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<title>Reverse Mode autodiff policies</title>
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<div class="section">
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<div class="titlepage"><div><div><h3 class="title">
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<a name="math_toolkit.gd_opt.policies"></a><a class="link" href="policies.html" title="Reverse Mode autodiff policies">Reverse Mode autodiff policies</a>
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</h3></div></div></div>
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<p>
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This header provides default policy implementations for using the gradient-based
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optimizers with <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">differentiation</span><span class="special">::</span><span class="identifier">reverse_mode</span><span class="special">::</span><span class="identifier">rvar</span></code> These policies handle:
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</p>
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<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
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<li class="listitem">
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preparing the reverse-mode tape before evaluating an objective,
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</li>
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<li class="listitem">
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extracting gradients from rvar arguments after backpropagation,
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</li>
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<li class="listitem">
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initializing <code class="computeroutput"><span class="identifier">rvar</span></code> containers
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and establishing tape checkpoints.
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</li>
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</ul></div>
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<h5>
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<a name="math_toolkit.gd_opt.policies.h0"></a>
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<span class="phrase"><a name="math_toolkit.gd_opt.policies.synopsis"></a></span><a class="link" href="policies.html#math_toolkit.gd_opt.policies.synopsis">Synopsis</a>
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</h5>
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<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">optimization</span><span class="special">/</span><span class="identifier">detail</span><span class="special">/</span><span class="identifier">rdiff_optimization_policies</span><span class="special">></span>
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<span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
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<span class="keyword">namespace</span> <span class="identifier">math</span> <span class="special">{</span>
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<span class="keyword">namespace</span> <span class="identifier">optimization</span> <span class="special">{</span>
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<span class="keyword">namespace</span> <span class="identifier">rdiff</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">differentiation</span><span class="special">::</span><span class="identifier">reverse_mode</span><span class="special">;</span>
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<span class="comment">/**
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* @brief> function evaluation policy for reverse mode autodiff
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* @arg objective> objective function to evaluate
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* @arg x> argument list
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*/</span>
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<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">RealType</span><span class="special">></span>
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<span class="keyword">struct</span> <span class="identifier">reverse_mode_function_eval_policy</span>
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<span class="special">{</span>
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<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">Objective</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">ArgumentContainer</span><span class="special">></span>
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<span class="identifier">rdiff</span><span class="special">::</span><span class="identifier">rvar</span><span class="special"><</span><span class="identifier">RealType</span><span class="special">,</span> <span class="number">1</span><span class="special">></span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">Objective</span><span class="special">&&</span> <span class="identifier">objective</span><span class="special">,</span>
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<span class="identifier">ArgumentContainer</span><span class="special">&</span> <span class="identifier">x</span><span class="special">);</span>
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<span class="special">};</span>
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<span class="comment">/**
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* @brief> gradient evaluation policy
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* @arg obj_f> objective
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* @arg x> argument list
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* @arg f_eval_olicy> funciton evaluation policy. These need to be
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* done in tandem
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* @arg obj_v> reference to variable inside gradient class
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*/</span>
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<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">RealType</span><span class="special">></span>
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<span class="keyword">struct</span> <span class="identifier">reverse_mode_gradient_evaluation_policy</span>
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<span class="special">{</span>
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<span class="keyword">template</span><span class="special"><</span><span class="keyword">class</span> <span class="identifier">Objective</span><span class="special">,</span>
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<span class="keyword">class</span> <span class="identifier">ArgumentContainer</span><span class="special">,</span>
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<span class="keyword">class</span> <span class="identifier">FunctionEvaluationPolicy</span><span class="special">></span>
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<span class="keyword">void</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">Objective</span><span class="special">&&</span> <span class="identifier">obj_f</span><span class="special">,</span>
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<span class="identifier">ArgumentContainer</span><span class="special">&</span> <span class="identifier">x</span><span class="special">,</span>
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<span class="identifier">FunctionEvaluationPolicy</span><span class="special">&&</span> <span class="identifier">f_eval_pol</span><span class="special">,</span>
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<span class="identifier">RealType</span><span class="special">&</span> <span class="identifier">obj_v</span><span class="special">,</span>
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<span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</span><span class="identifier">RealType</span><span class="special">>&</span> <span class="identifier">g</span><span class="special">)</span>
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<span class="special">};</span>
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<span class="comment">/*
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* init policies
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*/</span>
