[Scipy-svn] r6940 - trunk/scipy/special/specfun
scipy-svn at scipy.org
scipy-svn at scipy.org
Tue Nov 23 16:23:11 EST 2010
Author: ptvirtan
Date: 2010-11-23 15:23:10 -0600 (Tue, 23 Nov 2010)
New Revision: 6940
Modified:
trunk/scipy/special/specfun/specfun.f
Log:
STY: special: strip trailing whitespace from specfun.f
Modified: trunk/scipy/special/specfun/specfun.f
===================================================================
--- trunk/scipy/special/specfun/specfun.f 2010-11-23 14:28:52 UTC (rev 6939)
+++ trunk/scipy/special/specfun/specfun.f 2010-11-23 21:23:10 UTC (rev 6940)
@@ -1,15 +1,15 @@
C COMPUTATION OF SPECIAL FUNCTIONS
-C
+C
C Shanjie Zhang and Jianming Jin
C
-C Copyrighted but permission granted to use code in programs.
+C Copyrighted but permission granted to use code in programs.
C Buy their book "Computation of Special Functions", 1996, John Wiley & Sons, Inc.
C
C
C Compiled into a single source file and changed REAL To DBLE throughout.
C
C Changed according to ERRATA also.
-C
+C
C Changed GAMMA to GAMMA2 and PSI to PSI_SPEC to avoid potential conflicts.
C
@@ -65,7 +65,7 @@
END
-
+
C **********************************
SUBROUTINE CFS(Z,ZF,ZD)
@@ -135,7 +135,7 @@
C ==========================================================
C Purpose: Compute the associated Legendre functions of the
C second kind, Qmn(x) and Qmn'(x)
-C Input : x --- Argument of Qmn(x)
+C Input : x --- Argument of Qmn(x)
C m --- Order of Qmn(x) ( m = 0,1,2,… )
C n --- Degree of Qmn(x) ( n = 0,1,2,… )
C mm --- Physical dimension of QM and QD
@@ -224,8 +224,8 @@
SUBROUTINE CLPMN(MM,M,N,X,Y,CPM,CPD)
C
C =========================================================
-C Purpose: Compute the associated Legendre functions Pmn(z)
-C and their derivatives Pmn'(z) for a complex
+C Purpose: Compute the associated Legendre functions Pmn(z)
+C and their derivatives Pmn'(z) for a complex
C argument
C Input : x --- Real part of z
C y --- Imaginary part of z
@@ -336,7 +336,7 @@
END
-
+
C **********************************
C SciPy: Changed P from a character array to an integer array.
SUBROUTINE JDZO(NT,N,M,P,ZO)
@@ -357,9 +357,9 @@
C P(L) --- 0 (TM) or 1 (TE), a code for designating the
C zeros of Jn(x) or Jn'(x).
C In the waveguide applications, the zeros
-C of Jn(x) correspond to TM modes and
+C of Jn(x) correspond to TM modes and
C those of Jn'(x) correspond to TE modes
-C Routine called: BJNDD for computing Jn(x), Jn'(x) and
+C Routine called: BJNDD for computing Jn(x), Jn'(x) and
C Jn''(x)
C =============================================================
C
@@ -449,7 +449,7 @@
END
-
+
C **********************************
SUBROUTINE CBK(M,N,C,CV,QT,CK,BK)
@@ -519,13 +519,13 @@
END
-
+
C **********************************
SUBROUTINE CJY01(Z,CBJ0,CDJ0,CBJ1,CDJ1,CBY0,CDY0,CBY1,CDY1)
C
C =======================================================
-C Purpose: Compute Bessel functions J0(z), J1(z), Y0(z),
+C Purpose: Compute Bessel functions J0(z), J1(z), Y0(z),
C Y1(z), and their derivatives for a complex
C argument
C Input : z --- Complex argument
@@ -670,9 +670,9 @@
C of the second kind with a small argument
C Routines called:
C (1) LPMNS for computing the associated Legendre
