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sine_transform_prb_output.txt
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19 February 2012 08:07:54 PM
SINE_TRANSFORM_TEST
C++ version.
Test the SINE_TRANSFORM library.
SINE_TRANSFORM_TEST01:
SINE_TRANSFORM_DATA does a sine transform of data
defined by a vector.
Demonstrate that the transform is its own inverse.
Let R be a random N vector.
Let S be the transform of D.
Let T be the transform of E.
Then R and T will be equal.
I R(I) S(I) T(I)
0 0.218418 1.15667 0.218418
1 0.956318 0.701776 0.956318
2 0.829509 0.628231 0.829509
3 0.561695 -0.162421 0.561695
4 0.415307 0.0817916 0.415307
5 0.0661187 -0.381461 0.0661187
6 0.257578 0.130254 0.257578
7 0.109957 -0.452064 0.109957
8 0.043829 -0.00109167 0.043829
9 0.633966 0.00102277 0.633966
SINE_TRANSFORM_TEST02:
SINE_TRANSFORM_FUNCTION does a sine transform of data
defined by a function F(X) evaluated at equally spaced
points in an interval [A,B].
Demonstrate that the transform is its own inverse.
Let X(0:N+1) be N+2 equally spaced points in [A,B].
Let S be the transform of F(X(1:N)).
Let F1 be the linear interpolant of (A,F(A)), (B,F(B)).
Let F2 be the transform of S.
Then F(X(1:N)) = F1(X(1:N)) + F2(1:N).
I X(I) F(X(I)) S F1 F2 F1+F2
0 1 0.9504 0 0.9504 0 0.9504
1 1.2 1.4256 -1.1557 0.85536 0.57024 1.4256
2 1.4 1.7472 4.25108 0.76032 0.98688 1.7472
3 1.6 1.764 -1.58847 0.66528 1.09872 1.764
4 1.8 1.37088 0.687471 0.57024 0.80064 1.37088
5 2 0.5472 -0.359345 0.4752 0.072 0.5472
6 2.2 -0.6048 0.199698 0.38016 -0.98496 -0.6048
7 2.4 -1.8216 -0.117457 0.28512 -2.10672 -1.8216
8 2.6 -2.64 0.0654377 0.19008 -2.83008 -2.64
9 2.8 -2.35872 -0.0298847 0.09504 -2.45376 -2.35872
10 3 0 0 0 0 0
SINE_TRANSFORM_TEST03:
SINE_TRANSFORM_FUNCTION does a sine transform of data
defined by a function F(X) evaluated at N equally spaced
points in an interval [A,B].
SINE_TRANSFORM_INTERPOLANT evaluates the interpolant.
The interpolant will be 0 at the 0th and (N+1)-th points.
It equals the function at points 1 through N.
In between, it can approximate smooth functions,
and the approximation improves with N.
I X(I) F(X(I)) S(I)
0 1.3 1.61568 -134.083
1 1.6 1.764 50.9253
2 1.9 1.0098 -17.4326
3 2.2 -0.6048 7.52496
4 2.5 -2.3184 -3.86908
5 2.8 -2.35872 2.15858
6 3.1 2.349 -1.2589
7 3.4 16.4736 0.704712
8 3.7 46.5696 -0.31985
I X F(X) FHAT(X)
0 1 0.9504 0.9504
1 1.15 1.31483 1.28162
2 1.3 1.61568 1.61568
3 1.45 1.78516 1.82066
4 1.6 1.764 1.764
5 1.75 1.51052 1.47117
6 1.9 1.0098 1.0098
7 2.05 0.282738 0.328656
8 2.2 -0.6048 -0.6048
9 2.35 -1.53288 -1.58983
10 2.5 -2.3184 -2.3184
11 2.65 -2.70595 -2.62979
12 2.8 -2.35872 -2.35872
13 2.95 -0.849389 -0.961698
14 3.1 2.349 2.349
15 3.25 7.87215 8.0621
16 3.4 16.4736 16.4736
17 3.55 29.0339 28.6364
18 3.7 46.5696 46.5696
19 3.85 70.2425 71.4652
20 4 101.369 101.369
SINE_TRANSFORM_TEST04:
SINE_TRANSFORM_FUNCTION does a sine transform of data
defined by a function F(X) evaluated at N equally spaced
points in an interval [A,B].
