LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine claqsy ( character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, real, dimension( * ) S, real SCOND, real AMAX, character EQUED )

CLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ.

Purpose:
``` CLAQSY equilibrates a symmetric 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,out] A ``` A is COMPLEX array, dimension (LDA,N) On entry, the symmetric 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 = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).```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.```
Date
September 2012

Definition at line 136 of file claqsy.f.

136 *
137 * -- LAPACK auxiliary routine (version 3.4.2) --
138 * -- LAPACK is a software package provided by Univ. of Tennessee, --
139 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
140 * September 2012
141 *
142 * .. Scalar Arguments ..
143  CHARACTER equed, uplo
144  INTEGER lda, n
145  REAL amax, scond
146 * ..
147 * .. Array Arguments ..
148  REAL s( * )
149  COMPLEX a( lda, * )
150 * ..
151 *
152 * =====================================================================
153 *
154 * .. Parameters ..
155  REAL one, thresh
156  parameter ( one = 1.0e+0, thresh = 0.1e+0 )
157 * ..
158 * .. Local Scalars ..
159  INTEGER i, j
160  REAL cj, large, small
161 * ..
162 * .. External Functions ..
163  LOGICAL lsame
164  REAL slamch
165  EXTERNAL lsame, slamch
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
197  a( i, j ) = cj*s( i )*a( i, j )
198  10 CONTINUE
199  20 CONTINUE
200  ELSE
201 *
202 * Lower triangle of A is stored.
203 *
204  DO 40 j = 1, n
205  cj = s( j )
206  DO 30 i = j, n
207  a( i, j ) = cj*s( i )*a( i, j )
208  30 CONTINUE
209  40 CONTINUE
210  END IF
211  equed = 'Y'
212  END IF
213 *
214  RETURN
215 *
216 * End of CLAQSY
217 *
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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