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69 lines
2.2 KiB
Fortran
69 lines
2.2 KiB
Fortran
*DECK DXPMU
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SUBROUTINE DXPMU (NU1, NU2, MU1, MU2, THETA, X, SX, ID, PQA, IPQA,
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1 IERROR)
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C***BEGIN PROLOGUE DXPMU
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C***SUBSIDIARY
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C***PURPOSE To compute the values of Legendre functions for DXLEGF.
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C Method: backward mu-wise recurrence for P(-MU,NU,X) for
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C fixed nu to obtain P(-MU2,NU1,X), P(-(MU2-1),NU1,X), ...,
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C P(-MU1,NU1,X) and store in ascending mu order.
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C***LIBRARY SLATEC
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C***CATEGORY C3A2, C9
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C***TYPE DOUBLE PRECISION (XPMU-S, DXPMU-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 DXADD, DXADJ, DXPQNU
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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 Changed all specific intrinsics to generic. (WRB)
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C 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 DXPMU
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DOUBLE PRECISION PQA,NU1,NU2,P0,X,SX,THETA,X1,X2
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DIMENSION PQA(*),IPQA(*)
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C
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C CALL DXPQNU TO OBTAIN P(-MU2,NU,X)
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C
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C***FIRST EXECUTABLE STATEMENT DXPMU
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IERROR=0
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CALL DXPQNU(NU1,NU2,MU2,THETA,ID,PQA,IPQA,IERROR)
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IF (IERROR.NE.0) RETURN
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P0=PQA(1)
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IP0=IPQA(1)
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MU=MU2-1
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C
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C CALL DXPQNU TO OBTAIN P(-MU2-1,NU,X)
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C
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CALL DXPQNU(NU1,NU2,MU,THETA,ID,PQA,IPQA,IERROR)
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IF (IERROR.NE.0) RETURN
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N=MU2-MU1+1
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PQA(N)=P0
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IPQA(N)=IP0
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IF(N.EQ.1) GO TO 300
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PQA(N-1)=PQA(1)
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IPQA(N-1)=IPQA(1)
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IF(N.EQ.2) GO TO 300
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J=N-2
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290 CONTINUE
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C
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C BACKWARD RECURRENCE IN MU TO OBTAIN
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C P(-MU2,NU1,X),P(-(MU2-1),NU1,X),....P(-MU1,NU1,X)
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C USING
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C (NU-MU)*(NU+MU+1.)*P(-(MU+1),NU,X)=
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C 2.*MU*X*SQRT((1./(1.-X**2))*P(-MU,NU,X)-P(-(MU-1),NU,X)
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C
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X1=2.D0*MU*X*SX*PQA(J+1)
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X2=-(NU1-MU)*(NU1+MU+1.D0)*PQA(J+2)
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CALL DXADD(X1,IPQA(J+1),X2,IPQA(J+2),PQA(J),IPQA(J),IERROR)
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IF (IERROR.NE.0) RETURN
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CALL DXADJ(PQA(J),IPQA(J),IERROR)
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IF (IERROR.NE.0) RETURN
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IF(J.EQ.1) GO TO 300
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J=J-1
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MU=MU-1
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GO TO 290
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300 RETURN
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END
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