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+ SUBROUTINE DLAQGE( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
+ $ EQUED )
+*
+* -- LAPACK auxiliary routine (version 3.1) --
+* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
+* November 2006
+*
+* .. Scalar Arguments ..
+ CHARACTER EQUED
+ INTEGER LDA, M, N
+ DOUBLE PRECISION AMAX, COLCND, ROWCND
+* ..
+* .. Array Arguments ..
+ DOUBLE PRECISION A( LDA, * ), C( * ), R( * )
+* ..
+*
+* Purpose
+* =======
+*
+* DLAQGE equilibrates a general M by N matrix A using the row and
+* column 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.
+*
+* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
+* On entry, the M by N matrix A.
+* On exit, the equilibrated matrix. See EQUED for the form of
+* the equilibrated matrix.
+*
+* LDA (input) INTEGER
+* The leading dimension of the array A. LDA >= max(M,1).
+*
+* R (input) DOUBLE PRECISION array, dimension (M)
+* The row scale factors for A.
+*
+* C (input) DOUBLE PRECISION array, dimension (N)
+* The column scale factors for A.
+*
+* ROWCND (input) DOUBLE PRECISION
+* Ratio of the smallest R(i) to the largest R(i).
+*
+* COLCND (input) DOUBLE PRECISION
+* Ratio of the smallest C(i) to the largest C(i).
+*
+* AMAX (input) DOUBLE PRECISION
+* 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 ..
+ DOUBLE PRECISION ONE, THRESH
+ PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
+* ..
+* .. Local Scalars ..
+ INTEGER I, J
+ DOUBLE PRECISION CJ, LARGE, SMALL
+* ..
+* .. External Functions ..
+ DOUBLE PRECISION DLAMCH
+ EXTERNAL DLAMCH
+* ..
+* .. 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 = DLAMCH( 'Safe minimum' ) / DLAMCH( '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 = 1, M
+ A( I, J ) = CJ*A( I, 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 = 1, M
+ A( I, J ) = R( I )*A( I, J )
+ 30 CONTINUE
+ 40 CONTINUE
+ EQUED = 'R'
+ ELSE
+*
+* Row and column scaling
+*
+ DO 60 J = 1, N
+ CJ = C( J )
+ DO 50 I = 1, M
+ A( I, J ) = CJ*R( I )*A( I, J )
+ 50 CONTINUE
+ 60 CONTINUE
+ EQUED = 'B'
+ END IF
+*
+ RETURN
+*
+* End of DLAQGE
+*
+ END