stedc(3)

NAME
stedc - stedc: eig, divide and conquer

SYNOPSIS

  Functions

subroutine cstedc (compz, n, d, e, z, ldz, work, lwork, rwork, lrwork, iwork, liwork, info)
CSTEDC
subroutine dstedc (compz, n, d, e, z, ldz, work, lwork, iwork, liwork, info)
DSTEDC
subroutine sstedc (compz, n, d, e, z, ldz, work, lwork, iwork, liwork, info)
SSTEDC
subroutine zstedc (compz, n, d, e, z, ldz, work, lwork, rwork, lrwork, iwork, liwork, info)
ZSTEDC

Detailed Description

Function Documentation

  subroutine cstedc (character compz, integer n, real, dimension( * ) d, real, dimension( * ) e, complex, dimension( ldz, * ) z, integer ldz, complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork, integer liwork, integer info)

CSTEDC

Purpose:

    !>
    !> CSTEDC computes all eigenvalues and, optionally, eigenvectors of a
    !> symmetric tridiagonal matrix using the divide and conquer method.
    !> The eigenvectors of a full or band complex Hermitian matrix can also
    !> be found if CHETRD or CHPTRD or CHBTRD has been used to reduce this
    !> matrix to tridiagonal form.
    !>
    !>

Parameters
    COMPZ

    !>          COMPZ is CHARACTER*1
    !>          = 'N':  Compute eigenvalues only.
    !>          = 'I':  Compute eigenvectors of tridiagonal matrix also.
    !>          = 'V':  Compute eigenvectors of original Hermitian matrix
    !>                  also.  On entry, Z contains the unitary matrix used
    !>                  to reduce the original matrix to tridiagonal form.
    !>

    N

    !>          N is INTEGER
    !>          The dimension of the symmetric tridiagonal matrix.  N >= 0.
    !>

    D

    !>          D is REAL array, dimension (N)
    !>          On entry, the diagonal elements of the tridiagonal matrix.
    !>          On exit, if INFO = 0, the eigenvalues in ascending order.
    !>

    E

    !>          E is REAL array, dimension (N-1)
    !>          On entry, the subdiagonal elements of the tridiagonal matrix.
    !>          On exit, E has been destroyed.
    !>

    Z

    !>          Z is COMPLEX array, dimension (LDZ,N)
    !>          On entry, if COMPZ = 'V', then Z contains the unitary
    !>          matrix used in the reduction to tridiagonal form.
    !>          On exit, if INFO = 0, then if COMPZ = 'V', Z contains the
    !>          orthonormal eigenvectors of the original Hermitian matrix,
    !>          and if COMPZ = 'I', Z contains the orthonormal eigenvectors
    !>          of the symmetric tridiagonal matrix.
    !>          If  COMPZ = 'N', then Z is not referenced.
    !>

    LDZ

    !>          LDZ is INTEGER
    !>          The leading dimension of the array Z.  LDZ >= 1.
    !>          If eigenvectors are desired, then 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 COMPZ = 'N' or 'I', or N <= 1, LWORK must be at least 1.
    !>          If COMPZ = 'V' and N > 1, LWORK must be at least N*N.
    !>          Note that for COMPZ = 'V', then if N is less than or
    !>          equal to the minimum divide size, usually 25, then LWORK need
    !>          only be 1.
    !>
    !>          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 (MAX(1,LRWORK))
    !>          On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
    !>

    LRWORK

    !>          LRWORK is INTEGER
    !>          The dimension of the array RWORK.
    !>          If COMPZ = 'N' or N <= 1, LRWORK must be at least 1.
    !>          If COMPZ = 'V' and N > 1, LRWORK must be at least
    !>                         1 + 3*N + 2*N*lg N + 4*N**2 ,
    !>                         where lg( N ) = smallest integer k such
    !>                         that 2**k >= N.
    !>          If COMPZ = 'I' and N > 1, LRWORK must be at least
    !>                         1 + 4*N + 2*N**2 .
    !>          Note that for COMPZ = 'I' or 'V', then if N is less than or
    !>          equal to the minimum divide size, usually 25, then LRWORK
    !>          need only be max(1,2*(N-1)).
    !>
    !>          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 COMPZ = 'N' or N <= 1, LIWORK must be at least 1.
    !>          If COMPZ = 'V' or N > 1,  LIWORK must be at least
    !>                                    6 + 6*N + 5*N*lg N.
    !>          If COMPZ = 'I' or N > 1,  LIWORK must be at least
    !>                                    3 + 5*N .
    !>          Note that for COMPZ = 'I' or 'V', then if N is less than or
    !>          equal to the minimum divide size, usually 25, then LIWORK
    !>          need only be 1.
    !>
    !>          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:  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

