#### NAME
dsbevd.f -
#### SYNOPSIS
Functions/Subroutines
subroutine dsbevd (JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, LWORK,
IWORK, LIWORK, INFO)
DSBEVD computes the eigenvalues and, optionally, the left and/or
right eigenvectors for OTHER matrices
#### Function/Subroutine Documentation
subroutine dsbevd (characterJOBZ, characterUPLO, integerN, integerKD,
double precision, dimension( ldab, * )AB, integerLDAB, double
precision, dimension( * )W, double precision, dimension( ldz, * )Z,
integerLDZ, double precision, dimension( * )WORK, integerLWORK,
integer, dimension( * )IWORK, integerLIWORK, integerINFO)
DSBEVD computes the eigenvalues and, optionally, the left and/or right
eigenvectors for OTHER matrices
Purpose:
DSBEVD computes all the eigenvalues and, optionally, eigenvectors of
a real symmetric band matrix A. If eigenvectors are desired, it uses
a divide and conquer algorithm.
The divide and conquer algorithm 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.
Parameters:
__JOBZ__
JOBZ is CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
__UPLO__
UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
__N__
N is INTEGER
The order of the matrix A. N >= 0.
__KD__
KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KD >= 0.
__AB__
AB is DOUBLE PRECISION array, dimension (LDAB, N)
On entry, the upper or lower triangle of the symmetric band
matrix A, stored in the first KD+1 rows of the array. The
j-th column of A is stored in the j-th column of the array AB
as follows:
if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
On exit, AB is overwritten by values generated during the
reduction to tridiagonal form. If UPLO = 'U', the first
superdiagonal and the diagonal of the tridiagonal matrix T
are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
the diagonal and first subdiagonal of T are returned in the
first two rows of AB.
__LDAB__
LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD + 1.
__W__
W is DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
__Z__
Z is DOUBLE PRECISION array, dimension (LDZ, N)
If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
eigenvectors of the matrix A, with the i-th column of Z
holding the eigenvector associated with W(i).
If JOBZ = 'N', then Z is not referenced.
__LDZ__
LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = 'V', LDZ >= max(1,N).
__WORK__
WORK is DOUBLE PRECISION array,
dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
__LWORK__
LWORK is INTEGER
The dimension of the array WORK.
IF N <= 1, LWORK must be at least 1.
If JOBZ = 'N' and N > 2, LWORK must be at least 2*N.
If JOBZ = 'V' and N > 2, LWORK must be at least
( 1 + 5*N + 2*N**2 ).
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK and IWORK
arrays, returns these values as the first entries of the WORK
and IWORK arrays, and no error message related to LWORK or
LIWORK is issued by XERBLA.
__IWORK__
IWORK is INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
__LIWORK__
LIWORK is INTEGER
The dimension of the array IWORK.
If JOBZ = 'N' or N <= 1, LIWORK must be at least 1.
If JOBZ = 'V' and N > 2, LIWORK must be at least 3 + 5*N.
If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK and
IWORK arrays, returns these values as the first entries of
the WORK and IWORK arrays, and no error message related to
LWORK or LIWORK is issued by XERBLA.
__INFO__
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the algorithm failed to converge; i
off-diagonal elements of an intermediate tridiagonal
form did not converge to zero.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Definition at line 193 of file dsbevd.f.
#### Author
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