dgeequb-f(3)

dgeequb.f –

Synopsis

Functions/Subroutines

subroutine dgeequb (M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO)
DGEEQUB

Function/Subroutine Documentation

subroutine dgeequb (integerM, integerN, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( * )R, double precision, dimension( * )C, double precisionROWCND, double precisionCOLCND, double precisionAMAX, integerINFO)

DGEEQUB

Purpose:

 DGEEQUB computes row and column scalings intended to equilibrate an
 M-by-N matrix A and reduce its condition number. R returns the row
 scale factors and C the column scale factors, chosen to try to make
 the largest element in each row and column of the matrix B with
 elements B(i,j)=R(i)*A(i,j)*C(j) have an absolute value of at most
 the radix.
 R(i) and C(j) are restricted to be a power of the radix between
 SMLNUM = smallest safe number and BIGNUM = largest safe number. Use
 of these scaling factors is not guaranteed to reduce the condition
 number of A but works well in practice.
 This routine differs from DGEEQU by restricting the scaling factors
 to a power of the radix. Baring over- and underflow, scaling by
 these factors introduces no additional rounding errors. However, the
 scaled entries' magnitured are no longer approximately 1 but lie
 between sqrt(radix) and 1/sqrt(radix).

 

Parameters:

M

 M is INTEGER
 The number of rows of the matrix A. M >= 0.

N

 N is INTEGER
 The number of columns of the matrix A. N >= 0.

A

 A is DOUBLE PRECISION array, dimension (LDA,N)
 The M-by-N matrix whose equilibration factors are
 to be computed.

LDA

 LDA is INTEGER
 The leading dimension of the array A. LDA >= max(1,M).

R

 R is DOUBLE PRECISION array, dimension (M)
 If INFO = 0 or INFO > M, R contains the row scale factors
 for A.

C

 C is DOUBLE PRECISION array, dimension (N)
 If INFO = 0, C contains the column scale factors for A.

ROWCND

 ROWCND is DOUBLE PRECISION
 If INFO = 0 or INFO > M, ROWCND contains the ratio of the
 smallest R(i) to the largest R(i). If ROWCND >= 0.1 and
 AMAX is neither too large nor too small, it is not worth
 scaling by R.

COLCND

 COLCND is DOUBLE PRECISION
 If INFO = 0, COLCND contains the ratio of the smallest
 C(i) to the largest C(i). If COLCND >= 0.1, it is not
 worth scaling by C.

AMAX

 AMAX is DOUBLE PRECISION
 Absolute value of largest matrix element. If AMAX is very
 close to overflow or very close to underflow, the matrix
 should be scaled.

INFO

 INFO is INTEGER
 = 0: successful exit
 < 0: if INFO = -i, the i-th argument had an illegal value
 > 0: if INFO = i, and i is
 <= M: the i-th row of A is exactly zero
 > M: the (i-M)-th column of A is exactly zero

 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Definition at line 146 of file dgeequb.f.

Author

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