LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ zlaqhe()

subroutine zlaqhe ( character  UPLO,
integer  N,
complex*16, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( * )  S,
double precision  SCOND,
double precision  AMAX,
character  EQUED 
)

ZLAQHE scales a Hermitian matrix.

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

Purpose:
 ZLAQHE equilibrates a Hermitian 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
          Hermitian matrix A is stored.
          = 'U':  Upper triangular
          = 'L':  Lower triangular
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in,out]A
          A is COMPLEX*16 array, dimension (LDA,N)
          On entry, the Hermitian matrix A.  If UPLO = 'U', the leading
          n by n upper triangular part of A contains the upper
          triangular part of the matrix A, and the strictly lower
          triangular part of A is not referenced.  If UPLO = 'L', the
          leading n by n lower triangular part of A contains the lower
          triangular part of the matrix A, and the strictly upper
          triangular part of A is not referenced.

          On exit, if EQUED = 'Y', the equilibrated matrix:
          diag(S) * A * diag(S).
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(N,1).
[in]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          = 'Y':  Equilibration was done, i.e., A has been replaced by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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 133 of file zlaqhe.f.

134*
135* -- LAPACK auxiliary routine --
136* -- LAPACK is a software package provided by Univ. of Tennessee, --
137* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
138*
139* .. Scalar Arguments ..
140 CHARACTER EQUED, UPLO
141 INTEGER LDA, N
142 DOUBLE PRECISION AMAX, SCOND
143* ..
144* .. Array Arguments ..
145 DOUBLE PRECISION S( * )
146 COMPLEX*16 A( LDA, * )
147* ..
148*
149* =====================================================================
150*
151* .. Parameters ..
152 DOUBLE PRECISION ONE, THRESH
153 parameter( one = 1.0d+0, thresh = 0.1d+0 )
154* ..
155* .. Local Scalars ..
156 INTEGER I, J
157 DOUBLE PRECISION CJ, LARGE, SMALL
158* ..
159* .. External Functions ..
160 LOGICAL LSAME
161 DOUBLE PRECISION DLAMCH
162 EXTERNAL lsame, dlamch
163* ..
164* .. Intrinsic Functions ..
165 INTRINSIC dble
166* ..
167* .. Executable Statements ..
168*
169* Quick return if possible
170*
171 IF( n.LE.0 ) THEN
172 equed = 'N'
173 RETURN
174 END IF
175*
176* Initialize LARGE and SMALL.
177*
178 small = dlamch( 'Safe minimum' ) / dlamch( 'Precision' )
179 large = one / small
180*
181 IF( scond.GE.thresh .AND. amax.GE.small .AND. amax.LE.large ) THEN
182*
183* No equilibration
184*
185 equed = 'N'
186 ELSE
187*
188* Replace A by diag(S) * A * diag(S).
189*
190 IF( lsame( uplo, 'U' ) ) THEN
191*
192* Upper triangle of A is stored.
193*
194 DO 20 j = 1, n
195 cj = s( j )
196 DO 10 i = 1, j - 1
197 a( i, j ) = cj*s( i )*a( i, j )
198 10 CONTINUE
199 a( j, j ) = cj*cj*dble( a( j, j ) )
200 20 CONTINUE
201 ELSE
202*
203* Lower triangle of A is stored.
204*
205 DO 40 j = 1, n
206 cj = s( j )
207 a( j, j ) = cj*cj*dble( a( j, j ) )
208 DO 30 i = j + 1, n
209 a( i, j ) = cj*s( i )*a( i, j )
210 30 CONTINUE
211 40 CONTINUE
212 END IF
213 equed = 'Y'
214 END IF
215*
216 RETURN
217*
218* End of ZLAQHE
219*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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