LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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◆ claqhe()

 subroutine claqhe ( character uplo, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real scond, real amax, character equed )

CLAQHE scales a Hermitian matrix.

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 = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).```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

Definition at line 133 of file claqhe.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 REAL AMAX, SCOND
143* ..
144* .. Array Arguments ..
145 REAL S( * )
146 COMPLEX A( LDA, * )
147* ..
148*
149* =====================================================================
150*
151* .. Parameters ..
152 REAL ONE, THRESH
153 parameter( one = 1.0e+0, thresh = 0.1e+0 )
154* ..
155* .. Local Scalars ..
156 INTEGER I, J
157 REAL CJ, LARGE, SMALL
158* ..
159* .. External Functions ..
160 LOGICAL LSAME
161 REAL SLAMCH
162 EXTERNAL lsame, slamch
163* ..
164* .. Intrinsic Functions ..
165 INTRINSIC real
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 = slamch( 'Safe minimum' ) / slamch( '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*real( 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*real( 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 CLAQHE
219*
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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