LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

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 = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).```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