ForBrent.html

<pre class="sourceCode haskell"><code class="sourceCode haskell"><span style="">&gt;</span> <span style="color: green;">{-# OPTIONS_GHC -Wall                      #-}</span>
<span style="">&gt;</span> <span style="color: green;">{-# OPTIONS_GHC -fno-warn-name-shadowing   #-}</span>
<span style="">&gt;</span> <span style="color: green;">{-# OPTIONS_GHC -fno-warn-type-defaults    #-}</span>
<span style="">&gt;</span> <span style="color: green;">{-# OPTIONS_GHC -fno-warn-unused-do-bind   #-}</span>
<span style="">&gt;</span> <span style="color: green;">{-# OPTIONS_GHC -fno-warn-missing-methods  #-}</span>
<span style="">&gt;</span> <span style="color: green;">{-# OPTIONS_GHC -fno-warn-orphans          #-}</span>
<span style="">&gt;</span> 
<span style="">&gt;</span> <span style="color: blue; font-weight: bold;">import</span> <span style="">Symplectic</span>
<span style="">&gt;</span> 
<span style="">&gt;</span> <span style="">main</span> <span style="color: red;">::</span> <span style="">IO</span> <span style="">()</span>
<span style="">&gt;</span> <span style="">main</span> <span style="color: red;">=</span> <span style="color: blue; font-weight: bold;">do</span>
<span style="">&gt;</span>   <span style="">putStrLn</span> <span style="">$</span> <span style="">show</span> <span style="">$</span> <span style="">reallyRunSteps'</span> <span class="hs-num">10</span>
</code></pre>
<pre class="sourceCode haskell"><code class="sourceCode haskell"><span style="color: green;">{-# OPTIONS_GHC -Wall                      #-}</span>
<span style="color: green;">{-# OPTIONS_GHC -fno-warn-name-shadowing   #-}</span>
<span style="color: green;">{-# OPTIONS_GHC -fno-warn-type-defaults    #-}</span>
<span style="color: green;">{-# OPTIONS_GHC -fno-warn-unused-do-bind   #-}</span>
<span style="color: green;">{-# OPTIONS_GHC -fno-warn-missing-methods  #-}</span>
<span style="color: green;">{-# OPTIONS_GHC -fno-warn-orphans          #-}</span>

<span style="color: blue; font-weight: bold;">import</span> <span style="">Symplectic</span>

<span style="">main</span> <span style="color: red;">::</span> <span style="">IO</span> <span style="">()</span>
<span style="">main</span> <span style="color: red;">=</span> <span style="color: blue; font-weight: bold;">do</span>
  <span style="">putStrLn</span> <span style="">$</span> <span style="">show</span> <span style="">$</span> <span style="">reallyRunSteps'</span> <span class="hs-num">10</span></code></pre>
<div class="sourceCode"><table class="sourceCode python numberLines"><tr class="sourceCode"><td class="lineNumbers"><pre>1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
</pre></td><td class="sourceCode"><pre><code class="sourceCode python"><span class="kw">def</span> gauss(alpha,beta):
    <span class="co">&quot;&quot;&quot;</span>
<span class="co">    Compute the Gauss nodes and weights from the recursion</span>
<span class="co">    coefficients associated with a set of orthogonal polynomials</span>

<span class="co">    Inputs:</span>
<span class="co">    alpha - recursion coefficients</span>
<span class="co">    beta - recursion coefficients</span>

<span class="co">    Outputs:</span>
<span class="co">    x - quadrature nodes</span>
<span class="co">    w - quadrature weights</span>

<span class="co">    Adapted from the MATLAB code by Walter Gautschi</span>
<span class="co">    http://www.cs.purdue.edu/archives/2002/wxg/codes/gauss.m</span>
<span class="co">    &quot;&quot;&quot;</span>

    <span class="im">from</span> scipy.linalg <span class="im">import</span> eig_banded

    A <span class="op">=</span> np.vstack((np.sqrt(beta),alpha))
    x,V <span class="op">=</span> eig_banded(A,lower<span class="op">=</span><span class="va">False</span>)
    w <span class="op">=</span> beta[<span class="dv">0</span>]<span class="op">*</span>sp.real(sp.power(V[<span class="dv">0</span>,:],<span class="dv">2</span>))
    <span class="cf">return</span> x,w</code></pre></td></tr></table></div>

ForBrent.lhs

% Rao-Blackwellisation
% Dominic Steinitz
% 9th April 2017

> {-# OPTIONS_GHC -Wall                      #-}
> {-# OPTIONS_GHC -fno-warn-name-shadowing   #-}
> {-# OPTIONS_GHC -fno-warn-type-defaults    #-}
> {-# OPTIONS_GHC -fno-warn-unused-do-bind   #-}
> {-# OPTIONS_GHC -fno-warn-missing-methods  #-}
> {-# OPTIONS_GHC -fno-warn-orphans          #-}
>
> import Symplectic
>
> main :: IO ()
> main = do
>   putStrLn $ show $ reallyRunSteps' 10

``` {.haskell .numberLines include="RunAccGPU.hs"}
{-# OPTIONS_GHC -Wall                      #-}
{-# OPTIONS_GHC -fno-warn-name-shadowing   #-}
{-# OPTIONS_GHC -fno-warn-type-defaults    #-}
{-# OPTIONS_GHC -fno-warn-unused-do-bind   #-}
{-# OPTIONS_GHC -fno-warn-missing-methods  #-}
{-# OPTIONS_GHC -fno-warn-orphans          #-}

import Symplectic

main :: IO ()
main = do
  putStrLn $ show $ reallyRunSteps' 10
```

``` {.python .numberLines}
def gauss(alpha,beta):
    """
    Compute the Gauss nodes and weights from the recursion
    coefficients associated with a set of orthogonal polynomials

    Inputs:
    alpha - recursion coefficients
    beta - recursion coefficients

    Outputs:
    x - quadrature nodes
    w - quadrature weights

    Adapted from the MATLAB code by Walter Gautschi
    http://www.cs.purdue.edu/archives/2002/wxg/codes/gauss.m
    """

    from scipy.linalg import eig_banded

    A = np.vstack((np.sqrt(beta),alpha))
    x,V = eig_banded(A,lower=False)
    w = beta[0]*sp.real(sp.power(V[0,:],2))
    return x,w
```

ForBrent.sh

Library/Haskell/ghc-8.0.2/lib/BlogLiterately-0.8.4.3/bin/BlogLiterately --math=mathjax ForBrent.lhs > ForBrent.html