Thu Sep 13 17:09:45 2018 SINE_TRANSFORM_TEST Python version: 3.6.5 Test the SINE_TRANSFORM library. R8VEC_LINSPACE2_TEST Python version: 3.6.5 R8VEC_LINSPACE2 returns evenly spaced values between A and B omitting the endpoints. The linspace2 vector: 0: 12 1: 14 2: 16 3: 18 R8VEC_LINSPACE2_TEST Normal end of execution. R8VEC_PRINT_TEST Python version: 3.6.5 R8VEC_PRINT prints an R8VEC. Here is an R8VEC: 0: 123.456 1: 5e-06 2: -1e+06 3: 3.14159 R8VEC_PRINT_TEST: Normal end of execution. R8VEC_UNIFORM_01_TEST Python version: 3.6.5 R8VEC_UNIFORM_01 computes a random R8VEC. Initial seed is 123456789 Random R8VEC: 0: 0.218418 1: 0.956318 2: 0.829509 3: 0.561695 4: 0.415307 5: 0.0661187 6: 0.257578 7: 0.109957 8: 0.043829 9: 0.633966 R8VEC_UNIFORM_01_TEST: Normal end of execution. R8VEC3_PRINT_TEST Python version: 3.6.5 R8VEC3_PRINT prints an R8VEC. X, X^2, X+X^2's: 0: 0 0 0 1: 0.2 0.04 0.24 2: 0.4 0.16 0.56 3: 0.6 0.36 0.96 4: 0.8 0.64 1.44 5: 1 1 2 R8VEC3_PRINT_TEST: Normal end of execution. SINE_TRANSFORM_DATA_TEST Python version: 3.6.5 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 S T 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_DATA_TEST Normal end of execution. SINE_TRANSFORM_FUNCTION_TEST: Python version: 3.6.5 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_FUNCTION_TEST Normal end of execution. SINE_TRANSFORM_INTERPOLANT_TEST: Python version: 3.6.5 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 Created plot file "sine_interpolant.png" SINE_TRANSFORM_INTERPOLANT_TEST Normal end of execution. SINE_TRANSFORM_INTERPOLANT_TEST2: Python version: 3.6.5 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. Created plot file "sine_interpolant2.png" SINE_TRANSFORM_INTERPOLANT2_TEST Normal end of execution. SINE_TRANSFORM_TEST Normal end of execution. Thu Sep 13 17:09:45 2018