Visible to Intel only — GUID: GUID-D3C929A9-8E33-4540-8854-AA8BE61BB08F
Visible to Intel only — GUID: GUID-D3C929A9-8E33-4540-8854-AA8BE61BB08F
?sbev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix.
Syntax
call ssbev(jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, info)
call dsbev(jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, info)
call sbev(ab, w [,uplo] [,z] [,info])
Include Files
- mkl.fi, lapack.f90
Description
The routine computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A.
Input Parameters
- jobz
-
CHARACTER*1. Must be 'N' or 'V'.
If jobz = 'N', then only eigenvalues are computed.
If jobz = 'V', then eigenvalues and eigenvectors are computed.
- uplo
-
CHARACTER*1. Must be 'U' or 'L'.
If uplo = 'U', ab stores the upper triangular part of A.
If uplo = 'L', ab stores the lower triangular part of A.
- n
-
INTEGER. The order of the matrix A (n≥ 0).
- kd
-
INTEGER. The number of super- or sub-diagonals in A
(kd≥ 0).
- ab, work
-
REAL for ssbev
DOUBLE PRECISION for dsbev.
Arrays:
ab(lda,*) is an array containing either upper or lower triangular part of the symmetric matrix A (as specified by uplo) in band storage format.
The second dimension of ab must be at least max(1, n).
work (*) is a workspace array.
The dimension of work must be at least max(1, 3n-2).
- ldab
-
INTEGER. The leading dimension of ab; must be at least kd +1.
- ldz
-
INTEGER. The leading dimension of the output array z.
Constraints:
if jobz = 'N', then ldz≥ 1;
if jobz = 'V', then ldz≥ max(1, n) .
Output Parameters
- w, z
-
REAL for ssbev
DOUBLE PRECISION for dsbev
Arrays:
w(*), size at least max(1, n).
If info = 0, contains the eigenvalues of the matrix A in ascending order.
z(ldz,*).
The second dimension of z must be at least max(1, 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.
- ab
-
On exit, this array is overwritten by the values generated during the reduction to tridiagonal form (see the description of ?sbtrd).
- info
-
INTEGER.
If info = 0, the execution is successful.
If info = -i, the i-th parameter had an illegal value.
If info = i, then the algorithm failed to converge; i indicates the number of elements of an intermediate tridiagonal form which did not converge to zero.
LAPACK 95 Interface Notes
Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or restorable arguments, see LAPACK 95 Interface Conventions.
Specific details for the routine sbev interface are the following:
- ab
-
Holds the array A of size (kd+1,n).
- w
-
Holds the vector with the number of elements n.
- z
-
Holds the matrix Z of size (n, n).
- uplo
-
Must be 'U' or 'L'. The default value is 'U'.
- jobz
-
Restored based on the presence of the argument z as follows:
jobz = 'V', if z is present,
jobz = 'N', if z is omitted.