.TH "stein" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
stein \- stein: eig, inverse iteration
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBcstein\fP (n, d, e, m, w, iblock, isplit, z, ldz, work, iwork, ifail, info)"
.br
.RI "\fBCSTEIN\fP "
.ti -1c
.RI "subroutine \fBdstein\fP (n, d, e, m, w, iblock, isplit, z, ldz, work, iwork, ifail, info)"
.br
.RI "\fBDSTEIN\fP "
.ti -1c
.RI "subroutine \fBsstein\fP (n, d, e, m, w, iblock, isplit, z, ldz, work, iwork, ifail, info)"
.br
.RI "\fBSSTEIN\fP "
.ti -1c
.RI "subroutine \fBzstein\fP (n, d, e, m, w, iblock, isplit, z, ldz, work, iwork, ifail, info)"
.br
.RI "\fBZSTEIN\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "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)"

.PP
\fBCSTEIN\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> 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\&.
!>
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fID\fP 
.PP
.nf
!>          D is REAL array, dimension (N)
!>          The n diagonal elements of the tridiagonal matrix T\&.
!> 
.fi
.PP
.br
\fIE\fP 
.PP
.nf
!>          E is REAL array, dimension (N-1)
!>          The (n-1) subdiagonal elements of the tridiagonal matrix
!>          T, stored in elements 1 to N-1\&.
!> 
.fi
.PP
.br
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The number of eigenvectors to be found\&.  0 <= M <= N\&.
!> 
.fi
.PP
.br
\fIW\fP 
.PP
.nf
!>          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\&. )
!> 
.fi
.PP
.br
\fIIBLOCK\fP 
.PP
.nf
!>          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\&. )
!> 
.fi
.PP
.br
\fIISPLIT\fP 
.PP
.nf
!>          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\&. )
!> 
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILDZ\fP 
.PP
.nf
!>          LDZ is INTEGER
!>          The leading dimension of the array Z\&.  LDZ >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is REAL array, dimension (5*N)
!> 
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
!>          IWORK is INTEGER array, dimension (N)
!> 
.fi
.PP
.br
\fIIFAIL\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBInternal Parameters:\fP
.RS 4

.PP
.nf
!>  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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB180\fP of file \fBcstein\&.f\fP\&.
.SS "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)"

.PP
\fBDSTEIN\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> 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)\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fID\fP 
.PP
.nf
!>          D is DOUBLE PRECISION array, dimension (N)
!>          The n diagonal elements of the tridiagonal matrix T\&.
!> 
.fi
.PP
.br
\fIE\fP 
.PP
.nf
!>          E is DOUBLE PRECISION array, dimension (N-1)
!>          The (n-1) subdiagonal elements of the tridiagonal matrix
!>          T, in elements 1 to N-1\&.
!> 
.fi
.PP
.br
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The number of eigenvectors to be found\&.  0 <= M <= N\&.
!> 
.fi
.PP
.br
\fIW\fP 
.PP
.nf
!>          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\&. )
!> 
.fi
.PP
.br
\fIIBLOCK\fP 
.PP
.nf
!>          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\&. )
!> 
.fi
.PP
.br
\fIISPLIT\fP 
.PP
.nf
!>          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\&. )
!> 
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILDZ\fP 
.PP
.nf
!>          LDZ is INTEGER
!>          The leading dimension of the array Z\&.  LDZ >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is DOUBLE PRECISION array, dimension (5*N)
!> 
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
!>          IWORK is INTEGER array, dimension (N)
!> 
.fi
.PP
.br
\fIIFAIL\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBInternal Parameters:\fP
.RS 4

.PP
.nf
!>  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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB172\fP of file \fBdstein\&.f\fP\&.
.SS "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)"

.PP
\fBSSTEIN\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> 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)\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fID\fP 
.PP
.nf
!>          D is REAL array, dimension (N)
!>          The n diagonal elements of the tridiagonal matrix T\&.
!> 
.fi
.PP
.br
\fIE\fP 
.PP
.nf
!>          E is REAL array, dimension (N-1)
!>          The (n-1) subdiagonal elements of the tridiagonal matrix
!>          T, in elements 1 to N-1\&.
!> 
.fi
.PP
.br
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The number of eigenvectors to be found\&.  0 <= M <= N\&.
!> 
.fi
.PP
.br
\fIW\fP 
.PP
.nf
!>          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\&. )
!> 
.fi
.PP
.br
\fIIBLOCK\fP 
.PP
.nf
!>          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\&. )
!> 
.fi
.PP
.br
\fIISPLIT\fP 
.PP
.nf
!>          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\&. )
!> 
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILDZ\fP 
.PP
.nf
!>          LDZ is INTEGER
!>          The leading dimension of the array Z\&.  LDZ >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is REAL array, dimension (5*N)
!> 
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
!>          IWORK is INTEGER array, dimension (N)
!> 
.fi
.PP
.br
\fIIFAIL\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBInternal Parameters:\fP
.RS 4

.PP
.nf
!>  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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB172\fP of file \fBsstein\&.f\fP\&.
.SS "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)"

.PP
\fBZSTEIN\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> 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\&.
!>
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fID\fP 
.PP
.nf
!>          D is DOUBLE PRECISION array, dimension (N)
!>          The n diagonal elements of the tridiagonal matrix T\&.
!> 
.fi
.PP
.br
\fIE\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The number of eigenvectors to be found\&.  0 <= M <= N\&.
!> 
.fi
.PP
.br
\fIW\fP 
.PP
.nf
!>          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\&. )
!> 
.fi
.PP
.br
\fIIBLOCK\fP 
.PP
.nf
!>          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\&. )
!> 
.fi
.PP
.br
\fIISPLIT\fP 
.PP
.nf
!>          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\&. )
!> 
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILDZ\fP 
.PP
.nf
!>          LDZ is INTEGER
!>          The leading dimension of the array Z\&.  LDZ >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is DOUBLE PRECISION array, dimension (5*N)
!> 
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
!>          IWORK is INTEGER array, dimension (N)
!> 
.fi
.PP
.br
\fIIFAIL\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBInternal Parameters:\fP
.RS 4

.PP
.nf
!>  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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB180\fP of file \fBzstein\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.