去除前景发射并获得宇宙微波背景的干净地图的.zip

# CleanCMB This package contains functions to enable extraction of clean maps of the cosmic microwave background (CMB). Some functions can be used to extract non-CMB astrophysical components as well. If you came here to reproduce the results in Section 6 of the [science forecast paper](https://arxiv.org/abs/2107.10364) for CCAT-prime's Prime-Cam on the [Fred Young Submillimeter Telescope (FYST)](https://www.ccatobservatory.org/index.cfm), please go to [ccatprime/sciencepaper/](https://github.com/komatsu5147/CleanCMB.jl/tree/master/ccatprime/sciencepaper). Different algorithms exist for extraction of clean maps of the CMB (as well as of astrophysical components). The package currently supports: - Internal Linear Combination (ILC) Method - Parametric Maximum Likelihood Method See [this note](https://github.com/komatsu5147/CleanCMB.jl/tree/master/note_on_ilc_vs_ml.pdf) for the relationship between them. ## Installation From the Julia REPL, run ```Julia using Pkg Pkg.add(url="https://github.com/komatsu5147/CleanCMB.jl") ``` ## Internal Linear Combination (ILC) Method - `ilc_weights(cij[, e, ℓid=3])`: return weights for the internal linear combination (ILC) method, following Equation (12) of [Tegmark et al., PRD, 68, 123523 (2003)](https://journals.aps.org/prd/abstract/10.1103/PhysRevD.68.123523). - `cilc_weights(cij, a, b[, ℓid=3])`: return weights for the constrained internal linear combination (CILC) method for two components, following Equation (20) of [Remazeilles, et al., MNRAS, 410, 2481 (2011)](https://academic.oup.com/mnras/article/410/4/2481/1007333). - `milca_weights(cij, a, B[, ℓid=3])`: return weights for the modified internal linear combination algorithm (MILCA) method (CILC for N components), following Equation (15) of [Hurier, et al., A&A, 558, A118 (2013)](https://www.aanda.org/articles/aa/abs/2013/10/aa21891-13/aa21891-13.html). - Note: These papers define weights in various domain, including harmonic, wavelet, and pixel domain. You can choose to work in any domain by supplying a covariance matrix `cij` in the appropriate domain. - `ilc_clean_cij(cij, w)`: return a covariance matrix multiplied by weights, `w' * cij * w`, with `w` returned by any of the above functions, e.g., `w = cilc_weights(cij, a, b)`. - This would be a variance of the extracted component if `cij` were the same as that used in `ilc_weights()`, `cilc_weights()` or `milca_weights()`. - If `cij` is a noise covariance matrix, this function returns the noise variance of the cleaned map for each multipole, band-power bin, pixel, etc. ### Arguments - `cij::Array{<:AbstractFloat,2}`: `nν`-by-`nν` symmetric covariance matrix, where `nν` is the number of frequency bands. - or, `cij::Array{<:AbstractFloat,3}`:symmetric covariance matrix with the dimention of `(nℓ, nν, nν)`, `(nν, nℓ, nν)` or `(nν, nν, nℓ)` (default). Here, `nℓ` is the number of elements in the relevant domain, e.g., multipoles, band-power bins, pixels, etc. - The functions `ilc_weights()`, `cilc_weights()` and `milca_weights()` are *multiple dispatch*, which detect the dimension of the input `cij` automatically. - `a::Array{<:AbstractFloat,1}`: vector of the frequency response, for the component to be extracted. E.g., `a=[1,...,1]` for CMB. The number of elements is `nν`. - `b::Array{<:AbstractFloat,1}`: vector of the frequency response, for the component to be nulled. The number of elements is `nν`. - `B::Array{<:AbstractFloat,2}`: `nν`-by-`nrc` matrix of the frequency response, for `nrc` components to be nulled. ### Optional arguments - `e::Array{<:AbstractFloat,1}`: vector of the frequency response, for the component to be extracted. The default value is `e=[1,...,1]`, i.e., CMB. The number of elements is `nν`. - `ℓid::Integer=3`: location of the index for the `nℓ` domain, if the dimension of the input `cij` is `(nℓ, nν, nν)`, `(nν, nℓ, nν)` or `(nν, nν, nℓ)`. `ℓid=1` if `cij[nℓ,nν,nν]`, `ℓid=2` if `cij[nν,nℓ,nν]`, and `ℓid=3` (the default value) if `cij[nν,nν,nℓ]`. ## Parametric Maximum Likelihood Method - `loglike_beta(nij, A, d)` or `loglike_beta(nij, A, cij)`:: return log(likelihood) for frequency response vectors `A` given a data vector `d` or data covariance matrix `cij`, based on Equation (9) of [Stompor et al., MNRAS, 392, 216 (2009)](https://academic.oup.com/mnras/article/392/1/216/1071929). <!