sspevd.f(3)

NAME
sspevd.f -

SYNOPSIS

  Functions/Subroutines
subroutine sspevd (JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO)
SSPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Function/Subroutine Documentation

  subroutine sspevd (characterJOBZ, characterUPLO, integerN, real, dimension( * )AP, real, dimension( * )W, real, dimension( ldz, * )Z, integerLDZ, real, dimension( * )WORK, integerLWORK, integer, dimension( * )IWORK, integerLIWORK, integerINFO)

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

Purpose:

     SSPEVD computes all the eigenvalues and, optionally, eigenvectors
     of a real symmetric matrix A in packed storage. If eigenvectors are
     desired, it uses a divide and conquer algorithm.
     The divide and conquer algorithm makes very mild assumptions about
     floating point arithmetic. It will work on machines with a guard
     digit in add/subtract, or on those binary machines without guard
     digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
     Cray-2. It could conceivably fail on hexadecimal or decimal machines
     without guard digits, but we know of none.

Parameters:
    JOBZ

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

    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.

    AP

              AP is REAL array, dimension (N*(N+1)/2)
              On entry, the upper or lower triangle of the symmetric 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.

    W

              W is REAL array, dimension (N)
              If INFO = 0, the eigenvalues in ascending order.

    Z

              Z is REAL array, dimension (LDZ, N)
              If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
              eigenvectors of the matrix A, with the i-th column of Z
              holding the eigenvector associated with W(i).
              If JOBZ = 'N', then Z is not referenced.

    LDZ

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

    WORK

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

    LWORK

              LWORK is INTEGER
              The dimension of the array WORK.
              If N <= 1,               LWORK must be at least 1.
              If JOBZ = 'N' and N > 1, LWORK must be at least 2*N.
              If JOBZ = 'V' and N > 1, LWORK must be at least
                                                     1 + 6*N + N**2.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the required sizes of the WORK and IWORK
              arrays, returns these values as the first entries of the WORK
              and IWORK arrays, and no error message related to LWORK or
              LIWORK is issued by XERBLA.

    IWORK

              IWORK is INTEGER array, dimension (MAX(1,LIWORK))
              On exit, if INFO = 0, IWORK(1) returns the required LIWORK.

    LIWORK

              LIWORK is INTEGER
              The dimension of the array IWORK.
              If JOBZ  = 'N' or N <= 1, LIWORK must be at least 1.
              If JOBZ  = 'V' and N > 1, LIWORK must be at least 3 + 5*N.
              If LIWORK = -1, then a workspace query is assumed; the
              routine only calculates the required sizes of the WORK and
              IWORK arrays, returns these values as the first entries of
              the WORK and IWORK arrays, and no error message related to
              LWORK or LIWORK is issued by XERBLA.

    INFO

              INFO is INTEGER
              = 0:  successful exit
              < 0:  if INFO = -i, the i-th argument had an illegal value.
              > 0:  if INFO = i, the algorithm failed to converge; i
                    off-diagonal elements of an intermediate tridiagonal
                    form did not converge to zero.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    November 2011

Definition at line 178 of file sspevd.f.

Author

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