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annotate libinterp/corefcn/kron.cc @ 18794:03c2671493f9

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maint: Periodic merge of gui-release to default.
author Rik <rik@octave.org>
date Mon, 02 Jun 2014 11:17:59 -0700
parents 6a71e5030df5
children 9ac2357f19bc
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1 /*
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2
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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
79a90a0f0eff [project @ 2002-04-25 05:36:52 by jwe]
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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 octave_idx_type *pa = a.data ();
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140 const octave_idx_type *pb = b.data ();
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141 PermMatrix c(na*nb); // Row permutation.
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142 octave_idx_type *pc = c.fortran_vec ();
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143
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144 bool cola = a.is_col_perm ();
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145 bool colb = b.is_col_perm ();
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146 if (cola && colb)
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147 {
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148 for (octave_idx_type i = 0; i < na; i++)
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149 for (octave_idx_type j = 0; j < nb; j++)
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150 pc[pa[i]*nb+pb[j]] = i*nb+j;
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151 }
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152 else if (cola)
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153 {
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154 for (octave_idx_type i = 0; i < na; i++)
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155 for (octave_idx_type j = 0; j < nb; j++)
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156 pc[pa[i]*nb+j] = i*nb+pb[j];
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157 }
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158 else if (colb)
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159 {
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160 for (octave_idx_type i = 0; i < na; i++)
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161 for (octave_idx_type j = 0; j < nb; j++)
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162 pc[i*nb+pb[j]] = pa[i]*nb+j;
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163 }
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164 else
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165 {
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166 for (octave_idx_type i = 0; i < na; i++)
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167 for (octave_idx_type j = 0; j < nb; j++)
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168 pc[i*nb+j] = pa[i]*nb+pb[j];
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169 }
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170
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171 return c;
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172 }
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173
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174 template <class MTA, class MTB>
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175 octave_value
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176 do_kron (const octave_value& a, const octave_value& b)
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177 {
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178 MTA am = octave_value_extract<MTA> (a);
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179 MTB bm = octave_value_extract<MTB> (b);
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180 return octave_value (kron (am, bm));
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181 }
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182
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183 octave_value
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184 dispatch_kron (const octave_value& a, const octave_value& b)
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185 {
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186 octave_value retval;
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187 if (a.is_perm_matrix () && b.is_perm_matrix ())
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188 retval = do_kron<PermMatrix, PermMatrix> (a, b);
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189 else if (a.is_sparse_type () || b.is_sparse_type ())
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190 {
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191 if (a.is_complex_type () || b.is_complex_type ())
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192 retval = do_kron<SparseComplexMatrix, SparseComplexMatrix> (a, b);
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193 else
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194 retval = do_kron<SparseMatrix, SparseMatrix> (a, b);
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195 }
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196 else if (a.is_diag_matrix ())
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197 {
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198 if (b.is_diag_matrix () && a.rows () == a.columns ()
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199 && b.rows () == b.columns ())
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200 {
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201 // We have two diagonal matrices, the product of those will be
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202 // another diagonal matrix. To do that efficiently, extract
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203 // the diagonals as vectors and compute the product. That
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204 // will be another vector, which we then use to construct a
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205 // diagonal matrix object. Note that this will fail if our
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206 // digaonal matrix object is modified to allow the non-zero
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207 // values to be stored off of the principal diagonal (i.e., if
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208 // diag ([1,2], 3) is modified to return a diagonal matrix
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209 // object instead of a full matrix object).
