LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ slaqge()

 subroutine slaqge ( integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) r, real, dimension( * ) c, real rowcnd, real colcnd, real amax, character equed )

SLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ.

Purpose:
``` SLAQGE equilibrates a general M by N matrix A using the row and
column 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,out] A ``` A is REAL 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.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(M,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 = 'B': Both row and column equilibration, i.e., A has been replaced by diag(R) * A * diag(C).```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.```

Definition at line 140 of file slaqge.f.

142*
143* -- LAPACK auxiliary routine --
144* -- LAPACK is a software package provided by Univ. of Tennessee, --
145* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
146*
147* .. Scalar Arguments ..
148 CHARACTER EQUED
149 INTEGER LDA, M, N
150 REAL AMAX, COLCND, ROWCND
151* ..
152* .. Array Arguments ..
153 REAL A( LDA, * ), C( * ), R( * )
154* ..
155*
156* =====================================================================
157*
158* .. Parameters ..
159 REAL ONE, THRESH
160 parameter( one = 1.0e+0, thresh = 0.1e+0 )
161* ..
162* .. Local Scalars ..
163 INTEGER I, J
164 REAL CJ, LARGE, SMALL
165* ..
166* .. External Functions ..
167 REAL SLAMCH
168 EXTERNAL slamch
169* ..
170* .. Executable Statements ..
171*
172* Quick return if possible
173*
174 IF( m.LE.0 .OR. n.LE.0 ) THEN
175 equed = 'N'
176 RETURN
177 END IF
178*
179* Initialize LARGE and SMALL.
180*
181 small = slamch( 'Safe minimum' ) / slamch( 'Precision' )
182 large = one / small
183*
184 IF( rowcnd.GE.thresh .AND. amax.GE.small .AND. amax.LE.large )
185 \$ THEN
186*
187* No row scaling
188*
189 IF( colcnd.GE.thresh ) THEN
190*
191* No column scaling
192*
193 equed = 'N'
194 ELSE
195*
196* Column scaling
197*
198 DO 20 j = 1, n
199 cj = c( j )
200 DO 10 i = 1, m
201 a( i, j ) = cj*a( i, j )
202 10 CONTINUE
203 20 CONTINUE
204 equed = 'C'
205 END IF
206 ELSE IF( colcnd.GE.thresh ) THEN
207*
208* Row scaling, no column scaling
209*
210 DO 40 j = 1, n
211 DO 30 i = 1, m
212 a( i, j ) = r( i )*a( i, j )
213 30 CONTINUE
214 40 CONTINUE
215 equed = 'R'
216 ELSE
217*
218* Row and column scaling
219*
220 DO 60 j = 1, n
221 cj = c( j )
222 DO 50 i = 1, m
223 a( i, j ) = cj*r( i )*a( i, j )
224 50 CONTINUE
225 60 CONTINUE
226 equed = 'B'
227 END IF
228*
229 RETURN
230*
231* End of SLAQGE
232*
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
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