19-Dec-2022 15:03:58 hermite_product_polynomial_test(): MATLAB/Octave version 4.2.2 Test hermite_product_polynomial(). hermite_product_polynomial_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 19 5: 3 2 11 4: 0 4 10 3: 3 0 19 5: 3 2 14 4: 3 1 comp_random_grlex() randomly selects a composition between given lower and upper ranks. Rank Sum Components 18 5: 2 3 15 4: 4 0 12 4: 1 3 8 3: 1 2 6 2: 2 0 COMP_RANK_GRLEX returns the rank of a given composition. Rank Sum Components 15 4: 4 0 148 16: 11 5 hermite_product_polynomial_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). hermite_product_polynomial_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 5.000000 1 1 0 1 5.000000 5 5 0 2 5.000000 24 24 0 3 5.000000 110 110 0 4 5.000000 478 478 0 5 5.000000 1950 1950 0 6 5.000000 7360 7360 0 7 5.000000 25100 25100 0 8 5.000000 73980 73980 0 9 5.000000 169100 169100 0 10 5.000000 179680 179680 0 11 5.000000 -792600 -792600 0 12 5.000000 -5.93948e+06 -5.93948e+06 0 5 0.000000 0 0 0 5 0.500000 6.28125 6.28125 0 5 1.000000 6 6 0 5 3.000000 18 18 0 5 10.000000 90150 90150 0 hermite_product_polynomial_test03(): hepp_value() evaluates a Hermite product polynomial. polynomial_value() evaluates a polynomial. Evaluate at X = ( -0.912153, 0.604582, 0.376243 ) 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 0.376243 0.376243 3 0 1 0 0.604582 0.604582 4 1 0 0 -0.912153 -0.912153 5 0 0 2 -0.858441 -0.858441 6 0 1 1 0.22747 0.22747 7 0 2 0 -0.63448 -0.63448 8 1 0 1 -0.343191 -0.343191 9 1 1 0 -0.551472 -0.551472 10 2 0 0 -0.167977 -0.167977 11 0 0 3 -1.07547 -1.07547 12 0 1 2 -0.518998 -0.518998 13 0 2 1 -0.238719 -0.238719 14 0 3 0 -1.59276 -1.59276 15 1 0 2 0.78303 0.78303 16 1 1 1 -0.207487 -0.207487 17 1 2 0 0.578743 0.578743 18 2 0 1 -0.0632 -0.0632 19 2 1 0 -0.101556 -0.101556 20 3 0 0 1.97753 1.97753 hermite_product_polynomial_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. 19-Dec-2022 15:03:58