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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Linear Algebra · juobs Documentation</title><script data-outdated-warner src="assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.039/juliamono-regular.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.3/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.3/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.3/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.11/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"><a href="index.html">juobs Documentation</a></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 class="is-active"><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="linalg.html">Linear Algebra</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href="linalg.html">Linear Algebra</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://gitlab.ift.uam-csic.es/jugarrio/juobs" title="Edit on GitLab"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitLab</span></a><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 class="content" id="documenter-page"><h1 id="Linear-Algebra"><a class="docs-heading-anchor" href="#Linear-Algebra">Linear Algebra</a><a id="Linear-Algebra-1"></a><a class="docs-heading-anchor-permalink" href="#Linear-Algebra" title="Permalink"></a></h1><article class="docstring"><header><a class="docstring-binding" id="juobs.uweigvals" href="#juobs.uweigvals"><code>juobs.uweigvals</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">uweigvals(a::Matrix{uwreal}; iter = 30)
uweigvals(a::Matrix{uwreal}, b::Matrix{uwreal}; iter = 30)</code></pre><p>This function computes the eigenvalues of a matrix of uwreal objects. If a second matrix b is given as input, it returns the generalised eigenvalues instead. It takes as input:</p><ul><li><p><code>a::Matrix{uwreal}</code> : a matrix of uwreal</p></li><li><p><code>b::Matrix{uwreal}</code> : a matrix of uwreal, optional</p></li><li><p><code>iter=30</code>: optional flag to set the iterations of the qr algorithm used to solve the eigenvalue problem</p></li></ul><p>It returns:</p><ul><li><code>res = Vector{uwreal}</code>: a vector where each elements is an eigenvalue </li></ul><pre><code class="language- hljs">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</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://gitlab.ift.uam-csic.es/jugarrio/juobs">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="juobs.uweigvecs" href="#juobs.uweigvecs"><code>juobs.uweigvecs</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">uweigvecs(a::Matrix{uwreal}; iter = 30)
uweigvecs(a::Matrix{uwreal}, b::Matrix{uwreal}; iter = 30)</code></pre><p>This function computes the eigenvectors of a matrix of uwreal objects. If a second matrix b is given as input, it returns the generalised eigenvectors instead. It takes as input:</p><ul><li><p><code>a::Matrix{uwreal}</code> : a matrix of uwreal</p></li><li><p><code>b::Matrix{uwreal}</code> : a matrix of uwreal, optional</p></li><li><p><code>iter=30</code> : the number of iterations of the qr algorithm used to extract the eigenvalues </p></li></ul><p>It returns:</p><ul><li><code>res = Matrix{uwreal}</code>: a matrix where each column is an eigenvector </li></ul><p>Examples:</p><pre><code class="language- hljs">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 </code></pre></div><a class="docs-sourcelink" target="_blank" href="https://gitlab.ift.uam-csic.es/jugarrio/juobs">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="juobs.uweigen" href="#juobs.uweigen"><code>juobs.uweigen</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">uweigen(a::Matrix{uwreal}; iter = 30)
uweigen(a::Matrix{uwreal}, b::Matrix{uwreal}; iter = 30)</code></pre><p>This function computes the eigenvalues and the eigenvectors of a matrix of uwreal objects. If a second matrix b is given as input, it returns the generalised eigenvalues and eigenvectors instead. It takes as input:</p><ul><li><p><code>a::Matrix{uwreal}</code> : a matrix of uwreal</p></li><li><p><code>b::Matrix{uwreal}</code> : a matrix of uwreal, optional</p></li><li><p><code>iter=30</code> : the number of iterations of the qr algorithm used to extract the eigenvalues </p></li></ul><p>It returns:</p><ul><li><p><code>evals = Vector{uwreal}</code>: a vector where each elements is an eigenvalue </p></li><li><p><code>evecs = Matrix{uwreal}</code>: a matrix where the i-th column is the eigenvector of the i-th eigenvalue</p></li></ul><p>Examples:</p><pre><code class="language- hljs">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) </code></pre></div><a class="docs-sourcelink" target="_blank" href="https://gitlab.ift.uam-csic.es/jugarrio/juobs">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="juobs.get_matrix" href="#juobs.get_matrix"><code>juobs.get_matrix</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">get_matrix(diag::Vector{Array}, upper::Vector{Array} )</code></pre><p>This