SolverErrors

SolverError

An abstract supertype for structures that track and/or evaluate the quality of a solution for a linear system or least squares.

SolverErrorRecipe

An abstract supertype for structures that contain the user-controlled parameters, linear system dependent parameters, and preallocated memory for techniques that evaluate the solution to a linear solver.

FullResidual <: SolverError

A SolverError structure for computing the norm of the full residual, $b-Ax$.

Fields

• None

FullResidual <: SolverErrorRecipe

A SolverErrorResidual structure for computing the norm of the full residual, $b-Ax$

Fields

• residual::AbstractVector, a container for the residual $b-Ax$.

LSGradient <: SolverError

A SolverError structure for monitoring the residual of the normal equations of a linear system (equivalently, the gradient of the least squares problem), $-A^\top (b - Ax)$.

Fields

• None

LSGradientRecipe <: SolverErrorRecipe

A SolverErrorRecipe structure for storing the residual of the normal equations of a linear system (equivalently, the gradeint of the least squares problem), $-A^\intercal (b - Ax)$.

Fields

• gradient::AbstractVector, $-A^\top (b - Ax)$.

CompressedResidual <: ErrorRecipe

A structure for the compressed residual, Sb-SAx.

Fields

• None

CompressedResidualRecipe <: ErrorRecipe

A structure containing the preallocated structures for the compressed residual, Sb-SAx.

Fields

• residual::AbstractVector, a container for the compressed residual, Sb-SAx.
• residual_view::SubArray, a view of the residual container to handle varying compression sizes.

complete_error(
    error::SolverError, 
    solver::Solver,
    A::AbstractMatrix, 
    b::AbstractVector
)

A function that generates a SolverErrorRecipe given the arguments.

Arguments

• error::SolverError, a user-specified solver error method.
• solver::Solver, a user-specified solver method.
• A::AbstractMatrix, a coefficient matrix.
• b::AbstractVector, a constant vector.

Returns

• A SolverErrorRecipe object.

compute_error(
    error::SolverErrorRecipe, 
    solver::SolverRecipe, 
    x::AbstractVector,
    A::AbstractMatrix, 
    b::AbstractVector
)

A function that evaluates the error for a proposed solution vector.

Arguments

• error::SolverErrorRecipe, a fully initialized realization for a solver error method for a specific linear system or least squares problem.
• solver::SolverRecipe, a fully initialized realization for a solver method for a specific linear system.
• x::AbstractVector, a vector for the proposed solution.
• A::AbstractMatrix, a coefficient matrix.
• b::AbstractVector, a constant vector.

Returns

• Returns nothing