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SUBROUTINE SLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
$ AMAX, EQUED )
*
* -- LAPACK auxiliary routine (version 2.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* February 29, 1992
*
* .. Scalar Arguments ..
CHARACTER EQUED
INTEGER KL, KU, LDAB, M, N
REAL AMAX, COLCND, ROWCND
* ..
* .. Array Arguments ..
REAL AB( LDAB, * ), C( * ), R( * )
* ..
*
* 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.
*
* 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/output) 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.
*
* LDAB (input) INTEGER
* The leading dimension of the array AB. LDA >= KL+KU+1.
*
* R (output) REAL array, dimension (M)
* The row scale factors for A.
*
* C (output) REAL array, dimension (N)
* The column scale factors for A.
*
* ROWCND (output) REAL
* Ratio of the smallest R(i) to the largest R(i).
*
* COLCND (output) REAL
* Ratio of the smallest C(i) to the largest C(i).
*
* AMAX (input) REAL
* Absolute value of largest matrix entry.
*
* EQUED (output) 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.
*
* =====================================================================
*
* .. 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
*
END
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