TREX/qmckl
1
0
Fork 0
mirror of https://github.com/TREX-CoE/qmckl.git synced 2025-05-01 12:54:46 +02:00
Code Issues Projects Releases Wiki Activity
qmckl/qmckl_distance.html

1651 lines
75 KiB
HTML
Raw Blame History

<?xml version="1.0" encoding="utf-8"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2025-04-29 Tue 08:44 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Inter-particle distances</title>
<meta name="author" content="TREX CoE" />
<meta name="generator" content="Org Mode" />
<style>
#content { max-width: 60em; margin: auto; }
.title { text-align: center;
margin-bottom: .2em; }
.subtitle { text-align: center;
font-size: medium;
font-weight: bold;
margin-top:0; }
.todo { font-family: monospace; color: red; }
.done { font-family: monospace; color: green; }
.priority { font-family: monospace; color: orange; }
.tag { background-color: #eee; font-family: monospace;
padding: 2px; font-size: 80%; font-weight: normal; }
.timestamp { color: #bebebe; }
.timestamp-kwd { color: #5f9ea0; }
.org-right { margin-left: auto; margin-right: 0px; text-align: right; }
.org-left { margin-left: 0px; margin-right: auto; text-align: left; }
.org-center { margin-left: auto; margin-right: auto; text-align: center; }
.underline { text-decoration: underline; }
#postamble p, #preamble p { font-size: 90%; margin: .2em; }
p.verse { margin-left: 3%; }
pre {
border: 1px solid #e6e6e6;
border-radius: 3px;
background-color: #f2f2f2;
padding: 8pt;
font-family: monospace;
overflow: auto;
margin: 1.2em;
}
pre.src {
position: relative;
overflow: auto;
}
pre.src:before {
display: none;
position: absolute;
top: -8px;
right: 12px;
padding: 3px;
color: #555;
background-color: #f2f2f299;
}
pre.src:hover:before { display: inline; margin-top: 14px;}
/* Languages per Org manual */
pre.src-asymptote:before { content: 'Asymptote'; }
pre.src-awk:before { content: 'Awk'; }
pre.src-authinfo::before { content: 'Authinfo'; }
pre.src-C:before { content: 'C'; }
/* pre.src-C++ doesn't work in CSS */
pre.src-clojure:before { content: 'Clojure'; }
pre.src-css:before { content: 'CSS'; }
pre.src-D:before { content: 'D'; }
pre.src-ditaa:before { content: 'ditaa'; }
pre.src-dot:before { content: 'Graphviz'; }
pre.src-calc:before { content: 'Emacs Calc'; }
pre.src-emacs-lisp:before { content: 'Emacs Lisp'; }
pre.src-fortran:before { content: 'Fortran'; }
pre.src-gnuplot:before { content: 'gnuplot'; }
pre.src-haskell:before { content: 'Haskell'; }
pre.src-hledger:before { content: 'hledger'; }
pre.src-java:before { content: 'Java'; }
pre.src-js:before { content: 'Javascript'; }
pre.src-latex:before { content: 'LaTeX'; }
pre.src-ledger:before { content: 'Ledger'; }
pre.src-lisp:before { content: 'Lisp'; }
pre.src-lilypond:before { content: 'Lilypond'; }
pre.src-lua:before { content: 'Lua'; }
pre.src-matlab:before { content: 'MATLAB'; }
pre.src-mscgen:before { content: 'Mscgen'; }
pre.src-ocaml:before { content: 'Objective Caml'; }
pre.src-octave:before { content: 'Octave'; }
pre.src-org:before { content: 'Org mode'; }
pre.src-oz:before { content: 'OZ'; }
pre.src-plantuml:before { content: 'Plantuml'; }
pre.src-processing:before { content: 'Processing.js'; }
pre.src-python:before { content: 'Python'; }
pre.src-R:before { content: 'R'; }
pre.src-ruby:before { content: 'Ruby'; }
pre.src-sass:before { content: 'Sass'; }
pre.src-scheme:before { content: 'Scheme'; }
pre.src-screen:before { content: 'Gnu Screen'; }
pre.src-sed:before { content: 'Sed'; }
pre.src-sh:before { content: 'shell'; }
pre.src-sql:before { content: 'SQL'; }
pre.src-sqlite:before { content: 'SQLite'; }
/* additional languages in org.el's org-babel-load-languages alist */
pre.src-forth:before { content: 'Forth'; }
pre.src-io:before { content: 'IO'; }
pre.src-J:before { content: 'J'; }
pre.src-makefile:before { content: 'Makefile'; }
pre.src-maxima:before { content: 'Maxima'; }
pre.src-perl:before { content: 'Perl'; }
pre.src-picolisp:before { content: 'Pico Lisp'; }
pre.src-scala:before { content: 'Scala'; }
pre.src-shell:before { content: 'Shell Script'; }
pre.src-ebnf2ps:before { content: 'ebfn2ps'; }
/* additional language identifiers per "defun org-babel-execute"
in ob-*.el */
pre.src-cpp:before { content: 'C++'; }
pre.src-abc:before { content: 'ABC'; }
pre.src-coq:before { content: 'Coq'; }
pre.src-groovy:before { content: 'Groovy'; }
/* additional language identifiers from org-babel-shell-names in
ob-shell.el: ob-shell is the only babel language using a lambda to put
the execution function name together. */
pre.src-bash:before { content: 'bash'; }
pre.src-csh:before { content: 'csh'; }
pre.src-ash:before { content: 'ash'; }
pre.src-dash:before { content: 'dash'; }
pre.src-ksh:before { content: 'ksh'; }
pre.src-mksh:before { content: 'mksh'; }
pre.src-posh:before { content: 'posh'; }
/* Additional Emacs modes also supported by the LaTeX listings package */
pre.src-ada:before { content: 'Ada'; }
pre.src-asm:before { content: 'Assembler'; }
pre.src-caml:before { content: 'Caml'; }
pre.src-delphi:before { content: 'Delphi'; }
pre.src-html:before { content: 'HTML'; }
pre.src-idl:before { content: 'IDL'; }
pre.src-mercury:before { content: 'Mercury'; }
pre.src-metapost:before { content: 'MetaPost'; }
pre.src-modula-2:before { content: 'Modula-2'; }
pre.src-pascal:before { content: 'Pascal'; }
pre.src-ps:before { content: 'PostScript'; }
pre.src-prolog:before { content: 'Prolog'; }
pre.src-simula:before { content: 'Simula'; }
pre.src-tcl:before { content: 'tcl'; }
pre.src-tex:before { content: 'TeX'; }
pre.src-plain-tex:before { content: 'Plain TeX'; }
pre.src-verilog:before { content: 'Verilog'; }
pre.src-vhdl:before { content: 'VHDL'; }
pre.src-xml:before { content: 'XML'; }
pre.src-nxml:before { content: 'XML'; }
/* add a generic configuration mode; LaTeX export needs an additional
(add-to-list 'org-latex-listings-langs '(conf " ")) in .emacs */
pre.src-conf:before { content: 'Configuration File'; }
table { border-collapse:collapse; }
caption.t-above { caption-side: top; }
caption.t-bottom { caption-side: bottom; }
td, th { vertical-align:top; }
th.org-right { text-align: center; }
th.org-left { text-align: center; }
th.org-center { text-align: center; }
td.org-right { text-align: right; }
td.org-left { text-align: left; }
td.org-center { text-align: center; }
dt { font-weight: bold; }
.footpara { display: inline; }
.footdef { margin-bottom: 1em; }
.figure { padding: 1em; }
.figure p { text-align: center; }
.equation-container {
display: table;
text-align: center;
width: 100%;
}
.equation {
vertical-align: middle;
}
.equation-label {
display: table-cell;
text-align: right;
vertical-align: middle;
}
.inlinetask {
padding: 10px;
border: 2px solid gray;
margin: 10px;
background: #ffffcc;
}
#org-div-home-and-up
{ text-align: right; font-size: 70%; white-space: nowrap; }
textarea { overflow-x: auto; }
.linenr { font-size: smaller }
.code-highlighted { background-color: #ffff00; }
.org-info-js_info-navigation { border-style: none; }
#org-info-js_console-label
{ font-size: 10px; font-weight: bold; white-space: nowrap; }
.org-info-js_search-highlight
{ background-color: #ffff00; color: #000000; font-weight: bold; }
.org-svg { }
</style>
<link rel="stylesheet" title="Standard" href="qmckl.css" type="text/css" />
<script src="org-info.js">
// @license magnet:?xt=urn:btih:1f739d935676111cfff4b4693e3816e664797050&amp;dn=gpl-3.0.txt GPL-v3-or-Later
// @license-end
</script>
<script>
// @license magnet:?xt=urn:btih:1f739d935676111cfff4b4693e3816e664797050&amp;dn=gpl-3.0.txt GPL-v3-or-Later
org_html_manager.set("TOC_DEPTH", "4");
org_html_manager.set("LINK_HOME", "index.html");
org_html_manager.set("LINK_UP", "");
org_html_manager.set("LOCAL_TOC", "1");
org_html_manager.set("VIEW_BUTTONS", "0");
org_html_manager.set("MOUSE_HINT", "underline");
org_html_manager.set("FIXED_TOC", "0");
org_html_manager.set("TOC", "1");
org_html_manager.set("VIEW", "info");
org_html_manager.setup(); // activate after the parameters are set
// @license-end
</script>
<script>
window.MathJax = {
tex: {
ams: {
multlineWidth: '85%'
},
tags: 'ams',
tagSide: 'right',
tagIndent: '.8em'
},
chtml: {
scale: 1.0,
displayAlign: 'center',
displayIndent: '0em'
},
svg: {
scale: 1.0,
displayAlign: 'center',
displayIndent: '0em'
},
output: {
font: 'mathjax-modern',
displayOverflow: 'overflow'
}
};
</script>
<script
id="MathJax-script"
async
src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js">
</script>
</head>
<body>
<div id="org-div-home-and-up">
<a accesskey="h" href=""> UP </a>
|
<a accesskey="H" href="index.html"> HOME </a>
</div><div id="content" class="content">
<h1 class="title">Inter-particle distances</h1>
<div id="table-of-contents" role="doc-toc">
<h2>Table of Contents</h2>
<div id="text-table-of-contents" role="doc-toc">
<ul>
<li><a href="#orgd12afd3">1. Squared distance</a>
<ul>
<li><a href="#orgf44467f">1.1. <code>qmckl_distance_sq</code></a>
<ul>
<li><a href="#org3996e2a">1.1.1. Performance</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="#org31e63c6">2. Distance</a>
<ul>
<li><a href="#org9e56505">2.1. <code>qmckl_distance</code></a>
<ul>
<li><a href="#org676a534">2.1.1. Requirements</a></li>
<li><a href="#orgcca461a">2.1.2. C header</a></li>
<li><a href="#org0622776">2.1.3. Source</a></li>
<li><a href="#org521329d">2.1.4. Performance</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="#orgcc8a08d">3. Rescaled Distance</a>
<ul>
<li><a href="#org9bb806f">3.1. <code>qmckl_distance_rescaled</code></a>
<ul>
<li><a href="#orgc0cfb39">3.1.1. Requirements</a></li>
<li><a href="#org4aafa08">3.1.2. C header</a></li>
<li><a href="#org4f8c847">3.1.3. Source</a></li>
<li><a href="#org435bcf3">3.1.4. Performance</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="#orgd72cafc">4. Rescaled Distance Derivatives</a>
<ul>
<li><a href="#org77cae89">4.1. <code>qmckl_distance_rescaled_gl</code></a></li>
</ul>
</li>
</ul>
</div>
</div>
<div id="outline-container-orgd12afd3" class="outline-2">
<h2 id="orgd12afd3"><span class="section-number-2">1.</span> Squared distance</h2>
<div class="outline-text-2" id="text-1">
</div>
<div id="outline-container-orgf44467f" class="outline-3">
<h3 id="orgf44467f"><span class="section-number-3">1.1.</span> <code>qmckl_distance_sq</code></h3>
<div class="outline-text-3" id="text-1-1">
<p>
<code>qmckl_distance_sq</code> computes the matrix of the squared distances
between all pairs of points in two sets, one point within each set:
</p>
<p>
\[
C_{ij} = \sum_{k=1}^3 (A_{k,i}-B_{k,j})^2
\]
</p>
<table id="org0c5c37b" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Variable</th>
<th scope="col" class="org-left">Type</th>
<th scope="col" class="org-left">In/Out</th>
