Mercurial > octave-nkf
annotate libinterp/corefcn/kron.cc @ 20607:db3286201347 stable
doc: Add explanation of ':' optional input to numel().
* data.cc (Fnumel): Add explanation of ':' optional input.
author | Rik <rik@octave.org> |
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date | Wed, 07 Oct 2015 14:52:01 -0700 |
parents | 4f45eaf83908 |
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rev | line source |
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3910 | 1 /* |
2 | |
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3 Copyright (C) 2002-2015 John W. Eaton |
3910 | 4 |
5 This file is part of Octave. | |
6 | |
7 Octave is free software; you can redistribute it and/or modify it | |
8 under the terms of the GNU General Public License as published by the | |
7016 | 9 Free Software Foundation; either version 3 of the License, or (at your |
10 option) any later version. | |
3910 | 11 |
12 Octave is distributed in the hope that it will be useful, but WITHOUT | |
13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
15 for more details. | |
16 | |
17 You should have received a copy of the GNU General Public License | |
7016 | 18 along with Octave; see the file COPYING. If not, see |
19 <http://www.gnu.org/licenses/>. | |
3910 | 20 |
21 */ | |
22 | |
3911 | 23 // Author: Paul Kienzle <pkienzle@users.sf.net> |
24 | |
3910 | 25 #ifdef HAVE_CONFIG_H |
26 #include <config.h> | |
27 #endif | |
28 | |
29 #include "dMatrix.h" | |
10461 | 30 #include "fMatrix.h" |
3910 | 31 #include "CMatrix.h" |
10461 | 32 #include "fCMatrix.h" |
33 | |
34 #include "dSparse.h" | |
35 #include "CSparse.h" | |
36 | |
37 #include "dDiagMatrix.h" | |
38 #include "fDiagMatrix.h" | |
39 #include "CDiagMatrix.h" | |
40 #include "fCDiagMatrix.h" | |
41 | |
42 #include "PermMatrix.h" | |
43 | |
44 #include "mx-inlines.cc" | |
4153 | 45 #include "quit.h" |
3910 | 46 |
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47 #include "defun.h" |
3910 | 48 #include "error.h" |
49 #include "oct-obj.h" | |
50 | |
10461 | 51 template <class R, class T> |
52 static MArray<T> | |
53 kron (const MArray<R>& a, const MArray<T>& b) | |
54 { | |
55 assert (a.ndims () == 2); | |
56 assert (b.ndims () == 2); | |
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 (); |
3910 | 62 |
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63 MArray<T> c (dim_vector (nra*nrb, nca*ncb)); |
10461 | 64 T *cv = c.fortran_vec (); |
65 | |
66 for (octave_idx_type ja = 0; ja < nca; ja++) | |
67 for (octave_idx_type jb = 0; jb < ncb; jb++) | |
68 for (octave_idx_type ia = 0; ia < nra; ia++) | |
69 { | |
70 octave_quit (); | |
71 mx_inline_mul (nrb, cv, a(ia, ja), b.data () + nrb*jb); | |
72 cv += nrb; | |
73 } | |
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74 |
10461 | 75 return c; |
76 } | |
77 | |
78 template <class R, class T> | |
79 static MArray<T> | |
80 kron (const MDiagArray2<R>& a, const MArray<T>& b) | |
81 { | |
82 assert (b.ndims () == 2); | |
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 ()); |
10461 | 91 |
92 for (octave_idx_type ja = 0; ja < dla; ja++) | |
93 for (octave_idx_type jb = 0; jb < ncb; jb++) | |
94 { | |
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); |
10461 | 98 } |
99 | |
100 return c; | |
101 } | |
3910 | 102 |
103 template <class T> | |
10461 | 104 static MSparse<T> |
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 { |
10461 | 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 } |
10461 | 130 |
131 return C; | |
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132 } |
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133 |
10461 | 134 static PermMatrix |
135 kron (const PermMatrix& a, const PermMatrix& b) | |
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 (dim_vector (na * nb, 1)); |
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142 octave_idx_type rescol = 0; |
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143 for (octave_idx_type i = 0; i < na; i++) |
10461 | 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); |
10461 | 148 } |
149 | |
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150 return PermMatrix (res_perm, true); |
10461 | 151 } |
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152 |
10461 | 153 template <class MTA, class MTB> |
154 octave_value | |
155 do_kron (const octave_value& a, const octave_value& b) | |
156 { | |
157 MTA am = octave_value_extract<MTA> (a); | |
158 MTB bm = octave_value_extract<MTB> (b); | |
159 return octave_value (kron (am, bm)); | |
160 } | |
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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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.\n\ |
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238 \n\ |
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239 This is defined block by block as\n\ |
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241 @example\n\ | |
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242 x = [ a(i,j)*b ]\n\ |
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244 \n\ | |
10840 | 245 For example:\n\ |
3910 | 246 \n\ |
247 @example\n\ | |
248 @group\n\ | |
249 kron (1:4, ones (3, 1))\n\ | |
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250 @result{} 1 2 3 4\n\ |
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251 1 2 3 4\n\ |
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252 1 2 3 4\n\ |
3910 | 253 @end group\n\ |
254 @end example\n\ | |
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255 \n\ |
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256 If there are more than two input arguments @var{A1}, @var{A2}, @dots{},\n\ |
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257 @var{An} the Kronecker product is computed as\n\ |
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258 \n\ |
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259 @example\n\ |
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260 kron (kron (@var{A1}, @var{A2}), @dots{}, @var{An})\n\ |
