Mercurial > octave
view liboctave/array/fCMatrix.cc @ 21202:f7121e111991
maint: indent #ifdef blocks in liboctave and src directories.
* Array-C.cc, Array-b.cc, Array-ch.cc, Array-d.cc, Array-f.cc, Array-fC.cc,
Array-i.cc, Array-idx-vec.cc, Array-s.cc, Array-str.cc, Array-util.cc,
Array-voidp.cc, Array.cc, CColVector.cc, CDiagMatrix.cc, CMatrix.cc,
CNDArray.cc, CRowVector.cc, CSparse.cc, CSparse.h, DiagArray2.cc, MArray-C.cc,
MArray-d.cc, MArray-f.cc, MArray-fC.cc, MArray-i.cc, MArray-s.cc, MArray.cc,
MDiagArray2.cc, MSparse-C.cc, MSparse-d.cc, MSparse.h, MatrixType.cc,
PermMatrix.cc, Range.cc, Sparse-C.cc, Sparse-b.cc, Sparse-d.cc, Sparse.cc,
boolMatrix.cc, boolNDArray.cc, boolSparse.cc, chMatrix.cc, chNDArray.cc,
dColVector.cc, dDiagMatrix.cc, dMatrix.cc, dNDArray.cc, dRowVector.cc,
dSparse.cc, dSparse.h, dim-vector.cc, fCColVector.cc, fCDiagMatrix.cc,
fCMatrix.cc, fCNDArray.cc, fCRowVector.cc, fColVector.cc, fDiagMatrix.cc,
fMatrix.cc, fNDArray.cc, fRowVector.cc, idx-vector.cc, int16NDArray.cc,
int32NDArray.cc, int64NDArray.cc, int8NDArray.cc, intNDArray.cc,
uint16NDArray.cc, uint32NDArray.cc, uint64NDArray.cc, uint8NDArray.cc,
blaswrap.c, cquit.c, f77-extern.cc, f77-fcn.c, f77-fcn.h, lo-error.c, quit.cc,
quit.h, CmplxAEPBAL.cc, CmplxCHOL.cc, CmplxGEPBAL.cc, CmplxHESS.cc, CmplxLU.cc,
CmplxQR.cc, CmplxQRP.cc, CmplxSCHUR.cc, CmplxSVD.cc, CollocWt.cc, DASPK.cc,
DASRT.cc, DASSL.cc, EIG.cc, LSODE.cc, ODES.cc, Quad.cc, base-lu.cc, base-qr.cc,
dbleAEPBAL.cc, dbleCHOL.cc, dbleGEPBAL.cc, dbleHESS.cc, dbleLU.cc, dbleQR.cc,
dbleQRP.cc, dbleSCHUR.cc, dbleSVD.cc, eigs-base.cc, fCmplxAEPBAL.cc,
fCmplxCHOL.cc, fCmplxGEPBAL.cc, fCmplxHESS.cc, fCmplxLU.cc, fCmplxQR.cc,
fCmplxQRP.cc, fCmplxSCHUR.cc, fCmplxSVD.cc, fEIG.cc, floatAEPBAL.cc,
floatCHOL.cc, floatGEPBAL.cc, floatHESS.cc, floatLU.cc, floatQR.cc,
floatQRP.cc, floatSCHUR.cc, floatSVD.cc, lo-mappers.cc, lo-specfun.cc,
oct-convn.cc, oct-fftw.cc, oct-fftw.h, oct-norm.cc, oct-rand.cc,
oct-spparms.cc, randgamma.c, randmtzig.c, randpoisson.c, sparse-chol.cc,
sparse-dmsolve.cc, sparse-lu.cc, sparse-qr.cc, mx-defs.h, dir-ops.cc,
file-ops.cc, file-stat.cc, lo-sysdep.cc, mach-info.cc, oct-env.cc,
oct-group.cc, oct-openmp.h, oct-passwd.cc, oct-syscalls.cc, oct-time.cc,
oct-uname.cc, pathlen.h, sysdir.h, syswait.h, cmd-edit.cc, cmd-hist.cc,
data-conv.cc, f2c-main.c, glob-match.cc, lo-array-errwarn.cc,
lo-array-gripes.cc, lo-cutils.c, lo-cutils.h, lo-ieee.cc, lo-math.h,
lo-regexp.cc, lo-utils.cc, oct-base64.cc, oct-glob.cc, oct-inttypes.cc,
oct-inttypes.h, oct-locbuf.cc, oct-mutex.cc, oct-refcount.h, oct-rl-edit.c,
oct-rl-hist.c, oct-shlib.cc, oct-sort.cc, pathsearch.cc, singleton-cleanup.cc,
sparse-sort.cc, sparse-util.cc, statdefs.h, str-vec.cc, unwind-prot.cc,
url-transfer.cc, display-available.h, main-cli.cc, main-gui.cc, main.in.cc,
mkoctfile.in.cc, octave-config.in.cc, shared-fcns.h:
indent #ifdef blocks in liboctave and src directories.
| author | Rik <rik@octave.org> |
|---|---|
| date | Sat, 06 Feb 2016 06:40:13 -0800 |
| parents | 40051830f89b |
| children | e69eaee28737 |
line wrap: on
line source
// Matrix manipulations. /* Copyright (C) 1994-2015 John W. Eaton Copyright (C) 2008-2009 Jaroslav Hajek Copyright (C) 2009 VZLU Prague, a.s. This file is part of Octave. Octave is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version. Octave is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with Octave; see the file COPYING. If not, see <http://www.gnu.org/licenses/>. */ #ifdef HAVE_CONFIG_H # include <config.h> #endif #include <cfloat> #include <iostream> #include <vector> // FIXME #include <sys/types.h> #include "Array-util.h" #include "DET.h" #include "f77-fcn.h" #include "boolMatrix.h" #include "chMatrix.h" #include "fCMatrix.h" #include "fCNDArray.h" #include "fCDiagMatrix.h" #include "fCColVector.h" #include "fCRowVector.h" #include "fCmplxCHOL.h" #include "fCmplxSCHUR.h" #include "fCmplxSVD.h" #include "functor.h" #include "lo-error.h" #include "lo-ieee.h" #include "lo-mappers.h" #include "lo-utils.h" #include "mx-fcm-fdm.h" #include "mx-fcm-fs.h" #include "mx-fdm-fcm.h" #include "mx-inlines.cc" #include "mx-op-defs.h" #include "oct-cmplx.h" #include "oct-fftw.h" #include "oct-locbuf.h" #include "oct-norm.h" // Fortran functions we call. extern "C" { F77_RET_T F77_FUNC (xilaenv, XILAENV) (const octave_idx_type&, F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (cgebal, CGEBAL) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, FloatComplex*, const octave_idx_type&, octave_idx_type&, octave_idx_type&, float*, octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (sgebak, SGEBAK) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, float*, const octave_idx_type&, float*, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (cgemm, CGEMM) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, const FloatComplex&, const FloatComplex*, const octave_idx_type&, const FloatComplex*, const octave_idx_type&, const FloatComplex&, FloatComplex*, const octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (cgemv, CGEMV) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const FloatComplex&, const FloatComplex*, const octave_idx_type&, const FloatComplex*, const octave_idx_type&, const FloatComplex&, FloatComplex*, const octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (xcdotu, XCDOTU) (const octave_idx_type&, const FloatComplex*, const octave_idx_type&, const FloatComplex*, const octave_idx_type&, FloatComplex&); F77_RET_T F77_FUNC (xcdotc, XCDOTC) (const octave_idx_type&, const FloatComplex*, const octave_idx_type&, const FloatComplex*, const octave_idx_type&, FloatComplex&); F77_RET_T F77_FUNC (csyrk, CSYRK) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const FloatComplex&, const FloatComplex*, const octave_idx_type&, const FloatComplex&, FloatComplex*, const octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (cherk, CHERK) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const float&, const FloatComplex*, const octave_idx_type&, const float&, FloatComplex*, const octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (cgetrf, CGETRF) (const octave_idx_type&, const octave_idx_type&, FloatComplex*, const octave_idx_type&, octave_idx_type*, octave_idx_type&); F77_RET_T F77_FUNC (cgetrs, CGETRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, FloatComplex*, const octave_idx_type&, const octave_idx_type*, FloatComplex*, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (cgetri, CGETRI) (const octave_idx_type&, FloatComplex*, const octave_idx_type&, const octave_idx_type*, FloatComplex*, const octave_idx_type&, octave_idx_type&); F77_RET_T F77_FUNC (cgecon, CGECON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, FloatComplex*, const octave_idx_type&, const float&, float&, FloatComplex*, float*, octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (cgelsy, CGELSY) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, FloatComplex*, const octave_idx_type&, FloatComplex*, const octave_idx_type&, octave_idx_type*, float&, octave_idx_type&, FloatComplex*, const octave_idx_type&, float*, octave_idx_type&); F77_RET_T F77_FUNC (cgelsd, CGELSD) (const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, FloatComplex*, const octave_idx_type&, FloatComplex*, const octave_idx_type&, float*, float&, octave_idx_type&, FloatComplex*, const octave_idx_type&, float*, octave_idx_type*, octave_idx_type&); F77_RET_T F77_FUNC (cpotrf, CPOTRF) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, FloatComplex*, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (cpocon, CPOCON) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, FloatComplex*, const octave_idx_type&, const float&, float&, FloatComplex*, float*, octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (cpotrs, CPOTRS) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const FloatComplex*, const octave_idx_type&, FloatComplex*, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (ctrtri, CTRTRI) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const FloatComplex*, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (ctrcon, CTRCON) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const FloatComplex*, const octave_idx_type&, float&, FloatComplex*, float*, octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (ctrtrs, CTRTRS) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const FloatComplex*, const octave_idx_type&, FloatComplex*, const octave_idx_type&, octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (clartg, CLARTG) (const FloatComplex&, const FloatComplex&, float&, FloatComplex&, FloatComplex&); F77_RET_T F77_FUNC (ctrsyl, CTRSYL) (F77_CONST_CHAR_ARG_DECL, F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const octave_idx_type&, const FloatComplex*, const octave_idx_type&, const FloatComplex*, const octave_idx_type&, const FloatComplex*, const octave_idx_type&, float&, octave_idx_type& F77_CHAR_ARG_LEN_DECL F77_CHAR_ARG_LEN_DECL); F77_RET_T F77_FUNC (xclange, XCLANGE) (F77_CONST_CHAR_ARG_DECL, const octave_idx_type&, const octave_idx_type&, const FloatComplex*, const octave_idx_type&, float*, float& F77_CHAR_ARG_LEN_DECL); } static const FloatComplex FloatComplex_NaN_result (octave_Float_NaN, octave_Float_NaN); // FloatComplex Matrix class FloatComplexMatrix::FloatComplexMatrix (const FloatMatrix& a) : FloatComplexNDArray (a) { } FloatComplexMatrix::FloatComplexMatrix (const FloatRowVector& rv) : FloatComplexNDArray (rv) { } FloatComplexMatrix::FloatComplexMatrix (const FloatColumnVector& cv) : FloatComplexNDArray (cv) { } FloatComplexMatrix::FloatComplexMatrix (const FloatDiagMatrix& a) : FloatComplexNDArray (a.dims (), 0.0) { for (octave_idx_type i = 0; i < a.length (); i++) elem (i, i) = a.elem (i, i); } FloatComplexMatrix::FloatComplexMatrix (const MDiagArray2<float>& a) : FloatComplexNDArray (a.dims (), 0.0) { for (octave_idx_type i = 0; i < a.length (); i++) elem (i, i) = a.elem (i, i); } FloatComplexMatrix::FloatComplexMatrix (const DiagArray2<float>& a) : FloatComplexNDArray (a.dims (), 0.0) { for (octave_idx_type i = 0; i < a.length (); i++) elem (i, i) = a.elem (i, i); } FloatComplexMatrix::FloatComplexMatrix (const FloatComplexRowVector& rv) : FloatComplexNDArray (rv) { } FloatComplexMatrix::FloatComplexMatrix (const FloatComplexColumnVector& cv) : FloatComplexNDArray (cv) { } FloatComplexMatrix::FloatComplexMatrix (const FloatComplexDiagMatrix& a) : FloatComplexNDArray (a.dims (), 0.0) { for (octave_idx_type i = 0; i < a.length (); i++) elem (i, i) = a.elem (i, i); } FloatComplexMatrix::FloatComplexMatrix (const MDiagArray2<FloatComplex>& a) : FloatComplexNDArray (a.dims (), 0.0) { for (octave_idx_type i = 0; i < a.length (); i++) elem (i, i) = a.elem (i, i); } FloatComplexMatrix::FloatComplexMatrix (const DiagArray2<FloatComplex>& a) : FloatComplexNDArray (a.dims (), 0.0) { for (octave_idx_type i = 0; i < a.length (); i++) elem (i, i) = a.elem (i, i); } // FIXME: could we use a templated mixed-type copy function // here? FloatComplexMatrix::FloatComplexMatrix (const boolMatrix& a) : FloatComplexNDArray (a) { } FloatComplexMatrix::FloatComplexMatrix (const charMatrix& a) : FloatComplexNDArray (a.dims (), 0.0) { for (octave_idx_type i = 0; i < a.rows (); i++) for (octave_idx_type j = 0; j < a.cols (); j++) elem (i, j) = static_cast<unsigned char> (a.elem (i, j)); } FloatComplexMatrix::FloatComplexMatrix (const FloatMatrix& re, const FloatMatrix& im) : FloatComplexNDArray (re.dims ()) { if (im.rows () != rows () || im.cols () != cols ()) (*current_liboctave_error_handler) ("complex: internal error"); octave_idx_type nel = numel (); for (octave_idx_type i = 0; i < nel; i++) xelem (i) = FloatComplex (re(i), im(i)); } bool FloatComplexMatrix::operator == (const FloatComplexMatrix& a) const { if (rows () != a.rows () || cols () != a.cols ()) return false; return mx_inline_equal (numel (), data (), a.data ()); } bool FloatComplexMatrix::operator != (const FloatComplexMatrix& a) const { return !