rank_downdate


function rank_downdate(S:LLT, x:Real[_]) -> LLT

Rank one downdate of a Cholesky decomposition.

  • S: Existing Cholesky decomposition of the symmetric positive definite matrix S.
  • x: Vector x.

Returns: A new Cholesky decomposition of the symmetric positive definite matrix S - xx^\top.

function rank_downdate(S:LLT, X:Real[_,_]) -> LLT

Rank k downdate of a Cholesky decomposition.

  • S: Existing Cholesky decomposition of the symmetric positive definite matrix S.
  • X: Matrix X.

Returns: A new Cholesky decomposition of the symmetric positive definite matrix S - XX^\top.

The computation is performed as k separate rank-1 downdates using the columns of `X

function rank_downdate(y:Expression<LLT>, z:Expression<Real[_]>) -> MatrixRankDowndate<Expression<Real[_]>, Real[_], Real[_]>

Lazy rank 1 downdate.

function rank_downdate(y:LLT, z:Expression<Real[_]>) -> MatrixRankDowndate<Expression<Real[_]>, Real[_], Real[_]>

Lazy rank 1 downdate.

function rank_downdate(y:Expression<LLT>, z:Real[_]) -> MatrixRankDowndate<Expression<Real[_]>, Real[_], Real[_]>

Lazy rank 1 downdate.

function rank_downdate(y:Expression<LLT>, z:Expression<Real[_,_]>) -> MatrixRankDowndate<Expression<Real[_,_]>, Real[_,_], Real[_,_]>

Lazy rank k downdate.

function rank_downdate(y:LLT, z:Expression<Real[_,_]>) -> MatrixRankDowndate<Expression<Real[_,_]>, Real[_,_], Real[_,_]>

Lazy rank k downdate.

function rank_downdate(y:Expression<LLT>, z:Real[_,_]) -> MatrixRankDowndate<Expression<Real[_,_]>, Real[_,_], Real[_,_]>

Lazy rank k downdate.