/*! @file

    @id $Id$
*/
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#include <matrix.hxx>

/** @mainpage Neural Network with Hidden Layers

    @section neuro-intro Overview

    A complex neural network can be imitiated as a vector @c I of @c i
    input values, a vector @c O of @c o output values and any number
    @c l of hidden layers, where each of them contains @c h
    neurons.

    A neural network with double precision is inistialized as:
    @code
    NeuroNet<double, i, o, l+1, h> net;
    @endcode

    @dot
    digraph g {
      rankdir=LR;
      ranksep=1.5;
      subgraph clusterInput {
        label="Input Layer";
        I1 [label=<I<SUB>1</SUB>>];
        I2 [label=<I<SUB>2</SUB>>];
        Ix [label=<I<SUB>…</SUB>>];
        Ii [label=<I<SUB>i</SUB>>];
      }
      subgraph clusterHidden1 {
        label="First Hidden Layer";
        H11 [label=<H<SUB>11</SUB>>];
        H12 [label=<H<SUB>12</SUB>>];
        H1x [label=<H<SUB>1…</SUB>>];
        H1h [label=<H<SUB>1h</SUB>>];
      }
      subgraph clusterHidden2 {
        label="Second Hidden Layer";
        H21 [label=<H<SUB>21</SUB>>];
        H22 [label=<H<SUB>22</SUB>>];
        H2x [label=<H<SUB>2…</SUB>>];
        H2h [label=<H<SUB>2h</SUB>>];
      }
      subgraph clusterHiddenx {
        label="More Hidden Layers";
        Hx1 [label=<H<SUB>…1</SUB>>];
        Hx2 [label=<H<SUB>…2</SUB>>];
        Hxx [label=<H<SUB>……</SUB>>];
        Hxh [label=<H<SUB>…h</SUB>>];
      }
      subgraph clusterHiddenl {
        label="Last Hidden Layer";
        Hl1 [label=<H<SUB>l1</SUB>>];
        Hl2 [label=<H<SUB>l2</SUB>>];
        Hlx [label=<H<SUB>l…</SUB>>];
        Hlh [label=<H<SUB>lh</SUB>>];
      }
      subgraph clusterOutput {
        label="Output Layer";
        O1 [label=<O<SUB>1</SUB>>];
        O2 [label=<O<SUB>2</SUB>>];
        Ox [label=<O<SUB>…</SUB>>];
        Oo [label=<O<SUB>o</SUB>>];
      }
      I1 -> { H11; H12; H1x; H1h; }
      I2 -> { H11; H12; H1x; H1h; }
      Ix -> { H11; H12; H1x; H1h; }
      Ii -> { H11; H12; H1x; H1h; }
      H11 -> { H21; H22; H2x; H2h; }
      H12 -> { H21; H22; H2x; H2h; }
      H1x -> { H21; H22; H2x; H2h; }
      H1h -> { H21; H22; H2x; H2h; }
      H21 -> { Hx1; Hx2; Hxx; Hxh; }
      H22 -> { Hx1; Hx2; Hxx; Hxh; }
      H2x -> { Hx1; Hx2; Hxx; Hxh; }
      H2h -> { Hx1; Hx2; Hxx; Hxh; }
      Hx1 -> { Hl1; Hl2; Hlx; Hlh; }
      Hx2 -> { Hl1; Hl2; Hlx; Hlh; }
      Hxx -> { Hl1; Hl2; Hlx; Hlh; }
      Hxh -> { Hl1; Hl2; Hlx; Hlh; }
      Hl1 -> { O1; O2; Ox; Oo; }
      Hl2 -> { O1; O2; Ox; Oo; }
      Hlx -> { O1; O2; Ox; Oo; }
      Hlh -> { O1; O2; Ox; Oo; }
    }
    @enddot

    @section neuro-forward Forward Propagation
    
    The connections between two layers can be modelled as a
    Matrix. Then Matrix H<sub>1</sub> contains the weights from @c I
    to the first hidden layer, @c H<sub>2</sub> from the first to the
    second, and so on, until @c H<sub>l+1</sub> contains the weights
    from layer @c l to the output @c O.
    
    The output vector is then calculated as:
    O = I × H<sub>1</sub> × H<sub>2</sub> × H<sub>…</sub> × H<sub>l+1</sub>

    @code
    const size_type i(4);
    const size_type o(2);
    NeuroNet<double, i, o> net;
    Matrix<1, i> input(1.0, 2.0, 0.0, -1.0);
    Matrix<1, o> output = net(input);
    @endcode
    
    @section neuro-backward Back Propagation
    

    */
template
    <typename TYPE,
    size_t INPUT_LAYERS,
    size_t OUTPUT_LAYERS,
    size_t HIDDEN_LAYERS = INPUT_LAYERS+OUTPUT_LAYERS,
    size_t HIDDEN_LAYER_SIZE = INPUT_LAYERS+OUTPUT_LAYERS>
class NeuroNet {
};