(*this == a); } bool FloatComplexMatrix::is_hermitian (void) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (is_square () && nr > 0) { for (octave_idx_type i = 0; i < nr; i++) for (octave_idx_type j = i; j < nc; j++) if (elem (i, j) != conj (elem (j, i))) return false; return true; } return false; } // destructive insert/delete/reorder operations FloatComplexMatrix& FloatComplexMatrix::insert (const FloatMatrix& a, octave_idx_type r, octave_idx_type c) { octave_idx_type a_nr = a.rows (); octave_idx_type a_nc = a.cols (); if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) (*current_liboctave_error_handler) ("range error for insert"); if (a_nr >0 && a_nc > 0) { make_unique (); for (octave_idx_type j = 0; j < a_nc; j++) for (octave_idx_type i = 0; i < a_nr; i++) xelem (r+i, c+j) = a.elem (i, j); } return *this; } FloatComplexMatrix& FloatComplexMatrix::insert (const FloatRowVector& a, octave_idx_type r, octave_idx_type c) { octave_idx_type a_len = a.numel (); if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) (*current_liboctave_error_handler) ("range error for insert"); if (a_len > 0) { make_unique (); for (octave_idx_type i = 0; i < a_len; i++) xelem (r, c+i) = a.elem (i); } return *this; } FloatComplexMatrix& FloatComplexMatrix::insert (const FloatColumnVector& a, octave_idx_type r, octave_idx_type c) { octave_idx_type a_len = a.numel (); if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) (*current_liboctave_error_handler) ("range error for insert"); if (a_len > 0) { make_unique (); for (octave_idx_type i = 0; i < a_len; i++) xelem (r+i, c) = a.elem (i); } return *this; } FloatComplexMatrix& FloatComplexMatrix::insert (const FloatDiagMatrix& a, octave_idx_type r, octave_idx_type c) { octave_idx_type a_nr = a.rows (); octave_idx_type a_nc = a.cols (); if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) (*current_liboctave_error_handler) ("range error for insert"); fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); octave_idx_type a_len = a.length (); if (a_len > 0) { make_unique (); for (octave_idx_type i = 0; i < a_len; i++) xelem (r+i, c+i) = a.elem (i, i); } return *this; } FloatComplexMatrix& FloatComplexMatrix::insert (const FloatComplexMatrix& a, octave_idx_type r, octave_idx_type c) { Array<FloatComplex>::insert (a, r, c); return *this; } FloatComplexMatrix& FloatComplexMatrix::insert (const FloatComplexRowVector& a, octave_idx_type r, octave_idx_type c) { octave_idx_type a_len = a.numel (); if (r < 0 || r >= rows () || c < 0 || c + a_len > cols ()) (*current_liboctave_error_handler) ("range error for insert"); for (octave_idx_type i = 0; i < a_len; i++) elem (r, c+i) = a.elem (i); return *this; } FloatComplexMatrix& FloatComplexMatrix::insert (const FloatComplexColumnVector& a, octave_idx_type r, octave_idx_type c) { octave_idx_type a_len = a.numel (); if (r < 0 || r + a_len > rows () || c < 0 || c >= cols ()) (*current_liboctave_error_handler) ("range error for insert"); if (a_len > 0) { make_unique (); for (octave_idx_type i = 0; i < a_len; i++) xelem (r+i, c) = a.elem (i); } return *this; } FloatComplexMatrix& FloatComplexMatrix::insert (const FloatComplexDiagMatrix& a, octave_idx_type r, octave_idx_type c) { octave_idx_type a_nr = a.rows (); octave_idx_type a_nc = a.cols (); if (r < 0 || r + a_nr > rows () || c < 0 || c + a_nc > cols ()) (*current_liboctave_error_handler) ("range error for insert"); fill (0.0, r, c, r + a_nr - 1, c + a_nc - 1); octave_idx_type a_len = a.length (); if (a_len > 0) { make_unique (); for (octave_idx_type i = 0; i < a_len; i++) xelem (r+i, c+i) = a.elem (i, i); } return *this; } FloatComplexMatrix& FloatComplexMatrix::fill (float val) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr > 0 && nc > 0) { make_unique (); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = 0; i < nr; i++) xelem (i, j) = val; } return *this; } FloatComplexMatrix& FloatComplexMatrix::fill (const FloatComplex& val) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr > 0 && nc > 0) { make_unique (); for (octave_idx_type j = 0; j < nc; j++) for (octave_idx_type i = 0; i < nr; i++) xelem (i, j) = val; } return *this; } FloatComplexMatrix& FloatComplexMatrix::fill (float val, octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) (*current_liboctave_error_handler) ("range error for fill"); if (r1 > r2) { std::swap (r1, r2); } if (c1 > c2) { std::swap (c1, c2); } if (r2 >= r1 && c2 >= c1) { make_unique (); for (octave_idx_type j = c1; j <= c2; j++) for (octave_idx_type i = r1; i <= r2; i++) xelem (i, j) = val; } return *this; } FloatComplexMatrix& FloatComplexMatrix::fill (const FloatComplex& val, octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (r1 < 0 || r2 < 0 || c1 < 0 || c2 < 0 || r1 >= nr || r2 >= nr || c1 >= nc || c2 >= nc) (*current_liboctave_error_handler) ("range error for fill"); if (r1 > r2) { std::swap (r1, r2); } if (c1 > c2) { std::swap (c1, c2); } if (r2 >= r1 && c2 >=c1) { make_unique (); for (octave_idx_type j = c1; j <= c2; j++) for (octave_idx_type i = r1; i <= r2; i++) xelem (i, j) = val; } return *this; } FloatComplexMatrix FloatComplexMatrix::append (const FloatMatrix& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != a.rows ()) (*current_liboctave_error_handler) ("row dimension mismatch for append"); octave_idx_type nc_insert = nc; FloatComplexMatrix retval (nr, nc + a.cols ()); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } FloatComplexMatrix FloatComplexMatrix::append (const FloatRowVector& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != 1) (*current_liboctave_error_handler) ("row dimension mismatch for append"); octave_idx_type nc_insert = nc; FloatComplexMatrix retval (nr, nc + a.numel ()); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } FloatComplexMatrix FloatComplexMatrix::append (const FloatColumnVector& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != a.numel ()) (*current_liboctave_error_handler) ("row dimension mismatch for append"); octave_idx_type nc_insert = nc; FloatComplexMatrix retval (nr, nc + 1); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } FloatComplexMatrix FloatComplexMatrix::append (const FloatDiagMatrix& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != a.rows ()) (*current_liboctave_error_handler) ("row dimension mismatch for append"); octave_idx_type nc_insert = nc; FloatComplexMatrix retval (nr, nc + a.cols ()); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } FloatComplexMatrix FloatComplexMatrix::append (const FloatComplexMatrix& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != a.rows ()) (*current_liboctave_error_handler) ("row dimension mismatch for append"); octave_idx_type nc_insert = nc; FloatComplexMatrix retval (nr, nc + a.cols ()); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } FloatComplexMatrix FloatComplexMatrix::append (const FloatComplexRowVector& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != 1) (*current_liboctave_error_handler) ("row dimension mismatch for append"); octave_idx_type nc_insert = nc; FloatComplexMatrix retval (nr, nc + a.numel ()); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } FloatComplexMatrix FloatComplexMatrix::append (const FloatComplexColumnVector& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != a.numel ()) (*current_liboctave_error_handler) ("row dimension mismatch for append"); octave_idx_type nc_insert = nc; FloatComplexMatrix retval (nr, nc + 1); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } FloatComplexMatrix FloatComplexMatrix::append (const FloatComplexDiagMatrix& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != a.rows ()) (*current_liboctave_error_handler) ("row dimension mismatch for append"); octave_idx_type nc_insert = nc; FloatComplexMatrix retval (nr, nc + a.cols ()); retval.insert (*this, 0, 0); retval.insert (a, 0, nc_insert); return retval; } FloatComplexMatrix FloatComplexMatrix::stack (const FloatMatrix& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nc != a.cols ()) (*current_liboctave_error_handler) ("column dimension mismatch for stack"); octave_idx_type nr_insert = nr; FloatComplexMatrix retval (nr + a.rows (), nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } FloatComplexMatrix FloatComplexMatrix::stack (const FloatRowVector& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nc != a.numel ()) (*current_liboctave_error_handler) ("column dimension mismatch for stack"); octave_idx_type nr_insert = nr; FloatComplexMatrix retval (nr + 1, nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } FloatComplexMatrix FloatComplexMatrix::stack (const FloatColumnVector& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nc != 1) (*current_liboctave_error_handler) ("column dimension mismatch for stack"); octave_idx_type nr_insert = nr; FloatComplexMatrix retval (nr + a.numel (), nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } FloatComplexMatrix FloatComplexMatrix::stack (const FloatDiagMatrix& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nc != a.cols ()) (*current_liboctave_error_handler) ("column dimension mismatch for stack"); octave_idx_type nr_insert = nr; FloatComplexMatrix retval (nr + a.rows (), nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } FloatComplexMatrix FloatComplexMatrix::stack (const FloatComplexMatrix& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nc != a.cols ()) (*current_liboctave_error_handler) ("column dimension mismatch for stack"); octave_idx_type nr_insert = nr; FloatComplexMatrix retval (nr + a.rows (), nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } FloatComplexMatrix FloatComplexMatrix::stack (const FloatComplexRowVector& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nc != a.numel ()) (*current_liboctave_error_handler) ("column dimension mismatch for stack"); octave_idx_type nr_insert = nr; FloatComplexMatrix retval (nr + 1, nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } FloatComplexMatrix FloatComplexMatrix::stack (const FloatComplexColumnVector& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nc != 1) (*current_liboctave_error_handler) ("column dimension mismatch for stack"); octave_idx_type nr_insert = nr; FloatComplexMatrix retval (nr + a.numel (), nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } FloatComplexMatrix FloatComplexMatrix::stack (const FloatComplexDiagMatrix& a) const { octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nc != a.cols ()) (*current_liboctave_error_handler) ("column dimension mismatch for stack"); octave_idx_type nr_insert = nr; FloatComplexMatrix retval (nr + a.rows (), nc); retval.insert (*this, 0, 0); retval.insert (a, nr_insert, 0); return retval; } FloatComplexMatrix conj (const FloatComplexMatrix& a) { return do_mx_unary_map<FloatComplex, FloatComplex, std::conj<float> > (a); } // resize is the destructive equivalent for this one FloatComplexMatrix FloatComplexMatrix::extract (octave_idx_type r1, octave_idx_type c1, octave_idx_type r2, octave_idx_type c2) const { if (r1 > r2) { std::swap (r1, r2); } if (c1 > c2) { std::swap (c1, c2); } return index (idx_vector (r1, r2+1), idx_vector (c1, c2+1)); } FloatComplexMatrix FloatComplexMatrix::extract_n (octave_idx_type r1, octave_idx_type c1, octave_idx_type nr, octave_idx_type nc) const { return index (idx_vector (r1, r1 + nr), idx_vector (c1, c1 + nc)); } // extract row or column i. FloatComplexRowVector FloatComplexMatrix::row (octave_idx_type i) const { return index (idx_vector (i), idx_vector::colon); } FloatComplexColumnVector FloatComplexMatrix::column (octave_idx_type i) const { return index (idx_vector::colon, idx_vector (i)); } FloatComplexMatrix FloatComplexMatrix::inverse (void) const { octave_idx_type info; float rcon; MatrixType mattype (*this); return inverse (mattype, info, rcon, 0, 0); } FloatComplexMatrix FloatComplexMatrix::inverse (octave_idx_type& info) const { float rcon; MatrixType mattype (*this); return inverse (mattype, info, rcon, 0, 0); } FloatComplexMatrix FloatComplexMatrix::inverse (octave_idx_type& info, float& rcon, int force, int calc_cond) const { MatrixType mattype (*this); return inverse (mattype, info, rcon, force, calc_cond); } FloatComplexMatrix FloatComplexMatrix::inverse (MatrixType &mattype) const { octave_idx_type info; float rcon; return inverse (mattype, info, rcon, 0, 0); } FloatComplexMatrix FloatComplexMatrix::inverse (MatrixType &mattype, octave_idx_type& info) const { float rcon; return inverse (mattype, info, rcon, 0, 0); } FloatComplexMatrix FloatComplexMatrix::tinverse (MatrixType &mattype, octave_idx_type& info, float& rcon, int force, int calc_cond) const { FloatComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != nc || nr == 0 || nc == 0) (*current_liboctave_error_handler) ("inverse requires square matrix"); int typ = mattype.type (); char uplo = (typ == MatrixType::Lower ? 'L' : 'U'); char udiag = 'N'; retval = *this; FloatComplex *tmp_data = retval.fortran_vec (); F77_XFCN (ctrtri, CTRTRI, (F77_CONST_CHAR_ARG2 (&uplo, 1), F77_CONST_CHAR_ARG2 (&udiag, 1), nr, tmp_data, nr, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); // Throw-away extra info LAPACK gives so as to not change output. rcon = 0.0; if (info != 0) info = -1; else if (calc_cond) { octave_idx_type ztrcon_info = 0; char job = '1'; OCTAVE_LOCAL_BUFFER (FloatComplex, cwork, 2*nr); OCTAVE_LOCAL_BUFFER (float, rwork, nr); F77_XFCN (ctrcon, CTRCON, (F77_CONST_CHAR_ARG2 (&job, 1), F77_CONST_CHAR_ARG2 (&uplo, 1), F77_CONST_CHAR_ARG2 (&udiag, 1), nr, tmp_data, nr, rcon, cwork, rwork, ztrcon_info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); if (ztrcon_info != 0) info = -1; } if (info == -1 && ! force) retval = *this; // Restore matrix contents. return retval; } FloatComplexMatrix FloatComplexMatrix::finverse (MatrixType &mattype, octave_idx_type& info, float& rcon, int force, int calc_cond) const { FloatComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != nc) (*current_liboctave_error_handler) ("inverse requires square matrix"); Array<octave_idx_type> ipvt (dim_vector (nr, 1)); octave_idx_type *pipvt = ipvt.fortran_vec (); retval = *this; FloatComplex *tmp_data = retval.fortran_vec (); Array<FloatComplex> z (dim_vector (1, 1)); octave_idx_type lwork = -1; // Query the optimum work array size. F77_XFCN (cgetri, CGETRI, (nc, tmp_data, nr, pipvt, z.fortran_vec (), lwork, info)); lwork = static_cast<octave_idx_type> (std::real (z(0))); lwork = (lwork < 2 *nc ? 2*nc : lwork); z.resize (dim_vector (lwork, 1)); FloatComplex *pz = z.fortran_vec (); info = 0; // Calculate the norm of the matrix, for later use. float anorm; if (calc_cond) anorm = retval.abs ().sum ().row (static_cast<octave_idx_type>(0)) .max (); F77_XFCN (cgetrf, CGETRF, (nc, nc, tmp_data, nr, pipvt, info)); // Throw-away extra info LAPACK gives so as to not change output. rcon = 0.0; if (info != 0) info = -1; else if (calc_cond) { // Now calculate the condition number for non-singular matrix. octave_idx_type zgecon_info = 0; char job = '1'; Array<float> rz (dim_vector (2 * nc, 1)); float *prz = rz.fortran_vec (); F77_XFCN (cgecon, CGECON, (F77_CONST_CHAR_ARG2 (&job, 1), nc, tmp_data, nr, anorm, rcon, pz, prz, zgecon_info F77_CHAR_ARG_LEN (1))); if (zgecon_info != 0) info = -1; } if (info == -1 && ! force) retval = *this; // Restore contents. else { octave_idx_type zgetri_info = 0; F77_XFCN (cgetri, CGETRI, (nc, tmp_data, nr, pipvt, pz, lwork, zgetri_info)); if (zgetri_info != 0) info = -1; } if (info != 0) mattype.mark_as_rectangular (); return retval; } FloatComplexMatrix FloatComplexMatrix::inverse (MatrixType &mattype, octave_idx_type& info, float& rcon, int force, int calc_cond) const { int typ = mattype.type (false); FloatComplexMatrix ret; if (typ == MatrixType::Unknown) typ = mattype.type (*this); if (typ == MatrixType::Upper || typ == MatrixType::Lower) ret = tinverse (mattype, info, rcon, force, calc_cond); else { if (mattype.is_hermitian ()) { FloatComplexCHOL chol (*this, info, true, calc_cond); if (info == 0) { if (calc_cond) rcon = chol.rcond (); else rcon = 1.0; ret = chol.inverse (); } else mattype.mark_as_unsymmetric (); } if (! mattype.is_hermitian ()) ret = finverse (mattype, info, rcon, force, calc_cond); if ((mattype.is_hermitian () || calc_cond) && rcon == 0.) ret = FloatComplexMatrix (rows (), columns (), FloatComplex (octave_Float_Inf, 0.)); } return ret; } FloatComplexMatrix FloatComplexMatrix::pseudo_inverse (float tol) const { FloatComplexMatrix retval; FloatComplexSVD result (*this, SVD::economy); FloatDiagMatrix S = result.singular_values (); FloatComplexMatrix U = result.left_singular_matrix (); FloatComplexMatrix V = result.right_singular_matrix (); FloatColumnVector sigma = S.extract_diag (); octave_idx_type r = sigma.numel () - 1; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (tol <= 0.0) { if (nr > nc) tol = nr * sigma.elem (0) * std::numeric_limits<double>::epsilon (); else tol = nc * sigma.elem (0) * std::numeric_limits<double>::epsilon (); } while (r >= 0 && sigma.elem (r) < tol) r--; if (r < 0) retval = FloatComplexMatrix (nc, nr, 0.0); else { FloatComplexMatrix Ur = U.extract (0, 0, nr-1, r); FloatDiagMatrix D = FloatDiagMatrix (sigma.extract (0, r)) . inverse (); FloatComplexMatrix Vr = V.extract (0, 0, nc-1, r); retval = Vr * D * Ur.hermitian (); } return retval; } #if defined (HAVE_FFTW) FloatComplexMatrix FloatComplexMatrix::fourier (void) const { size_t nr = rows (); size_t nc = cols (); FloatComplexMatrix retval (nr, nc); size_t npts, nsamples; if (nr == 1 || nc == 1) { npts = nr > nc ? nr : nc; nsamples = 1; } else { npts = nr; nsamples = nc; } const FloatComplex *in (data ()); FloatComplex *out (retval.fortran_vec ()); octave_fftw::fft (in, out, npts, nsamples); return retval; } FloatComplexMatrix FloatComplexMatrix::ifourier (void) const { size_t nr = rows (); size_t nc = cols (); FloatComplexMatrix retval (nr, nc); size_t npts, nsamples; if (nr == 1 || nc == 1) { npts = nr > nc ? nr : nc; nsamples = 1; } else { npts = nr; nsamples = nc; } const FloatComplex *in (data ()); FloatComplex *out (retval.fortran_vec ()); octave_fftw::ifft (in, out, npts, nsamples); return retval; } FloatComplexMatrix FloatComplexMatrix::fourier2d (void) const { dim_vector dv (rows (), cols ()); FloatComplexMatrix retval (rows (), cols ()); const FloatComplex *in (data ()); FloatComplex *out (retval.fortran_vec ()); octave_fftw::fftNd (in, out, 2, dv); return retval; } FloatComplexMatrix FloatComplexMatrix::ifourier2d (void) const { dim_vector dv (rows (), cols ()); FloatComplexMatrix retval (rows (), cols ()); const FloatComplex *in (data ()); FloatComplex *out (retval.fortran_vec ()); octave_fftw::ifftNd (in, out, 2, dv); return retval; } #else extern "C" { F77_RET_T F77_FUNC (cffti, CFFTI) (const octave_idx_type&, FloatComplex*); F77_RET_T F77_FUNC (cfftf, CFFTF) (const octave_idx_type&, FloatComplex*, FloatComplex*); F77_RET_T F77_FUNC (cfftb, CFFTB) (const octave_idx_type&, FloatComplex*, FloatComplex*); } FloatComplexMatrix FloatComplexMatrix::fourier (void) const { FloatComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type npts, nsamples; if (nr == 1 || nc == 1) { npts = nr > nc ? nr : nc; nsamples = 1; } else { npts = nr; nsamples = nc; } octave_idx_type nn = 4*npts+15; Array<FloatComplex> wsave (dim_vector (nn, 1)); FloatComplex *pwsave = wsave.fortran_vec (); retval = *this; FloatComplex *tmp_data = retval.fortran_vec (); F77_FUNC (cffti, CFFTI) (npts, pwsave); for (octave_idx_type j = 0; j < nsamples; j++) { octave_quit (); F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); } return retval; } FloatComplexMatrix FloatComplexMatrix::ifourier (void) const { FloatComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type npts, nsamples; if (nr == 1 || nc == 1) { npts = nr > nc ? nr : nc; nsamples = 1; } else { npts = nr; nsamples = nc; } octave_idx_type nn = 4*npts+15; Array<FloatComplex> wsave (dim_vector (nn, 1)); FloatComplex *pwsave = wsave.fortran_vec (); retval = *this; FloatComplex *tmp_data = retval.fortran_vec (); F77_FUNC (cffti, CFFTI) (npts, pwsave); for (octave_idx_type