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.
Namespace: DotNumerics.LinearAlgebra.CSLapackAssembly: DWSIM.MathOps.DotNumerics (in DWSIM.MathOps.DotNumerics.dll) Version: 1.0.0.0 (1.0.0.0)
Syntax public void Run(
string JOBZ,
string UPLO,
int N,
int KD,
ref double[] AB,
int offset_ab,
int LDAB,
ref double[] W,
int offset_w,
ref double[] Z,
int offset_z,
int LDZ,
ref double[] WORK,
int offset_work,
int LWORK,
ref int[] IWORK,
int offset_iwork,
int LIWORK,
ref int INFO
)
Public Sub Run (
JOBZ As String,
UPLO As String,
N As Integer,
KD As Integer,
ByRef AB As Double(),
offset_ab As Integer,
LDAB As Integer,
ByRef W As Double(),
offset_w As Integer,
ByRef Z As Double(),
offset_z As Integer,
LDZ As Integer,
ByRef WORK As Double(),
offset_work As Integer,
LWORK As Integer,
ByRef IWORK As Integer(),
offset_iwork As Integer,
LIWORK As Integer,
ByRef INFO As Integer
)
Request Example
View SourceParameters
- JOBZ String
-
(input) CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
- UPLO String
-
(input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
- N Int32
-
(input) INTEGER
The order of the matrix A. N .GE. 0.
- KD Int32
-
(input) INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KD .GE. 0.
- AB Double
-
(input/output) 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).LE.i.LE.j;
if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j.LE.i.LE.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.
- offset_ab Int32
-
- LDAB Int32
-
(input) INTEGER
The leading dimension of the array AB. LDAB .GE. KD + 1.
- W Double
-
(output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
- offset_w Int32
-
- Z Double
-
(output) 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.
- offset_z Int32
-
- LDZ Int32
-
(input) INTEGER
The leading dimension of the array Z. LDZ .GE. 1, and if
JOBZ = 'V', LDZ .GE. max(1,N).
- WORK Double
-
(workspace/output) DOUBLE PRECISION array,
dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
- offset_work Int32
-
- LWORK Int32
-
(input) INTEGER
The dimension of the array WORK.
IF N .LE. 1, LWORK must be at least 1.
If JOBZ = 'N' and N .GT. 2, LWORK must be at least 2*N.
If JOBZ = 'V' and N .GT. 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 Int32
-
(workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
- offset_iwork Int32
-
- LIWORK Int32
-
(input) INTEGER
The dimension of the array LIWORK.
If JOBZ = 'N' or N .LE. 1, LIWORK must be at least 1.
If JOBZ = 'V' and N .GT. 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 Int32
-
(output) INTEGER
= 0: successful exit
.LT. 0: if INFO = -i, the i-th argument had an illegal value
.GT. 0: if INFO = i, the algorithm failed to converge; i
off-diagonal elements of an intermediate tridiagonal
form did not converge to zero.
See Also