cheevx.f (3) - Linux Manuals

NAME

cheevx.f -

SYNOPSIS


Functions/Subroutines


subroutine cheevx (JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, LWORK, RWORK, IWORK, IFAIL, INFO)
CHEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices

Function/Subroutine Documentation

subroutine cheevx (characterJOBZ, characterRANGE, characterUPLO, integerN, complex, dimension( lda, * )A, integerLDA, realVL, realVU, integerIL, integerIU, realABSTOL, integerM, real, dimension( * )W, complex, dimension( ldz, * )Z, integerLDZ, complex, dimension( * )WORK, integerLWORK, real, dimension( * )RWORK, integer, dimension( * )IWORK, integer, dimension( * )IFAIL, integerINFO)

CHEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices

Purpose:

 CHEEVX computes selected eigenvalues and, optionally, eigenvectors
 of a complex Hermitian matrix A.  Eigenvalues and eigenvectors can
 be selected by specifying either a range of values or a range of
 indices for the desired eigenvalues.


 

Parameters:

JOBZ

          JOBZ is CHARACTER*1
          = 'N':  Compute eigenvalues only;
          = 'V':  Compute eigenvalues and eigenvectors.


RANGE

          RANGE is CHARACTER*1
          = 'A': all eigenvalues will be found.
          = 'V': all eigenvalues in the half-open interval (VL,VU]
                 will be found.
          = 'I': the IL-th through IU-th eigenvalues will be found.


UPLO

          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.


N

          N is INTEGER
          The order of the matrix A.  N >= 0.


A

          A is COMPLEX 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.  If UPLO = 'L',
          the leading N-by-N lower triangular part of A contains
          the lower triangular part of the matrix A.
          On exit, the lower triangle (if UPLO='L') or the upper
          triangle (if UPLO='U') of A, including the diagonal, is
          destroyed.


LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).


VL

          VL is REAL


VU

          VU is REAL
          If RANGE='V', the lower and upper bounds of the interval to
          be searched for eigenvalues. VL < VU.
          Not referenced if RANGE = 'A' or 'I'.


IL

          IL is INTEGER


IU

          IU is INTEGER
          If RANGE='I', the indices (in ascending order) of the
          smallest and largest eigenvalues to be returned.
          1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
          Not referenced if RANGE = 'A' or 'V'.


ABSTOL

          ABSTOL is REAL
          The absolute error tolerance for the eigenvalues.
          An approximate eigenvalue is accepted as converged
          when it is determined to lie in an interval [a,b]
          of width less than or equal to

                  ABSTOL + EPS *   max( |a|,|b| ) ,

          where EPS is the machine precision.  If ABSTOL is less than
          or equal to zero, then  EPS*|T|  will be used in its place,
          where |T| is the 1-norm of the tridiagonal matrix obtained
          by reducing A to tridiagonal form.

          Eigenvalues will be computed most accurately when ABSTOL is
          set to twice the underflow threshold 2*SLAMCH('S'), not zero.
          If this routine returns with INFO>0, indicating that some
          eigenvectors did not converge, try setting ABSTOL to
          2*SLAMCH('S').

          See "Computing Small Singular Values of Bidiagonal Matrices
          with Guaranteed High Relative Accuracy," by Demmel and
          Kahan, LAPACK Working Note #3.


M

          M is INTEGER
          The total number of eigenvalues found.  0 <= M <= N.
          If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.


W

          W is REAL array, dimension (N)
          On normal exit, the first M elements contain the selected
          eigenvalues in ascending order.


Z

          Z is COMPLEX array, dimension (LDZ, max(1,M))
          If JOBZ = 'V', then if INFO = 0, the first M columns of Z
          contain the orthonormal eigenvectors of the matrix A
          corresponding to the selected eigenvalues, with the i-th
          column of Z holding the eigenvector associated with W(i).
          If an eigenvector fails to converge, then that column of Z
          contains the latest approximation to the eigenvector, and the
          index of the eigenvector is returned in IFAIL.
          If JOBZ = 'N', then Z is not referenced.
          Note: the user must ensure that at least max(1,M) columns are
          supplied in the array Z; if RANGE = 'V', the exact value of M
          is not known in advance and an upper bound must be used.


LDZ

          LDZ is INTEGER
          The leading dimension of the array Z.  LDZ >= 1, and if
          JOBZ = 'V', LDZ >= max(1,N).


WORK

          WORK is COMPLEX array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.


LWORK

          LWORK is INTEGER
          The length of the array WORK.  LWORK >= 1, when N <= 1;
          otherwise 2*N.
          For optimal efficiency, LWORK >= (NB+1)*N,
          where NB is the max of the blocksize for CHETRD and for
          CUNMTR as returned by ILAENV.

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.


RWORK

          RWORK is REAL array, dimension (7*N)


IWORK

          IWORK is INTEGER array, dimension (5*N)


IFAIL

          IFAIL is INTEGER array, dimension (N)
          If JOBZ = 'V', then if INFO = 0, the first M elements of
          IFAIL are zero.  If INFO > 0, then IFAIL contains the
          indices of the eigenvectors that failed to converge.
          If JOBZ = 'N', then IFAIL is not referenced.


INFO

          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
          > 0:  if INFO = i, then i eigenvectors failed to converge.
                Their indices are stored in array IFAIL.


 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Definition at line 251 of file cheevx.f.

Author

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