hbev#

Functions

void chbev(
    const char*          jobz,
    const char*          uplo,
    const INT            n,
    const INT            kd,
          c64*  restrict AB,
    const INT            ldab,
          f32*  restrict W,
          c64*  restrict Z,
    const INT            ldz,
          c64*  restrict work,
          f32*  restrict rwork,
          INT*           info
);
void chbev(const char *jobz, const char *uplo, const INT n, const INT kd, c64 *restrict AB, const INT ldab, f32 *restrict W, c64 *restrict Z, const INT ldz, c64 *restrict work, f32 *restrict rwork, INT *info)#

CHBEV computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A.

Parameters

in
jobz

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

in
uplo

= ‘U’: Upper triangle of A is stored; = ‘L’: Lower triangle of A is stored.

in
n

The order of the matrix A. n >= 0.

in
kd

The number of superdiagonals of the matrix A if uplo = ‘U’, or the number of subdiagonals if uplo = ‘L’. kd >= 0.

inout
AB

Complex array, dimension (ldab, n). On entry, the upper or lower triangle of the Hermitian band matrix A, stored in the first kd+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(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if uplo = ‘L’, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). On exit, AB is overwritten by values generated during the reduction to tridiagonal form. If uplo = ‘U’, the first superdiagonal and the diagonal of the tridiagonal matrix T are returned in rows kd and kd+1 of AB, and if uplo = ‘L’, the diagonal and first subdiagonal of T are returned in the first two rows of AB.

in
ldab

The leading dimension of the array AB. ldab >= kd+1.

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 orthonormal eigenvectors of the matrix A, with the i-th column of Z holding the eigenvector associated with W(i). If jobz = ‘N’, then Z is not referenced.

in
ldz

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

out
work

Complex array, dimension (n).

out
rwork

Single precision array, dimension (max(1, 3*n-2)).

out
info

= 0: successful exit. < 0: if info = -i, the i-th argument had an illegal value. > 0: if info = i, the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero.

Functions

void zhbev(
    const char*          jobz,
    const char*          uplo,
    const INT            n,
    const INT            kd,
          c128* restrict AB,
    const INT            ldab,
          f64*  restrict W,
          c128* restrict Z,
    const INT            ldz,
          c128* restrict work,
          f64*  restrict rwork,
          INT*           info
);
void zhbev(const char *jobz, const char *uplo, const INT n, const INT kd, c128 *restrict AB, const INT ldab, f64 *restrict W, c128 *restrict Z, const INT ldz, c128 *restrict work, f64 *restrict rwork, INT *info)#

ZHBEV computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A.

Parameters

in
jobz

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

in
uplo

= ‘U’: Upper triangle of A is stored; = ‘L’: Lower triangle of A is stored.

in
n

The order of the matrix A. n >= 0.

in
kd

The number of superdiagonals of the matrix A if uplo = ‘U’, or the number of subdiagonals if uplo = ‘L’. kd >= 0.

inout
AB

Complex array, dimension (ldab, n). On entry, the upper or lower triangle of the Hermitian band matrix A, stored in the first kd+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(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if uplo = ‘L’, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). On exit, AB is overwritten by values generated during the reduction to tridiagonal form. If uplo = ‘U’, the first superdiagonal and the diagonal of the tridiagonal matrix T are returned in rows kd and kd+1 of AB, and if uplo = ‘L’, the diagonal and first subdiagonal of T are returned in the first two rows of AB.

in
ldab

The leading dimension of the array AB. ldab >= kd+1.

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 orthonormal eigenvectors of the matrix A, with the i-th column of Z holding the eigenvector associated with W(i). If jobz = ‘N’, then Z is not referenced.

in
ldz

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

out
work

Complex array, dimension (n).

out
rwork

Double precision array, dimension (max(1, 3*n-2)).

out
info

= 0: successful exit. < 0: if info = -i, the i-th argument had an illegal value. > 0: if info = i, the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero.

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