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SUBROUTINE DMFSD

PURPOSE
   FACTOR A GIVEN SYMMETRIC POSITIVE DEFINITE MATRIX

USAGE
   CALL DMFSD(A,N,EPS,IER)

DESCRIPTION OF PARAMETERS
   A	  - DOUBLE PRECISION UPPER TRIANGULAR PART OF GIVEN
	    SYMMETRIC POSITIVE DEFINITE N BY N COEFFICIENT
	    MATRIX.
	    ON RETURN A CONTAINS THE RESULTANT UPPER
	    TRIANGULAR MATRIX IN DOUBLE PRECISION.
   N	  - THE NUMBER OF ROWS (COLUMNS) IN GIVEN MATRIX.
   EPS	  - SINGLE PRECISION INPUT CONSTANT WHICH IS USED
	    AS RELATIVE TOLERANCE FOR TEST ON LOSS OF
	    SIGNIFICANCE.
   IER	  - RESULTING ERROR PARAMETER CODED AS FOLLOWS
	    IER=0  - NO ERROR
	    IER=-1 - NO RESULT BECAUSE OF WRONG INPUT PARAME-
		     TER N OR BECAUSE SOME RADICAND IS NON-
		     POSITIVE (MATRIX A IS NOT POSITIVE
		     DEFINITE, POSSIBLY DUE TO LOSS OF SIGNI-
		     FICANCE)
	    IER=K  - WARNING WHICH INDICATES LOSS OF SIGNIFI-
		     CANCE. THE RADICAND FORMED AT FACTORIZA-
		     TION STEP K+1 WAS STILL POSITIVE BUT NO
		     LONGER GREATER THAN ABS(EPS*A(K+1,K+1)).

REMARKS
   THE UPPER TRIANGULAR PART OF GIVEN MATRIX IS ASSUMED TO BE
   STORED COLUMNWISE IN N*(N+1)/2 SUCCESSIVE STORAGE LOCATIONS.
   IN THE SAME STORAGE LOCATIONS THE RESULTING UPPER TRIANGU-
   LAR MATRIX IS STORED COLUMNWISE TOO.
   THE PROCEDURE GIVES RESULTS IF N IS GREATER THAN 0 AND ALL
   CALCULATED RADICANDS ARE POSITIVE.
   THE PRODUCT OF RETURNED DIAGONAL TERMS IS EQUAL TO THE
   SQUARE-ROOT OF THE DETERMINANT OF THE GIVEN MATRIX.

SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
   NONE

METHOD
   SOLUTION IS DONE USING THE SQUARE-ROOT METHOD OF CHOLESKY.
   THE GIVEN MATRIX IS REPRESENTED AS PRODUCT OF TWO TRIANGULAR
   MATRICES, WHERE THE LEFT HAND FACTOR IS THE TRANSPOSE OF
   THE RETURNED RIGHT HAND FACTOR.