Variables

Module for different variable representations, transforms between representations and operators that act on variables.

Exports

• FCVariable
• FSVariable
• FZVariable
• XCVariable
• XSVariable
• XZVariable
• cosine_transform
• cosine_transform!
• horizontal_counterpart
• horizontal_transform
• horizontal_transform!
• resolved
• sine_transform
• sine_transform!
• solve_poisson!
• transform!
• ∂x
• ∂x!
• ∂z
• ∂z!
• ∂z²
• ∂z²!
• ∫dx
• ∫dx!
• ∫dz
• ∫dz!
• ∫dz²
• ∫dz²!

Most of the operators have many methods signatures to allow for different combinations of input and output variables.

julia> ?
help?> ∂x!

A variable expressed in Fourier space in the horizontal and cosine space in the vertical.

A variable expressed in Fourier space in the horizontal and sine space in the vertical.

A variable expressed in Fourier space in the horizontal and physical space in the vertical.

A variable expressed in physical space in the horizontal and cosine space in the vertical.

A variable expressed in physical space in the horizontal and sine space in the vertical.

A variable expressed in physical space in the horizontal and vertical.

Transform the variable from physical space to cosine space or vice verse in the vertical.

cosine_transform!(out::XCVariable, in::XZVariable)

cosine_transform!(out::XZVariable, in::XCVariable)

Return the fourier (physical) counterpart to a physical (fourier) variable.

Transform the variable from physical space to Fourier space or vice verse in the horizontal.

horizontal_transform!(
    out::Union{FCVariable{T}, FSVariable{T}, FZVariable{T}} where T,
    in::Union{XCVariable{T}, XSVariable{T}, XZVariable{T}} where T
)

horizontal_transform!(
    out::Union{XCVariable{T}, XSVariable{T}, XZVariable{T}} where T,
    in::Union{FCVariable{T}, FSVariable{T}, FZVariable{T}} where T
)

Return a view into the resolved wavenumbers.

Transform the variable from physical space to sine space or vice verse in the vertical.

sine_transform!(out::XSVariable, in::XZVariable)

sine_transform!(out::XZVariable, in::XSVariable)

Solve the Poisson equation $\nabla^2\psi = -\zeta$ in Fourier–Sine space.

solve_poisson!(
    out::FSVariable,
    in::FSVariable
) -> SubArray{_A, 2, P, Tuple{UnitRange{Int64}, UnitRange{Int64}}, false} where {_A, P<:FSVariable}

Safe transforms with domain validation for public use.

Compute one or more (n) $x$–derivatives returning a new variable.

Compute one or more (n) $x$–derivatives.

∂x!(
    v::SawyerEliassenSolver.Variables.AbstractVariable,
    n::Int64
)

∂x!(v::SawyerEliassenSolver.Variables.AbstractVariable)

∂x!(
    v::Union{XCVariable{T}, XSVariable{T}, XZVariable{T}} where T,
    tmp::Union{FCVariable{T}, FSVariable{T}, FZVariable{T}} where T,
    n::Int64
)

∂x!(
    v::Union{XCVariable{T}, XSVariable{T}, XZVariable{T}} where T,
    tmp::Union{FCVariable{T}, FSVariable{T}, FZVariable{T}} where T
)

∂x!(
    out::Union{FCVariable{T}, FSVariable{T}, FZVariable{T}} where T,
    in::Union{FCVariable{T}, FSVariable{T}, FZVariable{T}} where T,
    n::Int64
)

∂x!(
    out::Union{XCVariable{T}, XSVariable{T}, XZVariable{T}} where T,
    in::Union{XCVariable{T}, XSVariable{T}, XZVariable{T}} where T,
    n::Int64
)

∂x!(
    out::Union{XCVariable{T}, XSVariable{T}, XZVariable{T}} where T,
    in::Union{XCVariable{T}, XSVariable{T}, XZVariable{T}} where T,
    tmp::Union{FCVariable{T}, FSVariable{T}, FZVariable{T}} where T,
    n::Int64
)

∂x!(
    out::Union{XCVariable{T}, XSVariable{T}, XZVariable{T}} where T,
    in::Union{XCVariable{T}, XSVariable{T}, XZVariable{T}} where T,
    tmp::Union{FCVariable{T}, FSVariable{T}, FZVariable{T}} where T
)

∂x!(v::SawyerEliassenSolver.Variables.AbstractVariable)

∂x(
    v::SawyerEliassenSolver.Variables.AbstractVariable
) -> Any

∂x(
    v::Union{FCVariable{T}, FSVariable{T}, FZVariable{T}} where T,
    n::Int64
) -> Any

∂x(
    v::Union{XCVariable{T}, XSVariable{T}, XZVariable{T}} where T,
    n::Int64
) -> Union{XCVariable, XSVariable, XZVariable}

∂x(
    v::Union{XCVariable{T}, XSVariable{T}, XZVariable{T}} where T,
    tmp::Union{FCVariable{T}, FSVariable{T}, FZVariable{T}} where T,
    n::Int64
) -> Union{XCVariable, XSVariable, XZVariable}

∂x(
    v::Union{XCVariable{T}, XSVariable{T}, XZVariable{T}} where T,
    tmp::Union{FCVariable{T}, FSVariable{T}, FZVariable{T}} where T
) -> Union{XCVariable, XSVariable, XZVariable}

Compute a $z$–derivative returning a new variable.

