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Updated juobs_linalg documentation with examples

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docs/build/assets/documenter.js
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...@@ -208,10 +208,6 @@ $(document).ready(function() { ...@@ -208,10 +208,6 @@ $(document).ready(function() {
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}) })
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docs/build/assets/search.js
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...@@ -181,7 +181,7 @@ $(document).ready(function() { ...@@ -181,7 +181,7 @@ $(document).ready(function() {
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}) })
$(function(){ $(function(){
...@@ -221,11 +221,7 @@ $(document).ready(function() { ...@@ -221,11 +221,7 @@ $(document).ready(function() {
data = store[result.ref] data = store[result.ref]
link = $('<a class="docs-label">'+data.title+'</a>') link = $('<a class="docs-label">'+data.title+'</a>')
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li = $('<li>').append(link).append(" ").append(cat) li = $('<li>').append(link).append(" ").append(cat)
searchresults.append(li) searchresults.append(li)
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docs/build/assets/themeswap.js
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// Small function to quickly swap out themes. Gets put into the <head> tag.. // Small function to quickly swap out themes. Gets put into the <head> tag..
function set_theme_from_local_storage() { function set_theme_from_local_storage() {
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...@@ -24,7 +14,7 @@ function set_theme_from_local_storage() { ...@@ -24,7 +14,7 @@ function set_theme_from_local_storage() {
// //
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// that are not the currently active theme) // that are not the currently active theme)
var active = null; var disabled = []; var darkTheme = null; var active = null; var disabled = [];
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// The <link> tag of each style sheet is expected to have a data-theme-name attribute // The <link> tag of each style sheet is expected to have a data-theme-name attribute
...@@ -35,12 +25,8 @@ function set_theme_from_local_storage() { ...@@ -35,12 +25,8 @@ function set_theme_from_local_storage() {
// To distinguish the default (primary) theme, it needs to have the data-theme-primary // To distinguish the default (primary) theme, it needs to have the data-theme-primary
// attribute set. // attribute set.
var isprimary = (ss.ownerNode.getAttribute("data-theme-primary") !== null); var isprimary = (ss.ownerNode.getAttribute("data-theme-primary") !== null);
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...@@ -52,15 +38,5 @@ function set_theme_from_local_storage() { ...@@ -52,15 +38,5 @@ function set_theme_from_local_storage() {
ss.disabled = true; ss.disabled = true;
}); });
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set_theme_from_local_storage(); set_theme_from_local_storage();
docs/build/index.html
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docs/build/search.html
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<!DOCTYPE html> <!DOCTYPE html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Search · juobs Documentation</title><link href="https://fonts.googleapis.com/css?family=Lato|Roboto+Mono" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.0/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.0/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.0/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.11.1/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="assets/documenter.js"></script><script src="siteinfo.js"></script><script src="../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit">juobs Documentation</span></div><form class="docs-search" action="search.html"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="index.html">Home</a></li><li><a class="tocitem" href="reader.html">Reader</a></li><li><a class="tocitem" href="tools.html">Tools</a></li><li><a class="tocitem" href="obs.html">Observables</a></li><li><a class="tocitem" href="linalg.html">Linear Algebra</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href="search.html">Search</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href="search.html">Search</a></li></ul></nav><div class="docs-right"><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article><p id="documenter-search-info">Loading search...</p><ul id="documenter-search-results"></ul></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Wednesday 24 February 2021 11:46">Wednesday 24 February 2021</span>. 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src/juobs_linalg.jl
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...@@ -13,45 +13,46 @@ end ...@@ -13,45 +13,46 @@ end
=# =#
@doc raw""" @doc raw"""
get_matrix(corr_diag::Vector{Array}, corr_upper::Vector{Array} ) get_matrix(diag::Vector{Array}, upper::Vector{Array} )
This method returns an array of dim `T` where each element is a symmetrix matrix of dimension n of `uwreal` correlators This function allows the user to build an array of matrices, where each matrix is a symmetric matrix of correlators at a given timeslice.
at fixed time i=1..T. It takes as input:
It takes as input:
`corr_diag`: vector of dimension n of correlators liying on the diagonal
`corr_upper`: vector of correlators liying on the upper diagonal. - `diag::Vector{Array}`: vector of correlators. Each correlator will constitute a diagonal element of the matrices A[i] where i runs over the timeslices, i.e.
