Preconditioner{T} = Union{AbstractLinearOperator{T}, opEye}

Abstract type accepted for preconditioners

Abstract type for statistics returned by a solver

Type for statistics returned by non-Lanczos solvers

Type for statistics returned by Lanczos solvers

Type for statistics returned by SYMMLQ

Type for statistics returned by adjoint systems solvers

Find the real roots of the quadratic

q(x) = q₂ x² + q₁ x + q₀,

where q₂, q₁ and q₀ are real. Care is taken to avoid numerical cancellation. Optionally, nitref steps of iterative refinement may be performed to improve accuracy. By default, nitref=1.

Numerically stable symmetric Givens reflection. Given a and b, return (c, s, ρ) such that

[ c  s ] [ a ] = [ ρ ]
[ s -c ] [ b ] = [ 0 ].

Given a trust-region radius radius, a vector x lying inside the trust-region and a direction d, return σ1 and σ2 such that

‖x + σi d‖ = radius, i = 1, 2

in the Euclidean norm. If known, ‖x‖² may be supplied in xNorm2.

If flip is set to true, σ1 and σ2 are computed such that

‖x - σi d‖ = radius, i = 1, 2.

Display an array in the form

[ -3.0e-01 -5.1e-01  1.9e-01 ... -2.3e-01 -4.4e-01  2.4e-01 ]

with (ndisp - 1)/2 elements on each side.