15 October 2012 03:12:58 PM LAGRANGE_INTERP_2D_TEST: C++ version Test the LAGRANGE_INTERP_2D library. The R8LIB library is needed. This test also needs the TEST_INTERP_2D library. LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #1 Using polynomial interpolant of product degree 1 x 1 Number of data points = 4 X, Y, Z data: 0: 0 0 0.766421 1: 1 0 0.107558 2: 0 1 0.270337 3: 1 1 0.0358696 X, Y, Z interpolation: 0: 0 0 0.766421 1: 1 0 0.107558 2: 0 1 0.270337 3: 1 1 0.0358696 RMS data interpolation error = 0 RMS data approximation error = 0.0307159 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #1 Using polynomial interpolant of product degree 2 x 2 Number of data points = 9 X, Y, Z data: 0: 0 0 0.766421 1: 0.5 0 0.434914 2: 1 0 0.107558 3: 0 0.5 0.481806 4: 0.5 0.5 0.325762 5: 1 0.5 0.161026 6: 0 1 0.270337 7: 0.5 1 0.145979 8: 1 1 0.0358696 X, Y, Z interpolation: 0: 0 0 0.766421 1: 0.5 0 0.434914 2: 1 0 0.107558 3: 0 0.5 0.481806 4: 0.5 0.5 0.325762 5: 1 0.5 0.161026 6: 0 1 0.270337 7: 0.5 1 0.145979 8: 1 1 0.0358696 RMS data interpolation error = 0 RMS data approximation error = 0.184386 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #1 Using polynomial interpolant of product degree 3 x 3 Number of data points = 16 X, Y, Z data: 0: 0 0 0.766421 1: 0.25 0 0.818854 2: 0.75 0 0.252062 3: 1 0 0.107558 4: 0 0.25 0.802583 5: 0.25 0.25 1.16528 6: 0.75 0.25 0.589359 7: 1 0.25 0.230218 8: 0 0.75 0.339527 9: 0.25 0.75 0.272413 10: 0.75 0.75 0.11597 11: 1 0.75 0.0503603 12: 0 1 0.270337 13: 0.25 1 0.22224 14: 0.75 1 0.0810474 15: 1 1 0.0358696 X, Y, Z interpolation: 0: 0 0 0.766421 1: 0.25 0 0.818854 2: 0.75 0 0.252062 3: 1 0 0.107558 4: 0 0.25 0.802583 5: 0.25 0.25 1.16528 6: 0.75 0.25 0.589359 7: 1 0.25 0.230218 8: 0 0.75 0.339527 9: 0.25 0.75 0.272413 10: 0.75 0.75 0.11597 11: 1 0.75 0.0503603 12: 0 1 0.270337 13: 0.25 1 0.22224 14: 0.75 1 0.0810474 15: 1 1 0.0358696 RMS data interpolation error = 0 RMS data approximation error = 0.065489 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #1 Using polynomial interpolant of product degree 4 x 4 Number of data points = 25 RMS data interpolation error = 0 RMS data approximation error = 0.0201751 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #1 Using polynomial interpolant of product degree 8 x 8 Number of data points = 81 RMS data interpolation error = 0 RMS data approximation error = 0.00171259 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #2 Using polynomial interpolant of product degree 1 x 1 Number of data points = 4 X, Y, Z data: 0: 0 0 0.111111 1: 1 0 3.38444e-09 2: 0 1 0.222222 3: 1 1 0.111111 X, Y, Z interpolation: 0: 0 0 0.111111 1: 1 0 3.38444e-09 2: 0 1 0.222222 3: 1 1 0.111111 RMS data interpolation error = 0 RMS data approximation error = 1.38778e-17 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #2 Using polynomial interpolant of product degree 2 x 2 Number of data points = 9 X, Y, Z data: 0: 0 0 0.111111 1: 0.5 0 2.7421e-05 2: 1 0 3.38444e-09 3: 0 0.5 0.222195 4: 0.5 0.5 0.111111 5: 1 0.5 2.7421e-05 6: 0 1 0.222222 7: 0.5 1 0.222195 8: 1 1 0.111111 X, Y, Z interpolation: 0: 0 0 0.111111 1: 0.5 0 2.7421e-05 2: 1 0 3.38444e-09 3: 0 0.5 0.222195 4: 0.5 0.5 0.111111 5: 1 0.5 2.7421e-05 6: 0 1 0.222222 7: 0.5 1 0.222195 8: 1 1 0.111111 RMS data interpolation error = 0 RMS data approximation error = 0.00490804 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #2 Using polynomial interpolant of product degree 3 x 3 Number of data points = 16 X, Y, Z data: 0: 0 0 0.111111 1: 0.25 0 0.00244154 2: 0.75 0 3.04657e-07 3: 1 0 3.38444e-09 4: 0 0.25 0.219781 5: 