Mercurial > octave
annotate libinterp/corefcn/sqrtm.cc @ 21100:e39e05d90788
Switch gripe_XXX to either err_XXX or warn_XXX naming scheme.
* libinterp/corefcn/errwarn.h, libinterp/corefcn/errwarn.cc: New header and .cc
file with common errors and warnings for libinterp.
* libinterp/corefcn/module.mk: Add errwarn.h, errwarn.cc to build system.
* liboctave/util/lo-array-errwarn.h, liboctave/util/lo-array-errwarn.cc: New
header and .cc file with common errors and warnings for liboctave.
* liboctave/util/module.mk: Add lo-array-errwarn.h, lo-array-errwarn.cc to
build system.
* lo-array-gripes.h: #include "lo-array-errwarn.h" for access to class
index_exception. Remove const char *error_id_XXX prototypes.
* lo-array-gripes.cc: Remove const char *error_id_XXX initializations.
Remove index_exception method definitions.
* Cell.cc, __pchip_deriv__.cc, __qp__.cc, balance.cc, betainc.cc, cellfun.cc,
daspk.cc, dasrt.cc, dassl.cc, data.cc, debug.cc, defaults.cc, det.cc,
dirfns.cc, eig.cc, fft.cc, fft2.cc, fftn.cc, find.cc, gammainc.cc, gcd.cc,
getgrent.cc, getpwent.cc, graphics.in.h, help.cc, hess.cc, hex2num.cc,
input.cc, inv.cc, jit-typeinfo.cc, load-save.cc, lookup.cc, ls-hdf5.cc,
ls-mat-ascii.cc, ls-mat4.cc, ls-mat5.cc, ls-oct-binary.cc, ls-oct-text.cc,
lsode.cc, lu.cc, luinc.cc, max.cc, mgorth.cc, oct-hist.cc, oct-procbuf.cc,
oct-stream.cc, oct.h, pager.cc, pinv.cc, pr-output.cc, quad.cc, qz.cc, rand.cc,
rcond.cc, regexp.cc, schur.cc, sparse-xdiv.cc, sparse-xpow.cc, sparse.cc,
spparms.cc, sqrtm.cc, str2double.cc, strfind.cc, strfns.cc, sub2ind.cc, svd.cc,
sylvester.cc, syscalls.cc, typecast.cc, utils.cc, variables.cc, xdiv.cc,
xnorm.cc, xpow.cc, __eigs__.cc, __glpk__.cc, __magick_read__.cc,
__osmesa_print__.cc, audiodevinfo.cc, audioread.cc, chol.cc, dmperm.cc,
fftw.cc, qr.cc, symbfact.cc, symrcm.cc, ov-base-diag.cc, ov-base-int.cc,
ov-base-mat.cc, ov-base-scalar.cc, ov-base-sparse.cc, ov-base.cc,
ov-bool-mat.cc, ov-bool-sparse.cc, ov-bool.cc, ov-builtin.cc, ov-cell.cc,
ov-ch-mat.cc, ov-class.cc, ov-complex.cc, ov-complex.h, ov-cs-list.cc,
ov-cx-diag.cc, ov-cx-mat.cc, ov-cx-sparse.cc, ov-fcn-handle.cc,
ov-fcn-inline.cc, ov-float.cc, ov-float.h, ov-flt-complex.cc, ov-flt-complex.h,
ov-flt-cx-diag.cc, ov-flt-cx-mat.cc, ov-flt-re-mat.cc, ov-int16.cc,
ov-int32.cc, ov-int64.cc, ov-int8.cc, ov-intx.h, ov-mex-fcn.cc, ov-perm.cc,