  subroutine dstedc (character compz, integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldz, * ) z, integer ldz, double precision, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer liwork, integer info)

DSTEDC

Purpose:

    !>
    !> DSTEDC computes all eigenvalues and, optionally, eigenvectors of a
    !> symmetric tridiagonal matrix using the divide and conquer method.
    !> The eigenvectors of a full or band real symmetric matrix can also be
    !> found if DSYTRD or DSPTRD or DSBTRD has been used to reduce this
    !> matrix to tridiagonal form.
    !>
    !>

Parameters
    COMPZ

    !>          COMPZ is CHARACTER*1
    !>          = 'N':  Compute eigenvalues only.
    !>          = 'I':  Compute eigenvectors of tridiagonal matrix also.
    !>          = 'V':  Compute eigenvectors of original dense symmetric
    !>                  matrix also.  On entry, Z contains the orthogonal
    !>                  matrix used to reduce the original matrix to
    !>                  tridiagonal form.
    !>

    N

    !>          N is INTEGER
    !>          The dimension of the symmetric tridiagonal matrix.  N >= 0.
    !>

    D

    !>          D is DOUBLE PRECISION array, dimension (N)
    !>          On entry, the diagonal elements of the tridiagonal matrix.
    !>          On exit, if INFO = 0, the eigenvalues in ascending order.
    !>

    E

    !>          E is DOUBLE PRECISION array, dimension (N-1)
    !>          On entry, the subdiagonal elements of the tridiagonal matrix.
    !>          On exit, E has been destroyed.
    !>

    Z

    !>          Z is DOUBLE PRECISION array, dimension (LDZ,N)
    !>          On entry, if COMPZ = 'V', then Z contains the orthogonal
    !>          matrix used in the reduction to tridiagonal form.
    !>          On exit, if INFO = 0, then if COMPZ = 'V', Z contains the
    !>          orthonormal eigenvectors of the original symmetric matrix,
    !>          and if COMPZ = 'I', Z contains the orthonormal eigenvectors
    !>          of the symmetric tridiagonal matrix.
    !>          If  COMPZ = 'N', then Z is not referenced.
    !>

    LDZ

    !>          LDZ is INTEGER
    !>          The leading dimension of the array Z.  LDZ >= 1.
    !>          If eigenvectors are desired, then LDZ >= max(1,N).
    !>

    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 dimension of the array WORK.
    !>          If COMPZ = 'N' or N <= 1 then LWORK must be at least 1.
    !>          If COMPZ = 'V' and N > 1 then LWORK must be at least
    !>                         ( 1 + 3*N + 2*N*lg N + 4*N**2 ),
    !>                         where lg( N ) = smallest integer k such
    !>                         that 2**k >= N.
    !>          If COMPZ = 'I' and N > 1 then LWORK must be at least
    !>                         ( 1 + 4*N + N**2 ).
    !>          Note that for COMPZ = 'I' or 'V', then if N is less than or
    !>          equal to the minimum divide size, usually 25, then LWORK need
    !>          only be max(1,2*(N-1)).
    !>
    !>          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.
    !>

