mirror of https://gitlab.com/QEF/q-e.git
51 lines
1.5 KiB
FortranFixed
51 lines
1.5 KiB
FortranFixed
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SUBROUTINE LAGZO(N,X,W)
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C
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C =========================================================
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C Purpose : Compute the zeros of Laguerre polynomial Ln(x)
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C in the interval [0,<2C>], and the corresponding
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C weighting coefficients for Gauss-Laguerre
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C integration
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C Input : n --- Order of the Laguerre polynomial
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C X(n) --- Zeros of the Laguerre polynomial
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C W(n) --- Corresponding weighting coefficients
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C =========================================================
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C
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IMPLICIT DOUBLE PRECISION (A-H,O-Z)
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DIMENSION X(N),W(N)
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HN=1.0D0/N
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DO 35 NR=1,N
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IF (NR.EQ.1) Z=HN
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IF (NR.GT.1) Z=X(NR-1)+HN*NR**1.27
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IT=0
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10 IT=IT+1
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Z0=Z
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P=1.0D0
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DO 15 I=1,NR-1
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15 P=P*(Z-X(I))
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F0=1.0D0
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F1=1.0D0-Z
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DO 20 K=2,N
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PF=((2.0D0*K-1.0D0-Z)*F1-(K-1.0D0)*F0)/K
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PD=K/Z*(PF-F1)
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F0=F1
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20 F1=PF
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FD=PF/P
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Q=0.0D0
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DO 30 I=1,NR-1
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WP=1.0D0
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DO 25 J=1,NR-1
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IF (J.EQ.I) GO TO 25
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WP=WP*(Z-X(J))
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25 CONTINUE
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Q=Q+WP
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30 CONTINUE
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GD=(PD-Q*FD)/P
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Z=Z-FD/GD
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IF (IT.LE.40.AND.DABS((Z-Z0)/Z).GT.1.0D-15) GO TO 10
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X(NR)=Z
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W(NR)=1.0D0/(Z*PD*PD)
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35 CONTINUE
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RETURN
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END
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