02 March 2022 07:07:51 AM HERMITE_PRODUCT_POLYNOMIAL_TEST: C++ version Test the HERMITE_PRODUCT_POLYNOMIAL library. HPP_TEST01: COMP_NEXT_GRLEX is given a composition, and computes the next composition in grlex order. Rank Sum Components 1 0 0 0 2 1 0 1 3 1 1 0 4 2 0 2 5 2 1 1 6 2 2 0 7 3 0 3 8 3 1 2 9 3 2 1 10 3 3 0 11 4 0 4 12 4 1 3 13 4 2 2 14 4 3 1 15 4 4 0 16 5 0 5 17 5 1 4 18 5 2 3 19 5 3 2 20 5 4 1 COMP_UNRANK_GRLEX is given a rank and returns the corresponding set of multinomial exponents. Rank Sum Components 5 2 1 1 20 5 4 1 17 5 1 4 12 4 1 3 9 3 2 1 COMP_RANDOM_GRLEX randomly selects a composition between given lower and upper ranks. Rank Sum Components 8 3 1 2 20 5 4 1 18 5 2 3 13 4 2 2 11 4 0 4 COMP_RANK_GRLEX returns the rank of a given composition. Rank Sum Components 15 4 4 0 148 16 11 5 HPP_TEST015: HEP_COEFFICIENTS computes the coefficients and exponents of the Hermite polynomial He(n,x). He(1,x) = + 1 * x^(1). He(2,x) = - 1 * x^(0) + 1 * x^(2). He(3,x) = - 3 * x^(1) + 1 * x^(3). He(4,x) = + 3 * x^(0) - 6 * x^(2) + 1 * x^(4). He(5,x) = + 15 * x^(1) - 10 * x^(3) + 1 * x^(5). HPP_TEST02: HEP_VALUES stores values of the Hermite polynomial He(o,x). HEP_VALUE evaluates a Hermite polynomial. Tabulated Computed O X He(O,X) He(O,X) Error 0 5 1 1 0 1 5 5 5 0 2 5 24 24 0 3 5 110 110 0 4 5 478 478 0 5 5 1950 1950 0 6 5 7360 7360 0 7 5 25100 25100 0 8 5 73980 73980 0 9 5 169100 169100 0 10 5 179680 179680 0 11 5 -792600 -792600 0 12 5 -5.93948e+06 -5.93948e+06 0 5 0 0 0 0 5 0.5 6.28125 6.28125 0 5 1 6 6 0 5 3 18 18 0 5 10 90150 90150 0 HPP_TEST03: HEPP_VALUE evaluates a Hermite product polynomial. POLYNOMIAL_VALUE evaluates a polynomial. Evaluate at X = -0.563163 0.912635 0.659018 Rank I1 I2 I3: He(I1,X1)*He(I2,X2)*He(I3,X3) P(X1,X2,X3) 1 0 0 0 1 1 2 0 0 1 0.659018 0.659018 3 0 1 0 0.912635 0.912635 4 1 0 0 -0.563163 -0.563163 5 0 0 2 -0.565695 -0.565695 6 0 1 1 0.601443 0.601443 7 0 2 0 -0.167097 -0.167097 8 1 0 1 -0.371135 -0.371135 9 1 1 0 -0.513963 -0.513963 10 2 0 0 -0.682847 -0.682847 11 0 0 3 -1.69084 -1.69084 12 0 1 2 -0.516273 -0.516273 13 0 2 1 -0.11012 -0.11012 14 0 3 0 -1.97777 -1.97777 15 1 0 2 0.318579 0.318579 16 1 1 1 -0.338711 -0.338711 17 1 2 0 0.094103 0.094103 18 2 0 1 -0.450009 -0.450009 19 2 1 0 -0.62319 -0.62319 20 3 0 0 1.51088 1.51088 HPP_TEST04: HEPP_TO_POLYNOMIAL is given a Hermite product polynomial and determines its polynomial representation. Using spatial dimension M = 2 HePP #1 = He(0,X)*He(0,Y) = + 1 * x^(0,0). HePP #2 = He(0,X)*He(1,Y) = + 1 * x^(0,1). HePP #3 = He(1,X)*He(0,Y) = + 1 * x^(1,0). HePP #4 = He(0,X)*He(2,Y) = - 1 * x^(0,0) + 1 * x^(0,2). HePP #5 = He(1,X)*He(1,Y) = + 1 * x^(1,1). HePP #6 = He(2,X)*He(0,Y) = - 1 * x^(0,0) + 1 * x^(2,0). HePP #7 = He(0,X)*He(3,Y) = - 3 * x^(0,1) + 1 * x^(0,3). HePP #8 = He(1,X)*He(2,Y) = - 1 * x^(1,0) + 1 * x^(1,2). HePP #9 = He(2,X)*He(1,Y) = - 1 * x^(0,1) + 1 * x^(2,1). HePP #10 = He(3,X)*He(0,Y) = - 3 * x^(1,0) + 1 * x^(3,0). HePP #11 = He(0,X)*He(4,Y) = + 3 * x^(0,0) - 6 * x^(0,2) + 1 * x^(0,4). HERMITE_PRODUCT_POLYNOMIAL_TEST: Normal end of execution. 02 March 2022 07:07:51 AM