F64ReferenceSparseLinearAlgebra
The portable sparse backend, available on every target. The sparse seams declare their routines and this implements them, so a binding that means to accelerate one cannot inherit the portable version by accident.
Properties
isPortable
Whether this is koblas's own implementation rather than a binding to a host library. The compiled-in SIMD kernels are portable however fast they are; only something calling out counts as accelerated.
name
Whether this backend can do work on this host. koblas's own implementations always can, so the default is true; a binding reports whether the library it calls resolved.
Relative preference among the backends offered for one half (F64Blas, F64Decompositions, F64Kernels or a sparse counterpart). registerBackend picks the highest; the portable reference is 0.
The sparse vector kernels used by operations around these matrix halves.
Whether factorBasis answers with a factorization that updates its factors in place. When false a replacement costs a factorization, so a caller pacing its own refactorizations has nothing left to pace.
Functions
asum
Sum |x_i| over the stored entries.
axpy
dot
factor
Factorize the square a into something solvable. A singular matrix comes back as a factorization reporting singular rather than as an exception, with a failedAt counting elimination steps rather than naming a column: the step that fails is the one with no acceptable pivot left, so there is no column of a to attribute it to.
Parameters
the square matrix to factorize.
scale rows by a power of two first; the solves undo it.
discard produced entries this far below the largest magnitude, giving an incomplete factorization.
gemv
In-place y = alpha · op(A) · x + beta · y, where op(A) is Aᵀ when transpose. Per BLAS convention beta == 0.0 overwrites y without reading it, so it may arrive uninitialized.
nrm2
Euclidean norm over the stored entries, rescaled as the dense euclideanNorm is.
scatter
trsv
Solve op(T) · x = b in place, op transposing when transpose. x holds the right-hand side on entry and the solution on return. Only the lower or upper triangle of a is read, and unitDiag takes the diagonal as 1 without reading it, as the dense com.eignex.koblas.dense.F64Blas.trsv does.
Unlike the dense half, which follows dtrsv in reporting nothing and answering a singular triangle with infinities, this reports it. There is no sparse BLAS routine whose silence it has to match, and the value is looked up to divide by it anyway, so a healthy solve pays nothing; only the failing column pays the extra scan that tells a stored zero from a missing entry.
Throws
if a diagonal entry is missing or zero and unitDiag is false, naming its position.
Factor a simplex basis for column replacements.
solveInto into a fresh vector.