stebz#

Functions

void sstebz(
    const char*          range,
    const char*          order,
    const INT            n,
    const f32            vl,
    const f32            vu,
    const INT            il,
    const INT            iu,
    const f32            abstol,
    const f32*  restrict D,
    const f32*  restrict E,
          INT*           m,
          INT*           nsplit,
          f32*  restrict W,
          INT*  restrict iblock,
          INT*  restrict isplit,
          f32*  restrict work,
          INT*  restrict iwork,
          INT*           info
);
void sstebz(const char *range, const char *order, const INT n, const f32 vl, const f32 vu, const INT il, const INT iu, const f32 abstol, const f32 *restrict D, const f32 *restrict E, INT *m, INT *nsplit, f32 *restrict W, INT *restrict iblock, INT *restrict isplit, f32 *restrict work, INT *restrict iwork, INT *info)#

SSTEBZ computes the eigenvalues of a symmetric tridiagonal matrix T.

The user may ask for all eigenvalues, all eigenvalues in the half-open interval (VL, VU], or the IL-th through IU-th eigenvalues.

To avoid overflow, the matrix must be scaled so that its largest element is no greater than overflow**(1/2) * underflow**(1/4) in absolute value, and for greatest accuracy, it should not be much smaller than that.

See W. Kahan “Accurate Eigenvalues of a Symmetric Tridiagonal

Matrix”, Report CS41, Computer Science Dept., Stanford University, July 21, 1966.

Parameters

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
order

= ‘B’: eigenvalues grouped by split-off block. = ‘E’: eigenvalues ordered from smallest to largest.

in
n

The order of the tridiagonal matrix T. n >= 0.

in
vl

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

in
vu

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

in
il

If range=’I’, the index of the smallest eigenvalue (0-based).

in
iu

If range=’I’, the index of the largest eigenvalue (0-based).

in
abstol

The absolute tolerance for the eigenvalues.

in
D

Double precision array, dimension (n). The diagonal elements.

in
E

Double precision array, dimension (n-1). The off-diagonal elements.

out
m

The actual number of eigenvalues found.

out
nsplit

The number of diagonal blocks in T.

out
W

Double precision array, dimension (n). The eigenvalues.

out
iblock

Integer array, dimension (n). Block number (0-based) for each eigenvalue.

out
isplit

Integer array, dimension (n). The splitting points (0-based endpoints).

out
work

Double precision array, dimension (4*n).

out
iwork

Integer array, dimension (3*n).

out
info

  • = 0: successful exit.

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

  • > 0: some eigenvalues failed to converge or were not computed.

Functions

void dstebz(
    const char*          range,
    const char*          order,
    const INT            n,
    const f64            vl,
    const f64            vu,
    const INT            il,
    const INT            iu,
    const f64            abstol,
    const f64*  restrict D,
    const f64*  restrict E,
          INT*           m,
          INT*           nsplit,
          f64*  restrict W,
          INT*  restrict iblock,
          INT*  restrict isplit,
          f64*  restrict work,
          INT*  restrict iwork,
          INT*           info
);
void dstebz(const char *range, const char *order, const INT n, const f64 vl, const f64 vu, const INT il, const INT iu, const f64 abstol, const f64 *restrict D, const f64 *restrict E, INT *m, INT *nsplit, f64 *restrict W, INT *restrict iblock, INT *restrict isplit, f64 *restrict work, INT *restrict iwork, INT *info)#

DSTEBZ computes the eigenvalues of a symmetric tridiagonal matrix T.

The user may ask for all eigenvalues, all eigenvalues in the half-open interval (VL, VU], or the IL-th through IU-th eigenvalues.

To avoid overflow, the matrix must be scaled so that its largest element is no greater than overflow**(1/2) * underflow**(1/4) in absolute value, and for greatest accuracy, it should not be much smaller than that.

See W. Kahan “Accurate Eigenvalues of a Symmetric Tridiagonal

Matrix”, Report CS41, Computer Science Dept., Stanford University, July 21, 1966.

Parameters

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
order

= ‘B’: eigenvalues grouped by split-off block. = ‘E’: eigenvalues ordered from smallest to largest.

in
n

The order of the tridiagonal matrix T. n >= 0.

in
vl

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

in
vu

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

in
il

If range=’I’, the index of the smallest eigenvalue (0-based).

in
iu

If range=’I’, the index of the largest eigenvalue (0-based).

in
abstol

The absolute tolerance for the eigenvalues.

in
D

Double precision array, dimension (n). The diagonal elements.

in
E

Double precision array, dimension (n-1). The off-diagonal elements.

out
m

The actual number of eigenvalues found.

out
nsplit

The number of diagonal blocks in T.

out
W

Double precision array, dimension (n). The eigenvalues.

out
iblock

Integer array, dimension (n). Block number (0-based) for each eigenvalue.

out
isplit

Integer array, dimension (n). The splitting points (0-based endpoints).

out
work

Double precision array, dimension (4*n).

out
iwork

Integer array, dimension (3*n).

out
info

  • = 0: successful exit.

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

  • > 0: some eigenvalues failed to converge or were not computed.

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