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629 lines
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HTML
629 lines
26 KiB
HTML
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</head>
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<body>
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<div id="org-div-home-and-up">
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<a accesskey="h" href=""> UP </a>
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<a accesskey="H" href="index.html"> HOME </a>
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</div><div id="content">
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<h1 class="title">Distances</h1>
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<div id="table-of-contents">
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#orge37b98f">1. Squared distance</a>
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<ul>
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<li>
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<ul>
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<li><a href="#orgae7b0c5">1.0.1. Requirements</a></li>
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<li><a href="#orgec00fc7">1.0.2. Performance</a></li>
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<li><a href="#org2e868c7">1.0.3. Source</a></li>
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</ul>
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</li>
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</ul>
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</li>
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</ul>
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</div>
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</div>
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<p>
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Functions for the computation of distances between particles.
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</p>
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<div id="outline-container-orge37b98f" class="outline-2">
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<h2 id="orge37b98f"><span class="section-number-2">1</span> Squared distance</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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<code>qmckl_distance_sq</code> computes the matrix of the squared distances
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between all pairs of points in two sets, one point within each set:
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</p>
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<p>
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\[
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C_{ij} = \sum_{k=1}^3 (A_{k,i}-B_{k,j})^2
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\]
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</p>
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||
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|
||
|
<col class="org-left" />
|
||
|
|
||
|
<col class="org-left" />
|
||
|
</colgroup>
|
||
|
<tbody>
|
||
|
<tr>
|
||
|
<td class="org-left"><code>context</code></td>
|
||
|
<td class="org-left">input</td>
|
||
|
<td class="org-left">Global state</td>
|
||
|
</tr>
|
||
|
|
||
|
<tr>
|
||
|
<td class="org-left"><code>transa</code></td>
|
||
|
<td class="org-left">input</td>
|
||
|
<td class="org-left">Array <code>A</code> is <code>N</code>: Normal, <code>T</code>: Transposed</td>
|
||
|
</tr>
|
||
|
|
||
|
<tr>
|
||
|
<td class="org-left"><code>transb</code></td>
|
||
|
<td class="org-left">input</td>
|
||
|
<td class="org-left">Array <code>B</code> is <code>N</code>: Normal, <code>T</code>: Transposed</td>
|
||
|
</tr>
|
||
|
|
||
|
<tr>
|
||
|
<td class="org-left"><code>m</code></td>
|
||
|
<td class="org-left">input</td>
|
||
|
