 0) return FloatMatrix (); if (nr != nc) err_nonsquare_matrix (); FloatComplexDiagMatrix r (nr, nc); for (octave_idx_type i = 0; i < nc; i++) r.dgxelem (i) = std::pow (a.dgxelem (i), b); retval = r; return retval; } // mixed octave_value xpow (const FloatComplexDiagMatrix& a, float b) { return xpow (a, static_cast<FloatComplex> (b)); } octave_value xpow (const FloatDiagMatrix& a, const FloatComplex& b) { return xpow (FloatComplexDiagMatrix (a), b); } // 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... // -*- 1 -*- octave_value elem_xpow (float a, const FloatMatrix& b) { octave_value retval; octave_idx_type nr = b.rows (); octave_idx_type nc = b.cols (); float d1, d2; if (a < 0.0 && ! b.all_integers (d1, d2)) { FloatComplex acplx (a); FloatComplexMatrix 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 (acplx, b(i, j)); } retval = result; } else { FloatMatrix 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 (float a, const FloatComplexMatrix& b) { octave_idx_type nr = b.rows (); octave_idx_type nc = b.cols (); FloatComplexMatrix result (nr, nc); FloatComplex acplx (a); 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 (acplx, b(i, j)); } return result; } // -*- 3 -*- octave_value elem_xpow (const FloatMatrix& a, float b) { octave_value retval; octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); if (! xisint (b) && a.any_element_is_negative ()) { FloatComplexMatrix result (nr, nc); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); FloatComplex acplx (a(i, j)); result(i, j) = std::pow (acplx, b); } retval = result; } else { FloatMatrix 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(i, j), b); } retval = result; } return retval; } // -*- 4 -*- octave_value elem_xpow (const FloatMatrix& a, const FloatMatrix& 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 (nr != b_nr || nc != b_nc) octave::err_nonconformant ("operator .^", nr, nc, b_nr, b_nc); bool convert_to_complex = false; for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); float atmp = a(i, j); float btmp = b(i, j); if (atmp < 0.0 && ! xisint (btmp)) { convert_to_complex = true; goto done; } } done: if (convert_to_complex) { FloatComplexMatrix complex_result (nr, nc); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); FloatComplex acplx (a(i, j)); FloatComplex bcplx (b(i, j)); complex_result(i, j) = std::pow (acplx, bcplx); } retval = complex_result; } else { FloatMatrix 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(i, j), b(i, j)); } retval = result; } return retval; } // -*- 5 -*- octave_value elem_xpow (const FloatMatrix& a, const FloatComplex& b) { octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); FloatComplexMatrix 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 (FloatComplex (a(i, j)), b); } return result; } // -*- 6 -*- octave_value elem_xpow (const FloatMatrix& a, const FloatComplexMatrix& 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 (nr != b_nr || nc != b_nc) octave::err_nonconformant ("operator .^", nr, nc, b_nr, b_nc); FloatComplexMatrix 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 (FloatComplex (a(i, j)), b(i, j)); } return result; } // -*- 7 -*- octave_value elem_xpow (const FloatComplex& a, const FloatMatrix& b) { octave_idx_type nr = b.rows (); octave_idx_type nc = b.cols (); FloatComplexMatrix result (nr, nc); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); float 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 FloatComplex& a, const FloatComplexMatrix& b) { octave_idx_type nr = b.rows (); octave_idx_type nc = b.cols (); FloatComplexMatrix 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 FloatComplexMatrix& a, float b) { octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); FloatComplexMatrix result (nr, nc); if (xisint (b)) { int bint = static_cast<int> (b); 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(i, j), bint); } } else { 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(i, j), b); } } return result; } // -*- 10 -*- octave_value elem_xpow (const FloatComplexMatrix& a, const FloatMatrix& 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 (nr != b_nr || nc != b_nc) octave::err_nonconformant ("operator .