 LAPACK  3.10.0 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.

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 = 'B': Both row and column equilibration, i.e., A has been replaced by diag(R) * A * diag(C).```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

Definition at line 158 of file zlaqgb.f.

160 *
161 * -- LAPACK auxiliary routine --
162 * -- LAPACK is a software package provided by Univ. of Tennessee, --
163 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
164 *
165 * .. Scalar Arguments ..
166  CHARACTER EQUED
167  INTEGER KL, KU, LDAB, M, N
168  DOUBLE PRECISION AMAX, COLCND, ROWCND
169 * ..
170 * .. Array Arguments ..
171  DOUBLE PRECISION C( * ), R( * )
172  COMPLEX*16 AB( LDAB, * )
173 * ..
174 *
175 * =====================================================================
176 *
177 * .. Parameters ..
178  DOUBLE PRECISION ONE, THRESH
179  parameter( one = 1.0d+0, thresh = 0.1d+0 )
180 * ..
181 * .. Local Scalars ..
182  INTEGER I, J
183  DOUBLE PRECISION CJ, LARGE, SMALL
184 * ..
185 * .. External Functions ..
186  DOUBLE PRECISION DLAMCH
187  EXTERNAL dlamch
188 * ..
189 * .. Intrinsic Functions ..
190  INTRINSIC max, min
191 * ..
192 * .. Executable Statements ..
193 *
194 * Quick return if possible
195 *
196  IF( m.LE.0 .OR. n.LE.0 ) THEN
197  equed = 'N'
198  RETURN
199  END IF
200 *
201 * Initialize LARGE and SMALL.
202 *
203  small = dlamch( 'Safe minimum' ) / dlamch( 'Precision' )
204  large = one / small
205 *
206  IF( rowcnd.GE.thresh .AND. amax.GE.small .AND. amax.LE.large )
207  \$ THEN
208 *
209 * No row scaling
210 *
211  IF( colcnd.GE.thresh ) THEN
212 *
213 * No column scaling
214 *
215  equed = 'N'
216  ELSE
217 *
218 * Column scaling
219 *
220  DO 20 j = 1, n
221  cj = c( j )
222  DO 10 i = max( 1, j-ku ), min( m, j+kl )
223  ab( ku+1+i-j, j ) = cj*ab( ku+1+i-j, j )
224  10 CONTINUE
225  20 CONTINUE
226  equed = 'C'
227  END IF
228  ELSE IF( colcnd.GE.thresh ) THEN
229 *
230 * Row scaling, no column scaling
231 *
232  DO 40 j = 1, n
233  DO 30 i = max( 1, j-ku ), min( m, j+kl )
234  ab( ku+1+i-j, j ) = r( i )*ab( ku+1+i-j, j )
235  30 CONTINUE
236  40 CONTINUE
237  equed = 'R'
238  ELSE
239 *
240 * Row and column scaling
241 *
242  DO 60 j = 1, n
243  cj = c( j )
244  DO 50 i = max( 1, j-ku ), min( m, j+kl )
245  ab( ku+1+i-j, j ) = cj*r( i )*ab( ku+1+i-j, j )
246  50 CONTINUE
247  60 CONTINUE
248  equed = 'B'
249  END IF
250 *
251  RETURN
252 *
253 * End of ZLAQGB
254 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
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