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   <div id="projectname">3DEX&#160;<span id="projectnumber">1.0</span></div>
   <div id="projectbrief">Three-dimensional Fourier-Bessel decomposition</div>
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<a href="#func-members">Functions/Subroutines</a>  </div>
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<div class="title">f3dex_stats Module Reference</div>  </div>
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<tr><td colspan="2"><h2><a name="func-members"></a>
Functions/Subroutines</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">REAL(DP)&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="namespacef3dex__stats.html#a2c704cb2c5b38f77b70a5c9783660912">CMODULE</a> (a)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">Computes the module of a complex number.  <a href="#a2c704cb2c5b38f77b70a5c9783660912"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">subroutine&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="namespacef3dex__stats.html#af82543b20c426be1736a4fed0d1ca80c">almn2cln_naive</a> (nnmax, nlmax, nmmax, almn, cln)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">Naive estimator for the almn's.  <a href="#af82543b20c426be1736a4fed0d1ca80c"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">REAL(DP)&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="namespacef3dex__stats.html#afc9d6ca61536648a01f8b6769080283e">dzrel</a> (cplxnb, cplxnbref)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">Relative error betwee two complex numbers.  <a href="#afc9d6ca61536648a01f8b6769080283e"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">subroutine&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="namespacef3dex__stats.html#a1f360b2a41b5a63c3379390a55ef07b2">legendre_vec</a> (x, pl, nlmax)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">Computes legendre coefs of a double using recurrence.  <a href="#a1f360b2a41b5a63c3379390a55ef07b2"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">subroutine&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="namespacef3dex__stats.html#aa2fb45e013179295e3b876ced9eff015">legendre_mat</a> (x, pl, nc, nlmax)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">Computes legendre coefs of an array using recurrence.  <a href="#aa2fb45e013179295e3b876ced9eff015"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">subroutine&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="namespacef3dex__stats.html#ac34a6421249816395b51048aa0a3dde3">gen_angles_map</a> (npix, ang_map, nside, nested, mask)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">Generates &lt;xxt&gt; correlation angles map.  <a href="#ac34a6421249816395b51048aa0a3dde3"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">REAL(DP)&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="namespacef3dex__stats.html#a70ed2d6cd6c25b9cd95b04e9223e5828">dzabs</a> (cplxnb, cplxnbref)</td></tr>
<tr><td class="memItemLeft" align="right" valign="top">subroutine&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="namespacef3dex__stats.html#ae67784686a6f0a1d26c1cef84c250b0d">EYEMAT</a> (A, s, e, val)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">Creates eye matrix.  <a href="#ae67784686a6f0a1d26c1cef84c250b0d"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">subroutine&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="namespacef3dex__stats.html#a564304481b43b3d55989683f03460410">INVERSE</a> (A, n, res)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">Inverts matrix.  <a href="#a564304481b43b3d55989683f03460410"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">subroutine&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="namespacef3dex__stats.html#afeef2b0049256649535f458d01e901c8">map2cl_QML</a> (map, cl, nside, nlmax, nlmax_recon, covarnoise, cltheo, logicalmask, covarest)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">Computes QML estimator of a healpix (masked) map.  <a href="#afeef2b0049256649535f458d01e901c8"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">subroutine&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="namespacef3dex__stats.html#aeff76c576e1699da5b3aa1f4efa4335d">map2cl_PCL</a> (map, cl, nside, nlmax, nlmax_recon, logicalmask, covarest)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">Computes QML estimator of a healpix (masked) map.  <a href="#aeff76c576e1699da5b3aa1f4efa4335d"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">REAL(DP)&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="namespacef3dex__stats.html#af0a10f88c8029206196ea18b3ad579ba">BILIN_FORM_PAR</a> (x, A, y, s, e)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">Parallel bilinear form.  <a href="#af0a10f88c8029206196ea18b3ad579ba"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">subroutine&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="namespacef3dex__stats.html#a046613d05a3a2eb1808a7ee99fba7509">MATMUL_PAR</a> (A, B, C, s, d1, d2, d3)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">Parallel matrix multiplication.  <a href="#a046613d05a3a2eb1808a7ee99fba7509"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">REAL(DP)&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="namespacef3dex__stats.html#aa88d6eefa32a9edc04b3d93af96f5a2e">TRACE</a> (mat, s, e)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">TRACE.  <a href="#aa88d6eefa32a9edc04b3d93af96f5a2e"></a><br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">REAL(DP)&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="namespacef3dex__stats.html#ae106140bb309de7d7779b6b086050bf4">TRACEPROD</a> (mat1, mat2, s, e)</td></tr>
<tr><td class="mdescLeft">&#160;</td><td class="mdescRight">TRACE of a product of matrices.  <a href="#ae106140bb309de7d7779b6b086050bf4"></a><br/></td></tr>
</table>
<hr/><h2>Function/Subroutine Documentation</h2>
<a class="anchor" id="af82543b20c426be1736a4fed0d1ca80c"></a><!-- doxytag: member="f3dex_stats::almn2cln_naive" ref="af82543b20c426be1736a4fed0d1ca80c" args="(nnmax, nlmax, nmmax, almn, cln)" -->
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          <td class="memname">subroutine f3dex_stats::almn2cln_naive </td>
          <td>(</td>
          <td class="paramtype">INTEGER(I4B),intent(in)&#160;</td>
          <td class="paramname"><em>nnmax</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INTEGER(I4B),intent(in)&#160;</td>
          <td class="paramname"><em>nlmax</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INTEGER(I4B),intent(in)&#160;</td>
          <td class="paramname"><em>nmmax</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">COMPLEX(DPC),dimension(1:nnmax,0:nlmax,0:nmmax),intent(in)&#160;</td>
          <td class="paramname"><em>almn</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">REAL(DP),dimension(0:nlmax, 1:nnmax),intent(out)&#160;</td>
          <td class="paramname"><em>cln</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
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<div class="memdoc">

