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*DECK SNQU07
SUBROUTINE SNQU07(NLF,X,W)
*
*-----------------------------------------------------------------------
*
*Purpose:
* To define Gauss-Lobatto points and weights (1D quadrature).
*
*Copyright:
* Copyright (C) 2008 Ecole Polytechnique de Montreal.
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version
*
*Author(s):
* C. Bienvenue
*
*Parameters: input
* NLF order of the SN approximation (even number).
*
*Parameters: output
* X base points in $\\mu$ of the quadrature.
* W weights of the quadrature.
*
*-----------------------------------------------------------------------
*
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER NLF
REAL X(NLF),W(NLF)
*----
* LOCAL VARIABLES
*----
PARAMETER(PI=3.141592654,NMAX=100,EPS=1.0E-6)
INTEGER N
REAL XOLD(NLF),P(NLF,NLF)
*----
* COMPUTE QUADRATURE PARAMETERS
*----
! INITIAL GUESS BASE POINTS
DO 10 I=1,NLF
X(I)=COS(PI*(I-1)/(NLF-1))
XOLD(I)=2.0
10 ENDDO
! NEWTON-RAPHSON METHOD TO COMPUTE BASE POINTS
P(:NLF,:NLF)=0.0
DO 20 I=1,NLF
N=1
DO WHILE (ABS(X(I)-XOLD(I)).GT.EPS)
XOLD(I) = X(I)
P(I,1)=1
P(I,2)=X(I)
DO 30 J=2,NLF-1
P(I,J+1)=((2*J-1)*X(I)*P(I,J)-(J-1)*P(I,J-1))/J
30 ENDDO
X(I)=XOLD(I)-(X(I)*P(I,NLF)-P(I,NLF-1))/(NLF*P(I,NLF))
IF(N.GT.NMAX) CALL XABORT('SNQU07: CONVERGENCE ISSUE.')
N=N+1
ENDDO
W(I)=2/((NLF-1)*NLF*P(I,NLF)**2)
20 ENDDO
! COMPUTE WEIGHTS
DO 40 I=1,NLF
W(I)=2/((NLF-1)*NLF*P(I,NLF)**2)
40 ENDDO
RETURN
END
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