<th scope="col" class="org-left">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left"><code>context</code></td>
<td class="org-left"><code>qmckl_context</code></td>
<td class="org-left">in</td>
<td class="org-left">Global state</td>
</tr>
<tr>
<td class="org-left"><code>transa</code></td>
<td class="org-left"><code>char</code></td>
<td class="org-left">in</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"><code>char</code></td>
<td class="org-left">in</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"><code>int64_t</code></td>
<td class="org-left">in</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"><code>int64_t</code></td>
<td class="org-left">in</td>
<td class="org-left">Number of points in the second set</td>
</tr>
<tr>
<td class="org-left"><code>A</code></td>
<td class="org-left"><code>double[][lda]</code></td>
<td class="org-left">in</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"><code>int64_t</code></td>
<td class="org-left">in</td>
<td class="org-left">Leading dimension of array <code>A</code></td>
</tr>
<tr>
<td class="org-left"><code>B</code></td>
<td class="org-left"><code>double[][ldb]</code></td>
<td class="org-left">in</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"><code>int64_t</code></td>
<td class="org-left">in</td>
<td class="org-left">Leading dimension of array <code>B</code></td>
</tr>
<tr>
<td class="org-left"><code>C</code></td>
<td class="org-left"><code>double[n][ldc]</code></td>
<td class="org-left">out</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"><code>int64_t</code></td>
<td class="org-left">in</td>
<td class="org-left">Leading dimension of array <code>C</code></td>
</tr>
</tbody>
</table>
<p>
Requirements:
</p>
<ul class="org-ul">
<li><code>context</code> is not <code>QMCKL_NULL_CONTEXT</code></li>
<li><code>m &gt; 0</code></li>
<li><code>n &gt; 0</code></li>
<li><code>lda &gt;= 3</code> if <code>transa == 'N'</code></li>
<li><code>lda &gt;= m</code> if <code>transa == 'T'</code></li>
<li><code>ldb &gt;= 3</code> if <code>transb == 'N'</code></li>
<li><code>ldb &gt;= n</code> if <code>transb == 'T'</code></li>
<li><code>ldc &gt;= m</code></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 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: #228b22;">double</span>* <span style="color: #a020f0;">const</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 class="org-src-container">
<pre class="src src-f90"><span style="color: #a020f0;">function</span> <span style="color: #0000ff;">qmckl_distance_sq</span>(context, transa, transb, m, n, <span style="color: #a020f0;">&amp;</span>
A, LDA, B, LDB, C, LDC) <span style="color: #a020f0;">&amp;</span>
<span style="color: #a020f0;">bind</span>(C) <span style="color: #a020f0;">result</span>(info)
<span style="color: #a020f0;">use</span> <span style="color: #0000ff;">qmckl_constants</span>
<span style="color: #a020f0;">implicit</span> <span style="color: #228b22;">none</span>
<span style="color: #228b22;">integer</span> (qmckl_context) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> context</span>
<span style="color: #228b22;">character</span>(<span style="color: #008b8b;">c_char</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> transa</span>
<span style="color: #228b22;">character</span>(<span style="color: #008b8b;">c_char</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> transb</span>
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> m</span>
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> n</span>
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> lda</span>
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> ldb</span>
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> ldc</span>
<span style="color: #228b22;">real</span> (<span style="color: #008b8b;">c_double</span> ) , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> A(lda,*)</span>
<span style="color: #228b22;">real</span> (<span style="color: #008b8b;">c_double</span> ) , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> B(ldb,*)</span>
<span style="color: #228b22;">real</span> (<span style="color: #008b8b;">c_double</span> ) , <span style="color: #a020f0;">intent</span>(out) ::<span style="color: #a0522d;"> C(ldc,n)</span>
<span style="color: #228b22;">integer</span>(qmckl_exit_code) ::<span style="color: #a0522d;"> info</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 = QMCKL_SUCCESS
<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 &lt;= 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 &lt;= 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> (transb == <span style="color: #8b2252;">'T'</span> <span style="color: #a020f0;">.or.</span> transb == <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 &lt; 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 &lt; 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 &lt; 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> LDB &lt; 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> LDB &lt; n) <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</span>
</pre>
</div>
</div>
<div id="outline-container-org3996e2a" class="outline-4">
<h4 id="org3996e2a"><span class="section-number-4">1.1.1.</span> Performance</h4>
<div class="outline-text-4" id="text-1-1-1">
<p>
This function is more efficient when <code>A</code> and <code>B</code> are
transposed.
