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Private Documentation

This page documents private functions which may be useful but which have no guarantee of stability across any change in versions of this package.

Contents

Generic utilities

CMB.quadprod — Method
quadprod(A::AbstractSparseMatrixCSC, b::AbstractVecOrMat, n::Integer)

Computes the quadratic product $ABA^\top$ efficiently for the case where $B$ is all zero except for a small number of columns b starting at the nth.

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Sphere Functions

CMB.Sphere.x̂ — Constant
const x̂ = SVector(1, 0, 0)
const ŷ = SVector(0, 1, 0)
const ẑ = SVector(0, 0, 1)

Constant unit vectors in the Cartesian directions.

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CMB.Sphere.ŷ — Constant
const x̂ = SVector(1, 0, 0)
const ŷ = SVector(0, 1, 0)
const ẑ = SVector(0, 0, 1)

Constant unit vectors in the Cartesian directions.

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CMB.Sphere.ẑ — Constant
const x̂ = SVector(1, 0, 0)
const ŷ = SVector(0, 1, 0)
const ẑ = SVector(0, 0, 1)

Constant unit vectors in the Cartesian directions.

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CMB.Sphere.:∥ — Method
∥(u, v) -> Bool

Test whether vector $u$ is parallel to vector $v$. Assumes that both are unit normalized.

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CMB.Sphere.cartvec — Method
r = cartvec(θ, ϕ)
r = cartvec((θ, ϕ))

Converts the colatitude-azimuth pair $(θ, ϕ)$ to a Cartesian unit vector $r$.

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CMB.Sphere.colataz — Method
θ, ϕ = colataz(δ, λ)
θ, ϕ = colataz((δ, λ))

Converts the latitude-longitude pair $(δ, λ)$ in degrees to colatitude-azimuth $(θ, ϕ)$ in radians.

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CMB.Sphere.colataz — Method
θ, ϕ = colataz(r)

Converts the Cartesian unit vector $r$ to a colatitude-azimuth pair $(θ, ϕ)$ in radians.

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CMB.Sphere.latlon — Method
δ, λ = latlon(θ, ϕ)
δ, λ = latlon((θ, ϕ))

Converts the colatitude-azimuth pair $(θ, ϕ)$ in radians to latitude-longitude $(δ, λ)$ in radians.

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CMB.Sphere.latlon — Method
δ, λ = latlon(r)

Converts the Cartesian unit vector $r$ to a latitude-longitude pair $(δ, λ)$ in degrees.

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Pixel Covariance