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Mojo function

apply_q

def apply_q[dtype: DType, element_layout: Layout](sigma: LayoutTensor[dtype, address_space=sigma.address_space, element_layout=element_layout, layout_int_type=sigma.layout_int_type, linear_idx_type=sigma.linear_idx_type, masked=sigma.masked, alignment=sigma.alignment], A: LayoutTensor[dtype, address_space=A.address_space, element_layout=element_layout, layout_int_type=A.layout_int_type, linear_idx_type=A.linear_idx_type, masked=A.masked, alignment=A.alignment], X: LayoutTensor[dtype, address_space=X.address_space, element_layout=element_layout, layout_int_type=X.layout_int_type, linear_idx_type=X.linear_idx_type, masked=X.masked, alignment=X.alignment])

Applies the implicit Q factor stored in A and sigma after calling qr_factorization to the X matrix.

See qr_factorization for more details on the construction of the Householder reflector.

Parameters:

dtype (DType): Element type of the matrices.
element_layout (Layout): Memory layout of the LayoutTensor inputs.

Args:

sigma (LayoutTensor[dtype, address_space=sigma.address_space, element_layout=element_layout, layout_int_type=sigma.layout_int_type, linear_idx_type=sigma.linear_idx_type, masked=sigma.masked, alignment=sigma.alignment]): Vector of length n holding the Householder scaling factors produced by qr_factorization.
A (LayoutTensor[dtype, address_space=A.address_space, element_layout=element_layout, layout_int_type=A.layout_int_type, linear_idx_type=A.linear_idx_type, masked=A.masked, alignment=A.alignment]): m×n matrix containing the implicit Q factor as produced by qr_factorization.
X (LayoutTensor[dtype, address_space=X.address_space, element_layout=element_layout, layout_int_type=X.layout_int_type, linear_idx_type=X.linear_idx_type, masked=X.masked, alignment=X.alignment]): m×q_n matrix to multiply by Q. Must have the same number of rows as A. Overwritten with Q·X in-place.