SUBROUTINE HRMSYM( NDIM, NF, MINPTS, MAXPTS, FUNSUB, EPSABS, 
     &     EPSREL, RESTAR, RESULT, ABSERR, NEVAL, IFAIL, WORK)
****BEGIN PROLOGUE HRMSYM
*
****AUTHOR
*            Alan Genz, 
*            Department of Mathematics 
*            Washington State University
*            Pullman, WA 99164-3113, USA
*            Email: alangenz@wsu.edu
*
*      Reference: Genz, A., and Keister, B. (1996), Fully Symmetric 
*      Interpolatory Rules for Multiple Integrals over Infinite 
*      Regions with Gaussian Weight, J. Comp. Appl. Math., 71, 299-309.
*
****KEYWORDS automatic multidimensional integrator,
*            n-dimensional region (-infin, infin)^n 
*            Gaussian weight
****PURPOSE  The routine calculates an approximation to a given
*            vector of definite integrals
*
*      infin     infin 
*     I    ...  I     w(X)(F ,F ,...,F  ) DX(NDIM)...DX(2)DX(1),
*     -infin    -infin      1  2      NF
*
*       where F = F (X ,X ,...,X    ), I = 1,2,...,NF,
*              I   I  1  2      NDIM
*
*       w(X) = EXP(-( X(1)**2 + ... + X(NDIM)**2 )/2)/SQRT(2*PI)**NDIM.
*
****DESCRIPTION Computation of integrals over infinite regions with
*               Gaussian weight.
*
*   ON ENTRY
*
*     NDIM   Integer, number of variables, with 1 < NDIM <= 1000.
*     NF     Integer, number of components of the integral.
*     MINPTS Integer, minimum number of function evaluations.
*     MAXPTS Integer, maximum number of function evaluations.
*     FUNSUB Externally declared subroutine for computing
*            all components of the integrand at the given
*            evaluation point.
*            It must have parameters (NDIM,X,NF,FUNVLS)
*            Input parameters:
*              NDIM   Integer that defines the dimension of the
*                     integral.
*              X      Real array of dimension NDIM
*                     that defines the evaluation point.
*              NF Integer that defines the number of components of I.
*            Output parameter:
*              FUNVLS Real array of dimension NF
*                     that defines NF components of the integrand.
*
*     EPSABS Real, requested absolute accuracy.
*     EPSREL Real, requested relative accuracy.
*     RESTAR Integer.
*            If RESTAR = 0, this is the first attempt to compute
*            the integral.
*            If RESTAR = 1, then we restart a previous attempt.
*     WORK   Real array of working storage, must have dimension at
*            least 2*NF + (NF+1)*NUMSMS. NUMSMS is the number 
*            of NDIM partitions of the integers 0,...,RULE, after
*            RULE+1 approximations to the integrals have been computed.
*            The required value for NUMSMS will never exceed 10000.
*
*   ON RETURN
*
*     RESULT Real array of dimension NF.
*            Approximations to all components of the integral.
*     ABSERR Real array of dimension NF.
*            Estimates of absolute accuracies.
*     NEVAL  Integer, number of function evaluations used.
*     IFAIL  Integer.
*            IFAIL = 0 for normal exit, when 
*              ABSERR(K) <= MAX( EPSABS, ABS(RESULT(K))*EPSREL ) for
*              all K, 0 < K <= NF, with <= MAXPTS function values. 
*            IFAIL = 1 if MAXPTS was too small to obtain the required 
*              accuracy. In this case values of RESULT are returned
*              with estimated absolute accuracies ABSERR.
*     WORK   Real array of working storage, that contains information
*            that might be needed for subsequent calls of HRMSYM. This
*            array should not be modified. 
*
****ROUTINES CALLED 
****END PROLOGUE HRMSYM
*
*   Global variables.