<p>Naive estimator for the almn's. </p>
<dl><dt><b>Parameters:</b></dt><dd>
  <table class="params">
    <tr><td class="paramdir">[in]</td><td class="paramname">alm(0:nnmax,0:nlmax,0:nmmax))</td><td>: input almn's </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">(nnmax,nlmax,nmmax)</td><td>: bounds </td></tr>
    <tr><td class="paramdir">[out]</td><td class="paramname">cl(0:nlmax,0:nnmax)</td><td>: output power spectrum </td></tr>
  </table>
  </dd>
</dl>

<p>Definition at line <a class="el" href="f3dex__stats_8f90_source.html#l00032">32</a> of file <a class="el" href="f3dex__stats_8f90_source.html">f3dex_stats.f90</a>.</p>

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<a class="anchor" id="af0a10f88c8029206196ea18b3ad579ba"></a><!-- doxytag: member="f3dex_stats::BILIN_FORM_PAR" ref="af0a10f88c8029206196ea18b3ad579ba" args="(x, A, y, s, e)" -->
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          <td class="memname">REAL(DP) f3dex_stats::BILIN_FORM_PAR </td>
          <td>(</td>
          <td class="paramtype">REAL(DP),dimension(s:e)&#160;</td>
          <td class="paramname"><em>x</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">REAL(DP),dimension(s:e,s:e)&#160;</td>
          <td class="paramname"><em>A</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">REAL(DP),dimension(s:e)&#160;</td>
          <td class="paramname"><em>y</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INTEGER(I4B)&#160;</td>
          <td class="paramname"><em>s</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INTEGER(I4B)&#160;</td>
          <td class="paramname"><em>e</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div>
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<p>Parallel bilinear form. </p>
<dl><dt><b>Parameters:</b></dt><dd>
  <table class="params">
    <tr><td class="paramdir">[in]</td><td class="paramname">(</td><td>x(s:e),y(s:e) ) : left and right vectors </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">A(s:e,s:e)</td><td>: middle matrix </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">(s,e)</td><td>: bounds </td></tr>
  </table>
  </dd>
</dl>