j = 0; j < nsamples; j++) { octave_quit (); F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); } for (octave_idx_type j = 0; j < npts*nsamples; j++) tmp_data[j] = tmp_data[j] / static_cast<float> (npts); return retval; } FloatComplexMatrix FloatComplexMatrix::fourier2d (void) const { FloatComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type npts, nsamples; if (nr == 1 || nc == 1) { npts = nr > nc ? nr : nc; nsamples = 1; } else { npts = nr; nsamples = nc; } octave_idx_type nn = 4*npts+15; Array<FloatComplex> wsave (dim_vector (nn, 1)); FloatComplex *pwsave = wsave.fortran_vec (); retval = *this; FloatComplex *tmp_data = retval.fortran_vec (); F77_FUNC (cffti, CFFTI) (npts, pwsave); for (octave_idx_type j = 0; j < nsamples; j++) { octave_quit (); F77_FUNC (cfftf, CFFTF) (npts, &tmp_data[npts*j], pwsave); } npts = nc; nsamples = nr; nn = 4*npts+15; wsave.resize (dim_vector (nn, 1)); pwsave = wsave.fortran_vec (); Array<FloatComplex> tmp (dim_vector (npts, 1)); FloatComplex *prow = tmp.fortran_vec (); F77_FUNC (cffti, CFFTI) (npts, pwsave); for (octave_idx_type j = 0; j < nsamples; j++) { octave_quit (); for (octave_idx_type i = 0; i < npts; i++) prow[i] = tmp_data[i*nr + j]; F77_FUNC (cfftf, CFFTF) (npts, prow, pwsave); for (octave_idx_type i = 0; i < npts; i++) tmp_data[i*nr + j] = prow[i]; } return retval; } FloatComplexMatrix FloatComplexMatrix::ifourier2d (void) const { FloatComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type npts, nsamples; if (nr == 1 || nc == 1) { npts = nr > nc ? nr : nc; nsamples = 1; } else { npts = nr; nsamples = nc; } octave_idx_type nn = 4*npts+15; Array<FloatComplex> wsave (dim_vector (nn, 1)); FloatComplex *pwsave = wsave.fortran_vec (); retval = *this; FloatComplex *tmp_data = retval.fortran_vec (); F77_FUNC (cffti, CFFTI) (npts, pwsave); for (octave_idx_type j = 0; j < nsamples; j++) { octave_quit (); F77_FUNC (cfftb, CFFTB) (npts, &tmp_data[npts*j], pwsave); } for (octave_idx_type j = 0; j < npts*nsamples; j++) tmp_data[j] = tmp_data[j] / static_cast<float> (npts); npts = nc; nsamples = nr; nn = 4*npts+15; wsave.resize (dim_vector (nn, 1)); pwsave = wsave.fortran_vec (); Array<FloatComplex> tmp (dim_vector (npts, 1)); FloatComplex *prow = tmp.fortran_vec (); F77_FUNC (cffti, CFFTI) (npts, pwsave); for (octave_idx_type j = 0; j < nsamples; j++) { octave_quit (); for (octave_idx_type i = 0; i < npts; i++) prow[i] = tmp_data[i*nr + j]; F77_FUNC (cfftb, CFFTB) (npts, prow, pwsave); for (octave_idx_type i = 0; i < npts; i++) tmp_data[i*nr + j] = prow[i] / static_cast<float> (npts); } return retval; } #endif FloatComplexDET FloatComplexMatrix::determinant (void) const { octave_idx_type info; float rcon; return determinant (info, rcon, 0); } FloatComplexDET FloatComplexMatrix::determinant (octave_idx_type& info) const { float rcon; return determinant (info, rcon, 0); } FloatComplexDET FloatComplexMatrix::determinant (octave_idx_type& info, float& rcon, int calc_cond) const { MatrixType mattype (*this); return determinant (mattype, info, rcon, calc_cond); } FloatComplexDET FloatComplexMatrix::determinant (MatrixType& mattype, octave_idx_type& info, float& rcon, int calc_cond) const { FloatComplexDET retval (1.0); info = 0; rcon = 0.0; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != nc) (*current_liboctave_error_handler) ("matrix must be square"); volatile int typ = mattype.type (); // Even though the matrix is marked as singular (Rectangular), we may // still get a useful number from the LU factorization, because it always // completes. if (typ == MatrixType::Unknown) typ = mattype.type (*this); else if (typ == MatrixType::Rectangular) typ = MatrixType::Full; if (typ == MatrixType::Lower || typ == MatrixType::Upper) { for (octave_idx_type i = 0; i < nc; i++) retval *= elem (i,i); } else if (typ == MatrixType::Hermitian) { FloatComplexMatrix atmp = *this; FloatComplex *tmp_data = atmp.fortran_vec (); float anorm = 0; if (calc_cond) anorm = xnorm (*this, 1); char job = 'L'; F77_XFCN (cpotrf, CPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, tmp_data, nr, info F77_CHAR_ARG_LEN (1))); if (info != 0) { rcon = 0.0; mattype.mark_as_unsymmetric (); typ = MatrixType::Full; } else { Array<FloatComplex> z (dim_vector (2 * nc, 1)); FloatComplex *pz = z.fortran_vec (); Array<float> rz (dim_vector (nc, 1)); float *prz = rz.fortran_vec (); F77_XFCN (cpocon, CPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), nr, tmp_data, nr, anorm, rcon, pz, prz, info F77_CHAR_ARG_LEN (1))); if (info != 0) rcon = 0.0; for (octave_idx_type i = 0; i < nc; i++) retval *= atmp (i,i); retval = retval.square (); } } else if (typ != MatrixType::Full) (*current_liboctave_error_handler) ("det: invalid dense matrix type"); if (typ == MatrixType::Full) { Array<octave_idx_type> ipvt (dim_vector (nr, 1)); octave_idx_type *pipvt = ipvt.fortran_vec (); FloatComplexMatrix atmp = *this; FloatComplex *tmp_data = atmp.fortran_vec (); info = 0; // Calculate the norm of the matrix, for later use. float anorm = 0; if (calc_cond) anorm = xnorm (*this, 1); F77_XFCN (cgetrf, CGETRF, (nr, nr, tmp_data, nr, pipvt, info)); // Throw-away extra info LAPACK gives so as to not change output. rcon = 0.0; if (info != 0) { info = -1; retval = FloatComplexDET (); } else { if (calc_cond) { // Now calc the condition number for non-singular matrix. char job = '1'; Array<FloatComplex> z (dim_vector (2 * nc, 1)); FloatComplex *pz = z.fortran_vec (); Array<float> rz (dim_vector (2 * nc, 1)); float *prz = rz.fortran_vec (); F77_XFCN (cgecon, CGECON, (F77_CONST_CHAR_ARG2 (&job, 1), nc, tmp_data, nr, anorm, rcon, pz, prz, info F77_CHAR_ARG_LEN (1))); } if (info != 0) { info = -1; retval = FloatComplexDET (); } else { for (octave_idx_type i = 0; i < nc; i++) { FloatComplex c = atmp(i,i); retval *= (ipvt(i) != (i+1)) ? -c : c; } } } } return retval; } float FloatComplexMatrix::rcond (void) const { MatrixType mattype (*this); return rcond (mattype); } float FloatComplexMatrix::rcond (MatrixType &mattype) const { float rcon = octave_NaN; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != nc) (*current_liboctave_error_handler) ("matrix must be square"); if (nr == 0 || nc == 0) rcon = octave_Inf; else { volatile int typ = mattype.type (); if (typ == MatrixType::Unknown) typ = mattype.type (*this); // Only calculate the condition number for LU/Cholesky if (typ == MatrixType::Upper) { const FloatComplex *tmp_data = fortran_vec (); octave_idx_type info = 0; char norm = '1'; char uplo = 'U'; char dia = 'N'; Array<FloatComplex> z (dim_vector (2 * nc, 1)); FloatComplex *pz = z.fortran_vec (); Array<float> rz (dim_vector (nc, 1)); float *prz = rz.fortran_vec (); F77_XFCN (ctrcon, CTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), F77_CONST_CHAR_ARG2 (&uplo, 1), F77_CONST_CHAR_ARG2 (&dia, 1), nr, tmp_data, nr, rcon, pz, prz, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); if (info != 0) rcon = 0; } else if (typ == MatrixType::Permuted_Upper) (*current_liboctave_error_handler) ("permuted triangular matrix not implemented"); else if (typ == MatrixType::Lower) { const FloatComplex *tmp_data = fortran_vec (); octave_idx_type info = 0; char norm = '1'; char uplo = 'L'; char dia = 'N'; Array<FloatComplex> z (dim_vector (2 * nc, 1)); FloatComplex *pz = z.fortran_vec (); Array<float> rz (dim_vector (nc, 1)); float *prz = rz.fortran_vec (); F77_XFCN (ctrcon, CTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), F77_CONST_CHAR_ARG2 (&uplo, 1), F77_CONST_CHAR_ARG2 (&dia, 1), nr, tmp_data, nr, rcon, pz, prz, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); if (info != 0) rcon = 0.0; } else if (typ == MatrixType::Permuted_Lower) (*current_liboctave_error_handler) ("permuted triangular matrix not implemented"); else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) { float anorm = -1.0; if (typ == MatrixType::Hermitian) { octave_idx_type info = 0; char job = 'L'; FloatComplexMatrix atmp = *this; FloatComplex *tmp_data = atmp.fortran_vec (); anorm = atmp.abs().sum(). row(static_cast<octave_idx_type>(0)).max(); F77_XFCN (cpotrf, CPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, tmp_data, nr, info F77_CHAR_ARG_LEN (1))); if (info != 0) { rcon = 0.0; mattype.mark_as_unsymmetric (); typ = MatrixType::Full; } else { Array<FloatComplex> z (dim_vector (2 * nc, 1)); FloatComplex *pz = z.fortran_vec (); Array<float> rz (dim_vector (nc, 1)); float *prz = rz.fortran_vec (); F77_XFCN (cpocon, CPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), nr, tmp_data, nr, anorm, rcon, pz, prz, info F77_CHAR_ARG_LEN (1))); if (info != 0) rcon = 0.0; } } if (typ == MatrixType::Full) { octave_idx_type info = 0; FloatComplexMatrix atmp = *this; FloatComplex *tmp_data = atmp.fortran_vec (); Array<octave_idx_type> ipvt (dim_vector (nr, 1)); octave_idx_type *pipvt = ipvt.fortran_vec (); if (anorm < 0.) anorm = atmp.abs ().sum (). row(static_cast<octave_idx_type>(0)).max (); Array<FloatComplex> z (dim_vector (2 * nc, 1)); FloatComplex *pz = z.fortran_vec (); Array<float> rz (dim_vector (2 * nc, 1)); float *prz = rz.fortran_vec (); F77_XFCN (cgetrf, CGETRF, (nr, nr, tmp_data, nr, pipvt, info)); if (info != 0) { rcon = 0.0; mattype.mark_as_rectangular (); } else { char job = '1'; F77_XFCN (cgecon, CGECON, (F77_CONST_CHAR_ARG2 (&job, 1), nc, tmp_data, nr, anorm, rcon, pz, prz, info F77_CHAR_ARG_LEN (1))); if (info != 0) rcon = 0.0; } } } else rcon = 0.0; } return rcon; } FloatComplexMatrix FloatComplexMatrix::utsolve (MatrixType &mattype, const FloatComplexMatrix& b, octave_idx_type& info, float& rcon, solve_singularity_handler sing_handler, bool calc_cond, blas_trans_type transt) const { FloatComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (nr == 0 || nc == 0 || b.cols () == 0) retval = FloatComplexMatrix (nc, b.cols (), FloatComplex (0.0, 0.0)); else { volatile int typ = mattype.type (); if (typ == MatrixType::Permuted_Upper || typ == MatrixType::Upper) { octave_idx_type b_nc = b.cols (); rcon = 1.; info = 0; if (typ == MatrixType::Permuted_Upper) (*current_liboctave_error_handler) ("permuted triangular matrix not implemented"); else { const FloatComplex *tmp_data = fortran_vec (); retval = b; FloatComplex *result = retval.fortran_vec (); char uplo = 'U'; char trans = get_blas_char (transt); char dia = 'N'; F77_XFCN (ctrtrs, CTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), F77_CONST_CHAR_ARG2 (&trans, 1), F77_CONST_CHAR_ARG2 (&dia, 1), nr, b_nc, tmp_data, nr, result, nr, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); if (calc_cond) { char norm = '1'; uplo = 'U'; dia = 'N'; Array<FloatComplex> z (dim_vector (2 * nc, 1)); FloatComplex *pz = z.fortran_vec (); Array<float> rz (dim_vector (nc, 1)); float *prz = rz.fortran_vec (); F77_XFCN (ctrcon, CTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), F77_CONST_CHAR_ARG2 (&uplo, 1), F77_CONST_CHAR_ARG2 (&dia, 1), nr, tmp_data, nr, rcon, pz, prz, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); if (info != 0) info = -2; volatile float rcond_plus_one = rcon + 1.0; if (rcond_plus_one == 1.0 || xisnan (rcon)) { info = -2; if (sing_handler) sing_handler (rcon); else warn_singular_matrix (rcon); } } } } else (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } FloatComplexMatrix FloatComplexMatrix::ltsolve (MatrixType &mattype, const FloatComplexMatrix& b, octave_idx_type& info, float& rcon, solve_singularity_handler sing_handler, bool calc_cond, blas_trans_type transt) const { FloatComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (nr == 0 || nc == 0 || b.cols () == 0) retval = FloatComplexMatrix (nc, b.cols (), FloatComplex (0.0, 0.0)); else { volatile int typ = mattype.type (); if (typ == MatrixType::Permuted_Lower || typ == MatrixType::Lower) { octave_idx_type b_nc = b.cols (); rcon = 1.; info = 0; if (typ == MatrixType::Permuted_Lower) (*current_liboctave_error_handler) ("permuted triangular matrix not implemented"); else { const FloatComplex *tmp_data = fortran_vec (); retval = b; FloatComplex *result = retval.fortran_vec (); char uplo = 'L'; char trans = get_blas_char (transt); char dia = 'N'; F77_XFCN (ctrtrs, CTRTRS, (F77_CONST_CHAR_ARG2 (&uplo, 1), F77_CONST_CHAR_ARG2 (&trans, 1), F77_CONST_CHAR_ARG2 (&dia, 1), nr, b_nc, tmp_data, nr, result, nr, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); if (calc_cond) { char norm = '1'; uplo = 'L'; dia = 'N'; Array<FloatComplex> z (dim_vector (2 * nc, 1)); FloatComplex *pz = z.fortran_vec (); Array<float> rz (dim_vector (nc, 1)); float *prz = rz.fortran_vec (); F77_XFCN (ctrcon, CTRCON, (F77_CONST_CHAR_ARG2 (&norm, 1), F77_CONST_CHAR_ARG2 (&uplo, 1), F77_CONST_CHAR_ARG2 (&dia, 1), nr, tmp_data, nr, rcon, pz, prz, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); if (info != 0) info = -2; volatile float rcond_plus_one = rcon + 1.0; if (rcond_plus_one == 1.0 || xisnan (rcon)) { info = -2; if (sing_handler) sing_handler (rcon); else warn_singular_matrix (rcon); } } } } else (*current_liboctave_error_handler) ("incorrect matrix type"); } return retval; } FloatComplexMatrix FloatComplexMatrix::fsolve (MatrixType &mattype, const FloatComplexMatrix& b, octave_idx_type& info, float& rcon, solve_singularity_handler sing_handler, bool calc_cond) const { FloatComplexMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr != nc || nr != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (nr == 0 || b.cols () == 0) retval = FloatComplexMatrix (nc, b.cols (), FloatComplex (0.0, 0.0)); else { volatile int typ = mattype.type (); // Calculate the norm of the matrix, for later use. float anorm = -1.; if (typ == MatrixType::Hermitian) { info = 0; char job = 'L'; FloatComplexMatrix atmp = *this; FloatComplex *tmp_data = atmp.fortran_vec (); anorm = atmp.abs().sum().row(static_cast<octave_idx_type>(0)).max(); F77_XFCN (cpotrf, CPOTRF, (F77_CONST_CHAR_ARG2 (&job, 1), nr, tmp_data, nr, info F77_CHAR_ARG_LEN (1))); // Throw-away extra info LAPACK gives so as to not change output. rcon = 0.0; if (info != 0) { info = -2; mattype.mark_as_unsymmetric (); typ = MatrixType::Full; } else { if (calc_cond) { Array<FloatComplex> z (dim_vector (2 * nc, 1)); FloatComplex *pz = z.fortran_vec (); Array<float> rz (dim_vector (nc, 1)); float *prz = rz.fortran_vec (); F77_XFCN (cpocon, CPOCON, (F77_CONST_CHAR_ARG2 (&job, 1), nr, tmp_data, nr, anorm, rcon, pz, prz, info F77_CHAR_ARG_LEN (1))); if (info != 0) info = -2; volatile float rcond_plus_one = rcon + 1.0; if (rcond_plus_one == 1.0 || xisnan (rcon)) { info = -2; if (sing_handler) sing_handler (rcon); else warn_singular_matrix (rcon); } } if (info == 0) { retval = b; FloatComplex *result = retval.fortran_vec (); octave_idx_type b_nc = b.cols (); F77_XFCN (cpotrs, CPOTRS, (F77_CONST_CHAR_ARG2 (&job, 1), nr, b_nc, tmp_data, nr, result, b.rows (), info F77_CHAR_ARG_LEN (1))); } else { mattype.mark_as_unsymmetric (); typ = MatrixType::Full; } } } if (typ == MatrixType::Full) { info = 0; Array<octave_idx_type> ipvt (dim_vector (nr, 1)); octave_idx_type *pipvt = ipvt.fortran_vec (); FloatComplexMatrix atmp = *this; FloatComplex *tmp_data = atmp.fortran_vec (); Array<FloatComplex> z (dim_vector (2 * nc, 1)); FloatComplex *pz = z.fortran_vec (); Array<float> rz (dim_vector (2 * nc, 1)); float *prz = rz.fortran_vec (); // Calculate the norm of the matrix, for later use. if (anorm < 0.) anorm = atmp.abs ().sum ().row (static_cast<octave_idx_type>(0)) .max (); F77_XFCN (cgetrf, CGETRF, (nr, nr, tmp_data, nr, pipvt, info)); // Throw-away extra info LAPACK gives so as to not change output. rcon = 0.0; if (info != 0) { info = -2; if (sing_handler) sing_handler (rcon); else warn_singular_matrix (); mattype.mark_as_rectangular (); } else { if (calc_cond) { // Now calculate the condition number for // non-singular matrix. char job = '1'; F77_XFCN (cgecon, CGECON, (F77_CONST_CHAR_ARG2 (&job, 1), nc, tmp_data, nr, anorm, rcon, pz, prz, info F77_CHAR_ARG_LEN (1))); if (info != 0) info = -2; volatile float rcond_plus_one = rcon + 1.0; if (rcond_plus_one == 1.0 || xisnan (rcon)) { info = -2; if (sing_handler) sing_handler (rcon); else warn_singular_matrix (rcon); } } if (info == 0) { retval = b; FloatComplex *result = retval.fortran_vec (); octave_idx_type b_nc = b.cols (); char job = 'N'; F77_XFCN (cgetrs, CGETRS, (F77_CONST_CHAR_ARG2 (&job, 1), nr, b_nc, tmp_data, nr, pipvt, result, b.rows (), info F77_CHAR_ARG_LEN (1))); } else mattype.mark_as_rectangular (); } } } return retval; } FloatComplexMatrix FloatComplexMatrix::solve (MatrixType &typ, const FloatMatrix& b) const { octave_idx_type info; float rcon; return solve (typ, b, info, rcon, 0); } FloatComplexMatrix FloatComplexMatrix::solve (MatrixType &typ, const FloatMatrix& b, octave_idx_type& info) const { float rcon; return solve (typ, b, info, rcon, 0); } FloatComplexMatrix FloatComplexMatrix::solve (MatrixType &typ, const FloatMatrix& b, octave_idx_type& info, float& rcon) const { return solve (typ, b, info, rcon, 0); } FloatComplexMatrix FloatComplexMatrix::solve (MatrixType &typ, const FloatMatrix& b, octave_idx_type& info, float& rcon, solve_singularity_handler sing_handler, bool singular_fallback, blas_trans_type transt) const { FloatComplexMatrix tmp (b); return solve (typ, tmp, info, rcon, sing_handler, singular_fallback, transt); } FloatComplexMatrix FloatComplexMatrix::solve (MatrixType &typ, const FloatComplexMatrix& b) const { octave_idx_type info; float rcon; return solve (typ, b, info, rcon, 0); } FloatComplexMatrix FloatComplexMatrix::solve (MatrixType &typ, const FloatComplexMatrix& b, octave_idx_type& info) const { float rcon; return solve (typ, b, info, rcon, 0); } FloatComplexMatrix FloatComplexMatrix::solve (MatrixType &typ, const FloatComplexMatrix& b, octave_idx_type& info, float& rcon) const { return solve (typ, b, info, rcon, 0); } FloatComplexMatrix FloatComplexMatrix::solve (MatrixType &mattype, const FloatComplexMatrix& b, octave_idx_type& info, float& rcon, solve_singularity_handler sing_handler, bool singular_fallback, blas_trans_type transt) const { FloatComplexMatrix retval; int typ = mattype.type (); if (typ == MatrixType::Unknown) typ = mattype.type (*this); // Only calculate the condition number for LU/Cholesky if (typ == MatrixType::Upper || typ == MatrixType::Permuted_Upper) retval = utsolve (mattype, b, info, rcon, sing_handler, true, transt); else if (typ == MatrixType::Lower || typ == MatrixType::Permuted_Lower) retval = ltsolve (mattype, b, info, rcon, sing_handler, true, transt); else if (transt == blas_trans) return transpose ().solve (mattype, b, info, rcon, sing_handler, singular_fallback); else if (transt == blas_conj_trans) retval = hermitian ().solve (mattype, b, info, rcon, sing_handler, singular_fallback); else if (typ == MatrixType::Full || typ == MatrixType::Hermitian) retval = fsolve (mattype, b, info, rcon, sing_handler, true); else if (typ != MatrixType::Rectangular) (*current_liboctave_error_handler) ("unknown matrix type"); // Rectangular or one of the above solvers flags a singular matrix if (singular_fallback && mattype.type () == MatrixType::Rectangular) { octave_idx_type rank; retval = lssolve (b, info, rank, rcon); } return retval; } FloatComplexColumnVector FloatComplexMatrix::solve (MatrixType &typ, const FloatColumnVector& b) const { octave_idx_type info; float rcon; return solve (typ, FloatComplexColumnVector (b), info, rcon, 0); } FloatComplexColumnVector FloatComplexMatrix::solve (MatrixType &typ, const FloatColumnVector& b, octave_idx_type& info) const { float rcon; return solve (typ, FloatComplexColumnVector (b), info, rcon, 0); } FloatComplexColumnVector FloatComplexMatrix::solve (MatrixType &typ, const FloatColumnVector& b, octave_idx_type& info, float& rcon) const { return solve (typ, FloatComplexColumnVector (b), info, rcon, 0); } FloatComplexColumnVector FloatComplexMatrix::solve (MatrixType &typ, const FloatColumnVector& b, octave_idx_type& info, float& rcon, solve_singularity_handler sing_handler, blas_trans_type transt) const { return solve (typ, FloatComplexColumnVector (b), info, rcon, sing_handler, transt); } FloatComplexColumnVector FloatComplexMatrix::solve (MatrixType &typ, const FloatComplexColumnVector& b) const { octave_idx_type info; float rcon; return solve (typ, b, info, rcon, 0); } FloatComplexColumnVector FloatComplexMatrix::solve (MatrixType &typ, const FloatComplexColumnVector& b, octave_idx_type& info) const { float rcon; return solve (typ, b, info, rcon, 0); } FloatComplexColumnVector FloatComplexMatrix::solve (MatrixType &typ, const FloatComplexColumnVector& b, octave_idx_type& info, float& rcon) const { return solve (typ, b, info, rcon, 0); } FloatComplexColumnVector FloatComplexMatrix::solve (MatrixType &typ, const FloatComplexColumnVector& b, octave_idx_type& info, float& rcon, solve_singularity_handler sing_handler, blas_trans_type transt) const { FloatComplexMatrix tmp (b); tmp = solve (typ, tmp, info, rcon, sing_handler, true, transt); return tmp.column (static_cast<octave_idx_type> (0)); } FloatComplexMatrix FloatComplexMatrix::solve (const FloatMatrix& b) const { octave_idx_type info; float rcon; return solve (b, info, rcon, 0); } FloatComplexMatrix FloatComplexMatrix::solve (const FloatMatrix& b, octave_idx_type& info) const { float rcon; return solve (b, info, rcon, 0); } FloatComplexMatrix FloatComplexMatrix::solve (const FloatMatrix& b, octave_idx_type& info, float& rcon) const { return solve (b, info, rcon, 0); } FloatComplexMatrix FloatComplexMatrix::solve (const FloatMatrix& b, octave_idx_type& info, float& rcon, solve_singularity_handler sing_handler, blas_trans_type transt) const { FloatComplexMatrix tmp (b); return solve (tmp, info, rcon, sing_handler, transt); } FloatComplexMatrix FloatComplexMatrix::solve (const FloatComplexMatrix& b) const { octave_idx_type info; float rcon; return solve (b, info, rcon, 0); } FloatComplexMatrix FloatComplexMatrix::solve (const FloatComplexMatrix& b, octave_idx_type& info) const { float rcon; return solve (b, info, rcon, 0); } FloatComplexMatrix FloatComplexMatrix::solve (const FloatComplexMatrix& b, octave_idx_type& info, float& rcon) const { return solve (b, info, rcon, 0); } FloatComplexMatrix FloatComplexMatrix::solve (const FloatComplexMatrix& b, octave_idx_type& info, float& rcon, solve_singularity_handler sing_handler, blas_trans_type transt) const { MatrixType mattype (*this); return solve (mattype, b, info, rcon, sing_handler, true, transt); } FloatComplexColumnVector FloatComplexMatrix::solve (const FloatColumnVector& b) const { octave_idx_type info; float rcon; return solve (FloatComplexColumnVector (b), info, rcon, 0); } FloatComplexColumnVector FloatComplexMatrix::solve (const FloatColumnVector& b, octave_idx_type& info) const { float rcon; return solve (FloatComplexColumnVector (b), info, rcon, 0); } FloatComplexColumnVector FloatComplexMatrix::solve (const FloatColumnVector& b, octave_idx_type& info, float& rcon) const { return solve (FloatComplexColumnVector (b), info, rcon, 0); } FloatComplexColumnVector FloatComplexMatrix::solve (const FloatColumnVector& b, octave_idx_type& info, float& rcon, solve_singularity_handler sing_handler, blas_trans_type transt) const { return solve (FloatComplexColumnVector (b), info, rcon, sing_handler, transt); } FloatComplexColumnVector FloatComplexMatrix::solve (const FloatComplexColumnVector& b) const { octave_idx_type info; float rcon; return solve (b, info, rcon, 0); } FloatComplexColumnVector FloatComplexMatrix::solve (const FloatComplexColumnVector& b, octave_idx_type& info) const { float rcon; return solve (b, info, rcon, 0); } FloatComplexColumnVector FloatComplexMatrix::solve (const FloatComplexColumnVector& b, octave_idx_type& info, float& rcon) const { return solve (b, info, rcon, 0); } FloatComplexColumnVector FloatComplexMatrix::solve (const FloatComplexColumnVector& b, octave_idx_type& info, float& rcon, solve_singularity_handler sing_handler, blas_trans_type transt) const { MatrixType mattype (*this); return solve (mattype, b, info, rcon, sing_handler, transt); } FloatComplexMatrix FloatComplexMatrix::lssolve (const FloatMatrix& b) const { octave_idx_type info; octave_idx_type rank; float rcon; return lssolve (FloatComplexMatrix (b), info, rank, rcon); } FloatComplexMatrix FloatComplexMatrix::lssolve (const FloatMatrix& b, octave_idx_type& info) const { octave_idx_type rank; float rcon; return lssolve (FloatComplexMatrix (b), info, rank, rcon); } FloatComplexMatrix FloatComplexMatrix::lssolve (const FloatMatrix& b, octave_idx_type& info, octave_idx_type& rank) const { float rcon; return lssolve (FloatComplexMatrix (b), info, rank, rcon); } FloatComplexMatrix FloatComplexMatrix::lssolve (const FloatMatrix& b, octave_idx_type& info, octave_idx_type& rank, float& rcon) const { return lssolve (FloatComplexMatrix (b), info, rank, rcon); } FloatComplexMatrix FloatComplexMatrix::lssolve (const FloatComplexMatrix& b) const { octave_idx_type info; octave_idx_type rank; float rcon; return lssolve (b, info, rank, rcon); } FloatComplexMatrix FloatComplexMatrix::lssolve (const FloatComplexMatrix& b, octave_idx_type& info) const { octave_idx_type rank; float rcon; return lssolve (b, info, rank, rcon); } FloatComplexMatrix FloatComplexMatrix::lssolve (const FloatComplexMatrix& b, octave_idx_type& info, octave_idx_type& rank) const { float rcon; return lssolve (b, info, rank, rcon); } FloatComplexMatrix FloatComplexMatrix::lssolve (const FloatComplexMatrix& b, octave_idx_type& info, octave_idx_type& rank, float& rcon) const { FloatComplexMatrix retval; octave_idx_type nrhs = b.cols (); octave_idx_type m = rows (); octave_idx_type n = cols (); if (m != b.rows ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (m== 0 || n == 0 || b.cols () == 0) retval = FloatComplexMatrix (n, b.cols (), FloatComplex (0.0, 0.0)); else { volatile octave_idx_type minmn = (m < n ? m : n); octave_idx_type maxmn = m > n ? m : n; rcon = -1.0; if (m != n) { retval = FloatComplexMatrix (maxmn, nrhs); for (octave_idx_type j = 0; j < nrhs; j++) for (octave_idx_type i = 0; i < m; i++) retval.elem (i, j) = b.elem (i, j); } else retval = b; FloatComplexMatrix atmp = *this; FloatComplex *tmp_data = atmp.fortran_vec (); FloatComplex *pretval = retval.fortran_vec (); Array<float> s (dim_vector (minmn, 1)); float *ps = s.fortran_vec (); // Ask ZGELSD what the dimension of WORK should be. octave_idx_type lwork = -1; Array<FloatComplex> work (dim_vector (1, 1)); octave_idx_type smlsiz; F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("CGELSD", 6), F77_CONST_CHAR_ARG2 (" ", 1), 0, 0, 0, 0, smlsiz F77_CHAR_ARG_LEN (6) F77_CHAR_ARG_LEN (1)); octave_idx_type mnthr; F77_FUNC (xilaenv, XILAENV) (6, F77_CONST_CHAR_ARG2 ("CGELSD", 6), F77_CONST_CHAR_ARG2 (" ", 1), m, n, nrhs, -1, mnthr F77_CHAR_ARG_LEN (6) F77_CHAR_ARG_LEN (1)); // We compute the size of rwork and iwork because ZGELSD in // older versions of LAPACK does not return them on a query // call. float dminmn = static_cast<float> (minmn); float dsmlsizp1 = static_cast<float> (smlsiz+1); float tmp = xlog2 (dminmn / dsmlsizp1); octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; if (nlvl < 0) nlvl = 0; octave_idx_type lrwork = minmn*(10 + 2*smlsiz + 8*nlvl) + 3*smlsiz*nrhs + std::max ((smlsiz+1)*(smlsiz+1), n*(1+nrhs) + 2*nrhs); if (lrwork < 1) lrwork = 1; Array<float> rwork (dim_vector (lrwork, 1)); float *prwork = rwork.fortran_vec (); octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; if (liwork < 1) liwork = 1; Array<octave_idx_type> iwork (dim_vector (liwork, 1)); octave_idx_type* piwork = iwork.fortran_vec (); F77_XFCN (cgelsd, CGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, ps, rcon, rank, work.fortran_vec (), lwork, prwork, piwork, info)); // The workspace query is broken in at least LAPACK 3.0.0 // through 3.1.1 when n >= mnthr. The obtuse formula below // should provide sufficient workspace for ZGELSD to operate // efficiently. if (n > m && n >= mnthr) { octave_idx_type addend = m; if (2*m-4 > addend) addend = 2*m-4; if (nrhs > addend) addend = nrhs; if (n-3*m > addend) addend = n-3*m; const octave_idx_type lworkaround = 4*m + m*m + addend; if (std::real (work(0)) < lworkaround) work(0) = lworkaround; } else if (m >= n) { octave_idx_type lworkaround = 2*m + m*nrhs; if (std::real (work(0)) < lworkaround) work(0) = lworkaround; } lwork = static_cast<octave_idx_type> (std::real (work(0))); work.resize (dim_vector (lwork, 1)); F77_XFCN (cgelsd, CGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, ps, rcon, rank, work.fortran_vec (), lwork, prwork, piwork, info)); if (s.elem (0) == 0.0) rcon = 0.0; else rcon = s.elem (minmn - 1) / s.elem (0); retval.resize (n, nrhs); } return retval; } FloatComplexColumnVector FloatComplexMatrix::lssolve (const FloatColumnVector& b) const { octave_idx_type info; octave_idx_type rank; float rcon; return lssolve (FloatComplexColumnVector (b), info, rank, rcon); } FloatComplexColumnVector FloatComplexMatrix::lssolve (const FloatColumnVector& b, octave_idx_type& info) const { octave_idx_type rank; float rcon; return lssolve (FloatComplexColumnVector (b), info, rank, rcon); } FloatComplexColumnVector FloatComplexMatrix::lssolve (const FloatColumnVector& b, octave_idx_type& info, octave_idx_type& rank) const { float rcon; return lssolve (FloatComplexColumnVector (b), info, rank, rcon); } FloatComplexColumnVector FloatComplexMatrix::lssolve (const FloatColumnVector& b, octave_idx_type& info, octave_idx_type& rank, float& rcon) const { return lssolve (FloatComplexColumnVector (b), info, rank, rcon); } FloatComplexColumnVector FloatComplexMatrix::lssolve (const FloatComplexColumnVector& b) const { octave_idx_type info; octave_idx_type rank; float rcon; return lssolve (b, info, rank, rcon); } FloatComplexColumnVector FloatComplexMatrix::lssolve (const FloatComplexColumnVector& b, octave_idx_type& info) const { octave_idx_type rank; float rcon; return lssolve (b, info, rank, rcon); } FloatComplexColumnVector FloatComplexMatrix::lssolve (const FloatComplexColumnVector& b, octave_idx_type& info, octave_idx_type& rank) const { float rcon; return lssolve (b, info, rank, rcon); } FloatComplexColumnVector FloatComplexMatrix::lssolve (const FloatComplexColumnVector& b, octave_idx_type& info, octave_idx_type& rank, float& rcon) const { FloatComplexColumnVector retval; octave_idx_type nrhs = 1; octave_idx_type m = rows (); octave_idx_type n = cols (); if (m != b.numel ()) (*current_liboctave_error_handler) ("matrix dimension mismatch solution of linear equations"); if (m == 0 || n == 0 || b.cols () == 0) retval = FloatComplexColumnVector (n, FloatComplex (0.0, 0.0)); else { volatile octave_idx_type minmn = (m < n ? m : n); octave_idx_type maxmn = m > n ? m : n; rcon = -1.0; if (m != n) { retval = FloatComplexColumnVector (maxmn); for (octave_idx_type i = 0; i < m; i++) retval.elem (i) = b.elem (i); } else retval = b; FloatComplexMatrix atmp = *this; FloatComplex *tmp_data = atmp.fortran_vec (); FloatComplex *pretval = retval.fortran_vec (); Array<float> s (dim_vector (minmn, 1)); float *ps = s.fortran_vec (); // Ask ZGELSD what the dimension of WORK should be. octave_idx_type lwork = -1; Array<FloatComplex> work (dim_vector (1, 1)); octave_idx_type smlsiz; F77_FUNC (xilaenv, XILAENV) (9, F77_CONST_CHAR_ARG2 ("CGELSD", 6), F77_CONST_CHAR_ARG2 (" ", 1), 0, 0, 0, 0, smlsiz F77_CHAR_ARG_LEN (6) F77_CHAR_ARG_LEN (1)); // We compute the size of rwork and iwork because ZGELSD in // older versions of LAPACK does not return them on a query // call. float dminmn = static_cast<float> (minmn); float dsmlsizp1 = static_cast<float> (smlsiz+1); float tmp = xlog2 (dminmn / dsmlsizp1); octave_idx_type nlvl = static_cast<octave_idx_type> (tmp) + 1; if (nlvl < 0) nlvl = 0; octave_idx_type lrwork = minmn*(10 + 2*smlsiz + 8*nlvl) + 3*smlsiz*nrhs + (smlsiz+1)*(smlsiz+1); if (lrwork < 1) lrwork = 1; Array<float> rwork (dim_vector (lrwork, 1)); float *prwork = rwork.fortran_vec (); octave_idx_type liwork = 3 * minmn * nlvl + 11 * minmn; if (liwork < 1) liwork = 1; Array<octave_idx_type> iwork (dim_vector (liwork, 