hpgvd

chpgvd

Functions

void chpgvd(
    const INT            itype,
    const char*          jobz,
    const char*          uplo,
    const INT            n,
          c64*  restrict AP,
          c64*  restrict BP,
          f32*  restrict W,
          c64*  restrict Z,
    const INT            ldz,
          c64*  restrict work,
    const INT            lwork,
          f32*  restrict rwork,
    const INT            lrwork,
          INT*  restrict iwork,
    const INT            liwork,
          INT*           info
);

void chpgvd(const INT itype, const char *jobz, const char *uplo, const INT n, c64 *restrict AP, c64 *restrict BP, f32 *restrict W, c64 *restrict Z, const INT ldz, c64 *restrict work, const INT lwork, f32 *restrict rwork, const INT lrwork, INT *restrict iwork, const INT liwork, INT *info)

CHPGVD computes all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*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.

Parameters

in

itype

Specifies the problem type to be solved: = 1: A*x = (lambda)*B*x = 2: A*B*x = (lambda)*x = 3: B*A*x = (lambda)*x

in

jobz

= ‘N’: Compute eigenvalues only; = ‘V’: Compute eigenvalues and eigenvectors.

in

uplo

= ‘U’: Upper triangles of A and B are stored; = ‘L’: Lower triangles of A and B are stored.

in

n

The order of the matrices A and B. n >= 0.

inout

AP

Complex array, dimension (n*(n+1)/2). On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. On exit, the contents of AP are destroyed.

inout

BP

Complex array, dimension (n*(n+1)/2). On entry, the upper or lower triangle of the Hermitian positive definite matrix B, packed columnwise. On exit, the triangular factor U or L from the Cholesky factorization B = U**H*U or B = L*L**H.

out

W

Single precision array, dimension (n). If info = 0, the eigenvalues in ascending order.

out

Z

Complex array, dimension (ldz, n). If jobz = ‘V’, then if info = 0, Z contains the matrix Z of eigenvectors.

in

ldz

The leading dimension of the array Z. ldz >= 1, and if jobz = ‘V’, ldz >= max(1,n).

out

work

Complex array, dimension (max(1,lwork)). On exit, if info = 0, work[0] returns the required lwork.

in

lwork

The dimension of the array work. If n <= 1, lwork >= 1. If jobz = ‘N’ and n > 1, lwork >= n. If jobz = ‘V’ and n > 1, lwork >= 2*n. If lwork = -1, then a workspace query is assumed.

out

rwork

Single precision array, dimension (max(1,lrwork)). On exit, if info = 0, rwork[0] returns the required lrwork.

in

lrwork

The dimension of array rwork. If n <= 1, lrwork >= 1. If jobz = ‘N’ and n > 1, lrwork >= n. If jobz = ‘V’ and n > 1, lrwork >= 1 + 5*n + 2*n**2. If lrwork = -1, then a workspace query is assumed.

out

iwork

Integer array, dimension (max(1,liwork)). On exit, if info = 0, iwork[0] returns the required liwork.

in

liwork

The dimension of array iwork. If jobz = ‘N’ or n <= 1, liwork >= 1. If jobz = ‘V’ and n > 1, liwork >= 3 + 5*n. If liwork = -1, then a workspace query is assumed.

out

info

= 0: successful exit < 0: if info = -i, the i-th argument had an illegal value > 0: CPPTRF or CHPEVD returned an error code: <= n: if info = i, CHPEVD 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 the leading principal minor of order i of B is not positive.

zhpgvd

Functions

void zhpgvd(
    const INT            itype,
    const char*          jobz,
    const char*          uplo,
    const INT            n,
          c128* restrict AP,
          c128* restrict BP,
          f64*  restrict W,
          c128* restrict Z,
    const INT            ldz,
          c128* restrict work,
    const INT            lwork,
          f64*  restrict rwork,
    const INT            lrwork,
          INT*  restrict iwork,
    const INT            liwork,
          INT*           info
);

void zhpgvd(const INT itype, const char *jobz, const char *uplo, const INT n, c128 *restrict AP, c128 *restrict BP, f64 *restrict W, c128 *restrict Z, const INT ldz, c128 *restrict work, const INT lwork, f64 *restrict rwork, const INT lrwork, INT *restrict iwork, const INT liwork, INT *info)

ZHPGVD computes all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*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.

Parameters

in

itype

Specifies the problem type to be solved: = 1: A*x = (lambda)*B*x = 2: A*B*x = (lambda)*x = 3: B*A*x = (lambda)*x

in

jobz

= ‘N’: Compute eigenvalues only; = ‘V’: Compute eigenvalues and eigenvectors.

in

uplo

= ‘U’: Upper triangles of A and B are stored; = ‘L’: Lower triangles of A and B are stored.

in

n

The order of the matrices A and B. n >= 0.

inout

AP

Complex array, dimension (n*(n+1)/2). On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. On exit, the contents of AP are destroyed.

inout

BP

Complex array, dimension (n*(n+1)/2). On entry, the upper or lower triangle of the Hermitian positive definite matrix B, packed columnwise. On exit, the triangular factor U or L from the Cholesky factorization B = U**H*U or B = L*L**H.

out

W

Double precision array, dimension (n). If info = 0, the eigenvalues in ascending order.

out

Z

Complex array, dimension (ldz, n). If jobz = ‘V’, then if info = 0, Z contains the matrix Z of eigenvectors.

in

ldz

The leading dimension of the array Z. ldz >= 1, and if jobz = ‘V’, ldz >= max(1,n).

out

work

Complex array, dimension (max(1,lwork)). On exit, if info = 0, work[0] returns the required lwork.

in

lwork

The dimension of the array work. If n <= 1, lwork >= 1. If jobz = ‘N’ and n > 1, lwork >= n. If jobz = ‘V’ and n > 1, lwork >= 2*n. If lwork = -1, then a workspace query is assumed.

out

rwork

Double precision array, dimension (max(1,lrwork)). On exit, if info = 0, rwork[0] returns the required lrwork.

in

lrwork

The dimension of array rwork. If n <= 1, lrwork >= 1. If jobz = ‘N’ and n > 1, lrwork >= n. If jobz = ‘V’ and n > 1, lrwork >= 1 + 5*n + 2*n**2. If lrwork = -1, then a workspace query is assumed.

out

iwork

Integer array, dimension (max(1,liwork)). On exit, if info = 0, iwork[0] returns the required liwork.

in

liwork

The dimension of array iwork. If jobz = ‘N’ or n <= 1, liwork >= 1. If jobz = ‘V’ and n > 1, liwork >= 3 + 5*n. If liwork = -1, then a workspace query is assumed.

out

info

= 0: successful exit < 0: if info = -i, the i-th argument had an illegal value > 0: ZPPTRF or ZHPEVD returned an error code: <= n: if info = i, ZHPEVD 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 the leading principal minor of order i of B is not positive.