hegvx#

Functions

void chegvx(
    const INT            itype,
    const char*          jobz,
    const char*          range,
    const char*          uplo,
    const INT            n,
          c64*  restrict A,
    const INT            lda,
          c64*  restrict B,
    const INT            ldb,
    const f32            vl,
    const f32            vu,
    const INT            il,
    const INT            iu,
    const f32            abstol,
          INT*           m,
          f32*  restrict W,
          c64*  restrict Z,
    const INT            ldz,
          c64*  restrict work,
    const INT            lwork,
          f32*  restrict rwork,
          INT*  restrict iwork,
          INT*  restrict ifail,
          INT*           info
);
void chegvx(const INT itype, const char *jobz, const char *range, const char *uplo, const INT n, c64 *restrict A, const INT lda, c64 *restrict B, const INT ldb, const f32 vl, const f32 vu, const INT il, const INT iu, const f32 abstol, INT *m, f32 *restrict W, c64 *restrict Z, const INT ldz, c64 *restrict work, const INT lwork, f32 *restrict rwork, INT *restrict iwork, INT *restrict ifail, INT *info)#

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

Here A and B are assumed to be Hermitian and B is also positive definite. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.

Parameters

in
itype

= 1: A*x = lambda*B*x; = 2: A*B*x = lambda*x; = 3: B*A*x = lambda*x

in
jobz

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

in
range

= ‘A’: all; = ‘V’: in (vl,vu]; = ‘I’: il-th through iu-th

in
uplo

= ‘U’: upper triangles stored; = ‘L’: lower triangles stored

in
n

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

inout
A

On entry, Hermitian matrix A. On exit, destroyed.

in
lda

Leading dimension of A. lda >= max(1, n).

inout
B

On entry, Hermitian positive definite B. On exit, Cholesky factor.

in
ldb

Leading dimension of B. ldb >= max(1, n).

in
vl

Lower bound of interval (if range=’V’).

in
vu

Upper bound of interval (if range=’V’).

in
il

Index of smallest eigenvalue (if range=’I’, 0-based).

in
iu

Index of largest eigenvalue (if range=’I’, 0-based).

in
abstol

Absolute error tolerance for eigenvalues.

out
m

Total number of eigenvalues found.

out
W

Selected eigenvalues in ascending order.

out
Z

Eigenvectors if jobz=’V’.

in
ldz

Leading dimension of Z. ldz >= 1, and if jobz=’V’, ldz >= n.

out
work

Complex workspace array, dimension (max(1, lwork)).

in
lwork

Length of work. lwork >= max(1, 2*n). If -1, workspace query.

out
rwork

Real workspace array, dimension (7*n).

out
iwork

Integer workspace array, dimension (5*n).

out
ifail

Indices of eigenvectors that failed to converge.

out
info

  • = 0: success; < 0: illegal argument; > 0: CPOTRF/CHEEVX error.

Functions

void zhegvx(
    const INT            itype,
    const char*          jobz,
    const char*          range,
    const char*          uplo,
    const INT            n,
          c128* restrict A,
    const INT            lda,
          c128* restrict B,
    const INT            ldb,
    const f64            vl,
    const f64            vu,
    const INT            il,
    const INT            iu,
    const f64            abstol,
          INT*           m,
          f64*  restrict W,
          c128* restrict Z,
    const INT            ldz,
          c128* restrict work,
    const INT            lwork,
          f64*  restrict rwork,
          INT*  restrict iwork,
          INT*  restrict ifail,
          INT*           info
);
void zhegvx(const INT itype, const char *jobz, const char *range, const char *uplo, const INT n, c128 *restrict A, const INT lda, c128 *restrict B, const INT ldb, const f64 vl, const f64 vu, const INT il, const INT iu, const f64 abstol, INT *m, f64 *restrict W, c128 *restrict Z, const INT ldz, c128 *restrict work, const INT lwork, f64 *restrict rwork, INT *restrict iwork, INT *restrict ifail, INT *info)#

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

Here A and B are assumed to be Hermitian and B is also positive definite. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.

Parameters

in
itype

= 1: A*x = lambda*B*x; = 2: A*B*x = lambda*x; = 3: B*A*x = lambda*x

in
jobz

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

in
range

= ‘A’: all; = ‘V’: in (vl,vu]; = ‘I’: il-th through iu-th

in
uplo

= ‘U’: upper triangles stored; = ‘L’: lower triangles stored

in
n

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

inout
A

On entry, Hermitian matrix A. On exit, destroyed.

in
lda

Leading dimension of A. lda >= max(1, n).

inout
B

On entry, Hermitian positive definite B. On exit, Cholesky factor.

in
ldb

Leading dimension of B. ldb >= max(1, n).

in
vl

Lower bound of interval (if range=’V’).

in
vu

Upper bound of interval (if range=’V’).

in
il

Index of smallest eigenvalue (if range=’I’, 0-based).

in
iu

Index of largest eigenvalue (if range=’I’, 0-based).

in
abstol

Absolute error tolerance for eigenvalues.

out
m

Total number of eigenvalues found.

out
W

Selected eigenvalues in ascending order.

out
Z

Eigenvectors if jobz=’V’.

in
ldz

Leading dimension of Z. ldz >= 1, and if jobz=’V’, ldz >= n.

out
work

Complex workspace array, dimension (max(1, lwork)).

in
lwork

Length of work. lwork >= max(1, 2*n). If -1, workspace query.

out
rwork

Real workspace array, dimension (7*n).

out
iwork

Integer workspace array, dimension (5*n).

out
ifail

Indices of eigenvectors that failed to converge.

out
info

  • = 0: success; < 0: illegal argument; > 0: ZPOTRF/ZHEEVX error.

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