Equilibration Scale Factors for a General Matrix in Banded Storage

Calling Sequence

CALL DGBEQU	(M, N, NSUB, NSUPER, DA, LDA, DROWSC, DCOLSC, DROWCN, DCOLCN, DAMAX, INFO)
CALL SGBEQU	(M, N, NSUB, NSUPER, SA, LDA, SROWSC, SCOLSC, SROWCN, SCOLCN, SAMAX, INFO)
CALL ZGBEQU	(M, N, NSUB, NSUPER, ZA, LDA, DROWSC, DCOLSC, DROWCN, DCOLCN, DAMAX, INFO)
CALL CGBEQU	(M, N, NSUB, NSUPER, CA, LDA, SROWSC, SCOLSC, SROWCN, SCOLCN, SAMAX, INFO)
void dgbequ	(int m, int n, int nsub, int nsuper, double *da, int lda, double *drowsc, double *dcolsc, double *drowcn, double *dcolcn, double *damax, int *info)
void sgbequ	(int m, int n, int nsub, int nsuper, float *sa, int lda, float *srowsc, float *scolsc, float *srowcn, float *scolcn, float *samax, int *info)
void zgbequ	(int m, int n, int nsub, int nsuper, doublecomplex *za, int lda, double *drowsc, double *dcolsc, double *drowcn, double *dcolcn, double *damax, int *info)
void cgbequ	(int m, int n, int nsub, int nsuper, complex *ca, int lda, float *srowsc, float *scolsc, float *srowcn, float *scolcn, float *samax, int *info)

Arguments

M	Number of rows in the matrix A. M 0.
N	Number of columns in the matrix A. N 0.
NSUB	Number of subdiagonals of A. N-1 NSUB 0 but if N = 0 then NSUB = 0.
NSUPER	Number of superdiagonals of A. N-1 NSUPER 0 but if N = 0 then NSUPER = 0.
xA	Matrix A.
LDA	Leading dimension of the array A as specified in a dimension or type statement. LDA NSUB + NSUPER + 1.
xROWSC	On exit, if INFO = 0 or INFO > M, ROWSC contains the row scale factors for the matrix A.
xCOLSC	On exit, if INFO = 0, COLSC contains the column scale factors for the matrix A.
xROWCN	On exit, if INFO = 0 or INFO > M, the ratio of the smallest ROWSC(i) to the largest ROWSC(i). If ROWCN 0.1 and AMAX is not close to overflow or underflow, then it is not worth scaling by ROWSC.
xCOLCN	On exit, if INFO = 0, the ratio of the smallest COLSC(i) to the largest COLSC(i). If COLCN 0.1 and AMAX is not close to overflow or underflow, then it is not worth scaling by COLSC.
xAMAX	On exit, the absolute value of the largest element of A. If AMAX is very close to overflow or underflow, A should be scaled regardless of the value of ROWCN or COLCN.
INFO	On exit:
	INFO = 0	Subroutine completed normally.
	INFO < 0	The ith argument, where i = |INFO|, had an illegal value.
	1 INFO M	Row INFO of the array A is exactly zero.
	INFO > M	Column (INFO-M) of array A is exactly zero.

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

INTEGER LDA, N, NSUB, NSUPER

PARAMETER (N = 4)

PARAMETER (NSUB = 1)

PARAMETER (NSUPER = 0)

PARAMETER (LDA = NSUB + 1 + NSUPER)

C

DOUBLE PRECISION A(LDA,N), AMAX, COLSCA(N), COLCND

DOUBLE PRECISION ROWCND, ROWSCA(N)

INTEGER ICOL, INFO, IROW

C

EXTERNAL DGBEQU

INTRINSIC ABS

C

C Initialize the array A to store in banded storage mode the

C 4x4 matrix A shown below.

C

C 2 0 0 0

C A = 4 4 0 0

C 0 4 4 0

C 0 0 2 2

C

DATA A / 2.0D0, 4.0D0, 4.0D0, 4.0D0, 4.0D0, 2.0D0, 2.0D0,

$ 8D8 /

C

PRINT 1000

PRINT 1010, A(1,1), 0.0D0, 0.0D0, 0.0D0

PRINT 1010, A(2,1), A(1,2), 0.0D0, 0.0D0

PRINT 1010, 0.0D0, A(2,2), A(1,3), 0.0D0

PRINT 1010, 0.0D0, 0.0D0, A(2,3), A(1,4)

PRINT 1020

PRINT 1010, ((A(IROW,ICOL), ICOL = 1, N), IROW = 1, LDA)

C

CALL DGBEQU (N, N, NSUB, NSUPER, A, LDA, ROWSCA, COLSCA,

$ ROWCND, COLCND, AMAX, INFO)

IF (INFO .NE. 0) THEN

PRINT 1030, ABS(INFO)

STOP 1

END IF

PRINT 1040

PRINT 1010, ROWSCA

PRINT 1050

PRINT 1010, COLSCA

C

1000 FORMAT (1X, 'A in full format:')

1010 FORMAT (4(3X, F8.5))

1020 FORMAT (/1X, 'A in banded form: (* in unused elements)')

1030 FORMAT (1X, 'Illegal argument to DGBEQU, INFO = ', I4)

1040 FORMAT (/1X, 'Row scale factors:')

1050 FORMAT (/1X, 'Column scale factors:')

C

END

Sample Output

A in full format:
2.00000 0.00000 0.00000 0.00000
4.00000 4.00000 0.00000 0.00000
0.00000 4.00000 4.00000 0.00000
0.00000 0.00000 2.00000 2.00000
A in banded form: (* in unused elements)
2.00000 4.00000 4.00000 2.00000
4.00000 4.00000 2.00000 ********
Row scale factors:
0.50000 0.25000 0.25000 0.50000
Column scale factors:
1.00000 1.00000 1.00000 1.00000