KWLinalg

Collection of functions to perform linear algebra operations in-place.

Non allocating updates LU decompositions

We extend the function LAPACK.getrf! to provide a pivot-vector ipiv as second argument. In this way, ipiv can be preallocated and LAPACK.getrf!(A, ipiv) does not cause any allocations. This allows one to update LU decompositions in-place.

For a matrix A the function lu!(A) still allocates workspaces.

using LinearAlgebra
n = 5
A = rand(n, n)
@allocated D = lu(A) # 384 bytes
@allocated Di = lu!(A) # 128 bytes

The function LAPACK.getrf! is only available to matrices and always allocates the pivot-vector ipiv. We provide a function LAPACK.getrf!(A, ipiv), such that a pivot vector can be provied and is not allocated everytime. For an lu-decomposition object, this can be used as follows

using KWLinalg
using LinearAlgebra
n = 5
A = rand(n, n)
D = lu(A)
# A is updated
A .= rand(n, n)
# We update the LU-decomposition in-place.
LAPACK.getrf!(D.factors, D.ipiv)

getrf!(A, ipiv) -> (A, ipiv, info)

Non allocating singular value decompositions