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<body>
<div id="content">
<h1 class="title">pochoir user manual</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#orgf1e1bc7">Introduction</a>
<ul>
<li><a href="#orgced7ad1">Overview of calculating response functions</a></li>
<li><a href="#org9765ae2">FDM for Laplace boundary value problem</a></li>
<li><a href="#org1eace20">RK4/5 for paths initial value problem</a></li>
</ul>
</li>
<li><a href="#orgd5e6fab">Getting started</a>
<ul>
<li><a href="#org0cd9beb">Installation</a></li>
<li><a href="#orgf7e744e">General usage</a></li>
<li><a href="#org081256a">Using CPU vs GPU</a></li>
<li><a href="#org4d2d806">Data and its storage</a></li>
</ul>
</li>
<li><a href="#orga9044d4">Tutorial</a>
<ul>
<li><a href="#orgb94f25c">Define the problem domain</a></li>
<li><a href="#org81a6911">Define initial and boundary value arrays</a></li>
<li><a href="#orgd00c747">Solve Laplace equation</a></li>
<li><a href="#orge9c1c5b">Calculate and visualize gradient fields</a></li>
<li><a href="#orgb436c02">Path initial value problem</a></li>
<li><a href="#org1cfab03">Calculate responses</a></li>
<li><a href="#org7a64c19">Convert to Wire-Cell</a></li>
<li><a href="#orge08789f">Automation with Snakemake</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div id="outline-container-orgf1e1bc7" class="outline-2">
<h2 id="orgf1e1bc7">Introduction</h2>
<div class="outline-text-2" id="text-orgf1e1bc7">
<p>
This describes how to use <code>pochoir</code>.
</p>
<p>
Following sections:
</p>
<ul class="org-ul">
<li>getting started</li>
<li>usage tutorial</li>
<li>developer guide</li>
</ul>
<p>
Remaining subsections describe <code>pochoir</code> concepts
</p>
</div>
<div id="outline-container-orgced7ad1" class="outline-3">
<h3 id="orgced7ad1">Overview of calculating response functions</h3>
<div class="outline-text-3" id="text-orgced7ad1">
<ul class="org-ul">
<li>describe the steps and data products</li>
</ul>
</div>
</div>
<div id="outline-container-org9765ae2" class="outline-3">
<h3 id="org9765ae2">FDM for Laplace boundary value problem</h3>
<div class="outline-text-3" id="text-org9765ae2">
<ul class="org-ul">
<li>characteristics of problem where FDM is applicable (grid vs geometry feature sizes)</li>
<li>define terms
<ul class="org-ul">
<li>domain</li>
<li>boundary value problem
<ul class="org-ul">
<li>boundary and initial values and boundary condition</li>
</ul></li>
<li>initial value problem
<ul class="org-ul">
<li>paths</li>
</ul></li>
</ul></li>
</ul>
</div>
</div>
<div id="outline-container-org1eace20" class="outline-3">
<h3 id="org1eace20">RK4/5 for paths initial value problem</h3>
</div>
</div>
<div id="outline-container-orgd5e6fab" class="outline-2">
<h2 id="orgd5e6fab">Getting started</h2>
<div class="outline-text-2" id="text-orgd5e6fab">
</div>
<div id="outline-container-org0cd9beb" class="outline-3">
<h3 id="org0cd9beb">Installation</h3>
<div class="outline-text-3" id="text-org0cd9beb">
<ul class="org-ul">
<li>get package</li>
<li>venv options (<code>python -m venv venv ; source venv/bin/activate</code> and <code>echo layout python3 > .envrc; direnv allow</code>)</li>
<li>install (<code>pip install -e .</code> or <code>pip install git@github.com:wirecell/pochoir.git</code> or whatever)</li>
<li>testing (<code>pytest</code>)</li>
</ul>
</div>
</div>
<div id="outline-container-orgf7e744e" class="outline-3">
<h3 id="orgf7e744e">General usage</h3>
<div class="outline-text-3" id="text-orgf7e744e">
<ul class="org-ul">
<li>CLI help</li>
<li>general CLI vs command-level options</li>
<li>environment variables (<code>POCHOIR_STORE</code>)</li>
</ul>
</div>
