naginterfaces.library.det.real_​band_​sym

naginterfaces.library.det.real_band_sym(uplo, kd, ab)[source]

real_band_sym computes the determinant of an symmetric positive definite banded matrix that has been stored in band-symmetric storage. lapacklin.dpbtrf must be called first to supply the Cholesky factorized form. The storage (upper or lower triangular) used by lapacklin.dpbtrf is relevant as this determines which elements of the stored factorized form are referenced.

For full information please refer to the NAG Library document for f03bh

https://support.nag.com/numeric/nl/nagdoc_30.1/flhtml/f03/f03bhf.html

Parameters
uplostr, length 1

Indicates whether the upper or lower triangular part of was stored and how it was factorized. This should not be altered following a call to lapacklin.dpbtrf.

The upper triangular part of was originally stored and was factorized as where is upper triangular.

The lower triangular part of was originally stored and was factorized as where is lower triangular.

kdint

, the number of superdiagonals or subdiagonals of the matrix .

abfloat, array-like, shape

The Cholesky factor of , as returned by lapacklin.dpbtrf.

Returns
dfloat

The determinant of is given by . It is given in this form to avoid overflow or underflow.

dexpint

The determinant of is given by . It is given in this form to avoid overflow or underflow.

Raises
NagValueError
(errno )

On entry, .

Constraint: or .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

The matrix is not positive definite.

Notes

The determinant of is calculated using the Cholesky factorization , where is an upper triangular band matrix, or , where is a lower triangular band matrix. The determinant of is the product of the squares of the diagonal elements of or .

References

Wilkinson, J H and Reinsch, C, 1971, Handbook for Automatic Computation II, Linear Algebra, Springer–Verlag