SIE Lens

init_SIELens(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 singular isothermal ellipsoid (SIE) 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 SIE 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::Real: x-coordinate of the lens (in $\rm \mathbf{arcseconds}$).
• θyc::Real: y-coordinate of the lens (in $\rm \mathbf{arcseconds}$).
• v_d::Real: Velocity dispersion of the lens (in $\rm \mathbf{km/s}$).
• θs::Real: Scale radius i.e., standard deviation of the Gaussian (in $\rm \mathbf{arcseconds}$).
• ϵ::Real: Ellipticity of the lens.
• pa::Real: 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 SIE 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::Real: x-coordinate of the lens (in $\rm \mathbf{arcseconds}$).
• θyc::Real: y-coordinate of the lens (in $\rm \mathbf{arcseconds}$).
• v_d::Real: Velocity dispersion of the lens (in $\rm \mathbf{km/s}$).
• θs::Real: Scale radius i.e., standard deviation of the Gaussian (in $\rm \mathbf{arcseconds}$).
• ϵ::Real: Ellipticity of the lens.
• pa::Real: 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 SIE lens and update the Jacobian values in-place.

Arguments

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