LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ claqhb()

subroutine claqhb ( character  UPLO,
integer  N,
integer  KD,
complex, dimension( ldab, * )  AB,
integer  LDAB,
real, dimension( * )  S,
real  SCOND,
real  AMAX,
character  EQUED 
)

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

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

Purpose:
 CLAQHB equilibrates an 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 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 REAL array, dimension (N)
          The scale factors for A.
[in]SCOND
          SCOND is REAL
          Ratio of the smallest S(i) to the largest S(i).
[in]AMAX
          AMAX is REAL
          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          = 'Y':  Equilibration was done, i.e., A has been replaced by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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 140 of file claqhb.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 REAL AMAX, SCOND
150* ..
151* .. Array Arguments ..
152 REAL S( * )
153 COMPLEX AB( LDAB, * )
154* ..
155*
156* =====================================================================
157*
158* .. Parameters ..
159 REAL ONE, THRESH
160 parameter( one = 1.0e+0, thresh = 0.1e+0 )
161* ..
162* .. Local Scalars ..
163 INTEGER I, J
164 REAL CJ, LARGE, SMALL
165* ..
166* .. External Functions ..
167 LOGICAL LSAME
168 REAL SLAMCH
169 EXTERNAL lsame, slamch
170* ..
171* .. Intrinsic Functions ..
172 INTRINSIC max, min, real
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 = slamch( 'Safe minimum' ) / slamch( '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*real( 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*real( 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 CLAQHB
226*
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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