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      <h1 class="title">manu</h1>
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    <ul class="simple simple-toc" id="toc-list">
  <li><a class="reference" id="manu-minus-nim-matrix-library_toc" href="#manu-minus-nim-matrix-library">Manu - Nim Matrix library</a></li>
<li>
  <a class="reference reference-toplevel" href="#6" id="56">Imports</a>
</li>
<li>
  <details open>
    <summary><a class="reference reference-toplevel" href="#12" id="62">Procs</a></summary>
    <ul class="simple simple-toc-section">
      <ul class="simple nested-toc-section">cond
  <li><a class="reference" href="#cond%2CsinkMatrix%5BT%5D" title="cond[T](m: sink Matrix[T]): T">cond[T](m: sink Matrix[T]): T</a></li>

</ul>
<ul class="simple nested-toc-section">det
  <li><a class="reference" href="#det%2CsinkMatrix%5BT%5D" title="det[T](m: sink Matrix[T]): T">det[T](m: sink Matrix[T]): T</a></li>

</ul>
<ul class="simple nested-toc-section">inverse
  <li><a class="reference" href="#inverse%2CsinkMatrix%5BT%5D" title="inverse[T](m: sink Matrix[T]): Matrix[T]">inverse[T](m: sink Matrix[T]): Matrix[T]</a></li>

</ul>
<ul class="simple nested-toc-section">norm2
  <li><a class="reference" href="#norm2%2CsinkMatrix%5BT%5D" title="norm2[T](m: sink Matrix[T]): T">norm2[T](m: sink Matrix[T]): T</a></li>

</ul>
<ul class="simple nested-toc-section">rank
  <li><a class="reference" href="#rank%2CsinkMatrix%5BT%5D" title="rank[T](m: sink Matrix[T]): int">rank[T](m: sink Matrix[T]): int</a></li>

</ul>
<ul class="simple nested-toc-section">solve
  <li><a class="reference" href="#solve%2CsinkMatrix%5BT%5D%2CMatrix%5BT%5D" title="solve[T](a: sink Matrix[T]; b: Matrix[T]): Matrix[T]">solve[T](a: sink Matrix[T]; b: Matrix[T]): Matrix[T]</a></li>

</ul>
<ul class="simple nested-toc-section">solveTranspose
  <li><a class="reference" href="#solveTranspose%2CMatrix%5BT%5D%2CMatrix%5BT%5D" title="solveTranspose[T](a, b: Matrix[T]): Matrix[T]">solveTranspose[T](a, b: Matrix[T]): Matrix[T]</a></li>

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  <a class="reference reference-toplevel" href="#19" id="69">Exports</a>
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  <div class="nine columns" id="content">
    <a href="https://github.com/planetis-m/manu/tree/master/manu.nim#L1" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
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    <p class="module-desc">
<h1><a class="toc-backref" id="manu-minus-nim-matrix-library" href="#manu-minus-nim-matrix-library">Manu - Nim Matrix library</a></h1><p>The manu module provides the fundamental operations of numerical linear algebra. Various constructors create Matrices from two dimensional arrays of double precision floating point numbers. Various &quot;gets&quot; and &quot;sets&quot; provide access to submatrices and matrix elements.  Several methods implement basic matrix arithmetic, including matrix addition and multiplication, matrix norms, and element-by-element array operations. Methods for reading and printing matrices are also included. All the operations in this version of the Matrix object involve real matrices. Complex matrices may be handled in a future version.</p>
<p>Five fundamental matrix decompositions, which consist of pairs or triples of matrices, permutation vectors, and the like, produce results in five decomposition classes. These decompositions are accessed by the manu module to compute solutions of simultaneous linear equations, determinants, inverses and other matrix functions. The five decompositions are:</p>
<ul class="simple"><li>Cholesky Decomposition of symmetric, positive definite matrices.</li>
<li>LU Decomposition of rectangular matrices.</li>
<li>QR Decomposition of rectangular matrices.</li>
<li>Singular Value Decomposition of rectangular matrices.</li>
<li>Eigenvalue Decomposition of both symmetric and nonsymmetric square matrices.</li>
</ul>