<p>Definition at line <a class="el" href="f3dex__stats_8f90_source.html#l00509">509</a> of file <a class="el" href="f3dex__stats_8f90_source.html">f3dex_stats.f90</a>.</p>

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<a class="anchor" id="a2c704cb2c5b38f77b70a5c9783660912"></a><!-- doxytag: member="f3dex_stats::CMODULE" ref="a2c704cb2c5b38f77b70a5c9783660912" args="(a)" -->
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          <td class="memname">REAL(DP) f3dex_stats::CMODULE </td>
          <td>(</td>
          <td class="paramtype">COMPLEX(DPC)&#160;</td>
          <td class="paramname"><em>a</em></td><td>)</td>
          <td></td>
        </tr>
      </table>
</div>
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<p>Computes the module of a complex number. </p>

<p>Definition at line <a class="el" href="f3dex__stats_8f90_source.html#l00018">18</a> of file <a class="el" href="f3dex__stats_8f90_source.html">f3dex_stats.f90</a>.</p>

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<a class="anchor" id="a70ed2d6cd6c25b9cd95b04e9223e5828"></a><!-- doxytag: member="f3dex_stats::dzabs" ref="a70ed2d6cd6c25b9cd95b04e9223e5828" args="(cplxnb, cplxnbref)" -->
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      <table class="memname">
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          <td class="memname">REAL(DP) f3dex_stats::dzabs </td>
          <td>(</td>
          <td class="paramtype">complex(DP)&#160;</td>
          <td class="paramname"><em>cplxnb</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">complex(DP)&#160;</td>
          <td class="paramname"><em>cplxnbref</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div>
<div class="memdoc">

<p>Definition at line <a class="el" href="f3dex__stats_8f90_source.html#l00193">193</a> of file <a class="el" href="f3dex__stats_8f90_source.html">f3dex_stats.f90</a>.</p>

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<a class="anchor" id="afc9d6ca61536648a01f8b6769080283e"></a><!-- doxytag: member="f3dex_stats::dzrel" ref="afc9d6ca61536648a01f8b6769080283e" args="(cplxnb, cplxnbref)" -->
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      <table class="memname">
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          <td class="memname">REAL(DP) f3dex_stats::dzrel </td>
          <td>(</td>
          <td class="paramtype">complex(DP)&#160;</td>
          <td class="paramname"><em>cplxnb</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">complex(DP)&#160;</td>
          <td class="paramname"><em>cplxnbref</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div>
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<p>Relative error betwee two complex numbers. </p>

<p>Definition at line <a class="el" href="f3dex__stats_8f90_source.html#l00063">63</a> of file <a class="el" href="f3dex__stats_8f90_source.html">f3dex_stats.f90</a>.</p>

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<a class="anchor" id="ae67784686a6f0a1d26c1cef84c250b0d"></a><!-- doxytag: member="f3dex_stats::EYEMAT" ref="ae67784686a6f0a1d26c1cef84c250b0d" args="(A, s, e, val)" -->
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          <td class="memname">subroutine f3dex_stats::EYEMAT </td>
          <td>(</td>
          <td class="paramtype">REAL(DP),dimension(s:e,s:e)&#160;</td>
          <td class="paramname"><em>A</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INTEGER&#160;</td>
          <td class="paramname"><em>s</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INTEGER&#160;</td>
          <td class="paramname"><em>e</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">REAL(DP),optional&#160;</td>
          <td class="paramname"><em>val</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div>
<div class="memdoc">

<p>Creates eye matrix. </p>
<dl><dt><b>Parameters:</b></dt><dd>
  <table class="params">
    <tr><td class="paramdir">[out]</td><td class="paramname">A(s:e,s:e)</td><td>: input matrix </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">(s,e)</td><td>: bounds [in] val : value to put on the diagonal </td></tr>
  </table>
  </dd>
</dl>

<p>Definition at line <a class="el" href="f3dex__stats_8f90_source.html#l00224">224</a> of file <a class="el" href="f3dex__stats_8f90_source.html">f3dex_stats.f90</a>.</p>

