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heevd - Man Page

{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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