1)); octave_idx_type* piwork = iwork.fortran_vec (); F77_XFCN (cgelsd, CGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, ps, rcon, rank, work.fortran_vec (), lwork, prwork, piwork, info)); lwork = static_cast<octave_idx_type> (std::real (work(0))); work.resize (dim_vector (lwork, 1)); rwork.resize (dim_vector (static_cast<octave_idx_type> (rwork(0)), 1)); iwork.resize (dim_vector (iwork(0), 1)); F77_XFCN (cgelsd, CGELSD, (m, n, nrhs, tmp_data, m, pretval, maxmn, ps, rcon, rank, work.fortran_vec (), lwork, prwork, piwork, info)); if (rank < minmn) { if (s.elem (0) == 0.0) rcon = 0.0; else rcon = s.elem (minmn - 1) / s.elem (0); retval.resize (n, nrhs); } } return retval; } // column vector by row vector -> matrix operations FloatComplexMatrix operator * (const FloatColumnVector& v, const FloatComplexRowVector& a) { FloatComplexColumnVector tmp (v); return tmp * a; } FloatComplexMatrix operator * (const FloatComplexColumnVector& a, const FloatRowVector& b) { FloatComplexRowVector tmp (b); return a * tmp; } FloatComplexMatrix operator * (const FloatComplexColumnVector& v, const FloatComplexRowVector& a) { FloatComplexMatrix retval; octave_idx_type len = v.numel (); if (len != 0) { octave_idx_type a_len = a.numel (); retval = FloatComplexMatrix (len, a_len); FloatComplex *c = retval.fortran_vec (); F77_XFCN (cgemm, CGEMM, (F77_CONST_CHAR_ARG2 ("N", 1), F77_CONST_CHAR_ARG2 ("N", 1), len, a_len, 1, 1.0, v.data (), len, a.data (), 1, 0.0, c, len F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); } return retval; } // matrix by diagonal matrix -> matrix operations FloatComplexMatrix& FloatComplexMatrix::operator += (const FloatDiagMatrix& a) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type a_nr = rows (); octave_idx_type a_nc = cols (); if (nr != a_nr || nc != a_nc) err_nonconformant ("operator +=", nr, nc, a_nr, a_nc); for (octave_idx_type i = 0; i < a.length (); i++) elem (i, i) += a.elem (i, i); return *this; } FloatComplexMatrix& FloatComplexMatrix::operator -= (const FloatDiagMatrix& a) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type a_nr = rows (); octave_idx_type a_nc = cols (); if (nr != a_nr || nc != a_nc) err_nonconformant ("operator -=", nr, nc, a_nr, a_nc); for (octave_idx_type i = 0; i < a.length (); i++) elem (i, i) -= a.elem (i, i); return *this; } FloatComplexMatrix& FloatComplexMatrix::operator += (const FloatComplexDiagMatrix& a) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type a_nr = rows (); octave_idx_type a_nc = cols (); if (nr != a_nr || nc != a_nc) err_nonconformant ("operator +=", nr, nc, a_nr, a_nc); for (octave_idx_type i = 0; i < a.length (); i++) elem (i, i) += a.elem (i, i); return *this; } FloatComplexMatrix& FloatComplexMatrix::operator -= (const FloatComplexDiagMatrix& a) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type a_nr = rows (); octave_idx_type a_nc = cols (); if (nr != a_nr || nc != a_nc) err_nonconformant ("operator -=", nr, nc, a_nr, a_nc); for (octave_idx_type i = 0; i < a.length (); i++) elem (i, i) -= a.elem (i, i); return *this; } // matrix by matrix -> matrix operations FloatComplexMatrix& FloatComplexMatrix::operator += (const FloatMatrix& a) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type a_nr = a.rows (); octave_idx_type a_nc = a.cols (); if (nr != a_nr || nc != a_nc) err_nonconformant ("operator +=", nr, nc, a_nr, a_nc); if (nr == 0 || nc == 0) return *this; FloatComplex *d = fortran_vec (); // Ensures only 1 reference to my privates! mx_inline_add2 (numel (), d, a.data ()); return *this; } FloatComplexMatrix& FloatComplexMatrix::operator -= (const FloatMatrix& a) { octave_idx_type nr = rows (); octave_idx_type nc = cols (); octave_idx_type a_nr = a.rows (); octave_idx_type a_nc = a.cols (); if (nr != a_nr || nc != a_nc) err_nonconformant ("operator -=", nr, nc, a_nr, a_nc); if (nr == 0 || nc == 0) return *this; FloatComplex *d = fortran_vec (); // Ensures only 1 reference to my privates! mx_inline_sub2 (numel (), d, a.data ()); return *this; } // unary operations boolMatrix FloatComplexMatrix::all (int dim) const { return FloatComplexNDArray::all (dim); } boolMatrix FloatComplexMatrix::any (int dim) const { return FloatComplexNDArray::any (dim); } FloatComplexMatrix FloatComplexMatrix::cumprod (int dim) const { return FloatComplexNDArray::cumprod (dim); } FloatComplexMatrix FloatComplexMatrix::cumsum (int dim) const { return FloatComplexNDArray::cumsum (dim); } FloatComplexMatrix FloatComplexMatrix::prod (int dim) const { return FloatComplexNDArray::prod (dim); } FloatComplexMatrix FloatComplexMatrix::sum (int dim) const { return FloatComplexNDArray::sum (dim); } FloatComplexMatrix FloatComplexMatrix::sumsq (int dim) const { return FloatComplexNDArray::sumsq (dim); } FloatMatrix FloatComplexMatrix::abs (void) const { return FloatComplexNDArray::abs (); } FloatComplexMatrix FloatComplexMatrix::diag (octave_idx_type k) const { return FloatComplexNDArray::diag (k); } FloatComplexDiagMatrix FloatComplexMatrix::diag (octave_idx_type m, octave_idx_type n) const { FloatComplexDiagMatrix retval; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr == 1 || nc == 1) retval = FloatComplexDiagMatrix (*this, m, n); else (*current_liboctave_error_handler) ("diag: expecting vector argument"); return retval; } bool FloatComplexMatrix::row_is_real_only (octave_idx_type i) const { bool retval = true; octave_idx_type nc = columns (); for (octave_idx_type j = 0; j < nc; j++) { if (std::imag (elem (i, j)) != 0.0) { retval = false; break; } } return retval; } bool FloatComplexMatrix::column_is_real_only (octave_idx_type j) const { bool retval = true; octave_idx_type nr = rows (); for (octave_idx_type i = 0; i < nr; i++) { if (std::imag (elem (i, j)) != 0.0) { retval = false; break; } } return retval; } FloatComplexColumnVector FloatComplexMatrix::row_min (void) const { Array<octave_idx_type> dummy_idx; return row_min (dummy_idx); } FloatComplexColumnVector FloatComplexMatrix::row_min (Array<octave_idx_type>& idx_arg) const { FloatComplexColumnVector result; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr > 0 && nc > 0) { result.resize (nr); idx_arg.resize (dim_vector (nr, 1)); for (octave_idx_type i = 0; i < nr; i++) { bool real_only = row_is_real_only (i); octave_idx_type idx_j; FloatComplex tmp_min; float abs_min = octave_Float_NaN; for (idx_j = 0; idx_j < nc; idx_j++) { tmp_min = elem (i, idx_j); if (! xisnan (tmp_min)) { abs_min = real_only ? std::real (tmp_min) : std::abs (tmp_min); break; } } for (octave_idx_type j = idx_j+1; j < nc; j++) { FloatComplex tmp = elem (i, j); if (xisnan (tmp)) continue; float abs_tmp = real_only ? std::real (tmp) : std::abs (tmp); if (abs_tmp < abs_min) { idx_j = j; tmp_min = tmp; abs_min = abs_tmp; } } if (xisnan (tmp_min)) { result.elem (i) = FloatComplex_NaN_result; idx_arg.elem (i) = 0; } else { result.elem (i) = tmp_min; idx_arg.elem (i) = idx_j; } } } return result; } FloatComplexColumnVector FloatComplexMatrix::row_max (void) const { Array<octave_idx_type> dummy_idx; return row_max (dummy_idx); } FloatComplexColumnVector FloatComplexMatrix::row_max (Array<octave_idx_type>& idx_arg) const { FloatComplexColumnVector result; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr > 0 && nc > 0) { result.resize (nr); idx_arg.resize (dim_vector (nr, 1)); for (octave_idx_type i = 0; i < nr; i++) { bool real_only = row_is_real_only (i); octave_idx_type idx_j; FloatComplex tmp_max; float abs_max = octave_Float_NaN; for (idx_j = 0; idx_j < nc; idx_j++) { tmp_max = elem (i, idx_j); if (! xisnan (tmp_max)) { abs_max = real_only ? std::real (tmp_max) : std::abs (tmp_max); break; } } for (octave_idx_type j = idx_j+1; j < nc; j++) { FloatComplex tmp = elem (i, j); if (xisnan (tmp)) continue; float abs_tmp = real_only ? std::real (tmp) : std::abs (tmp); if (abs_tmp > abs_max) { idx_j = j; tmp_max = tmp; abs_max = abs_tmp; } } if (xisnan (tmp_max)) { result.elem (i) = FloatComplex_NaN_result; idx_arg.elem (i) = 0; } else { result.elem (i) = tmp_max; idx_arg.elem (i) = idx_j; } } } return result; } FloatComplexRowVector FloatComplexMatrix::column_min (void) const { Array<octave_idx_type> dummy_idx; return column_min (dummy_idx); } FloatComplexRowVector FloatComplexMatrix::column_min (Array<octave_idx_type>& idx_arg) const { FloatComplexRowVector result; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr > 0 && nc > 0) { result.resize (nc); idx_arg.resize (dim_vector (1, nc)); for (octave_idx_type j = 0; j < nc; j++) { bool real_only = column_is_real_only (j); octave_idx_type idx_i; FloatComplex tmp_min; float abs_min = octave_Float_NaN; for (idx_i = 0; idx_i < nr; idx_i++) { tmp_min = elem (idx_i, j); if (! xisnan (tmp_min)) { abs_min = real_only ? std::real (tmp_min) : std::abs (tmp_min); break; } } for (octave_idx_type i = idx_i+1; i < nr; i++) { FloatComplex tmp = elem (i, j); if (xisnan (tmp)) continue; float abs_tmp = real_only ? std::real (tmp) : std::abs (tmp); if (abs_tmp < abs_min) { idx_i = i; tmp_min = tmp; abs_min = abs_tmp; } } if (xisnan (tmp_min)) { result.elem (j) = FloatComplex_NaN_result; idx_arg.elem (j) = 0; } else { result.elem (j) = tmp_min; idx_arg.elem (j) = idx_i; } } } return result; } FloatComplexRowVector FloatComplexMatrix::column_max (void) const { Array<octave_idx_type> dummy_idx; return column_max (dummy_idx); } FloatComplexRowVector FloatComplexMatrix::column_max (Array<octave_idx_type>& idx_arg) const { FloatComplexRowVector result; octave_idx_type nr = rows (); octave_idx_type nc = cols (); if (nr > 0 && nc > 0) { result.resize (nc); idx_arg.resize (dim_vector (1, nc)); for (octave_idx_type j = 0; j < nc; j++) { bool real_only = column_is_real_only (j); octave_idx_type idx_i; FloatComplex tmp_max; float abs_max = octave_Float_NaN; for (idx_i = 0; idx_i < nr; idx_i++) { tmp_max = elem (idx_i, j); if (! xisnan (tmp_max)) { abs_max = real_only ? std::real (tmp_max) : std::abs (tmp_max); break; } } for (octave_idx_type i = idx_i+1; i < nr; i++) { FloatComplex tmp = elem (i, j); if (xisnan (tmp)) continue; float abs_tmp = real_only ? std::real (tmp) : std::abs (tmp); if (abs_tmp > abs_max) { idx_i = i; tmp_max = tmp; abs_max = abs_tmp; } } if (xisnan (tmp_max)) { result.elem (j) = FloatComplex_NaN_result; idx_arg.elem (j) = 0; } else { result.elem (j) = tmp_max; idx_arg.elem (j) = idx_i; } } } return result; } // i/o std::ostream& operator << (std::ostream& os, const FloatComplexMatrix& a) { for (octave_idx_type i = 0; i < a.rows (); i++) { for (octave_idx_type j = 0; j < a.cols (); j++) { os << " "; octave_write_complex (os, a.elem (i, j)); } os << "\n"; } return os; } std::istream& operator >> (std::istream& is, FloatComplexMatrix& a) { octave_idx_type