LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ dlaqsp()

subroutine dlaqsp ( character  UPLO,
integer  N,
double precision, dimension( * )  AP,
double precision, dimension( * )  S,
double precision  SCOND,
double precision  AMAX,
character  EQUED 
)

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

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

Purpose:
 DLAQSP 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N)
          The scale factors for A.
[in]SCOND
          SCOND is DOUBLE PRECISION
          Ratio of the smallest S(i) to the largest S(i).
[in]AMAX
          AMAX is DOUBLE PRECISION
          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          = 'Y':  Equilibration was done, i.e., A has been replaced by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.
Date
December 2016

Definition at line 127 of file dlaqsp.f.

127 *
128 * -- LAPACK auxiliary routine (version 3.7.0) --
129 * -- LAPACK is a software package provided by Univ. of Tennessee, --
130 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
131 * December 2016
132 *
133 * .. Scalar Arguments ..
134  CHARACTER equed, uplo
135  INTEGER n
136  DOUBLE PRECISION amax, scond
137 * ..
138 * .. Array Arguments ..
139  DOUBLE PRECISION ap( * ), s( * )
140 * ..
141 *
142 * =====================================================================
143 *
144 * .. Parameters ..
145  DOUBLE PRECISION one, thresh
146  parameter( one = 1.0d+0, thresh = 0.1d+0 )
147 * ..
148 * .. Local Scalars ..
149  INTEGER i, j, jc
150  DOUBLE PRECISION cj, large, small
151 * ..
152 * .. External Functions ..
153  LOGICAL lsame
154  DOUBLE PRECISION dlamch
155  EXTERNAL lsame, dlamch
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 = dlamch( 'Safe minimum' ) / dlamch( '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 DLAQSP
211 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
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