ov-range.cc, ov-re-mat.cc, ov-re-sparse.cc, ov-scalar.cc, ov-scalar.h,
ov-str-mat.cc, ov-struct.cc, ov-type-conv.h, ov-uint16.cc, ov-uint32.cc,
ov-uint64.cc, ov-uint8.cc, ov-usr-fcn.cc, ov.cc, op-b-b.cc, op-b-bm.cc,
op-b-sbm.cc, op-bm-b.cc, op-bm-bm.cc, op-bm-sbm.cc, op-cdm-cdm.cc, op-cell.cc,
op-chm.cc, op-class.cc, op-cm-cm.cc, op-cm-cs.cc, op-cm-m.cc, op-cm-s.cc,
op-cm-scm.cc, op-cm-sm.cc, op-cs-cm.cc, op-cs-cs.cc, op-cs-m.cc, op-cs-s.cc,
op-cs-scm.cc, op-cs-sm.cc, op-dm-dm.cc, op-dm-scm.cc, op-dm-sm.cc,
op-dms-template.cc, op-double-conv.cc, op-fcdm-fcdm.cc, op-fcdm-fdm.cc,
op-fcm-fcm.cc, op-fcm-fcs.cc, op-fcm-fm.cc, op-fcm-fs.cc, op-fcn.cc,
op-fcs-fcm.cc, op-fcs-fcs.cc, op-fcs-fm.cc, op-fcs-fs.cc, op-fdm-fdm.cc,
op-float-conv.cc, op-fm-fcm.cc, op-fm-fcs.cc, op-fm-fm.cc, op-fm-fs.cc,
op-fs-fcm.cc, op-fs-fcs.cc, op-fs-fm.cc, op-fs-fs.cc, op-i16-i16.cc,
op-i32-i32.cc, op-i64-i64.cc, op-i8-i8.cc, op-int-concat.cc, op-int-conv.cc,
op-int.h, op-m-cm.cc, op-m-cs.cc, op-m-m.cc, op-m-s.cc, op-m-scm.cc,
op-m-sm.cc, op-pm-pm.cc, op-pm-scm.cc, op-pm-sm.cc, op-range.cc, op-s-cm.cc,
op-s-cs.cc, op-s-m.cc, op-s-s.cc, op-s-scm.cc, op-s-sm.cc, op-sbm-b.cc,
op-sbm-bm.cc, op-sbm-sbm.cc, op-scm-cm.cc, op-scm-cs.cc, op-scm-m.cc,
op-scm-s.cc, op-scm-scm.cc, op-scm-sm.cc, op-sm-cm.cc, op-sm-cs.cc, op-sm-m.cc,
op-sm-s.cc, op-sm-scm.cc, op-sm-sm.cc, op-str-m.cc, op-str-s.cc, op-str-str.cc,
op-struct.cc, op-ui16-ui16.cc, op-ui32-ui32.cc, op-ui64-ui64.cc, op-ui8-ui8.cc,
ops.h, lex.ll, pt-assign.cc, pt-eval.cc, pt-idx.cc, pt-loop.cc, pt-mat.cc,
pt-stmt.cc, Array-util.cc, Array-util.h, Array.cc, CColVector.cc,
CDiagMatrix.cc, CMatrix.cc, CNDArray.cc, CRowVector.cc, CSparse.cc,
DiagArray2.cc, MDiagArray2.cc, MSparse.cc, PermMatrix.cc, Range.cc, Sparse.cc,
dColVector.cc, dDiagMatrix.cc, dMatrix.cc, dNDArray.cc, dRowVector.cc,
dSparse.cc, fCColVector.cc, fCDiagMatrix.cc, fCMatrix.cc, fCNDArray.cc,
fCRowVector.cc, fColVector.cc, fDiagMatrix.cc, fMatrix.cc, fNDArray.cc,
fRowVector.cc, idx-vector.cc, CmplxGEPBAL.cc, dbleGEPBAL.cc, fCmplxGEPBAL.cc,
floatGEPBAL.cc, Sparse-diag-op-defs.h, Sparse-op-defs.h, Sparse-perm-op-defs.h,
mx-inlines.cc, mx-op-defs.h, oct-binmap.h:
Replace 'include "gripes.h"' with 'include "errwarn.h". Change all gripe_XXX
to err_XXX or warn_XXX or errwarn_XXX.