</div>
<div id="outline-container-org081256a" class="outline-3">
<h3 id="org081256a">Using CPU vs GPU</h3>
<div class="outline-text-3" id="text-org081256a">
<ul class="org-ul">
<li>devices: "best" vs "numpy" vs torch "cpu" and "gpu" (still needs actual implementation to pick "best" or otherwise globally set)</li>
<li>selection via CLI options</li>
<li>when to care what device is used</li>
</ul>
</div>
</div>
<div id="outline-container-org4d2d806" class="outline-3">
<h3 id="org4d2d806">Data and its storage</h3>
<div class="outline-text-3" id="text-org4d2d806">
<ul class="org-ul">
<li>main data objects
<ul class="org-ul">
<li>domain</li>
<li>scalar fields</li>
<li>vector fields</li>
<li>path start points</li>
<li>full paths</li>
<li>responses</li>
</ul></li>
<li>separate input and output vs input+output store</li>
<li>HDF5 vs NPZ+JSON+directory
<ul class="org-ul">
<li>latter can work with snakemake or similar</li>
<li>converting between the two</li>
</ul></li>
<li>export formats
<ul class="org-ul">
<li>vtk</li>
</ul></li>
<li>input formats
<ul class="org-ul">
<li>invent something for electrode shape description, probably JSON based
<ul class="org-ul">
<li>maybe jsonnet</li>
</ul></li>
<li>do we allow import of data object from, say, external NPZ?</li>
</ul></li>
</ul>
</div>
</div>
</div>
<div id="outline-container-orga9044d4" class="outline-2">
<h2 id="orga9044d4">Tutorial</h2>
<div class="outline-text-2" id="text-orga9044d4">
<p>
This tutorial walks through the individual steps of calculating field
responses for a 2D problem and ends with an example of how to automate
the entire workflow.
</p>
</div>
<div id="outline-container-orgb94f25c" class="outline-3">
<h3 id="orgb94f25c">Define the problem domain</h3>
<div class="outline-text-3" id="text-orgb94f25c">
<p>
A <i>domain</i> of a problem is the space on which it is defined. A <code>pochoir</code>
domain is a <i>finite, uniform, rectilinear</i> (Cartesian) grid of points.
In general, the grid may be N-dimensional though practical problems
will require either 2D or 3D (or possibly a mix of both).
</p>
<p>
A domain can be created simply with the <code>pochoir domain</code> command:
</p>
<div class="org-src-container">
<pre class="src src-shell">pochoir domain --help
</pre>
</div>
<pre class="example" id="orga921357">
Usage: pochoir domain [OPTIONS] NAME
Produce a "domain" and store it to the output dataset.
A domain describes a finite, uniform grid in N-D space in these terms:
- shape :: an N-D integer vector giving the number of grid
points in each dimension. Required.
- origin :: an N-D spatial vector identifying the location of
the grid point with all indices zero.
- spacing :: a scalar or N-D vector in same distance units as
used in origin and which gives a common or a per-dimension
spacing between neighboring grid points.
- first :: an N-D integer vector giving the first valid index in
each dimension (which is almost always the default, 0)
A vector is given as a comma-separated list of numbers.
Note: this description corresponds to vtk/paraview uniform rectilinear
grid, aka an "image".
Options:
-s, --shape TEXT The number of grid points in each dimension
-o, --origin TEXT The spatial location of zero index grid point (def=0's)
-s, --spacing TEXT The grid spacing as scalar or vector (def=1's)
-f, --first TEXT The first indices for each dimension (def=0's)
--help Show this message and exit.
</pre>
<p>
As shown in the help, each of the four vectors can be given on the
command line but only <code>shape</code> is required if the defaults are
sufficient. The size of the <code>shape</code> vector sets the dimension of the
domain.