-C functions of the first kind
+C functions of the first kind
C (2) LQMNS for computing the associated Legendre
-C functions of the second kind
+C functions of the second kind
C (3) KMN for computing expansion coefficients
C and joining factors
C ======================================================
@@ -767,7 +767,7 @@
END
-
+
C **********************************
SUBROUTINE BERNOB(N,BN)
@@ -780,7 +780,7 @@
C
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION BN(0:N)
- TPI=6.283185307179586D0
+ TPI=6.283185307179586D0
BN(0)=1.0D0
BN(1)=-0.5D0
BN(2)=1.0D0/6.0D0
@@ -847,7 +847,7 @@
10 SK=SK+CK(K+1)*CK(L-K+1)
15 S=S+SK*AP(I-L+1)
20 AP(I+1)=-R*S
- QS0=AP(M+1)
+ QS0=AP(M+1)
DO 30 L=1,M
R=1.0D0
DO 25 K=1,L
@@ -859,7 +859,7 @@
END
-
+
C **********************************
SUBROUTINE CV0(KD,M,Q,A0)
@@ -1026,7 +1026,7 @@
END
-
+
C **********************************
SUBROUTINE CVQM(M,Q,A0)
@@ -1083,7 +1083,7 @@
END
-
+
C **********************************
SUBROUTINE CSPHJY(N,Z,NM,CSJ,CDJ,CSY,CDY)
@@ -1169,12 +1169,12 @@
INTEGER FUNCTION MSTA1(X,MP)
C
C ===================================================
-C Purpose: Determine the starting point for backward
-C recurrence such that the magnitude of
+C Purpose: Determine the starting point for backward
+C recurrence such that the magnitude of
C Jn(x) at that point is about 10^(-MP)
C Input : x --- Argument of Jn(x)
C MP --- Value of magnitude
-C Output: MSTA1 --- Starting point
+C Output: MSTA1 --- Starting point
C ===================================================
C
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
@@ -1183,8 +1183,8 @@
F0=ENVJ(N0,A0)-MP
N1=N0+5
F1=ENVJ(N1,A0)-MP
- DO 10 IT=1,20
- NN=N1-(N1-N0)/(1.0D0-F0/F1)
+ DO 10 IT=1,20
+ NN=N1-(N1-N0)/(1.0D0-F0/F1)
F=ENVJ(NN,A0)-MP
IF(ABS(NN-N1).LT.1) GO TO 20
N0=N1
@@ -1442,7 +1442,7 @@
END
-
+
C **********************************
SUBROUTINE RMN2L(M,N,C,X,DF,KD,R2F,R2D,ID)
@@ -1453,7 +1453,7 @@
C c and a large cx
C Routine called:
C SPHY for computing the spherical Bessel
-C functions of the second kind
+C functions of the second kind
C ========================================================
C
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
@@ -1471,7 +1471,7 @@
R0=REG
DO 10 J=1,2*M+IP
10 R0=R0*J
- R=R0
+ R=R0
SUC=R*DF(1)
SW=0.0D0
DO 15 K=2,NM
@@ -1503,7 +1503,7 @@
ID=10
RETURN
ENDIF
- B0=KD*M/X**3.0D0/(1.0-KD/(X*X))*R2F
+ B0=KD*M/X**3.0D0/(1.0-KD/(X*X))*R2F
SUD=0.0D0
EPS2=0.0D0
DO 60 K=1,NM
@@ -1520,14 +1520,14 @@
EPS2=DABS(SUD-SW)
IF (K.GT.NM1.AND.EPS2.LT.DABS(SUD)*EPS) GO TO 65
60 SW=SUD
-65 R2D=B0+A0*C*SUD
+65 R2D=B0+A0*C*SUD
ID2=INT(LOG10(EPS2/DABS(SUD)+EPS))
ID=MAX(ID1,ID2)
RETURN
END
-
+
C **********************************
SUBROUTINE PSI_SPEC(X,PS)
@@ -1667,7 +1667,7 @@
END
-
+
C **********************************
SUBROUTINE LPMNS(M,N,X,PM,PD)
@@ -1719,7 +1719,7 @@
PM(K)=PM2
PMK=PM1
25 PM1=PM2
- PD(0)=((1.0D0-M)*PM(1)-X*PM(0))/(X*X-1.0)
+ PD(0)=((1.0D0-M)*PM(1)-X*PM(0))/(X*X-1.0)
DO 30 K=1,N
30 PD(K)=(K*X*PM(K)-(K+M)*PM(K-1))/(X*X-1.0D0)
DO 35 K=1,N
@@ -1822,11 +1822,11 @@
C the second kind
C Routines called:
C (1) SDMN for computing expansion coefficients dk
-C (2) RMN1 for computing prolate and oblate radial