*
      EXTERNAL FUNSUB
      INTEGER NDIM, NF, MINPTS, MAXPTS, RESTAR
      INTEGER NEVAL, IFAIL
      DOUBLE PRECISION EPSABS, EPSREL
      DOUBLE PRECISION RESULT(*), ABSERR(*), WORK(*)
*
*   Local variables.
*
      INTEGER I, MAXRUL, RULE, MNRULE, INTCLS, NUMSMS
      PARAMETER ( MAXRUL = 25 )
      DOUBLE PRECISION DIFFER, CLTOTL, RNTCLS, EPOWER
      PARAMETER ( EPOWER = 1.5 )
      SAVE RULE, MNRULE, CLTOTL
      IFAIL = 1
      IF ( NDIM .LE. 4 ) THEN 
*
*     Call product Gauss-Hermite Rule
*
         CALL HERMIT( NDIM, NF, MINPTS, MAXPTS, FUNSUB, EPSABS, EPSREL, 
     &                RESTAR, RESULT, ABSERR, NEVAL, IFAIL, WORK )
      ELSE
         IF ( RESTAR .EQ. 0 ) THEN
            MNRULE = -1
            RULE = 0
            CLTOTL = 0
            DO I = 1, NF
               WORK(I) = 0
               WORK(I+NF) = 0
            END DO
         END IF
         NEVAL = 0
         DO WHILE ( NEVAL .LE. MAXPTS .AND. RULE .LE. MAXRUL 
     &        .AND. ( IFAIL .GT. 0 .OR. NEVAL .LT. MINPTS ) ) 
            CALL HRMTRL( NDIM, NF, FUNSUB, MNRULE, RULE, RESULT, 
     &                   INTCLS, WORK(2*NF+1), WORK(3*NF+1), NUMSMS ) 
            RNTCLS = REAL( INTCLS )**EPOWER 
            CLTOTL = CLTOTL + RNTCLS
            DO I = 1, NF
               DIFFER = ( RESULT(I) - WORK(I) )/CLTOTL
               WORK(I) = WORK(I) + RNTCLS*DIFFER 
               WORK(NF+I) = ( CLTOTL - RNTCLS )
     &                     *( WORK(NF+I)/CLTOTL + RNTCLS*DIFFER**2 )
            END DO
            IFAIL = 0
            DO I = 1,NF
               IF ( RULE .GT. 0 ) THEN
                  ABSERR(I) = SQRT( WORK(NF+I) )
               ELSE
                  ABSERR(I) = ABS( RESULT(I) )
               END IF
               IF ( ABSERR(I) .GT. MAX(EPSABS,EPSREL*ABS(RESULT(I))) )
     &              IFAIL = 1
            END DO
            NEVAL = NEVAL + INTCLS
            RULE = RULE + 1
         END DO
      END IF
*
****END HRMSYM
*
      END
      SUBROUTINE HRMTRL( S, N, F, MINORD, MAXORD, INTVAL, INTCLS, 
     &                   WORK, FULSMS, NUMSMS )
*  MULTIDIMENSIONAL FULLY SYMMETRIC RULE INTEGRATION SUBROUTINE
*
*   THIS SUBROUTINE COMPUTES A SEQUENCE OF FULLY SYMMETRIC RULE
*   APPROXIMATIONS TO A FULLY SYMMETRIC MULTIPLE INTEGRAL. WRITTEN BY 
*     Alan Genz
*     Department of Mathematics
*     Washington State University
*     Pullman, Washington 99164-3113  USA
*     Telephone: 509-335-2131 
*     Electronic Mail: alangenz@wsu.edu
*     Fax: 509-335-1188 
*
***************  PARAMETERS FOR HRMTRL  ********************************
******INPUT PARAMETERS
*  S       INTEGER number of variables, with 0 < S <= 1000.
*  N       Integer, number of components of the integral.
*  F       EXTERNALly declared user defined integrand subroutine.
*          it must have parameters (S,X,N,F), where X is a REAL S-array
*          and F is a real N-array.
