PIEP Lens

init_PIEPLens(x_c::Real = 0.0, 
              y_c::Real = 0.0, 
              v_d::Real = NaN, 
              x_s::Real = NaN, 
              eps::Real = NaN, 
              pa::Real  = NaN)

Initialize pseudo isothermal elliptical potential (PIEP) lens with the given parameters.

Keyword Arguments

• x_c::Real = 0.0: x-coordinate of the lens (in $\rm \mathbf{arcseconds}$).
• y_c::Real = 0.0: y-coordinate of the lens (in $\rm \mathbf{arcseconds}$).
• v_d::Real = NaN: Velocity dispersion (in $\rm \mathbf{km/s}$).
• x_s::Real = NaN: Scale radius (in $\rm \mathbf{arcseconds}$).
• eps::Real = NaN: Ellipticity (dimensionless).
• pa::Real = NaN: Position angle (in $\rm \mathbf{deg}$).

potential!(ψ::U, θx::S, θy::S, θxc::T, θyc::T, v_d::T, θs::T, ϵ::T, pa::T) where {U<:Real, S<:Real, T<:Real}

potential!(ψ::U, θx::S, θy::S, θxc::T, θyc::T, v_d::T, θs::T, ϵ::T, pa::T) where {U<:ROA, S<:ROA, T<:Real}

Calculate potential at given coordinates for PIEP lens and update the potential values in-place.

Arguments

• ψ: Potential at given coordinates
• θx : x-coordinate(s) (in $\rm \mathbf{arcseconds}$).
• θy : y-coordinate(s) (in $\rm \mathbf{arcseconds}$).
• θxc: x-coordinate of the lens (in $\rm \mathbf{arcseconds}$).
• θyc: y-coordinate of the lens (in $\rm \mathbf{arcseconds}$).
• v_d: Velocity dispersion of the lens (in $\rm \mathbf{km/s}$).
• θs : Scale radius i.e., standard deviation of the Gaussian (in $\rm \mathbf{arcseconds}$).
• ϵ : Ellipticity of the lens.
• pa : Position angle of the lens (in $\rm \mathbf{degrees}$).

deflection!(ψx::U, ψy::U, θx::S, θy::S, θxc::T, θyc::T, v_d::T, θs::T, ϵ::T, pa::T) where {U<:Real, S<:Real, T<:Real}

deflection!(ψx::U, ψy::U, θx::S, θy::S, θxc::T, θyc::T, v_d::T, θs::T, ϵ::T, pa::T) where {U<:ROA, S<:ROA, T<:Real}

Calculate deflection at given coordinates for PIEP lens and update the deflection values in-place.

Arguments

• ψx : x-component of deflection at given coordinates
• ψy : y-component of deflection at given coordinates
• θx : x-coordinate(s) (in $\rm \mathbf{arcseconds}$).
• θy : y-coordinate(s) (in $\rm \mathbf{arcseconds}$).
• θxc: x-coordinate of the lens (in $\rm \mathbf{arcseconds}$).
• θyc: y-coordinate of the lens (in $\rm \mathbf{arcseconds}$).
• v_d: Velocity dispersion of the lens (in $\rm \mathbf{km/s}$).
• θs : Scale radius i.e., standard deviation of the Gaussian (in $\rm \mathbf{arcseconds}$).
• ϵ : Ellipticity of the lens.
• pa : Position angle of the lens (in $\rm \mathbf{degrees}$).

jacobian!(ψxx::U, ψyy::U, ψxy::U, θx::S, θy::S, θxc::T, θyc::T, v_d::T, θs::T, ϵ::T, pa::T) where {U<:Real, S<:Real, T<:Real}

jacobian!(ψxx::U, ψyy::U, ψxy::U, θx::S, θy::S, θxc::T, θyc::T, v_d::T, θs::T, ϵ::T, pa::T) where {U<:ROA, S<:ROA, T<:Real}

Calculate Jacobian at given coordinates for PIEP lens and update the Jacobian values in-place.

Arguments

• ψxx: x-component of Jacobian at given coordinates
• ψyy: y-component of Jacobian at given coordinates
• ψxy: xy-component of Jacobian at given coordinates
• θx : x-coordinate(s) (in $\rm \mathbf{arcseconds}$).
• θy : y-coordinate(s) (in $\rm \mathbf{arcseconds}$).
• θxc: x-coordinate of the lens (in $\rm \mathbf{arcseconds}$).
• θyc: y-coordinate of the lens (in $\rm \mathbf{arcseconds}$).
• v_d: Velocity dispersion of the lens (in $\rm \mathbf{km/s}$).
• θs : Scale radius i.e., standard deviation of the Gaussian (in $\rm \mathbf{arcseconds}$).
• ϵ : Ellipticity of the lens.
• pa : Position angle of the lens (in $\rm \mathbf{degrees}$).