# naginterfaces.library.lapackeig.dsbtrd¶

naginterfaces.library.lapackeig.dsbtrd(vect, uplo, kd, ab, q=None)[source]

dsbtrd reduces a real symmetric band matrix to tridiagonal form.

For full information please refer to the NAG Library document for f08he

https://www.nag.com/numeric/nl/nagdoc_28.7/flhtml/f08/f08hef.html

Parameters
vectstr, length 1

Indicates whether is to be returned.

is returned.

is updated (and the array must contain a matrix on entry).

is not required.

uplostr, length 1

Indicates whether the upper or lower triangular part of is stored.

The upper triangular part of is stored.

The lower triangular part of is stored.

kdint

If , the number of superdiagonals, , of the matrix .

If , the number of subdiagonals, , of the matrix .

abfloat, array-like, shape

The upper or lower triangle of the symmetric band matrix .

qNone or float, array-like, shape , optional

Note: the required extent for this argument in dimension 1 is determined as follows: if : ; if : ; otherwise: .

Note: the required extent for this argument in dimension 2 is determined as follows: if : ; if : ; otherwise: .

If , must contain the matrix formed in a previous stage of the reduction (for example, the reduction of a banded symmetric-definite generalized eigenproblem); otherwise need not be set.

Returns
abfloat, ndarray, shape

is overwritten by values generated during the reduction to tridiagonal form.

The first superdiagonal or subdiagonal and the diagonal of the tridiagonal matrix are returned in using the same storage format as described above.

dfloat, ndarray, shape

The diagonal elements of the tridiagonal matrix .

efloat, ndarray, shape

The off-diagonal elements of the tridiagonal matrix .

qNone or float, ndarray, shape

If or , the matrix .

If , is not referenced.

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: , or .

(errno )

On entry, error in parameter .

Constraint: or .

(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

Constraint: .

Notes

dsbtrd reduces a symmetric band matrix to symmetric tridiagonal form by an orthogonal similarity transformation:

The orthogonal matrix is determined as a product of Givens rotation matrices, and may be formed explicitly by the function if required.

The function uses a vectorizable form of the reduction, due to Kaufman (1984).

References

Kaufman, L, 1984, Banded eigenvalue solvers on vector machines, ACM Trans. Math. Software (10), 73–86

Parlett, B N, 1998, The Symmetric Eigenvalue Problem, SIAM, Philadelphia