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.

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

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          = 'Y':  Equilibration was done, i.e., A has been replaced by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

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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