naginterfaces.library.lapackeig.dgemqrt

naginterfaces.library.lapackeig.dgemqrt(side, trans, v, t, c)[source]

dgemqrt multiplies an arbitrary real matrix by the real orthogonal matrix from a factorization computed by dgeqrt().

For full information please refer to the NAG Library document for f08ac

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/f08/f08acf.html

Parameters
sidestr, length 1

Indicates how or is to be applied to .

or is applied to from the left.

or is applied to from the right.

transstr, length 1

Indicates whether or is to be applied to .

is applied to .

is applied to .

vfloat, array-like, shape

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

Details of the vectors which define the elementary reflectors, as returned by dgeqrt() in the first columns of its array argument .

tfloat, array-like, shape

Further details of the orthogonal matrix as returned by dgeqrt(). The number of blocks is , where and each block is of order except for the last block, which is of order . For the blocks the upper triangular block reflector factors are stored in the matrix as .

cfloat, array-like, shape

The matrix .

Returns
cfloat, ndarray, shape

is overwritten by or or or as specified by and .

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: .

(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

Constraint: .

Notes

dgemqrt is intended to be used after a call to dgeqrt() which performs a factorization of a real matrix . The orthogonal matrix is represented as a product of elementary reflectors.

This function may be used to form one of the matrix products

overwriting the result on (which may be any real rectangular matrix).

A common application of this function is in solving linear least squares problems, as described in the F08 Introduction.

References

Golub, G H and Van Loan, C F, 2012, Matrix Computations, (4th Edition), Johns Hopkins University Press, Baltimore