heevd(3)

NAME
heevd - {he,sy}evd: eig, divide and conquer

SYNOPSIS

  Functions
subroutine cheevd (jobz, uplo, n, a, lda, w, work, lwork, rwork, lrwork, iwork, liwork, info)
CHEEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices
subroutine dsyevd (jobz, uplo, n, a, lda, w, work, lwork, iwork, liwork, info)
DSYEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices
subroutine ssyevd (jobz, uplo, n, a, lda, w, work, lwork, iwork, liwork, info)
SSYEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices
subroutine zheevd (jobz, uplo, n, a, lda, w, work, lwork, rwork, lrwork, iwork, liwork, info)
ZHEEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices

Detailed Description

Function Documentation

  subroutine cheevd (character jobz, character uplo, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) w, complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork, integer liwork, integer info)

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

Purpose:

     CHEEVD computes all eigenvalues and, optionally, eigenvectors of a
     complex Hermitian matrix A.  If eigenvectors are desired, it uses a
     divide and conquer algorithm.

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.

    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, if JOBZ = 'V', then if INFO = 0, A contains the
              orthonormal eigenvectors of the matrix A.
              If JOBZ = 'N', then 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).

    W

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

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

    RWORK

              RWORK is REAL array,
                                             dimension (LRWORK)
              On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.

    LRWORK

              LRWORK is INTEGER
              The dimension of the array RWORK.
              If N <= 1,                LRWORK must be at least 1.
              If JOBZ  = 'N' and N > 1, LRWORK must be at least N.
              If JOBZ  = 'V' and N > 1, LRWORK must be at least
                             1 + 5*N + 2*N**2.
              If LRWORK = -1, then a workspace query is assumed; the
              routine only calculates the optimal sizes of the WORK, RWORK
              and IWORK arrays, returns these values as the first entries
              of the WORK, RWORK and IWORK arrays, and no error message
              related to LWORK or LRWORK or LIWORK is issued by XERBLA.

    IWORK

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

    LIWORK

              LIWORK is INTEGER
              The dimension of the array IWORK.
              If N <= 1,                LIWORK must be at least 1.
              If JOBZ  = 'N' and 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 optimal sizes of the WORK, RWORK
              and IWORK arrays, returns these values as the first entries
              of the WORK, RWORK and IWORK arrays, and no error message
              related to LWORK or LRWORK 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 and JOBZ = 'N', then the algorithm failed
                    to converge; i off-diagonal elements of an intermediate
                    tridiagonal form did not converge to zero;
                    if INFO = i and JOBZ = 'V', then the algorithm failed
                    to compute an eigenvalue while working on the submatrix
                    lying in rows and columns INFO/(N+1) through
                    mod(INFO,N+1).

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:
    Modified description of INFO. Sven, 16 Feb 05.

Contributors:
    Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

Definition at line 197 of file cheevd.f.

  subroutine dsyevd (character jobz, character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) w, double precision, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer liwork, integer info)

DSYEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices

Purpose:

     DSYEVD computes all eigenvalues and, optionally, eigenvectors of a
     real symmetric matrix A. If eigenvectors are desired, it uses a
     divide and conquer algorithm.
     Because of large use of BLAS of level 3, DSYEVD needs N**2 more
     workspace than DSYEVX.

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.

    A

              A is DOUBLE PRECISION array, dimension (LDA, N)
              On entry, the symmetric 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, if JOBZ = 'V', then if INFO = 0, A contains the
              orthonormal eigenvectors of the matrix A.
              If JOBZ = 'N', then 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).

    W

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

    WORK

              WORK is DOUBLE PRECISION array,
                                             dimension (LWORK)
              On exit, if INFO = 0, WORK(1) returns the optimal 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+1.
              If JOBZ = 'V' and N > 1, LWORK must be at least
                                                    1 + 6*N + 2*N**2.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal 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 optimal LIWORK.

    LIWORK

              LIWORK is INTEGER
              The dimension of the array IWORK.
              If N <= 1,                LIWORK must be at least 1.
              If JOBZ  = 'N' and 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 optimal 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 and JOBZ = 'N', then the algorithm failed
                    to converge; i off-diagonal elements of an intermediate
                    tridiagonal form did not converge to zero;
                    if INFO = i and JOBZ = 'V', then the algorithm failed
                    to compute an eigenvalue while working on the submatrix
                    lying in rows and columns INFO/(N+1) through
                    mod(INFO,N+1).

