Mercurial > octave-libtiff
view libinterp/corefcn/xpow.cc @ 21102:dfcb9d74b253
Rename local gripe_XXX functions to err_XXX or warn_XXX.
* graphics.cc (err_set_invalid): Add OCTAVE_NORETURN attribute.
* graphisc.cc: Rename gripe_set_invalid to err_set_invalid.
* jit-typeinfo.cc (err_bad_result): Rename from gripe_bad_result.
* load-save.cc (err_file_open): Rename from gripe_file_open.
* ls-mat5.cc (warn_dim_too_large): Rename from gripe_dim_too_large.
* oct-stream.cc (err_invalid_file_id): Rename from gripe_invalid_file_id.
* txt-eng-ft.cc (warn_missing_glyph, warn_glyph_render): Rename from
gripe_missing_glyph, gripe_glyph_render.
* xpow.cc: Add FIXME about strange gripe_failed_diagonalization function.
* ov-base-int.cc, ov-bool-mat.cc, ov-bool-sparse.cc, ov-bool.cc, ov-cell.cc,
ov-class.cc, ov-complex.cc, ov-cx-mat.cc, ov-cx-sparse.cc, ov-fcn-handle.cc,
ov-fcn-inline.cc, ov-float.cc, ov-flt-complex.cc, ov-flt-cx-mat.cc,
ov-flt-re-mat.cc, ov-range.cc, ov-re-mat.cc, ov-re-sparse.cc, ov-scalar.cc,
ov-str-mat.cc, ov-struct.cc
(warn_load, warn_save):
ov-base.cc (warn_load, warn_save, err_indexed_assignment,
err_assign_conversion_failed, err_no_conversion): Rename from gripe_XXX
version.
* ov-base.h (warn_load, warn_save): Rename from gripe_load, gripe_save.
* ov-classdef.cc (err_method_access, err_property_access): Rename from
gripe_method_access, gripe_property_access.
* ov-classdef.h (err_invalid_object): Rename from gripe_invalid_object.
* ov-oncleanup.h (gripe_internal): Delete function. Place single calling
instance directly in code.
* ov.cc (err_binary_op, err_binary_op_conv, err_unary_op, err_unary_op_conv,
err_unary_op_conversion_failed): Add OCTAVE_NORETURN attribute. Rename from
gripe_XXX.
* ov.cc (err_cat_op, err_cat_op_conv, ): Rename from gripe_XXX.
* lex.h (warn_single_quote_string, warn_language_extension,
maybe_warn_language_extension_comment, warn_language_extension_continuation,
warn_language_extension_operator): Rename from gripe_XXX.
* lex.ll (warn_single_quote_string, warn_language_extension,
maybe_warn_language_extension_comment, warn_language_extension_continuation,
warn_language_extension_operator): Rename from gripe_XXX.
* pt-check.cc (errmsg): Rename from gripe.
* pt-check.h (errmsg): Add OCTAVE_NORETURN attribute. Rename from gripe.
* PermMatrix.cc (err_invalid_permutation): Add OCTAVE_NORETURN attribute.
Rename from gripe_invalid_permutation.
* idx-vector.cc (err_invalid_range): Add OCTAVE_NORETURN attribute.
Rename from gripe_invalid_range.
liboctave/numeric/lo-specfun.cc (err_betainc_nonconformant): Add
OCTAVE_NORETURN attribute. Rename from gripe_betainc_nonconformant.
* oct-group.cc (err_invalid): New static function.
* oct-group.h (gripe_invalid): Delete private function.
* oct-passwd.cc (err_invalid): New static function.
* oct-passwd.h (gripe_invalid): Delete private function.
* data-conv.cc (err_unrecognized_float_fmt): Add OCTAVE_NORETURN attribute.
Rename from gripe_unrecognized_float_fmt.
* lo-cutils.c (warn_missing_wait_macro): Rename from gripe_missing_wait_macro.
* unwind-prot.cc (err_unhandled_exception): Rename from gripe_exception.
