LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ zlaqhb()

 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.

Download ZLAQHB + dependencies [TGZ] [ZIP] [TXT]

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 = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).```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.```

Definition at line 140 of file zlaqhb.f.

141*
142* -- LAPACK auxiliary routine --
143* -- LAPACK is a software package provided by Univ. of Tennessee, --
144* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
145*
146* .. Scalar Arguments ..
147 CHARACTER EQUED, UPLO
148 INTEGER KD, LDAB, N
149 DOUBLE PRECISION AMAX, SCOND
150* ..
151* .. Array Arguments ..
152 DOUBLE PRECISION S( * )
153 COMPLEX*16 AB( LDAB, * )
154* ..
155*
156* =====================================================================
157*
158* .. Parameters ..
159 DOUBLE PRECISION ONE, THRESH
160 parameter( one = 1.0d+0, thresh = 0.1d+0 )
161* ..
162* .. Local Scalars ..
163 INTEGER I, J
164 DOUBLE PRECISION CJ, LARGE, SMALL
165* ..
166* .. External Functions ..
167 LOGICAL LSAME
168 DOUBLE PRECISION DLAMCH
169 EXTERNAL lsame, dlamch
170* ..
171* .. Intrinsic Functions ..
172 INTRINSIC dble, max, min
173* ..
174* .. Executable Statements ..
175*
176* Quick return if possible
177*
178 IF( n.LE.0 ) THEN
179 equed = 'N'
180 RETURN
181 END IF
182*
183* Initialize LARGE and SMALL.
184*
185 small = dlamch( 'Safe minimum' ) / dlamch( 'Precision' )
186 large = one / small
187*
188 IF( scond.GE.thresh .AND. amax.GE.small .AND. amax.LE.large ) THEN
189*
190* No equilibration
191*
192 equed = 'N'
193 ELSE
194*
195* Replace A by diag(S) * A * diag(S).
196*
197 IF( lsame( uplo, 'U' ) ) THEN
198*
199* Upper triangle of A is stored in band format.
200*
201 DO 20 j = 1, n
202 cj = s( j )
203 DO 10 i = max( 1, j-kd ), j - 1
204 ab( kd+1+i-j, j ) = cj*s( i )*ab( kd+1+i-j, j )
205 10 CONTINUE
206 ab( kd+1, j ) = cj*cj*dble( ab( kd+1, j ) )
207 20 CONTINUE
208 ELSE
209*
210* Lower triangle of A is stored.
211*
212 DO 40 j = 1, n
213 cj = s( j )
214 ab( 1, j ) = cj*cj*dble( ab( 1, j ) )
215 DO 30 i = j + 1, min( n, j+kd )
216 ab( 1+i-j, j ) = cj*s( i )*ab( 1+i-j, j )
217 30 CONTINUE
218 40 CONTINUE
219 END IF
220 equed = 'Y'
221 END IF
222*
223 RETURN
224*
225* End of ZLAQHB
226*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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