| author | Rik <rik@octave.org> |
|---|---|
| date | Mon, 18 Jan 2016 18:28:06 -0800 |
| parents | 93748bcaec17 |
| children | 3d0d84305600 |
| rev | line source |
|---|---|
| 4331 | 1 /* |
| 2 | |
|
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3 Copyright (C) 2001-2015 Ross Lippert and Paul Kienzle |
| 10608 | 4 Copyright (C) 2010 VZLU Prague |
| 4331 | 5 |
| 7016 | 6 This file is part of Octave. |
| 4331 | 7 |
| 7016 | 8 Octave is free software; you can redistribute it and/or modify it |
| 9 under the terms of the GNU General Public License as published by the | |
| 10 Free Software Foundation; either version 3 of the License, or (at your | |
| 11 option) any later version. | |
| 12 | |
| 13 Octave is distributed in the hope that it will be useful, but WITHOUT | |
| 14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
| 15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
| 16 for more details. | |
| 4331 | 17 |
| 18 You should have received a copy of the GNU General Public License | |
| 7016 | 19 along with Octave; see the file COPYING. If not, see |
| 20 <http://www.gnu.org/licenses/>. | |
| 4331 | 21 |
| 22 */ | |
| 23 | |
| 24 #ifdef HAVE_CONFIG_H | |
| 25 #include <config.h> | |
| 26 #endif | |
| 27 | |
| 28 #include <float.h> | |
| 29 | |
| 30 #include "CmplxSCHUR.h" | |
|
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31 #include "fCmplxSCHUR.h" |
| 4331 | 32 #include "lo-ieee.h" |
| 33 #include "lo-mappers.h" | |
| 10608 | 34 #include "oct-norm.h" |
| 4331 | 35 |
|
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36 #include "defun.h" |
| 4331 | 37 #include "error.h" |
|
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38 #include "errwarn.h" |
| 4331 | 39 #include "utils.h" |
| 10608 | 40 #include "xnorm.h" |
| 4331 | 41 |
| 10608 | 42 template <class Matrix> |
| 43 static void | |
| 44 sqrtm_utri_inplace (Matrix& T) | |
| 4331 | 45 { |
| 10608 | 46 typedef typename Matrix::element_type element_type; |
| 4331 | 47 |
| 10608 | 48 const element_type zero = element_type (); |
| 4331 | 49 |
| 10608 | 50 bool singular = false; |
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51 |
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52 // The following code is equivalent to this triple loop: |
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53 // |
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54 // n = rows (T); |
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55 // for j = 1:n |
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56 // T(j,j) = sqrt (T(j,j)); |
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57 // for i = j-1:-1:1 |
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58 // T(i,j) /= (T(i,i) + T(j,j)); |
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59 // k = 1:i-1; |
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60 // T(k,j) -= T(k,i) * T(i,j); |
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61 // endfor |
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62 // endfor |
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63 // |
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64 // this is an in-place, cache-aligned variant of the code |
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65 // given in Higham's paper. |
| 4331 | 66 |
| 10608 | 67 const octave_idx_type n = T.rows (); |
| 68 element_type *Tp = T.fortran_vec (); | |
| 5275 | 69 for (octave_idx_type j = 0; j < n; j++) |
| 4331 | 70 { |
| 10608 | 71 element_type *colj = Tp + n*j; |
| 72 if (colj[j] != zero) | |
| 73 colj[j] = sqrt (colj[j]); | |
| 74 else | |
| 75 singular = true; | |
| 4331 | 76 |
| 10608 | 77 for (octave_idx_type i = j-1; i >= 0; i--) |
| 78 { | |
| 79 const element_type *coli = Tp + n*i; | |
| 80 const element_type colji = colj[i] /= (coli[i] + colj[j]); | |
| 81 for (octave_idx_type k = 0; k < i; k++) | |
| 82 colj[k] -= coli[k] * colji; | |
|
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83 } |
| 4331 | 84 } |
| 85 | |
| 10608 | 86 if (singular) |
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87 warning_with_id ("Octave:sqrtm:SingularMatrix", |
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88 "sqrtm: matrix is singular, may not have a square root"); |
| 4331 | 89 } |
| 90 | |
| 10608 | 91 template <class Matrix, class ComplexMatrix, class ComplexSCHUR> |
| 92 static octave_value | |
| 93 do_sqrtm (const octave_value& arg) | |
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94 { |
| 10608 | 95 |
| 96 octave_value retval; | |
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97 |
| 10608 | 98 MatrixType mt = arg.matrix_type (); |
| 99 | |
| 100 bool iscomplex = arg.is_complex_type (); | |
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101 |
| 10608 | 102 typedef typename Matrix::element_type real_type; |
| 103 | |
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104 real_type cutoff = 0; |
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105 real_type one = 1; |
| 10608 | 106 real_type eps = std::numeric_limits<real_type>::epsilon (); |
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107 |
