sbevx#

Functions

void ssbevx(
    const char*          jobz,
    const char*          range,
    const char*          uplo,
    const INT            n,
    const INT            kd,
          f32*  restrict AB,
    const INT            ldab,
          f32*  restrict Q,
    const INT            ldq,
    const f32            vl,
    const f32            vu,
    const INT            il,
    const INT            iu,
    const f32            abstol,
          INT*           m,
          f32*  restrict W,
          f32*  restrict Z,
    const INT            ldz,
          f32*  restrict work,
          INT*  restrict iwork,
          INT*  restrict ifail,
          INT*           info
);
void ssbevx(const char *jobz, const char *range, const char *uplo, const INT n, const INT kd, f32 *restrict AB, const INT ldab, f32 *restrict Q, const INT ldq, const f32 vl, const f32 vu, const INT il, const INT iu, const f32 abstol, INT *m, f32 *restrict W, f32 *restrict Z, const INT ldz, f32 *restrict work, INT *restrict iwork, INT *restrict ifail, INT *info)#

SSBEVX computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A.

Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.

Parameters

in
jobz

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

in
range

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

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 super-diagonals or sub-diagonals. kd >= 0.

inout
AB

The banded matrix A. Array of dimension (ldab, n).

in
ldab

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

out
Q

If jobz=’V’, the orthogonal matrix for reduction.

in
ldq

The leading dimension of Q. ldq >= max(1,n) if jobz=’V’.

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’).

in
iu

Index of largest eigenvalue (if range=’I’).

in
abstol

Absolute error tolerance for eigenvalues.

out
m

The total number of eigenvalues found.

out
W

The selected eigenvalues in ascending order.

out
Z

If jobz=’V’, the eigenvectors. Array of dimension (ldz, max(1,m)).

in
ldz

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

out
work

Workspace array of dimension (7*n).

out
iwork

Integer workspace array of dimension (5*n).

out
ifail

If jobz=’V’, indices of eigenvectors that failed to converge.

out
info

  • = 0: successful exit

  • < 0: if info = -i, the i-th argument had an illegal value

  • > 0: if info = i, then i eigenvectors failed to converge

Functions

void dsbevx(
    const char*          jobz,
    const char*          range,
    const char*          uplo,
    const INT            n,
    const INT            kd,
          f64*  restrict AB,
    const INT            ldab,
          f64*  restrict Q,
    const INT            ldq,
    const f64            vl,
    const f64            vu,
    const INT            il,
    const INT            iu,
    const f64            abstol,
          INT*           m,
          f64*  restrict W,
          f64*  restrict Z,
    const INT            ldz,
          f64*  restrict work,
          INT*  restrict iwork,
          INT*  restrict ifail,
          INT*           info
);
void dsbevx(const char *jobz, const char *range, const char *uplo, const INT n, const INT kd, f64 *restrict AB, const INT ldab, f64 *restrict Q, const INT ldq, const f64 vl, const f64 vu, const INT il, const INT iu, const f64 abstol, INT *m, f64 *restrict W, f64 *restrict Z, const INT ldz, f64 *restrict work, INT *restrict iwork, INT *restrict ifail, INT *info)#

DSBEVX computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A.

Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.

Parameters

in
jobz

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

in
range

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

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 super-diagonals or sub-diagonals. kd >= 0.

inout
AB

The banded matrix A. Array of dimension (ldab, n).

in
ldab

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

out
Q

If jobz=’V’, the orthogonal matrix for reduction.

in
ldq

The leading dimension of Q. ldq >= max(1,n) if jobz=’V’.

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’).

in
iu

Index of largest eigenvalue (if range=’I’).

in
abstol

Absolute error tolerance for eigenvalues.

out
m

The total number of eigenvalues found.

out
W

The selected eigenvalues in ascending order.

out
Z

If jobz=’V’, the eigenvectors. Array of dimension (ldz, max(1,m)).

in
ldz

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

out
work

Workspace array of dimension (7*n).

out
iwork

Integer workspace array of dimension (5*n).

out
ifail

If jobz=’V’, indices of eigenvectors that failed to converge.

out
info

  • = 0: successful exit

  • < 0: if info = -i, the i-th argument had an illegal value

  • > 0: if info = i, then i eigenvectors failed to converge

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