0.25 0.25 0.111111 6: 0.75 0.25 2.7421e-05 7: 1 0.25 3.04657e-07 8: 0 0.75 0.222222 9: 0.25 0.75 0.222195 10: 0.75 0.75 0.111111 11: 1 0.75 0.00244154 12: 0 1 0.222222 13: 0.25 1 0.222222 14: 0.75 1 0.219781 15: 1 1 0.111111 X, Y, Z interpolation: 0: 0 0 0.111111 1: 0.25 0 0.00244154 2: 0.75 0 3.04657e-07 3: 1 0 3.38444e-09 4: 0 0.25 0.219781 5: 0.25 0.25 0.111111 6: 0.75 0.25 2.7421e-05 7: 1 0.25 3.04657e-07 8: 0 0.75 0.222222 9: 0.25 0.75 0.222195 10: 0.75 0.75 0.111111 11: 1 0.75 0.00244154 12: 0 1 0.222222 13: 0.25 1 0.222222 14: 0.75 1 0.219781 15: 1 1 0.111111 RMS data interpolation error = 0 RMS data approximation error = 0.00143279 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #2 Using polynomial interpolant of product degree 4 x 4 Number of data points = 25 RMS data interpolation error = 0 RMS data approximation error = 0.000930276 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #2 Using polynomial interpolant of product degree 8 x 8 Number of data points = 81 RMS data interpolation error = 0 RMS data approximation error = 0.000109215 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #3 Using polynomial interpolant of product degree 1 x 1 Number of data points = 4 X, Y, Z data: 0: 0 0 0.1875 1: 1 0 0.075 2: 0 1 0.157058 3: 1 1 0.0628231 X, Y, Z interpolation: 0: 0 0 0.1875 1: 1 0 0.075 2: 0 1 0.157058 3: 1 1 0.0628231 RMS data interpolation error = 0 RMS data approximation error = 0.0744715 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #3 Using polynomial interpolant of product degree 2 x 2 Number of data points = 9 X, Y, Z data: 0: 0 0 0.1875 1: 0.5 0 0.3 2: 1 0 0.075 3: 0 0.5 0.0288273 4: 0.5 0.5 0.0461237 5: 1 0.5 0.0115309 6: 0 1 0.157058 7: 0.5 1 0.251292 8: 1 1 0.0628231 X, Y, Z interpolation: 0: 0 0 0.1875 1: 0.5 0 0.3 2: 1 0 0.075 3: 0 0.5 0.0288273 4: 0.5 0.5 0.0461237 5: 1 0.5 0.0115309 6: 0 1 0.157058 7: 0.5 1 0.251292 8: 1 1 0.0628231 RMS data interpolation error = 0 RMS data approximation error = 0.031092 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #3 Using polynomial interpolant of product degree 3 x 3 Number of data points = 16 X, Y, Z data: 0: 0 0 0.1875 1: 0.25 0 0.352941 2: 0.75 0 0.146341 3: 1 0 0.075 4: 0 0.25 0.122417 5: 0.25 0.25 0.230432 6: 0.75 0.25 0.0955452 7: 1 0.25 0.0489669 8: 0 0.75 0.0529165 9: 0.25 0.75 0.0996075 10: 0.75 0.75 0.0413007 11: 1 0.75 0.0211666 12: 0 1 0.157058 13: 0.25 1 0.295638 14: 0.75 1 0.122582 15: 1 1 0.0628231 X, Y, Z interpolation: 0: 0 0 0.1875 1: 0.25 0 0.352941 2: 0.75 0 0.146341 3: 1 0 0.075 4: 0 0.25 0.122417 5: 0.25 0.25 0.230432 6: 0.75 0.25 0.0955452 7: 1 0.25 0.0489669 8: 0 0.75 0.0529165 9: 0.25 0.75 0.0996075 10: 0.75 0.75 0.0413007 11: 1 0.75 0.0211666 12: 0 1 0.157058 13: 0.25 1 0.295638 14: 0.75 1 0.122582 15: 1 1 0.0628231 RMS data interpolation error = 0 RMS data approximation error = 0.00994526 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #3 Using polynomial interpolant of product degree 4 x 4 Number of data points = 25 RMS data interpolation error = 0 RMS data approximation error = 0.00418505 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #3 Using polynomial interpolant of product degree 8 x 8 Number of data points = 81 RMS data interpolation error = 0 RMS data approximation error = 0.000105732 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #4 Using polynomial interpolant of product degree 1 x 1 Number of data points = 4 X, Y, Z data: 0: 0 0 0.0265198 1: 1 0 0.0265198 2: 0 1 0.0265198 3: 1 1 0.0265198 X, Y, Z interpolation: 0: 0 0 0.0265198 1: 1 0 0.0265198 2: 0 1 0.0265198 3: 1 1 0.0265198 RMS data interpolation