subroutine slaqgb	(	integer	M,
		integer	N,
		integer	KL,
		integer	KU,
		real, dimension( ldab, * )	AB,
		integer	LDAB,
		real, dimension( * )	R,
		real, dimension( * )	C,
		real	ROWCND,
		real	COLCND,
		real	AMAX,
		character	EQUED
	)

SLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.

Download SLAQGB + dependencies [TGZ] [ZIP] [TXT]

Purpose:

 SLAQGB equilibrates a general M by N band matrix A with KL
 subdiagonals and KU superdiagonals using the row and scaling factors
 in the vectors R and C.

Parameters

[in]	M	M is INTEGER The number of rows of the matrix A. M >= 0.
[in]	N	N is INTEGER The number of columns of the matrix A. N >= 0.
[in]	KL	KL is INTEGER The number of subdiagonals within the band of A. KL >= 0.
[in]	KU	KU is INTEGER The number of superdiagonals within the band of A. KU >= 0.
[in,out]	AB	AB is REAL 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(m,j+kl) On exit, the equilibrated matrix, in the same storage format as A. See EQUED for the form of the equilibrated matrix.
[in]	LDAB	LDAB is INTEGER The leading dimension of the array AB. LDA >= KL+KU+1.
[in]	R	R is REAL array, dimension (M) The row scale factors for A.
[in]	C	C is REAL array, dimension (N) The column scale factors for A.
[in]	ROWCND	ROWCND is REAL Ratio of the smallest R(i) to the largest R(i).
[in]	COLCND	COLCND is REAL Ratio of the smallest C(i) to the largest C(i).
[in]	AMAX	AMAX is REAL Absolute value of largest matrix entry.
[out]	EQUED	EQUED is CHARACTER*1 Specifies the form of equilibration that was done. = 'N': No equilibration = 'R': Row equilibration, i.e., A has been premultiplied by diag(R). = 'C': Column equilibration, i.e., A has been postmultiplied by diag(C). = 'B': Both row and column equilibration, i.e., A has been replaced by diag(R) * A * diag(C).

Internal Parameters:

  THRESH is a threshold value used to decide if row or column scaling
  should be done based on the ratio of the row or column scaling
  factors.  If ROWCND < THRESH, row scaling is done, and if
  COLCND < THRESH, column scaling is done.

  LARGE and SMALL are threshold values used to decide if row scaling
  should be done based on the absolute size of the largest matrix
  element.  If AMAX > LARGE or AMAX < SMALL, row scaling is done.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date

September 2012

Definition at line 161 of file slaqgb.f.

*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          equed
      INTEGER            kl, ku, ldab, m, n
      REAL               amax, colcnd, rowcnd
*     ..
*     .. Array Arguments ..
      REAL               ab( ldab, * ), c( * ), r( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               one, thresh
      parameter                ( one = 1.0e+0, thresh = 0.1e+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            i, j
      REAL               cj, large, small
*     ..
*     .. External Functions ..
      REAL               slamch
      EXTERNAL           slamch
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max, min
*     ..
*     .. Executable Statements ..
*
*     Quick return if possible
*
      IF( m.LE.0 .OR. n.LE.0 ) THEN
         equed = 'N'
         RETURN
      END IF
*
*     Initialize LARGE and SMALL.
*
      small = slamch( 'Safe minimum' ) / slamch( 'Precision' )
      large = one / small
*
      IF( rowcnd.GE.thresh .AND. amax.GE.small .AND. amax.LE.large )
     $     THEN
*
*        No row scaling
*
         IF( colcnd.GE.thresh ) THEN
*
*           No column scaling
*
            equed = 'N'
         ELSE
*
*           Column scaling
*
            DO 20 j = 1, n
               cj = c( j )
               DO 10 i = max( 1, j-ku ), min( m, j+kl )
                  ab( ku+1+i-j, j ) = cj*ab( ku+1+i-j, j )
   10          CONTINUE
   20       CONTINUE
            equed = 'C'
         END IF
      ELSE IF( colcnd.GE.thresh ) THEN
*
*        Row scaling, no column scaling
*
         DO 40 j = 1, n
            DO 30 i = max( 1, j-ku ), min( m, j+kl )
               ab( ku+1+i-j, j ) = r( i )*ab( ku+1+i-j, j )
   30       CONTINUE
   40    CONTINUE
         equed = 'R'
      ELSE
*
*        Row and column scaling
*
         DO 60 j = 1, n
            cj = c( j )
            DO 50 i = max( 1, j-ku ), min( m, j+kl )
               ab( ku+1+i-j, j ) = cj*r( i )*ab( ku+1+i-j, j )
   50       CONTINUE
   60    CONTINUE
         equed = 'B'
      END IF
*
      RETURN
*
*     End of SLAQGB
*

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