*  MINORD  INTEGER minimum order parameter.  On entry MINORD specifies
*          the current highest order approximation to the integral,
*          available in the array INTVAL.  For the first call
*          MINORD should be set to -1. Otherwise a previous call is
*          assumed that computed INTVAL. On exit MINORD is set to MAXORD.
*  MAXORD  INTEGER maximum order parameter, must be greater than MINORD
*          and not exceed 25. The subroutine computes approximations of 
*          polynomial degree 2*MAXORD+1.
*******OUTPUT PARAMETERS
*  INTVAL  REAL array of length N.  Upon successful exit
*          INTVAL(1),..., INTVAL(N) are approximations to the components
*          of the integral.  These are all approximations of polynomial 
*          degree 2*MAXORD+1.
*  INTCLS  INTEGER number of F values needed for INTVAL
*  WORK    REAL working storage array. 
*  FULSMS  REAL working storage array with dimension (N+1,*). On exit
*          FULSMS(I,J) contains the fully symmetric basic rule sum
*          indexed by the jth s-partition of the integers 0,...,MAXORD, 
*          for the Ith component of the integrand.
*          FULSMS(N+1,J) contains number of points for the fully 
*          symmetric basic rule sum indexed by the Jth S-partition of 
*          the integers 0,...,MAXORD.
*  NUMSMS  INTEGER number of S-partitions of the integers 0,...,MAXORD.
************************************************************************
      EXTERNAL F
      INTEGER S, N, MAXDIM, MINORD, MAXORD, MAXRDM, NUMSMS
      PARAMETER ( MAXDIM = 1000, MAXRDM = 25 ) 
      DOUBLE PRECISION X(MAXDIM), FULWGT, WEIGHT, 
     &                 INTVAL(N), FULSMS(N+1,*), WORK(*) 
      INTEGER D, I, L, MODOFM, M(MAXDIM), K(MAXDIM), INTCLS, PRTCNT
      D = MINORD + 1
      INTCLS = 0
      IF ( D .EQ. 0 ) THEN
         DO I = 1,N
            INTVAL(I) = 0
         END DO
      END IF
*
****  Begin loop for each D
*      for each D find all distinct partitions M with |M| <= D
*
      DO WHILE( D .LE. MIN ( MAXORD, MAXRDM ) )
         PRTCNT = 0
         CALL NXPART( PRTCNT, S, M, MODOFM )
         DO WHILE( MODOFM .LE. D )
*     
****  Calculate updated weight for partition M alnd 
****     fully symmetric sums ( when necessary )
*
            FULWGT = WEIGHT( S, X, M, K, MODOFM, D )
            IF ( D .EQ. MODOFM ) THEN
               DO I = 1,N
                  FULSMS(I,PRTCNT) = 0
               END DO
               FULSMS(N+1,PRTCNT) = 0
            END IF
            IF ( FULSMS(N+1,PRTCNT) .EQ. 0 .AND. FULWGT .NE. 0 ) THEN
               CALL FULSMH( S, M, N, F, FULSMS(1,PRTCNT), X, WORK ) 
     &                      
               INTCLS = INTCLS + FULSMS(N+1,PRTCNT)
            END IF
            DO I = 1,N 
               INTVAL(I) = INTVAL(I) + FULWGT*FULSMS(I,PRTCNT)
            END DO
            CALL NXPART( PRTCNT, S, M, MODOFM )
         END DO
*     
****  End loop for each D
*
         D = D + 1
      END DO
      MINORD = MAXORD
      NUMSMS = PRTCNT - 1
      END
*
      SUBROUTINE FULSMH( S, M, N, F, FULSMS, X, FUNVAL )
*
****  To compute fully symmetric basic rule sums
*
      INTEGER S, M(*), SUMCLS, IX, LX, I,L, MI, ML, IL, N, MX
      DOUBLE PRECISION X(*), INTWGT, FULSMS(*), FUNVAL(*)
*
*        Generators for 1 + 2 + 6 + 10 + 16 = 35 point 
*        degree 51 rule, with degree 1, 5, 15 and 29 imbedded rules.     