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210
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211 octave_value tmp = dispatch_kron (a.diag (), b.diag ());
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212 retval = tmp.diag ();
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213 }
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214 else if (a.is_single_type () || b.is_single_type ())
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215 {
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216 if (a.is_complex_type ())
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217 retval = do_kron<FloatComplexDiagMatrix, FloatComplexMatrix> (a, b);
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218 else if (b.is_complex_type ())
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219 retval = do_kron<FloatDiagMatrix, FloatComplexMatrix> (a, b);
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220 else
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221 retval = do_kron<FloatDiagMatrix, FloatMatrix> (a, b);
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222 }
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223 else
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224 {
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225 if (a.is_complex_type ())
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226 retval = do_kron<ComplexDiagMatrix, ComplexMatrix> (a, b);
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227 else if (b.is_complex_type ())
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228 retval = do_kron<DiagMatrix, ComplexMatrix> (a, b);
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229 else
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230 retval = do_kron<DiagMatrix, Matrix> (a, b);
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231 }
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232 }
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233 else if (a.is_single_type () || b.is_single_type ())
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234 {
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235 if (a.is_complex_type ())
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236 retval = do_kron<FloatComplexMatrix, FloatComplexMatrix> (a, b);
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237 else if (b.is_complex_type ())
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238 retval = do_kron<FloatMatrix, FloatComplexMatrix> (a, b);
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239 else
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240 retval = do_kron<FloatMatrix, FloatMatrix> (a, b);
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241 }
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242 else
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243 {
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244 if (a.is_complex_type ())
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245 retval = do_kron<ComplexMatrix, ComplexMatrix> (a, b);
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246 else if (b.is_complex_type ())
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247 retval = do_kron<Matrix, ComplexMatrix> (a, b);
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248 else
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249 retval = do_kron<Matrix, Matrix> (a, b);
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250 }
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251 return retval;
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252 }
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253
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254
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255 DEFUN (kron, args, , "-*- texinfo -*-\n\
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256 @deftypefn {Built-in Function} {} kron (@var{A}, @var{B})\n\
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257 @deftypefnx {Built-in Function} {} kron (@var{A1}, @var{A2}, @dots{})\n\
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258 Form the Kronecker product of two or more matrices, defined block by \n\
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259 block as\n\
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260 \n\
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261 @example\n\
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262 x = [ a(i,j)*b ]\n\
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263 @end example\n\
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264 \n\
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265 For example:\n\
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266 \n\
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267 @example\n\
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268 @group\n\
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269 kron (1:4, ones (3, 1))\n\
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270 @result{} 1 2 3 4\n\
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271 1 2 3 4\n\
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272 1 2 3 4\n\
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273 @end group\n\
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274 @end example\n\
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275 \n\
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276 If there are more than two input arguments @var{A1}, @var{A2}, @dots{}, \n\
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277 @var{An} the Kronecker product is computed as\n\
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278 \n\
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279 @example\n\
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280 kron (kron (@var{A1}, @var{A2}), @dots{}, @var{An})\n\
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281 @end example\n\
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282 \n\
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283 @noindent\n\
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284 Since the Kronecker product is associative, this is well-defined.\n\
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285 @end deftypefn")
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286 {
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287 octave_value retval;
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288
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289 int nargin = args.length ();
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290
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291 if (nargin >= 2)
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292 {
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293 octave_value a = args(0);
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294 octave_value b = args(1);
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295 retval = dispatch_kron (a, b);
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296 for (octave_idx_type i = 2; i < nargin; i++)
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297 retval = dispatch_kron (retval, args(i));
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298 }
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299 else
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300 print_usage ();
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301
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302 return retval;
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303 }
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304
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305
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306 /*
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307 %!test
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308 %! x = ones (2);
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309 %! assert (kron (x, x), ones (4));
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310
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311 %!shared x, y, z
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312 %! x = [1, 2];
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313 %! y = [-1, -2];
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314 %! z = [1, 2, 3, 4; 1, 2, 3, 4; 1, 2, 3, 4];
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315 %!assert (kron (1:4, ones (3, 1)), z)
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316 %!assert (kron (x, y, z), kron (kron (x, y), z))
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317 %!assert (kron (x, y, z), kron (x, kron (y, z)))
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318
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319 %!assert (kron (diag ([1, 2]), diag ([3, 4])), diag ([3, 4, 6, 8]))
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320
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321 %% Test for two diag matrices. See the comments above in
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322 %% dispatch_kron for this case.
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323 %%
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324 %!test
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325 %! expected = zeros (16, 16);
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326 %! expected (1, 11) = 3;
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327 %! expected (2, 12) = 4;
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328 %! expected (5, 15) = 6;
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329 %! expected (6, 16) = 8;
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330 %! assert (kron (diag ([1, 2], 2), diag ([3, 4], 2)), expected)
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331 */