</p>
</div>
</div>
</div>
</div>
<div id="outline-container-org31e63c6" class="outline-2">
<h2 id="org31e63c6"><span class="section-number-2">2.</span> Distance</h2>
<div class="outline-text-2" id="text-2">
</div>
<div id="outline-container-org9e56505" class="outline-3">
<h3 id="org9e56505"><span class="section-number-3">2.1.</span> <code>qmckl_distance</code></h3>
<div class="outline-text-3" id="text-2-1">
<p>
<code>qmckl_distance</code> computes the matrix of the distances between all
pairs of points in two sets, one point within each set:
</p>
<p>
\[
C_{ij} = \sqrt{\sum_{k=1}^3 (A_{k,i}-B_{k,j})^2}
\]
</p>
<p>
If the input array is normal (<code>'N'</code>), the xyz coordinates are in
the leading dimension: <code>[n][3]</code> in C and <code>(3,n)</code> in Fortran.
</p>
<table id="orgd1ac06f" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Variable</th>
<th scope="col" class="org-left">Type</th>
<th scope="col" class="org-left">In/Out</th>
<th scope="col" class="org-left">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left"><code>context</code></td>
<td class="org-left"><code>qmckl_context</code></td>
<td class="org-left">in</td>
<td class="org-left">Global state</td>
</tr>
<tr>
<td class="org-left"><code>transa</code></td>
<td class="org-left"><code>char</code></td>
<td class="org-left">in</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"><code>char</code></td>
<td class="org-left">in</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"><code>int64_t</code></td>
<td class="org-left">in</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"><code>int64_t</code></td>
<td class="org-left">in</td>
<td class="org-left">Number of points in the second set</td>
</tr>
<tr>
<td class="org-left"><code>A</code></td>
<td class="org-left"><code>double[][lda]</code></td>
<td class="org-left">in</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"><code>int64_t</code></td>
<td class="org-left">in</td>
<td class="org-left">Leading dimension of array <code>A</code></td>
</tr>
<tr>
<td class="org-left"><code>B</code></td>
<td class="org-left"><code>double[][ldb]</code></td>
<td class="org-left">in</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"><code>int64_t</code></td>
<td class="org-left">in</td>
<td class="org-left">Leading dimension of array <code>B</code></td>
</tr>
<tr>
<td class="org-left"><code>C</code></td>
<td class="org-left"><code>double[n][ldc]</code></td>
<td class="org-left">out</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"><code>int64_t</code></td>
<td class="org-left">in</td>
<td class="org-left">Leading dimension of array <code>C</code></td>
</tr>
</tbody>
</table>
</div>
<div id="outline-container-org676a534" class="outline-4">
<h4 id="org676a534"><span class="section-number-4">2.1.1.</span> Requirements</h4>
<div class="outline-text-4" id="text-2-1-1">
<ul class="org-ul">
<li><code>context</code> is not <code>QMCKL_NULL_CONTEXT</code></li>
<li><code>m &gt; 0</code></li>
<li><code>n &gt; 0</code></li>
<li><code>lda &gt;= 3</code> if <code>transa == 'N'</code></li>
<li><code>lda &gt;= m</code> if <code>transa == 'T'</code></li>
<li><code>ldb &gt;= 3</code> if <code>transb == 'N'</code></li>
<li><code>ldb &gt;= n</code> if <code>transb == 'T'</code></li>
<li><code>ldc &gt;= m</code></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-orgcca461a" class="outline-4">
<h4 id="orgcca461a"><span class="section-number-4">2.1.2.</span> C header</h4>
<div class="outline-text-4" id="text-2-1-2">
<div class="org-src-container">
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_distance</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: #228b22;">double</span>* <span style="color: #a020f0;">const</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-org0622776" class="outline-4">
<h4 id="org0622776"><span class="section-number-4">2.1.3.</span> Source</h4>
<div class="outline-text-4" id="text-2-1-3">
<div class="org-src-container">
<pre class="src src-f90"><span style="color: #a020f0;">function</span> <span style="color: #0000ff;">qmckl_distance</span>(context, transa, transb, m, n, <span style="color: #a020f0;">&amp;</span>
A, LDA, B, LDB, C, LDC) <span style="color: #a020f0;">&amp;</span>
<span style="color: #a020f0;">bind</span>(C) <span style="color: #a020f0;">result</span>(info)
<span style="color: #a020f0;">use</span> <span style="color: #0000ff;">qmckl_constants</span>
<span style="color: #a020f0;">implicit</span> <span style="color: #228b22;">none</span>
<span style="color: #228b22;">integer</span>(qmckl_context), <span style="color: #a020f0;">intent</span>(in), <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> context</span>
<span style="color: #228b22;">character</span>(<span style="color: #008b8b;">c_char</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> transa</span>
<span style="color: #228b22;">character</span>(<span style="color: #008b8b;">c_char</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> transb</span>
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> m</span>
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> n</span>
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> lda</span>
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> ldb</span>
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> ldc</span>
<span style="color: #228b22;">real</span> (<span style="color: #008b8b;">c_double</span> ) , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> A(lda,*)</span>
<span style="color: #228b22;">real</span> (<span style="color: #008b8b;">c_double</span> ) , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> B(ldb,*)</span>
