LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ 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.

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 = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).```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.```
Date
December 2016

Definition at line 136 of file zlaqhe.f.

136 *
137 * -- LAPACK auxiliary routine (version 3.7.0) --
138 * -- LAPACK is a software package provided by Univ. of Tennessee, --
139 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
140 * December 2016
141 *
142 * .. Scalar Arguments ..
143  CHARACTER equed, uplo
144  INTEGER lda, n
145  DOUBLE PRECISION amax, scond
146 * ..
147 * .. Array Arguments ..
148  DOUBLE PRECISION s( * )
149  COMPLEX*16 a( lda, * )
150 * ..
151 *
152 * =====================================================================
153 *
154 * .. Parameters ..
155  DOUBLE PRECISION one, thresh
156  parameter( one = 1.0d+0, thresh = 0.1d+0 )
157 * ..
158 * .. Local Scalars ..
159  INTEGER i, j
160  DOUBLE PRECISION cj, large, small
161 * ..
162 * .. External Functions ..
163  LOGICAL lsame
164  DOUBLE PRECISION dlamch
165  EXTERNAL lsame, dlamch
166 * ..
167 * .. Intrinsic Functions ..
168  INTRINSIC dble
169 * ..
170 * .. Executable Statements ..
171 *
172 * Quick return if possible
173 *
174  IF( n.LE.0 ) THEN
175  equed = 'N'
176  RETURN
177  END IF
178 *
179 * Initialize LARGE and SMALL.
180 *
181  small = dlamch( 'Safe minimum' ) / dlamch( 'Precision' )
182  large = one / small
183 *
184  IF( scond.GE.thresh .AND. amax.GE.small .AND. amax.LE.large ) THEN
185 *
186 * No equilibration
187 *
188  equed = 'N'
189  ELSE
190 *
191 * Replace A by diag(S) * A * diag(S).
192 *
193  IF( lsame( uplo, 'U' ) ) THEN
194 *
195 * Upper triangle of A is stored.
196 *
197  DO 20 j = 1, n
198  cj = s( j )
199  DO 10 i = 1, j - 1
200  a( i, j ) = cj*s( i )*a( i, j )
201  10 CONTINUE
202  a( j, j ) = cj*cj*dble( a( j, j ) )
203  20 CONTINUE
204  ELSE
205 *
206 * Lower triangle of A is stored.
207 *
208  DO 40 j = 1, n
209  cj = s( j )
210  a( j, j ) = cj*cj*dble( a( j, j ) )
211  DO 30 i = j + 1, n
212  a( i, j ) = cj*s( i )*a( i, j )
213  30 CONTINUE
214  40 CONTINUE
215  END IF
216  equed = 'Y'
217  END IF
218 *
219  RETURN
220 *
221 * End of ZLAQHE
222 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
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