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annotate libinterp/corefcn/kron.cc @ 18849:aa9ca67f09fb

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make all permutation matrices column permutations (bug #42418) Making all permutation matrices column permutations allows permutation matrices to be iterated over in column-major order just like any other matrix. * PermMatrix.h, PermMatrix.cc (PermMatrix::_colp): Delete member variable and all uses. (PermMatrix::transpose): Create new matrix with internal representation flipped. (PermMatrix::pos_power): New function. (PermMatrix::eye): Call the one-argument constructor which already defaults to the identity matrix. (PermMatrix::is_col_perm): Unconditionally return true. (PermMatrix::is_row_perm): Unconditionally return false. (PermMatrix::data, PermMatrix::fortran_vec, PermMatrix::pvec): Delete. (PermMatrix::col_perm_vec): New function. * lu.cc: New test. * base-lu.cc (base_lu<lu_type>::base_lu): Call transpose in ipvt initialization. * find.cc, kron.cc, pr-output.cc, ov-perm.cc, PermMatrix.cc, PermMatrix.h, Sparse.cc, dMatrix.cc, fMatrix.cc, CmplxQRP.cc, base-lu.cc, dbleQRP.cc, fCmplxQRP.cc, floatQRP.cc, Sparse-perm-op-defs.h, mx-op-defs.h: Adapt to PermMatrix changes.
author David Spies <dnspies@gmail.com>
date Wed, 18 Jun 2014 19:38:40 -0600
parents 9ac2357f19bc
children 38c54d45d05f
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1 /*
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2
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d63878346099 maint: Update copyright notices for release.
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3 Copyright (C) 2002-2013 John W. Eaton
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4
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5 This file is part of Octave.
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6
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7 Octave is free software; you can redistribute it and/or modify it
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8 under the terms of the GNU General Public License as published by the
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9 Free Software Foundation; either version 3 of the License, or (at your
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10 option) any later version.
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11
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12 Octave is distributed in the hope that it will be useful, but WITHOUT
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13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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15 for more details.
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16
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17 You should have received a copy of the GNU General Public License
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18 along with Octave; see the file COPYING. If not, see
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19 <http://www.gnu.org/licenses/>.
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20
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21 */
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22
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23 // Author: Paul Kienzle <pkienzle@users.sf.net>
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24
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25 #ifdef HAVE_CONFIG_H
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26 #include <config.h>
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27 #endif
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28
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29 #include "dMatrix.h"
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30 #include "fMatrix.h"
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31 #include "CMatrix.h"
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32 #include "fCMatrix.h"
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33
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34 #include "dSparse.h"
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35 #include "CSparse.h"
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36
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37 #include "dDiagMatrix.h"
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38 #include "fDiagMatrix.h"
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39 #include "CDiagMatrix.h"
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40 #include "fCDiagMatrix.h"
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41
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42 #include "PermMatrix.h"
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43
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44 #include "mx-inlines.cc"
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45 #include "quit.h"
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46
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47 #include "defun.h"
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48 #include "error.h"
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49 #include "oct-obj.h"
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50
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51 template <class R, class T>
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52 static MArray<T>
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53 kron (const MArray<R>& a, const MArray<T>& b)
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54 {
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55 assert (a.ndims () == 2);
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56 assert (b.ndims () == 2);
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57
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58 octave_idx_type nra = a.rows ();
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59 octave_idx_type nrb = b.rows ();
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60 octave_idx_type nca = a.cols ();
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61 octave_idx_type ncb = b.cols ();
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62
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63 MArray<T> c (dim_vector (nra*nrb, nca*ncb));
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64 T *cv = c.fortran_vec ();
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65
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66 for (octave_idx_type ja = 0; ja < nca; ja++)
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67 for (octave_idx_type jb = 0; jb < ncb; jb++)
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68 for (octave_idx_type ia = 0; ia < nra; ia++)
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69 {
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70 octave_quit ();
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71 mx_inline_mul (nrb, cv, a(ia, ja), b.data () + nrb*jb);
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72 cv += nrb;
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73 }
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74
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75 return c;
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76 }
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77
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78 template <class R, class T>
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79 static MArray<T>
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80 kron (const MDiagArray2<R>& a, const MArray<T>& b)
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81 {
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82 assert (b.ndims () == 2);
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83
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84 octave_idx_type nra = a.rows ();
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85 octave_idx_type nrb = b.rows ();
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86 octave_idx_type dla = a.diag_length ();
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87 octave_idx_type nca = a.cols ();
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88 octave_idx_type ncb = b.cols ();
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89
