C 代码 计算雅可比多项式和相关函数.rar

03 March 2022 10:53:02 PM JACOBI_POLYNOMIAL_TEST C version Test the JACOBI_POLYNOMIAL library. TEST01: J_POLYNOMIAL_VALUES stores values of the Jacobi polynomials. J_POLYNOMIAL evaluates the polynomial. Tabulated Computed N A B X J(N,A,B,X) J(N,A,B,X) Error 0 0 1 0.5 1 1 0 1 0 1 0.5 0.25 0.25 0 2 0 1 0.5 -0.375 -0.375 0 3 0 1 0.5 -0.484375 -0.484375 0 4 0 1 0.5 -0.132812 -0.132812 0 5 0 1 0.5 0.275391 0.275391 0 5 1 1 0.5 -0.164062 -0.164062 0 5 2 1 0.5 -1.1748 -1.1748 0 5 3 1 0.5 -2.36133 -2.36133 0 5 4 1 0.5 -2.61621 -2.61621 0 5 5 1 0.5 0.117188 0.117188 0 5 0 2 0.5 0.421875 0.421875 0 5 0 3 0.5 0.504883 0.504883 0 5 0 4 0.5 0.509766 0.509766 0 5 0 5 0.5 0.430664 0.430664 0 5 0 1 -1 -6 -6 0 5 0 1 -0.8 0.03862 0.03862 5.06539e-16 5 0 1 -0.6 0.81184 0.81184 0 5 0 1 -0.4 0.03666 0.03666 -2.22045e-16 5 0 1 -0.2 -0.48512 -0.48512 5.55112e-17 5 0 1 0 -0.3125 -0.3125 0 5 0 1 0.2 0.18912 0.18912 -2.77556e-17 5 0 1 0.4 0.40234 0.40234 0 5 0 1 0.6 0.01216 0.01216 -2.77556e-17 5 0 1 0.8 -0.43962 -0.43962 -5.55112e-17 5 0 1 1 1 1 0 TEST02: J_POLYNOMIAL_ZEROS computes the zeros of J(n,a,b,x); Check by calling J_POLYNOMIAL there. Zeros for J(1,0.500000,0.500000) 0: 0.000000 Evaluate J(1,0.500000,0.500000) 0: 0.000000 Zeros for J(2,0.500000,0.500000) 0: -0.500000 1: 0.500000 Evaluate J(2,0.500000,0.500000) 0: -0.000000 1: -0.000000 Zeros for J(3,0.500000,0.500000) 0: -0.707107 1: 0.000000 2: 0.707107 Evaluate J(3,0.500000,0.500000) 0: 0.000000 1: -0.000000 2: -0.000000 Zeros for J(4,0.500000,0.500000) 0: -0.809017 1: -0.309017 2: 0.309017 3: 0.809017 Evaluate J(4,0.500000,0.500000) 0: 0.000000 1: 0.000000 2: 0.000000 3: 0.000000 Zeros for J(5,0.500000,0.500000) 0: -0.866025 1: -0.500000 2: 0.000000 3: 0.500000 4: 0.866025 Evaluate J(5,0.500000,0.500000) 0: -0.000000 1: -0.000000 2: 0.000000 3: 0.000000 4: 0.000000 Zeros for J(1,1.000000,1.500000) 0: 0.111111 Evaluate J(1,1.000000,1.500000) 0: 0.000000 Zeros for J(2,1.000000,1.500000) 0: -0.348215 1: 0.502061 Evaluate J(2,1.000000,1.500000) 0: -0.000000 1: -0.000000 Zeros for J(3,1.000000,1.500000) 0: -0.578486 1: 0.070894 2: 0.684062 Evaluate J(3,1.000000,1.500000) 0: 0.000000 1: -0.000000 2: -0.000000 Zeros for J(4,1.000000,1.500000) 0: -0.706793 1: -0.217417 2: 0.332314 3: 0.782371 Evaluate J(4,1.000000,1.500000) 0: 0.000000 1: -0.000000 2: -0.000000 3: -0.000000 Zeros for J(5,1.000000,1.500000) 0: -0.784837 1: -0.409111 2: 0.052074 3: 0.500669 4: 0.841205 Evaluate J(5,1.000000,1.500000) 0: -0.000000 1: -0.000000 2: 0.000000 3: 0.000000 4: -0.000000 Zeros for J(1,2.000000,0.500000) 0: -0.333333 Evaluate J(1,2.000000,0.500000) 0: 0.000000 Zeros for J(2,2.000000,0.500000) 0: -0.645661 1: 0.184123 Evaluate J(2,2.000000,0.500000) 0: -0.000000 1: -0.000000 Zeros for J(3,2.000000,0.500000) 0: -0.780044 1: -0.212793 2: 0.463425 Evaluate J(3,2.000000,0.500000) 0: -0.000000 1: 0.000000 2: 0.000000 Zeros for J(4,2.000000,0.500000) 0: -0.850186 1: -0.444336 2: 0.099507 3: 0.623586 Evaluate J(4,2.000000,0.500000) 0: 0.000000 1: 0.000000 2: -0.000000 3: 0.000000 Zeros for J(5,2.000000,0.500000) 0: -0.891404 1: -0.588710 2: -0.156285 3: 0.313970 4: 0.722429 Evaluate J(5,2.000000,0.500000) 0: -0.000000 1: 0.000000 2: 0.000000 3: -0.000000 4: 0.000000 TEST03: J_QUADRATURE_RULE computes the quadrature rule associated with J(n,a,b,x); X W 0: -0.810587 0.006203 1: -0.550876 0.061938 2: -0.230689 0.216462 3: 0.113888 0.398821 4: 0.443600 0.431011 5: 0.720815 0.259969 6: 0.913850 0.062257 Use the quadrature rule to estimate: Q = Integral (-1<x<+1) J(i,a,b,x) J(j,a,b,x) (1-x)^a (1+x)^b dx I J Q_Estimate Q_Exact 0 0 1.43666 1.43666 0 1 1.249e-16 0 0 2 2.22045e-16 0 0 3 8.32667e-17 0 0 4 2.77556e-16 0 0 5 1.38778e-17 0 1 1 1.54717 1.54717 1 2 -5.55112e-17 0 1 3 4.996e-16 0 1 4 -1.11022e-16 0 1 5 1.08247e-15 0 2 2 1.45203 1.45203 2 3 -2.77556e-16 0 2 4 1.66533e-15 0 2 5 2.77556e-17 0 3 3 1.32615 1.32615 3 4 -3.33067e-16 0 3 5 2.27596e-15 0 4 4 1.2068 1.2068 4 5 -9.15934e-16 0 5 5 1.10154 1.10154 TEST04: J_DOUBLE_PRODUCT_INTEGRAL returns the weighted integral of J(i,a,b,x) * J(j,a,b,x); Q = Integral (-1<x<+1) J(i,a,b,x) J(j,a,b,x) (1-x)^a (1+x)^b dx I J Q 0 0 1.