 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ 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.

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 = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).```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