C 代码 通过分段多项式函数插值或近似数据.rar

27 May 2021 03:26:18 PM SPLINE_TEST C version: Test the SPLINE library. parabola_val2_test parabola_val2() evaluates parabolas through 3 points in a table Our data tables will actually be parabolas: A: 2*x^2 + 3 * x + 1. B: 4*x^2 - 2 * x + 5. 0 2 15 17 1 4 45 61 2 6 91 137 3 8 153 245 4 10 231 385 Interpolated data: LEFT, X, Y1, Y2 1 1 6 7 2 3 28 35 3 5 66 95 3 7 120 187 3 9 190 311 TEST002 R8VEC_BRACKET finds a pair of entries in a sorted real array which bracket a value. Sorted array: 0: 1.000000 1: 2.000000 2: 3.000000 3: 4.000000 4: 5.000000 5: 5.000000 6: 7.000000 7: 8.000000 8: 9.000000 9: 10.000000 Search for XVAL = -10 X[0] = 1 X[1] = 2 Search for XVAL = 1 X[0] = 1 X[1] = 2 Search for XVAL = 4.5 X[3] = 4 X[4] = 5 Search for XVAL = 5 X[5] = 5 X[6] = 7 Search for XVAL = 10 X[8] = 9 X[9] = 10 Search for XVAL = 12 X[8] = 9 X[9] = 10 TEST003 R8VEC_BRACKET3 finds a pair of entries in a sorted real array which bracket a value. Sorted array: 0: 1.000000 1: 2.000000 2: 3.000000 3: 4.000000 4: 5.000000 5: 5.000000 6: 7.000000 7: 8.000000 8: 9.000000 9: 10.000000 Search for XVAL = -10 Starting guess for interval is = 5 Nearest interval: X[-1]= 12 X[0]= 1 Search for XVAL = 1 Starting guess for interval is = 0 Nearest interval: X[-1]= 12 X[0]= 1 Search for XVAL = 4.5 Starting guess for interval is = 0 Nearest interval: X[2]= 3 X[3]= 4 Search for XVAL = 5 Starting guess for interval is = 3 Nearest interval: X[2]= 3 X[3]= 4 Search for XVAL = 10 Starting guess for interval is = 3 Nearest interval: X[7]= 8 X[8]= 9 Search for XVAL = 12 Starting guess for interval is = 8 Nearest interval: X[7]= 8 X[8]= 9 TEST004 R8VEC_ORDER_TYPE classifies a real vector as -1: no order 0: all equal; 1: ascending; 2: strictly ascending; 3: descending; 4: strictly descending. Vector of order type -1: 0 1 1 3 2 2 3 4 Vector of order type 0: 0 2 1 2 2 2 3 2 Vector of order type 1: 0 1 1 2 2 2 3 4 Vector of order type 2: 0 1 1 2 2 3 3 4 Vector of order type 3: 0 4 1 4 2 3 3 1 Vector of order type 4: 0 9 1 7 2 3 3 0 TEST005 D3_NP_FS factors and solves a tridiagonal linear system. Computed solution: 0: 1.000000 1: 2.000000 2: 3.000000 3: 4.000000 4: 5.000000 5: 6.000000 6: 7.000000 7: 8.000000 8: 9.000000 9: 10.000000 TEST006 Approximate Y = EXP(X) using orders 1 to 8. Original data: X Y 0 1 1 2.71828 2 7.38906 3 20.0855 4 54.5982 5 148.413 6 403.429 7 1096.63 Evaluate at X = 2.5 where EXP(X) = 12.1825 Order Approximate Y Error 1 1 -11.1825 2 5.2957 -6.88679 3 10.8316 -1.35087 4 12.417 0.234513 5 12.0765 -0.106003 6 12.252 0.069528 7 12.1264 -0.0561433 8 12.2343 0.0518261 TEST01 BASIS_FUNCTION_B_VAL evaluates the B spline basis function. T B(T) -0.5 0 -0.375 0 -0.25 0 -0.125 0 * 0 0 0.25 0.00260417 0.5 0.0208333 0.75 0.0703125 * 1 0.166667 1.75 0.315104 2.5 0.479167 3.25 0.611979 * 4 0.666667 4.5 0.611979 5 0.479167 5.5 0.315104 * 6 0.166667 7 0.0703125 8 0.0208333 9 0.00260417 * 10 0 10.5 0 11 0 11.5 0 12 0 TEST02 BASIS_FUNCTION_BETA_VAL evaluates the Beta spline basis function. BETA1 = 1 BETA2 = 0 T B(T) -0.5 0 -0.375 0 -0.25 0 -0.125 0 * 0 0 0.25 0.00260417 0.5 0.0208333 0.75 0.0703125 * 1 0.166667 1.75 0.315104 2.5 0.479167 3.25 0.611979 * 4 0.666667 4.5 0.611979 5 0.479167 5.5 0.315104 * 6 0.166667 7 0.0703125 8 0.0208333 9 0.00260417 * 10 0 10.5 0 11 0 11.5 0 12 0 BETA1 = 1 BETA2 = 100 T B(T) -0.5 0 -0.375 0 -0.25 0 -0.125 0 * 0 0 0.25 0.000279018 0.5 0.00223214 0.75 0.00753348 * 1 0.0178571 1.75 0.17327 2.5 0.497768 3.25 0.818917 * 4 0.964286 4.5 0.818917 5 0.497768 5.5 0.17327 * 6 0.0178571 7 0.00753348 8 0.00223214 9 0.000279018 * 10 0 10.5 0 11 0 11.5 0 12 0 BETA1 = 100 BETA2 = 0 T B(T) -0.5 0 -0.375 0 -0.25 0 -0.125 0 * 0 0 0.25 1.53156e-08 0.5 1.22525e-07 0.75 4.13521e-07 * 1 9.80199e-07 1.75 0.00175767 2.5 0.00626188 3.25 0.0125854 * 4 0.0198 4.5 0.584721 5 0.871213 5.5 0.972099 * 6 0.980199 7 0.413521 8 0.122525 9 0.0153156 * 10 0 10.5 0 11 0 11.5 0 12 0 TEST03 BASIS_MATRIX_B_UNI sets up the basis matrix for the uniform B spline. TDATA, YDATA -1 4