* unwind-prot.h (err_unhandled_exception): Rename from gripe_exception.
author | Rik <rik@octave.org> |
---|---|
date | Mon, 18 Jan 2016 21:06:26 -0800 |
parents | e39e05d90788 |
children | 3ac9f47fb04b |
line wrap: on
line source
/* Copyright (C) 1993-2015 John W. Eaton Copyright (C) 2009-2010 VZLU Prague This file is part of Octave. Octave is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version. Octave is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with Octave; see the file COPYING. If not, see <http://www.gnu.org/licenses/>. */ #ifdef HAVE_CONFIG_H #include <config.h> #endif #include <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" // FIXME: Why does this routine call itself? static void gripe_failed_diagonalization (void) { gripe_failed_diagonalization (); } static inline int xisint (double x) { return (D_NINT (x) == x && ((x >= 0 && x < std::numeric_limits<int>::max ()) || (x <= 0 && 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 atmp (a); return std::pow (atmp, 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 || nr != nc) error ("for x^A, A must be a square matrix. Use .^ for elementwise power."); try { EIG b_eig (b); ComplexColumnVector lambda (b_eig.eigenvalues ()); ComplexMatrix Q (b_eig.eigenvectors ()); for (octave_idx_type i = 0; i < nr; i++) { Complex elt = lambda(i); if (std::imag (elt) == 0.0) lambda(i) = std::pow (a, std::real (elt)); else lambda(i) = std::pow (a, elt); } ComplexDiagMatrix D (lambda); ComplexMatrix C = Q * D * Q.inverse (); if (a > 0) retval = real (C); else retval = C; } catch (const octave_execution_exception&) { gripe_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 || nr != nc) error ("for x^A, A must be a square matrix. Use .^ for elementwise power."); EIG b_eig (b); try { ComplexColumnVector lambda (b_eig.eigenvalues ()); ComplexMatrix Q (b_eig.eigenvectors ()); for (octave_idx_type i = 0; i < nr; i++) { Complex elt = lambda(i); if (std::imag (elt) == 0.0) lambda(i) = std::pow (a, std::real (elt)); else lambda(i) = std::pow (a, elt); } ComplexDiagMatrix D (lambda); retval = ComplexMatrix (Q * D * Q.inverse ()); } catch (const octave_execution_exception&) { gripe_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 || nr != nc) error ("for A^b, A must be a square matrix. Use .^ for elementwise power."); if (static_cast<int> (b) == b) { int btmp = static_cast<int> (b); if (btmp == 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 (btmp < 0) { btmp = -btmp; 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); btmp--; while (btmp > 0) { if (btmp & 1) result = result * atmp; btmp >>= 1; if (btmp > 0) atmp = atmp * atmp; } retval = result; } } else { EIG a_eig (a); try { ComplexColumnVector lambda (a_eig.eigenvalues ()); ComplexMatrix Q (a_eig.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&) { gripe_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 || nr != nc) error ("for A^b, A must be a square matrix. Use .^ for elementwise power."); if (static_cast<int> (b) == b) { DiagMatrix r (nr, nc); for (octave_idx_type i = 0; i < nc; i++) r.dgelem (i) = std::pow (a.dgelem (i), b); retval = r; } else { ComplexDiagMatrix r (nr, nc); for (octave_idx_type i = 0; i < nc; i++) r.dgelem (i) = std::pow (static_cast<Complex> (a.dgelem (i)), b); retval = r; } return retval; } // -*- 5p -*- octave_value xpow (const PermMatrix& a, double b) { octave_value retval; int btmp = static_cast<int> (b); if (btmp == b) return a.power (btmp); 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 || nr != nc) error ("for A^b, A must be a square matrix. Use .^ for elementwise power."); EIG a_eig (a); try { ComplexColumnVector lambda (a_eig.eigenvalues ()); ComplexMatrix Q (a_eig.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&) { gripe_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 || nr != nc) error ("for x^A, A must be a square matrix. Use .^ for elementwise power."); EIG b_eig (b); try { ComplexColumnVector lambda (b_eig.eigenvalues ()); ComplexMatrix Q (b_eig.eigenvectors ()); for (octave_idx_type i = 0; i < nr; i++) { Complex elt = lambda(i); if (std::imag (elt) == 0.0) lambda(i) = std::pow (a, std::real (elt)); else lambda(i) = std::pow (a, elt); } ComplexDiagMatrix D (lambda); retval = ComplexMatrix (Q * D * Q.inverse ()); } catch (const octave_execution_exception&) { gripe_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 || nr != nc) error ("for x^A, A must be a square matrix. Use .^ for elementwise power."); EIG b_eig (b); try { ComplexColumnVector lambda (b_eig.eigenvalues ()); ComplexMatrix Q (b_eig.eigenvectors ()); for (octave_idx_type i = 0; i < nr; i++) { Complex elt = lambda(i); if (std::imag (elt) == 0.0) lambda(i) = std::pow (a, std::real (elt)); else lambda(i) = std::pow (a, elt); } ComplexDiagMatrix D (lambda); retval = ComplexMatrix (Q * D * Q.inverse ()); } catch (const octave_execution_exception&) { gripe_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 || nr != nc) error ("for A^b, A must be a square matrix. Use .