`A[i][1,1] = diag[1], .... A[i][n,n] = diag[n]`
`Given n=length(diag)`, the matrices will have dimension n*n
- `upper::Vector{Array}`: vector of correlators liying on the upper diagonal position.
`A[i][1,2] = upper[1], .. , A[i][1,n] = upper[n-1], `
`A[i][2,3] = upper[n], .. , A[i][n-1,n] = upper[n(n-1)/2]`
Given n, `length(upper)=n(n-1)/2`
The method returns an array of symmetric matrices of dimension n for each timeslice
Each correlator is an vector of uwreal variables of dimension `T`. Examples:
```@example
Example: ## load data
```@example pp_data = read_mesons(path, "G5", "G5")
for i in 1:n pa_data = read_mesons(path, "G5", "G0G5")
a[i,i] = Vector{uwreal} # vector of uwreal variables of dimension T. They will constitute the diagonal elements of the matrices aa_data = read_mesons(path, "G0G5", "G0G5")
for i in 1:n-1
for j in i+1:n
a[i,j] = Vector{uwreal} # vector of uwreal variables of dimension T. They will constitute the upper diagonal elements of the matrices. A matrix
of dimension n*n has n(n-1)/2 upper diagonal elements.
Assume n=4
diagonal = Vector{Array}()
push!(diagonal, a[1,1],a[2,2],a[3,3],a[4,4])
upsize = Vector{Array}()
push!(upsize, a[1,2], a[1,3], a[1,4], a[2,3], a[2,4], a[3,4])
array_of_matrices = get_matrix(diagonal, upsize)
Julia> T-element Array{Array,1} ## create Corr struct
corr_pp = corr_obs.(pp_data)
corr_pa = corr_obs.(pa_data)
corr_aa = corr_obs.(aa_data) # array of correlators for different \mu_q combinations
size(array_of_matrices) ## set up matrices
corr_diag = [corr_pp[1], corr_aa[1]]
corr_upper = [corr_pa[1]]
Julia> (T,) matrices = [corr_diag, corr_upper]
array_of_matrices[t] # t in 1:T Julia> matrices[i]
pp[i] ap[i]
pa[i] aa[i]
Julia> 4*4 Array{uwreal,2} ## where i runs over the timeslices
``` ```
""" """
function get_matrix(corr_diag::Vector{Vector{uwreal}}, corr_upper::Vector{Vector{uwreal}}) function get_matrix(corr_diag::Vector{Vector{uwreal}}, corr_upper::Vector{Vector{uwreal}})
...@@ -79,12 +80,41 @@ function get_matrix(corr_diag::Vector{Vector{uwreal}}, corr_upper::Vector{Vector ...@@ -79,12 +80,41 @@ function get_matrix(corr_diag::Vector{Vector{uwreal}}, corr_upper::Vector{Vector
return res return res
end end
get_matrix(corr_diag::Vector{Corr}, corr_upper::Vector{Corr}) = get_matrix(getfield.(corr_diag, :obs), getfield.(corr_upper, :obs)) get_matrix(corr_diag::Vector{Corr}, corr_upper::Vector{Corr}) = get_matrix(getfield.(corr_diag, :obs), getfield.(corr_upper, :obs))
@doc raw""" @doc raw"""
energies(evals::Vector{Array}) energies(evals::Vector{Array}; wpm::Union{Dict{Int64,Vector{Float64}},Dict{String,Vector{Float64}}, Nothing}=nothing)
This method computes the energy level from the eigenvalues according to:
``E_i(t) = \log(λ(t) / λ(t+1))``
Given a vector where each entry `evals[t]` is a `uwreal` array of eigenvalues, this method computes the effective energies of the first N states, where ```N=dim(evals[t])```. where `i=1,..,n` with `n=length(evals[1])` and `t=1,..,T` total time slices.