^", nr, nc, b_nr, b_nc); FloatComplexMatrix result (nr, nc); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); float btmp = b(i, j); if (xisint (btmp)) result(i, j) = std::pow (a(i, j), static_cast<int> (btmp)); else result(i, j) = std::pow (a(i, j), btmp); } return result; } // -*- 11 -*- octave_value elem_xpow (const FloatComplexMatrix& a, const FloatComplex& b) { octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); FloatComplexMatrix 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(i, j), b); } return result; } // -*- 12 -*- octave_value elem_xpow (const FloatComplexMatrix& a, const FloatComplexMatrix& 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 (nr != b_nr || nc != b_nc) octave::err_nonconformant ("operator .^", nr, nc, b_nr, b_nc); FloatComplexMatrix 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(i, j), b(i, j)); } return result; } // Safer pow functions that work elementwise for N-D arrays. // // op2 \ op1: s nd cs cnd // +-- +---+---+----+----+ // scalar | | * | 3 | * | 9 | // +---+---+----+----+ // N_d | 1 | 4 | 7 | 10 | // +---+---+----+----+ // complex_scalar | * | 5 | * | 11 | // +---+---+----+----+ // complex_N_d | 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... // -*- 1 -*- octave_value elem_xpow (float a, const FloatNDArray& b) { octave_value retval; if (a < 0.0 && ! b.all_integers ()) { FloatComplex acplx (a); FloatComplexNDArray result (b.dims ()); for (octave_idx_type i = 0; i < b.numel (); i++) { octave_quit (); result(i) = std::pow (acplx, b(i)); } retval = result; } else { FloatNDArray result (b.dims ()); for (octave_idx_type i = 0; i < b.numel (); i++) { octave_quit (); result(i) = std::pow (a, b(i)); } retval = result; } return retval; } // -*- 2 -*- octave_value elem_xpow (float a, const FloatComplexNDArray& b) { FloatComplexNDArray result (b.dims ()); for (octave_idx_type i = 0; i < b.numel (); i++) { octave_quit (); result(i) = std::pow (a, b(i)); } return result; } // -*- 3 -*- octave_value elem_xpow (const FloatNDArray& a, float b) { octave_value retval; if (xisint (b)) { FloatNDArray result (a.dims ()); int bint = static_cast<int> (b); if (bint == 2) { for (octave_idx_type i = 0; i < a.numel (); i++) result.xelem (i) = a(i) * a(i); } else if (bint == 3) { for (octave_idx_type i = 0; i < a.numel (); i++) result.xelem (i) = a(i) * a(i) * a(i); } else if (bint == -1) { for (octave_idx_type i = 0; i < a.numel (); i++) result.xelem (i) = 1.0f / a(i); } else { for (octave_idx_type i = 0; i < a.numel (); i++) { octave_quit (); result.xelem (i) = std::pow (a(i), bint); } } retval = result; } else { if (a.any_element_is_negative ()) { FloatComplexNDArray result (a.dims ()); for (octave_idx_type i = 0; i < a.numel (); i++) { octave_quit (); FloatComplex acplx (a(i)); result(i) = std::pow (acplx, b); } retval = result; } else { FloatNDArray result (a.dims ()); for (octave_idx_type i = 0; i < a.numel (); i++) { octave_quit (); result(i) = std::pow (a(i), b); } retval = result; } } return retval; } // -*- 4 -*- octave_value elem_xpow (const FloatNDArray& a, const FloatNDArray& b) { octave_value retval; dim_vector a_dims = a.dims (); dim_vector b_dims = b.dims (); if (a_dims != b_dims) { if (! is_valid_bsxfun ("operator .^", a_dims, b_dims)) octave::err_nonconformant ("operator .