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SUBROUTINE <a name="SLAQGE.1"></a><a href="slaqge.f.html#SLAQGE.1">SLAQGE</a>( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
$ EQUED )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK auxiliary routine (version 3.1) --
</span><span class="comment">*</span><span class="comment"> Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment"> November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> CHARACTER EQUED
INTEGER LDA, M, N
REAL AMAX, COLCND, ROWCND
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> REAL A( LDA, * ), C( * ), R( * )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="SLAQGE.20"></a><a href="slaqge.f.html#SLAQGE.1">SLAQGE</a> equilibrates a general M by N matrix A using the row and
</span><span class="comment">*</span><span class="comment"> column scaling factors in the vectors R and C.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> M (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The number of rows of the matrix A. M >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The number of columns of the matrix A. N >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> A (input/output) REAL array, dimension (LDA,N)
</span><span class="comment">*</span><span class="comment"> On entry, the M by N matrix A.
</span><span class="comment">*</span><span class="comment"> On exit, the equilibrated matrix. See EQUED for the form of
</span><span class="comment">*</span><span class="comment"> the equilibrated matrix.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDA (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array A. LDA >= max(M,1).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> R (input) REAL array, dimension (M)
</span><span class="comment">*</span><span class="comment"> The row scale factors for A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> C (input) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment"> The column scale factors for A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ROWCND (input) REAL
</span><span class="comment">*</span><span class="comment"> Ratio of the smallest R(i) to the largest R(i).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> COLCND (input) REAL
</span><span class="comment">*</span><span class="comment"> Ratio of the smallest C(i) to the largest C(i).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> AMAX (input) REAL
</span><span class="comment">*</span><span class="comment"> Absolute value of largest matrix entry.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> EQUED (output) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> Specifies the form of equilibration that was done.
</span><span class="comment">*</span><span class="comment"> = 'N': No equilibration
</span><span class="comment">*</span><span class="comment"> = 'R': Row equilibration, i.e., A has been premultiplied by
</span><span class="comment">*</span><span class="comment"> diag(R).
</span><span class="comment">*</span><span class="comment"> = 'C': Column equilibration, i.e., A has been postmultiplied
</span><span class="comment">*</span><span class="comment"> by diag(C).
</span><span class="comment">*</span><span class="comment"> = 'B': Both row and column equilibration, i.e., A has been
</span><span class="comment">*</span><span class="comment"> replaced by diag(R) * A * diag(C).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Internal Parameters
</span><span class="comment">*</span><span class="comment"> ===================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> THRESH is a threshold value used to decide if row or column scaling
</span><span class="comment">*</span><span class="comment"> should be done based on the ratio of the row or column scaling
</span><span class="comment">*</span><span class="comment"> factors. If ROWCND < THRESH, row scaling is done, and if
</span><span class="comment">*</span><span class="comment"> COLCND < THRESH, column scaling is done.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LARGE and SMALL are threshold values used to decide if row scaling
</span><span class="comment">*</span><span class="comment"> should be done based on the absolute size of the largest matrix
</span><span class="comment">*</span><span class="comment"> element. If AMAX > LARGE or AMAX < SMALL, row scaling is done.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Parameters ..
</span> REAL ONE, THRESH
PARAMETER ( ONE = 1.0E+0, THRESH = 0.1E+0 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> INTEGER I, J
REAL CJ, LARGE, SMALL
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> REAL <a name="SLAMCH.88"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>
EXTERNAL <a name="SLAMCH.89"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span> IF( M.LE.0 .OR. N.LE.0 ) THEN
EQUED = <span class="string">'N'</span>
RETURN
END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Initialize LARGE and SMALL.
</span><span class="comment">*</span><span class="comment">
</span> SMALL = <a name="SLAMCH.102"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>( <span class="string">'Safe minimum'</span> ) / <a name="SLAMCH.102"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>( <span class="string">'Precision'</span> )
LARGE = ONE / SMALL
<span class="comment">*</span><span class="comment">
</span> IF( ROWCND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE )
$ THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> No row scaling
</span><span class="comment">*</span><span class="comment">
</span> IF( COLCND.GE.THRESH ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> No column scaling
</span><span class="comment">*</span><span class="comment">
</span> EQUED = <span class="string">'N'</span>
ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Column scaling
</span><span class="comment">*</span><span class="comment">
</span> 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 = <span class="string">'C'</span>
END IF
ELSE IF( COLCND.GE.THRESH ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Row scaling, no column scaling
</span><span class="comment">*</span><span class="comment">
</span> DO 40 J = 1, N
DO 30 I = 1, M
A( I, J ) = R( I )*A( I, J )
30 CONTINUE
40 CONTINUE
EQUED = <span class="string">'R'</span>
ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Row and column scaling
</span><span class="comment">*</span><span class="comment">
</span> 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 = <span class="string">'B'</span>
END IF
<span class="comment">*</span><span class="comment">
</span> RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> End of <a name="SLAQGE.152"></a><a href="slaqge.f.html#SLAQGE.1">SLAQGE</a>
</span><span class="comment">*</span><span class="comment">
</span> END
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