SECTION 12.8 MONTE CARLO INTEGRATION OF NORMAL OVER THE                           INTERSECTION OF HALF-SPACES (MONCARL)

It is desired to integrate the multivariate normal density over the region given by

i=1,...,k, where the a_ij are given numbers. MONCARL accomplishes this via Monte Carlo integration.

The MAIN program should include

        COMMON/BPRINT/IPT,NFILE,NDIG,NPUNCH,JPT,MFILE
        CALL DFLT

        CALL MONCARL(NREP,NDIM,INDEP,ICONST,A,XMU,SIG,COV,ANS)

where

   NREP   = the number of samplings
   NDIM   = the dimensionality of the problem (i.e., n in the
            inequality above)
   INDEP  = a variable declared LOGICAL and set to .TRUE. if the
            X's are independent and to .FALSE. otherwise
   ICONST = the number of contraints (i.e., k in the inequality
            above)
   A      = a DOUBLE PRECISION array dimensioned A(ICONST,0:NDIM)
            where the column corresponding to column index 0
            should contain the right hand sides of the inequalities
   XMU    = a DOUBLE PRECISION array dimensioned XMU(NDIM)
            containing the mean vector
   SIG    = a DOUBLE PRECISION vector containing the standard
            deviations of the NDIM variables if INDEP=.TRUE.
            (SIG is irrelevant if INDEP=.FALSE.)
   COV    = a DOUBLE PRECISION array dimensioned COV(NDIM,NDIM)
            containing the covariance matrix if INDEP=.FALSE.
            (COV is irrelevant if INDEP=.TRUE.)
   ANS    = the required integral
   IER    = 0 for normal return, =-67 if the covariance matrix is
            not positive definite (relevant only if INDEP=.FALSE.)

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