stein(3)

NAME
stein - stein: eig, inverse iteration

SYNOPSIS

  Functions

subroutine cstein (n, d, e, m, w, iblock, isplit, z, ldz, work, iwork, ifail, info)
CSTEIN
subroutine dstein (n, d, e, m, w, iblock, isplit, z, ldz, work, iwork, ifail, info)
DSTEIN
subroutine sstein (n, d, e, m, w, iblock, isplit, z, ldz, work, iwork, ifail, info)
SSTEIN
subroutine zstein (n, d, e, m, w, iblock, isplit, z, ldz, work, iwork, ifail, info)
ZSTEIN

Detailed Description

Function Documentation

  subroutine cstein (integer n, real, dimension( * ) d, real, dimension( * ) e, integer m, real, dimension( * ) w, integer, dimension( * ) iblock, integer, dimension( * ) isplit, complex, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integer, dimension( * ) iwork, integer, dimension( * ) ifail, integer info)

CSTEIN

Purpose:

    !>
    !> CSTEIN computes the eigenvectors of a real symmetric tridiagonal
    !> matrix T corresponding to specified eigenvalues, using inverse
    !> iteration.
    !>
    !> The maximum number of iterations allowed for each eigenvector is
    !> specified by an internal parameter MAXITS (currently set to 5).
    !>
    !> Although the eigenvectors are real, they are stored in a complex
    !> array, which may be passed to CUNMTR or CUPMTR for back
    !> transformation to the eigenvectors of a complex Hermitian matrix
    !> which was reduced to tridiagonal form.
    !>
    !>

Parameters
    N

    !>          N is INTEGER
    !>          The order of the matrix.  N >= 0.
    !>

    D

    !>          D is REAL array, dimension (N)
    !>          The n diagonal elements of the tridiagonal matrix T.
    !>

    E

    !>          E is REAL array, dimension (N-1)
    !>          The (n-1) subdiagonal elements of the tridiagonal matrix
    !>          T, stored in elements 1 to N-1.
    !>

    M

    !>          M is INTEGER
    !>          The number of eigenvectors to be found.  0 <= M <= N.
    !>

    W

    !>          W is REAL array, dimension (N)
    !>          The first M elements of W contain the eigenvalues for
    !>          which eigenvectors are to be computed.  The eigenvalues
    !>          should be grouped by split-off block and ordered from
    !>          smallest to largest within the block.  ( The output array
    !>          W from SSTEBZ with ORDER = 'B' is expected here. )
    !>

    IBLOCK

    !>          IBLOCK is INTEGER array, dimension (N)
    !>          The submatrix indices associated with the corresponding
    !>          eigenvalues in W; IBLOCK(i)=1 if eigenvalue W(i) belongs to
    !>          the first submatrix from the top, =2 if W(i) belongs to
    !>          the second submatrix, etc.  ( The output array IBLOCK
    !>          from SSTEBZ is expected here. )
    !>

    ISPLIT

    !>          ISPLIT is INTEGER array, dimension (N)
    !>          The splitting points, at which T breaks up into submatrices.
    !>          The first submatrix consists of rows/columns 1 to
    !>          ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1
    !>          through ISPLIT( 2 ), etc.
    !>          ( The output array ISPLIT from SSTEBZ is expected here. )
    !>

    Z

    !>          Z is COMPLEX array, dimension (LDZ, M)
    !>          The computed eigenvectors.  The eigenvector associated
    !>          with the eigenvalue W(i) is stored in the i-th column of
    !>          Z.  Any vector which fails to converge is set to its current
    !>          iterate after MAXITS iterations.
    !>          The imaginary parts of the eigenvectors are set to zero.
    !>

    LDZ

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

    WORK

    !>          WORK is REAL array, dimension (5*N)
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension (N)
    !>

