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mod_functions.f90
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!***********************************************************
!* This program tests the subroutine BESSK to calculate the*
!* modified Bessel function of the third kind of order N *
!* for any real positive argument X. *
!* ------------------------------------------------------- *
!* SAMPLE RUN: *
!* *
!* X = 1.20970000000000 *
!* *
!* N = 0 *
!* Y = 0.314324491956902 *
!* *
!* N = 1 *
!* Y = 0.428050751380123 *
!* *
!* N = 2 *
!* Y = 1.02202185722122 *
!* *
!* N = 3 *
!* Y = 3.80747327670449 *
!* *
!* N = 4 *
!* Y = 19.9067367949966 *
!* *
!* ------------------------------------------------------- *
!* Reference: From Numath Library By Tuan Dang Trong *
!* in Fortran 77 [BIBLI 18]. *
!* *
!* F90 Version By J-P Moreau, Paris. *
!* (all variables declared) *
!* www.jpmoreau.fr *
!***********************************************************
FUNCTION BESSK(N,X)
IMPLICIT NONE
INTEGER N,J
REAL *8 X,BESSK,BESSK0,BESSK1,TOX,BK,BKM,BKP
! ------------------------------------------------------------------------
! CE SOUS-PROGRAMME CALCULE LA FONCTION BESSEL MODIFIFIEE 3E ESPECE
! D'ORDRE N ENTIER POUR TOUT X REEL POSITIF > 0. ON UTILISE ICI LA
! FORMULE DE RECURRENCE CLASSIQUE EN PARTANT DE BESSK0 ET BESSK1.
!
! THIS ROUTINE CALCULATES THE MODIFIED BESSEL FUNCTION OF THE THIRD
! KIND OF INTEGER ORDER, N FOR ANY POSITIVE REAL ARGUMENT, X. THE
! CLASSICAL RECURSION FORMULA IS USED, STARTING FROM BESSK0 AND BESSK1.
! ------------------------------------------------------------------------
! REFERENCE:
! C.W.CLENSHAW, CHEBYSHEV SERIES FOR MATHEMATICAL FUNCTIONS,
! MATHEMATICAL TABLES, VOL.5, 1962.
! ------------------------------------------------------------------------
IF (N.EQ.0) THEN
BESSK = BESSK0(X)
RETURN
ENDIF
IF (N.EQ.1) THEN
BESSK = BESSK1(X)
RETURN
ENDIF
IF (X.EQ.0.D0) THEN
BESSK = 1.D30
RETURN
ENDIF
TOX = 2.D0/X
BK = BESSK1(X)
BKM = BESSK0(X)
DO 11 J=1,N-1
BKP = BKM+DFLOAT(J)*TOX*BK
BKM = BK
BK = BKP
11 CONTINUE
BESSK = BK
RETURN
END
! ----------------------------------------------------------------------
FUNCTION BESSK0(X)
! CALCUL DE LA FONCTION BESSEL MODIFIEE DU 3EME ESPECE D'ORDRE 0
! POUR TOUT X REEL NON NUL.
!
! CALCULATES THE THE MODIFIED BESSEL FUNCTION OF THE THIRD KIND OF
! ORDER ZERO FOR ANY POSITIVE REAL ARGUMENT, X.
! ----------------------------------------------------------------------
IMPLICIT NONE
REAL*8 X,BESSK0,Y,AX,P1,P2,P3,P4,P5,P6,P7,Q1,Q2,Q3,Q4,Q5,Q6,Q7, &
BESSI0
DATA P1,P2,P3,P4,P5,P6,P7/-0.57721566D0,0.42278420D0,0.23069756D0, &
0.3488590D-1,0.262698D-2,0.10750D-3,0.74D-5/
DATA Q1,Q2,Q3,Q4,Q5,Q6,Q7/1.25331414D0,-0.7832358D-1,0.2189568D-1, &
-0.1062446D-1,0.587872D-2,-0.251540D-2,0.53208D-3/
IF(X.EQ.0.D0) THEN
BESSK0=1.D30
RETURN
ENDIF
IF(X.LE.2.D0) THEN
Y=X*X/4.D0
AX=-LOG(X/2.D0)*BESSI0(X)
BESSK0=AX+(P1+Y*(P2+Y*(P3+Y*(P4+Y*(P5+Y*(P6+Y*P7))))))
ELSE
Y=(2.D0/X)
AX=EXP(-X)/DSQRT(X)
BESSK0=AX*(Q1+Y*(Q2+Y*(Q3+Y*(Q4+Y*(Q5+Y*(Q6+Y*Q7))))))
ENDIF
RETURN
END
! ----------------------------------------------------------------------
FUNCTION BESSK1(X)
! CALCUL DE LA FONCTION BESSEL MODIFIEE DE 3EME ESPECE D'ORDRE 1
! POUR TOUT X REEL POSITF NON NUL.