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<a class="anchor" id="ac34a6421249816395b51048aa0a3dde3"></a><!-- doxytag: member="f3dex_stats::gen_angles_map" ref="ac34a6421249816395b51048aa0a3dde3" args="(npix, ang_map, nside, nested, mask)" -->
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          <td class="memname">subroutine f3dex_stats::gen_angles_map </td>
          <td>(</td>
          <td class="paramtype">INTEGER(I4B)&#160;</td>
          <td class="paramname"><em>npix</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">REAL(DP),dimension(0:npix-1,0:npix-1)&#160;</td>
          <td class="paramname"><em>ang_map</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INTEGER(I4B)&#160;</td>
          <td class="paramname"><em>nside</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">LOGICAL,optional&#160;</td>
          <td class="paramname"><em>nested</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">LOGICAL,dimension(0:12*nside**2-1),optional&#160;</td>
          <td class="paramname"><em>mask</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div>
<div class="memdoc">

<p>Generates &lt;xxt&gt; correlation angles map. </p>
<dl><dt><b>Parameters:</b></dt><dd>
  <table class="params">
    <tr><td class="paramdir">[in]</td><td class="paramname">(npix,nside)</td><td>: number of pixels and Healpix parameter </td></tr>
    <tr><td class="paramdir">[out]</td><td class="paramname">ang_map(0:npix-1,0:npix-1)</td><td>: angular map </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">nested</td><td>: logical for Healpix mode </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">mask</td><td>: optional mask </td></tr>
  </table>
  </dd>
</dl>

<p>Definition at line <a class="el" href="f3dex__stats_8f90_source.html#l00139">139</a> of file <a class="el" href="f3dex__stats_8f90_source.html">f3dex_stats.f90</a>.</p>

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<a class="anchor" id="a564304481b43b3d55989683f03460410"></a><!-- doxytag: member="f3dex_stats::INVERSE" ref="a564304481b43b3d55989683f03460410" args="(A, n, res)" -->
<div class="memitem">
<div class="memproto">
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        <tr>
          <td class="memname">subroutine f3dex_stats::INVERSE </td>
          <td>(</td>
          <td class="paramtype">DOUBLE PRECISION,dimension(n,n)&#160;</td>
          <td class="paramname"><em>A</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INTEGER&#160;</td>
          <td class="paramname"><em>n</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">LOGICAL&#160;</td>
          <td class="paramname"><em>res</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div>
<div class="memdoc">

<p>Inverts matrix. </p>
<dl><dt><b>Parameters:</b></dt><dd>
  <table class="params">
    <tr><td class="paramdir"></td><td class="paramname">inout]</td><td>A(n,n) : input/output matrix </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">n</td><td>: bounds [out] res : output result logical </td></tr>
  </table>
  </dd>
</dl>

<p>Definition at line <a class="el" href="f3dex__stats_8f90_source.html#l00246">246</a> of file <a class="el" href="f3dex__stats_8f90_source.html">f3dex_stats.f90</a>.</p>

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<a class="anchor" id="aa2fb45e013179295e3b876ced9eff015"></a><!-- doxytag: member="f3dex_stats::legendre_mat" ref="aa2fb45e013179295e3b876ced9eff015" args="(x, pl, nc, nlmax)" -->
<div class="memitem">
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          <td class="memname">subroutine f3dex_stats::legendre_mat </td>
          <td>(</td>
          <td class="paramtype">REAL(DP),dimension(0:nc-1)&#160;</td>
          <td class="paramname"><em>x</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">REAL(DP),dimension(0:nc-1, 0:nlmax)&#160;</td>
          <td class="paramname"><em>pl</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INTEGER(I4B)&#160;</td>
          <td class="paramname"><em>nc</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INTEGER(I4B)&#160;</td>
          <td class="paramname"><em>nlmax</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div>
<div class="memdoc">

