LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ zlaqsy()

subroutine zlaqsy ( character  UPLO,
integer  N,
complex*16, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( * )  S,
double precision  SCOND,
double precision  AMAX,
character  EQUED 
)

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

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

Purpose:
 ZLAQSY 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 COMPLEX*16 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          = 'Y':  Equilibration was done, i.e., A has been replaced by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 133 of file zlaqsy.f.

134 *
135 * -- LAPACK auxiliary routine --
136 * -- LAPACK is a software package provided by Univ. of Tennessee, --
137 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
138 *
139 * .. Scalar Arguments ..
140  CHARACTER EQUED, UPLO
141  INTEGER LDA, N
142  DOUBLE PRECISION AMAX, SCOND
143 * ..
144 * .. Array Arguments ..
145  DOUBLE PRECISION S( * )
146  COMPLEX*16 A( LDA, * )
147 * ..
148 *
149 * =====================================================================
150 *
151 * .. Parameters ..
152  DOUBLE PRECISION ONE, THRESH
153  parameter( one = 1.0d+0, thresh = 0.1d+0 )
154 * ..
155 * .. Local Scalars ..
156  INTEGER I, J
157  DOUBLE PRECISION CJ, LARGE, SMALL
158 * ..
159 * .. External Functions ..
160  LOGICAL LSAME
161  DOUBLE PRECISION DLAMCH
162  EXTERNAL lsame, dlamch
163 * ..
164 * .. Executable Statements ..
165 *
166 * Quick return if possible
167 *
168  IF( n.LE.0 ) THEN
169  equed = 'N'
170  RETURN
171  END IF
172 *
173 * Initialize LARGE and SMALL.
174 *
175  small = dlamch( 'Safe minimum' ) / dlamch( 'Precision' )
176  large = one / small
177 *
178  IF( scond.GE.thresh .AND. amax.GE.small .AND. amax.LE.large ) THEN
179 *
180 * No equilibration
181 *
182  equed = 'N'
183  ELSE
184 *
185 * Replace A by diag(S) * A * diag(S).
186 *
187  IF( lsame( uplo, 'U' ) ) THEN
188 *
189 * Upper triangle of A is stored.
190 *
191  DO 20 j = 1, n
192  cj = s( j )
193  DO 10 i = 1, j
194  a( i, j ) = cj*s( i )*a( i, j )
195  10 CONTINUE
196  20 CONTINUE
197  ELSE
198 *
199 * Lower triangle of A is stored.
200 *
201  DO 40 j = 1, n
202  cj = s( j )
203  DO 30 i = j, n
204  a( i, j ) = cj*s( i )*a( i, j )
205  30 CONTINUE
206  40 CONTINUE
207  END IF
208  equed = 'Y'
209  END IF
210 *
211  RETURN
212 *
213 * End of ZLAQSY
214 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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