dcylbs.f 2.37 KB
 Gregor Michalicek committed Jun 29, 2016 1 2 3 4 5 6 ``````!-------------------------------------------------------------------------------- ! Copyright (c) 2016 Peter Grünberg Institut, Forschungszentrum Jülich, Germany ! This file is part of FLEUR and available as free software under the conditions ! of the MIT license as expressed in the LICENSE file in more detail. !-------------------------------------------------------------------------------- `````` Markus Betzinger committed Apr 26, 2016 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 `````` MODULE m_dcylbs !******************************************************************** ! calculates the derivative of the cylindrical bessel functions ! for the given argument x amd m=-mmax,mmax ! for l=0,lmax and argument x ! note that the cylindrical bessel functions fj(m), m=-mmax,mmax are ! needed (call cylbes to generate those) ! Y.Mokrousov !******************************************************************** CONTAINS SUBROUTINE dcylbs( > mmax,x,fJ, < dfJ) IMPLICIT NONE ! .. ! .. Arguments .. INTEGER, INTENT (IN) :: mmax REAL, INTENT (IN) :: x REAL, INTENT (IN) :: fJ(-mmax:mmax) REAL, INTENT (OUT) :: dfJ(-mmax:mmax) ! ! .. Parameters .. REAL, PARAMETER :: xlim = 1.0e-04, zero = 0.0 ! .. ! .. Local Scalars .. INTEGER m REAL a,b dfJ(0) = -fJ(1) IF (x .EQ. zero) THEN dfJ(1) = 0.5 dfJ(-1) = -0.5 DO m = 2,mmax dfJ(m) = zero dfJ(-m) = zero END DO ELSE c---> possible calculation of the derivatives of cylindrical Bessel c---> functions using first two terms of series representation of c---> them for small x, error is ~xlim**2 (Y.Mokrousov) c IF (x .LT. xlim) THEN c a = 0.5 c b = 0.75 c dfJ(1) = a - b*((x/2.)**2) c dfJ(-1) = -dfJ(1) c DO m = 2,mmax c a = (1./(m-1))*a c b = b*(2+m)/((m+1)**2) c dfJ(m) = a*((x/2.)**(m-1)) - b*((x/2.)**(m+1)) c dfJ(-m) = ((-1)**m)*dfJ(m) c END DO c ELSE c------------------------------------------------------------------ DO m = 1,mmax dfJ(m) = fJ(m-1) - m*fJ(m)/x dfJ(-m) = ((-1)**m)*dfJ(m) ENDDO c ENDIF END IF RETURN END SUBROUTINE dcylbs END MODULE m_dcylbs ``````