*
      PARAMETER ( MX = 17 )
      DOUBLE PRECISION G(0:MX)
      SAVE G
      DATA G( 0),G( 1)/0D0                  , 0.17320508075688773D1/
      DATA G( 2),G( 3)/0.41849560176727319D1, 0.74109534999454084D0/
      DATA G( 4),G( 5)/0.28612795760570581D1, 0.63633944943363700D1/
      DATA G( 6),G( 7)/0.12304236340273060D1, 0.51870160399136561D1/
      DATA G( 8),G( 9)/0.25960831150492022D1, 0.32053337944991945D1/
      DATA G(10),G(11)/0.90169397898903025D1, 0.24899229757996061D0/
      DATA G(12),G(13)/0.79807717985905609D1, 0.22336260616769417D1/
      DATA G(14),G(15)/0.71221067008046167D1, 0.36353185190372782D1/
      DATA G(16),G(17)/0.56981777684881096D1, 0.47364330859522971D1/
      INTWGT = 1
      DO I = 1, S
        IF ( M(I) .NE. 0 ) INTWGT = INTWGT/2
      END DO
      SUMCLS = 0
      DO I = 1,N
         FULSMS(I) = 0
      END DO
*
********  Compute centrally symmetric sum for permutation M
*
 10   DO I = 1, S
         X(I) = -G(M(I))
      END DO
 20   SUMCLS = SUMCLS + 1
      CALL F( S, X, N, FUNVAL )
      DO I = 1,N
         FULSMS(I) = FULSMS(I) + INTWGT*FUNVAL(I)
      END DO
      DO I = 1, S
         X(I) = -X(I)
         IF ( X(I) .GT. 0 ) GO TO 20
      END DO
*
********  END Integration loop for M
*
*
********  Find next distinct permutation of M and loop back
*          to compute next centrally symmetric sum
*
      DO I = 2, S
         IF ( M(I-1) .GT. M(I) ) THEN
            MI = M(I)
            IX = I - 1
            IF ( I .GT. 2 ) THEN
               DO L = 1, IX/2
                  ML = M(L)
                  IL = I - L
                  M(L) = M(IL)
                  M(IL) = ML
                  IF ( ML .LE. MI ) IX = IX - 1
                  IF ( M(L) .GT. MI ) LX = L
               END DO
               IF ( M(IX) .LE. MI ) IX = LX
            END IF
            M(I) = M(IX)
            M(IX) = MI
            GO TO 10
         END IF
      END DO
*
****  END Loop for permutations of M and associated sums
*
*
**** Restore original order to M.
*
      DO I = 1, S/2
         MI = M(I)
         M(I) = M(S-I+1)
         M(S-I+1) = MI
      END DO
      FULSMS(N+1) = SUMCLS
      END
*
      DOUBLE PRECISION FUNCTION WEIGHT( S, INTRPS, M,K, MODOFM, D )
*
****  Subroutine to update weight for partition m
*
      INTEGER S, M(S), K(S), I, L, D, MAXRDM, NZRMAX, MODOFM
      PARAMETER ( MAXRDM = 25 )
      DOUBLE PRECISION INTRPS(S), MOMPRD(0:MAXRDM,0:MAXRDM), MOMNKN,
     &     INTMPA, INTMPB
      SAVE MOMPRD
*
*     Modified moments and generators for 1 + 2 + 6 + 10 + 16 = 35 point 
*        degree 51 rule, with degree 1, 5 and 19 imbedded rules.     
