1 | % Test code for the discrete quaternion Fourier transform. |
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2 | % This code tests the following functions: |
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3 | % |
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4 | % qdft qdft2 |
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5 | % iqdft iqdft2 |
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6 | % |
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7 | % It also verifies indirectly many of the basic quaternion operations |
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8 | % since the qdft depends on them. |
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9 | |
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10 | % Copyright © 2005 Stephen J. Sangwine and Nicolas Le Bihan. |
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11 | % See the file : Copyright.m for further details. |
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12 | |
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13 | % Since the two-dimensional qdft code calls the one-dimensional |
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14 | % code, we need only to test the two dimensionsal code in what |
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15 | % follows. |
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16 | |
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17 | % Define one real and one complex quaternion array. |
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18 | |
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19 | q = quaternion(randn(10,10), randn(10,10), randn(10,10), randn(10,10)); |
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20 | b = quaternion(complex(randn(10,10)),complex(randn(10,10)),... |
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21 | complex(randn(10,10)),complex(randn(10,10))); |
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22 | T = 1e-12; |
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23 | |
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24 | RA = unit(quaternion(1,1,1)); % Real axis. |
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25 | CA = complex(RA, quaternion(1,0,-1)); % Complex axis. |
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26 | |
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27 | if isreal(CA) error('Complex axis is not complex.'); end |
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28 | if ~isreal(RA) error('Real axis is complex.'); end |
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29 | |
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30 | % Test 1. Verify correct transform and inverse for a real quaternion |
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31 | % array with a real quaternion axis. |
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32 | |
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33 | compare(q, iqdft2(qdft2(q, RA, 'L'), RA, 'L'), T, 'qdft failed test 1L.'); |
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34 | compare(q, iqdft2(qdft2(q, RA, 'R'), RA, 'R'), T, 'qdft failed test 1R.'); |
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35 | |
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36 | % Test 2. Verify correct transform and inverse for a real quaternion |
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37 | % array with a complex axis. |
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38 | |
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39 | compare(q, iqdft2(qdft2(q, CA, 'L'), CA, 'L'), T, 'qdft failed test 2L.'); |
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40 | compare(q, iqdft2(qdft2(q, CA, 'R'), CA, 'R'), T, 'qdft failed test 2R.'); |
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41 | |
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42 | % Test 3. Verify correct transform and inverse for a complex quaternion |
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43 | % array with a complex axis. |
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44 | |
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45 | compare(b, iqdft2(qdft2(b, CA, 'L'), CA, 'L'), T, 'qdft failed test 3L.'); |
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46 | compare(b, iqdft2(qdft2(b, CA, 'R'), CA, 'R'), T, 'qdft failed test 3R.'); |
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47 | |
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48 | % Test 4. Verify correct transform and inverse for a complex quaternion |
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49 | % array with a real axis. |
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50 | |
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51 | compare(b, iqdft2(qdft2(b, RA, 'L'), RA, 'L'), T, 'qdft failed test 4L.'); |
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52 | compare(b, iqdft2(qdft2(b, RA, 'R'), RA, 'R'), T, 'qdft failed test 4R.'); |
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53 | |
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54 | clear q b T RA CA |
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