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:
    Jeff Rutter, Computer Science Division, University of California at Berkeley, USA
     Modified by Francoise Tisseur, University of Tennessee
     Modified description of INFO. Sven, 16 Feb 05.

Definition at line 176 of file dsyevd.f.

  subroutine ssyevd (character jobz, character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) w, real, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer liwork, integer info)

SSYEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices

Purpose:

     SSYEVD computes all eigenvalues and, optionally, eigenvectors of a
     real symmetric matrix A. If eigenvectors are desired, it uses a
     divide and conquer algorithm.
     Because of large use of BLAS of level 3, SSYEVD needs N**2 more
     workspace than SSYEVX.

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.

    A

              A is REAL array, dimension (LDA, N)
              On entry, the symmetric 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, if JOBZ = 'V', then if INFO = 0, A contains the
              orthonormal eigenvectors of the matrix A.
              If JOBZ = 'N', then 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).

    W

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

    WORK

              WORK is REAL array,
                                             dimension (LWORK)
              On exit, if INFO = 0, WORK(1) returns the optimal 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+1.
              If JOBZ = 'V' and N > 1, LWORK must be at least
                                                    1 + 6*N + 2*N**2.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal 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 optimal LIWORK.

    LIWORK

              LIWORK is INTEGER
              The dimension of the array IWORK.
              If N <= 1,                LIWORK must be at least 1.
              If JOBZ  = 'N' and 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 optimal 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 and JOBZ = 'N', then the algorithm failed
                    to converge; i off-diagonal elements of an intermediate
                    tridiagonal form did not converge to zero;
                    if INFO = i and JOBZ = 'V', then the algorithm failed
                    to compute an eigenvalue while working on the submatrix
                    lying in rows and columns INFO/(N+1) through
                    mod(INFO,N+1).

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:
    Jeff Rutter, Computer Science Division, University of California at Berkeley, USA
     Modified by Francoise Tisseur, University of Tennessee
     Modified description of INFO. Sven, 16 Feb 05.

Definition at line 174 of file ssyevd.f.

  subroutine zheevd (character jobz, character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) w, complex*16, dimension( * ) work, integer lwork, double precision, dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork, integer liwork, integer info)

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

Purpose:

     ZHEEVD computes all eigenvalues and, optionally, eigenvectors of a
     complex Hermitian matrix A.  If eigenvectors are desired, it uses a
     divide and conquer algorithm.

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.

    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.  If UPLO = 'L',
              the leading N-by-N lower triangular part of A contains
              the lower triangular part of the matrix A.
              On exit, if JOBZ = 'V', then if INFO = 0, A contains the
              orthonormal eigenvectors of the matrix A.
              If JOBZ = 'N', then 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).

    W

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

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

    RWORK

              RWORK is DOUBLE PRECISION array,
                                             dimension (LRWORK)
              On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.

    LRWORK

              LRWORK is INTEGER
              The dimension of the array RWORK.
              If N <= 1,                LRWORK must be at least 1.
              If JOBZ  = 'N' and N > 1, LRWORK must be at least N.
              If JOBZ  = 'V' and N > 1, LRWORK must be at least
                             1 + 5*N + 2*N**2.
              If LRWORK = -1, then a workspace query is assumed; the
              routine only calculates the optimal sizes of the WORK, RWORK
              and IWORK arrays, returns these values as the first entries
              of the WORK, RWORK and IWORK arrays, and no error message
              related to LWORK or LRWORK or LIWORK is issued by XERBLA.

    IWORK

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

    LIWORK

              LIWORK is INTEGER
              The dimension of the array IWORK.
              If N <= 1,                LIWORK must be at least 1.
              If JOBZ  = 'N' and 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 optimal sizes of the WORK, RWORK
              and IWORK arrays, returns these values as the first entries
              of the WORK, RWORK and IWORK arrays, and no error message
              related to LWORK or LRWORK 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 and JOBZ = 'N', then the algorithm failed
                    to converge; i off-diagonal elements of an intermediate
                    tridiagonal form did not converge to zero;
                    if INFO = i and JOBZ = 'V', then the algorithm failed
                    to compute an eigenvalue while working on the submatrix
                    lying in rows and columns INFO/(N+1) through
                    mod(INFO,N+1).

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:
    Modified description of INFO. Sven, 16 Feb 05.

Contributors:
    Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

Definition at line 197 of file zheevd.f.

Author

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