1 | % Test code for the fast quaternion Fourier transform. |
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2 | % This code tests the following functions: |
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3 | % |
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4 | % qfft qfft2 |
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5 | % iqfft iqfft2 |
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6 | |
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7 | % Copyright © 2005 Stephen J. Sangwine and Nicolas Le Bihan. |
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8 | % See the file : Copyright.m for further details. |
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9 | |
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10 | % We have to test all of the above functions separately, since they do not |
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11 | % call each other, as is the case with the corresponding dqft functions. In |
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12 | % addition, we need to verify the results of the FFTs against the DFT code |
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13 | % in the corresponding qdft functions, e.g. for qfft2, this is qdft2. For |
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14 | % each transform we need to verify that it inverts correctly for all four |
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15 | % combinations of real/complex data and real/complex axis, and for left and |
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16 | % right exponentials, and we need to verify each against the corresponding |
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17 | % DFT code. |
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18 | |
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19 | % Define one real and one complex quaternion array. |
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20 | |
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21 | q = quaternion(randn(10,10), randn(10,10), randn(10,10), randn(10,10)); |
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22 | b = quaternion(complex(randn(10,10)),complex(randn(10,10)),... |
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23 | complex(randn(10,10)),complex(randn(10,10))); |
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24 | T = 1e-12; |
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25 | |
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26 | RA = unit(quaternion(1,1,1)); % Real axis. |
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27 | CA = complex(quaternion(1,1,1), quaternion(0,1,-1)); % Complex axis. |
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28 | |
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29 | if isreal(CA) error('Complex axis is not complex.'); end |
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30 | if ~isreal(RA) error('Real axis is complex.'); end |
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31 | |
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32 | % 1D FFT code against its own inverse .... |
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33 | |
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34 | % Test 1. Verify correct transform and inverse for a real quaternion |
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35 | % array with a real quaternion axis. |
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36 | |
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37 | compare(q, iqfft(qfft(q, RA, 'L'), RA, 'L'), T, 'qfft failed test 1L.'); |
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38 | compare(q, iqfft(qfft(q, RA, 'R'), RA, 'R'), T, 'qfft failed test 1R.'); |
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39 | |
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40 | % Test 2. Verify correct transform and inverse for a real quaternion |
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41 | % array with a complex axis. |
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42 | |
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43 | compare(q, iqfft(qfft(q, CA, 'L'), CA, 'L'), T, 'qfft failed test 2L.'); |
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44 | compare(q, iqfft(qfft(q, CA, 'R'), CA, 'R'), T, 'qfft failed test 2R.'); |
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45 | |
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46 | % Test 3. Verify correct transform and inverse for a complex quaternion |
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47 | % array with a complex axis. |
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48 | |
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49 | compare(b, iqfft(qfft(b, CA, 'L'), CA, 'L'), T, 'qfft failed test 3L.'); |
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50 | compare(b, iqfft(qfft(b, CA, 'R'), CA, 'R'), T, 'qfft failed test 3R.'); |
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51 | |
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52 | % Test 4. Verify correct transform and inverse for a complex quaternion |
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53 | % array with a real axis. |
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54 | |
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55 | compare(b, iqfft(qfft(b, RA, 'L'), RA, 'L'), T, 'qfft failed test 4L.'); |
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56 | compare(b, iqfft(qfft(b, RA, 'R'), RA, 'R'), T, 'qfft failed test 4R.'); |
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57 | |
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58 | % 2D FFT code against its own inverse .... |
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59 | |
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60 | % Test 1. Verify correct transform and inverse for a real quaternion |
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61 | % array with a real quaternion axis. |
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62 | |
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63 | compare(q, iqfft2(qfft2(q, RA, 'L'), RA, 'L'), T, 'qfft2 failed test 1L.'); |
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64 | compare(q, iqfft2(qfft2(q, RA, 'R'), RA, 'R'), T, 'qfft2 failed test 1R.'); |
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65 | |
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66 | % Test 2. Verify correct transform and inverse for a real quaternion |
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67 | % array with a complex axis. |
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68 | |
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69 | compare(q, iqfft2(qfft2(q, CA, 'L'), CA, 'L'), T, 'qfft2 failed test 2L.'); |