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<span class="comment">/* default rvar policy */</span>
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<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">RealType</span><span class="special">></span>
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<span class="keyword">struct</span> <span class="identifier">tape_initializer_rvar</span>
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<span class="special">{</span>
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<span class="keyword">template</span><span class="special"><</span><span class="keyword">class</span> <span class="identifier">ArgumentContainer</span><span class="special">></span>
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<span class="keyword">void</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">ArgumentContainer</span><span class="special">&</span> <span class="identifier">x</span><span class="special">)</span> <span class="keyword">const</span> <span class="keyword">noexcept</span><span class="special">;</span>
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<span class="special">};</span>
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<span class="comment">/* random uniform */</span>
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<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">RealType</span><span class="special">></span>
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<span class="keyword">struct</span> <span class="identifier">random_uniform_initializer_rvar</span>
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<span class="special">{</span>
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<span class="identifier">RealType</span> <span class="identifier">low_</span><span class="special">,</span> <span class="identifier">high_</span><span class="special">;</span>
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<span class="identifier">size_t</span> <span class="identifier">seed_</span><span class="special">;</span>
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<span class="identifier">random_uniform_initializer_rvar</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">low</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span>
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<span class="identifier">RealType</span> <span class="identifier">high</span> <span class="special">=</span> <span class="number">1</span><span class="special">,</span>
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<span class="identifier">size_t</span> <span class="identifier">seed</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">random_device</span><span class="special">{}());</span>
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<span class="keyword">template</span><span class="special"><</span><span class="keyword">class</span> <span class="identifier">ArgumentContainer</span><span class="special">></span>
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<span class="keyword">void</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">ArgumentContainer</span><span class="special">&</span> <span class="identifier">x</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
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<span class="special">};</span>
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<span class="comment">/* constant initializer */</span>
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<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">RealType</span><span class="special">></span>
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<span class="keyword">struct</span> <span class="identifier">costant_initializer_rvar</span>
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<span class="special">{</span>
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<span class="identifier">RealType</span> <span class="identifier">constant</span><span class="special">;</span>
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<span class="keyword">explicit</span> <span class="identifier">costant_initializer_rvar</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">v</span> <span class="special">=</span> <span class="number">0</span><span class="special">);</span>
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<span class="keyword">template</span><span class="special"><</span><span class="keyword">class</span> <span class="identifier">ArgumentContainer</span><span class="special">></span>
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<span class="keyword">void</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">ArgumentContainer</span><span class="special">&</span> <span class="identifier">x</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
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<span class="special">};</span>
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<span class="special">}</span> <span class="comment">// namespace optimization</span>
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<span class="special">}</span> <span class="comment">// namespace math</span>
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<span class="special">}</span> <span class="comment">// namespace boost</span>
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</pre>
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<h5>
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<a name="math_toolkit.gd_opt.policies.h1"></a>
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<span class="phrase"><a name="math_toolkit.gd_opt.policies.function_evaluation_policies"></a></span><a class="link" href="policies.html#math_toolkit.gd_opt.policies.function_evaluation_policies">Function
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evaluation policies</a>
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</h5>
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<p>
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A function evaluation policy defines how an objective is evaluated at the
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current parameters, and is responsible for any AD bookkeeping required before
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the call.
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</p>
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<h5>
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<a name="math_toolkit.gd_opt.policies.h2"></a>
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<span class="phrase"><a name="math_toolkit.gd_opt.policies.reverse_mode_function_eval_polic"></a></span><a class="link" href="policies.html#math_toolkit.gd_opt.policies.reverse_mode_function_eval_polic">reverse_mode_function_eval_policy</a>
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</h5>
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<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">RealType</span><span class="special">></span> <span class="keyword">struct</span> <span class="identifier">reverse_mode_function_eval_policy</span> <span class="special">{</span> <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">Objective</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">ArgumentContainer</span><span class="special">></span> <span class="identifier">rdiff</span><span class="special">::</span><span class="identifier">rvar</span><span class="special"><</span><span class="identifier">RealType</span><span class="special">,</span> <span class="number">1</span><span class="special">></span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">Objective</span><span class="special">&&</span> <span class="identifier">objective</span><span class="special">,</span> <span class="identifier">ArgumentContainer</span><span class="special">&</span> <span class="identifier">x</span><span class="special">);</span> <span class="special">};</span>
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</pre>
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<p>
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This policy evaluates the objective objective(x) using reverse-mode AD and
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ensures the active tape is in a valid state before evaluation:
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</p>
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<p>
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ArgumentContainer must contain rdiff::rvar<RealType,1> values.
