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decuslib20-02
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decus/20-0026/mfgr.doc
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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.