+C (2) RMN1 for computing prolate and oblate radial
C functions of the first kind
C (3) RMN2L for computing prolate and oblate radial
C functions of the second kind for a large argument
-C (4) RMN2SP for computing the prolate radial function
+C (4) RMN2SP for computing the prolate radial function
C of the second kind for a small argument
C ==============================================================
C
@@ -1847,14 +1847,14 @@
END
-
+
C **********************************
SUBROUTINE JYNDD(N,X,BJN,DJN,FJN,BYN,DYN,FYN)
C
C ===========================================================
C Purpose: Compute Bessel functions Jn(x) and Yn(x), and
-C their first and second derivatives
+C their first and second derivatives
C Input: x --- Argument of Jn(x) and Yn(x) ( x > 0 )
C n --- Order of Jn(x) and Yn(x)
C Output: BJN --- Jn(x)
@@ -2012,7 +2012,7 @@
END
-
+
C **********************************
SUBROUTINE CISIA(X,CI,SI)
@@ -2314,7 +2314,7 @@
C KF=1 for Ai(x) and Ai'(x)
C KF=2 for Bi(x) and Bi'(x)
C Output: XA(m) --- a, the m-th zero of Ai(x) or
-C b, the m-th zero of Bi(x)
+C b, the m-th zero of Bi(x)
C XB(m) --- a', the m-th zero of Ai'(x) or
C b', the m-th zero of Bi'(x)
C XC(m) --- Ai(a') or Bi(b')
@@ -2395,7 +2395,7 @@
END
-
+
C **********************************
SUBROUTINE ERROR(X,ERR)
@@ -2473,8 +2473,8 @@
IF (CDABS(CR/CS).LT.1.0D-15) GO TO 15
10 CONTINUE
15 CER=2.0D0*C0*CS/DSQRT(PI)
- ELSE
- CL=1.0D0/Z1
+ ELSE
+ CL=1.0D0/Z1
CR=CL
C
C Asymptotic series; maximum K must be at most ~ R^2.
@@ -2535,7 +2535,7 @@
C
C ============================================================
C Purpose: Compute a sequence of characteristic values of
-C Mathieu functions
+C Mathieu functions
C Input : M --- Maximum order of Mathieu functions
C q --- Parameter of Mathieu functions
C KD --- Case code
@@ -2778,10 +2778,10 @@
C
C ========================================================
C Purpose: Compute the expansion coefficients for the
-C asymptotic expansion of Bessel functions
+C asymptotic expansion of Bessel functions
C with large orders
C Input : Km --- Maximum k
-C Output: A(L) --- Cj(k) where j and k are related to L
+C Output: A(L) --- Cj(k) where j and k are related to L
C by L=j+1+[k*(k+1)]/2; j,k=0,1,...,Km
C ========================================================
C
@@ -2887,12 +2887,12 @@
C Purpose: Compute lambda function with arbitrary order v,
C and their derivative
C Input : x --- Argument of lambda function
-C v --- Order of lambda function
+C v --- Order of lambda function
C Output: VL(n) --- Lambda function of order n+v0
-C DL(n) --- Derivative of lambda function
+C DL(n) --- Derivative of lambda function
C VM --- Highest order computed
C Routines called:
-C (1) MSTA1 and MSTA2 for computing the starting
+C (1) MSTA1 and MSTA2 for computing the starting
C point for backward recurrence
C (2) GAM0 for computing gamma function (|x| ≤ 1)
C =========================================================
@@ -3014,7 +3014,7 @@
END
-
+
C **********************************
SUBROUTINE CHGUIT(A,B,X,HU,ID)
@@ -3116,7 +3116,7 @@
END
-
+
C **********************************
SUBROUTINE KMN(M,N,C,CV,KD,DF,DN,CK1,CK2)
@@ -3136,7 +3136,7 @@
