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example_snia.html

@@ -316,7 +316,7 @@ <h1 class="title">Supernova Type Ia Analysis</h1>
 
 
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 <div class="sourceCode cell-code" id="cb1"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="kw">def</span> doc_theme():</span>
 <span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a>    <span class="cf">return</span> theme_minimal() <span class="op">+</span> theme(</span>
 <span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a>        panel_grid_minor<span class="op">=</span>element_line(color<span class="op">=</span><span class="st">"gray"</span>, linetype<span class="op">=</span><span class="st">"--"</span>),</span>
@@ -327,7 +327,7 @@ <h1 class="title">Supernova Type Ia Analysis</h1>
 <section id="computational-cosmology" class="level2 page-columns page-full">
 <h2 class="anchored" data-anchor-id="computational-cosmology">Computational Cosmology</h2>
 <p>NumCosmo provides tools for calculating cosmological observables with precision. For example, the comoving distance in an XCDM cosmology up to a redshift of <span class="math inline">\(z = 3.0\)</span> can be computed with a few lines of code using the parameters <span class="math inline">\(\Omega_{c0} = 0.25\)</span>, <span class="math inline">\(\Omega_{b0} = 0.05\)</span>, and <span class="math inline">\(w\)</span> varying from <span class="math inline">\(-1.5\)</span> to <span class="math inline">\(-0.5\)</span>.</p>
-<div id="8ea9741e" class="cell" data-execution_count="2">
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 <div class="sourceCode cell-code" id="cb2"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="im">import</span> numpy <span class="im">as</span> np</span>
 <span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a><span class="im">import</span> pandas <span class="im">as</span> pd</span>
 <span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a><span class="im">from</span> plotnine <span class="im">import</span> <span class="op">*</span></span>
@@ -386,7 +386,7 @@ <h2 class="anchored" data-anchor-id="computational-cosmology">Computational Cosm
 <section id="the-modeling" class="level3">
 <h3 class="anchored" data-anchor-id="the-modeling">The Modeling</h3>
 <p>NumCosmo’s computational objects are designed for direct use in statistical analyses. In the example above, the <code>HICosmoDEXcdm</code> class defines the cosmological model, which is a subclass of the <code>HICosmo</code> class representing a homogeneous isotropic cosmology. The model’s parameters can be accessed and managed within a model set, using the <code>MSet</code> class, which serves as the main container for all models in a given analysis.</p>
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 <div class="sourceCode cell-code" id="cb4"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a>mset <span class="op">=</span> Ncm.MSet.new_array([cosmo])</span>
 <span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a>mset.pretty_log()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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@@ -410,7 +410,7 @@ <h3 class="anchored" data-anchor-id="the-modeling">The Modeling</h3>
 <section id="fitting-model-to-data" class="level2 page-columns page-full">
 <h2 class="anchored" data-anchor-id="fitting-model-to-data">Fitting Model to Data</h2>
 <p>Once models are defined and the free parameters are set, they can be analyzed using a variety of statistical methods. For example, the best-fit parameters for a given model can be found by maximizing the likelihood function.</p>
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 <details class="code-fold">
 <summary>Code</summary>
 <div class="sourceCode cell-code" id="cb6"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a>cosmo.props.w_fit <span class="op">=</span> <span class="va">True</span></span>
@@ -437,7 +437,7 @@ <h2 class="anchored" data-anchor-id="fitting-model-to-data">Fitting Model to Dat
 #  - differentiation:   Numerical differentiantion (forward)
 #................