<td class="org-left">Number of points in the first set</td>
|
||
|
</tr>
|
||
|
|
||
|
<tr>
|
||
|
<td class="org-left"><code>n</code></td>
|
||
|
<td class="org-left">input</td>
|
||
|
<td class="org-left">Number of points in the second set</td>
|
||
|
</tr>
|
||
|
|
||
|
<tr>
|
||
|
<td class="org-left"><code>A(lda,3)</code></td>
|
||
|
<td class="org-left">input</td>
|
||
|
<td class="org-left">Array containing the \(m \times 3\) matrix \(A\)</td>
|
||
|
</tr>
|
||
|
|
||
|
<tr>
|
||
|
<td class="org-left"><code>lda</code></td>
|
||
|
<td class="org-left">input</td>
|
||
|
<td class="org-left">Leading dimension of array <code>A</code></td>
|
||
|
</tr>
|
||
|
|
||
|
<tr>
|
||
|
<td class="org-left"><code>B(ldb,3)</code></td>
|
||
|
<td class="org-left">input</td>
|
||
|
<td class="org-left">Array containing the \(n \times 3\) matrix \(B\)</td>
|
||
|
</tr>
|
||
|
|
||
|
<tr>
|
||
|
<td class="org-left"><code>ldb</code></td>
|
||
|
<td class="org-left">input</td>
|
||
|
<td class="org-left">Leading dimension of array <code>B</code></td>
|
||
|
</tr>
|
||
|
|
||
|
<tr>
|
||
|
<td class="org-left"><code>C(ldc,n)</code></td>
|
||
|
<td class="org-left">output</td>
|
||
|
<td class="org-left">Array containing the \(m \times n\) matrix \(C\)</td>
|
||
|
</tr>
|
||
|
|
||
|
<tr>
|
||
|
<td class="org-left"><code>ldc</code></td>
|
||
|
<td class="org-left">input</td>
|
||
|
<td class="org-left">Leading dimension of array <code>C</code></td>
|
||
|
</tr>
|
||
|
</tbody>
|
||
|
</table>
|
||
|
</div>
|
||
|
|
||
|
<div id="outline-container-orgae7b0c5" class="outline-4">
|
||
|
<h4 id="orgae7b0c5"><span class="section-number-4">1.0.1</span> Requirements</h4>
|
||
|
<div class="outline-text-4" id="text-1-0-1">
|
||
|
<ul class="org-ul">
|
||
|
<li><code>context</code> is not 0</li>
|
||
|
<li><code>m</code> > 0</li>
|
||
|
<li><code>n</code> > 0</li>
|
||
|
<li><code>lda</code> >= 3 if <code>transa</code> is <code>N</code></li>
|
||
|
<li><code>lda</code> >= m if <code>transa</code> is <code>T</code></li>
|
||
|
<li><code>ldb</code> >= 3 if <code>transb</code> is <code>N</code></li>
|
||
|
<li><code>ldb</code> >= n if <code>transb</code> is <code>T</code></li>
|
||
|
<li><code>ldc</code> >= m</li>
|
||
|
<li><code>A</code> is allocated with at least \(3 \times m \times 8\) bytes</li>
|
||
|
<li><code>B</code> is allocated with at least \(3 \times n \times 8\) bytes</li>
|
||
|
<li><code>C</code> is allocated with at least \(m \times n \times 8\) bytes</li>
|
||
|
</ul>
|
||
|
</div>
|
||
|
</div>
|
||
|
|
||
|
<div id="outline-container-orgec00fc7" class="outline-4">
|
||
|
<h4 id="orgec00fc7"><span class="section-number-4">1.0.2</span> Performance</h4>
|
||
|
<div class="outline-text-4" id="text-1-0-2">
|
||
|
<p>
|
||
|
This function might be more efficient when <code>A</code> and <code>B</code> are
|
||
|
transposed.
|
||
|
</p>
|
||
|
|
||
|
<div class="org-src-container">
|
||
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_distance_sq</span>(<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
||
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">char</span> <span style="color: #a0522d;">transa</span>, <span style="color: #a020f0;">const</span> <span style="color: #228b22;">char</span> <span style="color: #a0522d;">transb</span>,
|
||
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">m</span>, <span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">n</span>,
|
||
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> *<span style="color: #a0522d;">A</span>, <span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">lda</span>,
|
||
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> *<span style="color: #a0522d;">B</span>, <span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">ldb</span>,
|
||
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> *<span style="color: #a0522d;">C</span>, <span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">ldc</span>);
