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annotate test/test_diag_perm.m @ 10928:a93efb08dc7f

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author Ben Abbott <bpabbott@mac.com>
date Tue, 31 Aug 2010 07:41:18 -0400
parents 2e9af3363669
children fd0a3ac60b0e
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1 ## Copyright (C) 2009 E. Jason Riedy
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ########################################
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20 ## Permutation matrices
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21
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22 ## row permutation
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23 %!test
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24 %! n = 5;
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25 %! A = rand (n);
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26 %! perm = randperm (n);
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27 %! Prow = eye (n) (perm, :);
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28 %! assert (A(perm, :), Prow * A);
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29 %! invperm(perm) = 1:n;
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30 %! assert (Prow \ A, A(invperm, :));
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31 %! assert (Prow' * A, A(invperm, :));
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32
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33 ## column permutation
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34 %!test
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35 %! n = 7;
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36 %! A = rand (n);
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37 %! perm = randperm (n);
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38 %! Pcol = eye (n) (:, perm);
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39 %! assert (A(:, perm), A * Pcol);
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40 %! invperm(perm) = 1:n;
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41 %! assert (A / Pcol, A(:, invperm));
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42 %! assert (A * Pcol.', A(:, invperm));
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43
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44 ## fall back to a matrix in addition
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45 %!test
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46 %! n = 4;
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47 %! P1 = eye (n) (:, randperm (n));
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48 %! A = zeros (n) + P1;
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49 %! assert (sum (A), full (ones (1, n)));
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50 %! assert (sum (A, 2), full (ones (n, 1)));
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51
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52 ## preserve dense matrix structure
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53 %!test
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54 %! n = 7;
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55 %! Pc = eye (n) (:, randperm (n));
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56 %! Pr = eye (n) (randperm (n), :);
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57 %! assert (typeinfo (rand (n) * Pc), "matrix");
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58 %! assert (typeinfo (Pr * rand (n)), "matrix");
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59
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60 ## preserve sparse matrix structure
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61 %!test
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62 %! n = 7;
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63 %! Pc = eye (n) (:, randperm (n));
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64 %! Ac = sprand (n-3, n, .5) + I () * sprand (n-3, n, .5);
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65 %! Pr = eye (n) (randperm (n), :);
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66 %! Ar = sprand (n, n+2, .5);
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67 %! assert (typeinfo (Ac * Pc), "sparse complex matrix");
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68 %! assert (full (Ac * Pc), full (Ac) * Pc);
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69 %! assert (full (Ac / Pc), full (Ac) / Pc);
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70 %! assert (typeinfo (Pr * Ar), "sparse matrix");
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71 %! assert (full (Pr * Ar), Pr * full (Ar));
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72 %! assert (full (Pr \ Ar), Pr \ full (Ar));
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73
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74 ## structure rules for 1x1 dense / scalar and 1x1 perm
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75 %!test
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76 %! n = 7;
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77 %! P1 = eye (1) (:, [1]);
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78 %! A1 = 1;
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79 %! P = eye (n) (:, randperm (n));
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80 %! A = rand (n-3, n, .5);
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81 %! assert (typeinfo (A * P1), "matrix");
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82 %! assert (full (A * P1), full (A) * P1);
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83 %! assert (typeinfo (P1 * A), "matrix");
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84 %! assert (full (P1 * A), P1 * full (A));
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85 %! assert (typeinfo (A1 * P), "matrix");
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86 %! assert (full (A1 * P), full (A1) * P);
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87 %! assert (typeinfo (P * A1), "matrix");
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88 %! assert (full (P * A1), P * full (A1));
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89
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90 ## structure rules for 1x1 sparse and 1x1 perm
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91 %!test
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92 %! n = 7;
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93 %! P1 = eye (1) (:, [1]);
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94 %! A1 = sparse (1, 1, 2);
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95 %! P = eye (n) (:, randperm (n));
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96 %! A = sprand (n-3, n, .5);
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97 %! assert (typeinfo (A * P1), "sparse matrix");
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98 %! assert (full (A * P1), full (A) * P1);
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99 %! assert (typeinfo (P1 * A), "sparse matrix");
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100 %! assert (full (P1 * A), P1 * full (A));
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101 %! assert (typeinfo (A1 * P), "sparse matrix");
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102 %! assert (full (A1 * P), full (A1) * P);
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103 %! assert (typeinfo (P * A1), "sparse matrix");
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104 %! assert (full (P * A1), P * full (A1));
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105
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106 ## permuting a matrix with exceptional values does not introduce new ones.
