 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ zlaqge()

 subroutine zlaqge ( integer M, integer N, complex*16, dimension( lda, * ) A, integer LDA, double precision, dimension( * ) R, double precision, dimension( * ) C, double precision ROWCND, double precision COLCND, double precision AMAX, character EQUED )

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

Purpose:
``` ZLAQGE 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 COMPLEX*16 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 DOUBLE PRECISION array, dimension (M) The row scale factors for A.``` [in] C ``` C is DOUBLE PRECISION array, dimension (N) The column scale factors for A.``` [in] ROWCND ``` ROWCND is DOUBLE PRECISION Ratio of the smallest R(i) to the largest R(i).``` [in] COLCND ``` COLCND is DOUBLE PRECISION Ratio of the smallest C(i) to the largest C(i).``` [in] AMAX ``` AMAX is DOUBLE PRECISION 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 = 'B': Both row and column equilibration, i.e., A has been replaced by diag(R) * A * diag(C).```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 141 of file zlaqge.f.

143*
144* -- LAPACK auxiliary routine --
145* -- LAPACK is a software package provided by Univ. of Tennessee, --
146* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
147*
148* .. Scalar Arguments ..
149 CHARACTER EQUED
150 INTEGER LDA, M, N
151 DOUBLE PRECISION AMAX, COLCND, ROWCND
152* ..
153* .. Array Arguments ..
154 DOUBLE PRECISION C( * ), R( * )
155 COMPLEX*16 A( LDA, * )
156* ..
157*
158* =====================================================================
159*
160* .. Parameters ..
161 DOUBLE PRECISION ONE, THRESH
162 parameter( one = 1.0d+0, thresh = 0.1d+0 )
163* ..
164* .. Local Scalars ..
165 INTEGER I, J
166 DOUBLE PRECISION CJ, LARGE, SMALL
167* ..
168* .. External Functions ..
169 DOUBLE PRECISION DLAMCH
170 EXTERNAL dlamch
171* ..
172* .. Executable Statements ..
173*
174* Quick return if possible
175*
176 IF( m.LE.0 .OR. n.LE.0 ) THEN
177 equed = 'N'
178 RETURN
179 END IF
180*
181* Initialize LARGE and SMALL.
182*
183 small = dlamch( 'Safe minimum' ) / dlamch( 'Precision' )
184 large = one / small
185*
186 IF( rowcnd.GE.thresh .AND. amax.GE.small .AND. amax.LE.large )
187 \$ THEN
188*
189* No row scaling
190*
191 IF( colcnd.GE.thresh ) THEN
192*
193* No column scaling
194*
195 equed = 'N'
196 ELSE
197*
198* Column scaling
199*
200 DO 20 j = 1, n
201 cj = c( j )
202 DO 10 i = 1, m
203 a( i, j ) = cj*a( i, j )
204 10 CONTINUE
205 20 CONTINUE
206 equed = 'C'
207 END IF
208 ELSE IF( colcnd.GE.thresh ) THEN
209*
210* Row scaling, no column scaling
211*
212 DO 40 j = 1, n
213 DO 30 i = 1, m
214 a( i, j ) = r( i )*a( i, j )
215 30 CONTINUE
216 40 CONTINUE
217 equed = 'R'
218 ELSE
219*
220* Row and column scaling
221*
222 DO 60 j = 1, n
223 cj = c( j )
224 DO 50 i = 1, m
225 a( i, j ) = cj*r( i )*a( i, j )
226 50 CONTINUE
227 60 CONTINUE
228 equed = 'B'
229 END IF
230*
231 RETURN
232*
233* End of ZLAQGE
234*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
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