function allows the user to build an array of matrices, where each matrix is a symmetric matrix of correlators at a given timeslice. </p><p>It takes as input:</p><ul><li><p><code>diag::Vector{Array}</code>: vector of correlators. Each correlator will constitute a diagonal element of the matrices A[i] where i runs over the timeslices, i.e. <code>A[i][1,1] = diag[1], .... A[i][n,n] = diag[n]</code> <code>Given n=length(diag)</code>, the matrices will have dimension n*n </p></li><li><p><code>upper::Vector{Array}</code>: vector of correlators liying on the upper diagonal position. <code>A[i][1,2] = upper[1], .. , A[i][1,n] = upper[n-1],</code> <code>A[i][2,3] = upper[n], .. , A[i][n-1,n] = upper[n(n-1)/2]</code> Given n, <code>length(upper)=n(n-1)/2</code></p></li></ul><p>The method returns an array of symmetric matrices of dimension n for each timeslice </p><p>Examples:</p><pre><code class="language- hljs">## 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]
Julia> matrices[i]
pp[i] ap[i]
pa[i] aa[i]
## where i runs over the timeslices</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://gitlab.ift.uam-csic.es/jugarrio/juobs">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="juobs.energies" href="#juobs.energies"><code>juobs.energies</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">energies(evals::Vector{Array}; wpm::Union{Dict{Int64,Vector{Float64}},Dict{String,Vector{Float64}}, Nothing}=nothing)</code></pre><p>This method computes the energy level from the eigenvalues according to:</p><p><span>$E_i(t) = \log(λ(t) / λ(t+1))$</span></p><p>where <code>i=1,..,n</code> with <code>n=length(evals[1])</code> and <code>t=1,..,T</code> total time slices. It returns a vector array en where each entry en[i][t] contains the i-th states energy at time t </p><p>Examples:</p><pre><code class="language- hljs">## 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</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://gitlab.ift.uam-csic.es/jugarrio/juobs">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="juobs.getall_eigvals" href="#juobs.getall_eigvals"><code>juobs.getall_eigvals</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">getall_eigvals(a::Vector{Matrix}, t0; iter=30 )</code></pre><p>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:</p><p><span>$C(t_i)v_i = λ_i C(t_0) v_i$</span>, with i=1:lenght(a)</p><p>It takes as input:</p><ul><li><p><code>a::Vector{Matrix}</code> : a vector of matrices</p></li><li><p><code>t0::Int64</code> : idex value at which the fixed matrix is taken</p></li><li><p><code>iter=30</code> : the number of iterations of the qr algorithm used to extract the eigenvalues </p></li></ul><p>It returns:</p><ul><li><code>res</code> = Vector{Vector{uwreal}}</li></ul><p>where <code>res[i]</code> are the generalised eigenvalues of the i-th matrix of the input array. </p><p>Examples:</p><pre><code class="language- hljs">## 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
Julia></code></pre></div><a class="docs-sourcelink" target="_blank" href="https://gitlab.ift.uam-csic.es/jugarrio/juobs">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="juobs.getall_eigvecs" href="#juobs.getall_eigvecs"><code>juobs.getall_eigvecs</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">getall_eigvecs(a::Vector{Matrix}, delta_t; iter=30 )</code></pre><p>This function solves a GEVP problem, returning the eigenvectors, for a list of matrices.</p><p><span>$C(t_i)v_i = λ_i C(t_i-\delta_t) v_i$</span>, with i=1:lenght(a)</p><p>Here <code>delta_t</code> is the time shift within the two matrices of the problem, and is kept fixed. It takes as input:</p><ul><li><p><code>a::Vector{Matrix}</code> : a vector of matrices</p></li><li><p><code>delta_t::Int64</code> : the fixed time shift t-t_0</p></li><li><p><code>iter=30</code> : the number of iterations of the qr algorithm used to extract the eigenvalues </p></li></ul><p>It returns:</p><ul><li><code>res = Vector{Matrix{uwreal}}</code></li></ul><p>where each <code>res[i]</code> is a matrix with the eigenvectors as columns Examples:</p><pre><code class="language- hljs">mat_array = get_matrix(diag, upper_diag)
evecs = getall_eigvecs(mat_array, 5)</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://gitlab.ift.uam-csic.es/jugarrio/juobs">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="obs.html">« Observables</a><div class="flexbox-break"></div><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> version 0.27.15 on <span class="colophon-date" title="Friday 1 July 2022 12:33">Friday 1 July 2022</span>. Using Julia version 1.6.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>