*
      PARAMETER ( NZRMAX = 17 )
      DOUBLE PRECISION A(0:NZRMAX), G(0:NZRMAX)
      DATA A /  2*1D0, 0D0, 6D0, 
     &     -0.48378475125832451D2, 3*0D0, 34020D0, 
     &     -0.98606453173677489D6, 5*0D0, 0.12912054173706603D13, 
     &     -0.11268664521456168D15, 0.29248520348796280D16 /  
      DATA G( 0),G( 1)/0D0                  , 0.17320508075688773D1/
      DATA G( 2),G( 3)/0.41849560176727319D1, 0.74109534999454084D0/
      DATA G( 4),G( 5)/0.28612795760570581D1, 0.63633944943363700D1/
      DATA G( 6),G( 7)/0.12304236340273060D1, 0.51870160399136561D1/
      DATA G( 8),G( 9)/0.25960831150492022D1, 0.32053337944991945D1/
      DATA G(10),G(11)/0.90169397898903025D1, 0.24899229757996061D0/
      DATA G(12),G(13)/0.79807717985905609D1, 0.22336260616769417D1/
      DATA G(14),G(15)/0.71221067008046167D1, 0.36353185190372782D1/
      DATA G(16),G(17)/0.56981777684881096D1, 0.47364330859522971D1/
      DATA MOMPRD(0,0) / 0D0 /
      IF ( MOMPRD(0,0) .EQ. 0 ) THEN
*
****  Calculate moments 
*
         DO L = 0, MAXRDM 
            DO I = 0, MAXRDM 
               MOMPRD(L,I) = 0
            END DO
         END DO
         MOMPRD(0,0) = A(0)
         DO L = 0, NZRMAX
            MOMNKN = 1
            DO I = 1, NZRMAX
               IF ( I .LE. L ) THEN
                  MOMNKN = MOMNKN*( G(L)**2 - G(I-1)**2 )
               ELSE
                  MOMNKN = MOMNKN*( G(L)**2 - G(I)**2 )
               END IF
               IF ( I .GE. L ) MOMPRD(L,I) = A(I)/MOMNKN
            END DO
         END DO
      END IF
*
*     Determine Updated Weight Contribution
*
      DO I = 2,S
        INTRPS(I) = 0
        K(I) = M(I)
      END DO
      K(1) = D - MODOFM + M(1)
 10   INTRPS(1) = MOMPRD( M(1), K(1) )
      DO I = 2, S
        INTRPS(I) = INTRPS(I) + MOMPRD( M(I), K(I) )*INTRPS(I-1)
        INTRPS(I-1) = 0
        K(1) = K(1) - 1
        K(I) = K(I) + 1
        IF ( K(1) .GE. M(1) ) GO TO 10
        K(1) = K(1) + K(I) - M(I)
        K(I) = M(I)
      END DO
      WEIGHT = INTRPS(S)
      END
      SUBROUTINE NXPART( PRTCNT, S, M, MODOFM )
*
****  SUBROUTINE TO COMPUTE THE NEXT S PARTITION
*
      INTEGER S, M(S), PRTCNT, MODOFM, I, MSUM, L
      IF ( PRTCNT .EQ. 0 ) THEN
         DO I = 1, S
            M(I) = 0
         END DO
         PRTCNT = 1
         MODOFM = 0
      ELSE
         PRTCNT = PRTCNT + 1
         MSUM = M(1)
         DO I = 2, S
            MSUM = MSUM + M(I)
            IF ( M(1) .LE. M(I) + 1 ) THEN
               M(I) = 0
            ELSE
               M(1) = MSUM - (I-1)*(M(I)+1)
               DO L = 2, I
                  M(L) = M(I) + 1
               END DO
               RETURN
            END IF
         END DO
         M(1) = MSUM + 1
         MODOFM = M(1)
      END IF
      END
*
      SUBROUTINE MLTRUL( NDIM, NUMFUN, FUNSUB, NP, POINT, WEIGHT, 
     &                   INTVAL, FUNS, X, IC )
*
*     Computes product integration rule
*
      EXTERNAL FUNSUB
      INTEGER NDIM, NP, NUMFUN, ICI, I
      DOUBLE PRECISION POINT(*), WEIGHT(*), INTVAL(*)
      DOUBLE PRECISION WTPROD, X(*), FUNS(*), IC(*)
      DO I = 1, NDIM
         IC(I) = 1
      END DO
      DO I = 1, NUMFUN
         INTVAL(I) = 0
      END DO
 10   WTPROD = 1
      DO I = 1, NDIM
         ICI = IC(I)