| 10608 | 108 if (! iscomplex) |
| 109 { | |
| 110 Matrix x = octave_value_extract<Matrix> (arg); | |
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111 |
| 10608 | 112 if (mt.is_unknown ()) // if type is not known, compute it now. |
| 113 arg.matrix_type (mt = MatrixType (x)); | |
| 114 | |
| 115 switch (mt.type ()) | |
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116 { |
| 10608 | 117 case MatrixType::Upper: |
| 118 case MatrixType::Diagonal: | |
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119 if (! x.diag ().any_element_is_negative ()) |
| 10608 | 120 { |
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121 // Do it in real arithmetic. |
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122 sqrtm_utri_inplace (x); |
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123 retval = x; |
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124 retval.matrix_type (mt); |
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125 } |
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126 else |
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127 iscomplex = true; |
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128 break; |
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129 |
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130 case MatrixType::Lower: |
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131 if (! x.diag ().any_element_is_negative ()) |
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132 { |
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133 x = x.transpose (); |
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134 sqrtm_utri_inplace (x); |
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135 retval = x.transpose (); |
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136 retval.matrix_type (mt); |
| 10608 | 137 } |
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138 else |
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139 iscomplex = true; |
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140 break; |
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141 |
| 10608 | 142 default: |
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143 iscomplex = true; |
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144 break; |
| 10608 | 145 } |
| 146 | |
| 147 if (iscomplex) | |
| 148 cutoff = 10 * x.rows () * eps * xnorm (x, one); | |
| 149 } | |
| 150 | |
| 151 if (iscomplex) | |
| 152 { | |
| 153 ComplexMatrix x = octave_value_extract<ComplexMatrix> (arg); | |
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154 |
| 10608 | 155 if (mt.is_unknown ()) // if type is not known, compute it now. |
| 156 arg.matrix_type (mt = MatrixType (x)); | |
| 157 | |
| 158 switch (mt.type ()) | |
| 159 { | |
| 160 case MatrixType::Upper: | |
| 161 case MatrixType::Diagonal: | |
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162 sqrtm_utri_inplace (x); |
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163 retval = x; |
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164 retval.matrix_type (mt); |
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165 break; |
| 10608 | 166 |
| 167 case MatrixType::Lower: | |
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168 x = x.transpose (); |
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169 sqrtm_utri_inplace (x); |
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170 retval = x.transpose (); |
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171 retval.matrix_type (mt); |
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172 break; |
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173 |
| 10608 | 174 default: |
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175 { |
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176 ComplexMatrix u; |
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177 |
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178 do |
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179 { |
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180 ComplexSCHUR schur (x, "", true); |
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181 x = schur.schur_matrix (); |
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182 u = schur.unitary_matrix (); |
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183 } |
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184 while (0); // schur no longer needed. |
| 10608 | 185 |
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186 sqrtm_utri_inplace (x); |
| 10608 | 187 |
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188 x = u * x; // original x no longer needed. |
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189 ComplexMatrix res = xgemm (x, u, blas_no_trans, blas_conj_trans); |
| 10608 | 190 |
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191 if (cutoff > 0 && xnorm (imag (res), one) <= cutoff) |
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192 retval = real (res); |
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193 else |
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194 retval = res; |
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195 } |
