LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine zlaqhb ( character UPLO, integer N, integer KD, complex*16, dimension( ldab, * ) AB, integer LDAB, double precision, dimension( * ) S, double precision SCOND, double precision AMAX, character EQUED )

ZLAQHB scales a Hermitian band matrix, using scaling factors computed by cpbequ.

Purpose:
``` ZLAQHB equilibrates a Hermitian band matrix A
using the scaling factors in the vector S.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored. = 'U': Upper triangular = 'L': Lower triangular``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in] KD ``` KD is INTEGER The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 0.``` [in,out] AB ``` AB is COMPLEX*16 array, dimension (LDAB,N) On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first KD+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). On exit, if INFO = 0, the triangular factor U or L from the Cholesky factorization A = U**H *U or A = L*L**H of the band matrix A, in the same storage format as A.``` [in] LDAB ``` LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD+1.``` [out] S ``` S is DOUBLE PRECISION array, dimension (N) The scale factors for A.``` [in] SCOND ``` SCOND is DOUBLE PRECISION Ratio of the smallest S(i) to the largest S(i).``` [in] AMAX ``` AMAX is DOUBLE PRECISION Absolute value of largest matrix entry.``` [out] EQUED ``` EQUED is CHARACTER*1 Specifies whether or not equilibration was done. = 'N': No equilibration. = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).```
Internal Parameters:
```  THRESH is a threshold value used to decide if scaling should be done
based on the ratio of the scaling factors.  If SCOND < THRESH,
scaling is done.

LARGE and SMALL are threshold values used to decide if scaling should
be done based on the absolute size of the largest matrix element.
If AMAX > LARGE or AMAX < SMALL, scaling is done.```
Date
September 2012

Definition at line 143 of file zlaqhb.f.

143 *
144 * -- LAPACK auxiliary routine (version 3.4.2) --
145 * -- LAPACK is a software package provided by Univ. of Tennessee, --
146 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
147 * September 2012
148 *
149 * .. Scalar Arguments ..
150  CHARACTER equed, uplo
151  INTEGER kd, ldab, n
152  DOUBLE PRECISION amax, scond
153 * ..
154 * .. Array Arguments ..
155  DOUBLE PRECISION s( * )
156  COMPLEX*16 ab( ldab, * )
157 * ..
158 *
159 * =====================================================================
160 *
161 * .. Parameters ..
162  DOUBLE PRECISION one, thresh
163  parameter ( one = 1.0d+0, thresh = 0.1d+0 )
164 * ..
165 * .. Local Scalars ..
166  INTEGER i, j
167  DOUBLE PRECISION cj, large, small
168 * ..
169 * .. External Functions ..
170  LOGICAL lsame
171  DOUBLE PRECISION dlamch
172  EXTERNAL lsame, dlamch
173 * ..
174 * .. Intrinsic Functions ..
175  INTRINSIC dble, max, min
176 * ..
177 * .. Executable Statements ..
178 *
179 * Quick return if possible
180 *
181  IF( n.LE.0 ) THEN
182  equed = 'N'
183  RETURN
184  END IF
185 *
186 * Initialize LARGE and SMALL.
187 *
188  small = dlamch( 'Safe minimum' ) / dlamch( 'Precision' )
189  large = one / small
190 *
191  IF( scond.GE.thresh .AND. amax.GE.small .AND. amax.LE.large ) THEN
192 *
193 * No equilibration
194 *
195  equed = 'N'
196  ELSE
197 *
198 * Replace A by diag(S) * A * diag(S).
199 *
200  IF( lsame( uplo, 'U' ) ) THEN
201 *
202 * Upper triangle of A is stored in band format.
203 *
204  DO 20 j = 1, n
205  cj = s( j )
206  DO 10 i = max( 1, j-kd ), j - 1
207  ab( kd+1+i-j, j ) = cj*s( i )*ab( kd+1+i-j, j )
208  10 CONTINUE
209  ab( kd+1, j ) = cj*cj*dble( ab( kd+1, j ) )
210  20 CONTINUE
211  ELSE
212 *
213 * Lower triangle of A is stored.
214 *
215  DO 40 j = 1, n
216  cj = s( j )
217  ab( 1, j ) = cj*cj*dble( ab( 1, j ) )
218  DO 30 i = j + 1, min( n, j+kd )
219  ab( 1+i-j, j ) = cj*s( i )*ab( 1+i-j, j )
220  30 CONTINUE
221  40 CONTINUE
222  END IF
223  equed = 'Y'
224  END IF
225 *
226  RETURN
227 *
228 * End of ZLAQHB
229 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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