17 September 2021 11:53:53.080 PM TEST_INTERP_TEST FORTRAN90 version Test the TEST_INTERP library. This test also requires the R8LIB library. TEST01 P00_STORY prints the problem "story". Problem 1 This example is due to Hans-Joerg Wenz. It is an example of good data, which is dense enough in areas where the expected curvature of the interpolant is large. Good results can be expected with almost any reasonable interpolation method. Problem 2 This example is due to ETY Lee of Boeing. Data near the corners is more dense than in regions of small curvature. A local interpolation method will produce a more plausible interpolant than a nonlocal interpolation method, such as cubic splines. Problem 3 This example is due to Fred Fritsch and Ralph Carlson. This data can cause problems for interpolation methods. There are sudden changes in direction, and at the same time, sparsely-placed data. This can cause an interpolant to overshoot the data in a way that seems implausible. Problem 4 This example is due to Larry Irvine, Samuel Marin and Philip Smith. This data can cause problems for interpolation methods. There are sudden changes in direction, and at the same time, sparsely-placed data. This can cause an interpolant to overshoot the data in a way that seems implausible. Problem 5 This example is due to Larry Irvine, Samuel Marin and Philip Smith. This data can cause problems for interpolation methods. There are sudden changes in direction, and at the same time, sparsely-placed data. This can cause an interpolant to overshoot the data in a way that seems implausible. Problem 6 The data is due to deBoor and Rice. The data represents a temperature dependent property of titanium. The data has been used extensively as an example in spline approximation with variably-spaced knots. DeBoor considers two sets of knots: (595,675,755,835,915,995,1075) and (595,725,850,910,975,1040,1075). Problem 7 This data is a simple symmetric set of 4 points, for which it is interesting to develop the Shepard interpolants for varying values of the exponent p. Problem 8 This is equally spaced data for y = x^2, except for one extra point whose x value is close to another, but whose y value is not so close. A small disagreement in nearby data can be disaster. TEST02 P00_DATA_NUM returns N, the number of data points. P00_DIM_NUM returns M, the dimension of data. P00_DATA returns the actual (MxN) data. Problem 1 DATA_NUM 18 DIM_NUM 2 Data array: Row 1 2 Col 1: 0.00000 4.00000 2: 1.00000 5.00000 3: 2.00000 6.00000 4: 4.00000 6.00000 5: 5.00000 5.00000 6: 6.00000 3.00000 7: 7.00000 1.00000 8: 8.00000 1.00000 9: 9.00000 1.00000 10: 10.0000 3.00000 11: 11.0000 4.00000 12: 12.0000 4.00000 13: 13.0000 3.00000 14: 14.0000 3.00000 15: 15.0000 4.00000 16: 16.0000 4.00000 17: 17.0000 3.00000 18: 18.0000 0.00000 Problem 2 DATA_NUM 18 DIM_NUM 2 Data array: Row 1 2 Col 1: 0.00000 0.00000 2: 1.34000 5.00000 3: 5.00000 8.66000 4: 10.0000 10.0000 5: 10.6000 10.4000 6: 10.7000 12.0000 7: 10.7050 28.6000 8: 10.8000 30.2000 9: 11.4000 30.6000 10: 19.6000 30.6000 11: 20.2000 30.2000 12: 20.2950 28.6000 13: 20.3000 12.0000 14: 20.4000 10.4000 15: 21.0000 10.0000 16: 26.0000 8.66000 17: 29.6600 5.00000 18: 31.0000 0.00000 Problem 3 DATA_NUM 11 DIM_NUM 2 Data array: Row 1 2 Col 1: 0.00000 0.00000 2: 2.00000 10.0000 3: 3.00000 10.0000 4: 5.00000 10.0000 5: 6.00000 10.0000 6: 8.00000 10.0000 7: 9.00000 10.5000 8: 11.0000 15.0000 9: 12.0000 50.0000 10: 14.0000 60.0000 11: 15.0000 85.0000 Problem 4 DATA_NUM 8 DIM_NUM 2 Data array: Row 1 2 Col 1: 0.00000 0.00000 2: 0.500000E-01 0.700000 3: 0.100000 1.00000 4: 0.200000 1.00000 5: 0.800000 0.300000 6: 0.850000 0.500000E-01 7: 0.900000 0.100000 8: 1.00000 1.00000 Problem 5 DATA_NUM 9 DIM_NUM 2 Data array: Row 1 2 Col 1: 0.00000 0.00000 2: 0.100000 0.900000 3: 0.200000 0.950000 4: 0.300000 0.900000 5: 0.400000 0.100000 6: 0.500000 0.500000E-01 7: 0.600000 0.500000E-01 8: 0.800000 0.200000 9: 1.00000 1.00000 Problem 6 DATA_NUM 49 DIM_NUM 2 Data array: Row 1 2 Col 1: 595.000 0.644000 2: 605.000 0.622000 3: 615.000 0.638000 4: 625.000 0.649000 5: 635.000 0.652000 6: 645.000 0.639000 7: 655.000 0.646000 8: 665.000 0.657000 9: 675.000 0.652000 10: 685.000 0.655000 11: 695.000 0.644000 12: 705.000 0.663000 13: 715.000 0.663000 14: 725.000 0.668000 15: 735.000 0.676000 16: 745.000 0.676000 17: 755.000 0.686000 18: 765.000 0.679000 19: 775.000 0.678000 20: 785.000 0.683000 21: 795.000 0.694000 22: 805.000 0.699000 23: 815.000 0.710000 24: 825.000 0.730000 25: 835.000 0.763000 26: 845.000 0.812000 27: 855.000 0.907000 28: 865.000 1.04400 29: 875.000 1.33600 30: 885.000 1.88100 31: 895.000 2.16900 32: 905.000 2.07500 33: 915.000 1.59800 34: 925.000 1.21100 35: 935.000 0.916000 36: 945.000 0.746000 37: 955.000 0.672000 38: 965.000 0.627000 39: 975.000 0.615000 40: 985.000 0.607000 41: 995.000 0.606000 42: 1005.00 0.609000 43: 1015.00 0.603000 44: 1025.00 0.601000 45: 1035.00 0.603000 46: 1045.00 0.601000 47: 1055.00 0.611000 48: 1065.00 0.601000 49: 1075.00 0.608000 Problem 7 DATA_NUM 4 DIM_NUM 2 Data array: Row 1 2 Col 1: 0.00000 1.00000 2: 1.00000 2.00000 3: 4.00000 2.00000 4: 5.00000 1.00000 Problem 8 DATA_NUM 12 DIM_NUM 2 Data array: Row 1 2 Col 1: -1.00000 1.00000 2: -0.800000 0.640000 3: -0.600000 0.360000 4: -0.400000 0.160000 5: -0.200000 0.400000E-01 6: 0.00000 0.00000 7: 0.200000 0.400000E-01 8: 0.200010 0.500000E-01 9: 0.400000 0.160000 10: 0.600000 0.360000 11: 0.800000 0.640000 12: 1.00000 1.00000 TEST_INTERP_TEST Normal end of execution. 17 September 2021 11:53:53.081 PM