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 = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).```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

Definition at line 127 of file slaqsp.f.

127 *
128 * -- LAPACK auxiliary routine (version 3.4.2) --
129 * -- LAPACK is a software package provided by Univ. of Tennessee, --
130 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
131 * September 2012
132 *
133 * .. Scalar Arguments ..
134  CHARACTER equed, uplo
135  INTEGER n
136  REAL amax, scond
137 * ..
138 * .. Array Arguments ..
139  REAL ap( * ), s( * )
140 * ..
141 *
142 * =====================================================================
143 *
144 * .. Parameters ..
145  REAL one, thresh
146  parameter ( one = 1.0e+0, thresh = 0.1e+0 )
147 * ..
148 * .. Local Scalars ..
149  INTEGER i, j, jc
150  REAL cj, large, small
151 * ..
152 * .. External Functions ..
153  LOGICAL lsame
154  REAL slamch
155  EXTERNAL lsame, slamch
156 * ..
157 * .. Executable Statements ..
158 *
159 * Quick return if possible
160 *
161  IF( n.LE.0 ) THEN
162  equed = 'N'
163  RETURN
164  END IF
165 *
166 * Initialize LARGE and SMALL.
167 *
168  small = slamch( 'Safe minimum' ) / slamch( 'Precision' )
169  large = one / small
170 *
171  IF( scond.GE.thresh .AND. amax.GE.small .AND. amax.LE.large ) THEN
172 *
173 * No equilibration
174 *
175  equed = 'N'
176  ELSE
177 *
178 * Replace A by diag(S) * A * diag(S).
179 *
180  IF( lsame( uplo, 'U' ) ) THEN
181 *
182 * Upper triangle of A is stored.
183 *
184  jc = 1
185  DO 20 j = 1, n
186  cj = s( j )
187  DO 10 i = 1, j
188  ap( jc+i-1 ) = cj*s( i )*ap( jc+i-1 )
189  10 CONTINUE
190  jc = jc + j
191  20 CONTINUE
192  ELSE
193 *
194 * Lower triangle of A is stored.
195 *
196  jc = 1
197  DO 40 j = 1, n
198  cj = s( j )
199  DO 30 i = j, n
200  ap( jc+i-j ) = cj*s( i )*ap( jc+i-j )
201  30 CONTINUE
202  jc = jc + n - j + 1
203  40 CONTINUE
204  END IF
205  equed = 'Y'
206  END IF
207 *
208  RETURN
209 *
210 * End of SLAQSP
211 *
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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