    IFAIL

    !>          IFAIL is INTEGER array, dimension (M)
    !>          On normal exit, all elements of IFAIL are zero.
    !>          If one or more eigenvectors fail to converge after
    !>          MAXITS iterations, then their indices are stored in
    !>          array IFAIL.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          < 0: if INFO = -i, the i-th argument had an illegal value
    !>          > 0: if INFO = i, then i eigenvectors failed to converge
    !>               in MAXITS iterations.  Their indices are stored in
    !>               array IFAIL.
    !>

Internal Parameters:

    !>  MAXITS  INTEGER, default = 5
    !>          The maximum number of iterations performed.
    !>
    !>  EXTRA   INTEGER, default = 2
    !>          The number of iterations performed after norm growth
    !>          criterion is satisfied, should be at least 1.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine dstein (integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, integer m, double precision, dimension( * ) w, integer, dimension( * ) iblock, integer, dimension( * ) isplit, double precision, dimension( ldz, * ) z, integer ldz, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer, dimension( * ) ifail, integer info)

DSTEIN

Purpose:

    !>
    !> DSTEIN computes the eigenvectors of a real symmetric tridiagonal
    !> matrix T corresponding to specified eigenvalues, using inverse
    !> iteration.
    !>
    !> The maximum number of iterations allowed for each eigenvector is
    !> specified by an internal parameter MAXITS (currently set to 5).
    !>

Parameters
    N

    !>          N is INTEGER
    !>          The order of the matrix.  N >= 0.
    !>

    D

    !>          D is DOUBLE PRECISION array, dimension (N)
    !>          The n diagonal elements of the tridiagonal matrix T.
    !>

    E

    !>          E is DOUBLE PRECISION array, dimension (N-1)
    !>          The (n-1) subdiagonal elements of the tridiagonal matrix
    !>          T, in elements 1 to N-1.
    !>

    M

    !>          M is INTEGER
    !>          The number of eigenvectors to be found.  0 <= M <= N.
    !>

    W

    !>          W is DOUBLE PRECISION array, dimension (N)
    !>          The first M elements of W contain the eigenvalues for
    !>          which eigenvectors are to be computed.  The eigenvalues
    !>          should be grouped by split-off block and ordered from
    !>          smallest to largest within the block.  ( The output array
    !>          W from DSTEBZ with ORDER = 'B' is expected here. )
    !>

    IBLOCK

    !>          IBLOCK is INTEGER array, dimension (N)
    !>          The submatrix indices associated with the corresponding
    !>          eigenvalues in W; IBLOCK(i)=1 if eigenvalue W(i) belongs to
    !>          the first submatrix from the top, =2 if W(i) belongs to
    !>          the second submatrix, etc.  ( The output array IBLOCK
    !>          from DSTEBZ is expected here. )
    !>

    ISPLIT

    !>          ISPLIT is INTEGER array, dimension (N)
    !>          The splitting points, at which T breaks up into submatrices.
    !>          The first submatrix consists of rows/columns 1 to
    !>          ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1
    !>          through ISPLIT( 2 ), etc.
    !>          ( The output array ISPLIT from DSTEBZ is expected here. )
    !>

    Z

    !>          Z is DOUBLE PRECISION array, dimension (LDZ, M)
    !>          The computed eigenvectors.  The eigenvector associated
    !>          with the eigenvalue W(i) is stored in the i-th column of
    !>          Z.  Any vector which fails to converge is set to its current
    !>          iterate after MAXITS iterations.
    !>

    LDZ

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

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension (5*N)
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension (N)
    !>

    IFAIL

    !>          IFAIL is INTEGER array, dimension (M)
    !>          On normal exit, all elements of IFAIL are zero.
    !>          If one or more eigenvectors fail to converge after
    !>          MAXITS iterations, then their indices are stored in
    !>          array IFAIL.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit.
    !>          < 0: if INFO = -i, the i-th argument had an illegal value
    !>          > 0: if INFO = i, then i eigenvectors failed to converge
    !>               in MAXITS iterations.  Their indices are stored in
    !>               array IFAIL.
    !>