^ for elementwise power."); if (static_cast<int> (b) == b) { int btmp = static_cast<int> (b); if (btmp == 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 (btmp < 0) { btmp = -btmp; 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); btmp--; while (btmp > 0) { if (btmp & 1) result = result * atmp; btmp >>= 1; if (btmp > 0) atmp = atmp * atmp; } retval = result; } } else { EIG a_eig (a); try { ComplexColumnVector lambda (a_eig.eigenvalues ()); ComplexMatrix Q (a_eig.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&) { gripe_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 || nr != nc) error ("for A^b, A must be a square matrix. Use .^ for elementwise power."); EIG a_eig (a); try { ComplexColumnVector lambda (a_eig.eigenvalues ()); ComplexMatrix Q (a_eig.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&) { gripe_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 || nr != nc) error ("for A^b, A must be a square matrix. Use .^ for elementwise power."); ComplexDiagMatrix r (nr, nc); for (octave_idx_type i = 0; i < nc; i++) r(i, i) = std::pow (a(i, 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 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 ComplexMatrix& b) { octave_idx_type nr = b.rows (); octave_idx_type nc = b.cols (); ComplexMatrix result (nr, nc); Complex atmp (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 (atmp, 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 Range& 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.inc ())) { double base = std::pow (a, r.base ()); double inc = std::pow (a, r.inc ()); result(0) = base; for (octave_idx_type i = 1; i < n; i++) result(i) = (base *= inc); } else { // Don't use Range::limit () here. double limit = std::pow (a, r.base () + (n-1) * r.inc ()); double inc = std::pow (a, -r.inc ()); result(n-1) = limit; for (octave_idx_type i = n-2; i >= 0; i--) result(i) = (limit *= inc); } retval = result; } else retval = elem_xpow (a, r.matrix_value ()); 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 atmp (a (i, j)); result (i, j) = std::pow (atmp, 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) 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 = 0; i < nr; i++) { octave_quit (); double atmp = a (i, j); double btmp = b (i, j); if (atmp < 0.0 && static_cast<int> (btmp) != btmp) { convert_to_complex = 1; 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 atmp (a (i, j)); Complex btmp (b (i, j)); complex_result (i, j) = std::pow (atmp, btmp); } 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) 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 Range& 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.inc ())) { Complex base = std::pow (a, r.base ()); Complex inc = std::pow (a, r.inc ()); result(0) = base; for (octave_idx_type i = 1; i < n; i++) result(i) = (base *= inc); } else { // Don't use Range::limit () here. Complex limit = std::pow (a, r.base () + (n-1) * r.inc ()); Complex inc = std::pow (a, -r.inc ()); result(n-1) = limit; for (octave_idx_type i = n-2; i >= 0; i--) result(i) = (limit *= inc); } retval = result; } else retval = elem_xpow (a, r.matrix_value ()); 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)) { 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), static_cast<int> (b)); } } 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) 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) 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 atmp (a); ComplexNDArray result (b.dims ()); for (octave_idx_type i = 0; i < b.numel (); i++) { octave_quit (); result(i) = std::pow (atmp, 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)) { if (a.any_element_is_negative ()) { ComplexNDArray result (a.dims ()); for (octave_idx_type i = 0; i < a.numel (); i++) { octave_quit (); Complex atmp (a (i)); result(i) = std::pow (atmp, 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; } } else { NoAlias<NDArray> result (a.dims ()); int ib = static_cast<int> (b); if (ib == 2) { for (octave_idx_type i = 0; i < a.numel (); i++) result(i) = a(i) * a(i); } else if (ib == 3) { for (octave_idx_type i = 0; i < a.numel (); i++) result(i) = a(i) * a(i) * a(i); } else if (ib == -1) { for (octave_idx_type i = 0; i < a.numel (); i++) result(i) = 1.0 / a(i); } else { for (octave_idx_type i = 0; i < a.numel (); i++) { octave_quit (); result(i) = std::pow (a(i), ib); } } 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)) { //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)); } else err_nonconformant ("operator .