 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ zlaqgb()

 subroutine zlaqgb ( integer M, integer N, integer KL, integer KU, complex*16, dimension( ldab, * ) AB, integer LDAB, double precision, dimension( * ) R, double precision, dimension( * ) C, double precision ROWCND, double precision COLCND, double precision AMAX, character EQUED )

ZLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.

Download ZLAQGB + dependencies [TGZ] [ZIP] [TXT]

Purpose:
``` ZLAQGB equilibrates a general M by N band matrix A with KL
subdiagonals and KU superdiagonals using the row and 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] KL ``` KL is INTEGER The number of subdiagonals within the band of A. KL >= 0.``` [in] KU ``` KU is INTEGER The number of superdiagonals within the band of A. KU >= 0.``` [in,out] AB ``` AB is COMPLEX*16 array, dimension (LDAB,N) On entry, the matrix A in band storage, in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows: AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) On exit, the equilibrated matrix, in the same storage format as A. See EQUED for the form of the equilibrated matrix.``` [in] LDAB ``` LDAB is INTEGER The leading dimension of the array AB. LDA >= KL+KU+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 = 'B': Both row and column equilibration, i.e., A has been replaced by diag(R) * A * diag(C).```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
December 2016

Definition at line 162 of file zlaqgb.f.

162 *
163 * -- LAPACK auxiliary routine (version 3.7.0) --
164 * -- LAPACK is a software package provided by Univ. of Tennessee, --
165 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
166 * December 2016
167 *
168 * .. Scalar Arguments ..
169  CHARACTER equed
170  INTEGER kl, ku, ldab, m, n
171  DOUBLE PRECISION amax, colcnd, rowcnd
172 * ..
173 * .. Array Arguments ..
174  DOUBLE PRECISION c( * ), r( * )
175  COMPLEX*16 ab( ldab, * )
176 * ..
177 *
178 * =====================================================================
179 *
180 * .. Parameters ..
181  DOUBLE PRECISION one, thresh
182  parameter( one = 1.0d+0, thresh = 0.1d+0 )
183 * ..
184 * .. Local Scalars ..
185  INTEGER i, j
186  DOUBLE PRECISION cj, large, small
187 * ..
188 * .. External Functions ..
189  DOUBLE PRECISION dlamch
190  EXTERNAL dlamch
191 * ..
192 * .. Intrinsic Functions ..
193  INTRINSIC max, min
194 * ..
195 * .. Executable Statements ..
196 *
197 * Quick return if possible
198 *
199  IF( m.LE.0 .OR. n.LE.0 ) THEN
200  equed = 'N'
201  RETURN
202  END IF
203 *
204 * Initialize LARGE and SMALL.
205 *
206  small = dlamch( 'Safe minimum' ) / dlamch( 'Precision' )
207  large = one / small
208 *
209  IF( rowcnd.GE.thresh .AND. amax.GE.small .AND. amax.LE.large )
210  \$ THEN
211 *
212 * No row scaling
213 *
214  IF( colcnd.GE.thresh ) THEN
215 *
216 * No column scaling
217 *
218  equed = 'N'
219  ELSE
220 *
221 * Column scaling
222 *
223  DO 20 j = 1, n
224  cj = c( j )
225  DO 10 i = max( 1, j-ku ), min( m, j+kl )
226  ab( ku+1+i-j, j ) = cj*ab( ku+1+i-j, j )
227  10 CONTINUE
228  20 CONTINUE
229  equed = 'C'
230  END IF
231  ELSE IF( colcnd.GE.thresh ) THEN
232 *
233 * Row scaling, no column scaling
234 *
235  DO 40 j = 1, n
236  DO 30 i = max( 1, j-ku ), min( m, j+kl )
237  ab( ku+1+i-j, j ) = r( i )*ab( ku+1+i-j, j )
238  30 CONTINUE
239  40 CONTINUE
240  equed = 'R'
241  ELSE
242 *
243 * Row and column scaling
244 *
245  DO 60 j = 1, n
246  cj = c( j )
247  DO 50 i = max( 1, j-ku ), min( m, j+kl )
248  ab( ku+1+i-j, j ) = cj*r( i )*ab( ku+1+i-j, j )
249  50 CONTINUE
250  60 CONTINUE
251  equed = 'B'
252  END IF
253 *
254  RETURN
255 *
256 * End of ZLAQGB
257 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
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