error = 0 RMS data approximation error = 0.306813 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #4 Using polynomial interpolant of product degree 2 x 2 Number of data points = 9 X, Y, Z data: 0: 0 0 0.0265198 1: 0.5 0 0.094021 2: 1 0 0.0265198 3: 0 0.5 0.094021 4: 0.5 0.5 0.333333 5: 1 0.5 0.094021 6: 0 1 0.0265198 7: 0.5 1 0.094021 8: 1 1 0.0265198 X, Y, Z interpolation: 0: 0 0 0.0265198 1: 0.5 0 0.094021 2: 1 0 0.0265198 3: 0 0.5 0.094021 4: 0.5 0.5 0.333333 5: 1 0.5 0.094021 6: 0 1 0.0265198 7: 0.5 1 0.094021 8: 1 1 0.0265198 RMS data interpolation error = 0 RMS data approximation error = 0.0236917 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #4 Using polynomial interpolant of product degree 3 x 3 Number of data points = 16 X, Y, Z data: 0: 0 0 0.0265198 1: 0.25 0 0.068519 2: 0.75 0 0.068519 3: 1 0 0.0265198 4: 0 0.25 0.068519 5: 0.25 0.25 0.177032 6: 0.75 0.25 0.177032 7: 1 0.25 0.068519 8: 0 0.75 0.068519 9: 0.25 0.75 0.177032 10: 0.75 0.75 0.177032 11: 1 0.75 0.068519 12: 0 1 0.0265198 13: 0.25 1 0.068519 14: 0.75 1 0.068519 15: 1 1 0.0265198 X, Y, Z interpolation: 0: 0 0 0.0265198 1: 0.25 0 0.068519 2: 0.75 0 0.068519 3: 1 0 0.0265198 4: 0 0.25 0.068519 5: 0.25 0.25 0.177032 6: 0.75 0.25 0.177032 7: 1 0.25 0.068519 8: 0 0.75 0.068519 9: 0.25 0.75 0.177032 10: 0.75 0.75 0.177032 11: 1 0.75 0.068519 12: 0 1 0.0265198 13: 0.25 1 0.068519 14: 0.75 1 0.068519 15: 1 1 0.0265198 RMS data interpolation error = 0 RMS data approximation error = 0.00945138 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #4 Using polynomial interpolant of product degree 4 x 4 Number of data points = 25 RMS data interpolation error = 0 RMS data approximation error = 0.000685056 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #4 Using polynomial interpolant of product degree 8 x 8 Number of data points = 81 RMS data interpolation error = 0 RMS data approximation error = 1.53585e-06 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #5 Using polynomial interpolant of product degree 1 x 1 Number of data points = 4 X, Y, Z data: 0: 0 0 1.33551e-05 1: 1 0 1.33551e-05 2: 0 1 1.33551e-05 3: 1 1 1.33551e-05 X, Y, Z interpolation: 0: 0 0 1.33551e-05 1: 1 0 1.33551e-05 2: 0 1 1.33551e-05 3: 1 1 1.33551e-05 RMS data interpolation error = 0 RMS data approximation error = 0.33332 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #5 Using polynomial interpolant of product degree 2 x 2 Number of data points = 9 X, Y, Z data: 0: 0 0 1.33551e-05 1: 0.5 0 0.00210991 2: 1 0 1.33551e-05 3: 0 0.5 0.00210991 4: 0.5 0.5 0.333333 5: 1 0.5 0.00210991 6: 0 1 1.33551e-05 7: 0.5 1 0.00210991 8: 1 1 1.33551e-05 X, Y, Z interpolation: 0: 0 0 1.33551e-05 1: 0.5 0 0.00210991 2: 1 0 1.33551e-05 3: 0 0.5 0.00210991 4: 0.5 0.5 0.333333 5: 1 0.5 0.00210991 6: 0 1 1.33551e-05 7: 0.5 1 0.00210991 8: 1 1 1.33551e-05 RMS data interpolation error = 0 RMS data approximation error = 0.0808861 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #5 Using polynomial interpolant of product degree 3 x 3 Number of data points = 16 X, Y, Z data: 0: 0 0 1.33551e-05 1: 0.25 0 0.000595126 2: 0.75 0 0.000595126 3: 1 0 1.33551e-05 4: 0 0.25 0.000595126 5: 0.25 0.25 0.0265198 6: 0.75 0.25 0.0265198 7: 1 0.25 0.000595126 8: 0 0.75 0.000595126 9: 0.25 0.75 0.0265198 10: 0.75 0.75 0.0265198 11: 1 0.75 0.000595126 12: 0 1 1.33551e-05 13: 0.25 1 0.000595126 14: 0.75 1 0.000595126 15: 1 1 1.33551e-05 X, Y, Z interpolation: 0: 0 0 1.33551e-05 1: 0.25 0 0.000595126 2: 0.75 0 0.000595126 3: 1 0 1.33551e-05 4: 0 0.25 0.000595126 5: 0.25 0.25 0.0265198 6: 0.75 0.25 0.0265198 7: 1 0.25 0.000595126 8: 0 