^", a_dims, b_dims); } 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 && static_cast<int> (btmp) != 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 atmp (a(i)); complex_result(i) = std::pow (atmp, 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)) { return bsxfun_pow (a, b); } else err_nonconformant ("operator .^", a_dims, b_dims); } 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)) { if (b == -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), static_cast<int> (b)); } } } 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)) { return bsxfun_pow (a, b); } else err_nonconformant ("operator .^", a_dims, b_dims); } 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)) { return bsxfun_pow (a, b); } else err_nonconformant ("operator .^", a_dims, b_dims); } 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; } static inline int xisint (float x) { return (D_NINT (x) == x && ((x >= 0 && x < std::numeric_limits<int>::max ()) || (x <= 0 && 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 (float a, float b) { float retval; if (a < 0.0 && ! xisint (b)) { FloatComplex atmp (a); return std::pow (atmp, 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 || nr != nc) error ("for x^A, A must be a square matrix. Use .^ for elementwise power."); FloatEIG b_eig (b); try { FloatComplexColumnVector lambda (b_eig.eigenvalues ()); FloatComplexMatrix Q (b_eig.eigenvectors ()); for (octave_idx_type i = 0; i < nr; i++) { FloatComplex elt = lambda(i); if (std::imag (elt) == 0.0) lambda(i) = std::pow (a, std::real (elt)); else lambda(i) = std::pow (a, elt); } FloatComplexDiagMatrix D (lambda); FloatComplexMatrix C = Q * D * Q.inverse (); if (a > 0) retval = real (C); else retval = C; } catch (const octave_execution_exception&) { gripe_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 || nr != nc) error ("for x^A, A must be a square matrix. Use .^ for elementwise power."); FloatEIG b_eig (b); try { FloatComplexColumnVector lambda (b_eig.eigenvalues ()); FloatComplexMatrix Q (b_eig.eigenvectors ()); for (octave_idx_type i = 0; i < nr; i++) { FloatComplex elt = lambda(i); if (std::imag (elt) == 0.0) lambda(i) = std::pow (a, std::real (elt)); else lambda(i) = std::pow (a, elt); } FloatComplexDiagMatrix D (lambda); retval = FloatComplexMatrix (Q * D * Q.inverse ()); } catch (const octave_execution_exception&) { gripe_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 || nr != nc) error ("for A^b, A must be a square matrix. Use .^ for elementwise power."); if (static_cast<int> (b) == b) { int btmp = static_cast<int> (b); if (btmp == 0) { retval = FloatDiagMatrix (nr, nr, 1.0); } else { // Too much copying? // FIXME: we shouldn't do this if the exponent is large... FloatMatrix atmp; if (btmp < 0) { btmp = -btmp; 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); btmp--; while (btmp > 0) { if (btmp & 1) result = result * atmp; btmp >>= 1; if (btmp > 0) atmp = atmp * atmp; } retval = result; } } else { FloatEIG a_eig (a); try { FloatComplexColumnVector lambda (a_eig.eigenvalues ()); FloatComplexMatrix Q (a_eig.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&) { gripe_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 || nr != nc) error ("for A^b, A must be a square matrix. Use .^ for elementwise power."); if (static_cast<int> (b) == b) { FloatDiagMatrix r (nr, nc); for (octave_idx_type i = 0; i < nc; i++) r.dgelem (i) = std::pow (a.dgelem (i), b); retval = r; } else { FloatComplexDiagMatrix r (nr, nc); for (octave_idx_type i = 0; i < nc; i++) r.dgelem (i) = std::pow (static_cast<FloatComplex> (a.dgelem (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 || nr != nc) error ("for A^b, A must be a square matrix. Use .^ for elementwise power."); FloatEIG a_eig (a); try { FloatComplexColumnVector lambda (a_eig.eigenvalues ()); FloatComplexMatrix Q (a_eig.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&) { gripe_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 || nr != nc) error ("for x^A, A must be a square matrix. Use .^ for elementwise power."); FloatEIG b_eig (b); try { FloatComplexColumnVector lambda (b_eig.eigenvalues ()); FloatComplexMatrix Q (b_eig.eigenvectors ()); for (octave_idx_type i = 0; i < nr; i++) { FloatComplex elt = lambda(i); if (std::imag (elt) == 0.0) lambda(i) = std::pow (a, std::real (elt)); else lambda(i) = std::pow (a, elt); } FloatComplexDiagMatrix D (lambda); retval = FloatComplexMatrix (Q * D * Q.inverse ()); } catch (const octave_execution_exception&) { gripe_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 || nr != nc) error ("for x^A, A must be a square matrix. Use .