 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ 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 = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).```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 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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