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70 | compare(q, iqfft2(qfft2(q, CA, 'R'), CA, 'R'), T, 'qfft2 failed test 2R.'); |
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71 | |
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72 | % Test 3. Verify correct transform and inverse for a complex quaternion |
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73 | % array with a complex axis. |
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74 | |
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75 | compare(b, iqfft2(qfft2(b, CA, 'L'), CA, 'L'), T, 'qfft2 failed test 3L.'); |
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76 | compare(b, iqfft2(qfft2(b, CA, 'R'), CA, 'R'), T, 'qfft2 failed test 3R.'); |
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77 | |
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78 | % Test 4. Verify correct transform and inverse for a complex quaternion |
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79 | % array with a real axis. |
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80 | |
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81 | compare(b, iqfft2(qfft2(b, RA, 'L'), RA, 'L'), T, 'qfft2 failed test 4L.'); |
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82 | compare(b, iqfft2(qfft2(b, RA, 'R'), RA, 'R'), T, 'qfft2 failed test 4R.'); |
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83 | |
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84 | % 1D FFT code against DFT inverse .... |
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85 | |
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86 | % Test 5. Verify correct transform and inverse for a real quaternion |
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87 | % array with a real quaternion axis. |
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88 | |
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89 | compare(q, iqdft(qfft(q, RA, 'L'), RA, 'L'), T, 'qfft failed test 5L.'); |
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90 | compare(q, iqdft(qfft(q, RA, 'R'), RA, 'R'), T, 'qfft failed test 5R.'); |
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91 | |
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92 | % Test 6. Verify correct transform and inverse for a real quaternion |
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93 | % array with a complex axis. |
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94 | |
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95 | compare(q, iqdft(qfft(q, CA, 'L'), CA, 'L'), T, 'qfft failed test 6L.'); |
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96 | compare(q, iqdft(qfft(q, CA, 'R'), CA, 'R'), T, 'qfft failed test 6R.'); |
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97 | |
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98 | % Test 7. Verify correct transform and inverse for a complex quaternion |
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99 | % array with a complex axis. |
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100 | |
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101 | compare(b, iqdft(qfft(b, CA, 'L'), CA, 'L'), T, 'qfft failed test 7L.'); |
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102 | compare(b, iqdft(qfft(b, CA, 'R'), CA, 'R'), T, 'qfft failed test 7R.'); |
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103 | |
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104 | % Test 9. Verify correct transform and inverse for a complex quaternion |
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105 | % array with a real axis. |
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106 | |
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107 | compare(b, iqdft(qfft(b, RA, 'L'), RA, 'L'), T, 'qfft failed test 8L.'); |
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108 | compare(b, iqdft(qfft(b, RA, 'R'), RA, 'R'), T, 'qfft failed test 8R.'); |
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109 | |
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110 | % 2D FFT code against DFT inverse .... |
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111 | |
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112 | % Test 5. Verify correct transform and inverse for a real quaternion |
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113 | % array with a real quaternion axis. |
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114 | |
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115 | compare(q, iqdft2(qfft2(q, RA, 'L'), RA, 'L'), T, 'qfft2 failed test 5L.'); |
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116 | compare(q, iqdft2(qfft2(q, RA, 'R'), RA, 'R'), T, 'qfft2 failed test 5R.'); |
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117 | |
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118 | % Test 6. Verify correct transform and inverse for a real quaternion |
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119 | % array with a complex axis. |
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120 | |
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121 | compare(q, iqdft2(qfft2(q, CA, 'L'), CA, 'L'), T, 'qfft2 failed test 6L.'); |
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122 | compare(q, iqdft2(qfft2(q, CA, 'R'), CA, 'R'), T, 'qfft2 failed test 6R.'); |
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123 | |
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124 | % Test 7. Verify correct transform and inverse for a complex quaternion |
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125 | % array with a complex axis. |
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126 | |
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127 | compare(b, iqdft2(qfft2(b, CA, 'L'), CA, 'L'), T, 'qfft2 failed test 7L.'); |
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128 | compare(b, iqdft2(qfft2(b, CA, 'R'), CA, 'R'), T, 'qfft2 failed test 7R.'); |
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129 | |
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130 | % Test 8. Verify correct transform and inverse for a complex quaternion |
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131 | % array with a real axis. |
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132 | |
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133 | compare(b, iqdft2(qfft2(b, RA, 'L'), RA, 'L'), T, 'qfft2 failed test 8L.'); |
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134 | compare(b, iqdft2(qfft2(b, RA, 'R'), RA, 'R'), T, 'qfft2 failed test 8R.'); |
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135 | |
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136 | clear q b T RA CA |
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