LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ 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 = 'B': Both row and column equilibration, i.e., A has been replaced by diag(R) * A * diag(C).```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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