<span style="color: #228b22;">real</span> (<span style="color: #008b8b;">c_double</span> ) , <span style="color: #a020f0;">intent</span>(out) ::<span style="color: #a0522d;"> C(ldc,n)</span>
<span style="color: #228b22;">integer</span> (qmckl_exit_code) ::<span style="color: #a0522d;"> info</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 = QMCKL_SUCCESS
<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 &lt;= 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 &lt;= 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> (transb == <span style="color: #8b2252;">'T'</span> <span style="color: #a020f0;">.or.</span> transb == <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 &lt; 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: #b22222;">check for LDA</span>
<span style="color: #a020f0;">if</span> (<span style="color: #a020f0;">iand</span>(transab,1) == 0 <span style="color: #a020f0;">.and.</span> LDA &lt; 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 &lt; 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: #b22222;">check for LDB</span>
<span style="color: #a020f0;">if</span> (<span style="color: #a020f0;">iand</span>(transab,1) == 0 <span style="color: #a020f0;">.and.</span> LDB &lt; 3) <span style="color: #a020f0;">then</span>
info = QMCKL_INVALID_ARG_9
<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> LDB &lt; n) <span style="color: #a020f0;">then</span>
info = QMCKL_INVALID_ARG_9
<span style="color: #a020f0;">return</span>
<span style="color: #a020f0;">endif</span>
! <span style="color: #b22222;">check for LDC</span>
<span style="color: #a020f0;">if</span> (LDC &lt; m) <span style="color: #a020f0;">then</span>
info = QMCKL_INVALID_ARG_11
<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>
C(:,j) = dsqrt(C(:,j))
<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>
C(:,j) = dsqrt(C(:,j))
<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>
C(:,j) = dsqrt(C(:,j))
<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>
C(:,j) = dsqrt(C(:,j))
<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</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-org521329d" class="outline-4">
<h4 id="org521329d"><span class="section-number-4">2.1.4.</span> Performance</h4>
<div class="outline-text-4" id="text-2-1-4">
<p>
This function is more efficient when <code>A</code> and <code>B</code> are transposed.
</p>
</div>
</div>
</div>
</div>
<div id="outline-container-orgcc8a08d" class="outline-2">
<h2 id="orgcc8a08d"><span class="section-number-2">3.</span> Rescaled Distance</h2>
<div class="outline-text-2" id="text-3">
</div>
<div id="outline-container-org9bb806f" class="outline-3">
<h3 id="org9bb806f"><span class="section-number-3">3.1.</span> <code>qmckl_distance_rescaled</code></h3>
<div class="outline-text-3" id="text-3-1">
<p>
<code>qmckl_distance_rescaled</code> computes the matrix of the rescaled distances between all
pairs of points in two sets, one point within each set:
</p>
<p>
\[
C_{ij} = \frac{ 1 - e^{-\kappa r_{ij}}}{\kappa}
\]
</p>
<p>
If the input array is normal (<code>'N'</code>), the xyz coordinates are in
the leading dimension: <code>[n][3]</code> in C and <code>(3,n)</code> in Fortran.
</p>
<table id="org4422481" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Variable</th>
<th scope="col" class="org-left">Type</th>
<th scope="col" class="org-left">In/Out</th>
<th scope="col" class="org-left">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left"><code>context</code></td>
<td class="org-left"><code>qmckl_context</code></td>
<td class="org-left">in</td>
<td class="org-left">Global state</td>
</tr>
<tr>
<td class="org-left"><code>transa</code></td>
<td class="org-left"><code>char</code></td>
<td class="org-left">in</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"><code>char</code></td>
<td class="org-left">in</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"><code>int64_t</code></td>
<td class="org-left">in</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"><code>int64_t</code></td>
<td class="org-left">in</td>
<td class="org-left">Number of points in the second set</td>
</tr>
<tr>
<td class="org-left"><code>A</code></td>
<td class="org-left"><code>double[][lda]</code></td>
<td class="org-left">in</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"><code>int64_t</code></td>
<td class="org-left">in</td>
<td class="org-left">Leading dimension of array <code>A</code></td>
</tr>
<tr>
<td class="org-left"><code>B</code></td>
<td class="org-left"><code>double[][ldb]</code></td>
<td class="org-left">in</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"><code>int64_t</code></td>
<td class="org-left">in</td>
<td class="org-left">Leading dimension of array <code>B</code></td>
</tr>
<tr>
<td class="org-left"><code>C</code></td>
<td class="org-left"><code>double[n][ldc]</code></td>
<td class="org-left">out</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"><code>int64_t</code></td>
<td class="org-left">in</td>
<td class="org-left">Leading dimension of array <code>C</code></td>
</tr>
<tr>
<td class="org-left"><code>rescale_factor_kappa</code></td>
<td class="org-left"><code>double</code></td>
<td class="org-left">in</td>
<td class="org-left">Factor for calculating rescaled distances</td>
</tr>
</tbody>
</table>
</div>
<div id="outline-container-orgc0cfb39" class="outline-4">
<h4 id="orgc0cfb39"><span class="section-number-4">3.1.1.</span> Requirements</h4>
<div class="outline-text-4" id="text-3-1-1">
<ul class="org-ul">
<li><code>context</code> is not <code>QMCKL_NULL_CONTEXT</code></li>
<li><code>m &gt; 0</code></li>
<li><code>n &gt; 0</code></li>
<li><code>lda &gt;= 3</code> if <code>transa == 'N'</code></li>