0.75 0.000595126 9: 0.25 0.75 0.0265198 10: 0.75 0.75 0.0265198 11: 1 0.75 0.000595126 12: 0 1 1.33551e-05 13: 0.25 1 0.000595126 14: 0.75 1 0.000595126 15: 1 1 1.33551e-05 RMS data interpolation error = 0 RMS data approximation error = 0.0319109 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #5 Using polynomial interpolant of product degree 4 x 4 Number of data points = 25 RMS data interpolation error = 0 RMS data approximation error = 0.00871518 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #5 Using polynomial interpolant of product degree 8 x 8 Number of data points = 81 RMS data interpolation error = 0 RMS data approximation error = 0.000210653 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #6 Using polynomial interpolant of product degree 1 x 1 Number of data points = 4 X, Y, Z data: 0: 0 0 0.0386311 1: 1 0 0.0386311 2: 0 1 0.0386311 3: 1 1 0.0386311 X, Y, Z interpolation: 0: 0 0 0.0386311 1: 1 0 0.0386311 2: 0 1 0.0386311 3: 1 1 0.0386311 RMS data interpolation error = 0 RMS data approximation error = 0.350258 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #6 Using polynomial interpolant of product degree 2 x 2 Number of data points = 9 X, Y, Z data: 0: 0 0 0.0386311 1: 0.5 0 0.234931 2: 1 0 0.0386311 3: 0 0.5 0.234931 4: 0.5 0.5 0.388889 5: 1 0.5 0.234931 6: 0 1 0.0386311 7: 0.5 1 0.234931 8: 1 1 0.0386311 X, Y, Z interpolation: 0: 0 0 0.0386311 1: 0.5 0 0.234931 2: 1 0 0.0386311 3: 0 0.5 0.234931 4: 0.5 0.5 0.388889 5: 1 0.5 0.234931 6: 0 1 0.0386311 7: 0.5 1 0.234931 8: 1 1 0.0386311 RMS data interpolation error = 0 RMS data approximation error = 0.00314374 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #6 Using polynomial interpolant of product degree 3 x 3 Number of data points = 16 X, Y, Z data: 0: 0 0 0.0386311 1: 0.25 0 0.191103 2: 0.75 0 0.191103 3: 1 0 0.0386311 4: 0 0.25 0.191103 5: 0.25 0.25 0.315551 6: 0.75 0.25 0.315551 7: 1 0.25 0.191103 8: 0 0.75 0.191103 9: 0.25 0.75 0.315551 10: 0.75 0.75 0.315551 11: 1 0.75 0.191103 12: 0 1 0.0386311 13: 0.25 1 0.191103 14: 0.75 1 0.191103 15: 1 1 0.0386311 X, Y, Z interpolation: 0: 0 0 0.0386311 1: 0.25 0 0.191103 2: 0.75 0 0.191103 3: 1 0 0.0386311 4: 0 0.25 0.191103 5: 0.25 0.25 0.315551 6: 0.75 0.25 0.315551 7: 1 0.25 0.191103 8: 0 0.75 0.191103 9: 0.25 0.75 0.315551 10: 0.75 0.75 0.315551 11: 1 0.75 0.191103 12: 0 1 0.0386311 13: 0.25 1 0.191103 14: 0.75 1 0.191103 15: 1 1 0.0386311 RMS data interpolation error = 0 RMS data approximation error = 0.00173866 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #6 Using polynomial interpolant of product degree 4 x 4 Number of data points = 25 RMS data interpolation error = 0 RMS data approximation error = 8.36377e-05 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #6 Using polynomial interpolant of product degree 8 x 8 Number of data points = 81 RMS data interpolation error = 0 RMS data approximation error = 3.56374e-07 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #7 Using polynomial interpolant of product degree 1 x 1 Number of data points = 4 X, Y, Z data: 0: 0 0 0 1: 1 0 0 2: 0 1 -1.08804 3: 1 1 0.368924 X, Y, Z interpolation: 0: 0 0 0 1: 1 0 0 2: 0 1 -1.08804 3: 1 1 0.368924 RMS data interpolation error = 0 RMS data approximation error = 0.234231 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #7 Using polynomial interpolant of product degree 2 x 2 Number of data points = 9 X, Y, Z data: 0: 0 0 0 1: 0.5 0 0 2: 1 0 0 3: 0 0.5 -1.91785 4: 0.5 0.5 0.054451 5: 1 0.5 0.650288 6: 0 1 -1.08804 7: 0.5 1 -1.26756 8: 1 1 0.368924 X, Y, Z interpolation: 0: 0 0 0 1: 0.5 0 0 2: 1 0 0 3: 0 0.5 -1.91785 4: 0.5 0.5 0.054451 5: 1 0.5 0.650288 6: 0 1 -1.08804 7: 0.5 1 -1.26756 8: 1 1 0.368924 RMS data interpolation error = 0 RMS data approximation error = 0.26276 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #7 Using polynomial interpolant of product degree 3 x 3 Number of data points = 16 X, Y, Z data: 0: 0 0 0 1: 0.25 0 0 2: 0.75 0 0 3: 1 0 0 4: 0 0.25 1.19694 5: 0.25 0.25 -0.373827 6: 0.75 0.25 1.36899 7: 1 0.25 -0.40585 8: 0 0.75 1.876 9: 0.25 0.75 -0.54886 10: 0.75 0.75 0.0386056 11: 1 0.75 -0.636098 12: 0 1 -1.08804 13: 0.25 1 1.47015 14: 0.75 1 0.560846 15: 1 1 0.368924 X, Y, Z interpolation: 0: 0 0 0 1: 0.25 0 0 2: 0.75 0 0 3: 1 0 0 4: 0 0.25 1.19694 5: 0.25 0.25 -0.373827 6: 0.75 0.25 1.36899 7: 1 0.25 -0.40585 8: 0 0.75 1.876 9: 0.25 0.75 -0.54886 10: 0.75 0.75 0.0386056 11: 1 0.75 -0.636098 12: 0 1 -1.08804 13: 0.25 1 1.47015 14: 0.75 1 0.560846 15: 1 1 0.368924 RMS data interpolation error = 0 RMS data approximation error = 0.22209 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #7 Using polynomial interpolant of product degree 4 x 4 Number of data points = 25 RMS data interpolation error = 0 RMS data approximation error = 0.15835 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #7 Using polynomial interpolant of product degree 8 x 8 Number of data points = 81 RMS data interpolation error = 0 RMS data approximation error = 0.00256233 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #8 Using polynomial interpolant of product degree 1 x 1 Number of data points = 4 X, Y, Z data: 0: 0 0 6.52165e-06 1: 1 0 6.52165e-06 2: 0 1 6.52165e-06 3: 1 1 6.52165e-06 X, Y, Z interpolation: 0: 0 0 6.52165e-06 1: 1 0 6.52165e-06 2: 0 1 6.52165e-06 3: 1 1 6.52165e-06 RMS data interpolation error = 0 RMS data approximation error = 2.49999 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #8 Using polynomial interpolant of product degree 2 x 2 Number of data points = 9 X, Y, Z data: 0: 0 0 6.52165e-06 1: 0.5 0 1.00001 2: 1 0 6.52165e-06 3: 0 0.5 0.750007 4: 0.5 0.5 2.5 5: 1 0.5 0.750007 6: 0 1 6.52165e-06 7: 0.5 1 1.00001 8: 1 1 6.52165e-06 X, Y, Z interpolation: 0: 0 0 6.52165e-06 1: 0.5 0 1.00001 2: 1 0 6.52165e-06 3: 0 0.5 0.750007 4: 0.5 0.5 2.5 5: 1 0.5 0.750007 6: 0 1 6.52165e-06 7: 0.5 1 1.00001 8: 1 1 6.52165e-06 RMS data interpolation error = 0 RMS data approximation error = 0.82802 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #8 Using polynomial interpolant of product degree 3 x 3 Number of data points = 16 X, Y, Z data: 0: 0 0 6.52165e-06 1: 0.25 0 0.0439399 2: 0.75 0 0.0439399 3: 1 0 6.52165e-06 4: 0 0.25 0.0329565 5: 0.25 0.25 0.0783375 6: 0.75 0.25 0.0783375 7: 1 0.25 0.0329565 8: 0 0.75 0.0329565 9: 0.25 0.75 0.0783375 10: 0.75 0.75 0.0783375 11: 1 0.75 0.0329565 12: 0 1 6.52165e-06 13: 0.25 1 0.0439399 14: 0.75 1 0.0439399 15: 1 1 6.52165e-06 X, Y, Z interpolation: 0: 0 0 6.52165e-06 1: 0.25 0 0.0439399 2: 0.75 0 0.0439399 3: 1 0 6.52165e-06 4: 0 0.25 0.0329565 5: 0.25 0.25 0.0783375 6: 0.75 0.25 0.0783375 7: 1 0.25 0.0329565 8: 0 0.75 0.0329565 9: 0.25 0.75 0.0783375 10: 0.75 0.75 0.0783375 11: 1 0.75 0.0329565 12: 0 1 6.52165e-06 13: 0.25 1 0.0439399 14: 0.75 1 0.0439399 15: 1 1 6.52165e-06 RMS data interpolation error = 0 RMS data approximation error = 0.321494 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #8 Using polynomial interpolant of product degree 4 x 4 Number of data points = 25 RMS data interpolation error = 0 RMS data approximation error = 0.142802 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #8 Using polynomial interpolant of product degree 8 x 8 Number of data points = 81 