<p><strong class="examples_text">Example:</strong></p>
<pre class="listing"><span class="Keyword">import</span> <span class="Identifier">manu</span>
<span class="Comment"># Solve a linear system A x = b and compute the residual norm, ||b - A x||.</span>
<span class="Keyword">let</span> <span class="Identifier">vals</span> <span class="Operator">=</span> <span class="Operator">@</span><span class="Punctuation">[</span><span class="Operator">@</span><span class="Punctuation">[</span><span class="FloatNumber">1.0</span><span class="Punctuation">,</span> <span class="DecNumber">2</span><span class="Punctuation">,</span> <span class="DecNumber">3</span><span class="Punctuation">]</span><span class="Punctuation">,</span> <span class="Operator">@</span><span class="Punctuation">[</span><span class="FloatNumber">4.0</span><span class="Punctuation">,</span> <span class="DecNumber">5</span><span class="Punctuation">,</span> <span class="DecNumber">6</span><span class="Punctuation">]</span><span class="Punctuation">,</span> <span class="Operator">@</span><span class="Punctuation">[</span><span class="FloatNumber">7.0</span><span class="Punctuation">,</span> <span class="DecNumber">8</span><span class="Punctuation">,</span> <span class="DecNumber">10</span><span class="Punctuation">]</span><span class="Punctuation">]</span>
<span class="Keyword">let</span> <span class="Identifier">A</span> <span class="Operator">=</span> <span class="Identifier">matrix</span><span class="Punctuation">(</span><span class="Identifier">vals</span><span class="Punctuation">)</span>
<span class="Keyword">let</span> <span class="Identifier">b</span> <span class="Operator">=</span> <span class="Identifier">randMatrix64</span><span class="Punctuation">(</span><span class="DecNumber">3</span><span class="Punctuation">,</span> <span class="DecNumber">1</span><span class="Punctuation">)</span>
<span class="Keyword">let</span> <span class="Identifier">x</span> <span class="Operator">=</span> <span class="Identifier">A</span><span class="Operator">.</span><span class="Identifier">solve</span><span class="Punctuation">(</span><span class="Identifier">b</span><span class="Punctuation">)</span>
<span class="Keyword">let</span> <span class="Identifier">r</span> <span class="Operator">=</span> <span class="Identifier">A</span> <span class="Operator">*</span> <span class="Identifier">x</span> <span class="Operator">-</span> <span class="Identifier">b</span>
<span class="Keyword">let</span> <span class="Identifier">rnorm</span> <span class="Operator">=</span> <span class="Identifier">r</span><span class="Operator">.</span><span class="Identifier">normInf</span><span class="Punctuation">(</span><span class="Punctuation">)</span>
<span class="Identifier">echo</span><span class="Punctuation">(</span><span class="StringLit">&quot;x =</span><span class="EscapeSequence">\n</span><span class="StringLit">&quot;</span><span class="Punctuation">,</span> <span class="Identifier">x</span><span class="Punctuation">)</span>
<span class="Identifier">echo</span><span class="Punctuation">(</span><span class="StringLit">&quot;residual norm = &quot;</span><span class="Punctuation">,</span> <span class="Identifier">rnorm</span><span class="Punctuation">)</span></pre></p>
    <div class="section" id="6">
  <h1><a class="toc-backref" href="#6">Imports</a></h1>
  <dl class="item">
    <a class="reference external" href="manu/matrix.html">manu/matrix</a>, <a class="reference external" href="manu/cholesky.html">manu/cholesky</a>, <a class="reference external" href="manu/qr.html">manu/qr</a>, <a class="reference external" href="manu/lu.html">manu/lu</a>, <a class="reference external" href="manu/svd.html">manu/svd</a>, <a class="reference external" href="manu/eigen.html">manu/eigen</a>
  </dl>
</div>
<div class="section" id="12">
  <h1><a class="toc-backref" href="#12">Procs</a></h1>
  <dl class="item">
    <div id="cond-procs-all">
  <div id="cond,sinkMatrix[T]">
  <dt><pre><span class="Keyword">proc</span> <a href="#cond%2CsinkMatrix%5BT%5D"><span class="Identifier">cond</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">m</span><span class="Other">:</span> <span class="Identifier">sink</span> <a href="manu/matrix.html#Matrix"><span class="Identifier">Matrix</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <span class="Identifier">T</span></pre></dt>
  <dd>
    
    <p>Matrix condition (2 norm)</p>
<p><tt class="docutils literal"><span class="pre">return</span></tt>: ratio of largest to smallest singular value.</p>

    <a href="https://github.com/planetis-m/manu/tree/master/manu.nim#L79" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/planetis-m/manu/edit/master/manu.nim#L79" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;

  </dd>
</div>

</div>
<div id="det-procs-all">
  <div id="det,sinkMatrix[T]">
  <dt><pre><span class="Keyword">proc</span> <a href="#det%2CsinkMatrix%5BT%5D"><span class="Identifier">det</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">m</span><span class="Other">:</span> <span class="Identifier">sink</span> <a href="manu/matrix.html#Matrix"><span class="Identifier">Matrix</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <span class="Identifier">T</span></pre></dt>
  <dd>
    
    Matrix determinant
    <a href="https://github.com/planetis-m/manu/tree/master/manu.nim#L69" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/planetis-m/manu/edit/master/manu.nim#L69" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;

  </dd>
</div>

</div>
<div id="inverse-procs-all">
  <div id="inverse,sinkMatrix[T]">
  <dt><pre><span class="Keyword">proc</span> <a href="#inverse%2CsinkMatrix%5BT%5D"><span class="Identifier">inverse</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">m</span><span class="Other">:</span> <span class="Identifier">sink</span> <a href="manu/matrix.html#Matrix"><span class="Identifier">Matrix</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="manu/matrix.html#Matrix"><span class="Identifier">Matrix</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
  <dd>
    
    <p>Matrix inverse or pseudoinverse</p>
<p><tt class="docutils literal"><span class="pre">return</span></tt>: inverse(A) if A is square, pseudoinverse otherwise.</p>

    <a href="https://github.com/planetis-m/manu/tree/master/manu.nim#L62" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/planetis-m/manu/edit/master/manu.nim#L62" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;

  </dd>
</div>

</div>
<div id="norm2-procs-all">
  <div id="norm2,sinkMatrix[T]">
  <dt><pre><span class="Keyword">proc</span> <a href="#norm2%2CsinkMatrix%5BT%5D"><span class="Identifier">norm2</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">m</span><span class="Other">:</span> <span class="Identifier">sink</span> <a href="manu/matrix.html#Matrix"><span class="Identifier">Matrix</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <span class="Identifier">T</span></pre></dt>
  <dd>
    
    <p>Two norm</p>
<p><tt class="docutils literal"><span class="pre">return</span></tt>: maximum singular value.</p>

    <a href="https://github.com/planetis-m/manu/tree/master/manu.nim#L39" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/planetis-m/manu/edit/master/manu.nim#L39" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;

  </dd>
</div>

</div>
<div id="rank-procs-all">
  <div id="rank,sinkMatrix[T]">
  <dt><pre><span class="Keyword">proc</span> <a href="#rank%2CsinkMatrix%5BT%5D"><span class="Identifier">rank</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">m</span><span class="Other">:</span> <span class="Identifier">sink</span> <a href="manu/matrix.html#Matrix"><span class="Identifier">Matrix</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <span class="Identifier">int</span></pre></dt>
  <dd>
    
    <p>Matrix rank</p>
<p><tt class="docutils literal"><span class="pre">return</span></tt>: effective numerical rank, obtained from SVD.</p>

    <a href="https://github.com/planetis-m/manu/tree/master/manu.nim#L73" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/planetis-m/manu/edit/master/manu.nim#L73" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;

  </dd>
</div>

</div>
<div id="solve-procs-all">
  <div id="solve,sinkMatrix[T],Matrix[T]">
  <dt><pre><span class="Keyword">proc</span> <a href="#solve%2CsinkMatrix%5BT%5D%2CMatrix%5BT%5D"><span class="Identifier">solve</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">a</span><span class="Other">:</span> <span class="Identifier">sink</span> <a href="manu/matrix.html#Matrix"><span class="Identifier">Matrix</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">;</span> <span class="Identifier">b</span><span class="Other">:</span> <a href="manu/matrix.html#Matrix"><span class="Identifier">Matrix</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="manu/matrix.html#Matrix"><span class="Identifier">Matrix</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
  <dd>
    
    Solve <tt class="docutils literal"><span class="pre">A*X = B</span></tt><ul class="simple"><li>parameter <tt class="docutils literal"><span class="pre">b</span></tt>: the right hand side</li>
<li><tt class="docutils literal"><span class="pre">return</span></tt>: solution if A is square, least squares solution otherwise.</li>
</ul>

    <a href="https://github.com/planetis-m/manu/tree/master/manu.nim#L45" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/planetis-m/manu/edit/master/manu.nim#L45" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;

  </dd>
</div>

</div>
<div id="solveTranspose-procs-all">
  <div id="solveTranspose,Matrix[T],Matrix[T]">
  <dt><pre><span class="Keyword">proc</span> <a href="#solveTranspose%2CMatrix%5BT%5D%2CMatrix%5BT%5D"><span class="Identifier">solveTranspose</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">(</span><span class="Identifier">a</span><span class="Other">,</span> <span class="Identifier">b</span><span class="Other">:</span> <a href="manu/matrix.html#Matrix"><span class="Identifier">Matrix</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span><span class="Other">)</span><span class="Other">:</span> <a href="manu/matrix.html#Matrix"><span class="Identifier">Matrix</span></a><span class="Other">[</span><span class="Identifier">T</span><span class="Other">]</span></pre></dt>
  <dd>
    
    Solve <tt class="docutils literal"><span class="pre">X*A = B</span></tt>, which is also <tt class="docutils literal"><span class="pre">A'*X' = B'</span></tt><ul class="simple"><li>parameter <tt class="docutils literal"><span class="pre">b</span></tt>: the right hand side</li>
<li><tt class="docutils literal"><span class="pre">return</span></tt>: solution if A is square, least squares solution otherwise.</li>
</ul>

    <a href="https://github.com/planetis-m/manu/tree/master/manu.nim#L55" class="link-seesrc" target="_blank">Source</a>&nbsp;&nbsp;
<a href="https://github.com/planetis-m/manu/edit/master/manu.nim#L55" class="link-seesrc" target="_blank" >Edit</a>&nbsp;&nbsp;

  </dd>
</div>

</div>

  </dl>
</div>
<div class="section" id="19">
  <h1><a class="toc-backref" href="#19">Exports</a></h1>
  <dl class="item">
    <a href="manu/matrix.html#getArray,Matrix[T]"><span class="Identifier">getArray</span></a>, <a href="manu/matrix.html#Matrix32"><span class="Identifier">Matrix32</span></a>, <a href="manu/matrix.html#ColVector32"><span class="Identifier">ColVector32</span></a>, <a href="manu/matrix.html#-,sink,T"><span class="Identifier">-</span></a>, <a href="manu/matrix.html#sqrt,sink"><span class="Identifier">sqrt</span></a>, <a href="manu/matrix.html#cosh,sink"><span class="Identifier">cosh</span></a>, <a href="manu/matrix.html#*.,,sink"><span class="Identifier">*.</span></a>, <a href="manu/matrix.html#randNMatrix,int,int,T,T"><span class="Identifier">randNMatrix</span></a>, <a href="manu/matrix.html#randMatrix32,int,int"><span class="Identifier">randMatrix32</span></a>, <a href="manu/matrix.html#columnDimension,Matrix[T]"><span class="Identifier">columnDimension</span></a>, <a href="manu/matrix.html#randMatrix,int,int,Slice[T: SomeFloat]"><span class="Identifier">randMatrix</span></a>, <a href="manu/matrix.html#*.,sink,"><span class="Identifier">*.</span></a>, <a href="manu/matrix.html#/=,,T"><span class="Identifier">/=</span></a>, <a href="manu/matrix.html#-,,"><span class="Identifier">-</span></a>, <a href="manu/matrix.html#[]=,ColVector[T],int,T"><span class="Identifier">[]=</span></a>, <a href="manu/matrix.html#-,T,sink"><span class="Identifier">-</span></a>, <a href="manu/matrix.html#/.,sink,"><span class="Identifier">/.</span></a>, <a href="manu/matrix.html#[],Matrix[T],HSlice[U,V],openArray[SomeInteger]"><span class="Identifier">[]</span></a>, <a href="manu/matrix.html#/,sink,T"><span class="Identifier">/</span></a>, <a href="manu/matrix.html#$,Matrix[T]"><span class="Identifier">$</span></a>, <a href="manu/matrix.html#-,sink"><span class="Identifier">-</span></a>, <a href="manu/matrix.html#*.=,,"><span class="Identifier">*.=</span></a>, <a href="manu/matrix.html#+=,,"><span class="Identifier">+=</span></a>, <a href="manu/matrix.html#matrix,int,int,T"><span class="Identifier">matrix</span></a>, <a href="manu/matrix.html#*.,,sink_2"><span class="Identifier">*.</span></a>, <a href="manu/matrix.html#[],Matrix[T],openArray[SomeInteger],HSlice[U,V]"><span class="Identifier">[]</span></a>, <a href="manu/matrix.html#*.,sink,_2"><span class="Identifier">*.</span></a>, <a href="manu/matrix.html#ones64,int,int"><span class="Identifier">ones64</span></a>, <a href="manu/matrix.html#randNMatrix,int,int"><span class="Identifier">randNMatrix</span></a>, <a href="manu/matrix.html#+=,,T"><span class="Identifier">+=</span></a>, <a href="manu/matrix.html#rowDimension,Matrix[T]"><span class="Identifier">rowDimension</span></a>, <a href="manu/matrix.html#-,,_2"><span class="Identifier">-</span></a>, <a href="manu/matrix.html#randMatrix,int,int,T"><span class="Identifier">randMatrix</span></a>, <a href="manu/matrix.html#/.,,"><span class="Identifier">/.</span></a>, <a href="manu/matrix.html#[]=,RowVector[T],int,T"><span class="Identifier">[]=</span></a>, <a 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class="Identifier">getImagEigenvalues</span></a>, <a href="manu/eigen.html#getV,EigenvalueDecomposition[T]"><span class="Identifier">getV</span></a>, <a href="manu/eigen.html#EigenvalueDecomposition"><span class="Identifier">EigenvalueDecomposition</span></a>, <a href="manu/eigen.html#getD,EigenvalueDecomposition[T]"><span class="Identifier">getD</span></a>, <a href="manu/eigen.html#eig,sinkMatrix[T]"><span class="Identifier">eig</span></a>
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