ZSTEDC(1) LAPACK routine (version 3.2) ZSTEDC(1)NAME
ZSTEDC - computes all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using the divide and conquer method
SYNOPSIS
SUBROUTINE ZSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, RWORK, LRWORK,
IWORK, LIWORK, INFO )
CHARACTER COMPZ
INTEGER INFO, LDZ, LIWORK, LRWORK, LWORK, N
INTEGER IWORK( * )
DOUBLE PRECISION D( * ), E( * ), RWORK( * )
COMPLEX*16 WORK( * ), Z( LDZ, * )
PURPOSE
ZSTEDC computes all eigenvalues and, optionally, eigenvectors of a sym‐
metric 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.
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.
ARGUMENTS
COMPZ (input) 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 (input) INTEGER
The dimension of the symmetric tridiagonal matrix. N >= 0.
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.
E (input/output) DOUBLE PRECISION array, dimension (N-1)
On entry, the subdiagonal elements of the tridiagonal matrix.
On exit, E has been destroyed.
Z (input/output) 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 con‐
tains the orthonormal eigenvectors of the symmetric tridiagonal
matrix. If COMPZ = 'N', then Z is not referenced.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1. If eigenvec‐
tors are desired, then LDZ >= max(1,N).
WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) 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 (workspace/output) DOUBLE PRECISION array,
dimension (LRWORK) On exit, if INFO = 0, RWORK(1) returns the
optimal LRWORK.
LRWORK (input) 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 + 3*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 min‐
imum 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 mes‐
sage related to LWORK or LRWORK or LIWORK is issued by XERBLA.
IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
LIWORK (input) 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 (output) 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 work‐
ing on the submatrix lying in rows and columns INFO/(N+1)
through mod(INFO,N+1).
FURTHER DETAILS
Based on contributions by
Jeff Rutter, Computer Science Division, University of California
at Berkeley, USA
LAPACK routine (version 3.2) November 2008 ZSTEDC(1)