 #  Minimum found with precision: |df|/f =  1.00000e-08 and |dx| =  1.00000e-05
-#  Elapsed time: 00 days, 00:00:00.8083140
+#  Elapsed time: 00 days, 00:00:00.8229960
 #  iteration            [000074]
 #  function evaluations [000076]
 #  gradient evaluations [000000]
@@ -470,7 +470,7 @@ <h2 class="anchored" data-anchor-id="fitting-model-to-data">Fitting Model to Dat
 </div>
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 <p>The code above fits the XCDM model to the Union2.1 dataset, which contains supernova type Ia data. It computes the best-fit parameters for the model and the covariance matrix of the parameters using the Fisher matrix.</p>
-<div id="3620389d" class="cell" data-execution_count="6">
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 <div class="sourceCode cell-code" id="cb8"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a>lhr2d <span class="op">=</span> Ncm.LHRatio2d.new(</span>
 <span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a>    fit,</span>
 <span id="cb8-3"><a href="#cb8-3" aria-hidden="true" tabindex="-1"></a>    mset.fparam_get_pi_by_name(<span class="st">"Omegac"</span>),</span>
@@ -538,7 +538,7 @@ <h2 class="anchored" data-anchor-id="fitting-model-to-data">Fitting Model to Dat
 <section id="running-a-mcmc-analysis" class="level2 page-columns page-full">
 <h2 class="anchored" data-anchor-id="running-a-mcmc-analysis">Running a MCMC Analysis</h2>
 <p>NumCosmo also provides tools for running Markov Chain Monte Carlo (MCMC) analyses. The code below runs an MCMC analysis using the <code>APES</code> algorithm.</p>
-<div id="be5b4ab2" class="cell" data-execution_count="8">
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 <div class="sourceCode cell-code" id="cb10"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a>init_sampler <span class="op">=</span> Ncm.MSetTransKernGauss.new(<span class="dv">0</span>)</span>
 <span id="cb10-2"><a href="#cb10-2" aria-hidden="true" tabindex="-1"></a>init_sampler.set_mset(mset)</span>
 <span id="cb10-3"><a href="#cb10-3" aria-hidden="true" tabindex="-1"></a>init_sampler.set_prior_from_mset()</span>

search.json

@@ -30,7 +30,7 @@
     "href": "example_snia.html#fitting-model-to-data",
     "title": "Supernova Type Ia Analysis",
     "section": "Fitting Model to Data",
-    "text": "Fitting Model to Data\nOnce models are defined and the free parameters are set, they can be analyzed using a variety of statistical methods. For example, the best-fit parameters for a given model can be found by maximizing the likelihood function.\n\n\nCode\ncosmo.props.w_fit = True\ncosmo.props.Omegac_fit = True\nmset.prepare_fparam_map()\n\nlh = Ncm.Likelihood(\n    dataset=Ncm.Dataset.new_array(\n        [Nc.DataDistMu.new_from_id(dist, Nc.DataSNIAId.SIMPLE_UNION2_1)]\n    )\n)\nfit = Ncm.Fit.factory(\n    Ncm.FitType.NLOPT, \"ln-neldermead\", lh, mset, Ncm.FitGradType.NUMDIFF_FORWARD\n)\nfit.run(Ncm.FitRunMsgs.SIMPLE)\nfit.log_info()\nfit.fisher()\nfit.log_covar()\n\n\n#----------------------------------------------------------------------------------\n# Model fitting. Interating using:\n#  - solver:            NLOpt:ln-neldermead\n#  - differentiation:   Numerical differentiantion (forward)\n#................