Computes all eigenvalues and, optionally, eigenvectors of a real generalized symmetric definite eigenproblem with banded matrices. If eigenvectors are desired, it uses a divide and conquer method.
FORTRAN 77:
call ssbgvd(jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, w, z, ldz, work, lwork, iwork, liwork, info)
call dsbgvd(jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, w, z, ldz, work, lwork, iwork, liwork, info)
Fortran 95:
call sbgvd(ab, bb, w [,uplo] [,z] [,info])
C:
lapack_int LAPACKE_<?>sbgvd( int matrix_order, char jobz, char uplo, lapack_int n, lapack_int ka, lapack_int kb, <datatype>* ab, lapack_int ldab, <datatype>* bb, lapack_int ldbb, <datatype>* w, <datatype>* z, lapack_int ldz );
The FORTRAN 77 interfaces are specified in the mkl_lapack.fi and mkl_lapack.h include files, the Fortran 95 interfaces are specified in the lapack.f90 include file, and the C interfaces are specified in the mkl_lapacke.h include file.
The routine computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x = λ*B*x. Here A and B are assumed to be symmetric and banded, and B is also positive definite.
If eigenvectors are desired, it uses a divide and conquer algorithm.
The data types are given for the Fortran interface. A <datatype> placeholder, if present, is used for the C interface data types in the C interface section above. See C Interface Conventions for the C interface principal conventions and type definitions.
CHARACTER*1. Must be 'N' or 'V'.
If jobz = 'N', then compute eigenvalues only.
If jobz = 'V', then compute eigenvalues and eigenvectors.
CHARACTER*1. Must be 'U' or 'L'.
If uplo = 'U', arrays ab and bb store the upper triangles of A and B;
If uplo = 'L', arrays ab and bb store the lower triangles of A and B.
INTEGER. The order of the matrices A and B (n ≥ 0).
INTEGER. The number of super- or sub-diagonals in A
(ka ≥ 0).
INTEGER. The number of super- or sub-diagonals in B (kb ≥ 0).
REAL for ssbgvd
DOUBLE PRECISION for dsbgvd
Arrays:
ab (ldab,*) 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 the array ab must be at least max(1, n).
bb(ldbb,*) is an array containing either upper or lower triangular part of the symmetric matrix B (as specified by uplo) in band storage format.
The second dimension of the array bb must be at least max(1, n).
work is a workspace array, its dimension max(1, lwork).
INTEGER. The leading dimension of the array ab; must be at least ka+1.
INTEGER. The leading dimension of the array bb; must be at least kb+1.
INTEGER. The leading dimension of the output array z; ldz ≥ 1. If jobz = 'V', ldz ≥ max(1, n).
INTEGER.
The dimension of the array work.
Constraints:
If n ≤ 1, lwork ≥ 1;
If jobz = 'N' and n>1, lwork ≥ 3n;
If jobz = 'V' and n>1, lwork ≥ 2n2+5n+1.
If lwork = -1, then a workspace query is assumed; the routine only calculates the optimal size 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. See Application Notes for details.
INTEGER.
Workspace array, its dimension max(1, liwork).
INTEGER.
The dimension of the array iwork.
Constraints:
If n ≤ 1, liwork ≥ 1;
If jobz = 'N' and n>1, liwork ≥ 1;
If jobz = 'V' and n>1, liwork ≥ 5n+3.
If liwork = -1, then a workspace query is assumed; the routine only calculates the optimal size 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. See Application Notes for details.
On exit, the contents of ab are overwritten.
On exit, contains the factor S from the split Cholesky factorization B = ST*S, as returned by spbstf/dpbstf.
REAL for ssbgvd
DOUBLE PRECISION for dsbgvd
Arrays:
w(*), DIMENSION at least max(1, n).
If info = 0, contains the eigenvalues 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 matrix Z of eigenvectors, with the i-th column of z holding the eigenvector associated with w(i). The eigenvectors are normalized so that ZT*B*Z = I.
If jobz = 'N', then z is not referenced.
On exit, if info = 0, then work(1) returns the required minimal size of lwork.
On exit, if info = 0, then iwork(1) returns the required minimal size of liwork.
INTEGER.
If info = 0, the execution is successful.
If info = -i, the i-th argument had an illegal value.
If info > 0, and
if i ≤ n, the algorithm failed to converge, and i off-diagonal elements of an intermediate tridiagonal did not converge to zero;
if info = n + i, for 1 ≤ i ≤ n, then spbstf/dpbstf returned info = i and B is not positive-definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.
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 Fortran 95 Interface Conventions.
Specific details for the routine sbgvd interface are the following:
Holds the array A of size (ka+1,n).
Holds the array B of size (kb+1,n).
Holds the vector with the number of elements n.
Holds the matrix Z of size (n, n).
Must be 'U' or 'L'. The default value is 'U'.
Restored based on the presence of the argument z as follows:
jobz = 'V', if z is present,
jobz = 'N', if z is omitted.
If it is not clear how much workspace to supply, use a generous value of lwork (or liwork) for the first run or set lwork = -1 (liwork = -1).
If lwork (or liwork) has any of admissible sizes, which is no less than the minimal value described, the routine completes the task, though probably not so fast as with a recommended workspace, and provides the recommended workspace in the first element of the corresponding array (work, iwork) on exit. Use this value (work(1), iwork(1)) for subsequent runs.
If lwork = -1 (liwork = -1), the routine returns immediately and provides the recommended workspace in the first element of the corresponding array (work, iwork). This operation is called a workspace query.
Note that if work (liwork) is less than the minimal required value and is not equal to -1, the routine returns immediately with an error exit and does not provide any information on the recommended workspace.
Copyright © 1994 - 2011, Intel Corporation. All rights reserved.