 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ claqsp()

 subroutine claqsp ( character UPLO, integer N, complex, dimension( * ) AP, real, dimension( * ) S, real SCOND, real AMAX, character EQUED )

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

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Purpose:
``` CLAQSP 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 COMPLEX 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 = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).```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 125 of file claqsp.f.

126 *
127 * -- LAPACK auxiliary routine --
128 * -- LAPACK is a software package provided by Univ. of Tennessee, --
129 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130 *
131 * .. Scalar Arguments ..
132  CHARACTER EQUED, UPLO
133  INTEGER N
134  REAL AMAX, SCOND
135 * ..
136 * .. Array Arguments ..
137  REAL S( * )
138  COMPLEX AP( * )
139 * ..
140 *
141 * =====================================================================
142 *
143 * .. Parameters ..
144  REAL ONE, THRESH
145  parameter( one = 1.0e+0, thresh = 0.1e+0 )
146 * ..
147 * .. Local Scalars ..
148  INTEGER I, J, JC
149  REAL CJ, LARGE, SMALL
150 * ..
151 * .. External Functions ..
152  LOGICAL LSAME
153  REAL SLAMCH
154  EXTERNAL lsame, slamch
155 * ..
156 * .. Executable Statements ..
157 *
158 * Quick return if possible
159 *
160  IF( n.LE.0 ) THEN
161  equed = 'N'
162  RETURN
163  END IF
164 *
165 * Initialize LARGE and SMALL.
166 *
167  small = slamch( 'Safe minimum' ) / slamch( 'Precision' )
168  large = one / small
169 *
170  IF( scond.GE.thresh .AND. amax.GE.small .AND. amax.LE.large ) THEN
171 *
172 * No equilibration
173 *
174  equed = 'N'
175  ELSE
176 *
177 * Replace A by diag(S) * A * diag(S).
178 *
179  IF( lsame( uplo, 'U' ) ) THEN
180 *
181 * Upper triangle of A is stored.
182 *
183  jc = 1
184  DO 20 j = 1, n
185  cj = s( j )
186  DO 10 i = 1, j
187  ap( jc+i-1 ) = cj*s( i )*ap( jc+i-1 )
188  10 CONTINUE
189  jc = jc + j
190  20 CONTINUE
191  ELSE
192 *
193 * Lower triangle of A is stored.
194 *
195  jc = 1
196  DO 40 j = 1, n
197  cj = s( j )
198  DO 30 i = j, n
199  ap( jc+i-j ) = cj*s( i )*ap( jc+i-j )
200  30 CONTINUE
201  jc = jc + n - j + 1
202  40 CONTINUE
203  END IF
204  equed = 'Y'
205  END IF
206 *
207  RETURN
208 *
209 * End of CLAQSP
210 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68