IP=1
IF (N-M.EQ.2*INT((N-M)/2)) IP=0
K=0
- DO 10 I=1,NN+3
+ DO 10 I=1,NN+3
IF (IP.EQ.0) K=-2*(I-1)
IF (IP.EQ.1) K=-(2*I-3)
GK0=2.0D0*M+K
@@ -3204,7 +3204,7 @@
END
-
+
C **********************************
SUBROUTINE LAGZO(N,X,W)
@@ -3298,13 +3298,13 @@
END
-
+
C **********************************
SUBROUTINE CJYVA(V,Z,VM,CBJ,CDJ,CBY,CDY)
C
C ===========================================================
-C Purpose: Compute Bessel functions Jv(z), Yv(z) and their
+C Purpose: Compute Bessel functions Jv(z), Yv(z) and their
C derivatives for a complex argument
C Input : z --- Complex argument
C v --- Order of Jv(z) and Yv(z)
@@ -3345,7 +3345,7 @@
ELSE
CDJ(0)=(1.0D+300,0.0D0)
ENDIF
- VM=V
+ VM=V
RETURN
ENDIF
LB0=0.0D0
@@ -3554,13 +3554,13 @@
END
-
+
C **********************************
SUBROUTINE CJYVB(V,Z,VM,CBJ,CDJ,CBY,CDY)
C
C ===========================================================
-C Purpose: Compute Bessel functions Jv(z), Yv(z) and their
+C Purpose: Compute Bessel functions Jv(z), Yv(z) and their
C derivatives for a complex argument
C Input : z --- Complex argument
C v --- Order of Jv(z) and Yv(z)
@@ -3716,7 +3716,7 @@
END
-
+
C **********************************
SUBROUTINE JY01A(X,BJ0,DJ0,BJ1,DJ1,BY0,DY0,BY1,DY1)
@@ -3852,7 +3852,7 @@
C Purpose: Compute the incomplete gamma function
C r(a,x), Г(a,x) and P(a,x)
C Input : a --- Parameter ( a ≤ 170 )
-C x --- Argument
+C x --- Argument
C Output: GIN --- r(a,x)
C GIM --- Г(a,x)
C GIP --- P(a,x)
@@ -3895,7 +3895,7 @@
END
-
+
C **********************************
SUBROUTINE ITIKB(X,TI,TK)
@@ -4075,7 +4075,7 @@
ELSE
DJ(0)=1.0D+300
ENDIF
- VM=V
+ VM=V
RETURN
ENDIF
BJV0=0.0D0
@@ -4225,7 +4225,7 @@
END
-
+
C **********************************
SUBROUTINE JYNB(N,X,NM,BJ,DJ,BY,DY)
@@ -4253,7 +4253,7 @@
DJ(K) = 0.0D0
10 DY(K) = 1.0D+300
DJ(1)=0.5D0
- ELSE
+ ELSE
DJ(0)=-BJ(1)
DO 40 K=1,NM
40 DJ(K)=BJ(K-1)-K/X*BJ(K)
@@ -4278,7 +4278,7 @@
C BY(n-NMIN) --- Yn(x) ; if indexing starts at 0
C NM --- Highest order computed
C Routines called:
-C MSTA1 and MSTA2 to calculate the starting
+C MSTA1 and MSTA2 to calculate the starting
C point for backward recurrence
C =====================================================
C
@@ -4544,7 +4544,7 @@
END
-
+
C **********************************
SUBROUTINE JYNA(N,X,NM,BJ,DJ,BY,DY)
@@ -4561,7 +4561,7 @@
C NM --- Highest order computed
C Routines called:
C (1) JY01B to calculate J0(x), J1(x), Y0(x) & Y1(x)
-C (2) MSTA1 and MSTA2 to calculate the starting
+C (2) MSTA1 and MSTA2 to calculate the starting
C point for backward recurrence
C =========================================================
C
@@ -4632,7 +4632,7 @@
END
-
+
C **********************************
SUBROUTINE PBDV(V,X,DV,DP,PDF,PDD)
@@ -4644,7 +4644,7 @@
C v --- Order of Dv(x)
C Output: DV(na) --- Dn+v0(x)
C DP(na) --- Dn+v0'(x)
-C ( na = |n|, v0 = v-n, |v0| < 1,
+C ( na = |n|, v0 = v-n, |v0| < 1,
C n = 0,±1,±2,… )
C PDF --- Dv(x)
C PDD --- Dv'(x)
@@ -4748,7 +4748,7 @@
END
-
+
C **********************************
SUBROUTINE ITSH0(X,TH0)
@@ -4763,7 +4763,7 @@
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION A(25)
PI=3.141592653589793D0
- R=1.0D0
+ R=1.0D0
IF (X.LE.30.0) THEN
