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module paramdef
type parameters
sequence
integer :: n
integer :: m
real*4 :: beta
real*4 :: gamma
real*4 :: delta
real*4 :: l
real*4 :: tau(3)
real*4 :: theta(3)
real*4 :: lambda
end type parameters
end module
module param
use paramdef
type (parameters) :: params
real*8 :: ALPHA(25)
end module
PROGRAM BESSEL_TEST
use paramdef ! Used to define the "parameters" type
use param !
implicit none
real*8 :: ALPHAJ1(25),RY0(25),RY1(25)
real*8 :: A,B,BESSJ0
call JYZO(0,25,ALPHA,ALPHAJ1,RY0,RY1)
!case 1
A=1
B=BESSJ0(1)
print*,A,B
!case 2
A=real(1,8)
B=BESSJ0(A)
print*,A,B
!case 3
A=1
B=BESSJ0(real(1,8))
print*,A,B
!case 4
A=1
B=BESSJ0(real(A,8))
print*,A,B
!case 4
A=1
B=BESSJ0(A)
print*,A,B
!case 5
A=real(ALPHA(5),8)
B=BESSJ0(A)
print*,A,B
!case 6
A=ALPHA(5)
B=BESSJ0(real(A,8))
print*,A,B
!case 7
A=14.930917708487785
B=BESSJ0(A)
print*,A,B
!case 7
A=14.930917708487785
B=BESSJ0(real(A,8))
print*,A,B
!case 7
A=real(14.930,8)
B=BESSJ0(A)
print*,A,B
return
END PROGRAM BESSEL_TEST
!-----------------------------------------------------------------------
FUNCTION BESSJ0 (X)
REAL *8 X,BESSJ0,AX,FR,FS,Z,FP,FQ,XX
!-----------------------------------------------------------------------
! This subroutine calculates the First Kind Bessel Function of
! order 0, for any real number X. The polynomial approximation by
! series of Chebyshev polynomials is used for 0<X<8 and 0<8/X<1.
! REFERENCES:
! M.ABRAMOWITZ,I.A.STEGUN, HANDBOOK OF MATHEMATICAL FUNCTIONS, 1965.
! C.W.CLENSHAW, NATIONAL PHYSICAL LABORATORY MATHEMATICAL TABLES,
! VOL.5, 1962.
REAL *8 Y,P1,P2,P3,P4,P5,R1,R2,R3,R4,R5,R6 &
,Q1,Q2,Q3,Q4,Q5,S1,S2,S3,S4,S5,S6
DATA P1,P2,P3,P4,P5 /1.D0,-.1098628627D-2,.2734510407D-4, &
-.2073370639D-5,.2093887211D-6 /
DATA Q1,Q2,Q3,Q4,Q5 /-.1562499995D-1,.1430488765D-3, &
-.6911147651D-5,.7621095161D-6,-.9349451520D-7 /
DATA R1,R2,R3,R4,R5,R6 /57568490574.D0,-13362590354.D0, &
651619640.7D0,-11214424.18D0,77392.33017D0,-184.9052456D0 /
DATA S1,S2,S3,S4,S5,S6 /57568490411.D0,1029532985.D0, &
9494680.718D0,59272.64853D0,267.8532712D0,1.D0 /
IF(X.EQ.0.D0) GO TO 1
AX = ABS (X)
IF (AX.LT.8.) THEN
Y = X*X
FR = R1+Y*(R2+Y*(R3+Y*(R4+Y*(R5+Y*R6))))
FS = S1+Y*(S2+Y*(S3+Y*(S4+Y*(S5+Y*S6))))
BESSJ0 = FR/FS
ELSE
Z = 8./AX
Y = Z*Z
XX = AX-.785398164
FP = P1+Y*(P2+Y*(P3+Y*(P4+Y*P5)))
FQ = Q1+Y*(Q2+Y*(Q3+Y*(Q4+Y*Q5)))
BESSJ0 = SQRT(.636619772/AX)*(FP*COS(XX)-Z*FQ*SIN(XX))
ENDIF
RETURN
1 BESSJ0 = 1.D0
RETURN
END
! ---------------------------------------------------------------------------
FUNCTION BESSJ1 (X)
REAL *8 X,BESSJ1,AX,FR,FS,Z,FP,FQ,XX
! This subroutine calculates the First Kind Bessel Function of
! order 1, for any real number X. The polynomial approximation by
! series of Chebyshev polynomials is used for 0<X<8 and 0<8/X<1.