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107 %!test
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108 %! n = 5;
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109 %! pc = randperm (n);
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110 %! Pc = eye (n) (:, pc);
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111 %! pr = randperm (n);
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112 %! Pr = eye (n) (pr, :);
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113 %! A = rand (n);
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114 %! A(n, n-2) = NaN;
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115 %! A(3, 1) = Inf;
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116 %! assert (Pr * A * Pc, A(pr, pc));
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117
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118 ## conversion to sparse form
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119 %!test
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120 %! n = 7;
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121 %! P = eye (n) (:, randperm (n));
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122 %! sP = sparse (P);
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123 %! assert (full (sP), full (P));
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124 %! assert (size (find (sP), 1), n);
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125 %! [I, J, V] = find (sP);
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126 %! assert (all (V == 1));
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127
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128 ########################################
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129 ## Diagonal matrices
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130
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131 ## square row scaling
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132 %!test
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133 %! m = 7;
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134 %! n = 11;
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135 %! A = rand (m, n);
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136 %! scalefact = rand (m, 1);
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137 %! Dr = diag (scalefact);
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138 %! assert (Dr * A, repmat (scalefact, 1, n) .* A);
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139 %! assert (Dr \ A, A ./ repmat (scalefact, 1, n));
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140 %! scalefact(m-1) = Inf;
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141 %! Dr(m-1, m-1) = 0;
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142 %! assert (Dr \ A, A ./ repmat (scalefact, 1, n));
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143
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144 ## square column scaling
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145 %!test
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146 %! m = 13;
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147 %! n = 11;
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148 %! A = rand (m, n);
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149 %! scalefact = rand (1, n);
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150 %! Dc = diag (scalefact);
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151 %! assert (A * Dc, repmat (scalefact, m, 1) .* A);
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152 %! assert (A / Dc, A ./ repmat (scalefact, m, 1));
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153 %! scalefact(n-1) = Inf;
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154 %! Dc(n-1, n-1) = 0;
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155 %! assert (A / Dc, A ./ repmat (scalefact, m, 1));
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156
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157 ## arithmetic
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158 %!test
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159 %! m = 9;
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160 %! n = 7;
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161 %! mn = min (m, n);
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162 %! d1 = rand (mn, 1) + I () * rand (mn, 1);
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163 %! D1 = diag (d1, m, n);
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164 %! d2 = rand (mn, 1);
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165 %! D2 = diag (d2, m, n);
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166 %! D1D2 = D1 + D2;
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167 %! assert (typeinfo (D1D2), "complex diagonal matrix");
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168 %! assert (diag (D1D2), d1 + d2);
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169 %! D1D2 = D2.' * D1;
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170 %! assert (typeinfo (D1D2), "complex diagonal matrix");
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171 %! assert (diag (D1D2), d1 .* d2);
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172
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173 ## slicing
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174 %!test
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175 %! m = 13;
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176 %! n = 6;
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177 %! mn = min (m, n);
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178 %! d = rand (mn, 1);
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179 %! D = diag (d, m, n);
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180 %! Dslice = D (1:(m-3), 1:(n-2));
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181 %! assert (typeinfo (Dslice), "diagonal matrix");
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182
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183 ## preserve dense matrix structure when scaling
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184 %!assert (typeinfo (rand (8) * (3 * eye (8))), "matrix");
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185 %!assert (typeinfo ((3 * eye (8)) * rand (8)), "matrix");
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186
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187 ## preserve sparse matrix structure when scaling
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188 %!assert (typeinfo (sprand (8, 8, .5) * (3 * eye (8))), "sparse matrix");
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189 %!assert (typeinfo (sprand (8, 8, .5) * (3 * eye (8))'), "sparse matrix");
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190 %!assert (typeinfo (((3 + 2 * I ()) * eye (8)) * sprand (8, 8, .5)), "sparse complex matrix");
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191 %!assert (typeinfo (((3 + 2 * I ()) * eye (8))' * sprand (8, 8, .5)), "sparse complex matrix");
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192 %!assert (typeinfo (sprand (8, 8, .5) * ((3 + 2 * I ()) * eye (8)).'), "sparse complex matrix");
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193
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194 ## scaling a matrix with exceptional values does not introduce new ones.