Internal Parameters:

    !>  MAXITS  INTEGER, default = 5
    !>          The maximum number of iterations performed.
    !>
    !>  EXTRA   INTEGER, default = 2
    !>          The number of iterations performed after norm growth
    !>          criterion is satisfied, should be at least 1.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine sstein (integer n, real, dimension( * ) d, real, dimension( * ) e, integer m, real, dimension( * ) w, integer, dimension( * ) iblock, integer, dimension( * ) isplit, real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integer, dimension( * ) iwork, integer, dimension( * ) ifail, integer info)

SSTEIN

Purpose:

    !>
    !> SSTEIN computes the eigenvectors of a real symmetric tridiagonal
    !> matrix T corresponding to specified eigenvalues, using inverse
    !> iteration.
    !>
    !> The maximum number of iterations allowed for each eigenvector is
    !> specified by an internal parameter MAXITS (currently set to 5).
    !>

Parameters
    N

    !>          N is INTEGER
    !>          The order of the matrix.  N >= 0.
    !>

    D

    !>          D is REAL array, dimension (N)
    !>          The n diagonal elements of the tridiagonal matrix T.
    !>

    E

    !>          E is REAL array, dimension (N-1)
    !>          The (n-1) subdiagonal elements of the tridiagonal matrix
    !>          T, in elements 1 to N-1.
    !>

    M

    !>          M is INTEGER
    !>          The number of eigenvectors to be found.  0 <= M <= N.
    !>

    W

    !>          W is REAL array, dimension (N)
    !>          The first M elements of W contain the eigenvalues for
    !>          which eigenvectors are to be computed.  The eigenvalues
    !>          should be grouped by split-off block and ordered from
    !>          smallest to largest within the block.  ( The output array
    !>          W from SSTEBZ with ORDER = 'B' is expected here. )
    !>

    IBLOCK

    !>          IBLOCK is INTEGER array, dimension (N)
    !>          The submatrix indices associated with the corresponding
    !>          eigenvalues in W; IBLOCK(i)=1 if eigenvalue W(i) belongs to
    !>          the first submatrix from the top, =2 if W(i) belongs to
    !>          the second submatrix, etc.  ( The output array IBLOCK
    !>          from SSTEBZ is expected here. )
    !>

    ISPLIT

    !>          ISPLIT is INTEGER array, dimension (N)
    !>          The splitting points, at which T breaks up into submatrices.
    !>          The first submatrix consists of rows/columns 1 to
    !>          ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1
    !>          through ISPLIT( 2 ), etc.
    !>          ( The output array ISPLIT from SSTEBZ is expected here. )
    !>

    Z

    !>          Z is REAL array, dimension (LDZ, M)
    !>          The computed eigenvectors.  The eigenvector associated
    !>          with the eigenvalue W(i) is stored in the i-th column of
    !>          Z.  Any vector which fails to converge is set to its current
    !>          iterate after MAXITS iterations.
    !>

    LDZ

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

    WORK

    !>          WORK is REAL array, dimension (5*N)
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension (N)
    !>

    IFAIL

    !>          IFAIL is INTEGER array, dimension (M)
    !>          On normal exit, all elements of IFAIL are zero.
    !>          If one or more eigenvectors fail to converge after
    !>          MAXITS iterations, then their indices are stored in
    !>          array IFAIL.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit.
    !>          < 0: if INFO = -i, the i-th argument had an illegal value
    !>          > 0: if INFO = i, then i eigenvectors failed to converge
    !>               in MAXITS iterations.  Their indices are stored in
    !>               array IFAIL.
    !>

Internal Parameters:

    !>  MAXITS  INTEGER, default = 5
    !>          The maximum number of iterations performed.
    !>
    !>  EXTRA   INTEGER, default = 2
    !>          The number of iterations performed after norm growth
    !>          criterion is satisfied, should be at least 1.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine zstein (integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, integer m, double precision, dimension( * ) w, integer, dimension( * ) iblock, integer, dimension( * ) isplit, complex*16, dimension( ldz, * ) z, integer ldz, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer, dimension( * ) ifail, integer info)