</p>
<div class="org-src-container">
<pre class="src src-shell">pochoir domain --shape 100,100 --spacing 0.1 adomain
ls -l store/adomain/
</pre>
</div>
<pre class="example" id="org866e4a5">
total 16
-rw-rw-r-- 1 bv bv 280 Mar 19 15:35 first.npz
-rw-rw-r-- 1 bv bv 282 Mar 19 15:35 origin.npz
-rw-rw-r-- 1 bv bv 280 Mar 19 15:35 shape.npz
-rw-rw-r-- 1 bv bv 284 Mar 19 15:35 spacing.npz
</pre>
<div class="note" id="orgc95f524">
<p>
This listing assumes the NPZ based store is used. If using an HDF5 store,
these four arrays are stored as datasets in an HDF5 group named
<code>adomain</code>.
</p>
</div>
<p>
Once defined, a domain is referenced by the given name (<code>adomain</code> here).
</p>
</div>
</div>
<div id="outline-container-org81a6911" class="outline-3">
<h3 id="org81a6911">Define initial and boundary value arrays</h3>
<div class="outline-text-3" id="text-org81a6911">
<p>
An <i>initial value</i> array provides a scalar field from which the FDM
solution begins. Each element holds either a known, applied potential
or an initial guess. The <i>boundary value</i> array elements take a value
of 1 or 0. Unity indicates the corresponding element in the initial
value array should be considered a fixed applied potential and all
others are free to be adjusted by the FDM.
</p>
</div>
<div id="outline-container-orgab831cf" class="outline-4">
<h4 id="orgab831cf">Example initial and boundary value arrays</h4>
<div class="outline-text-4" id="text-orgab831cf">
<p>
A number of hard-wired examples are provided as examples:
</p>
<div class="org-src-container">
<pre class="src src-shell">pochoir example --help
pochoir example list
pochoir example caps
</pre>
</div>
<pre class="example" id="org4413fe4">
Usage: pochoir example [OPTIONS] NAME
Generate a boundary and initial array example (try "list")
Options:
--help Show this message and exit.
caps
sandh
</pre>
<p>
Here, the <code>caps</code> example is created. It represents a fictional set of
parallel plate capacitors. The example populates arrays named
<code>caps-initial</code> and <code>caps-boundary</code> and they may be visualized:
</p>
<div class="org-src-container">
<pre class="src src-shell">pochoir plot-image caps-boundary docs/caps-boundary.png
pochoir plot-image caps-initial docs/caps-initial.png
</pre>
</div>
<div id="org41c2913" class="figure">
<p><img src="docs/caps-boundary.png" alt="caps-boundary.png" />
</p>
</div>
<div id="orga6a6e49" class="figure">
<p><img src="docs/caps-initial.png" alt="caps-initial.png" />
</p>
</div>
</div>
</div>
<div id="outline-container-orgf9919dc" class="outline-4">
<h4 id="orgf9919dc">Custom electrode description</h4>
<div class="outline-text-4" id="text-orgf9919dc">
<p>
For arbitrary problems, the user may provide a description of the
electrodes and their applied potentials and <code>pochoir</code> will render them
to the domain grid.
</p>
<div class="caution" id="org911910a">
<p>
This is work still to be provided.
</p>
</div>
</div>
</div>
</div>
<div id="outline-container-orgd00c747" class="outline-3">
<h3 id="orgd00c747">Solve Laplace equation</h3>
<div class="outline-text-3" id="text-orgd00c747">
<p>
The Laplace equation can be solved by specifying <i>initial</i> and <i>boundary</i>
value arrays, boundary conditions and convergence requirements.
</p>
<div class="org-src-container">
<pre class="src src-shell">pochoir fdm --help
</pre>
</div>
<pre class="example" id="org969d3e7">
Usage: pochoir fdm [OPTIONS] SOLUTION ERROR
Solve a Laplace boundary value problem with finite difference method
storing the result as named solution. The error names an output array to
hold difference in last two iterations.
Options:
-i, --initial TEXT Name initial value array, elements include boundary
values
-b, --boundary TEXT Name the boundary array, zero value elemnts subject
to solving
-e, --edges TEXT Comma separated list of 'fixed' or 'periodic' giving
domain edge conditions
--precision FLOAT Finish when no changes larger than precision
--epoch INTEGER Number of iterations before any check
-n, --nepochs INTEGER Limit number of epochs (def: one epoch)
--help Show this message and exit.