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196 break; |
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197 } |
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198 } |
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199 |
| 10608 | 200 return retval; |
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201 } |
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202 |
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203 DEFUN (sqrtm, args, nargout, |
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204 "-*- texinfo -*-\n\ |
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205 @deftypefn {} {@var{s} =} sqrtm (@var{A})\n\ |
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206 @deftypefnx {} {[@var{s}, @var{error_estimate}] =} sqrtm (@var{A})\n\ |
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207 Compute the matrix square root of the square matrix @var{A}.\n\ |
| 4331 | 208 \n\ |
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209 Ref: @nospell{N.J. Higham}. @cite{A New sqrtm for @sc{matlab}}. Numerical\n\ |
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210 Analysis Report No. 336, Manchester @nospell{Centre} for Computational\n\ |
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211 Mathematics, Manchester, England, January 1999.\n\ |
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212 @seealso{expm, logm}\n\ |
| 5642 | 213 @end deftypefn") |
| 4331 | 214 { |
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215 if (args.length () != 1) |
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216 print_usage (); |
| 4331 | 217 |
| 218 octave_value arg = args(0); | |
| 219 | |
| 5275 | 220 octave_idx_type n = arg.rows (); |
| 221 octave_idx_type nc = arg.columns (); | |
| 4331 | 222 |
| 10608 | 223 if (n != nc || arg.ndims () > 2) |
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224 err_square_matrix_required ("sqrtm"); |
| 4331 | 225 |
| 20892 | 226 octave_value_list retval (nargout > 1 ? 3 : 1); |
| 227 | |
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228 if (nargout > 1) |
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229 { |
| 20892 | 230 // FIXME: Octave does not calculate a condition number with respect to |
| 231 // sqrtm. Should this return NaN instead of -1? | |
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232 retval(2) = -1.0; |
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233 } |
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234 |
| 10608 | 235 if (arg.is_diag_matrix ()) |
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236 // sqrtm of a diagonal matrix is just sqrt. |
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237 retval(0) = arg.sqrt (); |
| 10608 | 238 else if (arg.is_single_type ()) |
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239 retval(0) = do_sqrtm<FloatMatrix, FloatComplexMatrix, FloatComplexSCHUR> |
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240 (arg); |
| 10608 | 241 else if (arg.is_numeric_type ()) |
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242 retval(0) = do_sqrtm<Matrix, ComplexMatrix, ComplexSCHUR> (arg); |
| 4331 | 243 |
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244 if (nargout > 1) |
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245 { |
| 10608 | 246 // This corresponds to generic code |
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247 // |
| 10608 | 248 // norm (s*s - x, "fro") / norm (x, "fro"); |
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249 |
| 10608 | 250 octave_value s = retval(0); |
| 251 retval(1) = xfrobnorm (s*s - arg) / xfrobnorm (arg); | |
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252 } |
| 4331 | 253 |
| 254 return retval; | |
| 255 } | |
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256 |
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257 /* |
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258 %!assert (sqrtm (2*ones (2)), ones (2), 3*eps) |
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259 |
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260 ## The following two tests are from the reference in the docstring above. |
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261 %!test |
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262 %! x = [0 1; 0 0]; |
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263 %! assert (any (isnan (sqrtm (x))(:))); |
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264 |
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265 %!test |
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266 %! x = eye (4); x(2,2) = x(3,3) = 2^-26; x(1,4) = 1; |
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267 %! z = eye (4); z(2,2) = z(3,3) = 2^-13; z(1,4) = 0.5; |
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268 %! [y, err] = sqrtm (x); |
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269 %! assert (y, z); |
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270 %! assert (err, 0); # Yes, this one has to hold exactly |
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271 */ |