S=0.5D0
DO 10 K=1,100
@@ -4857,7 +4857,7 @@
END
-
+
C **********************************
SUBROUTINE GAMMA2(X,GA)
@@ -4992,7 +4992,7 @@
END
-
+
C **********************************
SUBROUTINE LAMN(N,X,NM,BL,DL)
@@ -5042,7 +5042,7 @@
35 DL(N)=-0.5D0*X/(N+1.0D0)*UK
RETURN
ENDIF
- IF (N.EQ.0) NM=1
+ IF (N.EQ.0) NM=1
M=MSTA1(X,200)
IF (M.LT.NM) THEN
NM=M
@@ -5150,7 +5150,7 @@
END
-
+
C **********************************
SUBROUTINE CVF(KD,M,Q,A,MJ,F)
@@ -5199,7 +5199,7 @@
END
-
+
C **********************************
SUBROUTINE CLPN(N,X,Y,CPN,CPD)
@@ -5412,7 +5412,7 @@
END
-
+
C **********************************
SUBROUTINE ELIT(HK,PHI,FE,EE)
@@ -5710,7 +5710,7 @@
END
-
+
C **********************************
SUBROUTINE STVH0(X,SH0)
@@ -5952,7 +5952,7 @@
END
-
+
C **********************************
SUBROUTINE CCHG(A,B,Z,CHG)
@@ -6069,13 +6069,13 @@
END
-
+
C **********************************
SUBROUTINE HYGFZ(A,B,C,Z,ZHF)
C
C ======================================================
-C Purpose: Compute the hypergeometric function for a
+C Purpose: Compute the hypergeometric function for a
C complex argument, F(a,b,c,z)
C Input : a --- Parameter
C b --- Parameter
@@ -6146,7 +6146,7 @@
ELSE IF (A0.LE.1.0D0) THEN
IF (X.LT.0.0D0) THEN
Z1=Z/(Z-1.0D0)
- IF (C.GT.A.AND.B.LT.A.AND.B.GT.0.0) THEN
+ IF (C.GT.A.AND.B.LT.A.AND.B.GT.0.0) THEN
A=BB
B=AA
ENDIF
@@ -6360,7 +6360,7 @@
END
-
+
C **********************************
SUBROUTINE ITAIRY(X,APT,BPT,ANT,BNT)
@@ -6481,7 +6481,7 @@
C NM --- Highest order computed
C Routines called:
C (1) IK01A for computing I0(x),I1(x),K0(x) & K1(x)
-C (2) MSTA1 and MSTA2 for computing the starting
+C (2) MSTA1 and MSTA2 for computing the starting
C point for backward recurrence
C ========================================================
C
@@ -6549,7 +6549,7 @@
END
-
+
C **********************************
SUBROUTINE CJYNA(N,Z,NM,CBJ,CDJ,CBY,CDY)
@@ -6566,7 +6566,7 @@
C NM --- Highest order computed
C Rouitines called:
C (1) CJY01 to calculate J0(z), J1(z), Y0(z), Y1(z)
-C (2) MSTA1 and MSTA2 to calculate the starting
+C (2) MSTA1 and MSTA2 to calculate the starting
C point for backward recurrence
C =======================================================
C
@@ -6635,7 +6635,7 @@
CG1=CBY1
DO 90 K=2,NM
CYK=2.0D0*(K-1.0D0)/Z*CG1-CG0
- IF (CDABS(CYK).GT.1.0D+290) GO TO 90
+ IF (CDABS(CYK).GT.1.0D+290) GO TO 90
YAK=CDABS(CYK)
YA1=CDABS(CG0)
IF (YAK.LT.YA0.AND.YAK.LT.YA1) LB=K
@@ -6696,7 +6696,7 @@
END
-
+
C **********************************
SUBROUTINE CJYNB(N,Z,NM,CBJ,CDJ,CBY,CDY)
@@ -6833,7 +6833,7 @@
END
-
+
C **********************************
SUBROUTINE IKNB(N,X,NM,BI,DI,BK,DK)
@@ -6849,7 +6849,7 @@
C DK(n) --- Kn'(x)
C NM --- Highest order computed
C Routines called:
-C MSTA1 and MSTA2 for computing the starting point
+C MSTA1 and MSTA2 for computing the starting point
C for backward recurrence
C ===========================================================
C
@@ -6931,7 +6931,7 @@
SUBROUTINE LPMN(MM,M,N,X,PM,PD)
C
C =====================================================
-C Purpose: Compute the associated Legendre functions
+C Purpose: Compute the associated Legendre functions
C Pmn(x) and their derivatives Pmn'(x)