|
||
|
</pre>
|
||
|
</div>
|
||
|
</div>
|
||
|
</div>
|
||
|
|
||
|
<div id="outline-container-org2e868c7" class="outline-4">
|
||
|
<h4 id="org2e868c7"><span class="section-number-4">1.0.3</span> Source</h4>
|
||
|
<div class="outline-text-4" id="text-1-0-3">
|
||
|
<div class="org-src-container">
|
||
|
<pre class="src src-f90"><span style="color: #228b22;">integer </span><span style="color: #a020f0;">function</span><span style="color: #a0522d;"> </span><span style="color: #0000ff;">qmckl_distance_sq_f</span><span style="color: #000000; background-color: #ffffff;">(context, transa, transb, m, n, A, LDA, B, LDB, C, LDC) result(info)</span>
|
||
|
<span style="color: #a020f0;">use</span> <span style="color: #0000ff;">qmckl</span>
|
||
|
<span style="color: #a020f0;">implicit</span> <span style="color: #228b22;">none</span>
|
||
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> context</span>
|
||
|
<span style="color: #228b22;">character</span> , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> transa, transb</span>
|
||
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> m, n</span>
|
||
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> lda</span>
|
||
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> A(lda,*)</span>
|
||
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> ldb</span>
|
||
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> B(ldb,*)</span>
|
||
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> ldc</span>
|
||
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(out) ::<span style="color: #a0522d;"> C(ldc,*)</span>
|
||
|
|
||
|
<span style="color: #228b22;">integer</span>*8 ::<span style="color: #a0522d;"> i,j</span>
|
||
|
<span style="color: #228b22;">real</span>*8 ::<span style="color: #a0522d;"> x, y, z</span>
|
||
|
<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> transab</span>
|
||
|
|
||
|
info = 0
|
||
|
|
||
|
<span style="color: #a020f0;">if</span> (context == QMCKL_NULL_CONTEXT) <span style="color: #a020f0;">then</span>
|
||
|
info = QMCKL_INVALID_CONTEXT
|
||
|
<span style="color: #a020f0;">return</span>
|
||
|
<span style="color: #a020f0;">endif</span>
|
||
|
|
||
|
<span style="color: #a020f0;">if</span> (m <= 0_8) <span style="color: #a020f0;">then</span>
|
||
|
info = QMCKL_INVALID_ARG_4
|
||
|
<span style="color: #a020f0;">return</span>
|
||
|
<span style="color: #a020f0;">endif</span>
|
||
|
|
||
|
<span style="color: #a020f0;">if</span> (n <= 0_8) <span style="color: #a020f0;">then</span>
|
||
|
info = QMCKL_INVALID_ARG_5
|
||
|
<span style="color: #a020f0;">return</span>
|
||
|
<span style="color: #a020f0;">endif</span>
|
||
|
|
||
|
<span style="color: #a020f0;">if</span> (transa == <span style="color: #8b2252;">'N'</span> <span style="color: #a020f0;">.or.</span> transa == <span style="color: #8b2252;">'n'</span>) <span style="color: #a020f0;">then</span>
|
||
|
transab = 0
|
||
|
<span style="color: #a020f0;">else if</span> (transa == <span style="color: #8b2252;">'T'</span> <span style="color: #a020f0;">.or.</span> transa == <span style="color: #8b2252;">'t'</span>) <span style="color: #a020f0;">then</span>
|
||
|
transab = 1
|
||
|
<span style="color: #a020f0;">else</span>
|
||
|
transab = -100
|
||
|
<span style="color: #a020f0;">endif</span>
|
||
|
|
||
|
<span style="color: #a020f0;">if</span> (transb == <span style="color: #8b2252;">'N'</span> <span style="color: #a020f0;">.or.</span> transb == <span style="color: #8b2252;">'n'</span>) <span style="color: #a020f0;">then</span>
|
||
|
<span style="color: #a020f0;">continue</span>
|
||
|
<span style="color: #a020f0;">else if</span> (transa == <span style="color: #8b2252;">'T'</span> <span style="color: #a020f0;">.or.</span> transa == <span style="color: #8b2252;">'t'</span>) <span style="color: #a020f0;">then</span>
|
||
|
