Equilibration Scale Factors for a General Matrix

Calling Sequence

CALL DGEEQU	(M, N, DA, LDA, DROWSC, DCOLSC, DROWCN, DCOLCN, DAMAX, INFO)
CALL SGEEQU	(M, N, SA, LDA, SROWSC, SCOLSC, SROWCN, SCOLCN, SAMAX, INFO)
CALL ZGEEQU	(M, N, ZA, LDA, DROWSC, DCOLSC, DROWCN, DCOLCN, DAMAX, INFO)
CALL CGEEQU	(M, N, CA, LDA, SROWSC, SCOLSC, SROWCN, SCOLCN, SAMAX, INFO)
void dgeequ	(int m, int n, double *da, int lda, double *drowsc, double *dcolsc, double *drowcn, double *dcolcn, double *damax, int *info)
void sgeequ	(int m, int n, float *sa, int lda, float *srowsc, float *scolsc, float *srowcn, float *scolcn, float *samax, int *info)
void zgeequ	(int m, int n, doublecomplex *za, int lda, double *drowcn, double *dcolcn,double *drowcn, double *dcolcn, double *damax, int *info)
void cgeequ	(int m, int n, 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.
xA	Matrix A.
LDA	Leading dimension of the array A as specified in a dimension or type statement. LDA max(1, M).
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, ROWCN contains 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, COLCN contains 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 the array A is exactly zero.

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

INTEGER LDA, N

PARAMETER (N = 3)

PARAMETER (LDA = N)

C

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

DOUBLE PRECISION ROWCND, ROWSCA(N)

INTEGER ICOL, INFO, IROW

C

EXTERNAL DGEEQU

INTRINSIC ABS

C

C Initialize the array A to store the 3x3 matrix A shown

C below.

C

C 2 4 8

C A = 2 8 16

C 2 16 32

C

DATA A / 2.0D0, 2.0D0, 2.0D0, 4.0D0, 8.0D0, 1.6D1,

$ 8.0D0, 1.6D1, 3.2D1 /

C

C Print the initial value of A.

C

PRINT 1000

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

C

C Compute and print the scale factors that will

C equilibrate A.

C

CALL DGEEQU (N, N, A, LDA, ROWSCA, COLSCA, ROWCND, COLCND,

$ AMAX, INFO)

IF (INFO .LT. 0) THEN

PRINT 1020, ABS(INFO)

STOP 1

ELSE IF (INFO .GT. N) THEN

PRINT 1030, INFO - N

STOP 2

ELSE IF (INFO .GT. 0) THEN

PRINT 1040, INFO

STOP 3

END IF

PRINT 1050

PRINT 1010, ROWSCA

PRINT 1060

PRINT 1010, COLSCA

C

C Use the scale factors to equilibrate A and print the

C equilibrated A.

C

DO 110, ICOL = 1, N

DO 100, IROW = 1, N

A(IROW,ICOL) = A(IROW,ICOL) * ROWSCA(IROW) *

$ COLSCA(ICOL)

100 CONTINUE

110 CONTINUE

PRINT 1070

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

C

1000 FORMAT (1X, 'A:')

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

1020 FORMAT (1X, 'Illegal argument to DGEEQU, argument #', I1)

1030 FORMAT (1X, 'Column ', I1, ' of A is exactly zero.')

1040 FORMAT (1X, 'Row ', I1, ' of A is exactly zero.')

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

1060 FORMAT (/1X, 'Column scale factors:')

1070 FORMAT (/1X, 'Scaled A:')

C

END

Sample Output

A:
2.00000 4.00000 8.00000
2.00000 8.00000 16.00000
2.00000 16.00000 32.00000
Row scale factors:
0.12500 0.06250 0.03125
Column scale factors:
4.00000 2.00000 1.00000
Scaled A:
1.00000 1.00000 1.00000
0.50000 1.00000 1.00000
0.25000 1.00000 1.00000