</pre>
<p>
We may make a trial solution which we save it and its error to <code>caps-solution1</code> and <code>caps-error1</code> arrays, respectively
</p>
<div class="org-src-container">
<pre class="src src-shell">pochoir fdm -e periodic,periodic \
-i caps-initial -b caps-boundary \
--epoch 10 -n 1 \
caps-solution1 caps-error1
</pre>
</div>
<pre class="example" id="org5addb1f">
maxerr: 43.046966552734375
</pre>
<p>
The maximum difference between the solution at the penultimate and
last iteration is the printed <code>maxerr</code>.
</p>
<p>
We can visualize solution and error:
</p>
<div class="org-src-container">
<pre class="src src-shell">pochoir plot-image caps-solution1 docs/caps-solution1.png
pochoir plot-image caps-error1 docs/caps-error1.png
</pre>
</div>
<div id="orga35f886" class="figure">
<p><img src="docs/caps-solution1.png" alt="caps-solution1.png" />
</p>
</div>
<div id="orga3471b6" class="figure">
<p><img src="docs/caps-error1.png" alt="caps-error1.png" />
</p>
</div>
<p>
The error is rather high and although this domain is small which makes
the solution fast, we may reuse this first solution as the <i>initial
value</i> array for continued solution:
</p>
<div class="org-src-container">
<pre class="src src-shell">pochoir fdm -e periodic,periodic \
-i caps-solution1 -b caps-boundary \
--epoch 10 -n 1 \
caps-solution2 caps-error2
</pre>
</div>
<pre class="example" id="orgc4864bb">
maxerr: 21.263214111328125
</pre>
<div class="org-src-container">
<pre class="src src-shell">pochoir plot-image caps-solution2 docs/caps-solution2.png
pochoir plot-image caps-error2 docs/caps-error2.png
</pre>
</div>
<div id="org49e157a" class="figure">
<p><img src="docs/caps-solution2.png" alt="caps-solution2.png" />
</p>
</div>
<div id="org05bf33d" class="figure">
<p><img src="docs/caps-error2.png" alt="caps-error2.png" />
</p>
</div>
<p>
We can continue this manual, high-level iteration or take a guess for
the total number of internal iterations to reach the desired error
level. Or, we may tell <code>pochoir fdm</code> to continue until either the
requested number of epochs are reached or the <code>maxerr</code> falls below a
requested precision. When using a precision, it is checked only after
each epoch is complete and so the result will typically be
over-precise.
</p>
<div class="org-src-container">
<pre class="src src-shell">pochoir fdm -e periodic,periodic \
-i caps-solution2 -b caps-boundary \
--epoch 10 -n 100 --precision 0.1 \
caps-solution3 caps-error3
</pre>
</div>
<pre class="example" id="org8f29fa2">
maxerr: 13.02484130859375
maxerr: 8.48162841796875
maxerr: 5.6507568359375
maxerr: 3.921722412109375
maxerr: 2.8282470703125
maxerr: 2.056884765625
maxerr: 1.50787353515625
maxerr: 1.12823486328125
maxerr: 0.855926513671875
maxerr: 0.65093994140625
maxerr: 0.496307373046875
maxerr: 0.37939453125
maxerr: 0.2906494140625
maxerr: 0.2232666015625
maxerr: 0.17201995849609375
maxerr: 0.13336181640625
maxerr: 0.10352325439453125
maxerr: 0.08056640625
</pre>
<p>
The solution is reached prior to 100 epochs. Again, let's see it:
</p>
<div class="org-src-container">
<pre class="src src-shell">pochoir plot-image caps-solution3 docs/caps-solution3.png
pochoir plot-image caps-error3 docs/caps-error3.png
</pre>
</div>
<div id="org93554cd" class="figure">
<p><img src="docs/caps-solution3.png" alt="caps-solution3.png" />
</p>
</div>
<div id="orgc5af1ce" class="figure">
<p><img src="docs/caps-error3.png" alt="caps-error3.png" />
</p>
</div>
</div>
<div id="outline-container-org70a1c4e" class="outline-4">
<h4 id="org70a1c4e">3D Laplace</h4>
<div class="outline-text-4" id="text-org70a1c4e">
<ul class="org-ul">
<li>change in args w.r.t. 2D</li>
<li>understand time/resource scaling with 2D</li>
<li>visualize (matplotlib and paraview)</li>
</ul>
</div>
</div>
<div id="outline-container-orgb14950a" class="outline-4">
<h4 id="orgb14950a">Use 2D as boundary condition for 3D</h4>
<div class="outline-text-4" id="text-orgb14950a">
<ul class="org-ul">
<li>derive 3D boundary values to 2D and merge with 3D boundary values</li>
<li>understand precision of 2D as a function of 3D domain size</li>
</ul>
</div>
</div>
<div id="outline-container-org89d4b9d" class="outline-4">
<h4 id="org89d4b9d">Weighting fields</h4>
<div class="outline-text-4" id="text-org89d4b9d">
<p>
The fantasy example of <code>caps</code> sets boundary values applicable for
calculating the "real", applied potential. The overall field response
is tabulated for each <i>sensitive electrode</i> by calculating that
electrode's <i>weighting potential</i>. Thus we must apply the <code>pochoir fdm</code>
command as above to a <i>boundary value</i> which sets the grid points on the
sensitive electrode to unity and all others to zero.
