.TH DSTEDC 1 "November 2006" " LAPACK driver routine (version 3.1) " " LAPACK driver routine (version 3.1) "
.SH NAME
DSTEDC - all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method
.SH SYNOPSIS
.TP 19
SUBROUTINE DSTEDC(
COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK,
LIWORK, INFO )
.TP 19
.ti +4
CHARACTER
COMPZ
.TP 19
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INTEGER
INFO, LDZ, LIWORK, LWORK, N
.TP 19
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INTEGER
IWORK( * )
.TP 19
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DOUBLE
PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )
.SH 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.
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This code makes very mild assumptions about floating point
arithmetic. It will work on machines with a guard digit in
add/subtract, or on those binary machines without guard digits
which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.
It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none. See DLAED3 for details.
.SH ARGUMENTS
.TP 8
COMPZ (input) CHARACTER*1
= \(aqN\(aq: Compute eigenvalues only.
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= \(aqI\(aq: Compute eigenvectors of tridiagonal matrix also.
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= \(aqV\(aq: Compute eigenvectors of original dense symmetric
matrix also. On entry, Z contains the orthogonal
matrix used to reduce the original matrix to
tridiagonal form.
.TP 8
N (input) INTEGER
The dimension of the symmetric tridiagonal matrix. N >= 0.
.TP 8
D (input/output) DOUBLE PRECISION array, dimension (N)
On entry, the diagonal elements of the tridiagonal matrix.
On exit, if INFO = 0, the eigenvalues in ascending order.
.TP 8
E (input/output) DOUBLE PRECISION array, dimension (N-1)
On entry, the subdiagonal elements of the tridiagonal matrix.
On exit, E has been destroyed.
.TP 8
Z (input/output) DOUBLE PRECISION array, dimension (LDZ,N)
On entry, if COMPZ = \(aqV\(aq, then Z contains the orthogonal
matrix used in the reduction to tridiagonal form.
On exit, if INFO = 0, then if COMPZ = \(aqV\(aq, Z contains the
orthonormal eigenvectors of the original symmetric matrix,
and if COMPZ = \(aqI\(aq, Z contains the orthonormal eigenvectors
of the symmetric tridiagonal matrix.
If COMPZ = \(aqN\(aq, then Z is not referenced.
.TP 8
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1.
If eigenvectors are desired, then LDZ >= max(1,N).
.TP 8
WORK (workspace/output) DOUBLE PRECISION array,
dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
.TP 8
LWORK (input) INTEGER
The dimension of the array WORK.
If COMPZ = \(aqN\(aq or N <= 1 then LWORK must be at least 1.
If COMPZ = \(aqV\(aq and N > 1 then LWORK must be at least
( 1 + 3*N + 2*N*lg N + 3*N**2 ),
where lg( N ) = smallest integer k such
that 2**k >= N.
If COMPZ = \(aqI\(aq and N > 1 then LWORK must be at least
( 1 + 4*N + N**2 ).
Note that for COMPZ = \(aqI\(aq or \(aqV\(aq, 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.
.TP 8
IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
.TP 8
LIWORK (input) INTEGER
The dimension of the array IWORK.
If COMPZ = \(aqN\(aq or N <= 1 then LIWORK must be at least 1.
If COMPZ = \(aqV\(aq and N > 1 then LIWORK must be at least
( 6 + 6*N + 5*N*lg N ).
If COMPZ = \(aqI\(aq and N > 1 then LIWORK must be at least
( 3 + 5*N ).
Note that for COMPZ = \(aqI\(aq or \(aqV\(aq, 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.
.TP 8
INFO (output) INTEGER
= 0: successful exit.
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< 0: if INFO = -i, the i-th argument had an illegal value.
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> 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).
.SH FURTHER DETAILS
Based on contributions by
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Jeff Rutter, Computer Science Division, University of California
at Berkeley, USA
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Modified by Francoise Tisseur, University of Tennessee.
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