08-Jan-2022 10:27:31 test_interp_test() MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test test_interp(). This test also requires r8lib(). TEST_INTERP_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 a disaster. TEST_INTERP_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 4 2: 1 5 3: 2 6 4: 4 6 5: 5 5 6: 6 3 7: 7 1 8: 8 1 9: 9 1 10: 10 3 11: 11 4 12: 12 4 13: 13 3 14: 14 3 15: 15 4 16: 16 4 17: 17 3 18: 18 0 Problem 2 DATA_NUM = 18 DIM_NUM = 2 Data array: Row: 1 2 Col 1: 0 0 2: 1.34 5 3: 5 8.66 4: 10 10 5: 10.6 10.4 6: 10.7 12 7: 10.705 28.6 8: 10.8 30.2 9: 11.4 30.6 10: 19.6 30.6 11: 20.2 30.2 12: 20.295 28.6 13: 20.3 12 14: 20.4 10.4 15: 21 10 16: 26 8.66 17: 29.66 5 18: 31 0 Problem 3 DATA_NUM = 11 DIM_NUM = 2 Data array: Row: 1 2 Col 1: 0 0 2: 2 10 3: 3 10 4: 5 10 5: 6 10 6: 8 10 7: 9 10.5 8: 11 15 9: 12 50 10: 14 60 11: 15 85 Problem 4 DATA_NUM = 8 DIM_NUM = 2 Data array: Row: 1 2 Col 1: 0 0 2: 0.05 0.7 3: 0.1 1 4: 0.2 1 5: 0.8 0.3 6: 0.85 0.05 7: 0.9 0.1 8: 1 1 Problem 5 DATA_NUM = 9 DIM_NUM = 2 Data array: Row: 1 2 Col 1: 0 0 2: 0.1 0.9 3: 0.2 0.95 4: 0.3 0.9 5: 0.4 0.1 6: 0.5 0.05 7: 0.6 0.05 8: 0.8 0.2 9: 1 1 Problem 6 DATA_NUM = 49 DIM_NUM = 2 Data array: Row: 1 2 Col 1: 595 0.644 2: 605 0.622 3: 615 0.638 4: 625 0.649 5: 635 0.652 6: 645 0.639 7: 655 0.646 8: 665 0.657 9: 675 0.652 10: 685 0.655 11: 695 0.644 12: 705 0.663 13: 715 0.663 14: 725 0.668 15: 735 0.676 16: 745 0.676 17: 755 0.686 18: 765 0.679 19: 775 0.678 20: 785 0.683 21: 795 0.694 22: 805 0.699 23: 815 0.71 24: 825 0.73 25: 835 0.763 26: 845 0.812 27: 855 0.907 28: 865 1.044 29: 875 1.336 30: 885 1.881 31: 895 2.169 32: 905 2.075 33: 915 1.598 34: 925 1.211 35: 935 0.916 36: 945 0.746 37: 955 0.672 38: 965 0.627 39: 975 0.615 40: 985 0.607 41: 995 0.606 42: 1005 0.609 43: 1015 0.603 44: 1025 0.601 45: 1035 0.603 46: 1045 0.601 47: 1055 0.611 48: 1065 0.601 49: 1075 0.608 Problem 7 DATA_NUM = 4 DIM_NUM = 2 Data array: Row: 1 2 Col 1: 0 1 2: 1 2 3: 4 2 4: 5 1 Problem 8 DATA_NUM = 12 DIM_NUM = 2 Data array: Row: 1 2 Col 1: -1 1 2: -0.8 0.64 3: -0.6 0.36 4: -0.4 0.16 5: -0.2 0.04 6: 0 0 7: 0.2 0.04 8: 0.20001 0.05 9: 0.4 0.16 10: 0.6 0.36 11: 0.8 0.64 12: 1 1 Created graphics file "p01_plot.png". Created graphics file "p02_plot.png". Created graphics file "p03_plot.png". Created graphics file "p04_plot.png". Created graphics file "p05_plot.png". Created graphics file "p06_plot.png". Created graphics file "p07_plot.png". Created graphics file "p08_plot.png". test_interp_test(): Normal end of execution. 08-Jan-2022 10:27:37