<p>Computes legendre coefs of an array using recurrence. </p>
<dl><dt><b>Parameters:</b></dt><dd>
  <table class="params">
    <tr><td class="paramdir">[in]</td><td class="paramname">x(0:nc-1)</td><td>: abs </td></tr>
    <tr><td class="paramdir">[out]</td><td class="paramname">pl(0:nc-1,0:nlmax)</td><td>: legendre matrix [in] (nc,nlmax) : dimensions </td></tr>
  </table>
  </dd>
</dl>

<p>Definition at line <a class="el" href="f3dex__stats_8f90_source.html#l00120">120</a> of file <a class="el" href="f3dex__stats_8f90_source.html">f3dex_stats.f90</a>.</p>

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<a class="anchor" id="a1f360b2a41b5a63c3379390a55ef07b2"></a><!-- doxytag: member="f3dex_stats::legendre_vec" ref="a1f360b2a41b5a63c3379390a55ef07b2" args="(x, pl, nlmax)" -->
<div class="memitem">
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          <td class="memname">subroutine f3dex_stats::legendre_vec </td>
          <td>(</td>
          <td class="paramtype">REAL(DP)&#160;</td>
          <td class="paramname"><em>x</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">REAL(DP),dimension(0:nlmax)&#160;</td>
          <td class="paramname"><em>pl</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INTEGER(I4B)&#160;</td>
          <td class="paramname"><em>nlmax</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div>
<div class="memdoc">

<p>Computes legendre coefs of a double using recurrence. </p>
<dl><dt><b>Parameters:</b></dt><dd>
  <table class="params">
    <tr><td class="paramdir">[in]</td><td class="paramname">x(0:nc-1)</td><td>: abs </td></tr>
    <tr><td class="paramdir">[out]</td><td class="paramname">pl(0:nc-1,0:nlmax)</td><td>: legendre matrix [in] (nc,nlmax) : dimensions </td></tr>
  </table>
  </dd>
</dl>

<p>Definition at line <a class="el" href="f3dex__stats_8f90_source.html#l00099">99</a> of file <a class="el" href="f3dex__stats_8f90_source.html">f3dex_stats.f90</a>.</p>

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<a class="anchor" id="aeff76c576e1699da5b3aa1f4efa4335d"></a><!-- doxytag: member="f3dex_stats::map2cl_PCL" ref="aeff76c576e1699da5b3aa1f4efa4335d" args="(map, cl, nside, nlmax, nlmax_recon, logicalmask, covarest)" -->
<div class="memitem">
<div class="memproto">
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          <td class="memname">subroutine f3dex_stats::map2cl_PCL </td>
          <td>(</td>
          <td class="paramtype">REAL(DP),dimension(0:(12*nside*nside-1))&#160;</td>
          <td class="paramname"><em>map</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">REAL(DP),dimension(0:nlmax_recon)&#160;</td>
          <td class="paramname"><em>cl</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INTEGER(I4B)&#160;</td>
          <td class="paramname"><em>nside</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INTEGER(I4B)&#160;</td>
          <td class="paramname"><em>nlmax</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INTEGER(I4B)&#160;</td>
          <td class="paramname"><em>nlmax_recon</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">LOGICAL,dimension(0:(12*nside*nside-1)),optional&#160;</td>
          <td class="paramname"><em>logicalmask</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">REAL(DP),dimension(0:nlmax_recon),optional&#160;</td>
          <td class="paramname"><em>covarest</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div>
<div class="memdoc">

<p>Computes QML estimator of a healpix (masked) map. </p>
<dl><dt><b>Parameters:</b></dt><dd>
  <table class="params">
    <tr><td class="paramdir">[in]</td><td class="paramname">map(0:12*nside*nside-1)</td><td>: input healpix map </td></tr>
    <tr><td class="paramdir">[out]</td><td class="paramname">cl(0:nlmax)</td><td>: output power spectrum estimates </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">nside</td><td>: healpix parameter </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">nlmax</td><td>: input nlmax for the theory signal covariance </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">nlmax_recon</td><td>: lmax for the reconstruction and estimation </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">logicalmask(0:12*nside*nside-1)</td><td>: (optional) healpix logical mask </td></tr>
    <tr><td class="paramdir">[out]</td><td class="paramname">covarest</td><td>: (optional) output covariance of the noise </td></tr>
  </table>
  </dd>
</dl>

