LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ 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.

Download CLAQSP + dependencies [TGZ] [ZIP] [TXT]

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          = 'Y':  Equilibration was done, i.e., A has been replaced by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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

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*
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48