zhegvx (3) - Linux Manuals

Command to display zhegvx manual in Linux: $ man 3 zhegvx

NAME

zhegvx.f -

SYNOPSIS

Functions/Subroutines

subroutine zhegvx (ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, LWORK, RWORK, IWORK, IFAIL, INFO)
ZHEGST

Function/Subroutine Documentation

subroutine zhegvx (integerITYPE, characterJOBZ, characterRANGE, characterUPLO, integerN, complex16, dimension( lda, )A, integerLDA, complex16, dimension( ldb, )B, integerLDB, double precisionVL, double precisionVU, integerIL, integerIU, double precisionABSTOL, integerM, double precision, dimension( * )W, complex16, dimension( ldz, )Z, integerLDZ, complex16, dimension( )WORK, integerLWORK, double precision, dimension( * )RWORK, integer, dimension( * )IWORK, integer, dimension( * )IFAIL, integerINFO)

ZHEGST

Purpose:

 ZHEGVX computes selected eigenvalues, and optionally, eigenvectors
 of a complex generalized Hermitian-definite eigenproblem, of the form
 A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.  Here A and
 B are assumed to be Hermitian and B is also positive definite.
 Eigenvalues and eigenvectors can be selected by specifying either a
 range of values or a range of indices for the desired eigenvalues.

Parameters:

ITYPE

          ITYPE is INTEGER
          Specifies the problem type to be solved:
          = 1:  A*x = (lambda)*B*x
          = 2:  A*B*x = (lambda)*x
          = 3:  B*A*x = (lambda)*x

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 triangles of A and B are stored;
          = 'L':  Lower triangles of A and B are stored.

          N is INTEGER
          The order of the matrices A and B.  N >= 0.

          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.  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).

          B is COMPLEX*16 array, dimension (LDB, N)
          On entry, the Hermitian matrix B.  If UPLO = 'U', the
          leading N-by-N upper triangular part of B contains the
          upper triangular part of the matrix B.  If UPLO = 'L',
          the leading N-by-N lower triangular part of B contains
          the lower triangular part of the matrix B.

          On exit, if INFO <= N, the part of B containing the matrix is
          overwritten by the triangular factor U or L from the Cholesky
          factorization B = U**H*U or B = L*L**H.

LDB

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

          VL is DOUBLE PRECISION

          VU is DOUBLE PRECISION

          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 is INTEGER

          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 DOUBLE PRECISION
          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 C to tridiagonal form, where C is the symmetric
          matrix of the standard symmetric problem to which the
          generalized problem is transformed.

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

          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 is DOUBLE PRECISION array, dimension (N)
          The first M elements contain the selected
          eigenvalues in ascending order.

          Z is COMPLEX*16 array, dimension (LDZ, max(1,M))
          If JOBZ = 'N', then Z is not referenced.
          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).
          The eigenvectors are normalized as follows:
          if ITYPE = 1 or 2, Z**T*B*Z = I;
          if ITYPE = 3, Z**T*inv(B)*Z = 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.
          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*16 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 >= max(1,2*N).
          For optimal efficiency, LWORK >= (NB+1)*N,
          where NB is the blocksize for ZHETRD 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 DOUBLE PRECISION 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:  ZPOTRF or ZHEEVX returned an error code:
             <= N:  if INFO = i, ZHEEVX failed to converge;
                    i eigenvectors failed to converge.  Their indices
                    are stored in array IFAIL.
             > N:   if INFO = N + i, for 1 <= i <= N, then the leading
                    minor of order i of B is not positive definite.
                    The factorization of B could not be completed and
                    no eigenvalues or eigenvectors were computed.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

Contributors:

: Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

Definition at line 297 of file zhegvx.f.

Author

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