sgbequb.f(3)							      LAPACK							      sgbequb.f(3)

NAME

       sgbequb.f -

SYNOPSIS

   Functions/Subroutines
       subroutine sgbequb (M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, INFO)
	   SGBEQUB

Function/Subroutine Documentation
   subroutine sgbequb (integerM, integerN, integerKL, integerKU, real, dimension( ldab, * )AB, integerLDAB, real, dimension( * )R, real,
       dimension( * )C, realROWCND, realCOLCND, realAMAX, integerINFO)
       SGBEQUB

       Purpose:

	    SGBEQUB 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 SGEEQU 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.

	   KL

		     KL is INTEGER
		     The number of subdiagonals within the band of A.  KL >= 0.

	   KU

		     KU is INTEGER
		     The number of superdiagonals within the band of A.  KU >= 0.

	   AB

		     AB is DOUBLE PRECISION array, dimension (LDAB,N)
		     On entry, the matrix A in band storage, 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(N,j+kl)

	   LDAB

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

	   R

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

	   C

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

	   ROWCND

		     ROWCND is 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

		     COLCND is 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

		     AMAX is 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

		     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 160 of file sgbequb.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.1							  Sun May 26 2013						      sgbequb.f(3)