naginterfaces.library.lapackeig.dgglse

naginterfaces.library.lapackeig.dgglse(n, a, b, c, d)[source]

dgglse solves a real linear equality-constrained least squares problem.

For full information please refer to the NAG Library document for f08za

https://www.nag.com/numeric/nl/nagdoc_28.7/flhtml/f08/f08zaf.html

Parameters
nint

, the number of columns of the matrices and .

afloat, array-like, shape

The matrix .

bfloat, array-like, shape

The matrix .

cfloat, array-like, shape

The right-hand side vector for the least squares part of the LSE problem.

dfloat, array-like, shape

The right-hand side vector for the equality constraints.

Returns
afloat, ndarray, shape

is overwritten.

bfloat, ndarray, shape

is overwritten.

cfloat, ndarray, shape

The residual sum of squares for the solution vector is given by the sum of squares of elements ; the remaining elements are overwritten.

dfloat, ndarray, shape

is overwritten.

xfloat, ndarray, shape

The solution vector of the LSE problem.

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

Constraint: .

(errno )

The upper triangular factor associated with in the generalized factorization of the pair is singular, so that ; the least squares solution could not be computed.

(errno )

The part of the upper trapezoidal factor associated with in the generalized factorization of the pair is singular, so that the rank of the matrix () comprising the rows of and is less than ; the least squares solutions could not be computed.

Notes

dgglse solves the real linear equality-constrained least squares (LSE) problem

where is an matrix, is a matrix, is an element vector and is a element vector. It is assumed that , and , where . These conditions ensure that the LSE problem has a unique solution, which is obtained using a generalized factorization of the matrices and .

References

Anderson, E, Bai, Z, Bischof, C, Blackford, S, Demmel, J, Dongarra, J J, Du Croz, J J, Greenbaum, A, Hammarling, S, McKenney, A and Sorensen, D, 1999, LAPACK Users’ Guide, (3rd Edition), SIAM, Philadelphia

Anderson, E, Bai, Z and Dongarra, J, 1992, Generalized factorization and its applications, Linear Algebra Appl. (Volume 162–164), 243–271

Eldèn, L, 1980, Perturbation theory for the least squares problem with linear equality constraints, SIAM J. Numer. Anal. (17), 338–350