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RedHat 9 (Linux i386) - man page for zgeequ (redhat section l)

ZGEEQU(l)					)					ZGEEQU(l)

NAME
       ZGEEQU  -  compute  row and column scalings intended to equilibrate an M-by-N matrix A and
       reduce its condition number

SYNOPSIS
       SUBROUTINE ZGEEQU( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO )

	   INTEGER	  INFO, LDA, M, N

	   DOUBLE	  PRECISION AMAX, COLCND, ROWCND

	   DOUBLE	  PRECISION C( * ), R( * )

	   COMPLEX*16	  A( LDA, * )

PURPOSE
       ZGEEQU 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 fac-
       tors, 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 absolute value 1.

       R(i)  and  C(j)	are  restricted  to be between SMLNUM = smallest safe number and BIGNUM =
       largest safe number.  Use of these scaling factors is not guaranteed to reduce the  condi-
       tion number of A but works well in practice.

ARGUMENTS
       M       (input) INTEGER
	       The number of rows of the matrix A.  M >= 0.

       N       (input) INTEGER
	       The number of columns of the matrix A.  N >= 0.

       A       (input) COMPLEX*16 array, dimension (LDA,N)
	       The M-by-N matrix whose equilibration factors are to be computed.

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

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

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

       ROWCND  (output) 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  (output) 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    (output) 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    (output) 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

LAPACK version 3.0			   15 June 2000 				ZGEEQU(l)


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