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195 %!test
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196 %! n = 6;
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197 %! dr = rand (n, 1);
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198 %! Dr = diag (dr);
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199 %! dc = rand (1, n);
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200 %! Dc = diag (dc);
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201 %! A = rand (n);
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202 %! A(n, n-2) = NaN;
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203 %! A(4, 1) = Inf;
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204 %! assert (Dr * A * Dc, A .* kron (dr, dc), eps);
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205
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206 ## sparse inverse row scaling with a zero factor
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207 %!test
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208 %! n = 8;
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209 %! A = sprand (n, n, .5);
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210 %! scalefact = rand (n, 1);
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211 %! Dr = diag (scalefact);
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212 %! scalefact(n-1) = Inf;
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213 %! Dr(n-1, n-1) = 0;
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214 %! assert (full (Dr \ A), full (A) ./ repmat (scalefact, 1, n));
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215
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216 ## narrow sparse inverse row scaling
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217 %!test
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218 %! n = 8;
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219 %! A = sprand (n, n, .5);
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220 %! scalefact = rand (n-2, 1);
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221 %! Dr = diag (scalefact, n, n-2);
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222 %! assert (full (Dr \ A), Dr \ full(A))
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223
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224 ## sparse inverse column scaling with a zero factor
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225 %!test
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226 %! n = 11;
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227 %! A = sprand (n, n, .5);
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228 %! scalefact = rand (1, n);
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229 %! Dc = diag (scalefact);
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230 %! scalefact(n-1) = Inf;
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231 %! Dc(n-1, n-1) = 0;
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232 %! assert (full (A / Dc), full(A) / Dc)
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233
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234 ## short sparse inverse column scaling
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235 %!test
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236 %! n = 7;
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237 %! A = sprand (n, n, .5);
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238 %! scalefact = rand (1, n-2) + I () * rand(1, n-2);
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239 %! Dc = diag (scalefact, n-2, n);
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240 %! assert (full (A / Dc), full(A) / Dc)
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241
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242 ## adding sparse and diagonal stays sparse
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243 %!test
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244 %! n = 9;
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245 %! A = sprand (n, n, .5);
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246 %! D = 2 * eye (n);
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247 %! assert (typeinfo (A + D), "sparse matrix")
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248 %! assert (typeinfo (A - D), "sparse matrix")
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249 %! D = D * I () + D;
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250 %! assert (typeinfo (A - D), "sparse complex matrix")
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251 %! A = A * I () + A;
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252 %! assert (typeinfo (D - A), "sparse complex matrix")
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253
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254 ## adding sparse and diagonal stays sparse
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255 %!test
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256 %! n = 9;
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257 %! A = sprand (n, n, .5);
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258 %! D = 2 * eye (n);
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259 %! assert (full (A + D), full (A) + D)
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260 %! assert (full (A - D), full (A) - D)
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261 %! D = D * I () + D;
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262 %! assert (full (D + A), D + full (A))
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263 %! A = A * I () + A;
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264 %! A(6, 4) = nan ();
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265 %! assert (full (D - A), D - full (A))