nr = a.rows (); octave_idx_type nc = a.cols (); if (nr > 0 && nc > 0) { FloatComplex tmp; for (octave_idx_type i = 0; i < nr; i++) for (octave_idx_type j = 0; j < nc; j++) { tmp = octave_read_value<FloatComplex> (is); if (is) a.elem (i, j) = tmp; else return is; } } return is; } FloatComplexMatrix Givens (const FloatComplex& x, const FloatComplex& y) { float cc; FloatComplex cs, temp_r; F77_FUNC (clartg, CLARTG) (x, y, cc, cs, temp_r); FloatComplexMatrix g (2, 2); g.elem (0, 0) = cc; g.elem (1, 1) = cc; g.elem (0, 1) = cs; g.elem (1, 0) = -conj (cs); return g; } FloatComplexMatrix Sylvester (const FloatComplexMatrix& a, const FloatComplexMatrix& b, const FloatComplexMatrix& c) { FloatComplexMatrix retval; // FIXME: need to check that a, b, and c are all the same // size. // Compute Schur decompositions FloatComplexSCHUR as (a, "U"); FloatComplexSCHUR bs (b, "U"); // Transform c to new coordinates. FloatComplexMatrix ua = as.unitary_matrix (); FloatComplexMatrix sch_a = as.schur_matrix (); FloatComplexMatrix ub = bs.unitary_matrix (); FloatComplexMatrix sch_b = bs.schur_matrix (); FloatComplexMatrix cx = ua.hermitian () * c * ub; // Solve the sylvester equation, back-transform, and return the // solution. octave_idx_type a_nr = a.rows (); octave_idx_type b_nr = b.rows (); float scale; octave_idx_type info; FloatComplex *pa = sch_a.fortran_vec (); FloatComplex *pb = sch_b.fortran_vec (); FloatComplex *px = cx.fortran_vec (); F77_XFCN (ctrsyl, CTRSYL, (F77_CONST_CHAR_ARG2 ("N", 1), F77_CONST_CHAR_ARG2 ("N", 1), 1, a_nr, b_nr, pa, a_nr, pb, b_nr, px, a_nr, scale, info F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); // FIXME: check info? retval = ua * cx * ub.hermitian (); return retval; } FloatComplexMatrix operator * (const FloatComplexMatrix& m, const FloatMatrix& a) { if (m.columns () > std::min (m.rows (), a.columns ()) / 10) return FloatComplexMatrix (real (m) * a, imag (m) * a); else return m * FloatComplexMatrix (a); } FloatComplexMatrix operator * (const FloatMatrix& m, const FloatComplexMatrix& a) { if (a.rows () > std::min (m.rows (), a.columns ()) / 10) return FloatComplexMatrix (m * real (a), m * imag (a)); else return FloatComplexMatrix (m) * a; } /* ## Simple Dot Product, Matrix-Vector, and Matrix-Matrix Unit tests %!assert (single ([1+i 2+i 3+i]) * single ([ 4+i ; 5+i ; 6+i]), single (29+21i), 5e-7) %!assert (single ([1+i 2+i ; 3+i 4+i]) * single ([5+i ; 6+i]), single ([15 + 14i ; 37 + 18i]), 5e-7) %!assert (single ([1+i 2+i ; 3+i 4+i ]) * single ([5+i 6+i ; 7+i 8+i]), single ([17 + 15i 20 + 17i; 41 + 19i 48 + 21i]), 5e-7) %!assert (single ([1 i])*single ([i 0])', single (-i)) ## Test some simple identities %!shared M, cv, rv %! M = single (randn (10,10))+ i*single (rand (10,10)); %! cv = single (randn (10,1))+ i*single (rand (10,1)); %! rv = single (randn (1,10))+ i*single (rand (1,10)); %!assert ([M*cv,M*cv], M*[cv,cv], 5e-6) %!assert ([M.'*cv,M.'*cv], M.'*[cv,cv], 5e-6) %!assert ([M'*cv,M'*cv], M'*[cv,cv], 5e-6) %!assert ([rv*M;rv*M], [rv;rv]*M, 5e-6) %!assert ([rv*M.';rv*M.'], [rv;rv]*M.', 5e-6) %!assert ([rv*M';rv*M'], [rv;rv]*M', 5e-6) %!assert (2*rv*cv, [rv,rv]*[cv;cv], 5e-6) */ static char get_blas_trans_arg (bool trans, bool conj) { return trans ? (conj ? 'C' : 'T') : 'N'; } // the general GEMM operation FloatComplexMatrix xgemm (const FloatComplexMatrix& a, const FloatComplexMatrix& b, blas_trans_type transa, blas_trans_type transb) { FloatComplexMatrix retval; bool tra = transa != blas_no_trans; bool trb = transb != blas_no_trans; bool cja = transa == blas_conj_trans; bool cjb = transb == blas_conj_trans; octave_idx_type a_nr = tra ? a.cols () : a.rows (); octave_idx_type a_nc = tra ? a.rows () : a.cols (); octave_idx_type b_nr = trb ? b.cols () : b.rows (); octave_idx_type b_nc = trb ? b.rows () : b.cols (); if (a_nc != b_nr) err_nonconformant ("operator *", a_nr, a_nc, b_nr, b_nc); if (a_nr == 0 || a_nc == 0 || b_nc == 0) retval = FloatComplexMatrix (a_nr, b_nc, 0.0); else if (a.data () == b.data () && a_nr == b_nc && tra != trb) { octave_idx_type lda = a.rows (); // FIXME: looking at the reference BLAS, it appears that it // should not be necessary to initialize the output matrix if // BETA is 0 in the call to CHERK, but ATLAS appears to // use the result matrix before zeroing the elements. retval = FloatComplexMatrix (a_nr, b_nc, 0.0); FloatComplex *c = retval.fortran_vec (); const char ctra = get_blas_trans_arg (tra, cja); if (cja || cjb) { F77_XFCN (cherk, CHERK, (F77_CONST_CHAR_ARG2 ("U", 1), F77_CONST_CHAR_ARG2 (&ctra, 1), a_nr, a_nc, 1.0, a.data (), lda, 0.0, c, a_nr F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); for (octave_idx_type j = 0; j < a_nr; j++) for (octave_idx_type i = 0; i < j; i++) retval.xelem (j,i) = std::conj (retval.xelem (i,j)); } else { F77_XFCN (csyrk, CSYRK, (F77_CONST_CHAR_ARG2 ("U", 1), F77_CONST_CHAR_ARG2 (&ctra, 1), a_nr, a_nc, 1.0, a.data (), lda, 0.0, c, a_nr F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); for (octave_idx_type j = 0; j < a_nr; j++) for (octave_idx_type i = 0; i < j; i++) retval.xelem (j,i) = retval.xelem (i,j); } } else { octave_idx_type lda = a.rows (); octave_idx_type tda = a.cols (); octave_idx_type ldb = b.rows (); octave_idx_type tdb = b.cols (); retval = FloatComplexMatrix (a_nr, b_nc, 0.0); FloatComplex *c = retval.fortran_vec (); if (b_nc == 1 && a_nr == 1) { if (cja == cjb) { F77_FUNC (xcdotu, XCDOTU) (a_nc, a.data (), 1, b.data (), 1, *c); if (cja) *c = std::conj (*c); } else if (cja) F77_FUNC (xcdotc, XCDOTC) (a_nc, a.data (), 1, b.data (), 1, *c); else F77_FUNC (xcdotc, XCDOTC) (a_nc, b.data (), 1, a.data (), 1, *c); } else if (b_nc == 1 && ! cjb) { const char ctra = get_blas_trans_arg (tra, cja); F77_XFCN (cgemv, CGEMV, (F77_CONST_CHAR_ARG2 (&ctra, 1), lda, tda, 1.0, a.data (), lda, b.data (), 1, 0.0, c, 1 F77_CHAR_ARG_LEN (1))); } else if (a_nr == 1 && ! cja && ! cjb) { const char crevtrb = get_blas_trans_arg (! trb, cjb); F77_XFCN (cgemv, CGEMV, (F77_CONST_CHAR_ARG2 (&crevtrb, 1), ldb, tdb, 1.0, b.data (), ldb, a.data (), 1, 0.0, c, 1 F77_CHAR_ARG_LEN (1))); } else { const char ctra = get_blas_trans_arg (tra, cja); const char ctrb = get_blas_trans_arg (trb, cjb); F77_XFCN (cgemm, CGEMM, (F77_CONST_CHAR_ARG2 (&ctra, 1), F77_CONST_CHAR_ARG2 (&ctrb, 1), a_nr, b_nc, a_nc, 1.0, a.data (), lda, b.data (), ldb, 0.0, c, a_nr F77_CHAR_ARG_LEN (1) F77_CHAR_ARG_LEN (1))); } } return retval; } FloatComplexMatrix operator * (const FloatComplexMatrix& a, const FloatComplexMatrix& b) { return xgemm (a, b); } // FIXME: it would be nice to share code among the min/max // functions below. #define EMPTY_RETURN_CHECK(T) \ if (nr == 0 || nc == 0) \ return T (nr, nc); FloatComplexMatrix min (const FloatComplex& c, const FloatComplexMatrix& m) { octave_idx_type nr = m.rows (); octave_idx_type nc = m.columns (); EMPTY_RETURN_CHECK (FloatComplexMatrix); 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) = xmin (c, m(i, j)); } return result; } FloatComplexMatrix min (const FloatComplexMatrix& m, const FloatComplex& c) { octave_idx_type nr = m.rows (); octave_idx_type nc = m.columns (); EMPTY_RETURN_CHECK (FloatComplexMatrix); 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) = xmin (m(i, j), c); } return result; } FloatComplexMatrix min (const FloatComplexMatrix& a, const FloatComplexMatrix& b) { octave_idx_type nr = a.rows (); octave_idx_type nc = a.columns (); if (nr != b.rows () || nc != b.columns ()) (*current_liboctave_error_handler) ("two-arg min requires same size arguments"); EMPTY_RETURN_CHECK (FloatComplexMatrix); FloatComplexMatrix result (nr, nc); for (octave_idx_type j = 0; j < nc; j++) { int columns_are_real_only = 1; for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); if (std::imag (a(i, j)) != 0.0 || std::imag (b(i, j)) != 0.0) { columns_are_real_only = 0; break; } } if (columns_are_real_only) { for (octave_idx_type i = 0; i < nr; i++) result(i, j) = xmin (std::real (a(i, j)), std::real (b(i, j))); } else { for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); result(i, j) = xmin (a(i, j), b(i, j)); } } } return result; } FloatComplexMatrix max (const FloatComplex& c, const FloatComplexMatrix& m) { octave_idx_type nr = m.rows (); octave_idx_type nc = m.columns (); EMPTY_RETURN_CHECK (FloatComplexMatrix); 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) = xmax (c, m(i, j)); } return result; } FloatComplexMatrix max (const FloatComplexMatrix& m, const FloatComplex& c) { octave_idx_type nr = m.rows (); octave_idx_type nc = m.columns (); EMPTY_RETURN_CHECK (FloatComplexMatrix); 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) = xmax (m(i, j), c); } return result; } FloatComplexMatrix max (const FloatComplexMatrix& a, const FloatComplexMatrix& b) { octave_idx_type nr = a.rows (); octave_idx_type nc = a.columns (); if (nr != b.rows () || nc != b.columns ()) (*current_liboctave_error_handler) ("two-arg max requires same size arguments"); EMPTY_RETURN_CHECK (FloatComplexMatrix); FloatComplexMatrix result (nr, nc); for (octave_idx_type j = 0; j < nc; j++) { int columns_are_real_only = 1; for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); if (std::imag (a(i, j)) != 0.0 || std::imag (b(i, j)) != 0.0) { columns_are_real_only = 0; break; } } if (columns_are_real_only) { for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); result(i, j) = xmax (std::real (a(i, j)), std::real (b(i, j))); } } else { for (octave_idx_type i = 0; i < nr; i++) { octave_quit (); result(i, j) = xmax (a(i, j), b(i, j)); } } } return result; } FloatComplexMatrix linspace (const FloatComplexColumnVector& x1, const FloatComplexColumnVector& x2, octave_idx_type n) { octave_idx_type m = x1.numel (); if (x2.numel () != m) (*current_liboctave_error_handler) ("linspace: vectors must be of equal length"); NoAlias<FloatComplexMatrix> retval; if (n < 1) { retval.clear (m, 0); return retval; } retval.clear (m, n); for (octave_idx_type i = 0; i < m; i++) retval(i, 0) = x1(i); // The last column is unused so temporarily store delta there FloatComplex *delta = &retval(0, n-1); for (octave_idx_type i = 0; i < m; i++) delta[i] = (x2(i) - x1(i)) / (n - 1.0f); for (octave_idx_type j = 1; j < n-1; j++) for (octave_idx_type i = 0; i < m; i++) retval(i, j) = x1(i) + static_cast<float> (j)*delta[i]; for (octave_idx_type i = 0; i < m; i++) retval(i, n-1) = x2(i); return retval; } MS_CMP_OPS (FloatComplexMatrix, FloatComplex) MS_BOOL_OPS (FloatComplexMatrix, FloatComplex) SM_CMP_OPS (FloatComplex, FloatComplexMatrix) SM_BOOL_OPS (FloatComplex, FloatComplexMatrix) MM_CMP_OPS (FloatComplexMatrix, FloatComplexMatrix) MM_BOOL_OPS (FloatComplexMatrix, FloatComplexMatrix)