         X(I) = POINT(ICI)
         WTPROD = WTPROD*WEIGHT(ICI)
      END DO
      CALL FUNSUB( NDIM, X, NUMFUN, FUNS ) 
      DO I = 1, NUMFUN
         INTVAL(I) = INTVAL(I) + WTPROD*FUNS(I)
      END DO
      DO I = 1, NDIM
         IC(I) = IC(I) + 1
         IF ( IC(I) .LE. NP ) GO TO 10
         IC(I) = 1
      END DO
      END
*
      SUBROUTINE HERMIT( NDIM, NUMFUN, MINPTS, MAXPTS, FUNSUB,
     &     EPSABS, EPSREL, RESTAR, RESULT, ABSERR, NEVAL, IFAIL, WORK ) 
****BEGIN PROLOGUE HERMIT
****CATEGORY NO. H2B1A1
****AUTHOR
*
*     Alan Genz
*     Department of Mathematics
*     Washington State University
*     Pullman, Washington 99164-3113  USA
*     Telephone: 509-335-2131 
*     Electronic Mail: alangenz@wsu.edu
*     Fax: 509-335-1188 
*
****KEYWORDS automatic multidimensional integrator, Gaussian weight
*            n-dimensional region (-infin, infin)^n 
****PURPOSE  The routine calculates an approximation to a vector of
*            definite integrals using Gauss-Hermite product rules.
*
*      infin     infin
*     I    ...  I       w(X) (F ,F ,...,F      ) DX(NDIM)...DX(2)DX(1),
*     -infin    -infin         1  2      NUMFUN
*
*       where F = F (X ,X ,...,X    ), I = 1,2,...,NUMFUN,
*              I   I  1  2      NDIM
*
*       w(X) = EXP(-( X(1)**2 + ... + X(NDIM)**2 )/2)/SQRT(2*PI)**NDIM.
*
****DESCRIPTION Computation of integrals over infinite regions with
*               Gaussian weight using Gauss-Hermite product rules.
*
*   ON ENTRY
*
*     NDIM   Integer, number of variables.
*     NUMFUN Integer, number of components of the integral.
*     MINPTS Integer, minimum number of function evaluations.
*     MAXPTS Integer, maximum number of function evaluations.
*     FUNSUB Externally declared subroutine for computing components of 
*            the integrand at the given evaluation point.
*            It must have parameters (NDIM,X,NUMFUN,FUNVLS)
*            Input parameters:
*              NDIM   Integer, number of dimensions for the integral.
*              X      Real NDIM-array for the evaluation point.
*              NUMFUN Integer, number of components of I.
*            Output parameter:
*              FUNVLS Real NUMFUN-array for integrand components.
*
*     EPSABS Real, requested absolute accuracy.
*     EPSREL Real, requested relative accuracy.
*     RESTAR Integer.
*            If RESTAR = 0, this is the first attempt to compute
*            the integral.
*            If RESTAR = 1, then we restart a previous attempt.
*     WORK   Real array of working storage, must have dimensions at
*            least 2*NUMFUN+2*NDIM
*
*   ON RETURN
*
*     RESULT Real NUMFUN-array of approximations to all components 
*            of the integral.
*     ABSERR Real NUMFUN-array of estimates of absolute accuracies.
*     NEVAL  Integer, number of function evaluations used.
*     IFAIL  Integer.
*            IFAIL = 0 for normal exit, when 
*              ABSERR(K) <= MAX( EPSABS, ABS(RESULT(K))*EPSREL ) for
*              all K, 0 < K <= NUMFUN, with <= MAXPTS function values. 
*            IFAIL = 1 if MAXPTS was too small to obtain the required 
*              accuracy. In this case values of RESULT are returned
*              with estimated absolute accuracies ABSERR.
