LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ 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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

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*
dlamch
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
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