04 March 2022 09:48:44 AM RBF_INTERP_ND_TEST: C++ version Test the RBF_INTERP_ND library. The R8LIB library is also needed. RBF_INTERP_ND_TEST01: RBF_WEIGHT computes weights for RBF interpolation. RBF_INTERP_ND evaluates the RBF interpolant. Use the multiquadratic basis function PHI1(R). The product points: Row: 0 1 Col 0: 0 0 1: 0.5 0 2: 1 0 3: 1.5 0 4: 2 0 5: 0 0.5 6: 0.5 0.5 7: 1 0.5 8: 1.5 0.5 9: 2 0.5 10: 0 1 11: 0.5 1 12: 1 1 13: 1.5 1 14: 2 1 15: 0 1.5 16: 0.5 1.5 17: 1 1.5 18: 1.5 1.5 19: 2 1.5 20: 0 2 21: 0.5 2 22: 1 2 23: 1.5 2 24: 2 2 Scale factor R0 = 0.4 Function data: 0: 0 1: 0 2: 0 3: 0 4: 0 5: 0 6: 0.1947 7: 0.303265 8: 0.354275 9: 0.367879 10: 0 11: 0.303265 12: 0.367879 13: 0.334695 14: 0.270671 15: 0 16: 0.354275 17: 0.334695 18: 0.237148 19: 0.149361 20: 0 21: 0.367879 22: 0.270671 23: 0.149361 24: 0.0732626 Weight vector: 0: -0.501359 1: 0.300861 2: 0.23295 3: 0.369441 4: 0.645573 5: 0.300861 6: -0.155096 7: -0.367322 8: -0.407046 9: -1.30006 10: 0.23295 11: -0.367322 12: 0.182323 13: 0.203404 14: 0.514794 15: 0.369441 16: -0.407046 17: 0.203404 18: -0.12928 19: 0.00990249 20: 0.645573 21: -1.30006 22: 0.514794 23: 0.00990249 24: 0.0666187 L2 interpolation error averaged per interpolant node = 2.96286e-16 L2 approximation error averaged per 1000 samples = 0.0031887 RBF_INTERP_ND_TEST02: RBF_WEIGHT computes weights for RBF interpolation. RBF_INTERP_ND evaluates the RBF interpolant. Use the inverse multiquadratic basis function PHI2(R). The product points: Row: 0 1 Col 0: 0 0 1: 0.5 0 2: 1 0 3: 1.5 0 4: 2 0 5: 0 0.5 6: 0.5 0.5 7: 1 0.5 8: 1.5 0.5 9: 2 0.5 10: 0 1 11: 0.5 1 12: 1 1 13: 1.5 1 14: 2 1 15: 0 1.5 16: 0.5 1.5 17: 1 1.5 18: 1.5 1.5 19: 2 1.5 20: 0 2 21: 0.5 2 22: 1 2 23: 1.5 2 24: 2 2 Scale factor R0 = 0.4 Function data: 0: 0 1: 0 2: 0 3: 0 4: 0 5: 0 6: 0.1947 7: 0.303265 8: 0.354275 9: 0.367879 10: 0 11: 0.303265 12: 0.367879 13: 0.334695 14: 0.270671 15: 0 16: 0.354275 17: 0.334695 18: 0.237148 19: 0.149361 20: 0 21: 0.367879 22: 0.270671 23: 0.149361 24: 0.0732626 Weight vector: 0: 0.00455693 1: -0.044454 2: -0.0711033 3: -0.0829322 4: -0.121156 5: -0.044454 6: 0.0524777 7: 0.0753675 8: 0.10031 9: 0.184681 10: -0.0711033 11: 0.0753675 12: 0.0199836 13: 0.00472747 14: -0.00972847 15: -0.0829322 16: 0.10031 17: 0.00472747 18: 0.00968919 19: -0.0108128 20: -0.121156 21: 0.184681 22: -0.00972847 23: -0.0108128 24: -0.0325387 L2 interpolation error averaged per interpolant node = 5.89813e-17 L2 approximation error averaged