LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 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 = 'B': Both row and column equilibration, i.e., A has been replaced by diag(R) * A * diag(C).```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.```
Date
September 2012

Definition at line 145 of file zlaqge.f.

145 *
146 * -- LAPACK auxiliary routine (version 3.4.2) --
147 * -- LAPACK is a software package provided by Univ. of Tennessee, --
148 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
149 * September 2012
150 *
151 * .. Scalar Arguments ..
152  CHARACTER equed
153  INTEGER lda, m, n
154  DOUBLE PRECISION amax, colcnd, rowcnd
155 * ..
156 * .. Array Arguments ..
157  DOUBLE PRECISION c( * ), r( * )
158  COMPLEX*16 a( lda, * )
159 * ..
160 *
161 * =====================================================================
162 *
163 * .. Parameters ..
164  DOUBLE PRECISION one, thresh
165  parameter ( one = 1.0d+0, thresh = 0.1d+0 )
166 * ..
167 * .. Local Scalars ..
168  INTEGER i, j
169  DOUBLE PRECISION cj, large, small
170 * ..
171 * .. External Functions ..
172  DOUBLE PRECISION dlamch
173  EXTERNAL dlamch
174 * ..
175 * .. Executable Statements ..
176 *
177 * Quick return if possible
178 *
179  IF( m.LE.0 .OR. n.LE.0 ) THEN
180  equed = 'N'
181  RETURN
182  END IF
183 *
184 * Initialize LARGE and SMALL.
185 *
186  small = dlamch( 'Safe minimum' ) / dlamch( 'Precision' )
187  large = one / small
188 *
189  IF( rowcnd.GE.thresh .AND. amax.GE.small .AND. amax.LE.large )
190  \$ THEN
191 *
192 * No row scaling
193 *
194  IF( colcnd.GE.thresh ) THEN
195 *
196 * No column scaling
197 *
198  equed = 'N'
199  ELSE
200 *
201 * Column scaling
202 *
203  DO 20 j = 1, n
204  cj = c( j )
205  DO 10 i = 1, m
206  a( i, j ) = cj*a( i, j )
207  10 CONTINUE
208  20 CONTINUE
209  equed = 'C'
210  END IF
211  ELSE IF( colcnd.GE.thresh ) THEN
212 *
213 * Row scaling, no column scaling
214 *
215  DO 40 j = 1, n
216  DO 30 i = 1, m
217  a( i, j ) = r( i )*a( i, j )
218  30 CONTINUE
219  40 CONTINUE
220  equed = 'R'
221  ELSE
222 *
223 * Row and column scaling
224 *
225  DO 60 j = 1, n
226  cj = c( j )
227  DO 50 i = 1, m
228  a( i, j ) = cj*r( i )*a( i, j )
229  50 CONTINUE
230  60 CONTINUE
231  equed = 'B'
232  END IF
233 *
234  RETURN
235 *
236 * End of ZLAQGE
237 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65

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