sbgvx#

Functions

void ssbgvx(
    const char*          jobz,
    const char*          range,
    const char*          uplo,
    const INT            n,
    const INT            ka,
    const INT            kb,
          f32*  restrict AB,
    const INT            ldab,
          f32*  restrict BB,
    const INT            ldbb,
          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 ssbgvx(const char *jobz, const char *range, const char *uplo, const INT n, const INT ka, const INT kb, f32 *restrict AB, const INT ldab, f32 *restrict BB, const INT ldbb, 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)#

SSBGVX computes selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x = lambda*B*x.

Here A and B are assumed to be symmetric and banded, and B is also positive definite. Eigenvalues and eigenvectors can be selected by specifying either all eigenvalues, 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 will be found = ‘V’: all eigenvalues in (vl,vu] will be found = ‘I’: the il-th through iu-th eigenvalues will be found

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.

in
ka

The number of superdiagonals (if uplo=’U’) or subdiagonals (if uplo=’L’) of A. ka >= 0.

in
kb

The number of superdiagonals (if uplo=’U’) or subdiagonals (if uplo=’L’) of B. kb >= 0.

inout
AB

The banded matrix A. Array of dimension (ldab, n). On exit, contents are destroyed.

in
ldab

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

inout
BB

The banded matrix B. Array of dimension (ldbb, n). On exit, the split Cholesky factor S from spbstf.

in
ldbb

The leading dimension of BB. ldbb >= kb+1.

out
Q

If jobz=’V’, the n-by-n transformation matrix. Array of dimension (ldq, n).

in
ldq

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

in
vl

If range=’V’, the lower bound of the interval.

in
vu

If range=’V’, the upper bound of the interval. vl < vu.

in
il

If range=’I’, the index of the smallest eigenvalue.

in
iu

If range=’I’, the index of the largest eigenvalue.

in
abstol

The absolute error tolerance for eigenvalues.

out
m

The total number of eigenvalues found.

out
W

The eigenvalues in ascending order. Array of dimension (n).

out
Z

If jobz=’V’, the eigenvectors. Array of dimension (ldz, n).

in
ldz

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

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. Array of dimension (n).

out
info

  • = 0: successful exit

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

  • <= n: i eigenvectors failed to converge

  • > n: spbstf returned info = i (B not positive definite)

Functions

void dsbgvx(
    const char*          jobz,
    const char*          range,
    const char*          uplo,
    const INT            n,
    const INT            ka,
    const INT            kb,
          f64*  restrict AB,
    const INT            ldab,
          f64*  restrict BB,
    const INT            ldbb,
          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 dsbgvx(const char *jobz, const char *range, const char *uplo, const INT n, const INT ka, const INT kb, f64 *restrict AB, const INT ldab, f64 *restrict BB, const INT ldbb, 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)#

DSBGVX computes selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x = lambda*B*x.

Here A and B are assumed to be symmetric and banded, and B is also positive definite. Eigenvalues and eigenvectors can be selected by specifying either all eigenvalues, 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 will be found = ‘V’: all eigenvalues in (vl,vu] will be found = ‘I’: the il-th through iu-th eigenvalues will be found

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.

in
ka

The number of superdiagonals (if uplo=’U’) or subdiagonals (if uplo=’L’) of A. ka >= 0.

in
kb

The number of superdiagonals (if uplo=’U’) or subdiagonals (if uplo=’L’) of B. kb >= 0.

inout
AB

The banded matrix A. Array of dimension (ldab, n). On exit, contents are destroyed.

in
ldab

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

inout
BB

The banded matrix B. Array of dimension (ldbb, n). On exit, the split Cholesky factor S from dpbstf.

in
ldbb

The leading dimension of BB. ldbb >= kb+1.

out
Q

If jobz=’V’, the n-by-n transformation matrix. Array of dimension (ldq, n).

in
ldq

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

in
vl

If range=’V’, the lower bound of the interval.

in
vu

If range=’V’, the upper bound of the interval. vl < vu.

in
il

If range=’I’, the index of the smallest eigenvalue.

in
iu

If range=’I’, the index of the largest eigenvalue.

in
abstol

The absolute error tolerance for eigenvalues.

out
m

The total number of eigenvalues found.

out
W

The eigenvalues in ascending order. Array of dimension (n).

out
Z

If jobz=’V’, the eigenvectors. Array of dimension (ldz, n).

in
ldz

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

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. Array of dimension (n).

out
info

  • = 0: successful exit

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

  • <= n: i eigenvectors failed to converge

  • > n: dpbstf returned info = i (B not positive definite)

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