C Input : x --- Argument of Pmn(x)
C m --- Order of Pmn(x), m = 0,1,2,...,n
@@ -7056,7 +7056,7 @@
END
-
+
C **********************************
SUBROUTINE CY01(KF,Z,ZF,ZD)
@@ -7207,7 +7207,7 @@
SUBROUTINE FFK(KS,X,FR,FI,FM,FA,GR,GI,GM,GA)
C
C =======================================================
-C Purpose: Compute modified Fresnel integrals F±(x)
+C Purpose: Compute modified Fresnel integrals F±(x)
C and K±(x)
C Input : x --- Argument of F±(x) and K±(x)
C KS --- Sign code
@@ -7378,7 +7378,7 @@
END
-
+
C **********************************
SUBROUTINE AIRYB(X,AI,BI,AD,BD)
@@ -7599,7 +7599,7 @@
END
-
+
C **********************************
SUBROUTINE SCKB(M,N,C,DF,CK)
@@ -7649,10 +7649,10 @@
30 R1=R1*I
35 CK(K+1)=FAC*SUM/R1
RETURN
- END
+ END
-
+
C **********************************
SUBROUTINE CPDLA(N,Z,CDN)
@@ -7680,7 +7680,7 @@
END
-
+
C **********************************
SUBROUTINE FCSZO(KF,NT,ZO)
@@ -7692,7 +7692,7 @@
C KF=1 for C(z) or KF=2 for S(z)
C NT --- Total number of zeros
C Output: ZO(L) --- L-th zero of C(z) or S(z)
-C Routines called:
+C Routines called:
C (1) CFC for computing Fresnel integral C(z)
C (2) CFS for computing Fresnel integral S(z)
C ==============================================================
@@ -7740,14 +7740,14 @@
END
-
+
C **********************************
SUBROUTINE E1XA(X,E1)
C
C ============================================
C Purpose: Compute exponential integral E1(x)
-C Input : x --- Argument of E1(x)
+C Input : x --- Argument of E1(x)
C Output: E1 --- E1(x) ( x > 0 )
C ============================================
C
@@ -7773,7 +7773,7 @@
C
C =======================================================
C Purpose: Compute the associated Legendre function
-C Pmv(x) with an integer order and an arbitrary
+C Pmv(x) with an integer order and an arbitrary
C nonnegative degree v
C Input : x --- Argument of Pm(x) ( -1 ≤ x ≤ 1 )
C m --- Order of Pmv(x)
@@ -7865,7 +7865,7 @@
END
-
+
C **********************************
SUBROUTINE CGAMA(X,Y,KF,GR,GI)
@@ -7998,7 +7998,7 @@
END
-
+
C **********************************
SUBROUTINE CHGUS(A,B,X,HU,ID)
@@ -8047,7 +8047,7 @@
END
-
+
C **********************************
SUBROUTINE ITTH0(X,TTH)
@@ -8185,7 +8185,7 @@
C ====================================================
C
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
- PI=3.141592653589793D0
+ PI=3.141592653589793D0
EPS=1.0D-12
EP=DEXP(-.25*X*X)
A0=DABS(X)**VA*EP
@@ -8207,7 +8207,7 @@
END
-
+
C **********************************
SUBROUTINE IK01A(X,BI0,DI0,BI1,DI1,BK0,DK0,BK1,DK1)
@@ -8322,7 +8322,7 @@
SUBROUTINE CPBDN(N,Z,CPB,CPD)
C
C ==================================================
-C Purpose: Compute the parabolic cylinder functions
+C Purpose: Compute the parabolic cylinder functions
C Dn(z) and Dn'(z) for a complex argument
C Input: z --- Complex argument of Dn(z)
C n --- Order of Dn(z) ( n=0,±1,±2,… )
@@ -8410,7 +8410,7 @@
END
-
+
C **********************************
SUBROUTINE IK01B(X,BI0,DI0,BI1,DI1,BK0,DK0,BK1,DK1)
@@ -8508,7 +8508,7 @@
END
-
+
C **********************************
SUBROUTINE LPN(N,X,PN,PD)
@@ -8730,13 +8730,13 @@
ENDIF
85 IF (FC(1).LT.0.0D0) THEN
DO 90 J=1,KM
-90 FC(J)=-FC(J)
