LAPACK  3.4.2
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zhpevx.f File Reference

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  ZHPEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Function/Subroutine Documentation

subroutine zhpevx ( character  JOBZ,
character  RANGE,
character  UPLO,
integer  N,
complex*16, dimension( * )  AP,
double precision  VL,
double precision  VU,
integer  IL,
integer  IU,
double precision  ABSTOL,
integer  M,
double precision, dimension( * )  W,
complex*16, dimension( ldz, * )  Z,
integer  LDZ,
complex*16, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
integer, dimension( * )  IWORK,
integer, dimension( * )  IFAIL,
integer  INFO 

ZHPEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Download ZHPEVX + dependencies [TGZ] [ZIP] [TXT]
 ZHPEVX computes selected eigenvalues and, optionally, eigenvectors
 of a complex Hermitian matrix A in packed storage.
 Eigenvalues/vectors can be selected by specifying either a range of
 values or a range of indices for the desired eigenvalues.
          JOBZ is CHARACTER*1
          = 'N':  Compute eigenvalues only;
          = 'V':  Compute eigenvalues and eigenvectors.
          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 is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.
          N is INTEGER
          The order of the matrix A.  N >= 0.
          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
          On entry, the upper or lower triangle of the Hermitian matrix
          A, packed columnwise in a linear array.  The j-th column of A
          is stored in the array AP as follows:
          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.

          On exit, AP is overwritten by values generated during the
          reduction to tridiagonal form.  If UPLO = 'U', the diagonal
          and first superdiagonal of the tridiagonal matrix T overwrite
          the corresponding elements of A, and if UPLO = 'L', the
          diagonal and first subdiagonal of T overwrite the
          corresponding elements of A.
          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'.
          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 AP to tridiagonal form.

          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

          See "Computing Small Singular Values of Bidiagonal Matrices
          with Guaranteed High Relative Accuracy," by Demmel and
          Kahan, LAPACK Working Note #3.
          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)
          If INFO = 0, the selected eigenvalues in ascending order.
          Z is COMPLEX*16 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 is INTEGER
          The leading dimension of the array Z.  LDZ >= 1, and if
          JOBZ = 'V', LDZ >= max(1,N).
          WORK is COMPLEX*16 array, dimension (2*N)
          RWORK is DOUBLE PRECISION array, dimension (7*N)
          IWORK is INTEGER array, dimension (5*N)
          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 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.
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
November 2011

Definition at line 232 of file zhpevx.f.

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