RMS data interpolation error = 0 RMS data approximation error = 0.0123551 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #9 Using polynomial interpolant of product degree 1 x 1 Number of data points = 4 X, Y, Z data: 0: 0 0 0.0996532 1: 1 0 -0.189352 2: 0 1 -0.189352 3: 1 1 0.359788 X, Y, Z interpolation: 0: 0 0 0.0996532 1: 1 0 -0.189352 2: 0 1 -0.189352 3: 1 1 0.359788 RMS data interpolation error = 0 RMS data approximation error = 0.0201845 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #9 Using polynomial interpolant of product degree 2 x 2 Number of data points = 9 X, Y, Z data: 0: 0 0 0.0996532 1: 0.5 0 0 2: 1 0 -0.189352 3: 0 0.5 0 4: 0.5 0.5 0 5: 1 0.5 -0 6: 0 1 -0.189352 7: 0.5 1 -0 8: 1 1 0.359788 X, Y, Z interpolation: 0: 0 0 0.0996532 1: 0.5 0 0 2: 1 0 -0.189352 3: 0 0.5 0 4: 0.5 0.5 0 5: 1 0.5 0 6: 0 1 -0.189352 7: 0.5 1 0 8: 1 1 0.359788 RMS data interpolation error = 0 RMS data approximation error = 15.391 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #9 Using polynomial interpolant of product degree 3 x 3 Number of data points = 16 X, Y, Z data: 0: 0 0 0.0996532 1: 0.25 0 1.32058 2: 0.75 0 -2.09804 3: 1 0 -0.189352 4: 0 0.25 1.32058 5: 0.25 0.25 17.4999 6: 0.75 0.25 -27.8026 7: 1 0.25 -2.50923 8: 0 0.75 -2.09804 9: 0.25 0.75 -27.8026 10: 0.75 0.75 44.1709 11: 1 0.75 3.9865 12: 0 1 -0.189352 13: 0.25 1 -2.50923 14: 0.75 1 3.9865 15: 1 1 0.359788 X, Y, Z interpolation: 0: 0 0 0.0996532 1: 0.25 0 1.32058 2: 0.75 0 -2.09804 3: 1 0 -0.189352 4: 0 0.25 1.32058 5: 0.25 0.25 17.4999 6: 0.75 0.25 -27.8026 7: 1 0.25 -2.50923 8: 0 0.75 -2.09804 9: 0.25 0.75 -27.8026 10: 0.75 0.75 44.1709 11: 1 0.75 3.9865 12: 0 1 -0.189352 13: 0.25 1 -2.50923 14: 0.75 1 3.9865 15: 1 1 0.359788 RMS data interpolation error = 0 RMS data approximation error = 4.94687 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #9 Using polynomial interpolant of product degree 4 x 4 Number of data points = 25 RMS data interpolation error = 0 RMS data approximation error = 7.09178 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #9 Using polynomial interpolant of product degree 8 x 8 Number of data points = 81 RMS data interpolation error = 0 RMS data approximation error = 0.682591 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #10 Using polynomial interpolant of product degree 1 x 1 Number of data points = 4 X, Y, Z data: 0: 0 0 -0.0830877 1: 1 0 -0.0830877 2: 0 1 -0.0830877 3: 1 1 -0.0830877 X, Y, Z interpolation: 0: 0 0 -0.0830877 1: 1 0 -0.0830877 2: 0 1 -0.0830877 3: 1 1 -0.0830877 RMS data interpolation error = 0 RMS data approximation error = 1.08309 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #10 Using polynomial interpolant of product degree 2 x 2 Number of data points = 9 X, Y, Z data: 0: 0 0 -0.0830877 1: 0.5 0 0.147613 2: 1 0 -0.0830877 3: 0 0.5 0.193855 4: 0.5 0.5 1 5: 1 0.5 0.193855 6: 0 1 -0.0830877 7: 0.5 1 0.147613 8: 1 1 -0.0830877 X, Y, Z interpolation: 0: 0 0 -0.0830877 1: 0.5 0 0.147613 2: 1 0 -0.0830877 3: 0 0.5 0.193855 4: 0.5 0.5 1 5: 1 0.5 0.193855 6: 0 1 -0.0830877 7: 0.5 1 0.147613 8: 1 1 -0.0830877 RMS data interpolation error = 0 RMS data approximation error = 0.339989 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #10 Using polynomial interpolant of product degree 3 x 3 Number of data points = 16 X, Y, Z data: 0: 0 0 -0.0830877 1: 0.25 0 0.0628413 2: 0.75 0 0.0628413 3: 1 0 -0.0830877 4: 0 0.25 0.131554 5: 0.25 0.25 -0.058646 6: 0.75 0.25 -0.058646 7: 1 0.25 0.131554 8: 0 0.75 0.131554 9: 0.25 0.75 -0.058646 10: 0.75 0.75 -0.058646 11: 1 0.75 0.131554 12: 0 1 -0.0830877 13: 0.25 1 0.0628413 14: 