scipy 1.8.0 Pypi GitHub Homepage
Other Docs
NotesParametersRaisesReturnsBackRef
qr(a, overwrite_a=False, lwork=None, mode='full', pivoting=False, check_finite=True)

Calculate the decomposition A = Q R where Q is unitary/orthogonal and R upper triangular.

Notes

This is an interface to the LAPACK routines dgeqrf, zgeqrf, dorgqr, zungqr, dgeqp3, and zgeqp3.

If mode=economic , the shapes of Q and R are (M, K) and (K, N) instead of (M,M) and (M,N), with K=min(M,N) .

Parameters

a : (M, N) array_like

Matrix to be decomposed

overwrite_a : bool, optional

Whether data in a is overwritten (may improve performance if :None:None:`overwrite_a` is set to True by reusing the existing input data structure rather than creating a new one.)

lwork : int, optional

Work array size, lwork >= a.shape[1]. If None or -1, an optimal size is computed.

mode : {'full', 'r', 'economic', 'raw'}, optional

Determines what information is to be returned: either both Q and R ('full', default), only R ('r') or both Q and R but computed in economy-size ('economic', see Notes). The final option 'raw' (added in SciPy 0.11) makes the function return two matrices (Q, TAU) in the internal format used by LAPACK.

pivoting : bool, optional

Whether or not factorization should include pivoting for rank-revealing qr decomposition. If pivoting, compute the decomposition A P = Q R as above, but where P is chosen such that the diagonal of R is non-increasing.

check_finite : bool, optional

Whether to check that the input matrix contains only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination) if the inputs do contain infinities or NaNs.

Raises

LinAlgError

Raised if decomposition fails

Returns

Q : float or complex ndarray

Of shape (M, M), or (M, K) for mode='economic' . Not returned if mode='r' .

R : float or complex ndarray

Of shape (M, N), or (K, N) for mode='economic' . K = min(M, N) .

P : int ndarray

Of shape (N,) for pivoting=True . Not returned if pivoting=False .

Compute QR decomposition of a matrix.

Examples

>>> from scipy import linalg
... rng = np.random.default_rng()
... a = rng.standard_normal((9, 6))
>>> q, r = linalg.qr(a)
... np.allclose(a, np.dot(q, r)) True
>>> q.shape, r.shape
((9, 9), (9, 6))
>>> r2 = linalg.qr(a, mode='r')
... np.allclose(r, r2) True
>>> q3, r3 = linalg.qr(a, mode='economic')
... q3.shape, r3.shape ((9, 6), (6, 6))
>>> q4, r4, p4 = linalg.qr(a, pivoting=True)
... d = np.abs(np.diag(r4))
... np.all(d[1:] <= d[:-1]) True
>>> np.allclose(a[:, p4], np.dot(q4, r4))
True
>>> q4.shape, r4.shape, p4.shape
((9, 9), (9, 6), (6,))
>>> q5, r5, p5 = linalg.qr(a, mode='economic', pivoting=True)
... q5.shape, r5.shape, p5.shape ((9, 6), (6, 6), (6,))
See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.linalg._decomp_update.qr_delete scipy.linalg._decomp_update.qr_update scipy.linalg._decomp_update.qr_insert scipy.linalg._decomp_qr.qr scipy.linalg._decomp_qr.qr_multiply

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them


GitHub : /scipy/linalg/_decomp_qr.py#26
type: <class 'function'>
Commit: