29-Jul-2021 15:34:17 sine_transform_test(): MATLAB/Octave version 9.9.0.1467703 (R2020b) Test sine_transform() 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) 1 0.814724 1.630842 0.814724 2 0.905792 0.036942 0.905792 3 0.126987 1.088972 0.126987 4 0.913376 -0.415716 0.913376 5 0.632359 0.674023 0.632359 6 0.097540 0.424403 0.097540 7 0.278498 0.343630 0.278498 8 0.546882 -0.254533 0.546882 9 0.957507 -0.324448 0.957507 10 0.964889 -0.161952 0.964889 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 1.000000 0.950400 0.000000 0.950400 0.000000 0.950400 1 1.200000 1.425600 -1.155704 0.855360 0.570240 1.425600 2 1.400000 1.747200 4.251083 0.760320 0.986880 1.747200 3 1.600000 1.764000 -1.588474 0.665280 1.098720 1.764000 4 1.800000 1.370880 0.687471 0.570240 0.800640 1.370880 5 2.000000 0.547200 -0.359345 0.475200 0.072000 0.547200 6 2.200000 -0.604800 0.199698 0.380160 -0.984960 -0.604800 7 2.400000 -1.821600 -0.117457 0.285120 -2.106720 -1.821600 8 2.600000 -2.640000 0.065438 0.190080 -2.830080 -2.640000 9 2.800000 -2.358720 -0.029885 0.095040 -2.453760 -2.358720 10 3.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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) 1 1.300000 1.615680 -134.082993 2 1.600000 1.764000 50.925281 3 1.900000 1.009800 -17.432578 4 2.200000 -0.604800 7.524957 5 2.500000 -2.318400 -3.869077 6 2.800000 -2.358720 2.158577 7 3.100000 2.349000 -1.258899 8 3.400000 16.473600 0.704712 9 3.700000 46.569600 -0.319850 I X F(X) FHAT(X) 1 1.000000 0.950400 0.950400 2 1.150000 1.314830 1.281618 3 1.300000 1.615680 1.615680 4 1.450000 1.785164 1.820661 5 1.600000 1.764000 1.764000 6 1.750000 1.510523 1.471165 7 1.900000 1.009800 1.009800 8 2.050000 0.282738 0.328656 9 2.200000 -0.604800 -0.604800 10 2.350000 -1.532883 -1.589835 11 2.500000 -2.318400 -2.318400 12 2.650000 -2.705948 -2.629789 13 2.800000 -2.358720 -2.358720 14 2.950000 -0.849389 -0.961698 15 3.100000 2.349000 2.349000 16 3.250000 7.872145 8.062100 17 3.400000 16.473600 16.473600 18 3.550000 29.033885 28.636424 19 3.700000 46.569600 46.569600 20 3.850000 70.242539 71.465247 21 4.000000 101.368800 101.368800 Function and interpolant plot saved as "sine_transform_test03.png" 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. Function and interpolant plot saved as "sine_transform_test04.png" sine_transform_test(): Normal end of execution. 29-Jul-2021 15:34:32