<li><code>lda &gt;= m</code> if <code>transa == 'T'</code></li>
<li><code>ldb &gt;= 3</code> if <code>transb == 'N'</code></li>
<li><code>ldb &gt;= n</code> if <code>transb == 'T'</code></li>
<li><code>ldc &gt;= m</code></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-org4aafa08" class="outline-4">
<h4 id="org4aafa08"><span class="section-number-4">3.1.2.</span> C header</h4>
<div class="outline-text-4" id="text-3-1-2">
<div class="org-src-container">
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_distance_rescaled</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: #228b22;">double</span>* <span style="color: #a020f0;">const</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>,
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">rescale_factor_kappa</span> );
</pre>
</div>
</div>
</div>
<div id="outline-container-org4f8c847" class="outline-4">
<h4 id="org4f8c847"><span class="section-number-4">3.1.3.</span> Source</h4>
<div class="outline-text-4" id="text-3-1-3">
<div class="org-src-container">
<pre class="src src-f90"><span style="color: #a020f0;">function</span> <span style="color: #0000ff;">qmckl_distance_rescaled</span>(context, transa, transb, m, n, <span style="color: #a020f0;">&amp;</span>
A, LDA, B, LDB, C, LDC, rescale_factor_kappa) <span style="color: #a020f0;">&amp;</span>
<span style="color: #a020f0;">bind</span>(C) <span style="color: #a020f0;">result</span>(info)
<span style="color: #a020f0;">use</span> <span style="color: #0000ff;">qmckl_constants</span>
<span style="color: #a020f0;">implicit</span> <span style="color: #228b22;">none</span>
<span style="color: #228b22;">integer</span> (qmckl_context), <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> context</span>
<span style="color: #228b22;">character</span>(<span style="color: #008b8b;">c_char</span> ) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> transa</span>
<span style="color: #228b22;">character</span>(<span style="color: #008b8b;">c_char</span> ) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> transb</span>
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> m</span>
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> n</span>
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> lda</span>
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> ldb</span>
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> ldc</span>
<span style="color: #228b22;">real</span> (<span style="color: #008b8b;">c_double</span> ) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> rescale_factor_kappa</span>
<span style="color: #228b22;">real</span> (<span style="color: #008b8b;">c_double</span> ) , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> A(lda,*)</span>
<span style="color: #228b22;">real</span> (<span style="color: #008b8b;">c_double</span> ) , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> B(ldb,*)</span>
<span style="color: #228b22;">real</span> (<span style="color: #008b8b;">c_double</span> ) , <span style="color: #a020f0;">intent</span>(out) ::<span style="color: #a0522d;"> C(ldc,n)</span>
<span style="color: #228b22;">integer</span>(qmckl_exit_code) ::<span style="color: #a0522d;"> info</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, dist, rescale_factor_kappa_inv</span>
<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> transab</span>
rescale_factor_kappa_inv = 1.0d0/rescale_factor_kappa;
info = QMCKL_SUCCESS
<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 &lt;= 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 &lt;= 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> (transb == <span style="color: #8b2252;">'T'</span> <span style="color: #a020f0;">.or.</span> transb == <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: #b22222;">check for LDA</span>
<span style="color: #a020f0;">if</span> (transab &lt; 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 &lt; 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 &lt; 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: #b22222;">check for LDB</span>
<span style="color: #a020f0;">if</span> (<span style="color: #a020f0;">iand</span>(transab,2) == 0 <span style="color: #a020f0;">.and.</span> LDB &lt; 3) <span style="color: #a020f0;">then</span>
info = QMCKL_INVALID_ARG_9
<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> LDB &lt; n) <span style="color: #a020f0;">then</span>
info = QMCKL_INVALID_ARG_9
<span style="color: #a020f0;">return</span>
<span style="color: #a020f0;">endif</span>
! <span style="color: #b22222;">check for LDC</span>
<span style="color: #a020f0;">if</span> (LDC &lt; m) <span style="color: #a020f0;">then</span>
info = QMCKL_INVALID_ARG_11
<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)
dist = dsqrt(x*x + y*y + z*z)
C(i,j) = (1.0d0 - dexp(-rescale_factor_kappa * dist)) * rescale_factor_kappa_inv
<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)
dist = dsqrt(x*x + y*y + z*z)
C(i,j) = (1.0d0 - dexp(-rescale_factor_kappa * dist)) * rescale_factor_kappa_inv
<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)
dist = dsqrt(x*x + y*y + z*z)
C(i,j) = (1.0d0 - dexp(-rescale_factor_kappa * dist)) * rescale_factor_kappa_inv
<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)
dist = dsqrt(x*x + y*y + z*z)
C(i,j) = (1.0d0 - dexp(-rescale_factor_kappa * dist)) * rescale_factor_kappa_inv
<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_rescaled</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-org435bcf3" class="outline-4">
<h4 id="org435bcf3"><span class="section-number-4">3.1.4.</span> Performance</h4>
<div class="outline-text-4" id="text-3-1-4">
<p>
This function is more efficient when <code>A</code> and <code>B</code> are transposed.