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90 MArray<T> c (dim_vector (nra*nrb, nca*ncb), T ());
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91
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92 for (octave_idx_type ja = 0; ja < dla; ja++)
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93 for (octave_idx_type jb = 0; jb < ncb; jb++)
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94 {
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95 octave_quit ();
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96 mx_inline_mul (nrb, &c.xelem (ja*nrb, ja*ncb + jb), a.dgelem (ja),
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97 b.data () + nrb*jb);
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98 }
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99
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100 return c;
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101 }
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102
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103 template <class T>
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104 static MSparse<T>
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105 kron (const MSparse<T>& A, const MSparse<T>& B)
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106 {
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107 octave_idx_type idx = 0;
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108 MSparse<T> C (A.rows () * B.rows (), A.columns () * B.columns (),
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109 A.nnz () * B.nnz ());
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110
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111 C.cidx (0) = 0;
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112
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113 for (octave_idx_type Aj = 0; Aj < A.columns (); Aj++)
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114 for (octave_idx_type Bj = 0; Bj < B.columns (); Bj++)
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115 {
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116 octave_quit ();
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117 for (octave_idx_type Ai = A.cidx (Aj); Ai < A.cidx (Aj+1); Ai++)
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118 {
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119 octave_idx_type Ci = A.ridx (Ai) * B.rows ();
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120 const T v = A.data (Ai);
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121
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122 for (octave_idx_type Bi = B.cidx (Bj); Bi < B.cidx (Bj+1); Bi++)
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123 {
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124 C.data (idx) = v * B.data (Bi);
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125 C.ridx (idx++) = Ci + B.ridx (Bi);
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126 }
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127 }
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128 C.cidx (Aj * B.columns () + Bj + 1) = idx;
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129 }
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130
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131 return C;
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132 }
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133
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134 static PermMatrix
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135 kron (const PermMatrix& a, const PermMatrix& b)
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136 {
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137 octave_idx_type na = a.rows ();
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138 octave_idx_type nb = b.rows ();
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139 const Array<octave_idx_type>& pa = a.col_perm_vec ();
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140 const Array<octave_idx_type>& pb = b.col_perm_vec ();
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141 Array<octave_idx_type> res_perm;
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142 octave_idx_type rescol = 0;
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143 for (octave_idx_type i = 0; i < na; i++)
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144 {
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145 octave_idx_type a_add = pa(i) * nb;
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146 for (octave_idx_type j = 0; j < nb; j++)
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147 res_perm.xelem (rescol++) = a_add + pb(j);
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148 }
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149
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150 return PermMatrix (res_perm, true);
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151 }
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152
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153 template <class MTA, class MTB>
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154 octave_value
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155 do_kron (const octave_value& a, const octave_value& b)
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156 {
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157 MTA am = octave_value_extract<MTA> (a);
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158 MTB bm = octave_value_extract<MTB> (b);
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159 return octave_value (kron (am, bm));
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160 }
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161
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162 octave_value
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163 dispatch_kron (const octave_value& a, const octave_value& b)
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164 {
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165 octave_value retval;
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166 if (a.is_perm_matrix () && b.is_perm_matrix ())
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167 retval = do_kron<PermMatrix, PermMatrix> (a, b);
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168 else if (a.is_sparse_type () || b.is_sparse_type ())
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169 {
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170 if (a.is_complex_type () || b.is_complex_type ())
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171 retval = do_kron<SparseComplexMatrix, SparseComplexMatrix> (a, b);
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172 else
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173 retval = do_kron<SparseMatrix, SparseMatrix> (a, b);
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174 }
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175 else if (a.is_diag_matrix ())
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176 {
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177 if (b.is_diag_matrix () && a.rows () == a.columns ()
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178 && b.rows () == b.columns ())
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179 {
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180 // We have two diagonal matrices, the product of those will be
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181 // another diagonal matrix. To do that efficiently, extract
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182 // the diagonals as vectors and compute the product. That
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183 // will be another vector, which we then use to construct a
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184 // diagonal matrix object. Note that this will fail if our
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185 // digaonal matrix object is modified to allow the nonzero
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186 // values to be stored off of the principal diagonal (i.e., if
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187 // diag ([1,2], 3) is modified to return a diagonal matrix
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188 // object instead of a full matrix object).
