1 | % Test code for the quaternion svd function. |
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2 | |
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3 | % Copyright © 2006 Stephen J. Sangwine and Nicolas Le Bihan. |
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4 | % See the file : Copyright.m for further details. |
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5 | |
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6 | T = 1e-10; |
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7 | |
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8 | % This is quite a long script because of the need to test the |
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9 | % function with square, wide and tall arrays, and with 1, 2 or |
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10 | % 3 output parameters, and with normal and economy decompositions. |
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11 | |
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12 | % Square array. |
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13 | |
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14 | display('svd on real quaternions ...') |
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15 | display('svd on square array ...') |
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16 | |
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17 | A = quaternion(randn(5,5),randn(5,5),randn(5,5),randn(5,5)); |
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18 | |
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19 | % Normal decomposition. |
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20 | |
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21 | [U, B, V] = svd(A); |
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22 | compare(U*B*V', A, T, 'quaternion/svd failed test 1A') |
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23 | |
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24 | [U, B] = svd(A); |
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25 | compare(U*B*V', A, T, 'quaternion/svd failed test 1B') |
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26 | |
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27 | S = svd(A); |
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28 | compare(S, diag(B), T, 'quaternion/svd failed test 1C') |
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29 | |
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30 | % Economy (0) decomposition. |
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31 | |
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32 | [U, B, V] = svd(A,0); |
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33 | compare(U*B*V', A, T, 'quaternion/svd failed test 2A') |
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34 | |
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35 | [U, B] = svd(A,0); |
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36 | compare(U*B*V', A, T, 'quaternion/svd failed test 2B') |
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37 | |
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38 | S = svd(A,0); |
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39 | compare(S, diag(B), T, 'quaternion/svd failed test 2C') |
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40 | |
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41 | % Economy (''econ'') decomposition. |
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42 | |
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43 | [U, B, V] = svd(A,'econ'); |
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44 | compare(U*B*V', A, T, 'quaternion/svd failed test 3A') |
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45 | |
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46 | [U, B] = svd(A,'econ'); |
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47 | compare(U*B*V', A, T, 'quaternion/svd failed test 3B') |
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48 | |
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49 | S = svd(A,'econ'); |
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50 | compare(S, diag(B), T, 'quaternion/svd failed test 3C') |
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51 | |
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52 | % Wide array. |
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53 | |
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54 | display('svd on wide array ...') |
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55 | |
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56 | A = quaternion(randn(5,7),randn(5,7),randn(5,7),randn(5,7)); |
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57 | |
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58 | % Normal decomposition. |
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59 | |
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60 | [U, B, V] = svd(A); |
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61 | compare(U*B*V', A, T, 'quaternion/svd failed test 4A') |
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62 | |
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63 | [U, B] = svd(A); |
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64 | compare(U*B*V', A, T, 'quaternion/svd failed test 4B') |
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65 | |
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66 | S = svd(A); |
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67 | compare(S, diag(B), T, 'quaternion/svd failed test 4C') |
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68 | |
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69 | % Economy (0) decomposition. |
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70 | |
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71 | [U, B, V] = svd(A,0); |
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72 | compare(U*B*V', A, T, 'quaternion/svd failed test 5A') |
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73 | |
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74 | [U, B] = svd(A,0); |
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75 | compare(U*B*V', A, T, 'quaternion/svd failed test 5B') |
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76 | |
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77 | S = svd(A,0); |
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78 | compare(S, diag(B), T, 'quaternion/svd failed test 5C') |
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79 | |
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80 | % Economy (''econ'') decomposition. |
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81 | |
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82 | [U, B, V] = svd(A,'econ'); |
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83 | compare(U*B*V', A, T, 'quaternion/svd failed test 6A') |
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84 | |
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85 | [U, B] = svd(A,'econ'); |
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86 | compare(U*B*V', A, T, 'quaternion/svd failed test 6B') |
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87 | |
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88 | S = svd(A,'econ'); |
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89 | compare(S, diag(B), T, 'quaternion/svd failed test 6C') |
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90 | |
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91 | % Tall array. |
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92 | |
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93 | display('svd on tall array ...') |
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94 | |
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95 | A = A.'; |
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96 | |
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97 | % Normal decomposition. |
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98 | |
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99 | [U, B, V] = svd(A); |
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100 | compare(U*B*V', A, T, 'quaternion/svd failed test 7A') |
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101 | |
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102 | [U, B] = svd(A); |
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103 | compare(U*B*V', A, T, 'quaternion/svd failed test 7B') |
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104 | |
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105 | S = svd(A); |
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106 | compare(S, diag(B), T, 'quaternion/svd failed test 7C') |
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107 | |
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108 | % Economy (0) decomposition. |
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109 | |
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110 | [U, B, V] = svd(A,0); |
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111 | compare(U*B*V', A, T, 'quaternion/svd failed test 8A') |
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112 | |
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113 | [U, B] = svd(A,0); |
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114 | compare(U*B*V', A, T, 'quaternion/svd failed test 8B') |
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115 | |
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116 | S = svd(A,0); |
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117 | compare(S, diag(B), T, 'quaternion/svd failed test 8C') |
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118 | |
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119 | % Economy (''econ'') decomposition. |
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120 | |
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121 | [U, B, V] = svd(A,'econ'); |
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122 | compare(U*B*V', A, T, 'quaternion/svd failed test 9A') |
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123 | |
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124 | [U, B] = svd(A,'econ'); |
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125 | compare(U*B*V', A, T, 'quaternion/svd failed test 9B') |
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126 | |
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127 | S = svd(A,'econ'); |
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128 | compare(S, diag(B), T, 'quaternion/svd failed test 9C') |
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129 | |
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130 | % Now repeat the whole lot with complex data ........ |
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131 | |
