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template<typename T>
void sbgv(char *jobz, char *uplo, integer *n, integer *ka, integer *kb, T *ab, integer *ldab, T *bb, integer *ldbb, T *w, T *z, integer *ldz, float *work, integer *info)# SBGV computes all the eigenvalues, and optionally, the eigenvectors.
Purpose:
SBGV computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric and banded, and B is also positive definite.
- Parameters:
JOBZ – [in]
JOBZ is CHARACTER*1
= ‘N’: Compute eigenvalues only;
= ‘V’: Compute eigenvalues and eigenvectors.UPLO – [in]
UPLO is CHARACTER*1
= ‘U’: Upper triangles of A and B are stored;
= ‘L’: Lower triangles of A and B are stored.N – [in]
N is INTEGER
The order of the matrices A and B. N >= 0.
KA – [in]
KA is INTEGER
The number of superdiagonals of the matrix A if UPLO = ‘U’, or the number of subdiagonals if UPLO = ‘L’. KA >= 0.
KB – [in]
KB is INTEGER
The number of superdiagonals of the matrix B if UPLO = ‘U’, or the number of subdiagonals if UPLO = ‘L’. KB >= 0.
AB – [inout]
AB is REAL array, dimension (LDAB, N)
On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first ka+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(ka+1+i-j,j) = A(i,j) for fla_max(1,j-ka)<=i<=j;
if UPLO = ‘L’, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).
On exit, the contents of AB are destroyed.LDAB – [in]
LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KA+1.
BB – [inout]
BB is REAL array, dimension (LDBB, N)
On entry, the upper or lower triangle of the symmetric band matrix B, stored in the first kb+1 rows of the array. The j-th column of B is stored in the j-th column of the array BB as follows:
if UPLO = ‘U’, BB(kb+1+i-j,j) = B(i,j) for fla_max(1,j-kb)<=i<=j;
if UPLO = ‘L’, BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb).
On exit, the factor S from the split Cholesky factorization B = S**T*S, as returned by SPBSTF.LDBB – [in]
LDBB is INTEGER
The leading dimension of the array BB. LDBB >= KB+1.
W – [out]
W is REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
Z – [out]
Z is REAL array, dimension (LDZ, 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 Z**T*B*Z = I.
If JOBZ = ‘N’, then Z is not referenced.LDZ – [in]
LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 1, and if JOBZ = ‘V’, LDZ >= N.
WORK – [out] WORK is REAL array, dimension (3*N)
INFO – [out]
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, and i is:
<= N: the algorithm failed to converge: i off-diagonal elements of an intermediate tridiagonal form did not converge to zero;
> N: if INFO = N + i, for 1 <= i <= N, then SPBSTF returned INFO = i: B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.