The Elk Code
hermite.f90
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1 
2 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl.
3 ! This file is distributed under the terms of the GNU Lesser General Public
4 ! License. See the file COPYING for license details.
5 
6 !BOP
7 ! !ROUTINE: hermite
8 ! !INTERFACE:
9 real(8) function hermite(n,x)
10 ! !INPUT/OUTPUT PARAMETERS:
11 ! n : order of Hermite polynomial (in,integer)
12 ! x : real argument (in,real)
13 ! !DESCRIPTION:
14 ! Returns the $n$th Hermite polynomial. The recurrence relation
15 ! $$ H_i(x)=2xH_{i-1}(x)-2nH_{i-2}(x), $$
16 ! with $H_0=1$ and $H_1=2x$, is used. This procedure is numerically stable
17 ! and accurate to near machine precision for $n\le 20$.
18 !
19 ! !REVISION HISTORY:
20 ! Created April 2003 (JKD)
21 !EOP
22 !BOC
23 implicit none
24 ! arguments
25 integer, intent(in) :: n
26 real(8), intent(in) :: x
27 ! local variables
28 integer i
29 real(8) h1,h2,ht
30 ! fast return if possible
31 if (n == 0) then
32  hermite=1.d0
33  return
34 else if (n == 1) then
35  hermite=2.d0*x
36  return
37 else if (n == 2) then
38  hermite=4.d0*x**2-2.d0
39  return
40 end if
41 if (n < 0) then
42  write(*,*)
43  write(*,'("Error(hermite): n < 0 : ",I8)') n
44  write(*,*)
45  stop
46 end if
47 if (n > 20) then
48  write(*,*)
49  write(*,'("Error(hermite): n out of range : ",I8)') n
50  write(*,*)
51  stop
52 end if
53 if (abs(x) > 1.d15) then
54  write(*,*)
55  write(*,'("Error(hermite): x out of range : ",G18.10)') x
56  write(*,*)
57  stop
58 end if
59 h1=2.d0*x
60 h2=1.d0
61 do i=2,n
62  ht=2.d0*(x*h1-dble(i-1)*h2)
63  h2=h1
64  h1=ht
65 end do
66 hermite=h1
67 end function
68 !EOC
69 
hermite
real(8) function hermite(n, x)
Definition: hermite.f90:10