transab = transab + 2
|
||
|
<span style="color: #a020f0;">else</span>
|
||
|
transab = -100
|
||
|
<span style="color: #a020f0;">endif</span>
|
||
|
|
||
|
<span style="color: #a020f0;">if</span> (transab < 0) <span style="color: #a020f0;">then</span>
|
||
|
info = QMCKL_INVALID_ARG_1
|
||
|
<span style="color: #a020f0;">return</span>
|
||
|
<span style="color: #a020f0;">endif</span>
|
||
|
|
||
|
<span style="color: #a020f0;">if</span> (<span style="color: #a020f0;">iand</span>(transab,1) == 0 <span style="color: #a020f0;">.and.</span> LDA < 3) <span style="color: #a020f0;">then</span>
|
||
|
info = QMCKL_INVALID_ARG_7
|
||
|
<span style="color: #a020f0;">return</span>
|
||
|
<span style="color: #a020f0;">endif</span>
|
||
|
|
||
|
<span style="color: #a020f0;">if</span> (<span style="color: #a020f0;">iand</span>(transab,1) == 1 <span style="color: #a020f0;">.and.</span> LDA < m) <span style="color: #a020f0;">then</span>
|
||
|
info = QMCKL_INVALID_ARG_7
|
||
|
<span style="color: #a020f0;">return</span>
|
||
|
<span style="color: #a020f0;">endif</span>
|
||
|
|
||
|
<span style="color: #a020f0;">if</span> (<span style="color: #a020f0;">iand</span>(transab,2) == 0 <span style="color: #a020f0;">.and.</span> LDA < 3) <span style="color: #a020f0;">then</span>
|
||
|
info = QMCKL_INVALID_ARG_7
|
||
|
<span style="color: #a020f0;">return</span>
|
||
|
<span style="color: #a020f0;">endif</span>
|
||
|
|
||
|
<span style="color: #a020f0;">if</span> (<span style="color: #a020f0;">iand</span>(transab,2) == 2 <span style="color: #a020f0;">.and.</span> LDA < m) <span style="color: #a020f0;">then</span>
|
||
|
info = QMCKL_INVALID_ARG_7
|
||
|
<span style="color: #a020f0;">return</span>
|
||
|
<span style="color: #a020f0;">endif</span>
|
||
|
|
||
|
|
||
|
<span style="color: #a020f0;">select case</span> (transab)
|
||
|
|
||
|
<span style="color: #a020f0;">case</span>(0)
|
||
|
|
||
|
<span style="color: #a020f0;">do</span> j=1,n
|
||
|
<span style="color: #a020f0;">do</span> i=1,m
|
||
|
x = A(1,i) - B(1,j)
|
||
|
y = A(2,i) - B(2,j)
|
||
|
z = A(3,i) - B(3,j)
|
||
|
C(i,j) = x*x + y*y + z*z
|
||
|
<span style="color: #a020f0;">end do</span>
|
||
|
<span style="color: #a020f0;">end do</span>
|
||
|
|
||
|
<span style="color: #a020f0;">case</span>(1)
|
||
|
|
||
|
<span style="color: #a020f0;">do</span> j=1,n
|
||
|
<span style="color: #a020f0;">do</span> i=1,m
|
||
|
x = A(i,1) - B(1,j)
|
||
|
y = A(i,2) - B(2,j)
|
||
|
z = A(i,3) - B(3,j)
|
||
|
C(i,j) = x*x + y*y + z*z
|
||
|
<span style="color: #a020f0;">end do</span>
|
||
|
<span style="color: #a020f0;">end do</span>
|
||
|
|
||
|
<span style="color: #a020f0;">case</span>(2)
|
||
|
|
||
|
<span style="color: #a020f0;">do</span> j=1,n
|
||
|
<span style="color: #a020f0;">do</span> i=1,m
|
||
|
x = A(1,i) - B(j,1)
|
||
|
y = A(2,i) - B(j,2)
|
||
|
z = A(3,i) - B(j,3)
|
||
|
C(i,j) = x*x + y*y + z*z
|
||
|
<span style="color: #a020f0;">end do</span>
|
||
|
<span style="color: #a020f0;">end do</span>
|
||
|
|
||
|
<span style="color: #a020f0;">case</span>(3)
|
||
|
|
||
|
<span style="color: #a020f0;">do</span> j=1,n
|
||
|
<span style="color: #a020f0;">do</span> i=1,m
|
||
|
x = A(i,1) - B(j,1)
|
||
|
y = A(i,2) - B(j,2)
|
||
|
z = A(i,3) - B(j,3)
|
||
|
C(i,j) = x*x + y*y + z*z
|
||
|
<span style="color: #a020f0;">end do</span>
|
||
|
<span style="color: #a020f0;">end do</span>
|
||
|
|
||
|
<span style="color: #a020f0;">end select</span>
|
||
|
|
||
|
<span style="color: #a020f0;">end function</span> <span style="color: #0000ff;">qmckl_distance_sq_f</span>
|
||
|
</pre>
|
||
|
</div>
|
||
|
</div>
|
||
|
</div>
|
||
|
</div>
|
||
|
</div>
|
||
|
<div id="postamble" class="status">
|
||
|
<p class="author">Author: TREX CoE</p>
|
||
|
<p class="date">Created: 2021-03-19 Fri 12:49</p>
|
||
|
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
||
|
</div>
|
||
|
</body>
|
||
|
</html>
|