<p>Definition at line <a class="el" href="f3dex__stats_8f90_source.html#l00411">411</a> of file <a class="el" href="f3dex__stats_8f90_source.html">f3dex_stats.f90</a>.</p>

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<a class="anchor" id="afeef2b0049256649535f458d01e901c8"></a><!-- doxytag: member="f3dex_stats::map2cl_QML" ref="afeef2b0049256649535f458d01e901c8" args="(map, cl, nside, nlmax, nlmax_recon, covarnoise, cltheo, logicalmask, covarest)" -->
<div class="memitem">
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      <table class="memname">
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          <td class="memname">subroutine f3dex_stats::map2cl_QML </td>
          <td>(</td>
          <td class="paramtype">REAL(DP),dimension(0:(12*nside*nside-1))&#160;</td>
          <td class="paramname"><em>map</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">REAL(DP),dimension(0:nlmax_recon)&#160;</td>
          <td class="paramname"><em>cl</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INTEGER(I4B)&#160;</td>
          <td class="paramname"><em>nside</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INTEGER(I4B)&#160;</td>
          <td class="paramname"><em>nlmax</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INTEGER(I4B)&#160;</td>
          <td class="paramname"><em>nlmax_recon</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">REAL(DP),dimension(0:12*nside**2-1,0:12*nside**2-1)&#160;</td>
          <td class="paramname"><em>covarnoise</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">REAL(DP),dimension(0:nlmax)&#160;</td>
          <td class="paramname"><em>cltheo</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">LOGICAL,dimension(0:(12*nside*nside-1)),optional&#160;</td>
          <td class="paramname"><em>logicalmask</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">REAL(DP),dimension(0:nlmax_recon),optional&#160;</td>
          <td class="paramname"><em>covarest</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div>
<div class="memdoc">

<p>Computes QML estimator of a healpix (masked) map. </p>
<dl><dt><b>Parameters:</b></dt><dd>
  <table class="params">
    <tr><td class="paramdir">[in]</td><td class="paramname">map(0:12*nside*nside-1)</td><td>: input healpix map </td></tr>
    <tr><td class="paramdir">[out]</td><td class="paramname">cl(0:nlmax)</td><td>: output power spectrum estimates </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">nside</td><td>: healpix parameter </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">nlmax</td><td>: input nlmax for the theory signal covariance </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">nlmax_recon</td><td>: lmax for the reconstruction and estimation </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">covarnoise</td><td>: covariance matrix of the noise </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">cltheo</td><td>: theoretical power spectrum </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">logicalmask(0:12*nside*nside-1)</td><td>: (optional) healpix logical mask </td></tr>
    <tr><td class="paramdir">[out]</td><td class="paramname">covarest</td><td>: (optional) output covariance of the noise </td></tr>
  </table>
  </dd>
</dl>

<p>Definition at line <a class="el" href="f3dex__stats_8f90_source.html#l00280">280</a> of file <a class="el" href="f3dex__stats_8f90_source.html">f3dex_stats.f90</a>.</p>

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<a class="anchor" id="a046613d05a3a2eb1808a7ee99fba7509"></a><!-- doxytag: member="f3dex_stats::MATMUL_PAR" ref="a046613d05a3a2eb1808a7ee99fba7509" args="(A, B, C, s, d1, d2, d3)" -->
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          <td class="memname">subroutine f3dex_stats::MATMUL_PAR </td>
          <td>(</td>
          <td class="paramtype">REAL(DP),dimension(s:d1,s:d2)&#160;</td>
          <td class="paramname"><em>A</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">REAL(DP),dimension(s:d2,s:d3)&#160;</td>
          <td class="paramname"><em>B</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">REAL(DP),dimension(s:d1,s:d3)&#160;</td>
          <td class="paramname"><em>C</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INTEGER(I4B)&#160;</td>
          <td class="paramname"><em>s</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INTEGER(I4B)&#160;</td>
          <td class="paramname"><em>d1</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INTEGER(I4B)&#160;</td>
          <td class="paramname"><em>d2</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INTEGER(I4B)&#160;</td>
          <td class="paramname"><em>d3</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div>
<div class="memdoc">

