extendr_api::prelude::modules::qr::col_pivoting::compute

Function qr_in_place

pub fn qr_in_place<'out, I, E>(
    matrix: MatMut<'_, E>,
    householder_factor: MatMut<'_, E>,
    col_perm: &'out mut [I],
    col_perm_inv: &'out mut [I],
    parallelism: Parallelism<'_>,
    stack: PodStack<'_>,
    params: ColPivQrComputeParams,
) -> (ColPivQrInfo, PermRef<'out, I>)
where
    I: Index,
    E: ComplexField,
Expand description

Computes the QR decomposition with pivoting of a rectangular matrix $A$, into a unitary matrix $Q$, represented as a block Householder sequence, and an upper trapezoidal matrix $R$, such that $$AP^\top = QR.$$

The Householder bases of $Q$ are stored in the strictly lower trapezoidal part of matrix with an implicit unit diagonal, and its upper triangular Householder factors are stored in householder_factor, blockwise in chunks of blocksize×blocksize.

The block size is chosen as the number of rows of householder_factor.

After the function returns, col_perm contains the order of the columns after pivoting, i.e. the result is the same as computing the non-pivoted QR decomposition of the matrix matrix[:, col_perm]. col_perm_inv contains its inverse permutation.

§Output

  • The number of transpositions that constitute the permutation.
  • a structure representing the permutation $P$.

§Panics

  • Panics if the number of columns of the householder factor is not equal to the minimum of the number of rows and the number of columns of the input matrix.
  • Panics if the block size is zero.
  • Panics if the length of col_perm and col_perm_inv is not equal to the number of columns of matrix.
  • Panics if the provided memory in stack is insufficient (see qr_in_place_req).