    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 COMPZ = 'N' or N <= 1 then LIWORK must be at least 1.
    !>          If COMPZ = 'V' and N > 1 then LIWORK must be at least
    !>                         ( 6 + 6*N + 5*N*lg N ).
    !>          If COMPZ = 'I' and N > 1 then LIWORK must be at least
    !>                         ( 3 + 5*N ).
    !>          Note that for COMPZ = 'I' or 'V', then if N is less than or
    !>          equal to the minimum divide size, usually 25, then LIWORK
    !>          need only be 1.
    !>
    !>          If LIWORK = -1, then a workspace query is assumed; the
    !>          routine only calculates the optimal size of the IWORK array,
    !>          returns this value as the first entry of the IWORK array, and
    !>          no error message related to 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:  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

  subroutine sstedc (character compz, integer n, real, dimension( * ) d, real, dimension( * ) e, real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer liwork, integer info)

SSTEDC

Purpose:

    !>
    !> SSTEDC computes all eigenvalues and, optionally, eigenvectors of a
    !> symmetric tridiagonal matrix using the divide and conquer method.
    !> The eigenvectors of a full or band real symmetric matrix can also be
    !> found if SSYTRD or SSPTRD or SSBTRD has been used to reduce this
    !> matrix to tridiagonal form.
    !>
    !>

Parameters
    COMPZ

    !>          COMPZ is CHARACTER*1
    !>          = 'N':  Compute eigenvalues only.
    !>          = 'I':  Compute eigenvectors of tridiagonal matrix also.
    !>          = 'V':  Compute eigenvectors of original dense symmetric
    !>                  matrix also.  On entry, Z contains the orthogonal
    !>                  matrix used to reduce the original matrix to
    !>                  tridiagonal form.
    !>

    N

    !>          N is INTEGER
    !>          The dimension of the symmetric tridiagonal matrix.  N >= 0.
    !>

    D

    !>          D is REAL array, dimension (N)
    !>          On entry, the diagonal elements of the tridiagonal matrix.
    !>          On exit, if INFO = 0, the eigenvalues in ascending order.
    !>

    E

    !>          E is REAL array, dimension (N-1)
    !>          On entry, the subdiagonal elements of the tridiagonal matrix.
    !>          On exit, E has been destroyed.
    !>

    Z

    !>          Z is REAL array, dimension (LDZ,N)
    !>          On entry, if COMPZ = 'V', then Z contains the orthogonal
    !>          matrix used in the reduction to tridiagonal form.
    !>          On exit, if INFO = 0, then if COMPZ = 'V', Z contains the
    !>          orthonormal eigenvectors of the original symmetric matrix,
    !>          and if COMPZ = 'I', Z contains the orthonormal eigenvectors
    !>          of the symmetric tridiagonal matrix.
    !>          If  COMPZ = 'N', then Z is not referenced.
    !>

    LDZ

    !>          LDZ is INTEGER
    !>          The leading dimension of the array Z.  LDZ >= 1.
    !>          If eigenvectors are desired, then LDZ >= max(1,N).
    !>

    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 dimension of the array WORK.
    !>          If COMPZ = 'N' or N <= 1 then LWORK must be at least 1.
    !>          If COMPZ = 'V' and N > 1 then LWORK must be at least
    !>                         ( 1 + 3*N + 2*N*lg N + 4*N**2 ),
    !>                         where lg( N ) = smallest integer k such
    !>                         that 2**k >= N.
    !>          If COMPZ = 'I' and N > 1 then LWORK must be at least
    !>                         ( 1 + 4*N + N**2 ).
    !>          Note that for COMPZ = 'I' or 'V', then if N is less than or
    !>          equal to the minimum divide size, usually 25, then LWORK need
    !>          only be max(1,2*(N-1)).
    !>
    !>          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.
    !>

    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 COMPZ = 'N' or N <= 1 then LIWORK must be at least 1.
    !>          If COMPZ = 'V' and N > 1 then LIWORK must be at least
    !>                         ( 6 + 6*N + 5*N*lg N ).
    !>          If COMPZ = 'I' and N > 1 then LIWORK must be at least
    !>                         ( 3 + 5*N ).
    !>          Note that for COMPZ = 'I' or 'V', then if N is less than or
    !>          equal to the minimum divide size, usually 25, then LIWORK
    !>          need only be 1.
    !>
    !>          If LIWORK = -1, then a workspace query is assumed; the
    !>          routine only calculates the optimal size of the IWORK array,
    !>          returns this value as the first entry of the IWORK array, and
    !>          no error message related to 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:  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

  subroutine zstedc (character compz, integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, 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)