! REFERENCES:
! M.ABRAMOWITZ,I.A.STEGUN, HANDBOOK OF MATHEMATICAL FUNCTIONS, 1965.
! C.W.CLENSHAW, NATIONAL PHYSICAL LABORATORY MATHEMATICAL TABLES,
! VOL.5, 1962.
REAL *8 Y,P1,P2,P3,P4,P5,P6,R1,R2,R3,R4,R5,R6 &
,Q1,Q2,Q3,Q4,Q5,S1,S2,S3,S4,S5,S6
DATA P1,P2,P3,P4,P5 /1.D0,.183105D-2,-.3516396496D-4, &
.2457520174D-5,-.240337019D-6 /,P6 /.636619772D0 /
DATA Q1,Q2,Q3,Q4,Q5 /.04687499995D0,-.2002690873D-3, &
.8449199096D-5,-.88228987D-6,.105787412D-6 /
DATA R1,R2,R3,R4,R5,R6 /72362614232.D0,-7895059235.D0, &
242396853.1D0,-2972611.439D0,15704.48260D0,-30.16036606D0 /
DATA S1,S2,S3,S4,S5,S6 /144725228442.D0,2300535178.D0, &
18583304.74D0,99447.43394D0,376.9991397D0,1.D0 /
AX = ABS(X)
IF (AX.LT.8.) THEN
Y = X*X
FR = R1+Y*(R2+Y*(R3+Y*(R4+Y*(R5+Y*R6))))
FS = S1+Y*(S2+Y*(S3+Y*(S4+Y*(S5+Y*S6))))
BESSJ1 = X*(FR/FS)
ELSE
Z = 8./AX
Y = Z*Z
XX = AX-2.35619491
FP = P1+Y*(P2+Y*(P3+Y*(P4+Y*P5)))
FQ = Q1+Y*(Q2+Y*(Q3+Y*(Q4+Y*Q5)))
BESSJ1 = SQRT(P6/AX)*(COS(XX)*FP-Z*SIN(XX)*FQ)*SIGN(S6,X)
ENDIF
RETURN
END
SUBROUTINE JYNDD(N,X,BJN,DJN,FJN,BYN,DYN,FYN)
! ===========================================================
! Purpose: Compute Bessel functions Jn(x) and Yn(x), and
! their first and second derivatives
! Input: x --- Argument of Jn(x) and Yn(x) ( x > 0 )
! n --- Order of Jn(x) and Yn(x)
! Output: BJN --- Jn(x)
! DJN --- Jn'(x)
! FJN --- Jn"(x)
! BYN --- Yn(x)
! DYN --- Yn'(x)
! FYN --- Yn"(x)
! ===========================================================
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION BJ(102),BY(102)
DO 10 NT=1,900
MT=INT(0.5*LOG10(6.28*NT)-NT*LOG10(1.36*DABS(X)/NT))
IF (MT.GT.20) GO TO 15
10 CONTINUE
15 M=NT
BS=0.0D0
F0=0.0D0
F1=1.0D-35
SU=0.0D0
DO 20 K=M,0,-1
F=2.0D0*(K+1.0D0)*F1/X-F0
IF (K.LE.N+1) BJ(K+1)=F
IF (K.EQ.2*INT(K/2)) THEN
BS=BS+2.0D0*F
IF (K.NE.0) SU=SU+(-1)**(K/2)*F/K
ENDIF
F0=F1
20 F1=F
DO 25 K=0,N+1
25 BJ(K+1)=BJ(K+1)/(BS-F)
BJN=BJ(N+1)
EC=0.5772156649015329D0
E0=0.3183098861837907D0
S1=2.0D0*E0*(DLOG(X/2.0D0)+EC)*BJ(1)
F0=S1-8.0D0*E0*SU/(BS-F)
F1=(BJ(2)*F0-2.0D0*E0/X)/BJ(1)
BY(1)=F0
BY(2)=F1
DO 30 K=2,N+1
F=2.0D0*(K-1.0D0)*F1/X-F0
BY(K+1)=F
F0=F1
30 F1=F
BYN=BY(N+1)
DJN=-BJ(N+2)+N*BJ(N+1)/X
DYN=-BY(N+2)+N*BY(N+1)/X
FJN=(N*N/(X*X)-1.0D0)*BJN-DJN/X
FYN=(N*N/(X*X)-1.0D0)*BYN-DYN/X
RETURN
END
! End of file mjyzo.f90
!*********************************************************************
SUBROUTINE JYZO(N,NT,RJ0,RJ1,RY0,RY1)
! ======================================================
! Purpose: Compute the zeros of Bessel functions Jn(x),
! Yn(x), and their derivatives
! Input : n --- Order of Bessel functions (0 to 100)
! NT --- Number of zeros (roots)
! Output: RJ0(L) --- L-th zero of Jn(x), L=1,2,...,NT
! RJ1(L) --- L-th zero of Jn'(x), L=1,2,...,NT
! RY0(L) --- L-th zero of Yn(x), L=1,2,...,NT
! RY1(L) --- L-th zero of Yn'(x), L=1,2,...,NT
! Routine called: JYNDD for computing Jn(x), Yn(x), and
! their first and second derivatives
! ======================================================
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION RJ0(NT),RJ1(NT),RY0(NT),RY1(NT)
IF (N.LE.20) THEN
X=2.82141+1.15859*N
ELSE
X=N+1.85576*N**0.33333+1.03315/N**0.33333
ENDIF
L=0
10 X0=X
CALL JYNDD(N,X,BJN,DJN,FJN,BYN,DYN,FYN)
X=X-BJN/DJN
IF (DABS(X-X0).GT.1.0D-9) GO TO 10
L=L+1
RJ0(L)=X
X=X+3.1416+(0.0972+0.0679*N-0.000354*N**2)/L
IF (L.LT.NT) GO TO 10
IF (N.LE.20) THEN
X=0.961587+1.07703*N
ELSE
X=N+0.80861*N**0.33333+0.07249/N**0.33333
ENDIF
IF (N.EQ.0) X=3.8317
L=0
15 X0=X
CALL JYNDD(N,X,BJN,DJN,FJN,BYN,DYN,FYN)
X=X-DJN/FJN
IF (DABS(X-X0).GT.1.0D-9) GO TO 15
L=L+1
RJ1(L)=X
X=X+3.1416+(0.4955+0.0915*N-0.000435*N**2)/L
IF (L.LT.NT) GO TO 15
IF (N.LE.20) THEN
X=1.19477+1.08933*N
ELSE
X=N+0.93158*N**0.33333+0.26035/N**0.33333
ENDIF
L=0
20 X0=X
CALL JYNDD(N,X,BJN,DJN,FJN,BYN,DYN,FYN)
X=X-BYN/DYN
IF (DABS(X-X0).GT.1.0D-9) GO TO 20
L=L+1
RY0(L)=X
X=X+3.1416+(0.312+0.0852*N-0.000403*N**2)/L
IF (L.LT.NT) GO TO 20
IF (N.LE.20) THEN
X=2.67257+1.16099*N
ELSE
X=N+1.8211*N**0.33333+0.94001/N**0.33333
ENDIF
L=0
25 X0=X
CALL JYNDD(N,X,BJN,DJN,FJN,BYN,DYN,FYN)
X=X-DYN/FYN
IF (DABS(X-X0).GT.1.0D-9) GO TO 25
L=L+1
RY1(L)=X
X=X+3.1416+(0.197+0.0643*N-0.000286*N**2)/L
IF (L.LT.NT) GO TO 25
RETURN
END |
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