-- - `loglike_beta_deriv(nij, A, dAdβ, d)` and `loglike_beta_hessian(nij, A, dAdβI, dAdβJ, d)`: return the gradient and hessian of log(likelihood) with respect to foreground parameters, using Equation (A1) and (5) of [Errard et al., PRD, 84, 063005 (2011)](https://journals.aps.org/prd/abstract/10.1103/PhysRevD.84.063005), respectively. These functions may be used to make the maximisation of `loglike_beta(nij, A, d)` more efficient. --> ### Arguments - `nij::Array{<:AbstractFloat,2}`: `nν`-by-`nν` symmetric noise covariance matrix, where `nν` is the number of frequency bands. - `A::Array{<:AbstractFloat,2}`: `nν`-by-`nc` matrix of the frequency response, for `nc` components in sky. - E.g., ``A = [a B]`` where `a = ones(nν)` for CMB and `B` is a `nν`-by-`nc-1` matrix for the frequency response of foreground components. - `d::Array{<:AbstractFloat,1}`: data vector for a given pixel, (ℓ,m), or any other appropriate domain. The number of elements is `nν`. - `cij::Array{<:AbstractFloat,2}`: `nν`-by-`nν` symmetric covariance matrix for a given multipole, pixel, or any other appropriate domain. <!-- - `dAdβ::Array{<:AbstractFloat,2}`, `dAdβI::Array{<:AbstractFloat,2}` and `dAdβJ::Array{<:AbstractFloat,2}`: `nν`-by-`nc` matrix of the derivative of the frequency response with respect to a foreground parameter. - E.g., ``dAdβ = [zeros(nν) dsynch/dβs zeros(nν)]`` where `zeros(nν)` for CMB and dust because they do not depend on the synchrotron index `βs`. --> ## Foreground models The package contains the following functions to return frequency dependence of foreground components: - `tsz(νGHz; units="cmb", Tcmb=2.7255)`: Spectrum of the thermal Sunyaev-Zeldovich effect given in Equation (V) in Appendix of [Zeldovich, Sunyaev, Astrophys. Space Sci. 4, 301 (1969)](http://articles.adsabs.harvard.edu/pdf/1969Ap%26SS...4..301Z). - `dust1(νGHz; Td=19.6, βd=1.6, νd=353, units="cmb", Tcmb=2.7255)`: Spectrum of 1-component modified black-body thermal dust emission. The output is normalized to unity at `νGHz = νd`. - `synch(νGHz; βs=-3, νs=23, Cs=0, νC=40, units="cmb", Tcmb=2.7255)`: Spectrum of synchrotron emission. The output is normalized to unity at `νGHz = νs`. ### Arguments - `νGHz::Real`: frequency in units of GHz. ### Optional keyword arguments - `units::String`: units of the spectrum. For Rayleigh-Jeans temperature (brightness temperature) units, set `units = "rj"`. The default is the CMB units. - `Tcmb::Real`: present-day temperature of the CMB in units of Kelvin. The default value is `2.7255`. - `Td::Real`: dust temperature. The default value is `19.6` (Kelvin). - `βd::Real`: dust emissivity index. The default value is `1.6`. - `νd::Real`: frequency at which the output dust spectrum is normalized to unity. The default value is `353` (GHz). - `βs::Real`: synchrotron power-law index. The default is `-3`. - `νs::Real`: frequency at which the output synchrotron spectrum is normalized to unity. The default is `23` (GHz). - `Cs::Real`: curvature of the synchrotron spectrum. The default value is `0`. - `νC::Real`: pivot frequency for curvature of the synchrotron spectrum. The default value is `40` (GHz). ## Example Julia Codes - [examples/CleanWMAP.jl](https://github.com/komatsu5147/CleanCMB.jl/tree/master/examples/CleanWMAP.jl) - This code applies `ilc_weights()` in pixel domain to produce a clean map of CMB from the temperature maps of Wilkinson Microwave Anisotropy Probe (WMAP) at five frequency bands. - The code requires [Healpix.jl](https://github.com/ziotom78/Healpix.jl). ### Pipeli