23 October 2014 08:30:37 AM
HPP_PRB:
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).
HPP_PRB:
Normal end of execution.
23 October 2014 08:30:37 AM