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SUBROUTINE DMFGR

PURPOSE
   FOR A GIVEN M BY N MATRIX THE FOLLOWING CALCULATIONS
   ARE PERFORMED
   (1) DETERMINE RANK AND LINEARLY INDEPENDENT ROWS AND
       COLUMNS (BASIS).
   (2) FACTORIZE A SUBMATRIX OF MAXIMAL RANK.
   (3) EXPRESS NON-BASIC ROWS IN TERMS OF BASIC ONES.
   (4) EXPRESS BASIC VARIABLES IN TERMS OF FREE ONES.

USAGE
   CALL DMFGR(A,M,N,EPS,IRANK,IROW,ICOL)

DESCRIPTION OF PARAMETERS
   A	  - DOUBLE PRECISION GIVEN MATRIX WITH M ROWS
	    AND N COLUMNS.
	    ON RETURN A CONTAINS THE TRIANGULAR FACTORS
	    OF A SUBMATRIX OF MAXIMAL RANK.
   M	  - NUMBER OF ROWS OF MATRIX A.
   N	  - NUMBER OF COLUMNS OF MATRIX A.
   EPS	  - SINGLE PRECISION TESTVALUE FOR ZERO AFFECTED BY
	    ROUNDOFF NOISE.
   IRANK  - RESULTANT RANK OF GIVEN MATRIX.
   IROW   - INTEGER VECTOR OF DIMENSION M CONTAINING THE
	    SUBSCRIPTS OF BASIC ROWS IN IROW(1),...,IROW(IRANK)
   ICOL   - INTEGER VECTOR OF DIMENSION N CONTAINING THE
	    SUBSCRIPTS OF BASIC COLUMNS IN ICOL(1) UP TO
	    ICOL(IRANK).

REMARKS
   THE LEFT HAND TRIANGULAR FACTOR IS NORMALIZED SUCH THAT
   THE DIAGONAL CONTAINS ALL ONES THUS ALLOWING TO STORE ONLY
   THE SUBDIAGONAL PART.

SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
   NONE

METHOD
   GAUSSIAN ELIMINATION TECHNIQUE IS USED FOR CALCULATION
   OF THE TRIANGULAR FACTORS OF A GIVEN MATRIX.
   COMPLETE PIVOTING IS BUILT IN.
   IN CASE OF A SINGULAR MATRIX ONLY THE TRIANGULAR FACTORS
   OF A SUBMATRIX OF MAXIMAL RANK ARE RETAINED.
   THE REMAINING PARTS OF THE RESULTANT MATRIX GIVE THE
   DEPENDENCIES OF ROWS AND THE SOLUTION OF THE HOMOGENEOUS
   MATRIX EQUATION A*X=0.