linalg_householder_product {torch} | R Documentation |
Computes the first n
columns of a product of Householder matrices.
Description
Letting be
or
,
for a matrix
with columns
with
and a vector
with
,
this function computes the first
columns of the matrix
Usage
linalg_householder_product(A, tau)
Arguments
A |
(Tensor): tensor of shape |
tau |
(Tensor): tensor of shape |
Details
Math could not be displayed. Please visit the package website.
where is the
m
-dimensional identity matrix and
is the conjugate transpose when
is complex, and the transpose when
is real-valued.
See Representation of Orthogonal or Unitary Matrices for
further details.
Supports inputs of float, double, cfloat and cdouble dtypes. Also supports batches of matrices, and if the inputs are batches of matrices then the output has the same batch dimensions.
Note
This function only uses the values strictly below the main diagonal of A
.
The other values are ignored.
See Also
-
torch_geqrf()
can be used together with this function to form theQ
from thelinalg_qr()
decomposition. -
torch_ormqr()
is a related function that computes the matrix multiplication of a product of Householder matrices with another matrix. However, that function is not supported by autograd.
Other linalg:
linalg_cholesky_ex()
,
linalg_cholesky()
,
linalg_det()
,
linalg_eigh()
,
linalg_eigvalsh()
,
linalg_eigvals()
,
linalg_eig()
,
linalg_inv_ex()
,
linalg_inv()
,
linalg_lstsq()
,
linalg_matrix_norm()
,
linalg_matrix_power()
,
linalg_matrix_rank()
,
linalg_multi_dot()
,
linalg_norm()
,
linalg_pinv()
,
linalg_qr()
,
linalg_slogdet()
,
linalg_solve_triangular()
,
linalg_solve()
,
linalg_svdvals()
,
linalg_svd()
,
linalg_tensorinv()
,
linalg_tensorsolve()
,
linalg_vector_norm()
Examples
if (torch_is_installed()) {
A <- torch_randn(2, 2)
h_tau <- torch_geqrf(A)
Q <- linalg_householder_product(h_tau[[1]], h_tau[[2]])
torch_allclose(Q, linalg_qr(A)[[1]])
}