LAPACK  3.10.0
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.

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          = 'Y':  Equilibration was done, i.e., A has been replaced by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