naginterfaces.library.lapackeig.dorgbr¶
- naginterfaces.library.lapackeig.dorgbr(vect, k, a, tau)[source]¶
dorgbr
generates one of the real orthogonal matrices or which were determined bydgebrd()
when reducing a real matrix to bidiagonal form.For full information please refer to the NAG Library document for f08kf
https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/f08/f08kff.html
- Parameters
- vectstr, length 1
Indicates whether the orthogonal matrix or is generated.
is generated.
is generated.
- kint
If , the number of columns in the original matrix .
If , the number of rows in the original matrix .
- afloat, array-like, shape
Details of the vectors which define the elementary reflectors, as returned by
dgebrd()
.- taufloat, array-like, shape
Note: the required length for this argument is determined as follows: if : ; if : ; otherwise: .
Further details of the elementary reflectors, as returned by
dgebrd()
in its argument if , or in its argument if .
- Returns
- afloat, ndarray, shape
The orthogonal matrix or , or the leading rows or columns thereof, as specified by , and .
- Raises
- NagValueError
- (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: .
- (errno )
On entry, error in parameter .
Constraint: .
- Notes
dorgbr
is intended to be used after a call todgebrd()
, which reduces a real rectangular matrix to bidiagonal form by an orthogonal transformation: .dgebrd()
represents the matrices and as products of elementary reflectors.This function may be used to generate or explicitly as square matrices, or in some cases just the leading columns of or the leading rows of .
The various possibilities are specified by the arguments , , and . The appropriate values to cover the most likely cases are as follows (assuming that was an matrix):
To form the full matrix : set , and (note that the array must have at least columns).
If , to form the leading columns of : set , and
To form the full matrix : set , and (note that the array must have at least rows).
If , to form the leading rows of : set and
- References
Golub, G H and Van Loan, C F, 1996, Matrix Computations, (3rd Edition), Johns Hopkins University Press, Baltimore