^", a_dims, b_dims); // Potentially complex results FloatNDArray xa = octave_value_extract<FloatNDArray> (a); FloatNDArray xb = octave_value_extract<FloatNDArray> (b); if (! xb.all_integers () && xa.any_element_is_negative ()) return octave_value (bsxfun_pow (FloatComplexNDArray (xa), xb)); else return octave_value (bsxfun_pow (xa, xb)); } int len = a.numel (); bool convert_to_complex = false; for (octave_idx_type i = 0; i < len; i++) { octave_quit (); float atmp = a(i); float btmp = b(i); if (atmp < 0.0 && ! xisint (btmp)) { convert_to_complex = true; goto done; } } done: if (convert_to_complex) { FloatComplexNDArray complex_result (a_dims); for (octave_idx_type i = 0; i < len; i++) { octave_quit (); FloatComplex acplx (a(i)); complex_result(i) = std::pow (acplx, b(i)); } retval = complex_result; } else { FloatNDArray result (a_dims); for (octave_idx_type i = 0; i < len; i++) { octave_quit (); result(i) = std::pow (a(i), b(i)); } retval = result; } return retval; } // -*- 5 -*- octave_value elem_xpow (const FloatNDArray& a, const FloatComplex& b) { FloatComplexNDArray result (a.dims ()); for (octave_idx_type i = 0; i < a.numel (); i++) { octave_quit (); result(i) = std::pow (a(i), b); } return result; } // -*- 6 -*- octave_value elem_xpow (const FloatNDArray& a, const FloatComplexNDArray& b) { dim_vector a_dims = a.dims (); dim_vector b_dims = b.dims (); if (a_dims != b_dims) { if (! is_valid_bsxfun ("operator .^", a_dims, b_dims)) octave::err_nonconformant ("operator .^", a_dims, b_dims); return bsxfun_pow (a, b); } FloatComplexNDArray result (a_dims); for (octave_idx_type i = 0; i < a.numel (); i++) { octave_quit (); result(i) = std::pow (a(i), b(i)); } return result; } // -*- 7 -*- octave_value elem_xpow (const FloatComplex& a, const FloatNDArray& b) { FloatComplexNDArray result (b.dims ()); for (octave_idx_type i = 0; i < b.numel (); i++) { octave_quit (); float btmp = b(i); if (xisint (btmp)) result(i) = std::pow (a, static_cast<int> (btmp)); else result(i) = std::pow (a, btmp); } return result; } // -*- 8 -*- octave_value elem_xpow (const FloatComplex& a, const FloatComplexNDArray& b) { FloatComplexNDArray result (b.dims ()); for (octave_idx_type i = 0; i < b.numel (); i++) { octave_quit (); result(i) = std::pow (a, b(i)); } return result; } // -*- 9 -*- octave_value elem_xpow (const FloatComplexNDArray& a, float b) { FloatComplexNDArray result (a.dims ()); if (xisint (b)) { int bint = static_cast<int> (b); if (bint == -1) { for (octave_idx_type i = 0; i < a.numel (); i++) result.xelem (i) = 1.0f / a(i); } else { for (octave_idx_type i = 0; i < a.numel (); i++) { octave_quit (); result(i) = std::pow (a(i), bint); } } } else { for (octave_idx_type i = 0; i < a.numel (); i++) { octave_quit (); result(i) = std::pow (a(i), b); } } return result; } // -*- 10 -*- octave_value elem_xpow (const FloatComplexNDArray& a, const FloatNDArray& b) { dim_vector a_dims = a.dims (); dim_vector b_dims = b.dims (); if (a_dims != b_dims) { if (! is_valid_bsxfun ("operator .^", a_dims, b_dims)) octave::err_nonconformant ("operator .^", a_dims, b_dims); return bsxfun_pow (a, b); } FloatComplexNDArray result (a_dims); for (octave_idx_type i = 0; i < a.numel (); i++) { octave_quit (); float btmp = b(i); if (xisint (btmp)) result(i) = std::pow (a(i), static_cast<int> (btmp)); else result(i) = std::pow (a(i), btmp); } return result; } // -*- 11 -*- octave_value elem_xpow (const FloatComplexNDArray& a, const FloatComplex& b) { FloatComplexNDArray result (a.dims ()); for (octave_idx_type i = 0; i < a.numel (); i++) { octave_quit (); result(i) = std::pow (a(i), b); } return result; } // -*- 12 -*- octave_value elem_xpow (const FloatComplexNDArray& a, const FloatComplexNDArray& b) { dim_vector a_dims = a.dims (); dim_vector b_dims = b.dims (); if (a_dims != b_dims) { if (! is_valid_bsxfun ("operator .^", a_dims, b_dims)) octave::err_nonconformant ("operator .^", a_dims, b_dims); return bsxfun_pow (a, b); } FloatComplexNDArray result (a_dims); for (octave_idx_type i = 0; i < a.numel (); i++) { octave_quit (); result(i) = std::pow (a(i), b(i)); } return result; } OCTAVE_END_NAMESPACE(octave)