Computes all eigenvalues and, optionally, eigenvectors of a real generalized symmetric definite eigenproblem using a divide and conquer method.
lapack_int LAPACKE_ssygvd (int matrix_layout, lapack_int itype, char jobz, char uplo, lapack_int n, float* a, lapack_int lda, float* b, lapack_int ldb, float* w);
lapack_int LAPACKE_dsygvd (int matrix_layout, lapack_int itype, char jobz, char uplo, lapack_int n, double* a, lapack_int lda, double* b, lapack_int ldb, double* w);
The routine computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form
A*x = λ*B*x, A*B*x = λ*x, or B*A*x = λ*x .
Here A and B are assumed to be symmetric and B is also positive definite.
It uses a divide and conquer algorithm.
Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).
Must be 1 or 2 or 3. Specifies the problem type to be solved:
if itype = 1, the problem type is A*x = lambda*B*x;
if itype = 2, the problem type is A*B*x = lambda*x;
if itype = 3, the problem type is B*A*x = lambda*x.
Must be 'N' or 'V'.
If jobz = 'N', then compute eigenvalues only.
If jobz = 'V', then compute eigenvalues and eigenvectors.
Must be 'U' or 'L'.
If uplo = 'U', arrays a and b store the upper triangles of A and B;
If uplo = 'L', arrays a and b store the lower triangles of A and B.
The order of the matrices A and B (n≥ 0).
- a, b
a (size at least lda*n) contains the upper or lower triangle of the symmetric matrix A, as specified by uplo.
b (size at least ldb*n) contains the upper or lower triangle of the symmetric positive definite matrix B, as specified by uplo.
The leading dimension of a; at least max(1, n).
The leading dimension of b; at least max(1, n).
On exit, if jobz = 'V', then if info = 0, a contains the matrix Z of eigenvectors. The eigenvectors are normalized as follows:
if itype = 1 or 2, ZT*B*Z = I;
if itype = 3, ZT*inv(B)*Z = I;
If jobz = 'N', then on exit the upper triangle (if uplo = 'U') or the lower triangle (if uplo = 'L') of A, including the diagonal, is destroyed.
On exit, if info≤n, the part of b containing the matrix is overwritten by the triangular factor U or L from the Cholesky factorization B = UT*U or B = L*LT.
Array, size at least max(1, n).
If info = 0, contains the eigenvalues in ascending order.
This function returns a value info.
If info=0, the execution is successful.
If info = -i, the i-th parameter had an illegal value.
If info > 0, an error code is returned as specified below.
If info = i and jobz = 'N', then the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero.
If jobz = 'V', then the algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns info/(n+1) through mod(info,n+1).
For info > n:
If info = n + i, for 1 ≤i≤n, then the leading minor of order i of B is not positive-definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.