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</p>
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<h5>
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<a name="math_toolkit.gd_opt.policies.h3"></a>
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<span class="phrase"><a name="math_toolkit.gd_opt.policies.gradient_evaluation_policies"></a></span><a class="link" href="policies.html#math_toolkit.gd_opt.policies.gradient_evaluation_policies">Gradient
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evaluation policies</a>
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</h5>
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<p>
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A gradient evaluation policy defines how gradients are computed and extracted
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into an ordinary numeric container.
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</p>
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<h5>
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<a name="math_toolkit.gd_opt.policies.h4"></a>
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<span class="phrase"><a name="math_toolkit.gd_opt.policies.reverse_mode_gradient_evaluation"></a></span><a class="link" href="policies.html#math_toolkit.gd_opt.policies.reverse_mode_gradient_evaluation">reverse_mode_gradient_evaluation_policy</a>
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</h5>
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<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">RealType</span><span class="special">></span> <span class="keyword">struct</span> <span class="identifier">reverse_mode_gradient_evaluation_policy</span> <span class="special">{</span> <span class="keyword">template</span><span class="special"><</span><span class="keyword">class</span> <span class="identifier">Objective</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">ArgumentContainer</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">FunctionEvaluationPolicy</span><span class="special">></span> <span class="keyword">void</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">Objective</span><span class="special">&&</span> <span class="identifier">obj_f</span><span class="special">,</span> <span class="identifier">ArgumentContainer</span><span class="special">&</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">FunctionEvaluationPolicy</span><span class="special">&&</span> <span class="identifier">f_eval_pol</span><span class="special">,</span> <span class="identifier">RealType</span><span class="special">&</span> <span class="identifier">obj_v</span><span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</span><span class="identifier">RealType</span><span class="special">>&</span> <span class="identifier">g</span><span class="special">);</span> <span class="special">};</span>
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</pre>
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<p>
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This policy computes the objective value and gradient using reverse-mode
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autodiff
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</p>
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<h5>
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<a name="math_toolkit.gd_opt.policies.h5"></a>
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<span class="phrase"><a name="math_toolkit.gd_opt.policies.initialization_policies"></a></span><a class="link" href="policies.html#math_toolkit.gd_opt.policies.initialization_policies">Initialization
|
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policies</a>
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</h5>
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<p>
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Initialization policies prepare the argument container and the reverse-mode
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tape for optimization. They establish tape checkpoints that are later used
|
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by function/gradient evaluation policies.