SINE_TRANSFORM_INTERPOLANT evaluates the interpolant.
The interpolant will be 0 at the 0th and (N+1)-th points.
It equals the function at points 1 through N.
In between, it can approximate smooth functions,
and the approximation improves with N.
Expect exact agreement every 5th sample.
0 0 16 16
1 0.0875 13.5345 12.1185
2 0.175 7.40993 8.14431
3 0.2625 0.718525 4.08778
4 0.35 -3.37481 0.127658
5 0.4375 -3.38709 -3.38709
6 0.525 -0.261986 -6.00473
7 0.6125 3.31412 -7.29108
8 0.7 4.60251 -6.96841
9 0.7875 2.49725 -5.03072
10 0.875 -1.79798 -1.79798
11 0.9625 -5.50363 2.11236
12 1.05 -5.97239 5.89563
13 1.1375 -2.35477 8.72778
14 1.225 3.77527 9.94989
15 1.3125 9.22252 9.22252
16 1.4 10.9479 6.60982
17 1.4875 7.79106 2.57105
18 1.575 1.13422 -2.13952
19 1.6625 -5.87902 -6.64004
20 1.75 -10.1153 -10.1153
21 1.8375 -10.1816 -11.9913
22 1.925 -7.11132 -12.0493
23 2.0125 -3.62422 -10.4554
24 2.1 -2.41286 -7.70271
25 2.1875 -4.48318 -4.48318
26 2.275 -8.53577 -1.52287
27 2.3625 -11.7561 0.57908
28 2.45 -11.5442 1.47206
29 2.5375 -7.15363 1.11104
30 2.625 -0.258664 -0.258664
31 2.7125 5.90462 -2.18004
32 2.8 8.33648 -4.10374
33 2.8875 5.96864 -5.5186
34 2.975 0.268963 -6.06345
35 3.0625 -5.59725 -5.59725
36 3.15 -8.55986 -4.21524
37 3.2375 -7.34674 -2.21145
38 3.325 -3.11101 0.000922866
39 3.4125 1.36686 1.99141
40 3.5 3.41326 3.41326
41 3.5875 2.09478 4.08137
42 3.675 -1.22106 4.01059
43 3.7625 -3.71076 3.40642
44 3.85 -2.843 2.61026
45 3.9375 2.01118 2.01118
46 4.025 9.07165 1.94371
47 4.1125 15.064 2.5953
48 4.2 17.0369 3.94595
49 4.2875 14.0285 5.75635
50 4.375 7.61085 7.61085
51 4.4625 0.994622 9.00863
52 4.55 -2.78267 9.4842
53 4.6375 -2.53121 8.72961
54 4.725 0.523216 6.68794
55 4.8125 3.59227 3.59227
56 4.9 4.07749 -0.0640166
57 4.9875 1.17416 -3.62349
58 5.075 -3.62787 -6.40811
59 5.1625 -7.44431 -7.87739
60 5.25 -7.76263 -7.76263
61 5.3375 -4.02272 -6.14256
62 5.425 1.93559 -3.43872
63 5.5125 6.84124 -0.32848
64 5.6 7.82541 2.40583
65 5.6875 4.0559 4.0559
66 5.775 -2.7801 4.15137
67 5.8625 -9.42686 2.56828
68 5.95 -12.8901 -0.444089
69 6.0375 -12.0812 -4.32348
70 6.125 -8.325 -8.325
71 6.2125 -4.45199 -11.6869
72 6.3 -3.02927 -13.7891
73 6.3875 -4.78675 -14.2657
74 6.475 -8.1757 -13.0461
75 6.5625 -10.3216 -10.3216
76 6.65 -8.80462 -6.45294
77 6.7375 -3.20757 -1.85263
78 6.825 4.49863 3.12251
79 6.9125 10.978 8.23613
80 7 13.3791 13.3791
SINE_TRANSFORM_TEST
Normal end of execution.
19 February 2012 08:07:54 PM