^ for elementwise power."); FloatEIG b_eig (b); try { FloatComplexColumnVector lambda (b_eig.eigenvalues ()); FloatComplexMatrix Q (b_eig.eigenvectors ()); for (octave_idx_type i = 0; i < nr; i++) { FloatComplex elt = lambda(i); if (std::imag (elt) == 0.0) lambda(i) = std::pow (a, std::real (elt)); else lambda(i) = std::pow (a, elt); } FloatComplexDiagMatrix D (lambda); retval = FloatComplexMatrix (Q * D * Q.inverse ()); } catch (const octave_execution_exception&) { gripe_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 || nr != nc) error ("for A^b, A must be a square matrix. Use .^ for elementwise power."); if (static_cast<int> (b) == b) { int btmp = static_cast<int> (b); if (btmp == 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 (btmp < 0) { btmp = -btmp; 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); btmp--; while (btmp > 0) { if (btmp & 1) result = result * atmp; btmp >>= 1; if (btmp > 0) atmp = atmp * atmp; } retval = result; } } else { FloatEIG a_eig (a); try { FloatComplexColumnVector lambda (a_eig.eigenvalues ()); FloatComplexMatrix Q (a_eig.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&) { gripe_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 || nr != nc) error ("for A^b, A must be a square matrix. Use .^ for elementwise power."); FloatEIG a_eig (a); try { FloatComplexColumnVector lambda (a_eig.eigenvalues ()); FloatComplexMatrix Q (a_eig.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&) { gripe_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 || nr != nc) error ("for A^b, A must be a square matrix. Use .^ for elementwise power."); FloatComplexDiagMatrix r (nr, nc); for (octave_idx_type i = 0; i < nc; i++) r(i, i) = std::pow (a(i, 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 atmp (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 (atmp, 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 atmp (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 (atmp, 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 atmp (a (i, j)); result (i, j) = std::pow (atmp, 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) 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 = 0; i < nr; i++) { octave_quit (); float atmp = a (i, j); float btmp = b (i, j); if (atmp < 0.0 && static_cast<int> (btmp) != btmp) { convert_to_complex = 1; 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 atmp (a (i, j)); FloatComplex btmp (b (i, j)); complex_result (i, j) = std::pow (atmp, btmp); } 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) 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)) { 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), static_cast<int> (b)); } } 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) 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) 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 atmp (a); FloatComplexNDArray result (b.dims ()); for (octave_idx_type i = 0; i < b.numel (); i++) { octave_quit (); result(i) = std::pow (atmp, 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)) { if (a.any_element_is_negative ()) { FloatComplexNDArray result (a.dims ()); for (octave_idx_type i = 0; i < a.numel (); i++) { octave_quit (); FloatComplex atmp (a (i)); result(i) = std::pow (atmp, 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; } } else { NoAlias<FloatNDArray> result (a.dims ()); int ib = static_cast<int> (b); if (ib == 2) { for (octave_idx_type i = 0; i < a.numel (); i++) result(i) = a(i) * a(i); } else if (ib == 3) { for (octave_idx_type i = 0; i < a.numel (); i++) result(i) = a(i) * a(i) * a(i); } else if (ib == -1) { for (octave_idx_type i = 0; i < a.numel (); i++) result(i) = 1.0f / a(i); } else { for (octave_idx_type i = 0; i < a.numel (); i++) { octave_quit (); result(i) = std::pow (a(i), ib); } } 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)) { //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)); } else err_nonconformant ("operator .^", a_dims, b_dims); } 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 && static_cast<int> (btmp) != 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 atmp (a(i)); complex_result(i) = std::pow (atmp, 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)) { return bsxfun_pow (a, b); } else err_nonconformant ("operator .^", a_dims, b_dims); } 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)) { if (b == -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), static_cast<int> (b)); } } } 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)) { return bsxfun_pow (a, b); } else err_nonconformant ("operator .^", a_dims, b_dims); } 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)) { return bsxfun_pow (a, b); } else err_nonconformant ("operator .^", a_dims, b_dims); } 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; }