*
****ROUTINES CALLED MLTRUL
****END PROLOGUE HERMIT
*
*   Global variables.
*
      EXTERNAL FUNSUB
      INTEGER NDIM, NUMFUN, MINPTS, MAXPTS, RESTAR
      INTEGER NEVAL, IFAIL
      DOUBLE PRECISION EPSABS, EPSREL
      DOUBLE PRECISION RESULT(*), ABSERR(*), WORK(*)
*
*   Local variables.
*
      INTEGER I, K, MAXRUL, RULE
      PARAMETER ( MAXRUL = 50 )
      DOUBLE PRECISION POINT(MAXRUL), WEIGHT(MAXRUL)
      SAVE RULE
      DOUBLE PRECISION W(25,50), T(25,50)
      SAVE W, T
      IF ( RESTAR .EQ. 0 ) RULE = 1
      NEVAL = 0
 10   IF ( NEVAL + RULE**NDIM .LE. MAXPTS .AND. RULE .LT. MAXRUL ) THEN
         DO I = 1, RULE/2
            POINT( I) = -T(I,RULE)
            WEIGHT(I) =  W(I,RULE)
            POINT( RULE-I+1) = T(I,RULE)
            WEIGHT(RULE-I+1) = W(I,RULE)
         END DO
         IF ( MOD( RULE, 2 ) .EQ. 1 ) THEN
            POINT(  RULE/2 + 1 ) = 0
            WEIGHT( RULE/2 + 1 ) = W( RULE/2 + 1, RULE ) 
         END IF
         CALL MLTRUL( NDIM, NUMFUN, FUNSUB, RULE, POINT, WEIGHT, 
     &        RESULT, WORK, WORK(NUMFUN+1), WORK(NUMFUN+NDIM+1) )
         NEVAL = NEVAL + RULE**NDIM
         IFAIL = 0
         DO I = 1,NUMFUN
            IF ( RULE .GT. 1 ) THEN
               ABSERR(I) = ABS( RESULT(I) - WORK(2*NDIM+NUMFUN+I)  )
            ELSE
               ABSERR(I) = ABS( RESULT(I) )
            ENDIF
            WORK(2*NDIM+NUMFUN+I) = RESULT(I)
            IF ( ABSERR(I) .GT. MAX( EPSABS, EPSREL*ABS(RESULT(I)) ) )
     &           IFAIL = 1
         END DO
         RULE = RULE + 1
         IF ( IFAIL .GT. 0 .OR. NEVAL .LT. MINPTS ) GO TO 10 
      END IF
*
*     Gauss Hermite Weights and Points, N = 1,50
*
      DATA   W(1, 1), T(1, 1) / 1D0, 0D0 /
      DATA ( W(I, 2), T(I, 2), I = 1, 1) /
     &  0.5000000000000001D+00, 0.1000000000000000D+01/
      DATA ( W(I, 3), T(I, 3), I = 1, 2) /
     &  0.1666666666666667D+00, 0.1732050807568877D+01,
     &  0.6666666666666664D+00, 0.1107367643833737D-15/
      DATA ( W(I, 4), T(I, 4), I = 1, 2) /
     &  0.4587585476806855D-01, 0.2334414218338977D+01,
     &  0.4541241452319317D+00, 0.7419637843027258D+00/
      DATA ( W(I, 5), T(I, 5), I = 1, 3) /
     &  0.1125741132772071D-01, 0.2856970013872805D+01,
     &  0.2220759220056126D+00, 0.1355626179974265D+01,
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      DATA ( W(I,46), T(I,46), I = 1,23) /
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      DATA ( W(I,47), T(I,47), I = 1,24) /
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      DATA ( W(I,48), T(I,48), I = 1,24) /
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      DATA ( W(I,49), T(I,49), I = 1,25) /
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      DATA ( W(I,50), T(I,50), I = 1,25) /
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*
*
****END HERMIT
*
      END