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124 lines
3.2 KiB
Fortran
124 lines
3.2 KiB
Fortran
*DECK XQNU
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SUBROUTINE XQNU (NU1, NU2, MU1, THETA, X, SX, ID, PQA, IPQA,
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1 IERROR)
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C***BEGIN PROLOGUE XQNU
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C***SUBSIDIARY
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C***PURPOSE To compute the values of Legendre functions for XLEGF.
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C Method: backward nu-wise recurrence for Q(MU,NU,X) for
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C fixed mu to obtain Q(MU1,NU1,X), Q(MU1,NU1+1,X), ...,
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C Q(MU1,NU2,X).
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C***LIBRARY SLATEC
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C***CATEGORY C3A2, C9
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C***TYPE SINGLE PRECISION (XQNU-S, DXQNU-D)
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C***KEYWORDS LEGENDRE FUNCTIONS
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C***AUTHOR Smith, John M., (NBS and George Mason University)
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C***ROUTINES CALLED XADD, XADJ, XPQNU
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C***REVISION HISTORY (YYMMDD)
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C 820728 DATE WRITTEN
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C 890126 Revised to meet SLATEC CML recommendations. (DWL and JMS)
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C 901019 Revisions to prologue. (DWL and WRB)
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C 901106 Corrected order of sections in prologue and added TYPE
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C section. (WRB)
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C 920127 Revised PURPOSE section of prologue. (DWL)
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C***END PROLOGUE XQNU
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DIMENSION PQA(*),IPQA(*)
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REAL DMU,NU,NU1,NU2,PQ,PQA,PQ1,PQ2,SX,X,X1,X2
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REAL THETA,PQL1,PQL2
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C***FIRST EXECUTABLE STATEMENT XQNU
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IERROR=0
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K=0
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PQ2=0.0
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IPQ2=0
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PQL2=0.0
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IPQL2=0
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IF(MU1.EQ.1) GO TO 290
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MU=0
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C
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C CALL XPQNU TO OBTAIN Q(0.,NU2,X) AND Q(0.,NU2-1,X)
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C
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CALL XPQNU(NU1,NU2,MU,THETA,ID,PQA,IPQA,IERROR)
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IF (IERROR.NE.0) RETURN
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IF(MU1.EQ.0) RETURN
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K=(NU2-NU1+1.5)
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PQ2=PQA(K)
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IPQ2=IPQA(K)
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PQL2=PQA(K-1)
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IPQL2=IPQA(K-1)
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290 MU=1
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C
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C CALL XPQNU TO OBTAIN Q(1.,NU2,X) AND Q(1.,NU2-1,X)
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C
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CALL XPQNU(NU1,NU2,MU,THETA,ID,PQA,IPQA,IERROR)
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IF (IERROR.NE.0) RETURN
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IF(MU1.EQ.1) RETURN
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NU=NU2
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PQ1=PQA(K)
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IPQ1=IPQA(K)
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PQL1=PQA(K-1)
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IPQL1=IPQA(K-1)
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300 MU=1
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DMU=1.
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320 CONTINUE
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C
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C FORWARD RECURRENCE IN MU TO OBTAIN Q(MU1,NU2,X) AND
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C Q(MU1,NU2-1,X) USING
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C Q(MU+1,NU,X)=-2.*MU*X*SQRT(1./(1.-X**2))*Q(MU,NU,X)
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C -(NU+MU)*(NU-MU+1.)*Q(MU-1,NU,X)
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C
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C FIRST FOR NU=NU2
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C
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X1=-2.*DMU*X*SX*PQ1
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X2=(NU+DMU)*(NU-DMU+1.)*PQ2
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CALL XADD(X1,IPQ1,-X2,IPQ2,PQ,IPQ,IERROR)
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IF (IERROR.NE.0) RETURN
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CALL XADJ(PQ,IPQ,IERROR)
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IF (IERROR.NE.0) RETURN
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PQ2=PQ1
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IPQ2=IPQ1
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PQ1=PQ
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IPQ1=IPQ
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MU=MU+1
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DMU=DMU+1.
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IF(MU.LT.MU1) GO TO 320
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PQA(K)=PQ
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IPQA(K)=IPQ
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IF(K.EQ.1) RETURN
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IF(NU.LT.NU2) GO TO 340
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C
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C THEN FOR NU=NU2-1
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C
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NU=NU-1.
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PQ2=PQL2
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IPQ2=IPQL2
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PQ1=PQL1
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IPQ1=IPQL1
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K=K-1
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GO TO 300
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C
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C BACKWARD RECURRENCE IN NU TO OBTAIN
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C Q(MU1,NU1,X),Q(MU1,NU1+1,X),....,Q(MU1,NU2,X)
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C USING
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C (NU-MU+1.)*Q(MU,NU+1,X)=
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C (2.*NU+1.)*X*Q(MU,NU,X)-(NU+MU)*Q(MU,NU-1,X)
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C
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340 PQ1=PQA(K)
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IPQ1=IPQA(K)
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PQ2=PQA(K+1)
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IPQ2=IPQA(K+1)
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350 IF(NU.LE.NU1) RETURN
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K=K-1
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X1=(2.*NU+1.)*X*PQ1/(NU+DMU)
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X2=-(NU-DMU+1.)*PQ2/(NU+DMU)
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CALL XADD(X1,IPQ1,X2,IPQ2,PQ,IPQ,IERROR)
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IF (IERROR.NE.0) RETURN
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CALL XADJ(PQ,IPQ,IERROR)
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IF (IERROR.NE.0) RETURN
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PQ2=PQ1
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IPQ2=IPQ1
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PQ1=PQ
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IPQ1=IPQ
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PQA(K)=PQ
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IPQA(K)=IPQ
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NU=NU-1.
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GO TO 350
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END
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