LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 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 = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).```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.```
Date
September 2012

Definition at line 135 of file slaqsy.f.

135 *
136 * -- LAPACK auxiliary routine (version 3.4.2) --
137 * -- LAPACK is a software package provided by Univ. of Tennessee, --
138 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
139 * September 2012
140 *
141 * .. Scalar Arguments ..
142  CHARACTER equed, uplo
143  INTEGER lda, n
144  REAL amax, scond
145 * ..
146 * .. Array Arguments ..
147  REAL a( lda, * ), s( * )
148 * ..
149 *
150 * =====================================================================
151 *
152 * .. Parameters ..
153  REAL one, thresh
154  parameter ( one = 1.0e+0, thresh = 0.1e+0 )
155 * ..
156 * .. Local Scalars ..
157  INTEGER i, j
158  REAL cj, large, small
159 * ..
160 * .. External Functions ..
161  LOGICAL lsame
162  REAL slamch
163  EXTERNAL lsame, slamch
164 * ..
165 * .. Executable Statements ..
166 *
167 * Quick return if possible
168 *
169  IF( n.LE.0 ) THEN
170  equed = 'N'
171  RETURN
172  END IF
173 *
174 * Initialize LARGE and SMALL.
175 *
176  small = slamch( 'Safe minimum' ) / slamch( 'Precision' )
177  large = one / small
178 *
179  IF( scond.GE.thresh .AND. amax.GE.small .AND. amax.LE.large ) THEN
180 *
181 * No equilibration
182 *
183  equed = 'N'
184  ELSE
185 *
186 * Replace A by diag(S) * A * diag(S).
187 *
188  IF( lsame( uplo, 'U' ) ) THEN
189 *
190 * Upper triangle of A is stored.
191 *
192  DO 20 j = 1, n
193  cj = s( j )
194  DO 10 i = 1, j
195  a( i, j ) = cj*s( i )*a( i, j )
196  10 CONTINUE
197  20 CONTINUE
198  ELSE
199 *
200 * Lower triangle of A is stored.
201 *
202  DO 40 j = 1, n
203  cj = s( j )
204  DO 30 i = j, n
205  a( i, j ) = cj*s( i )*a( i, j )
206  30 CONTINUE
207  40 CONTINUE
208  END IF
209  equed = 'Y'
210  END IF
211 *
212  RETURN
213 *
214 * End of SLAQSY
215 *
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

Here is the caller graph for this function: