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<span class="Comment">/*</span><span class="Comment">*************************************************************************\</span>

<span class="Comment">MODULE: matrix</span>

<span class="Comment">SUMMARY:</span>

<span class="Comment">Matrix templates.</span>

<span class="Comment">The declaration </span>

<span class="Comment">   Mat&lt;T&gt; M;</span>

<span class="Comment">creates a 0 x 0 matrix.  </span>

<span class="Comment">We can make it have 10 rows and 20 columns like this:</span>

<span class="Comment">   M.SetDims(10, 20);</span>

<span class="Comment">A row can be accessed as M[i], indexing from 0, or as M(i), indexing from 1.</span>
<span class="Comment">A matrix entry can be accessed as M[i][j], indexing from 0, or as</span>
<span class="Comment">M(i, j), indexing from 1.</span>

<span class="Comment">A matrix is represented as a Vec&lt; Vec&lt;T&gt; &gt;: a vector of rows, where</span>
<span class="Comment">each row is a Vec&lt;T&gt;.  Any attempt to resize one of the rows so</span>
<span class="Comment">as to create a non-rectangular matrix will result in a run-time </span>
<span class="Comment">error.</span>

<span class="Comment">The dimensions of an existing matrix may be changed.  If the number of</span>
<span class="Comment">columns does not change, then the matrix is just &quot;resized&quot; like a vector,</span>
<span class="Comment">and no information is lost.  Otherwise, if the number of columns changes,</span>
<span class="Comment">the matrix is completely destroyed, and a new matrix is created</span>


<span class="Comment">\*************************************************************************</span><span class="Comment">*/</span>


<span class="Comment">// EXCEPTIONS: all functions below do not throw any exceptions,</span>
<span class="Comment">//   except as noted</span>

<span class="Type">template</span>&lt;<span class="Type">class</span> T&gt;
<span class="Type">class</span> Mat {

   <span class="Type">typedef</span> <span class="Type">typename</span> Vec&lt;T&gt;::value_type value_type;
   <span class="Type">typedef</span> <span class="Type">typename</span> Vec&lt;T&gt;::reference reference;
   <span class="Type">typedef</span> <span class="Type">typename</span> Vec&lt;T&gt;::const_reference const_reference;


   Mat(); <span class="Comment">// initially 0 x 0</span>

   Mat(<span class="Type">const</span> Mat&lt;T&gt;&amp; a);
   <span class="Comment">// copy constructor</span>

   <span class="Comment">// EXCEPTIONS: may throw</span>


   Mat&amp; <span class="Statement">operator</span>=(<span class="Type">const</span> Mat&lt;T&gt;&amp; a);
   <span class="Comment">// assignment</span>

   <span class="Comment">// EXCEPTIONS: may throw, weak ES (but dimensions of LHS</span>
   <span class="Comment">//   will be either that of old LHS or RHS)</span>

   ~Mat();
   <span class="Comment">// destructor</span>

   Mat(INIT_SIZE_TYPE, <span class="Type">long</span> n, <span class="Type">long</span> m);
   <span class="Comment">// Mat(INIT_SIZE, n, m) initializes an n x m matrix, invoking</span>
   <span class="Comment">// the default constructor for T to initialize entries.</span>

   <span class="Comment">// EXCEPTIONS: may throw</span>

   <span class="Type">void</span> SetDims(<span class="Type">long</span> n, <span class="Type">long</span> m);
   <span class="Comment">// M.SetDims(n, m) makes M have dimension n x m.  If the number of</span>
   <span class="Comment">// columns (m) changes, previous storage is freed, and space for M</span>
   <span class="Comment">// is reallocated and initialized; otherwise, more rows are</span>
   <span class="Comment">// allocated as necessary (when number of rows increases), </span>
   <span class="Comment">// excess rows are retained (when number of rows decreases),</span>
   <span class="Comment">// and--importantly--the contents do not change.</span>

   <span class="Comment">// EXCEPTIONS: strong ES (although underlying vector representation</span>
   <span class="Comment">//    may be reallocated)</span>

   <span class="Type">void</span> kill(); free storage <span class="Statement">and</span> make <span class="Constant">0</span> x <span class="Constant">0</span>

   <span class="Type">long</span> NumRows() <span class="Type">const</span>;
   <span class="Comment">// M.NumRows() returns the number of rows of M</span>

   <span class="Type">long</span> NumCols() <span class="Type">const</span>;
   <span class="Comment">// M.NumCols() returns the number of columns of M</span>

   Vec&lt;T&gt;&amp; <span class="Statement">operator</span>[](<span class="Type">long</span> i);
   <span class="Type">const</span> Vec&lt;T&gt;&amp; <span class="Statement">operator</span>[](<span class="Type">long</span> i) <span class="Type">const</span>;
   <span class="Comment">// access row i, initial index 0.  </span>
   <span class="Comment">// Even if one has read/write access to a row, any attempt</span>
   <span class="Comment">// to change its length will raise an error.</span>

   <span class="Comment">// EXCEPTIONS: may throw if range checking is turned on</span>

   Vec&lt;T&gt;&amp; <span class="Statement">operator</span>()(<span class="Type">long</span> i);
   <span class="Type">const</span> Vec&lt;T&gt;&amp; <span class="Statement">operator</span>()(<span class="Type">long</span> i) <span class="Type">const</span>;
   <span class="Comment">// access row i, initial index 1. </span>
   <span class="Comment">// Even if one has read/write access to a row, any attempt</span>
   <span class="Comment">// to change its length will raise an error.</span>
   <span class="Comment">// of this row will raise an error.</span>

   <span class="Comment">// EXCEPTIONS: may throw if range checking is turned on</span>

   reference <span class="Statement">operator</span>()(<span class="Type">long</span> i, <span class="Type">long</span> j);
   const_reference <span class="Statement">operator</span>()(<span class="Type">long</span> i, <span class="Type">long</span> j) <span class="Type">const</span>;
   <span class="Comment">// access element (i, j), both indices starting at 1</span>

   <span class="Comment">// EXCEPTIONS: may throw if range checking is turned on</span>

   const_reference get(<span class="Type">long</span> i, <span class="Type">long</span> j) <span class="Type">const</span>;
   <span class="Comment">// access element (i, j), both indices starting at 0</span>

   <span class="Comment">// EXCEPTIONS: may throw if range checking is turned on</span>

   <span class="Type">void</span> put(<span class="Type">long</span> i, <span class="Type">long</span> j, <span class="Type">const</span> T&amp; a);
   <span class="Comment">// same as M[i].put(j, a)</span>

   <span class="Type">template</span> &lt;<span class="Type">class</span> U&gt;
   <span class="Type">void</span> put(<span class="Type">long</span> i, <span class="Type">long</span> j, <span class="Type">const</span> U&amp; a);
   <span class="Comment">// same as M[i].put(j, a)</span>

   <span class="Type">long</span> position(<span class="Type">const</span> Vec&lt;T&gt;&amp; a) <span class="Type">const</span>;
   <span class="Comment">// returns index of a in matrix, or -1 if not present;</span>
   <span class="Comment">// equivalent to rep(*this).position(a).</span>

   <span class="Type">long</span> position1(<span class="Type">const</span> Vec&lt;T&gt;&amp; a) <span class="Type">const</span>;
   <span class="Comment">// returns index of a in matrix, or -1 if not present;</span>
   <span class="Comment">// equivalent to rep(*this).position1(a).</span>

   <span class="Type">void</span> swap(Mat&lt;T&gt;&amp; other);
   <span class="Comment">// quick swap *this and other</span>

};

<span class="Type">template</span>&lt;<span class="Type">class</span> T&gt;
<span class="Type">const</span> Vec&lt; Vec&lt;T&gt; &gt;&amp; rep(<span class="Type">const</span> Mat&lt;T&gt;&amp; a);
<span class="Comment">// read-only access to underlying representation</span>

<span class="Type">template</span>&lt;<span class="Type">class</span> T&gt;
<span class="Type">void</span> swap(Mat&lt;T&gt;&amp; X, Mat&lt;T&gt;&amp; Y);
<span class="Comment">// quick swap of X and Y </span>

<span class="Type">template</span>&lt;<span class="Type">class</span> T&gt;
<span class="Type">void</span> MakeMatrix(Mat&lt;T&gt;&amp; x, <span class="Type">const</span> vec_vec_T&amp; a);
<span class="Comment">// copies a to x, checking that it is &quot;rectangular&quot;</span>

<span class="Comment">// EXCEPTIONS: may thow, weak ES (but dimensions of x either</span>
<span class="Comment">//    remain unchanged or are set to the new dimensions implied by a)</span>

<span class="Comment">/*</span><span class="Comment">*************************************************************************\</span>

<span class="Comment">                            Input/Output</span>

<span class="Comment">\*************************************************************************</span><span class="Comment">*/</span>


<span class="Type">template</span>&lt;<span class="Type">class</span> T&gt;
istream&amp; <span class="Statement">operator</span>&gt;&gt;(istream&amp;, Mat&lt;T&gt;&amp;);

<span class="Comment">// EXCEPTIONS: may throw, weak ES</span>

<span class="Type">template</span>&lt;<span class="Type">class</span> T&gt;
ostream&amp; <span class="Statement">operator</span>&lt;&lt;(ostream&amp;, <span class="Type">const</span> Mat&lt;T&gt;&amp;);

<span class="Comment">// EXCEPTIONS: may throw, weak ES</span>


<span class="Comment">/*</span><span class="Comment">*************************************************************************\</span>

<span class="Comment">                              Equality Testing</span>


<span class="Comment">\*************************************************************************</span><span class="Comment">*/</span>


<span class="Type">template</span>&lt;<span class="Type">class</span> T&gt;
<span class="Type">long</span> <span class="Statement">operator</span>==(<span class="Type">const</span> Mat&lt;T&gt;&amp; a, <span class="Type">const</span> Mat&lt;T&gt;&amp; b);

<span class="Type">template</span>&lt;<span class="Type">class</span> T&gt;
<span class="Type">long</span> <span class="Statement">operator</span>!=(<span class="Type">const</span> Mat&lt;T&gt;&amp; a, <span class="Type">const</span> Mat&lt;T&gt;&amp; b);

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