0.75 1 0.0628413 15: 1 1 -0.0830877 X, Y, Z interpolation: 0: 0 0 -0.0830877 1: 0.25 0 0.0628413 2: 0.75 0 0.0628413 3: 1 0 -0.0830877 4: 0 0.25 0.131554 5: 0.25 0.25 -0.058646 6: 0.75 0.25 -0.058646 7: 1 0.25 0.131554 8: 0 0.75 0.131554 9: 0.25 0.75 -0.058646 10: 0.75 0.75 -0.058646 11: 1 0.75 0.131554 12: 0 1 -0.0830877 13: 0.25 1 0.0628413 14: 0.75 1 0.0628413 15: 1 1 -0.0830877 RMS data interpolation error = 0 RMS data approximation error = 0.138405 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #10 Using polynomial interpolant of product degree 4 x 4 Number of data points = 25 RMS data interpolation error = 0 RMS data approximation error = 0.110323 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #10 Using polynomial interpolant of product degree 8 x 8 Number of data points = 81 RMS data interpolation error = 0 RMS data approximation error = 0.00999769 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #11 Using polynomial interpolant of product degree 1 x 1 Number of data points = 4 X, Y, Z data: 0: 0 0 0 1: 1 0 1 2: 0 1 0 3: 1 1 2 X, Y, Z interpolation: 0: 0 0 0 1: 1 0 1 2: 0 1 0 3: 1 1 2 RMS data interpolation error = 0 RMS data approximation error = 0 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #11 Using polynomial interpolant of product degree 2 x 2 Number of data points = 9 X, Y, Z data: 0: 0 0 0 1: 0.5 0 0.5 2: 1 0 1 3: 0 0.5 0 4: 0.5 0.5 0.75 5: 1 0.5 1.5 6: 0 1 0 7: 0.5 1 1 8: 1 1 2 X, Y, Z interpolation: 0: 0 0 0 1: 0.5 0 0.5 2: 1 0 1 3: 0 0.5 0 4: 0.5 0.5 0.75 5: 1 0.5 1.5 6: 0 1 0 7: 0.5 1 1 8: 1 1 2 RMS data interpolation error = 0 RMS data approximation error = 0 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #11 Using polynomial interpolant of product degree 3 x 3 Number of data points = 16 X, Y, Z data: 0: 0 0 0 1: 0.25 0 0.25 2: 0.75 0 0.75 3: 1 0 1 4: 0 0.25 0 5: 0.25 0.25 0.3125 6: 0.75 0.25 0.9375 7: 1 0.25 1.25 8: 0 0.75 0 9: 0.25 0.75 0.4375 10: 0.75 0.75 1.3125 11: 1 0.75 1.75 12: 0 1 0 13: 0.25 1 0.5 14: 0.75 1 1.5 15: 1 1 2 X, Y, Z interpolation: 0: 0 0 0 1: 0.25 0 0.25 2: 0.75 0 0.75 3: 1 0 1 4: 0 0.25 0 5: 0.25 0.25 0.3125 6: 0.75 0.25 0.9375 7: 1 0.25 1.25 8: 0 0.75 0 9: 0.25 0.75 0.4375 10: 0.75 0.75 1.3125 11: 1 0.75 1.75 12: 0 1 0 13: 0.25 1 0.5 14: 0.75 1 1.5 15: 1 1 2 RMS data interpolation error = 0 RMS data approximation error = 5.02977e-17 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #11 Using polynomial interpolant of product degree 4 x 4 Number of data points = 25 RMS data interpolation error = 0 RMS data approximation error = 4.31507e-17 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #11 Using polynomial interpolant of product degree 8 x 8 Number of data points = 81 RMS data interpolation error = 0 RMS data approximation error = 4.76462e-17 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #12 Using polynomial interpolant of product degree 1 x 1 Number of data points = 4 X, Y, Z data: 0: 0 0 0 1: 1 0 0 2: 0 1 0.688241 3: 1 1 1.87271 X, Y, Z interpolation: 0: 0 0 0 1: 1 0 0 2: 0 1 0.688241 3: 1 1 1.87271 RMS data interpolation error = 0 RMS data approximation error = 0.179861 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #12 Using polynomial interpolant of product degree 2 x 2 Number of data points = 9 X, Y, Z data: 0: 0 0 0 1: 0.5 0 0 2: 1 0 0 3: 0 0.5 0.748896 4: 0.5 0.5 0.460375 5: 1 0.5 0.666271 6: 0 1 0.688241 7: 0.5 1 1.16513 8: 1 1 1.87271 X, Y, Z interpolation: 0: 0 0 0 1: 0.5 0 0 2: 1 0 0 3: 0 0.5 0.748896 4: 0.5 0.5 0.460375 5: 1 0.5 0.666271 6: 0 1 0.688241 7: 0.5 1 1.16513 8: 1 1 1.87271 RMS data interpolation error = 0 RMS data approximation