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Enhance first demo.
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schoi32 committed Dec 25, 2019
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71 changes: 38 additions & 33 deletions docs/_sources/rst_from_demos/qmcpy_intro.rst.txt
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Welcome to QMCPy
================

Import
------
Importing QMCPy
---------------

Here we show three different ways to import QMCPy in a Python
environment. First, we can import the package ``qmcpy`` under the alias
``qp``.

.. code:: ipython3
import qmcpy
print(qmcpy.name, qmcpy.__version__)
import qmcpy as qp
print(qp.name, qp.__version__)
.. parsed-literal::
qmcpy 0.1
Alternatively, we can import individual objects from ‘qmcpy’ as shown
below.

.. code:: ipython3
# Individual Imports
from qmcpy import integrate
from qmcpy.integrand import *
from qmcpy.true_measure import *
from qmcpy.discrete_distribution import *
from qmcpy.stopping_criterion import *
Lastly, we can import all objects from the package using an asterisk.

.. code:: ipython3
# Complete Import
from qmcpy import *
Important Notes
===============
---------------

IID vs LDS
----------
~~~~~~~~~~

Low discrepancy sequences (LDS) such as lattice and Sobol are not
independent like IID points - The below code generates 1 replication
(squeezed out) of 4 samples of 2 dimensions
independent like IID (independent identically distributed) points.

The code below generates 1 replication (squeezed out) of 4 lattice
samples of 2 dimensions.

.. code:: ipython3
Expand All @@ -58,14 +67,14 @@ independent like IID points - The below code generates 1 replication
Multi-Dimensional Inputs
------------------------
~~~~~~~~~~~~~~~~~~~~~~~~

Suppose we want to create an integrand in QMCPy for evaluating the
following integral:

.. math:: \int_{[0,1]^d} \|x\|_2^{\|x\|_2^{1/2}} dx,
.. math:: \int_{[0,1]^d} \|x\|_2^{\|x\|_2^{1/2}} dx,

where :math:`[0,1]^d` is the unit hypercube in :math:`\mathbb{R}^d`.
\ where :math:`[0,1]^d` is the unit hypercube in :math:`\mathbb{R}^d`.
The integrand is defined everywhere except at :math:`x=0` and hence the
definite integral is also defined.

Expand Down Expand Up @@ -143,9 +152,9 @@ function.
Numpy’s norm(x) is obviously a matrix norm, but we want it to be vector
2-norm that acts on each row of x. To that end, let’s add an axis
argument to the function:
Numpy’s ``norm(x)`` is obviously a matrix norm, but we want it to be
vector 2-norm that acts on each row of ``x``. To that end, let’s add an
axis argument to the function:

.. code:: ipython3
Expand All @@ -160,8 +169,8 @@ argument to the function:
Now it’s working! Let’s make sure that the sqrt function is acting on
each element of the vector norm results:
Now it’s working! Let’s make sure that the ``sqrt`` function is acting
on each element of the vector norm results:

.. code:: ipython3
Expand Down Expand Up @@ -199,8 +208,8 @@ We have got our proper function definition now.
x_norms = norm(x, axis = 1)
return x_norms ** sqrt(x_norms)
We can now create an integrand instance with our QuickConstruct class in
QMCPy and then invoke QMCPy’s integrate function:
We can now create an ``integrand`` instance with our ``QuickConstruct``
class in QMCPy and then invoke QMCPy’s ``integrate`` function:

.. code:: ipython3
Expand All @@ -212,7 +221,7 @@ QMCPy and then invoke QMCPy’s integrate function:
.. parsed-literal::
Solution: 0.6616
Solution: 0.6632
QuickConstruct (Integrand Object)
IIDStdUniform (Discrete Distribution Object)
mimics StdUniform
Expand All @@ -227,9 +236,9 @@ QMCPy and then invoke QMCPy’s integrate function:
inflate 1.200
alpha 0.010
MeanVarData (AccumData Object)
n 3166
n_total 4190
confid_int [ 0.651 0.672]
n 3317
n_total 4341
confid_int [ 0.653 0.673]
time_total 0.002
Expand All @@ -253,9 +262,6 @@ solution is accurate enough:
It’s good. Shall we test the function with :math:`d=2` by simply
changing the input parameter value of dimension for QuickConstruct?