</p>
</div>
</div>
</div>
</div>
<div id="outline-container-orgd72cafc" class="outline-2">
<h2 id="orgd72cafc"><span class="section-number-2">4.</span> Rescaled Distance Derivatives</h2>
<div class="outline-text-2" id="text-4">
</div>
<div id="outline-container-org77cae89" class="outline-3">
<h3 id="org77cae89"><span class="section-number-3">4.1.</span> <code>qmckl_distance_rescaled_gl</code></h3>
<div class="outline-text-3" id="text-4-1">
<p>
<code>qmckl_distance_rescaled_gl</code> computes the matrix of the gradient and Laplacian of the
rescaled distance with respect to the electron coordinates. The derivative is a rank 3 tensor.
The first dimension has a dimension of 4 of which the first three coordinates
contains the gradient vector and the last index is the Laplacian.
</p>
<p>
\[
C(r_{ij}) = \left( 1 - \exp(-\kappa\, r_{ij})\right)/\kappa
\]
</p>
<p>
Here the gradient is defined as follows:
</p>
<p>
\[
\nabla_i C(r_{ij}) = \left(\frac{\partial C(r_{ij})}{\partial x_i},\frac{\partial C(r_{ij})}{\partial y_i},\frac{\partial C(r_{ij})}{\partial z_i} \right)
\]
and the Laplacian is defined as follows:
</p>
<p>
\[
\Delta_i C(r_{ij}) = \frac{\partial^2}{\partial x_i^2} + \frac{\partial^2}{\partial y_i^2} + \frac{\partial^2}{\partial z_i^2}
\]
</p>
<p>
Using the above three formulas, the expression for the gradient and Laplacian is:
</p>
<p>
\[
\frac{\partial C(r_{ij})}{\partial x_i} = \frac{|(x_i -
x_j)|}{r_{ij}} \exp (- \kappa \, r_{ij})
\]
</p>
<p>
\[
\Delta C_{ij}(r_{ij}) = \left[ \frac{2}{r_{ij}} - \kappa \right] \exp (- \kappa \, r_{ij})
\]
</p>
<p>
If the input array is normal (<code>'N'</code>), the xyz coordinates are in
the leading dimension: <code>[n][3]</code> in C and <code>(3,n)</code> in Fortran.
</p>
<table id="org664922a" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Variable</th>
<th scope="col" class="org-left">Type</th>
<th scope="col" class="org-left">In/Out</th>
<th scope="col" class="org-left">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left"><code>context</code></td>
<td class="org-left"><code>qmckl_context</code></td>
<td class="org-left">in</td>
<td class="org-left">Global state</td>
</tr>
<tr>
<td class="org-left"><code>transa</code></td>
<td class="org-left"><code>char</code></td>
<td class="org-left">in</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"><code>char</code></td>
<td class="org-left">in</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"><code>int64_t</code></td>
<td class="org-left">in</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"><code>int64_t</code></td>
<td class="org-left">in</td>
<td class="org-left">Number of points in the second set</td>
</tr>
<tr>
<td class="org-left"><code>A</code></td>
<td class="org-left"><code>double[][lda]</code></td>
<td class="org-left">in</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"><code>int64_t</code></td>
<td class="org-left">in</td>
<td class="org-left">Leading dimension of array <code>A</code></td>
</tr>
<tr>
<td class="org-left"><code>B</code></td>
<td class="org-left"><code>double[][ldb]</code></td>
<td class="org-left">in</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"><code>int64_t</code></td>
<td class="org-left">in</td>
<td class="org-left">Leading dimension of array <code>B</code></td>
</tr>
<tr>
<td class="org-left"><code>C</code></td>
<td class="org-left"><code>double[n][ldc][4]</code></td>
<td class="org-left">out</td>
<td class="org-left">Array containing the \(4 \times m \times n\) matrix \(C\)</td>
</tr>
<tr>
<td class="org-left"><code>ldc</code></td>
<td class="org-left"><code>int64_t</code></td>
<td class="org-left">in</td>
<td class="org-left">Leading dimension of array <code>C</code></td>
</tr>
<tr>
<td class="org-left"><code>rescale_factor_kappa</code></td>
<td class="org-left"><code>double</code></td>
<td class="org-left">in</td>
<td class="org-left">Factor for calculating rescaled distances derivatives</td>
</tr>
</tbody>
</table>
<p>
Requirements:
</p>
<ul class="org-ul">
<li><code>context</code> is not <code>QMCKL_NULL_CONTEXT</code></li>
<li><code>m &gt; 0</code></li>
<li><code>n &gt; 0</code></li>
<li><code>lda &gt;= 3</code> if <code>transa == 'N'</code></li>
<li><code>lda &gt;= m</code> if <code>transa == 'T'</code></li>
<li><code>ldb &gt;= 3</code> if <code>transb == 'N'</code></li>
<li><code>ldb &gt;= n</code> if <code>transb == 'T'</code></li>
<li><code>ldc &gt;= m</code></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 \(4 \times m \times n \times 8\) bytes</li>
</ul>
<div class="org-src-container">
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_distance_rescaled_gl</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: #228b22;">double</span>* <span style="color: #a020f0;">const</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>,
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> <span style="color: #a0522d;">rescale_factor_kappa</span> );
</pre>
</div>
<div class="org-src-container">
<pre class="src src-f90"><span style="color: #a020f0;">function</span> <span style="color: #0000ff;">qmckl_distance_rescaled_gl</span>(context, transa, transb, m, n, <span style="color: #a020f0;">&amp;</span>
A, LDA, B, LDB, C, LDC, rescale_factor_kappa) <span style="color: #a020f0;">&amp;</span>
