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DRANDMULTINORMALREFERENCE / SRANDMULTINORMALREFERENCE

Initializes a reference vector for use with DRANDMULTINORMALR. Reference vector is for a Multivariate Normal distribution with probability density function, f(X), where: f(X) = sqrt([det(C^(-1))] / [(2 * Pi)^M]) * exp(-(X - u)^T * C^(-1) * (X - u)), where u is the vector of means, XMU.

(Note that SRANDMULTINORMALREFERENCE is the single precision version of DRANDMULTINORMALREFERENCE. The argument lists of both routines are identical except that any double precision arguments of DRANDMULTINORMALREFERENCE are replaced in SRANDMULTINORMALREFERENCE by single precision arguments - type REAL in FORTRAN or type float in C).

— SUBROUTINE: DRANDMULTINORMALREFERENCE (M,XMU,C,LDC,REF,LREF,INFO)
— Input: INTEGER M

On input: number of dimensions for the distribution.
Constraint: M>=1.

— Input: DOUBLE PRECISION XMU(M)

On input: vector of means for the distribution.

— Input: DOUBLE PRECISION C(LDC,M)

On input: variance / covariance matrix for the distribution.

— Input: INTEGER LDC

On input: leading dimension of C in the calling routine.
Constraint: LDC>=N.

— Output: DOUBLE PRECISION REF(LREF)

On output: if INFO returns with a value of 0 then REF contains reference information required to generate values from a Multivariate Normal distribution using DRANDMULTINORMALR.

— Input/Output: INTEGER LREF

On input: either the length of the reference vector REF, or -1.
On output: if LREF=-1 on input, then LREF is set to the recommended length of the reference vector and the routine returns. Otherwise LREF is left unchanged.

— Output: INTEGER INFO

On output: INFO is an error indicator. If INFO = -i on exit, the i-th argument had an illegal value. If INFO =1 on exit, then LREF has been set to the recommended length for the reference vector REF. If INFO = 0 then the reference vector, REF, has been successfully initialized. 

     Example:
     

     
          C      Generate 100 values from the
          C      Multivariate Normal distribution
                 INTEGER LSTATE,N, MM
                 PARAMETER (LSTATE=16,N=100,MM=10)
                 INTEGER I,J,INFO,SEED(1),STATE(LSTATE)
                 INTEGER LDC,LDX,M
                 DOUBLE PRECISION X(N,MM),XMU(MM),C(MM,MM)
                 INTEGER LREF
                 DOUBLE PRECISION REF(1000)
          
          C      Set array sizes
                 LDC = MM
                 LDX = N
          
          C      Set the seed
                 SEED(1) = 1234
          
          C      Read in the distributional parameters
                 READ(5,*) M
                 READ(5,*) (XMU(I),I=1,M)
                 DO 20 I = 1,M
                   READ(5,*) (C(I,J),J=1,M)
          20     CONTINUE
          
          C      Initialize the STATE vector
                 CALL DRANDINITIALIZE(1,1,SEED,1,STATE,LSTATE,INFO)
          
          C      Initialize the reference vector
                 LREF = 1000
                 CALL DRANDMULTINORMALREFERENCE(M,XMU,C,LDC,REF,LREF,INFO)
          
          C      Generate N variates from the
          C      Multivariate Normal distribution
                 CALL DRANDMULTINORMALR(N,REF,STATE,X,LDX,INFO)
          C      Print the results
                 DO 40 I = 1,N
                   WRITE(6,*) (X(I,J),J=1,M)
          40     CONTINUE