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132 | T = 1e-8; % The error margin for complex data is much more |
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133 | % relaxed than for real data, because the results |
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134 | % are not so accurate. |
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135 | |
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136 | % Square array. |
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137 | |
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138 | display('svd on complex quaternions ...') |
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139 | display('svd on square array ...') |
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140 | |
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141 | A = quaternion(complex(randn(5,5),randn(5,5)),... |
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142 | complex(randn(5,5),randn(5,5)),... |
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143 | complex(randn(5,5),randn(5,5)),... |
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144 | complex(randn(5,5),randn(5,5))); |
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145 | |
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146 | % Normal decomposition. |
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147 | |
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148 | [U, B, V] = svd(A); |
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149 | compare(U*B*V', A, T, 'quaternion/svd failed test 10A') |
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150 | |
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151 | [U, B] = svd(A); |
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152 | compare(U*B*V', A, T, 'quaternion/svd failed test 10B') |
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153 | |
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154 | S = svd(A); |
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155 | compare(S, diag(B), T, 'quaternion/svd failed test 10C') |
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156 | |
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157 | % Economy (0) decomposition. |
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158 | |
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159 | [U, B, V] = svd(A,0); |
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160 | compare(U*B*V', A, T, 'quaternion/svd failed test 11A') |
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161 | |
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162 | [U, B] = svd(A,0); |
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163 | compare(U*B*V', A, T, 'quaternion/svd failed test 11B') |
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164 | |
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165 | S = svd(A,0); |
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166 | compare(S, diag(B), T, 'quaternion/svd failed test 11C') |
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167 | |
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168 | % Economy (''econ'') decomposition. |
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169 | |
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170 | [U, B, V] = svd(A,'econ'); |
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171 | compare(U*B*V', A, T, 'quaternion/svd failed test 12A') |
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172 | |
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173 | [U, B] = svd(A,'econ'); |
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174 | compare(U*B*V', A, T, 'quaternion/svd failed test 12B') |
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175 | |
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176 | S = svd(A,'econ'); |
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177 | compare(S, diag(B), T, 'quaternion/svd failed test 12C') |
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178 | |
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179 | % Wide array. |
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180 | |
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181 | display('svd on wide array ...') |
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182 | |
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183 | A = quaternion(complex(randn(5,7),randn(5,7)),... |
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184 | complex(randn(5,7),randn(5,7)),... |
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185 | complex(randn(5,7),randn(5,7)),... |
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186 | complex(randn(5,7),randn(5,7))); |
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187 | |
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188 | % Normal decomposition. |
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189 | |
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190 | [U, B, V] = svd(A); |
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191 | compare(U*B*V', A, T, 'quaternion/svd failed test 13A') |
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192 | |
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193 | [U, B] = svd(A); |
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194 | compare(U*B*V', A, T, 'quaternion/svd failed test 13B') |
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195 | |
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196 | S = svd(A); |
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197 | compare(S, diag(B), T, 'quaternion/svd failed test 13C') |
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198 | |
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199 | % Economy (0) decomposition. |
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200 | |
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201 | [U, B, V] = svd(A,0); |
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202 | compare(U*B*V', A, T, 'quaternion/svd failed test 14A') |
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203 | |
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204 | [U, B] = svd(A,0); |
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205 | compare(U*B*V', A, T, 'quaternion/svd failed test 14B') |
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206 | |
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207 | S = svd(A,0); |
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208 | compare(S, diag(B), T, 'quaternion/svd failed test 14C') |
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209 | |
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210 | % Economy (''econ'') decomposition. |
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211 | |
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212 | [U, B, V] = svd(A,'econ'); |
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213 | compare(U*B*V', A, T, 'quaternion/svd failed test 15A') |
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214 | |
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215 | [U, B] = svd(A,'econ'); |
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216 | compare(U*B*V', A, T, 'quaternion/svd failed test 15B') |
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217 | |
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218 | S = svd(A,'econ'); |
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219 | compare(S, diag(B), T, 'quaternion/svd failed test 15C') |
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220 | |
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221 | % Tall array. |
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222 | |
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223 | display('svd on tall array ...') |
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224 | |
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225 | A = A.'; |
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226 | |
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227 | % Normal decomposition. |
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228 | |
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229 | [U, B, V] = svd(A); |
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230 | compare(U*B*V', A, T, 'quaternion/svd failed test 16A') |
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231 | |
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232 | [U, B] = svd(A); |
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233 | compare(U*B*V', A, T, 'quaternion/svd failed test 16B') |
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234 | |
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235 | S = svd(A); |
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236 | compare(S, diag(B), T, 'quaternion/svd failed test 16C') |
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237 | |
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238 | % Economy (0) decomposition. |
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239 | |
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240 | [U, B, V] = svd(A,0); |
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241 | compare(U*B*V', A, T, 'quaternion/svd failed test 17A') |
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242 | |
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243 | [U, B] = svd(A,0); |
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244 | compare(U*B*V', A, T, 'quaternion/svd failed test 17B') |
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245 | |
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246 | S = svd(A,0); |
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247 | compare(S, diag(B), T, 'quaternion/svd failed test 17C') |
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248 | |
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249 | % Economy (''econ'') decomposition. |
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250 | |
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251 | [U, B, V] = svd(A,'econ'); |
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252 | compare(U*B*V', A, T, 'quaternion/svd failed test 18A') |
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253 | |
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254 | [U, B] = svd(A,'econ'); |
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255 | compare(U*B*V', A, T, 'quaternion/svd failed test 18B') |
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256 | |
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257 | S = svd(A,'econ'); |
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258 | compare(S, diag(B), T, 'quaternion/svd failed test 18C') |
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259 | |
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260 | clear A U B V S |
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