!
! CALCULATES THE THE MODIFIED BESSEL FUNCTION OF THE THIRD KIND OF
! ORDER ONE FOR ANY POSITIVE REAL ARGUMENT, X.
! ----------------------------------------------------------------------
IMPLICIT NONE
REAL*8 X,BESSK1,Y,AX,P1,P2,P3,P4,P5,P6,P7,Q1,Q2,Q3,Q4,Q5,Q6,Q7,BESSI1
DATA P1,P2,P3,P4,P5,P6,P7/1.D0,0.15443144D0,-0.67278579D0, &
-0.18156897D0,-0.1919402D-1,-0.110404D-2,-0.4686D-4/
DATA Q1,Q2,Q3,Q4,Q5,Q6,Q7/1.25331414D0,0.23498619D0,-0.3655620D-1, &
0.1504268D-1,-0.780353D-2,0.325614D-2,-0.68245D-3/
IF(X.EQ.0.D0) THEN
BESSK1=1.D32
RETURN
ENDIF
IF(X.LE.2.D0) THEN
Y=X*X/4.D0
AX=LOG(X/2.D0)*BESSI1(X)
BESSK1=AX+(1.D0/X)*(P1+Y*(P2+Y*(P3+Y*(P4+Y*(P5+Y*(P6+Y*P7))))))
ELSE
Y=(2.D0/X)
AX=EXP(-X)/DSQRT(X)
BESSK1=AX*(Q1+Y*(Q2+Y*(Q3+Y*(Q4+Y*(Q5+Y*(Q6+Y*Q7))))))
ENDIF
RETURN
END
!
! Bessel Function of the 1st kind of order zero.
!
FUNCTION BESSI0(X)
IMPLICIT NONE
REAL *8 X,BESSI0,Y,P1,P2,P3,P4,P5,P6,P7,Q1,Q2,Q3,Q4,Q5,Q6,Q7,Q8,Q9,AX,BX
DATA P1,P2,P3,P4,P5,P6,P7/1.D0,3.5156229D0,3.0899424D0,1.2067429D0, &
0.2659732D0,0.360768D-1,0.45813D-2/
DATA Q1,Q2,Q3,Q4,Q5,Q6,Q7,Q8,Q9/0.39894228D0,0.1328592D-1, &
0.225319D-2,-0.157565D-2,0.916281D-2,-0.2057706D-1, &
0.2635537D-1,-0.1647633D-1,0.392377D-2/
IF(ABS(X).LT.3.75D0) THEN
Y=(X/3.75D0)**2
BESSI0=P1+Y*(P2+Y*(P3+Y*(P4+Y*(P5+Y*(P6+Y*P7)))))
ELSE
AX=ABS(X)
Y=3.75D0/AX
BX=EXP(AX)/DSQRT(AX)
AX=Q1+Y*(Q2+Y*(Q3+Y*(Q4+Y*(Q5+Y*(Q6+Y*(Q7+Y*(Q8+Y*Q9)))))))
BESSI0=AX*BX
ENDIF
RETURN
END
!
! Bessel Function of the 1st kind of order one.
!
FUNCTION BESSI1(X)
IMPLICIT NONE
REAL *8 X,BESSI1,Y,P1,P2,P3,P4,P5,P6,P7,Q1,Q2,Q3,Q4,Q5,Q6,Q7,Q8,Q9,AX,BX
DATA P1,P2,P3,P4,P5,P6,P7/0.5D0,0.87890594D0,0.51498869D0, &
0.15084934D0,0.2658733D-1,0.301532D-2,0.32411D-3/
DATA Q1,Q2,Q3,Q4,Q5,Q6,Q7,Q8,Q9/0.39894228D0,-0.3988024D-1, &
-0.362018D-2,0.163801D-2,-0.1031555D-1,0.2282967D-1, &
-0.2895312D-1,0.1787654D-1,-0.420059D-2/
IF(ABS(X).LT.3.75D0) THEN
Y=(X/3.75D0)**2
BESSI1=X*(P1+Y*(P2+Y*(P3+Y*(P4+Y*(P5+Y*(P6+Y*P7))))))
ELSE
AX=ABS(X)
Y=3.75D0/AX
BX=EXP(AX)/DSQRT(AX)
AX=Q1+Y*(Q2+Y*(Q3+Y*(Q4+Y*(Q5+Y*(Q6+Y*(Q7+Y*(Q8+Y*Q9)))))))
BESSI1=AX*BX
ENDIF
RETURN
END
! End of file Tbessk.f90