</p>
<div class="warning" id="org916cbb0">
<p>
FIXME: How best to specify this and manage the results is a WIP.
</p>
</div>
</div>
</div>
</div>
<div id="outline-container-orge9c1c5b" class="outline-3">
<h3 id="orge9c1c5b">Calculate and visualize gradient fields</h3>
<div class="outline-text-3" id="text-orge9c1c5b">
<p>
The <i>gradient</i> of a scalar field gives a vector field. The E-field is
the gradient of the applied potential scalar field and is needed for
the next step of calculating paths. The W-fields, one per sensitive
electrode are needed for the step after, calculating responses to
paths.
</p>
<p>
The <code>pochoir grad</code> command will calculate and store the gradient
allowing for visualization and later use.
</p>
<div class="org-src-container">
<pre class="src src-shell">pochoir grad --help
</pre>
</div>
<pre class="example" id="org6a6436f">
Usage: pochoir grad [OPTIONS] SCALAR VECTOR
Calculate the gradient of a scalar field.
Options:
-d, --domain TEXT Use named dataset for the domain, (def: indices)
--help Show this message and exit.
</pre>
<div class="org-src-container">
<pre class="src src-shell">pochoir grad \
--domain adomain \
caps-solution3 caps-efield3
</pre>
</div>
<p>
We may visualize this field with:
</p>
<div class="org-src-container">
<pre class="src src-shell">pochoir plot-quiver \
--domain adomain \
caps-efield3 docs/caps-efield3.png
</pre>
</div>
<div id="org5a3f5c7" class="figure">
<p><img src="docs/caps-efield3.png" alt="caps-efield3.png" />
</p>
</div>
<ul class="org-ul">
<li>2D and 3D matplotlib</li>
<li>paraview</li>
</ul>
</div>
</div>
<div id="outline-container-orgb436c02" class="outline-3">
<h3 id="orgb436c02">Path initial value problem</h3>
<div class="outline-text-3" id="text-orgb436c02">
<ul class="org-ul">
<li>specify problem to solve</li>
<li>specify initial value</li>
<li>apply solver</li>
<li>store result</li>
<li>visualize (matplotlib and paraview)</li>
</ul>
</div>
</div>
<div id="outline-container-org1cfab03" class="outline-3">
<h3 id="org1cfab03">Calculate responses</h3>
<div class="outline-text-3" id="text-org1cfab03">
<ul class="org-ul">
<li>combine path and fields for schockley-ramo</li>
<li>exploit symmetry and equivalences</li>
<li>visualize</li>
</ul>
</div>
</div>
<div id="outline-container-org7a64c19" class="outline-3">
<h3 id="org7a64c19">Convert to Wire-Cell</h3>
</div>
<div id="outline-container-orge08789f" class="outline-3">
<h3 id="orge08789f">Automation with Snakemake</h3>
<div class="outline-text-3" id="text-orge08789f">
<ul class="org-ul">
<li>full chain, repeatable, performant processing</li>
<li>what knobs to tune</li>
</ul>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Brett Viren</p>
<p class="date">Created: 2021-03-19 Fri 15:35</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
</body>
</html>