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

CGBEQU(l)					)					CGBEQU(l)

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

SYNOPSIS
       SUBROUTINE CGBEQU( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, INFO )

	   INTEGER	  INFO, KL, KU, LDAB, M, N

	   REAL 	  AMAX, COLCND, ROWCND

	   REAL 	  C( * ), R( * )

	   COMPLEX	  AB( LDAB, * )

PURPOSE
       CGBEQU computes row and column scalings intended to equilibrate an M-by-N  band	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 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.

       KL      (input) INTEGER
	       The number of subdiagonals within the band of A.  KL >= 0.

       KU      (input) INTEGER
	       The number of superdiagonals within the band of A.  KU >= 0.

       AB      (input) COMPLEX array, dimension (LDAB,N)
	       The band matrix A, stored in rows 1 to KL+KU+1.	The j-th column of A is stored in
	       the j-th column of the array AB as follows: AB(ku+1+i-j,j) = A(i,j)  for  max(1,j-
	       ku)<=i<=min(m,j+kl).

       LDAB    (input) INTEGER
	       The leading dimension of the array AB.  LDAB >= KL+KU+1.

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

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

       ROWCND  (output) REAL
	       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) REAL
	       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) REAL
	       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 				CGBEQU(l)


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