Purpose
=======
LA_SBEV and LA_SBEVD compute all eigenvalues and, optionally, all
eigenvectors of a real symmetric matrix A in band form.
LA_HBEV and LA_HBEVD compute all eigenvalues and, optionally, all
eigenvectors of a complex Hermitian matrix A in band form.
LA_SBEVD and LA_HBEVD use a divide and conquer algorithm. They are
much faster than LA_SBEV and LA_HBEV for large matrices but use more
workspace.
=========
SUBROUTINE LA_SBEV / LA_HBEV / LA_SBEVD /
LA_HBEVD( AB, W, UPLO=uplo, Z=z, INFO=info )
(), INTENT(INOUT) :: AB(:,:)
REAL(), INTENT(OUT) :: W(:)
CHARACTER(LEN=1), INTENT(IN), OPTIONAL :: UPLO
(), INTENT(OUT), OPTIONAL :: Z(:,:)
INTEGER, INTENT(OUT), OPTIONAL :: INFO
where
::= REAL | COMPLEX
::= KIND(1.0) | KIND(1.0D0)
Arguments
=========
AB (input/output) REAL or COMPLEX array, shape (:,:) with
size(AB,1) = kd + 1 and
size(AB,2) = n, where kd is the number of subdiagonals or
superdiagonals in the band and n is the order of A.
On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L')
triangle of matrix A in band storage. The kd + 1 diagonals of A
are stored in the rows of AB so that the j-th column of A is
stored in the j-th column of AB as follows:
if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j
1<=j<=n
if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd)
1<=j<=n.
On exit, AB is overwritten by values generated during the
reduction of A to a tridiagonal matrix T . If UPLO = 'U', the
first superdiagonal and the diagonal of T are returned in rows
kd and kd + 1 of AB. If UPLO = 'L', the diagonal and first
subdiagonal of T are returned in the first two rows of AB.
W (output) REAL array, shape (:) with size(W) = n.
The eigenvalues in ascending order.
UPLO Optional (input) CHARACTER(LEN=1).
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
Default value: 'U'.
Z Optional (output) REAL or COMPLEX square array, shape (:,:) with
size(Z,1) = n.
The columns of Z contain the orthonormal eigenvectors of A in
the order of the eigenvalues.
INFO Optional (output) INTEGER.
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = i, then i off-diagonal elements of an intermediate
tridiagonal form did not converge to zero.
If INFO is not present and an error occurs, then the program is
terminated with an error message.