LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ dlaqsy()

subroutine dlaqsy ( character  UPLO,
integer  N,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( * )  S,
double precision  SCOND,
double precision  AMAX,
character  EQUED 
)

DLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ.

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

Purpose:
 DLAQSY 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]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
          n by n upper triangular part of A contains the upper
          triangular part of the matrix A, and the strictly lower
          triangular part of A is not referenced.  If UPLO = 'L', the
          leading n by n lower triangular part of A contains the lower
          triangular part of the matrix A, and the strictly upper
          triangular part of A is not referenced.

          On exit, if EQUED = 'Y', the equilibrated matrix:
          diag(S) * A * diag(S).
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(N,1).
[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          = 'Y':  Equilibration was done, i.e., A has been replaced by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.

Definition at line 132 of file dlaqsy.f.

133 *
134 * -- LAPACK auxiliary routine --
135 * -- LAPACK is a software package provided by Univ. of Tennessee, --
136 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
137 *
138 * .. Scalar Arguments ..
139  CHARACTER EQUED, UPLO
140  INTEGER LDA, N
141  DOUBLE PRECISION AMAX, SCOND
142 * ..
143 * .. Array Arguments ..
144  DOUBLE PRECISION A( LDA, * ), S( * )
145 * ..
146 *
147 * =====================================================================
148 *
149 * .. Parameters ..
150  DOUBLE PRECISION ONE, THRESH
151  parameter( one = 1.0d+0, thresh = 0.1d+0 )
152 * ..
153 * .. Local Scalars ..
154  INTEGER I, J
155  DOUBLE PRECISION CJ, LARGE, SMALL
156 * ..
157 * .. External Functions ..
158  LOGICAL LSAME
159  DOUBLE PRECISION DLAMCH
160  EXTERNAL lsame, dlamch
161 * ..
162 * .. Executable Statements ..
163 *
164 * Quick return if possible
165 *
166  IF( n.LE.0 ) THEN
167  equed = 'N'
168  RETURN
169  END IF
170 *
171 * Initialize LARGE and SMALL.
172 *
173  small = dlamch( 'Safe minimum' ) / dlamch( 'Precision' )
174  large = one / small
175 *
176  IF( scond.GE.thresh .AND. amax.GE.small .AND. amax.LE.large ) THEN
177 *
178 * No equilibration
179 *
180  equed = 'N'
181  ELSE
182 *
183 * Replace A by diag(S) * A * diag(S).
184 *
185  IF( lsame( uplo, 'U' ) ) THEN
186 *
187 * Upper triangle of A is stored.
188 *
189  DO 20 j = 1, n
190  cj = s( j )
191  DO 10 i = 1, j
192  a( i, j ) = cj*s( i )*a( i, j )
193  10 CONTINUE
194  20 CONTINUE
195  ELSE
196 *
197 * Lower triangle of A is stored.
198 *
199  DO 40 j = 1, n
200  cj = s( j )
201  DO 30 i = j, n
202  a( i, j ) = cj*s( i )*a( i, j )
203  30 CONTINUE
204  40 CONTINUE
205  END IF
206  equed = 'Y'
207  END IF
208 *
209  RETURN
210 *
211 * End of DLAQSY
212 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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