SubSolvers

SubSolver

An abstract supertype for structures specifying solution methods for a linear system or least squares problem.

SubSolverRecipe

An abstract supertype for structures with pre-allocated memory for methods that solve a linear system or least squares problem.

LQSolver <: SubSolver

A type containing information relevant to solving the linear subsystems created by the Solver routines with the LQ factorization. As there are no user controlled parameters, if the user wishes to use this method they can simply specify LQSolver().

LQSolverRecipe <: SubSolverRecipe{M<:AbstractArray}

A mutable type containing informtation relevant to solving the linear subsytems created by the Solver routines with the LQ factorization.

Fields

• A::M, The matrix in the linear system that will be solved with the LQ solver.

QRSolver <: SubSolver

A type containing information relevant to solving the linear subsystems created by the Solver routines with the QR factorization. As there are no user controlled parameters, if the user wishes to use this method they can simply specify QRSolver().

Fields

• None

QRSolverRecipe{M<:AbstractArray} <: SubSolverRecipe

A mutable type containing information relevant to solving the linear subsystems created by the Solver routines with the QR factorization.

Fields

• A::M, The matrix in the linear system that will be solved with the QR solver.

complete_sub_solver(solver::SubSolver, A::AbstractArray)

A function that generates a SubSolverRecipe given the arguments.

Arguments

• solver::SubSolver, a user-specified sub-solving method.
• A::AbstractArray, a coefficient matrix or vector.

Returns

• A SubSolverRecipe object.

Throws

• ArgumentError if no method for completing the sub-solver exists for the given sub-solver type.

complete_sub_solver(solver::SubSolver, A::AbstractArray, b::AbstractArray)

A function that generates a SubSolverRecipe given the arguments.

Arguments

• solver::SubSolver, a user-specified sub-solving method.
• A::AbstractArray, a coefficient matrix or vector.
• b::AbstractArray, a constant matrix or vector.

Returns

• A SubSolverRecipe object.

Throws

• ArgumentError if no method for completing the sub-solver exists for the given sub-solver type.

update_sub_solver!(solver::SubSolverRecipe, A::AbstractArray)

A function that updates the SubSolver in place given arguments.

Arguments

• solver::SubSolverRecipe, a fully initialized realization for a linear sub-solver.
• A::AbstractArray, a coefficient matrix or vector.

Returns

• Modifies the SubSolverRecipe in place given the arguments.and returns nothing.

Throws

• ArgumentError if no method for updating the sub-solver exists for the given sub-solver type.

ldiv!(x::AbstractVector, solver::SubSolverRecipe, b::AbstractVector)

An extension of LinearAlgebra.ldiv! that solves a linear system using the SubSolverRecipe and stores the result in x.

Arguments

• x::AbstractVector, the output vector to store the solution.
• solver::SubSolverRecipe, a fully initialized realization for a linear sub-solver.
• b::AbstractVector, the right-hand side vector.

Returns

• Writes the solution to solver applied to the constant vector b into x and returns x.

Throws

• ArgumentError if no method for solving with the sub-solver exists for the given sub-solver type.