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</p>
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<h5>
|
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<a name="math_toolkit.gd_opt.policies.h6"></a>
|
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<span class="phrase"><a name="math_toolkit.gd_opt.policies.tape_initializer_rvar"></a></span><a class="link" href="policies.html#math_toolkit.gd_opt.policies.tape_initializer_rvar">tape_initializer_rvar</a>
|
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</h5>
|
||
<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">RealType</span><span class="special">></span> <span class="keyword">struct</span> <span class="identifier">tape_initializer_rvar</span> <span class="special">{</span> <span class="keyword">template</span><span class="special"><</span><span class="keyword">class</span> <span class="identifier">ArgumentContainer</span><span class="special">></span> <span class="keyword">void</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">ArgumentContainer</span><span class="special">&</span> <span class="identifier">x</span><span class="special">)</span> <span class="keyword">const</span> <span class="keyword">noexcept</span><span class="special">;</span> <span class="special">};</span>
|
||
</pre>
|
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<p>
|
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This policy: * statically requires <code class="computeroutput"><span class="identifier">ArgumentContainer</span><span class="special">::</span><span class="identifier">value_type</span></code>
|
||
to be <code class="computeroutput"><span class="identifier">rdiff</span><span class="special">::</span><span class="identifier">rvar</span><span class="special"><</span><span class="identifier">RealType</span><span class="special">,</span><span class="number">1</span><span class="special">></span></code>, * adds
|
||
a checkpoint to the active reverse-mode tape via <code class="computeroutput"><span class="identifier">tape</span><span class="special">.</span><span class="identifier">add_checkpoint</span><span class="special">()</span></code>
|
||
</p>
|
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<h5>
|
||
<a name="math_toolkit.gd_opt.policies.h7"></a>
|
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<span class="phrase"><a name="math_toolkit.gd_opt.policies.random_uniform_initializer_rvar"></a></span><a class="link" href="policies.html#math_toolkit.gd_opt.policies.random_uniform_initializer_rvar">random_uniform_initializer_rvar</a>
|
||
</h5>
|
||
<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">RealType</span><span class="special">></span>
|
||
<span class="keyword">struct</span> <span class="identifier">random_uniform_initializer_rvar</span>
|
||
<span class="special">{</span>
|
||
<span class="identifier">random_uniform_initializer_rvar</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">low</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span>
|
||
<span class="identifier">RealType</span> <span class="identifier">high</span> <span class="special">=</span> <span class="number">1</span><span class="special">,</span>
|
||
<span class="identifier">size_t</span> <span class="identifier">seed</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">random_device</span><span class="special">{}());</span>
|
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<span class="keyword">template</span><span class="special"><</span><span class="keyword">class</span> <span class="identifier">ArgumentContainer</span><span class="special">></span>
|
||
<span class="keyword">void</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">ArgumentContainer</span><span class="special">&</span> <span class="identifier">x</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
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<span class="special">};</span>
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</pre>
|
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<p>
|
||
This policy initializes each element of x independently as:
|
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</p>
|
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<pre class="programlisting"><span class="identifier">x</span><span class="special">[</span><span class="identifier">i</span><span class="special">]</span> <span class="special">=</span> <span class="identifier">rdiff</span><span class="special">::</span><span class="identifier">rvar</span><span class="special"><</span><span class="identifier">RealType</span><span class="special">,</span><span class="number">1</span><span class="special">>(</span><span class="identifier">U</span><span class="special">(</span><span class="identifier">low</span><span class="special">,</span> <span class="identifier">high</span><span class="special">))</span>
|
||
</pre>
|
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<p>
|
||
using
|
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</p>
|
||
<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">random</span><span class="special">::</span><span class="identifier">mt19937</span>
|
||
</pre>
|
||
<p>
|
||
and
|
||
</p>
|
||
<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">random</span><span class="special">::</span><span class="identifier">uniform_real_distribution</span><span class="special"><</span><span class="identifier">RealType</span><span class="special">></span>
|
||
</pre>
|
||
<h5>
|
||
<a name="math_toolkit.gd_opt.policies.h8"></a>
|
||
<span class="phrase"><a name="math_toolkit.gd_opt.policies.costant_initializer_rvar"></a></span><a class="link" href="policies.html#math_toolkit.gd_opt.policies.costant_initializer_rvar">costant_initializer_rvar</a>
|
||
</h5>
|
||
<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">RealType</span><span class="special">></span>
|
||
<span class="keyword">struct</span> <span class="identifier">costant_initializer_rvar</span>
|
||
<span class="special">{</span>
|
||
<span class="keyword">explicit</span> <span class="identifier">costant_initializer_rvar</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">v</span> <span class="special">=</span> <span class="number">0</span><span class="special">);</span>
|
||
|
||
<span class="keyword">template</span><span class="special"><</span><span class="keyword">class</span> <span class="identifier">ArgumentContainer</span><span class="special">></span>
|
||
<span class="keyword">void</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">ArgumentContainer</span><span class="special">&</span> <span class="identifier">x</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
|
||
<span class="special">};</span>
|
||
</pre>
|
||
<p>
|
||
This policy initializes each element of x to the constant value v
|
||
</p>
|
||
</div>
|
||
<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
|
||
Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
|
||
Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||
Walker, Xiaogang Zhang, and Maksym Zhelyeznyakov<p>
|
||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
||
</p>
|
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</div>
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