\n#  Minimum found with precision: |df|/f =  1.00000e-08 and |dx| =  1.00000e-05\n#  Elapsed time: 00 days, 00:00:00.8083140\n#  iteration            [000074]\n#  function evaluations [000076]\n#  gradient evaluations [000000]\n#  degrees of freedom   [000577]\n#  m2lnL     =     562.219163105056 (     562.21916 )\n#  Fit parameters:\n#     0.230499952926549     -1.02959391499341      \n#----------------------------------------------------------------------------------\n# Data used:\n#   - Union2.1 sample\n#----------------------------------------------------------------------------------\n# Model[03000]:\n#   - NcHICosmo : XCDM - Constant EOS\n#----------------------------------------------------------------------------------\n# Model parameters\n#   -      H0[00]:  67.36               [FIXED]\n#   -  Omegac[01]:  0.230499952926549   [FREE]\n#   -  Omegax[02]:  0.7                 [FIXED]\n#   - Tgamma0[03]:  2.7245              [FIXED]\n#   -      Yp[04]:  0.24                [FIXED]\n#   -    ENnu[05]:  3.046               [FIXED]\n#   -  Omegab[06]:  0.05                [FIXED]\n#   -       w[07]: -1.02959391499341    [FREE]\n#----------------------------------------------------------------------------------\n# NcmMSet parameters covariance matrix\n#                                                  -------------------------------\n# Omegac[03000:01] =  0.2305      +/-  0.06233     |  1           | -0.9297      |\n#      w[03000:07] = -1.03        +/-  0.08595     | -0.9297      |  1           |\n#                                                  -------------------------------\n\n\nThe code above fits the XCDM model to the Union2.1 dataset, which contains supernova type Ia data. It computes the best-fit parameters for the model and the covariance matrix of the parameters using the Fisher matrix.\n\nlhr2d = Ncm.LHRatio2d.new(\n    fit,\n    mset.fparam_get_pi_by_name(\"Omegac\"),\n    mset.fparam_get_pi_by_name(\"w\"),\n    1.0e-3,\n)\n\nbest_fit = pd.DataFrame(\n    {\n        \"Omegac\": [cosmo.props.Omegac],\n        \"w\": [cosmo.props.w],\n        \"sigma\": \"Best-fit\",\n        \"region\": \"Best-fit\",\n    }\n)\n\n\nregions_pd_list = []\nfor i, sigma in enumerate(\n    [Ncm.C.stats_1sigma(), Ncm.C.stats_2sigma(), Ncm.C.stats_3sigma()]\n):\n    fisher_rg = lhr2d.fisher_border(sigma, 300.0, Ncm.FitRunMsgs.NONE)\n    Omegac_a = np.array(fisher_rg.p1.dup_array())\n    w_a = np.array(fisher_rg.p2.dup_array())\n    regions_pd_list.append(\n        pd.DataFrame(\n            {\n                \"Omegac\": Omegac_a,\n                \"w\": w_a,\n                \"sigma\": rf\"{i+1}$\\sigma$\",\n                \"region\": \"Fisher\",\n            }\n        )\n    )\n\nregions_pd = pd.concat(regions_pd_list)\n\nThe code above computes the confidence regions for the best-fit parameters using the Fisher matrix.\n\n\nCode\n(\n    ggplot(regions_pd, aes(\"Omegac\", \"w\", fill=\"sigma\", color=\"sigma\"))\n    + geom_polygon(alpha=0.3)\n    + geom_point(data=best_fit)\n    + labs(x=r\"$\\Omega_c$\", y=r\"$w$\", fill=r\"Confidence\")\n    + guides(fill=guide_legend(), color=False)\n    + doc_theme()\n)\n\n\n\n\n\n\n\n\nFigure 2: Best-fit parameters and confidence regions for the XCDM model.",
+    "text": "Fitting Model to Data\nOnce models are defined and the free parameters are set, they can be analyzed using a variety of statistical methods. For example, the best-fit parameters for a given model can be found by maximizing the likelihood function.\n\n\nCode\ncosmo.props.w_fit = True\ncosmo.props.Omegac_fit = True\nmset.prepare_fparam_map()\n\nlh = Ncm.Likelihood(\n    dataset=Ncm.Dataset.new_array(\n        [Nc.DataDistMu.new_from_id(dist, Nc.DataSNIAId.SIMPLE_UNION2_1)]\n    )\n)\nfit = Ncm.Fit.factory(\n    Ncm.FitType.NLOPT, \"ln-neldermead\", lh, mset, Ncm.FitGradType.NUMDIFF_FORWARD\n)\nfit.run(Ncm.FitRunMsgs.SIMPLE)\nfit.log_info()\nfit.fisher()\nfit.log_covar()\n\n\n#----------------------------------------------------------------------------------\n# Model fitting. Interating using:\n#  - solver:            NLOpt:ln-neldermead\n#  - differentiation:   Numerical differentiantion (forward)\n#................