Compute a $z$–derivative inplace.

∂z!(out::FCVariable, in::FSVariable)

∂z!(out::FSVariable, in::FCVariable)

∂z!(out::XCVariable, in::XSVariable)

∂z!(out::XSVariable, in::XCVariable)

∂z!(
    out::Union{FZVariable, XZVariable},
    in::Union{FZVariable, XZVariable}
)

∂z(v::FCVariable) -> FSVariable

∂z(v::FSVariable) -> FCVariable

∂z(v::FZVariable) -> FZVariable

∂z(v::XCVariable) -> XSVariable

∂z(v::XSVariable) -> XCVariable

∂z(v::XZVariable) -> XZVariable

Compute a second $z$–derivative returning a new variable.

Compute a second $z$–derivative inplace.

∂z²!(v::SawyerEliassenSolver.Variables.AbstractVariable)

∂z²!(
    out::Union{FCVariable, XCVariable},
    in::Union{FCVariable, XCVariable}
)

∂z²!(
    out::Union{FSVariable, XSVariable},
    in::Union{FSVariable, XSVariable}
)

∂z²(
    v::Union{FCVariable, FSVariable, XCVariable, XSVariable}
) -> Union{FCVariable, FSVariable, XCVariable, XSVariable}

Compute one or more $x$–antiderivatives returning a new variable.

Compute one or more $x$–antiderivatives inplace.

∫dx!(
    v::SawyerEliassenSolver.Variables.AbstractVariable,
    n::Int64
)

∫dx!(v::SawyerEliassenSolver.Variables.AbstractVariable)

∫dx!(
    v::Union{XCVariable{T}, XSVariable{T}, XZVariable{T}} where T,
    tmp::Union{FCVariable{T}, FSVariable{T}, FZVariable{T}} where T,
    n::Int64
)

∫dx!(
    v::Union{XCVariable{T}, XSVariable{T}, XZVariable{T}} where T,
    tmp::Union{FCVariable{T}, FSVariable{T}, FZVariable{T}} where T
)

∫dx!(v::SawyerEliassenSolver.Variables.AbstractVariable)

∫dx!(
    out::Union{XCVariable{T}, XSVariable{T}, XZVariable{T}} where T,
    in::Union{XCVariable{T}, XSVariable{T}, XZVariable{T}} where T,
    tmp::Union{FCVariable{T}, FSVariable{T}, FZVariable{T}} where T,
    n::Int64
)

∫dx!(
    out::Union{XCVariable{T}, XSVariable{T}, XZVariable{T}} where T,
    in::Union{XCVariable{T}, XSVariable{T}, XZVariable{T}} where T,
    tmp::Union{FCVariable{T}, FSVariable{T}, FZVariable{T}} where T
)

∫dx!(v::SawyerEliassenSolver.Variables.AbstractVariable)

∫dx(
    v::SawyerEliassenSolver.Variables.AbstractVariable,
    n::Int64
) -> Any

∫dx(
    v::SawyerEliassenSolver.Variables.AbstractVariable
) -> Any

∫dx(
    v::Union{XCVariable{T}, XSVariable{T}, XZVariable{T}} where T,
    tmp::Union{FCVariable{T}, FSVariable{T}, FZVariable{T}} where T,
    n::Int64
) -> Union{XCVariable, XSVariable, XZVariable}

∫dx(
    v::Union{XCVariable{T}, XSVariable{T}, XZVariable{T}} where T,
    tmp::Union{FCVariable{T}, FSVariable{T}, FZVariable{T}} where T
) -> Union{XCVariable, XSVariable, XZVariable}

Compute a $z$–antiderivative returning a new variable.

Compute a $z$-antiderivative inplace.

∫dz!(out::FCVariable, in::FSVariable)

∫dz!(out::FSVariable, in::FCVariable)

∫dz!(out::XCVariable, in::XSVariable)

∫dz!(out::XSVariable, in::XCVariable)

∫dz(v::FCVariable) -> FSVariable

∫dz(v::FSVariable) -> FCVariable

∫dz(v::XCVariable) -> XSVariable

∫dz(v::XSVariable) -> XCVariable

Compute a second $z$–antiderivative returning a new variable.

Compute a second $z$–antiderivative inplace.

∫dz²!(v::SawyerEliassenSolver.Variables.AbstractVariable)

∫dz²!(
    out::Union{FCVariable, XCVariable},
    in::Union{FCVariable, XCVariable}
)

∫dz²!(
    out::Union{FSVariable, XSVariable},
    in::Union{FSVariable, XSVariable}
)

∫dz²(
    v::Union{FCVariable, FSVariable, XCVariable, XSVariable}
) -> Union{FCVariable, FSVariable, XCVariable, XSVariable}