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261 @end example\n\ |
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262 \n\ |
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263 @noindent\n\ |
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264 Since the Kronecker product is associative, this is well-defined.\n\ |
3910 | 265 @end deftypefn") |
266 { | |
10461 | 267 octave_value retval; |
3910 | 268 |
269 int nargin = args.length (); | |
270 | |
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271 if (nargin >= 2) |
3910 | 272 { |
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273 octave_value a = args(0); |
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274 octave_value b = args(1); |
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275 retval = dispatch_kron (a, b); |
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276 for (octave_idx_type i = 2; i < nargin; i++) |
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277 retval = dispatch_kron (retval, args(i)); |
3910 | 278 } |
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279 else |
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280 print_usage (); |
3910 | 281 |
282 return retval; | |
283 } | |
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284 |
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285 |
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286 /* |
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287 %!test |
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288 %! x = ones (2); |
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289 %! assert (kron (x, x), ones (4)); |
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290 |
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291 %!shared x, y, z, p1, p2, d1, d2 |
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292 %! x = [1, 2]; |
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293 %! y = [-1, -2]; |
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294 %! z = [1, 2, 3, 4; 1, 2, 3, 4; 1, 2, 3, 4]; |
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295 %! p1 = eye (3)([2, 3, 1], :); ## Permutation matrix |
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296 %! p2 = [0 1 0; 0 0 1; 1 0 0]; ## Non-permutation equivalent |
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297 %! d1 = diag ([1 2 3]); ## Diag type matrix |
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298 %! d2 = [1 0 0; 0 2 0; 0 0 3]; ## Non-diag equivalent |
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299 %!assert (kron (1:4, ones (3, 1)), z) |
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300 %!assert (kron (single (1:4), ones (3, 1)), single (z)) |
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301 %!assert (kron (sparse (1:4), ones (3, 1)), sparse (z)) |
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302 %!assert (kron (complex (1:4), ones (3, 1)), z) |
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303 %!assert (kron (complex (single(1:4)), ones (3, 1)), single(z)) |
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304 %!assert (kron (x, y, z), kron (kron (x, y), z)) |
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305 %!assert (kron (x, y, z), kron (x, kron (y, z))) |
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306 %!assert (kron (p1, p1), kron (p2, p2)) |
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307 %!assert (kron (p1, p2), kron (p2, p1)) |
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308 %!assert (kron (d1, d1), kron (d2, d2)) |
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309 %!assert (kron (d1, d2), kron (d2, d1)) |
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310 |
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311 |
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312 %!assert (kron (diag ([1, 2]), diag ([3, 4])), diag ([3, 4, 6, 8])) |
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313 |
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314 %% Test for two diag matrices. See the comments above in |
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315 %% dispatch_kron for this case. |
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allow kron to work for two diag matrix arguments (bug #35647)
John W. Eaton <jwe@octave.org>
parents:
14138
diff
changeset
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316 %% |
6eabd81604b5
allow kron to work for two diag matrix arguments (bug #35647)
John W. Eaton <jwe@octave.org>
parents:
14138
diff
changeset
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317 %!test |
6eabd81604b5
allow kron to work for two diag matrix arguments (bug #35647)
John W. Eaton <jwe@octave.org>
parents:
14138
diff
changeset
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318 %! expected = zeros (16, 16); |
6eabd81604b5
allow kron to work for two diag matrix arguments (bug #35647)
John W. Eaton <jwe@octave.org>
parents:
14138
diff
changeset
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319 %! expected (1, 11) = 3; |
6eabd81604b5
allow kron to work for two diag matrix arguments (bug #35647)
John W. Eaton <jwe@octave.org>
parents:
14138
diff
changeset
|
320 %! expected (2, 12) = 4; |
6eabd81604b5
allow kron to work for two diag matrix arguments (bug #35647)
John W. Eaton <jwe@octave.org>
parents:
14138
diff
changeset
|
321 %! expected (5, 15) = 6; |
6eabd81604b5
allow kron to work for two diag matrix arguments (bug #35647)
John W. Eaton <jwe@octave.org>
parents:
14138
diff
changeset
|
322 %! expected (6, 16) = 8; |
6eabd81604b5
allow kron to work for two diag matrix arguments (bug #35647)
John W. Eaton <jwe@octave.org>
parents:
14138
diff
changeset
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323 %! assert (kron (diag ([1, 2], 2), diag ([3, 4], 2)), expected) |
12790
5ecdb60ddf0f
codesprint: Write two tests for kron.cc
Jordi Gutiérrez Hermoso <jordigh@gmail.com>
parents:
11586
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324 */ |