hbevd(3)

NAME
hbevd - {hb,sb}evd: eig, divide and conquer

SYNOPSIS

  Functions
subroutine chbevd (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, lwork, rwork, lrwork, iwork, liwork, info)
CHBEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
subroutine dsbevd (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, lwork, iwork, liwork, info)
DSBEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
subroutine ssbevd (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, lwork, iwork, liwork, info)
SSBEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
subroutine zhbevd (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, lwork, rwork, lrwork, iwork, liwork, info)
ZHBEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Detailed Description

Function Documentation

  subroutine chbevd (character jobz, character uplo, integer n, integer kd, complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) w, complex, dimension( ldz, * ) z, integer ldz, complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork, integer liwork, integer info)

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

Purpose:

     CHBEVD computes all the eigenvalues and, optionally, eigenvectors of
     a complex Hermitian band 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.

    KD

              KD is INTEGER
              The number of superdiagonals of the matrix A if UPLO = 'U',
              or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

    AB

              AB is COMPLEX array, dimension (LDAB, N)
              On entry, the upper or lower triangle of the Hermitian band
              matrix A, stored in the first KD+1 rows of the array.  The
              j-th column of A is stored in the j-th column of the array AB
              as follows:
              if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
              if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
              On exit, AB is overwritten by values generated during the
              reduction to tridiagonal form.  If UPLO = 'U', the first
              superdiagonal and the diagonal of the tridiagonal matrix T
              are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
              the diagonal and first subdiagonal of T are returned in the
              first two rows of AB.

    LDAB

              LDAB is INTEGER
              The leading dimension of the array AB.  LDAB >= KD + 1.

    W

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

    Z

              Z is COMPLEX 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 COMPLEX array, dimension (MAX(1,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 N.
              If JOBZ = 'V' and N > 1, LWORK must be at least 2*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 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 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 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, 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.

Definition at line 207 of file chbevd.f.

  subroutine dsbevd (character jobz, character uplo, integer n, integer kd, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) w, double precision, dimension( ldz, * ) z, integer ldz, double precision, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer liwork, integer info)

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

Purpose:

     DSBEVD computes all the eigenvalues and, optionally, eigenvectors of
     a real symmetric band 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.

    KD

              KD is INTEGER
              The number of superdiagonals of the matrix A if UPLO = 'U',
              or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

    AB

              AB is DOUBLE PRECISION array, dimension (LDAB, N)
              On entry, the upper or lower triangle of the symmetric band
              matrix A, stored in the first KD+1 rows of the array.  The
              j-th column of A is stored in the j-th column of the array AB
              as follows:
              if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
              if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
              On exit, AB is overwritten by values generated during the
              reduction to tridiagonal form.  If UPLO = 'U', the first
              superdiagonal and the diagonal of the tridiagonal matrix T
              are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
              the diagonal and first subdiagonal of T are returned in the
              first two rows of AB.

    LDAB

              LDAB is INTEGER
              The leading dimension of the array AB.  LDAB >= KD + 1.

    W

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

    Z

              Z is DOUBLE PRECISION 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 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 > 2, LWORK must be at least 2*N.
              If JOBZ  = 'V' and N > 2, LWORK must be at least
                             ( 1 + 5*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 JOBZ  = 'N' or N <= 1, LIWORK must be at least 1.
              If JOBZ  = 'V' and N > 2, 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, 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.

Definition at line 185 of file dsbevd.f.

  subroutine ssbevd (character jobz, character uplo, integer n, integer kd, real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) w, real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer liwork, integer info)

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

Purpose:

     SSBEVD computes all the eigenvalues and, optionally, eigenvectors of
     a real symmetric band 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.

    KD

              KD is INTEGER
              The number of superdiagonals of the matrix A if UPLO = 'U',
              or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

    AB

              AB is REAL array, dimension (LDAB, N)
              On entry, the upper or lower triangle of the symmetric band
              matrix A, stored in the first KD+1 rows of the array.  The
              j-th column of A is stored in the j-th column of the array AB
              as follows:
              if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
              if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
              On exit, AB is overwritten by values generated during the
              reduction to tridiagonal form.  If UPLO = 'U', the first
              superdiagonal and the diagonal of the tridiagonal matrix T
              are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
              the diagonal and first subdiagonal of T are returned in the
              first two rows of AB.

    LDAB

              LDAB is INTEGER
              The leading dimension of the array AB.  LDAB >= KD + 1.

    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 (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 > 2, LWORK must be at least 2*N.
              If JOBZ  = 'V' and N > 2, LWORK must be at least
                             ( 1 + 5*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 JOBZ  = 'N' or N <= 1, LIWORK must be at least 1.
              If JOBZ  = 'V' and N > 2, 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, 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.

Definition at line 185 of file ssbevd.f.

  subroutine zhbevd (character jobz, character uplo, integer n, integer kd, complex*16, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) w, complex*16, dimension( ldz, * ) z, integer ldz, complex*16, dimension( * ) work, integer lwork, double precision, dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork, integer liwork, integer info)

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

Purpose:

     ZHBEVD computes all the eigenvalues and, optionally, eigenvectors of
     a complex Hermitian band 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.

    KD

              KD is INTEGER
              The number of superdiagonals of the matrix A if UPLO = 'U',
              or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

    AB

              AB is COMPLEX*16 array, dimension (LDAB, N)
              On entry, the upper or lower triangle of the Hermitian band
              matrix A, stored in the first KD+1 rows of the array.  The
              j-th column of A is stored in the j-th column of the array AB
              as follows:
              if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
              if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
              On exit, AB is overwritten by values generated during the
              reduction to tridiagonal form.  If UPLO = 'U', the first
              superdiagonal and the diagonal of the tridiagonal matrix T
              are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
              the diagonal and first subdiagonal of T are returned in the
              first two rows of AB.

    LDAB

              LDAB is INTEGER
              The leading dimension of the array AB.  LDAB >= KD + 1.

    W

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

    Z

              Z is COMPLEX*16 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 COMPLEX*16 array, dimension (MAX(1,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 N.
              If JOBZ = 'V' and N > 1, LWORK must be at least 2*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 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 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 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, 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.

Definition at line 207 of file zhbevd.f.

Author

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