LAPACK
3.6.1
LAPACK: Linear Algebra PACKage
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subroutine dsbgv | ( | character | JOBZ, |
character | UPLO, | ||
integer | N, | ||
integer | KA, | ||
integer | KB, | ||
double precision, dimension( ldab, * ) | AB, | ||
integer | LDAB, | ||
double precision, dimension( ldbb, * ) | BB, | ||
integer | LDBB, | ||
double precision, dimension( * ) | W, | ||
double precision, dimension( ldz, * ) | Z, | ||
integer | LDZ, | ||
double precision, dimension( * ) | WORK, | ||
integer | INFO | ||
) |
DSBGV
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DSBGV 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.
[in] | JOBZ | JOBZ is CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. |
[in] | UPLO | UPLO is CHARACTER*1 = 'U': Upper triangles of A and B are stored; = 'L': Lower triangles of A and B are stored. |
[in] | N | N is INTEGER The order of the matrices A and B. N >= 0. |
[in] | KA | KA is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KA >= 0. |
[in] | KB | KB is INTEGER The number of superdiagonals of the matrix B if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KB >= 0. |
[in,out] | AB | AB is DOUBLE PRECISION 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 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. |
[in] | LDAB | LDAB is INTEGER The leading dimension of the array AB. LDAB >= KA+1. |
[in,out] | BB | BB is DOUBLE PRECISION 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 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 DPBSTF. |
[in] | LDBB | LDBB is INTEGER The leading dimension of the array BB. LDBB >= KB+1. |
[out] | W | W is DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order. |
[out] | Z | Z is DOUBLE PRECISION 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. |
[in] | LDZ | LDZ is INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= N. |
[out] | WORK | WORK is DOUBLE PRECISION array, dimension (3*N) |
[out] | INFO | 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 DPBSTF returned INFO = i: B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed. |
Definition at line 179 of file dsbgv.f.