\n#  Minimum found with precision: |df|/f =  1.00000e-08 and |dx| =  1.00000e-05\n#  Elapsed time: 00 days, 00:00:00.8229960\n#  iteration            [000074]\n#  function evaluations [000076]\n#  gradient evaluations [000000]\n#  degrees of freedom   [000577]\n#  m2lnL     =     562.219163105056 (     562.21916 )\n#  Fit parameters:\n#     0.230499952926549     -1.02959391499341      \n#----------------------------------------------------------------------------------\n# Data used:\n#   - Union2.1 sample\n#----------------------------------------------------------------------------------\n# Model[03000]:\n#   - NcHICosmo : XCDM - Constant EOS\n#----------------------------------------------------------------------------------\n# Model parameters\n#   -      H0[00]:  67.36               [FIXED]\n#   -  Omegac[01]:  0.230499952926549   [FREE]\n#   -  Omegax[02]:  0.7                 [FIXED]\n#   - Tgamma0[03]:  2.7245              [FIXED]\n#   -      Yp[04]:  0.24                [FIXED]\n#   -    ENnu[05]:  3.046               [FIXED]\n#   -  Omegab[06]:  0.05                [FIXED]\n#   -       w[07]: -1.02959391499341    [FREE]\n#----------------------------------------------------------------------------------\n# NcmMSet parameters covariance matrix\n#                                                  -------------------------------\n# Omegac[03000:01] =  0.2305      +/-  0.06233     |  1           | -0.9297      |\n#      w[03000:07] = -1.03        +/-  0.08595     | -0.9297      |  1           |\n#                                                  -------------------------------\n\n\nThe code above fits the XCDM model to the Union2.1 dataset, which contains supernova type Ia data. It computes the best-fit parameters for the model and the covariance matrix of the parameters using the Fisher matrix.\n\nlhr2d = Ncm.LHRatio2d.new(\n    fit,\n    mset.fparam_get_pi_by_name(\"Omegac\"),\n    mset.fparam_get_pi_by_name(\"w\"),\n    1.0e-3,\n)\n\nbest_fit = pd.DataFrame(\n    {\n        \"Omegac\": [cosmo.props.Omegac],\n        \"w\": [cosmo.props.w],\n        \"sigma\": \"Best-fit\",\n        \"region\": \"Best-fit\",\n    }\n)\n\n\nregions_pd_list = []\nfor i, sigma in enumerate(\n    [Ncm.C.stats_1sigma(), Ncm.C.stats_2sigma(), Ncm.C.stats_3sigma()]\n):\n    fisher_rg = lhr2d.fisher_border(sigma, 300.0, Ncm.FitRunMsgs.NONE)\n    Omegac_a = np.array(fisher_rg.p1.dup_array())\n    w_a = np.array(fisher_rg.p2.dup_array())\n    regions_pd_list.append(\n        pd.DataFrame(\n            {\n                \"Omegac\": Omegac_a,\n                \"w\": w_a,\n                \"sigma\": rf\"{i+1}$\\sigma$\",\n                \"region\": \"Fisher\",\n            }\n        )\n    )\n\nregions_pd = pd.concat(regions_pd_list)\n\nThe code above computes the confidence regions for the best-fit parameters using the Fisher matrix.\n\n\nCode\n(\n    ggplot(regions_pd, aes(\"Omegac\", \"w\", fill=\"sigma\", color=\"sigma\"))\n    + geom_polygon(alpha=0.3)\n    + geom_point(data=best_fit)\n    + labs(x=r\"$\\Omega_c$\", y=r\"$w$\", fill=r\"Confidence\")\n    + guides(fill=guide_legend(), color=False)\n    + doc_theme()\n)\n\n\n\n\n\n\n\n\nFigure 2: Best-fit parameters and confidence regions for the XCDM model.",
     "crumbs": [
       "About NumCosmo",
       "Examples",