<span style="color: #a020f0;">bind</span>(C) <span style="color: #a020f0;">result</span>(info)
<span style="color: #a020f0;">use</span> <span style="color: #0000ff;">qmckl_constants</span>
<span style="color: #a020f0;">implicit</span> <span style="color: #228b22;">none</span>
<span style="color: #228b22;">integer</span>(qmckl_exit_code) ::<span style="color: #a0522d;"> info</span>
<span style="color: #228b22;">integer</span> (qmckl_context), <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> context</span>
<span style="color: #228b22;">character</span>(<span style="color: #008b8b;">c_char</span> ) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> transa</span>
<span style="color: #228b22;">character</span>(<span style="color: #008b8b;">c_char</span> ) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> transb</span>
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> m</span>
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> n</span>
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> lda</span>
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> ldb</span>
<span style="color: #228b22;">integer</span> (<span style="color: #008b8b;">c_int64_t</span>) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> ldc</span>
<span style="color: #228b22;">real</span> (<span style="color: #008b8b;">c_double</span> ) , <span style="color: #a020f0;">intent</span>(in) , <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> rescale_factor_kappa</span>
<span style="color: #228b22;">real</span> (<span style="color: #008b8b;">c_double</span> ) , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> A(lda,*)</span>
<span style="color: #228b22;">real</span> (<span style="color: #008b8b;">c_double</span> ) , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> B(ldb,*)</span>
<span style="color: #228b22;">real</span> (<span style="color: #008b8b;">c_double</span> ) , <span style="color: #a020f0;">intent</span>(out) ::<span style="color: #a0522d;"> C(4,ldc,n)</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, dist, dist_inv</span>
<span style="color: #228b22;">real</span>*8 ::<span style="color: #a0522d;"> rij</span>
<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> transab</span>
info = QMCKL_SUCCESS
<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 &lt;= 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 &lt;= 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> (transb == <span style="color: #8b2252;">'T'</span> <span style="color: #a020f0;">.or.</span> transb == <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: #b22222;">check for LDA</span>
<span style="color: #a020f0;">if</span> (transab &lt; 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 &lt; 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 &lt; 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: #b22222;">check for LDB</span>
<span style="color: #a020f0;">if</span> (<span style="color: #a020f0;">iand</span>(transab,2) == 0 <span style="color: #a020f0;">.and.</span> LDB &lt; 3) <span style="color: #a020f0;">then</span>
info = QMCKL_INVALID_ARG_9
<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> LDB &lt; n) <span style="color: #a020f0;">then</span>
info = QMCKL_INVALID_ARG_9
<span style="color: #a020f0;">return</span>
<span style="color: #a020f0;">endif</span>
! <span style="color: #b22222;">check for LDC</span>
<span style="color: #a020f0;">if</span> (LDC &lt; m) <span style="color: #a020f0;">then</span>
info = QMCKL_INVALID_ARG_11
<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)
dist = <span style="color: #a020f0;">max</span>(1.d-20, dsqrt(x*x + y*y + z*z))
dist_inv = 1.0d0/dist
rij = dexp(-rescale_factor_kappa * dist)
C(1,i,j) = x * dist_inv * rij
C(2,i,j) = y * dist_inv * rij
C(3,i,j) = z * dist_inv * rij
C(4,i,j) = (2.0d0 * dist_inv - rescale_factor_kappa) * rij
<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)
dist = <span style="color: #a020f0;">max</span>(1.d-20, dsqrt(x*x + y*y + z*z))
dist_inv = 1.0d0/dist
rij = dexp(-rescale_factor_kappa * dist)
C(1,i,j) = x * dist_inv * rij
C(2,i,j) = y * dist_inv * rij
C(3,i,j) = z * dist_inv * rij
C(4,i,j) = (2.0d0 * dist_inv - rescale_factor_kappa) * rij
<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)
dist = <span style="color: #a020f0;">max</span>(1.d-20, dsqrt(x*x + y*y + z*z))
dist_inv = 1.0d0/dist
rij = dexp(-rescale_factor_kappa * dist)
C(1,i,j) = x * dist_inv * rij
C(2,i,j) = y * dist_inv * rij
C(3,i,j) = z * dist_inv * rij
C(4,i,j) = (2.0d0 * dist_inv - rescale_factor_kappa) * rij
<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)
dist = <span style="color: #a020f0;">max</span>(1.d-20, dsqrt(x*x + y*y + z*z))
dist_inv = 1.0d0/dist
rij = dexp(-rescale_factor_kappa * dist)
C(1,i,j) = x * dist_inv * rij
C(2,i,j) = y * dist_inv * rij
C(3,i,j) = z * dist_inv * rij
C(4,i,j) = (2.0d0 * dist_inv - rescale_factor_kappa) * rij
<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_rescaled_gl</span>
</pre>
</div>
<p>
This function is more efficient when <code>A</code> and <code>B</code> are transposed.
</p>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: TREX CoE</p>
<p class="date">Created: 2025-04-29 Tue 08:44</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
</body>
</html>
Reference in New Issue View Git Blame Copy Permalink