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189
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190 octave_value tmp = dispatch_kron (a.diag (), b.diag ());
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191 retval = tmp.diag ();
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192 }
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193 else if (a.is_single_type () || b.is_single_type ())
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194 {
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195 if (a.is_complex_type ())
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196 retval = do_kron<FloatComplexDiagMatrix, FloatComplexMatrix> (a, b);
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197 else if (b.is_complex_type ())
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198 retval = do_kron<FloatDiagMatrix, FloatComplexMatrix> (a, b);
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199 else
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200 retval = do_kron<FloatDiagMatrix, FloatMatrix> (a, b);
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201 }
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202 else
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203 {
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204 if (a.is_complex_type ())
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205 retval = do_kron<ComplexDiagMatrix, ComplexMatrix> (a, b);
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206 else if (b.is_complex_type ())
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207 retval = do_kron<DiagMatrix, ComplexMatrix> (a, b);
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208 else
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209 retval = do_kron<DiagMatrix, Matrix> (a, b);
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210 }
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211 }
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212 else if (a.is_single_type () || b.is_single_type ())
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213 {
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214 if (a.is_complex_type ())
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215 retval = do_kron<FloatComplexMatrix, FloatComplexMatrix> (a, b);
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216 else if (b.is_complex_type ())
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217 retval = do_kron<FloatMatrix, FloatComplexMatrix> (a, b);
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218 else
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219 retval = do_kron<FloatMatrix, FloatMatrix> (a, b);
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220 }
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221 else
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222 {
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223 if (a.is_complex_type ())
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224 retval = do_kron<ComplexMatrix, ComplexMatrix> (a, b);
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225 else if (b.is_complex_type ())
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226 retval = do_kron<Matrix, ComplexMatrix> (a, b);
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227 else
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228 retval = do_kron<Matrix, Matrix> (a, b);
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229 }
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230 return retval;
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231 }
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232
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233
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234 DEFUN (kron, args, , "-*- texinfo -*-\n\
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235 @deftypefn {Built-in Function} {} kron (@var{A}, @var{B})\n\
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236 @deftypefnx {Built-in Function} {} kron (@var{A1}, @var{A2}, @dots{})\n\
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237 Form the Kronecker product of two or more matrices, defined block by \n\
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238 block as\n\
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239 \n\
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240 @example\n\
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241 x = [ a(i,j)*b ]\n\
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242 @end example\n\
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243 \n\
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244 For example:\n\
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245 \n\
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246 @example\n\
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247 @group\n\
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248 kron (1:4, ones (3, 1))\n\
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249 @result{} 1 2 3 4\n\
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250 1 2 3 4\n\
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251 1 2 3 4\n\
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252 @end group\n\
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253 @end example\n\
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254 \n\
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255 If there are more than two input arguments @var{A1}, @var{A2}, @dots{}, \n\
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256 @var{An} the Kronecker product is computed as\n\
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257 \n\
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258 @example\n\
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259 kron (kron (@var{A1}, @var{A2}), @dots{}, @var{An})\n\
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260 @end example\n\
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261 \n\
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262 @noindent\n\
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263 Since the Kronecker product is associative, this is well-defined.\n\
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264 @end deftypefn")
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265 {
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266 octave_value retval;
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267
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268 int nargin = args.length ();
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269
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270 if (nargin >= 2)
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271 {
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272 octave_value a = args(0);
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273 octave_value b = args(1);
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274 retval = dispatch_kron (a, b);
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275 for (octave_idx_type i = 2; i < nargin; i++)
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276 retval = dispatch_kron (retval, args(i));
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277 }
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278 else
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279 print_usage ();
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280
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281 return retval;
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282 }
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283
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284
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285 /*
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286 %!test
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287 %! x = ones (2);
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288 %! assert (kron (x, x), ones (4));
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289
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290 %!shared x, y, z
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291 %! x = [1, 2];
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292 %! y = [-1, -2];
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293 %! z = [1, 2, 3, 4; 1, 2, 3, 4; 1, 2, 3, 4];
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294 %!assert (kron (1:4, ones (3, 1)), z)
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295 %!assert (kron (x, y, z), kron (kron (x, y), z))
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296 %!assert (kron (x, y, z), kron (x, kron (y, z)))
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297
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298 %!assert (kron (diag ([1, 2]), diag ([3, 4])), diag ([3, 4, 6, 8]))
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299
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300 %% Test for two diag matrices. See the comments above in
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301 %% dispatch_kron for this case.
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302 %%
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303 %!test
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304 %! expected = zeros (16, 16);
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305 %! expected (1, 11) = 3;
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306 %! expected (2, 12) = 4;
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307 %! expected (5, 15) = 6;
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308 %! expected (6, 16) = 8;
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309 %! assert (kron (diag ([1, 2], 2), diag ([3, 4], 2)), expected)
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310 */