 LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine dlaqgb ( integer M, integer N, integer KL, integer KU, double precision, dimension( ldab, * ) AB, integer LDAB, double precision, dimension( * ) R, double precision, dimension( * ) C, double precision ROWCND, double precision COLCND, double precision AMAX, character EQUED )

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

Purpose:
``` DLAQGB 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 DOUBLE PRECISION 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 = 'B': Both row and column equilibration, i.e., A has been replaced by diag(R) * A * diag(C).```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
September 2012

Definition at line 161 of file dlaqgb.f.

161 *
162 * -- LAPACK auxiliary routine (version 3.4.2) --
163 * -- LAPACK is a software package provided by Univ. of Tennessee, --
164 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
165 * September 2012
166 *
167 * .. Scalar Arguments ..
168  CHARACTER equed
169  INTEGER kl, ku, ldab, m, n
170  DOUBLE PRECISION amax, colcnd, rowcnd
171 * ..
172 * .. Array Arguments ..
173  DOUBLE PRECISION ab( ldab, * ), c( * ), r( * )
174 * ..
175 *
176 * =====================================================================
177 *
178 * .. Parameters ..
179  DOUBLE PRECISION one, thresh
180  parameter ( one = 1.0d+0, thresh = 0.1d+0 )
181 * ..
182 * .. Local Scalars ..
183  INTEGER i, j
184  DOUBLE PRECISION cj, large, small
185 * ..
186 * .. External Functions ..
187  DOUBLE PRECISION dlamch
188  EXTERNAL dlamch
189 * ..
190 * .. Intrinsic Functions ..
191  INTRINSIC max, min
192 * ..
193 * .. Executable Statements ..
194 *
195 * Quick return if possible
196 *
197  IF( m.LE.0 .OR. n.LE.0 ) THEN
198  equed = 'N'
199  RETURN
200  END IF
201 *
202 * Initialize LARGE and SMALL.
203 *
204  small = dlamch( 'Safe minimum' ) / dlamch( 'Precision' )
205  large = one / small
206 *
207  IF( rowcnd.GE.thresh .AND. amax.GE.small .AND. amax.LE.large )
208  \$ THEN
209 *
210 * No row scaling
211 *
212  IF( colcnd.GE.thresh ) THEN
213 *
214 * No column scaling
215 *
216  equed = 'N'
217  ELSE
218 *
219 * Column scaling
220 *
221  DO 20 j = 1, n
222  cj = c( j )
223  DO 10 i = max( 1, j-ku ), min( m, j+kl )
224  ab( ku+1+i-j, j ) = cj*ab( ku+1+i-j, j )
225  10 CONTINUE
226  20 CONTINUE
227  equed = 'C'
228  END IF
229  ELSE IF( colcnd.GE.thresh ) THEN
230 *
231 * Row scaling, no column scaling
232 *
233  DO 40 j = 1, n
234  DO 30 i = max( 1, j-ku ), min( m, j+kl )
235  ab( ku+1+i-j, j ) = r( i )*ab( ku+1+i-j, j )
236  30 CONTINUE
237  40 CONTINUE
238  equed = 'R'
239  ELSE
240 *
241 * Row and column scaling
242 *
243  DO 60 j = 1, n
244  cj = c( j )
245  DO 50 i = max( 1, j-ku ), min( m, j+kl )
246  ab( ku+1+i-j, j ) = cj*r( i )*ab( ku+1+i-j, j )
247  50 CONTINUE
248  60 CONTINUE
249  equed = 'B'
250  END IF
251 *
252  RETURN
253 *
254 * End of DLAQGB
255 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65

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