Corrected a typo in GD
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@@ -630,45 +630,6 @@ Subtracting this equation from that of $\hat{x}_{i+1}$ we have
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!et
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!eblock
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!split
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===== Simple example and demonstration =====
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!bblock
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The function $f$ can be either the energy or the variance. If we choose the energy then we have
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!bt
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\begin{equation*}
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\hat{\alpha}_{i+1}-\hat{\alpha}_i=\hat{A}^{-1}(\nabla E(\hat{\alpha}_{i+1})-\nabla E(\hat{\alpha}_i)).
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\end{equation*}
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!et
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In the simple harmonic oscillator model, the gradient and the Hessian $\hat{A}$ are
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!bt
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\begin{equation*}
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\frac{d\langle E_L[\alpha]\rangle}{d\alpha} = \alpha-\frac{1}{4\alpha^3}
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\end{equation*}
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!et
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and a second derivative which is always positive (meaning that we find a minimum)
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!bt
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\begin{equation*}
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\hat{A}= \frac{d^2\langle E_L[\alpha]\rangle}{d\alpha^2} = 1+\frac{3}{4\alpha^4}
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\end{equation*}
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!et
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!eblock
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!split
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===== Simple example and demonstration =====
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!bblock
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We get then
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!bt
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\begin{equation*}
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\alpha_{i+1}=\frac{4}{3}\alpha_i-\frac{\alpha_i^4}{3\alpha_{i+1}^3},
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\end{equation*}
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!et
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which can be rewritten as
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!bt
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\begin{equation*}
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\alpha_{i+1}^4-\frac{4}{3}\alpha_i\alpha_{i+1}^4+\frac{1}{3}\alpha_i^4.
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\end{equation*}
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!et
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!eblock
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!split
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===== Conjugate gradient method =====
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@@ -44,11 +44,12 @@ system doconce split_html $html.html --method=space10
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# Bootstrap style
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html=${name}-bs
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system doconce format html $name --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=$html $opt
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#system doconce split_html $html.html --method=split --pagination --nav_button=bottom
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system doconce split_html $html.html --method=split --pagination --nav_button=bottom
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# IPython notebook
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system doconce format ipynb $name $opt
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# Ordinary plain LaTeX document
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rm -f *.aux # important after beamer
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system doconce format pdflatex $name --minted_latex_style=trac --latex_admon=paragraph $opt
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