ZSTEDC

Purpose:

    !>
    !> ZSTEDC computes all eigenvalues and, optionally, eigenvectors of a
    !> symmetric tridiagonal matrix using the divide and conquer method.
    !> The eigenvectors of a full or band complex Hermitian matrix can also
    !> be found if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this
    !> matrix to tridiagonal form.
    !>
    !>

Parameters
    COMPZ

    !>          COMPZ is CHARACTER*1
    !>          = 'N':  Compute eigenvalues only.
    !>          = 'I':  Compute eigenvectors of tridiagonal matrix also.
    !>          = 'V':  Compute eigenvectors of original Hermitian matrix
    !>                  also.  On entry, Z contains the unitary matrix used
    !>                  to reduce the original matrix to tridiagonal form.
    !>

    N

    !>          N is INTEGER
    !>          The dimension of the symmetric tridiagonal matrix.  N >= 0.
    !>

    D

    !>          D is DOUBLE PRECISION array, dimension (N)
    !>          On entry, the diagonal elements of the tridiagonal matrix.
    !>          On exit, if INFO = 0, the eigenvalues in ascending order.
    !>

    E

    !>          E is DOUBLE PRECISION array, dimension (N-1)
    !>          On entry, the subdiagonal elements of the tridiagonal matrix.
    !>          On exit, E has been destroyed.
    !>

    Z

    !>          Z is COMPLEX*16 array, dimension (LDZ,N)
    !>          On entry, if COMPZ = 'V', then Z contains the unitary
    !>          matrix used in the reduction to tridiagonal form.
    !>          On exit, if INFO = 0, then if COMPZ = 'V', Z contains the
    !>          orthonormal eigenvectors of the original Hermitian matrix,
    !>          and if COMPZ = 'I', Z contains the orthonormal eigenvectors
    !>          of the symmetric tridiagonal matrix.
    !>          If  COMPZ = 'N', then Z is not referenced.
    !>

    LDZ

    !>          LDZ is INTEGER
    !>          The leading dimension of the array Z.  LDZ >= 1.
    !>          If eigenvectors are desired, then 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 COMPZ = 'N' or 'I', or N <= 1, LWORK must be at least 1.
    !>          If COMPZ = 'V' and N > 1, LWORK must be at least N*N.
    !>          Note that for COMPZ = 'V', then if N is less than or
    !>          equal to the minimum divide size, usually 25, then LWORK need
    !>          only be 1.
    !>
    !>          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 (MAX(1,LRWORK))
    !>          On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
    !>

    LRWORK

    !>          LRWORK is INTEGER
    !>          The dimension of the array RWORK.
    !>          If COMPZ = 'N' or N <= 1, LRWORK must be at least 1.
    !>          If COMPZ = 'V' and N > 1, LRWORK must be at least
    !>                         1 + 3*N + 2*N*lg N + 4*N**2 ,
    !>                         where lg( N ) = smallest integer k such
    !>                         that 2**k >= N.
    !>          If COMPZ = 'I' and N > 1, LRWORK must be at least
    !>                         1 + 4*N + 2*N**2 .
    !>          Note that for COMPZ = 'I' or 'V', then if N is less than or
    !>          equal to the minimum divide size, usually 25, then LRWORK
    !>          need only be max(1,2*(N-1)).
    !>
    !>          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 COMPZ = 'N' or N <= 1, LIWORK must be at least 1.
    !>          If COMPZ = 'V' or N > 1,  LIWORK must be at least
    !>                                    6 + 6*N + 5*N*lg N.
    !>          If COMPZ = 'I' or N > 1,  LIWORK must be at least
    !>                                    3 + 5*N .
    !>          Note that for COMPZ = 'I' or 'V', then if N is less than or
    !>          equal to the minimum divide size, usually 25, then LIWORK
    !>          need only be 1.
    !>
    !>          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:  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

Author

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