ZSTEIN

Purpose:

    !>
    !> ZSTEIN computes the eigenvectors of a real symmetric tridiagonal
    !> matrix T corresponding to specified eigenvalues, using inverse
    !> iteration.
    !>
    !> The maximum number of iterations allowed for each eigenvector is
    !> specified by an internal parameter MAXITS (currently set to 5).
    !>
    !> Although the eigenvectors are real, they are stored in a complex
    !> array, which may be passed to ZUNMTR or ZUPMTR for back
    !> transformation to the eigenvectors of a complex Hermitian matrix
    !> which was reduced to tridiagonal form.
    !>
    !>

Parameters
    N

    !>          N is INTEGER
    !>          The order of the matrix.  N >= 0.
    !>

    D

    !>          D is DOUBLE PRECISION array, dimension (N)
    !>          The n diagonal elements of the tridiagonal matrix T.
    !>

    E

    !>          E is DOUBLE PRECISION array, dimension (N-1)
    !>          The (n-1) subdiagonal elements of the tridiagonal matrix
    !>          T, stored in elements 1 to N-1.
    !>

    M

    !>          M is INTEGER
    !>          The number of eigenvectors to be found.  0 <= M <= N.
    !>

    W

    !>          W is DOUBLE PRECISION array, dimension (N)
    !>          The first M elements of W contain the eigenvalues for
    !>          which eigenvectors are to be computed.  The eigenvalues
    !>          should be grouped by split-off block and ordered from
    !>          smallest to largest within the block.  ( The output array
    !>          W from DSTEBZ with ORDER = 'B' is expected here. )
    !>

    IBLOCK

    !>          IBLOCK is INTEGER array, dimension (N)
    !>          The submatrix indices associated with the corresponding
    !>          eigenvalues in W; IBLOCK(i)=1 if eigenvalue W(i) belongs to
    !>          the first submatrix from the top, =2 if W(i) belongs to
    !>          the second submatrix, etc.  ( The output array IBLOCK
    !>          from DSTEBZ is expected here. )
    !>

    ISPLIT

    !>          ISPLIT is INTEGER array, dimension (N)
    !>          The splitting points, at which T breaks up into submatrices.
    !>          The first submatrix consists of rows/columns 1 to
    !>          ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1
    !>          through ISPLIT( 2 ), etc.
    !>          ( The output array ISPLIT from DSTEBZ is expected here. )
    !>

    Z

    !>          Z is COMPLEX*16 array, dimension (LDZ, M)
    !>          The computed eigenvectors.  The eigenvector associated
    !>          with the eigenvalue W(i) is stored in the i-th column of
    !>          Z.  Any vector which fails to converge is set to its current
    !>          iterate after MAXITS iterations.
    !>          The imaginary parts of the eigenvectors are set to zero.
    !>

    LDZ

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

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension (5*N)
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension (N)
    !>

    IFAIL

    !>          IFAIL is INTEGER array, dimension (M)
    !>          On normal exit, all elements of IFAIL are zero.
    !>          If one or more eigenvectors fail to converge after
    !>          MAXITS iterations, then their indices are stored in
    !>          array IFAIL.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          < 0: if INFO = -i, the i-th argument had an illegal value
    !>          > 0: if INFO = i, then i eigenvectors failed to converge
    !>               in MAXITS iterations.  Their indices are stored in
    !>               array IFAIL.
    !>

Internal Parameters:

    !>  MAXITS  INTEGER, default = 5
    !>          The maximum number of iterations performed.
    !>
    !>  EXTRA   INTEGER, default = 2
    !>          The number of iterations performed after norm growth
    !>          criterion is satisfied, should be at least 1.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Author

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