stein(3) Library Functions Manual stein(3)

stein - stein: eig, inverse iteration


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

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.

Definition at line 180 of file cstein.f.

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.

Definition at line 172 of file dstein.f.

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.

Definition at line 172 of file sstein.f.

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.

Definition at line 180 of file zstein.f.

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