error = 0.141766 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #12 Using polynomial interpolant of product degree 3 x 3 Number of data points = 16 X, Y, Z data: 0: 0 0 0 1: 0.25 0 0 2: 0.75 0 0 3: 1 0 0 4: 0 0.25 0.721902 5: 0.25 0.25 0.787472 6: 0.75 0.25 0.197944 7: 1 0.25 0.270804 8: 0 0.75 0.44832 9: 0.25 0.75 0.486641 10: 0.75 0.75 0.82212 11: 1 0.75 1.25848 12: 0 1 0.688241 13: 0.25 1 0.854796 14: 0.75 1 1.58342 15: 1 1 1.87271 X, Y, Z interpolation: 0: 0 0 0 1: 0.25 0 0 2: 0.75 0 0 3: 1 0 0 4: 0 0.25 0.721902 5: 0.25 0.25 0.787472 6: 0.75 0.25 0.197944 7: 1 0.25 0.270804 8: 0 0.75 0.44832 9: 0.25 0.75 0.486641 10: 0.75 0.75 0.82212 11: 1 0.75 1.25848 12: 0 1 0.688241 13: 0.25 1 0.854796 14: 0.75 1 1.58342 15: 1 1 1.87271 RMS data interpolation error = 0 RMS data approximation error = 0.0161854 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #12 Using polynomial interpolant of product degree 4 x 4 Number of data points = 25 RMS data interpolation error = 0 RMS data approximation error = 0.00619069 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #12 Using polynomial interpolant of product degree 8 x 8 Number of data points = 81 RMS data interpolation error = 0 RMS data approximation error = 0.00015455 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #13 Using polynomial interpolant of product degree 1 x 1 Number of data points = 4 X, Y, Z data: 0: 0 0 0.0196078 1: 1 0 0.0196078 2: 0 1 0.0196078 3: 1 1 0.0196078 X, Y, Z interpolation: 0: 0 0 0.0196078 1: 1 0 0.0196078 2: 0 1 0.0196078 3: 1 1 0.0196078 RMS data interpolation error = 0 RMS data approximation error = 0.980392 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #13 Using polynomial interpolant of product degree 2 x 2 Number of data points = 9 X, Y, Z data: 0: 0 0 0.0196078 1: 0.5 0 0.0384615 2: 1 0 0.0196078 3: 0 0.5 0.0384615 4: 0.5 0.5 1 5: 1 0.5 0.0384615 6: 0 1 0.0196078 7: 0.5 1 0.0384615 8: 1 1 0.0196078 X, Y, Z interpolation: 0: 0 0 0.0196078 1: 0.5 0 0.0384615 2: 1 0 0.0196078 3: 0 0.5 0.0384615 4: 0.5 0.5 1 5: 1 0.5 0.0384615 6: 0 1 0.0196078 7: 0.5 1 0.0384615 8: 1 1 0.0196078 RMS data interpolation error = 0 RMS data approximation error = 0.252037 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #13 Using polynomial interpolant of product degree 3 x 3 Number of data points = 16 X, Y, Z data: 0: 0 0 0.0196078 1: 0.25 0 0.0310078 2: 0.75 0 0.0310078 3: 1 0 0.0196078 4: 0 0.25 0.0310078 5: 0.25 0.25 0.0740741 6: 0.75 0.25 0.0740741 7: 1 0.25 0.0310078 8: 0 0.75 0.0310078 9: 0.25 0.75 0.0740741 10: 0.75 0.75 0.0740741 11: 1 0.75 0.0310078 12: 0 1 0.0196078 13: 0.25 1 0.0310078 14: 0.75 1 0.0310078 15: 1 1 0.0196078 X, Y, Z interpolation: 0: 0 0 0.0196078 1: 0.25 0 0.0310078 2: 0.75 0 0.0310078 3: 1 0 0.0196078 4: 0 0.25 0.0310078 5: 0.25 0.25 0.0740741 6: 0.75 0.25 0.0740741 7: 1 0.25 0.0310078 8: 0 0.75 0.0310078 9: 0.25 0.75 0.0740741 10: 0.75 0.75 0.0740741 11: 1 0.75 0.0310078 12: 0 1 0.0196078 13: 0.25 1 0.0310078 14: 0.75 1 0.0310078 15: 1 1 0.0196078 RMS data interpolation error = 0 RMS data approximation error = 0.0993214 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #13 Using polynomial interpolant of product degree 4 x 4 Number of data points = 25 RMS data interpolation error = 0 RMS data approximation error = 0.0437172 LAGRANGE_INTERP_2D_TEST01: Interpolate data from TEST_INTERP_2D problem #13 Using polynomial interpolant of product degree 8 x 8 Number of data points = 81 RMS data interpolation error = 0 RMS data approximation error = 0.00690114 LAGRANGE_INTERP_2D_TEST: Normal end of execution. 15 October 2012 03:12:58 PM