<p>Parallel matrix multiplication. </p>
<dl><dt><b>Parameters:</b></dt><dd>
  <table class="params">
    <tr><td class="paramdir">[in]</td><td class="paramname">A(s:d1,s:d2)</td><td>: first matrix </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">B(s:d2,s:d3)</td><td>: second matrix </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">C(s:d1,s:d3)</td><td>: output matrix </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">(s,d1,d2,d3)</td><td>: bounds </td></tr>
  </table>
  </dd>
</dl>

<p>Definition at line <a class="el" href="f3dex__stats_8f90_source.html#l00538">538</a> of file <a class="el" href="f3dex__stats_8f90_source.html">f3dex_stats.f90</a>.</p>

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<a class="anchor" id="aa88d6eefa32a9edc04b3d93af96f5a2e"></a><!-- doxytag: member="f3dex_stats::TRACE" ref="aa88d6eefa32a9edc04b3d93af96f5a2e" args="(mat, s, e)" -->
<div class="memitem">
<div class="memproto">
      <table class="memname">
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          <td class="memname">REAL(DP) f3dex_stats::TRACE </td>
          <td>(</td>
          <td class="paramtype">REAL(DP),dimension(s:e,s:e),intent(in)&#160;</td>
          <td class="paramname"><em>mat</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INTEGER(I4B)&#160;</td>
          <td class="paramname"><em>s</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INTEGER(I4B)&#160;</td>
          <td class="paramname"><em>e</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div>
<div class="memdoc">

<p>TRACE. </p>
<dl><dt><b>Parameters:</b></dt><dd>
  <table class="params">
    <tr><td class="paramdir">[in]</td><td class="paramname">mat(s:e,s:e)</td><td>: input matrix </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">(s,e)</td><td>: bounds </td></tr>
  </table>
  </dd>
</dl>

<p>Definition at line <a class="el" href="f3dex__stats_8f90_source.html#l00563">563</a> of file <a class="el" href="f3dex__stats_8f90_source.html">f3dex_stats.f90</a>.</p>

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<a class="anchor" id="ae106140bb309de7d7779b6b086050bf4"></a><!-- doxytag: member="f3dex_stats::TRACEPROD" ref="ae106140bb309de7d7779b6b086050bf4" args="(mat1, mat2, s, e)" -->
<div class="memitem">
<div class="memproto">
      <table class="memname">
        <tr>
          <td class="memname">REAL(DP) f3dex_stats::TRACEPROD </td>
          <td>(</td>
          <td class="paramtype">REAL(DP),dimension(s:e,s:e),intent(in)&#160;</td>
          <td class="paramname"><em>mat1</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">REAL(DP),dimension(s:e,s:e),intent(in)&#160;</td>
          <td class="paramname"><em>mat2</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INTEGER(I4B)&#160;</td>
          <td class="paramname"><em>s</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">INTEGER(I4B)&#160;</td>
          <td class="paramname"><em>e</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div>
<div class="memdoc">

<p>TRACE of a product of matrices. </p>
<dl><dt><b>Parameters:</b></dt><dd>
  <table class="params">
    <tr><td class="paramdir">[in]</td><td class="paramname">mat1(s:e,s:e)</td><td>: input matrix 1 </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">mat2(s:e,s:e)</td><td>: input matrix 2 </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">(s,e)</td><td>: bounds </td></tr>
  </table>
  </dd>
</dl>

<p>Definition at line <a class="el" href="f3dex__stats_8f90_source.html#l00589">589</a> of file <a class="el" href="f3dex__stats_8f90_source.html">f3dex_stats.f90</a>.</p>

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