heev(3)

NAME
heev - {he,sy}ev: eig, QR iteration

SYNOPSIS

  Functions

subroutine cheev (jobz, uplo, n, a, lda, w, work, lwork, rwork, info)
CHEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices
subroutine dsyev (jobz, uplo, n, a, lda, w, work, lwork, info)
DSYEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices
subroutine ssyev (jobz, uplo, n, a, lda, w, work, lwork, info)
SSYEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices
subroutine zheev (jobz, uplo, n, a, lda, w, work, lwork, rwork, info)
ZHEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices

Detailed Description

Function Documentation

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

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

Purpose:

    !>
    !> CHEEV computes all eigenvalues and, optionally, eigenvectors of a
    !> complex Hermitian matrix A.
    !>

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.  LWORK >= max(1,2*N-1).
    !>          For optimal efficiency, LWORK >= (NB+1)*N,
    !>          where NB is the blocksize for CHETRD 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 (max(1, 3*N-2))
    !>

    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.

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

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

Purpose:

    !>
    !> DSYEV computes all eigenvalues and, optionally, eigenvectors of a
    !> real symmetric matrix A.
    !>

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 (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(1,3*N-1).
    !>          For optimal efficiency, LWORK >= (NB+2)*N,
    !>          where NB is the blocksize for DSYTRD 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.
    !>

    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.

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

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

Purpose:

    !>
    !> SSYEV computes all eigenvalues and, optionally, eigenvectors of a
    !> real symmetric matrix A.
    !>

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 (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(1,3*N-1).
    !>          For optimal efficiency, LWORK >= (NB+2)*N,
    !>          where NB is the blocksize for SSYTRD 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.
    !>

    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.

  subroutine zheev (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 info)

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

Purpose:

    !>
    !> ZHEEV computes all eigenvalues and, optionally, eigenvectors of a
    !> complex Hermitian matrix A.
    !>

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.  LWORK >= max(1,2*N-1).
    !>          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 (max(1, 3*N-2))
    !>

    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.

Author

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