LAPACK  3.10.1
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          = 'Y':  Equilibration was done, i.e., A has been replaced by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.

Definition at line 133 of file zlaqhe.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 * .. Intrinsic Functions ..
165  INTRINSIC dble
166 * ..
167 * .. Executable Statements ..
168 *
169 * Quick return if possible
170 *
171  IF( n.LE.0 ) THEN
172  equed = 'N'
173  RETURN
174  END IF
175 *
176 * Initialize LARGE and SMALL.
177 *
178  small = dlamch( 'Safe minimum' ) / dlamch( 'Precision' )
179  large = one / small
180 *
181  IF( scond.GE.thresh .AND. amax.GE.small .AND. amax.LE.large ) THEN
182 *
183 * No equilibration
184 *
185  equed = 'N'
186  ELSE
187 *
188 * Replace A by diag(S) * A * diag(S).
189 *
190  IF( lsame( uplo, 'U' ) ) THEN
191 *
192 * Upper triangle of A is stored.
193 *
194  DO 20 j = 1, n
195  cj = s( j )
196  DO 10 i = 1, j - 1
197  a( i, j ) = cj*s( i )*a( i, j )
198  10 CONTINUE
199  a( j, j ) = cj*cj*dble( a( j, j ) )
200  20 CONTINUE
201  ELSE
202 *
203 * Lower triangle of A is stored.
204 *
205  DO 40 j = 1, n
206  cj = s( j )
207  a( j, j ) = cj*cj*dble( a( j, j ) )
208  DO 30 i = j + 1, n
209  a( i, j ) = cj*s( i )*a( i, j )
210  30 CONTINUE
211  40 CONTINUE
212  END IF
213  equed = 'Y'
214  END IF
215 *
216  RETURN
217 *
218 * End of ZLAQHE
219 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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