Hernquist lens

init_HernquistLens(D_d::Real  = NaN, 
                   x_c::Real  = 0.0, 
                   y_c::Real  = 0.0, 
                   mass::Real = NaN, 
                   x_s::Real  = NaN)

Initialize a Hernquist lens with the given parameters.

Keyword Arguments

• D_d::Real = NaN: ADD from observer to lens (in $\rm \mathbf{meters}$).
• 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 $\rm \mathbf{arcseconds}$).
• mass::Real= NaN: Mass of the lens (in $\rm \mathbf{M_\odot}$).
• x_s::Real = NaN: Scale radius (in $\rm \mathbf{arcseconds}$).

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

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

Calculate potential at given coordinates for Hernquist 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 $\rm \mathbf{arcseconds}$).
• D_d : Angular diameter distance to the lens (in $\rm \mathbf{meters}$).
• θxc : x-coordinate of the lens (in $\rm \mathbf{arcseconds}$).
• θyc : y-coordinate of the lens (in $\rm \mathbf{arcseconds}$).
• mass: Mass of the lens (in $\rm \mathbf{M_\odot}$).
• θs : Scale radius i.e., standard deviation of the Gaussian (in $\rm \mathbf{arcseconds}$).

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

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

Calculate deflection at given coordinates for Hernquist 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 $\rm \mathbf{arcseconds}$).
• D_d : Angular diameter distance to the lens (in $\rm \mathbf{meters}$).
• θxc : x-coordinate of the lens (in $\rm \mathbf{arcseconds}$).
• θyc : y-coordinate of the lens (in $\rm \mathbf{arcseconds}$).
• mass: Mass of the lens (in $\rm \mathbf{M_\odot}$).
• θs : Scale radius i.e., standard deviation of the Gaussian (in $\rm \mathbf{arcseconds}$).

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

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

Calculate Jacobian at given coordinates for Hernquist 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 $\rm \mathbf{arcseconds}$).
• D_d : Angular diameter distance to the lens (in $\rm \mathbf{meters}$).
• θxc : x-coordinate of the lens (in $\rm \mathbf{arcseconds}$).
• θyc : y-coordinate of the lens (in $\rm \mathbf{arcseconds}$).
• mass: Mass of the lens (in $\rm \mathbf{M_\odot}$).
• θs : Scale radius i.e., standard deviation of the Gaussian (in $\rm \mathbf{arcseconds}$).