Computes all eigenvalues and, optionally, eigenvectors of a complex generalized Hermitian positive-definite eigenproblem with matrices in packed storage using a divide and conquer method.
lapack_int LAPACKE_chpgvd( int matrix_layout, lapack_int itype, char jobz, char uplo, lapack_int n, lapack_complex_float* ap, lapack_complex_float* bp, float* w, lapack_complex_float* z, lapack_int ldz );
lapack_int LAPACKE_zhpgvd( int matrix_layout, lapack_int itype, char jobz, char uplo, lapack_int n, lapack_complex_double* ap, lapack_complex_double* bp, double* w, lapack_complex_double* z, lapack_int ldz );
The routine computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian positive-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 Hermitian, stored in packed format, and B is also positive definite.
If eigenvectors are desired, 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 ap and bp store the upper triangles of A and B;
If uplo = 'L', arrays ap and bp store the lower triangles of A and B.
The order of the matrices A and B (n≥ 0).
- ap, bp
ap contains the packed upper or lower triangle of the Hermitian matrix A, as specified by uplo.
The dimension of ap must be at least max(1, n*(n+1)/2).
bp contains the packed upper or lower triangle of the Hermitian matrix B, as specified by uplo.
The dimension of bp must be at least max(1, n*(n+1)/2).
The leading dimension of the output array z; ldz≥ 1. If jobz = 'V', ldz≥ max(1, n).
On exit, the contents of ap are overwritten.
On exit, contains the triangular factor U or L from the Cholesky factorization B = UH*U or B = L*LH, in the same storage format as B.
Array, size at least max(1, n).
If info = 0, contains the eigenvalues in ascending order.
Array z (size at least max(1, ldz*n)).
If jobz = 'V', then if info = 0, z contains the matrix Z of eigenvectors. The eigenvectors are normalized as follows:
if itype = 1 or 2, ZH*B*Z = I;
if itype = 3, ZH*inv(B)*Z = I;
If jobz = 'N', then z is not referenced.
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, cpptrf/zpptrf and chpevd/zhpevd returned an error code:
If info = i≤n, chpevd/zhpevd 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 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.