It’s good. Shall we test the function with :math:`d=2` by simply
changing the input parameter value of dimension for QuickConstruct

.. code:: ipython3
dim = 2
Expand All @@ -266,7 +272,7 @@ changing the input parameter value of dimension for QuickConstruct
.. parsed-literal::
Solution: 0.8244
Solution: 0.8317
QuickConstruct (Integrand Object)
IIDStdUniform (Discrete Distribution Object)
mimics StdUniform
Expand All @@ -281,10 +287,10 @@ changing the input parameter value of dimension for QuickConstruct
inflate 1.200
alpha 0.010
MeanVarData (AccumData Object)
n 5520
n_total 6544
confid_int [ 0.814 0.834]
time_total 0.002
n 5243
n_total 6267
confid_int [ 0.821 0.842]
time_total 0.003
Expand All @@ -303,4 +309,3 @@ value:
True
9 changes: 2 additions & 7 deletions docs/demos.html
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Expand Up @@ -90,7 +90,6 @@
<li class="toctree-l1"><a class="reference internal" href="algorithms.html">QMCPy Documentation</a></li>
<li class="toctree-l1 current"><a class="current reference internal" href="#">Demos</a><ul>
<li class="toctree-l2"><a class="reference internal" href="rst_from_demos/qmcpy_intro.html">Welcome to QMCPy</a></li>
<li class="toctree-l2"><a class="reference internal" href="rst_from_demos/qmcpy_intro.html#important-notes">Important Notes</a></li>
<li class="toctree-l2"><a class="reference internal" href="rst_from_demos/integration_examples.html">Integration Examples using QMCPy package</a></li>
<li class="toctree-l2"><a class="reference internal" href="rst_from_demos/sample_scatter_plots.html">Scatter Plots of Samples</a></li>
<li class="toctree-l2"><a class="reference internal" href="rst_from_demos/MC_vs_QMC.html">A Monte Carlo vs Quasi-Monte Carlo Comparison</a></li>
Expand Down Expand Up @@ -167,12 +166,8 @@ <h1>Demos<a class="headerlink" href="#demos" title="Permalink to this headline">
<div class="toctree-wrapper compound">
<ul>
<li class="toctree-l1"><a class="reference internal" href="rst_from_demos/qmcpy_intro.html">Welcome to QMCPy</a><ul>
<li class="toctree-l2"><a class="reference internal" href="rst_from_demos/qmcpy_intro.html#import">Import</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="rst_from_demos/qmcpy_intro.html#important-notes">Important Notes</a><ul>
<li class="toctree-l2"><a class="reference internal" href="rst_from_demos/qmcpy_intro.html#iid-vs-lds">IID vs LDS</a></li>
<li class="toctree-l2"><a class="reference internal" href="rst_from_demos/qmcpy_intro.html#multi-dimensional-inputs">Multi-Dimensional Inputs</a></li>
<li class="toctree-l2"><a class="reference internal" href="rst_from_demos/qmcpy_intro.html#importing-qmcpy">Importing QMCPy</a></li>
<li class="toctree-l2"><a class="reference internal" href="rst_from_demos/qmcpy_intro.html#important-notes">Important Notes</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="rst_from_demos/integration_examples.html">Integration Examples using QMCPy package</a><ul>
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8 changes: 2 additions & 6 deletions docs/index.html
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Expand Up @@ -210,12 +210,8 @@ <h1>Qmcpy Documentation<a class="headerlink" href="#qmcpy-documentation" title="
</li>
<li class="toctree-l1"><a class="reference internal" href="demos.html">Demos</a><ul>
<li class="toctree-l2"><a class="reference internal" href="rst_from_demos/qmcpy_intro.html">Welcome to QMCPy</a><ul>
<li class="toctree-l3"><a class="reference internal" href="rst_from_demos/qmcpy_intro.html#import">Import</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="rst_from_demos/qmcpy_intro.html#important-notes">Important Notes</a><ul>
<li class="toctree-l3"><a class="reference internal" href="rst_from_demos/qmcpy_intro.html#iid-vs-lds">IID vs LDS</a></li>
<li class="toctree-l3"><a class="reference internal" href="rst_from_demos/qmcpy_intro.html#multi-dimensional-inputs">Multi-Dimensional Inputs</a></li>
<li class="toctree-l3"><a class="reference internal" href="rst_from_demos/qmcpy_intro.html#importing-qmcpy">Importing QMCPy</a></li>
<li class="toctree-l3"><a class="reference internal" href="rst_from_demos/qmcpy_intro.html#important-notes">Important Notes</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="rst_from_demos/integration_examples.html">Integration Examples using QMCPy package</a><ul>
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