+90 FC(J)=-FC(J)
ENDIF
RETURN
END
-
+
C **********************************
SUBROUTINE SPHI(N,X,NM,SI,DI)
@@ -8892,7 +8892,7 @@
END
-
+
C **********************************
SUBROUTINE RMN1(M,N,C,X,DF,KD,R1F,R1D)
@@ -8904,7 +8904,7 @@
C Routines called:
C (1) SCKB for computing expansion coefficients c2k
C (2) SPHJ for computing the spherical Bessel
-C functions of the first kind
+C functions of the first kind
C =======================================================
C
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
@@ -8919,7 +8919,7 @@
R0=REG
DO 10 J=1,2*M+IP
10 R0=R0*J
- R=R0
+ R=R0
SUC=R*DF(1)
SW=0.0D0
DO 15 K=2,NM
@@ -8958,7 +8958,7 @@
CX=C*X
NM2=2*NM+M
CALL SPHJ(NM2,CX,NM2,SJ,DJ)
- A0=(1.0D0-KD/(X*X))**(0.5D0*M)/SUC
+ A0=(1.0D0-KD/(X*X))**(0.5D0*M)/SUC
R1F=0.0D0
SW=0.0D0
LG=0
@@ -8976,7 +8976,7 @@
IF (K.GT.NM1.AND.DABS(R1F-SW).LT.DABS(R1F)*EPS) GO TO 55
50 SW=R1F
55 R1F=R1F*A0
- B0=KD*M/X**3.0D0/(1.0-KD/(X*X))*R1F
+ B0=KD*M/X**3.0D0/(1.0-KD/(X*X))*R1F
SUD=0.0D0
SW=0.0D0
DO 60 K=1,NM
@@ -8997,7 +8997,7 @@
END
-
+
C **********************************
SUBROUTINE DVSA(VA,X,PD)
@@ -9049,7 +9049,7 @@
END
-
+
C **********************************
SUBROUTINE E1Z(Z,CE1)
@@ -9193,7 +9193,7 @@
END
-
+
C **********************************
SUBROUTINE GMN(M,N,C,X,BK,GF,GD)
@@ -9232,7 +9232,7 @@
END
-
+
C **********************************
SUBROUTINE ITJYA(X,TJ,TY)
@@ -9388,7 +9388,7 @@
END
-
+
C **********************************
SUBROUTINE RCTY(N,X,NM,RY,DY)
@@ -9751,14 +9751,14 @@
END
-
+
C **********************************
SUBROUTINE CYZO(NT,KF,KC,ZO,ZV)
C
C ===========================================================
C Purpose : Compute the complex zeros of Y0(z), Y1(z) and
-C Y1'(z), and their associated values at the zeros
+C Y1'(z), and their associated values at the zeros
C using the modified Newton's iteration method
C Input: NT --- Total number of zeros/roots
C KF --- Function choice code
@@ -9833,7 +9833,7 @@
END
-
+
C **********************************
SUBROUTINE KLVNB(X,BER,BEI,GER,GEI,DER,DEI,HER,HEI)
@@ -10009,7 +10009,7 @@
END
-
+
C **********************************
SUBROUTINE CSPHIK(N,Z,NM,CSI,CDI,CSK,CDK)
@@ -10033,7 +10033,7 @@
DOUBLE PRECISION A0,PI
DIMENSION CSI(0:N),CDI(0:N),CSK(0:N),CDK(0:N)
PI=3.141592653589793D0
- A0=CDABS(Z)
+ A0=CDABS(Z)
NM=N
IF (A0.LT.1.0D-60) THEN
DO 10 K=0,N
@@ -10199,7 +10199,7 @@
END
-
+
C **********************************
SUBROUTINE OTHPL(KF,N,X,PL,DPL)
@@ -10323,7 +10323,7 @@
END
-
+
C **********************************
SUBROUTINE RSWFO(M,N,C,X,CV,KF,R1F,R1D,R2F,R2D)
@@ -10376,7 +10376,7 @@
END
-
+
C **********************************
SUBROUTINE CH12N(N,Z,NM,CHF1,CHD1,CHF2,CHD2)
@@ -10441,7 +10441,7 @@
END
-
+
C **********************************
SUBROUTINE JYZO(N,NT,RJ0,RJ1,RY0,RY1)
@@ -10520,7 +10520,7 @@
X=1.19477+1.08933*N
ELSE
X=N+0.93158*N**0.33333+0.26035/N**0.33333
- ENDIF
+ ENDIF
L=0
XGUESS=X
20 X0=X
@@ -10544,7 +10544,7 @@
X=2.67257+1.16099*N
ELSE
X=N+1.8211*N**0.33333+0.94001/N**0.33333
- ENDIF
+ ENDIF
L=0
XGUESS=X
25 X0=X
@@ -10565,7 +10565,7 @@
END
-
+
C **********************************
SUBROUTINE IKV(V,X,VM,BI,DI,BK,DK)
@@ -10714,7 +10714,7 @@
END
-
+
