28-Jul-2021 14:34:26 legendre_product_test(): MATLAB/Octave version 9.9.0.1467703 (R2020b) Test legendre_product(). LEGENDRE_LINEAR_PRODUCT_TEST Compute a linearly weighted Legendre product table. Tij = integral ( -1 <= X <= +1 ) X^E Li(X) Lj(X) dx where Li(X) = Legendre polynomial of degree i. Maximum degree P = 5 Exponent of X, E = 0 Linearly weighted table: Col: 1 2 3 4 5 Row 1 : 1 -2.77556e-17 -2.22045e-16 0 0 2 : 0 1 0 -1.11022e-16 0 3 :-1.66533e-16 0 1 5.55112e-17 -2.77556e-17 4 : 0 -1.66533e-16 5.55112e-17 1 0 5 :-2.77556e-17 0 5.55112e-17 0 1 6 : 1.38778e-17 3.88578e-16 0 3.747e-16 -1.38778e-17 Col: 6 Row 1 : 1.38778e-17 2 : 3.60822e-16 3 : 0 4 : 3.46945e-16 5 : 1.38778e-17 6 : 1 LEGENDRE_LINEAR_PRODUCT_TEST Compute a linearly weighted Legendre product table. Tij = integral ( -1 <= X <= +1 ) X^E Li(X) Lj(X) dx where Li(X) = Legendre polynomial of degree i. Maximum degree P = 5 Exponent of X, E = 1 Linearly weighted table: Col: 1 2 3 4 5 Row 1 :-1.38778e-17 0.57735 1.38778e-17 3.33067e-16 0 2 : 0.57735 0 0.516398 0 3.33067e-16 3 : 0 0.516398 -2.77556e-17 0.507093 0 4 : 3.05311e-16 0 0.507093 -2.77556e-17 0.503953 5 : 0 3.33067e-16 0 0.503953 0 6 : 8.32667e-17 0 1.94289e-16 2.77556e-17 0.502519 Col: 6 Row 1 : 1.11022e-16 2 : 0 3 : 1.66533e-16 4 : 0 5 : 0.502519 6 :-1.38778e-17 LEGENDRE_LINEAR_PRODUCT_TEST Compute a linearly weighted Legendre product table. Tij = integral ( -1 <= X <= +1 ) X^E Li(X) Lj(X) dx where Li(X) = Legendre polynomial of degree i. Maximum degree P = 5 Exponent of X, E = 2 Linearly weighted table: Col: 1 2 3 4 5 Row 1 : 0.333333 0 0.298142 0 2.08167e-16 2 : 1.38778e-17 0.6 -2.77556e-17 0.261861 0 3 : 0.298142 -2.77556e-17 0.52381 0 0.255551 4 : 0 0.261861 0 0.511111 -2.77556e-17 5 : 2.08167e-16 0 0.255551 -2.77556e-17 0.506494 6 : 0 1.80411e-16 0 0.253246 1.38778e-17 Col: 6 Row 1 : 0 2 : 1.80411e-16 3 : 0 4 : 0.253246 5 : 0 6 : 0.504274 LEGENDRE_EXPONENTIAL_PRODUCT_TEST Compute an exponentially weighted Legendre product table. Tij = integral ( -1 <= X <= +1 ) exp(B*X) Li(X) Lj(X) dx where Li(X) = Legendre polynomial of degree i. Maximum degree P = 5 Exponential argument coefficient B = 0.000000 Exponentially weighted table: Col: 1 2 3 4 5 Row 1 : 1 1.38778e-17 -2.63678e-16 1.38778e-17 1.38778e-16 2 : 0 1 -5.55112e-17 -1.94289e-16 0 3 :-2.77556e-16 -2.77556e-17 1 0 -1.11022e-16 4 : 1.38778e-17 -1.94289e-16 0 1 -2.77556e-17 5 : 1.38778e-16 0 -1.11022e-16 0 1 6 : 0 1.38778e-16 0 -5.55112e-16 2.77556e-17 Col: 6 Row 1 : 0 2 : 1.11022e-16 3 : 0 4 :-5.55112e-16 5 : 2.77556e-17 6 : 1 LEGENDRE_EXPONENTIAL_PRODUCT_TEST Compute an exponentially weighted Legendre product table. Tij = integral ( -1 <= X <= +1 ) exp(B*X) Li(X) Lj(X) dx where Li(X) = Legendre polynomial of degree i. Maximum degree P = 5 Exponential argument coefficient B = 1.000000 Exponentially weighted table: Col: 1 2 3 4 5 Row 1 : 1.1752 0.637186 0.160019 0.0266297 0.00332171 2 : 0.637186 1.31833 0.593306 0.143446 0.0235329 3 : 0.160019 0.593306 1.28028 0.575807 0.139112 4 : 0.0266297 0.143446 0.575807 1.27245 0.570883 5 : 0.00332171 0.0235329 0.139112 0.570883 1.26977 6 : 0.000331538 0.00291515 0.0228114 0.137684 0.56876 Col: 6 Row 1 : 0.000331538 2 : 0.00291515 3 : 0.0228114 4 : 0.137684 5 : 0.56876 6 : 1.26849 legendre_product_test(): Normal end of execution. 28-Jul-2021 14:34:27