Enter your search terms Submit search form
	Web pdp-10.trailing-edge.com

SUBROUTINE MFGR

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 MFGR(A,M,N,EPS,IRANK,IROW,ICOL)

DESCRIPTION OF PARAMETERS
   A	  - GIVEN MATRIX WITH M ROWS AND N COLUMNS.
	    ON RETURN A CONTAINS THE FIVE SUBMATRICES
	    L, R, H, D, O.
   M	  - NUMBER OF ROWS OF MATRIX A.
   N	  - NUMBER OF COLUMNS OF MATRIX A.
   EPS	  - 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.