LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ dlaqgb()

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 = 'B': Both row and column equilibration, i.e., A has been replaced by diag(R) * A * diag(C).```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

Definition at line 157 of file dlaqgb.f.

159*
160* -- LAPACK auxiliary routine --
161* -- LAPACK is a software package provided by Univ. of Tennessee, --
162* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
163*
164* .. Scalar Arguments ..
165 CHARACTER EQUED
166 INTEGER KL, KU, LDAB, M, N
167 DOUBLE PRECISION AMAX, COLCND, ROWCND
168* ..
169* .. Array Arguments ..
170 DOUBLE PRECISION AB( LDAB, * ), C( * ), R( * )
171* ..
172*
173* =====================================================================
174*
175* .. Parameters ..
176 DOUBLE PRECISION ONE, THRESH
177 parameter( one = 1.0d+0, thresh = 0.1d+0 )
178* ..
179* .. Local Scalars ..
180 INTEGER I, J
181 DOUBLE PRECISION CJ, LARGE, SMALL
182* ..
183* .. External Functions ..
184 DOUBLE PRECISION DLAMCH
185 EXTERNAL dlamch
186* ..
187* .. Intrinsic Functions ..
188 INTRINSIC max, min
189* ..
190* .. Executable Statements ..
191*
192* Quick return if possible
193*
194 IF( m.LE.0 .OR. n.LE.0 ) THEN
195 equed = 'N'
196 RETURN
197 END IF
198*
199* Initialize LARGE and SMALL.
200*
201 small = dlamch( 'Safe minimum' ) / dlamch( 'Precision' )
202 large = one / small
203*
204 IF( rowcnd.GE.thresh .AND. amax.GE.small .AND. amax.LE.large )
205 \$ THEN
206*
207* No row scaling
208*
209 IF( colcnd.GE.thresh ) THEN
210*
211* No column scaling
212*
213 equed = 'N'
214 ELSE
215*
216* Column scaling
217*
218 DO 20 j = 1, n
219 cj = c( j )
220 DO 10 i = max( 1, j-ku ), min( m, j+kl )
221 ab( ku+1+i-j, j ) = cj*ab( ku+1+i-j, j )
222 10 CONTINUE
223 20 CONTINUE
224 equed = 'C'
225 END IF
226 ELSE IF( colcnd.GE.thresh ) THEN
227*
228* Row scaling, no column scaling
229*
230 DO 40 j = 1, n
231 DO 30 i = max( 1, j-ku ), min( m, j+kl )
232 ab( ku+1+i-j, j ) = r( i )*ab( ku+1+i-j, j )
233 30 CONTINUE
234 40 CONTINUE
235 equed = 'R'
236 ELSE
237*
238* Row and column scaling
239*
240 DO 60 j = 1, n
241 cj = c( j )
242 DO 50 i = max( 1, j-ku ), min( m, j+kl )
243 ab( ku+1+i-j, j ) = cj*r( i )*ab( ku+1+i-j, j )
244 50 CONTINUE
245 60 CONTINUE
246 equed = 'B'
247 END IF
248*
249 RETURN
250*
251* End of DLAQGB
252*
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
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