The index `t` here runs from 1:T=lenght(evals), while the index `i` stands for the number of energy levels computed: i = length(evals[t]) It returns a vector array en where each entry en[i][t] contains the i-th states energy at time t
It returns a vector array `eff_en` where each entry `eff_en[t]` contains the first N states energies as uwreal objects
Examples:
```@example
## load data
pp_data = read_mesons(path, "G5", "G5")
pa_data = read_mesons(path, "G5", "G0G5")
aa_data = read_mesons(path, "G0G5", "G0G5")
## create Corr struct
corr_pp = corr_obs.(pp_data)
corr_pa = corr_obs.(pa_data)
corr_aa = corr_obs.(aa_data) # array of correlators for different \mu_q combinations
## set up matrices
corr_diag = [corr_pp[1], corr_aa[1]]
corr_upper = [corr_pa[1]]
matrices = [corr_diag, corr_upper]
## solve the GEVP
evals = getall_eigvals(matrices, 5) #where t_0=5
en = energies(evals)
Julia> en[i] # i-th state energy at each timeslice
```
""" """
function energies(evals::Union{Vector{Vector{uwreal}},Array{Array{uwreal}} }; wpm::Union{Dict{Int64,Vector{Float64}},Dict{String,Vector{Float64}}, Nothing}=nothing) function energies(evals::Union{Vector{Vector{uwreal}},Array{Array{uwreal}} }; wpm::Union{Dict{Int64,Vector{Float64}},Dict{String,Vector{Float64}}, Nothing}=nothing)
time = length(evals) time = length(evals)
...@@ -108,7 +138,7 @@ end ...@@ -108,7 +138,7 @@ end
This function solves a GEVP problem, returning the eigenvalues, for a list of matrices, taking as generalised matrix the one This function solves a GEVP problem, returning the eigenvalues, for a list of matrices, taking as generalised matrix the one
at index t0, i.e: at index t0, i.e:
``C(t_i)v_i = λ_i C(t_0) v_i``, with i=1:lenght(a) ``C(t_i)v_i = λ_i C(t_0) v_i``, with i=1:lenght(a)
It takes as input: It takes as input:
...@@ -125,9 +155,28 @@ It returns: ...@@ -125,9 +155,28 @@ It returns:
where `res[i]` are the generalised eigenvalues of the i-th matrix of the input array. where `res[i]` are the generalised eigenvalues of the i-th matrix of the input array.
Examples: Examples:
```@example ```@example
mat_array = get_matrix(diag, upper_diag) ## load data
evals = getall_eigvals(mat_array, 5) pp_data = read_mesons(path, "G5", "G5")
pa_data = read_mesons(path, "G5", "G0G5")
aa_data = read_mesons(path, "G0G5", "G0G5")
## create Corr struct
corr_pp = corr_obs.(pp_data)
corr_pa = corr_obs.(pa_data)
corr_aa = corr_obs.(aa_data) # array of correlators for different \mu_q combinations
## set up matrices
corr_diag = [corr_pp[1], corr_aa[1]]
corr_upper = [corr_pa[1]]
matrices = [corr_diag, corr_upper]
## solve the GEVP
evals = getall_eigvals(matrices, 5) #where t_0=5
Julia>
``` ```
""" """
function getall_eigvals(a::Vector{Matrix}, t0::Int64; iter=30 ) function getall_eigvals(a::Vector{Matrix}, t0::Int64; iter=30 )
...@@ -150,9 +199,19 @@ It takes as input: ...@@ -150,9 +199,19 @@ It takes as input:
- `b::Matrix{uwreal}` : a matrix of uwreal, optional - `b::Matrix{uwreal}` : a matrix of uwreal, optional
- `iter=30`: optional flag to set the iterations of the qr algorithm used to solve the eigenvalue problem
It returns: It returns:
- `res = Vector{uwreal}`: a vector where each elements is an eigenvalue - `res = Vector{uwreal}`: a vector where each elements is an eigenvalue
```@example
a = Matrix{uwreal}(nothing, n,n) ## n*n matrix of uwreal with nothing entries
b = Matrix{uwreal}(nothing, n,n) ## n*n matrix of uwreal with nothing entries
res = uweigvals(a) ##eigenvalues
res1 = uweigvals(a,b) ## generalised eigenvalues
```
""" """
function uweigvals(a::Matrix{uwreal}; iter = 30) function uweigvals(a::Matrix{uwreal}; iter = 30)
n = size(a,1) n = size(a,1)
...@@ -176,7 +235,7 @@ end ...@@ -176,7 +235,7 @@ end
This function solves a GEVP problem, returning the eigenvectors, for a list of matrices. This function solves a GEVP problem, returning the eigenvectors, for a list of matrices.
