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

 subroutine slaqsp ( character uplo, integer n, real, dimension( * ) ap, real, dimension( * ) s, real scond, real amax, character equed )

SLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ.

Purpose:
``` SLAQSP 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] AP ``` AP is REAL array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. On exit, the equilibrated matrix: diag(S) * A * diag(S), in the same storage format as A.``` [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 = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).```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 124 of file slaqsp.f.

125*
126* -- LAPACK auxiliary routine --
127* -- LAPACK is a software package provided by Univ. of Tennessee, --
128* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129*
130* .. Scalar Arguments ..
131 CHARACTER EQUED, UPLO
132 INTEGER N
133 REAL AMAX, SCOND
134* ..
135* .. Array Arguments ..
136 REAL AP( * ), S( * )
137* ..
138*
139* =====================================================================
140*
141* .. Parameters ..
142 REAL ONE, THRESH
143 parameter( one = 1.0e+0, thresh = 0.1e+0 )
144* ..
145* .. Local Scalars ..
146 INTEGER I, J, JC
147 REAL CJ, LARGE, SMALL
148* ..
149* .. External Functions ..
150 LOGICAL LSAME
151 REAL SLAMCH
152 EXTERNAL lsame, slamch
153* ..
154* .. Executable Statements ..
155*
156* Quick return if possible
157*
158 IF( n.LE.0 ) THEN
159 equed = 'N'
160 RETURN
161 END IF
162*
163* Initialize LARGE and SMALL.
164*
165 small = slamch( 'Safe minimum' ) / slamch( 'Precision' )
166 large = one / small
167*
168 IF( scond.GE.thresh .AND. amax.GE.small .AND. amax.LE.large ) THEN
169*
170* No equilibration
171*
172 equed = 'N'
173 ELSE
174*
175* Replace A by diag(S) * A * diag(S).
176*
177 IF( lsame( uplo, 'U' ) ) THEN
178*
179* Upper triangle of A is stored.
180*
181 jc = 1
182 DO 20 j = 1, n
183 cj = s( j )
184 DO 10 i = 1, j
185 ap( jc+i-1 ) = cj*s( i )*ap( jc+i-1 )
186 10 CONTINUE
187 jc = jc + j
188 20 CONTINUE
189 ELSE
190*
191* Lower triangle of A is stored.
192*
193 jc = 1
194 DO 40 j = 1, n
195 cj = s( j )
196 DO 30 i = j, n
197 ap( jc+i-j ) = cj*s( i )*ap( jc+i-j )
198 30 CONTINUE
199 jc = jc + n - j + 1
200 40 CONTINUE
201 END IF
202 equed = 'Y'
203 END IF
204*
205 RETURN
206*
207* End of SLAQSP
208*
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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