C **********************************
SUBROUTINE SDMN(M,N,C,CV,KD,DF)
@@ -10742,7 +10742,7 @@
5 DF(I)=0D0
DF((N-M)/2+1)=1.0D0
RETURN
- ENDIF
+ ENDIF
CS=C*C*KD
IP=1
K=0
@@ -10776,7 +10776,7 @@
12 DF(K1)=DF(K1)*1.0D-100
F1=F1*1.0D-100
F0=F0*1.0D-100
- ENDIF
+ ENDIF
ELSE
KB=K
FL=DF(K+1)
@@ -10788,7 +10788,7 @@
ELSE IF (KB.EQ.2) THEN
DF(2)=F2
FS=-((D(2)-CV)*F2+G(2)*F1)/A(2)
- ELSE
+ ELSE
DF(2)=F2
DO 20 J=3,KB+1
F=-((D(J-1)-CV)*F2+G(J-1)*F1)/A(J-1)
@@ -10798,7 +10798,7 @@
15 DF(K1)=DF(K1)*1.0D-100
F=F*1.0D-100
F2=F2*1.0D-100
- ENDIF
+ ENDIF
F1=F2
20 F2=F
FS=F
@@ -10837,7 +10837,7 @@
-
+
C **********************************
SUBROUTINE AJYIK(X,VJ1,VJ2,VY1,VY2,VI1,VI2,VK1,VK2)
@@ -11168,7 +11168,7 @@
END
-
+
C **********************************
SUBROUTINE CIKVA(V,Z,VM,CBI,CDI,CBK,CDK)
@@ -11187,7 +11187,7 @@
C VM --- Highest order computed
C Routines called:
C (1) GAMMA2 for computing the gamma function
-C (2) MSTA1 and MSTA2 for computing the starting
+C (2) MSTA1 and MSTA2 for computing the starting
C point for backward recurrence
C ============================================================
C
@@ -11336,7 +11336,7 @@
END
-
+
C **********************************
SUBROUTINE CFC(Z,ZF,ZD)
@@ -11399,7 +11399,7 @@
END
-
+
C **********************************
SUBROUTINE FCS(X,C,S)
@@ -11808,7 +11808,7 @@
END
-
+
C **********************************
SUBROUTINE GAIH(X,GA)
@@ -11958,7 +11958,7 @@
END
-
+
C **********************************
SUBROUTINE CLQMN(MM,M,N,X,Y,CQM,CQD)
@@ -12081,7 +12081,7 @@
DO 5 I=1,N-M+1
5 EG(I)=(I+M)*(I+M-1.0D0)
GO TO 70
- ENDIF
+ ENDIF
ICM=(N-M+2)/2
NM=10+INT(0.5*(N-M)+C)
CS=C*C*KD
@@ -12339,7 +12339,7 @@
END
-
+
C **********************************
SUBROUTINE MTU12(KF,KC,M,Q,X,F1R,D1R,F2R,D2R)
@@ -12385,7 +12385,7 @@
ELSE
QM=17.0+3.1*SQRT(Q)-.126*Q+.0037*SQRT(Q)*Q
ENDIF
- KM=INT(QM+0.5*M)
+ KM=INT(QM+0.5*M)
CALL FCOEF(KD,M,Q,A,FG)
IC=INT(M/2)+1
IF (KD.EQ.4) IC=M/2
@@ -12465,14 +12465,14 @@
END
-
+
C **********************************
SUBROUTINE CIK01(Z,CBI0,CDI0,CBI1,CDI1,CBK0,CDK0,CBK1,CDK1)
C
C ==========================================================
-C Purpose: Compute modified Bessel functions I0(z), I1(z),
-C K0(z), K1(z), and their derivatives for a
+C Purpose: Compute modified Bessel functions I0(z), I1(z),
+C K0(z), K1(z), and their derivatives for a
C complex argument
C Input : z --- Complex argument
C Output: CBI0 --- I0(z)
@@ -12682,7 +12682,7 @@
SY(0)=-DCOS(X)/X
F0=SY(0)
DY(0)=(DSIN(X)+DCOS(X)/X)/X
- IF (N.LT.1) THEN
+ IF (N.LT.1) THEN
RETURN
ENDIF
SY(1)=(SY(0)-DSIN(X))/X
@@ -12690,7 +12690,7 @@
DO 15 K=2,N
F=(2.0D0*K-1.0D0)*F1/X-F0
SY(K)=F
- IF (DABS(F).GE.1.0D+300) GO TO 20
+ IF (DABS(F).GE.1.0D+300) GO TO 20
F0=F1
15 F1=F
20 NM=K-1
@@ -12700,7 +12700,7 @@
END
-
+
C **********************************
SUBROUTINE JELP(U,HK,ESN,ECN,EDN,EPH)
@@ -12862,7 +12862,7 @@
BJ0=SR*(PU0*DCOS(T0)-QU0*DSIN(T0))
BJ1=SR*(PU1*DCOS(T1)-QU1*DSIN(T1))
C Forward recurrence for J_|v| (Abm & Stg 9.1.27)
-C It's OK for the limited range -8.0 ≤ v ≤ 12.5,
+C It's OK for the limited range -8.0 ≤ v ≤ 12.5,
C since x >= 20 here; but would be unstable for v <~ -20
BF0=BJ0
BF1=BJ1
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