per 1000 samples = 0.00410702 RBF_INTERP_ND_TEST03: RBF_WEIGHT computes weights for RBF interpolation. RBF_INTERP_ND evaluates the RBF interpolant. Use the thin-plate spline basis function PHI3(R). The product points: Row: 0 1 Col 0: 0 0 1: 0.5 0 2: 1 0 3: 1.5 0 4: 2 0 5: 0 0.5 6: 0.5 0.5 7: 1 0.5 8: 1.5 0.5 9: 2 0.5 10: 0 1 11: 0.5 1 12: 1 1 13: 1.5 1 14: 2 1 15: 0 1.5 16: 0.5 1.5 17: 1 1.5 18: 1.5 1.5 19: 2 1.5 20: 0 2 21: 0.5 2 22: 1 2 23: 1.5 2 24: 2 2 Scale factor R0 = 0.4 Function data: 0: 0 1: 0 2: 0 3: 0 4: 0 5: 0 6: 0.1947 7: 0.303265 8: 0.354275 9: 0.367879 10: 0 11: 0.303265 12: 0.367879 13: 0.334695 14: 0.270671 15: 0 16: 0.354275 17: 0.334695 18: 0.237148 19: 0.149361 20: 0 21: 0.367879 22: 0.270671 23: 0.149361 24: 0.0732626 Weight vector: 0: 0.433461 1: -0.204877 2: -0.0872454 3: -0.246184 4: -0.0676362 5: -0.204877 6: -0.0378926 7: 0.133989 8: 0.127043 9: 0.441877 10: -0.0872454 11: 0.133989 12: -0.0423124 13: -0.107041 14: -0.183447 15: -0.246184 16: 0.127043 17: -0.107041 18: -0.0378467 19: -0.107503 20: -0.0676362 21: 0.441877 22: -0.183447 23: -0.107503 24: 0.141281 L2 interpolation error averaged per interpolant node = 9.00541e-16 L2 approximation error averaged per 1000 samples = 0.0026366 RBF_INTERP_ND_TEST04: RBF_WEIGHT computes weights for RBF interpolation. RBF_INTERP_ND evaluates the RBF interpolant. Use the gaussian basis function PHI4(R). The product points: Row: 0 1 Col 0: 0 0 1: 0.5 0 2: 1 0 3: 1.5 0 4: 2 0 5: 0 0.5 6: 0.5 0.5 7: 1 0.5 8: 1.5 0.5 9: 2 0.5 10: 0 1 11: 0.5 1 12: 1 1 13: 1.5 1 14: 2 1 15: 0 1.5 16: 0.5 1.5 17: 1 1.5 18: 1.5 1.5 19: 2 1.5 20: 0 2 21: 0.5 2 22: 1 2 23: 1.5 2 24: 2 2 Scale factor R0 = 0.4 Function data: 0: 0 1: 0 2: 0 3: 0 4: 0 5: 0 6: 0.1947 7: 0.303265 8: 0.354275 9: 0.367879 10: 0 11: 0.303265 12: 0.367879 13: 0.334695 14: 0.270671 15: 0 16: 0.354275 17: 0.334695 18: 0.237148 19: 0.149361 20: 0 21: 0.367879 22: 0.270671 23: 0.149361 24: 0.0732626 Weight vector: 0: 0.0247652 1: -0.0461165 2: -0.0818427 3: -0.0622022 4: -0.17306 5: -0.0461165 6: 0.0838087 7: 0.173681 8: 0.128662 9: 0.37891 10: -0.0818427 11: 0.173681 12: 0.051454 13: 0.0737542 14: -0.0110253 15: -0.0622022 16: 0.128662 17: 0.0737542 18: 0.0630212 19: 0.076087 20: -0.17306 21: 0.37891 22: -0.0110253 23: 0.076087 24: -0.0125014 L2 interpolation error averaged per interpolant node = 3.90968e-17 L2 approximation error averaged per 1000 samples = 0.00413716 RBF_INTERP_ND_TEST: Normal end of execution. 04 March 2022 09:48:44 AM