LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ zlaqhe()

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

ZLAQHE scales a Hermitian matrix.

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

Purpose:
 ZLAQHE equilibrates a Hermitian 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
          Hermitian 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 Hermitian 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          = 'Y':  Equilibration was done, i.e., A has been replaced by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.
Date
December 2016

Definition at line 136 of file zlaqhe.f.

136 *
137 * -- LAPACK auxiliary routine (version 3.7.0) --
138 * -- LAPACK is a software package provided by Univ. of Tennessee, --
139 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
140 * December 2016
141 *
142 * .. Scalar Arguments ..
143  CHARACTER equed, uplo
144  INTEGER lda, n
145  DOUBLE PRECISION amax, scond
146 * ..
147 * .. Array Arguments ..
148  DOUBLE PRECISION s( * )
149  COMPLEX*16 a( lda, * )
150 * ..
151 *
152 * =====================================================================
153 *
154 * .. Parameters ..
155  DOUBLE PRECISION one, thresh
156  parameter( one = 1.0d+0, thresh = 0.1d+0 )
157 * ..
158 * .. Local Scalars ..
159  INTEGER i, j
160  DOUBLE PRECISION cj, large, small
161 * ..
162 * .. External Functions ..
163  LOGICAL lsame
164  DOUBLE PRECISION dlamch
165  EXTERNAL lsame, dlamch
166 * ..
167 * .. Intrinsic Functions ..
168  INTRINSIC dble
169 * ..
170 * .. Executable Statements ..
171 *
172 * Quick return if possible
173 *
174  IF( n.LE.0 ) THEN
175  equed = 'N'
176  RETURN
177  END IF
178 *
179 * Initialize LARGE and SMALL.
180 *
181  small = dlamch( 'Safe minimum' ) / dlamch( 'Precision' )
182  large = one / small
183 *
184  IF( scond.GE.thresh .AND. amax.GE.small .AND. amax.LE.large ) THEN
185 *
186 * No equilibration
187 *
188  equed = 'N'
189  ELSE
190 *
191 * Replace A by diag(S) * A * diag(S).
192 *
193  IF( lsame( uplo, 'U' ) ) THEN
194 *
195 * Upper triangle of A is stored.
196 *
197  DO 20 j = 1, n
198  cj = s( j )
199  DO 10 i = 1, j - 1
200  a( i, j ) = cj*s( i )*a( i, j )
201  10 CONTINUE
202  a( j, j ) = cj*cj*dble( a( j, j ) )
203  20 CONTINUE
204  ELSE
205 *
206 * Lower triangle of A is stored.
207 *
208  DO 40 j = 1, n
209  cj = s( j )
210  a( j, j ) = cj*cj*dble( a( j, j ) )
211  DO 30 i = j + 1, n
212  a( i, j ) = cj*s( i )*a( i, j )
213  30 CONTINUE
214  40 CONTINUE
215  END IF
216  equed = 'Y'
217  END IF
218 *
219  RETURN
220 *
221 * End of ZLAQHE
222 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
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