LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ slaqsy()

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

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

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 = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).```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

Definition at line 132 of file slaqsy.f.

133*
134* -- LAPACK auxiliary routine --
135* -- LAPACK is a software package provided by Univ. of Tennessee, --
136* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
137*
138* .. Scalar Arguments ..
139 CHARACTER EQUED, UPLO
140 INTEGER LDA, N
141 REAL AMAX, SCOND
142* ..
143* .. Array Arguments ..
144 REAL A( LDA, * ), S( * )
145* ..
146*
147* =====================================================================
148*
149* .. Parameters ..
150 REAL ONE, THRESH
151 parameter( one = 1.0e+0, thresh = 0.1e+0 )
152* ..
153* .. Local Scalars ..
154 INTEGER I, J
155 REAL CJ, LARGE, SMALL
156* ..
157* .. External Functions ..
158 LOGICAL LSAME
159 REAL SLAMCH
160 EXTERNAL lsame, slamch
161* ..
162* .. Executable Statements ..
163*
164* Quick return if possible
165*
166 IF( n.LE.0 ) THEN
167 equed = 'N'
168 RETURN
169 END IF
170*
171* Initialize LARGE and SMALL.
172*
173 small = slamch( 'Safe minimum' ) / slamch( 'Precision' )
174 large = one / small
175*
176 IF( scond.GE.thresh .AND. amax.GE.small .AND. amax.LE.large ) THEN
177*
178* No equilibration
179*
180 equed = 'N'
181 ELSE
182*
183* Replace A by diag(S) * A * diag(S).
184*
185 IF( lsame( uplo, 'U' ) ) THEN
186*
187* Upper triangle of A is stored.
188*
189 DO 20 j = 1, n
190 cj = s( j )
191 DO 10 i = 1, j
192 a( i, j ) = cj*s( i )*a( i, j )
193 10 CONTINUE
194 20 CONTINUE
195 ELSE
196*
197* Lower triangle of A is stored.
198*
199 DO 40 j = 1, n
200 cj = s( j )
201 DO 30 i = j, n
202 a( i, j ) = cj*s( i )*a( i, j )
203 30 CONTINUE
204 40 CONTINUE
205 END IF
206 equed = 'Y'
207 END IF
208*
209 RETURN
210*
211* End of SLAQSY
212*
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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