``C(t_i)v_i = λ_i C(t_i-\delta_t) v_i``, with i=1:lenght(a) ``C(t_i)v_i = λ_i C(t_i-\delta_t) v_i ``, with i=1:lenght(a)
Here `delta_t` is the time shift within the two matrices of the problem, and is kept fixed. Here `delta_t` is the time shift within the two matrices of the problem, and is kept fixed.
It takes as input: It takes as input:
...@@ -189,7 +248,7 @@ It takes as input: ...@@ -189,7 +248,7 @@ It takes as input:
It returns: It returns:
- `res` = Vector{Matrix{uwreal}} - `res = Vector{Matrix{uwreal}}`
where each `res[i]` is a matrix with the eigenvectors as columns where each `res[i]` is a matrix with the eigenvectors as columns
Examples: Examples:
...@@ -203,7 +262,6 @@ function getall_eigvecs(a::Vector{Matrix}, delta_t; iter=30) ...@@ -203,7 +262,6 @@ function getall_eigvecs(a::Vector{Matrix}, delta_t; iter=30)
res = Vector{Matrix{uwreal}}(undef, n) res = Vector{Matrix{uwreal}}(undef, n)
[res[i] = uweigvecs(a[i+delta_t], a[i]) for i=1:n] [res[i] = uweigvecs(a[i+delta_t], a[i]) for i=1:n]
return res return res
end end
@doc raw""" @doc raw"""
...@@ -219,9 +277,19 @@ It takes as input: ...@@ -219,9 +277,19 @@ It takes as input:
- `b::Matrix{uwreal}` : a matrix of uwreal, optional - `b::Matrix{uwreal}` : a matrix of uwreal, optional
- `iter=30` : the number of iterations of the qr algorithm used to extract the eigenvalues
It returns: It returns:
- `res = Matrix{uwreal}`: a matrix where each column is an eigenvector - `res = Matrix{uwreal}`: a matrix where each column is an eigenvector
Examples:
```@example
a = Matrix{uwreal}(nothing, n,n) ## n*n matrix of uwreal with nothing entries
b = Matrix{uwreal}(nothing, n,n) ## n*n matrix of uwreal with nothing entries
res = uweigvecs(a) ##eigenvectors in column
res1 = uweigvecs(a,b) ## generalised eigenvectors in column
```
""" """
function uweigvecs(a::Matrix{uwreal}; iter = 30) function uweigvecs(a::Matrix{uwreal}; iter = 30)
n = size(a,1) n = size(a,1)
...@@ -258,9 +326,22 @@ It takes as input: ...@@ -258,9 +326,22 @@ It takes as input:
- `b::Matrix{uwreal}` : a matrix of uwreal, optional - `b::Matrix{uwreal}` : a matrix of uwreal, optional
- `iter=30` : the number of iterations of the qr algorithm used to extract the eigenvalues
It returns: It returns:
- `evals = Vector{uwreal}`: a vector where each elements is an eigenvalue - `evals = Vector{uwreal}`: a vector where each elements is an eigenvalue
- `evecs = Matrix{uwreal}`: a matrix where the i-th column is the eigenvector of the i-th eigenvalue - `evecs = Matrix{uwreal}`: a matrix where the i-th column is the eigenvector of the i-th eigenvalue
Examples:
```@example
a = Matrix{uwreal}(nothing, n,n) ## n*n matrix of uwreal with nothing entries
b = Matrix{uwreal}(nothing, n,n) ## n*n matrix of uwreal with nothing entries
eval, evec = uweigen(a)
eval1, evec1 = uweigvecs(a,b)
```
""" """
function uweigen(a::Matrix{uwreal}; iter = 30) function uweigen(a::Matrix{uwreal}; iter = 30)
return uweigvals(a, iter=iter), uweigvecs(a, iter=iter) return uweigvals(a, iter=iter), uweigvecs(a, iter=iter)
......
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