Add demos to PDF documentation of QMCPy.

QMCSoftware · Dec 24, 2019 · 13c1c8d · 13c1c8d
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diff --git a/docs/_sources/demos.rst.txt b/docs/_sources/demos.rst.txt
@@ -1,27 +1,15 @@
 Demos
 =====
 
-QMCPy Intro
-------------
-.. raw:: html
-   :file: html_from_demos/qmcpy_intro.html
+.. toctree::
+    :maxdepth: 2
 
-Integration Examples
---------------------
-.. raw:: html
-   :file: html_from_demos/integration_examples.html
+    rst_from_demos/qmcpy_intro.rst
 
-Sampling Points Visualization
------------------------------
-.. raw:: html
-   :file: html_from_demos/sample_scatter_plots.html
+    rst_from_demos/integration_examples.rst
 
-MC and QMC Comparison
----------------------
-.. raw:: html
-   :file: html_from_demos/MC_vs_QMC.html
+    rst_from_demos/sample_scatter_plots.rst
 
-Quasi-Random Sequence Generators
---------------------------------
-.. raw:: html
-   :file: html_from_demos/quasirandom_generators.html
+    rst_from_demos/MC_vs_QMC.rst
+
+    rst_from_demos/quasirandom_generators.rst
diff --git a/docs/_sources/rst_from_demos/MC_vs_QMC.rst.txt b/docs/_sources/rst_from_demos/MC_vs_QMC.rst.txt
diff --git a/docs/_sources/rst_from_demos/integration_examples.rst.txt b/docs/_sources/rst_from_demos/integration_examples.rst.txt
@@ -0,0 +1,194 @@
+Integration Examples using QMCPy package
+========================================
+
+.. code:: ipython3
+
+    from qmcpy import *
+    
+    from numpy import arange
+
+Keister Example
+---------------
+
+Keister Integrand: - :math:`y_i = \pi^{d/2} * \cos(||x_i||_2)`
+
+Gaussian True Measure: - :math:`\mathcal{N}(0,\frac{1}{2})`
+
+Sobol Discrete Distribution: -
+:math:`x_j \overset{lds}{\sim} \mathcal{U}(0,1)`
+
+.. code:: ipython3
+
+    dim = 3
+    integrand = Keister(dim)
+    discrete_distrib = Sobol(rng_seed=7)
+    true_measure = Gaussian(dim, variance=1 / 2)
+    stopping_criterion = CLTRep(discrete_distrib, true_measure, abs_tol=.05)
+    _, data = integrate(integrand, true_measure, discrete_distrib, stopping_criterion)
+    print(data)
+
+
+.. parsed-literal::
+
+    Solution: 2.1716         
+    Keister (Integrand Object)
+    Sobol (Discrete Distribution Object)
+    	mimics          StdUniform
+    	rng_seed        7
+    	backend         pytorch
+    Gaussian (True Measure Object)
+    	dimension       3
+    	mu              0
+    	sigma           0.707
+    CLTRep (Stopping Criterion Object)
+    	abs_tol         0.050
+    	rel_tol         0
+    	n_max           1073741824
+    	inflate         1.200
+    	alpha           0.010
+    MeanVarDataRep (AccumData Object)
+    	n               128
+    	n_total         128
+    	confid_int      [ 2.164  2.179]
+    	time_total      0.008
+    	r               16
+    
+
+
+Asian Option Pricing Example
+----------------------------
+
+Single Level
+~~~~~~~~~~~~
+
+Asian Call Option Integrand -
+:math:`S_i(t_j)=S(0)e^{(r-\frac{\sigma^2}{2})t_j+\sigma\mathcal{B}(t_j)}`
+- discounted put payoff
+:math:`= max(K-\frac{1}{d}\sum_{j=0}^{d-1} S(jT/d))\;,\: 0)`
+
+Brownian Motion True Measure: -
+:math:`\:\: \mathcal{B}(t_j)=B(t_{j-1})+Z_j\sqrt{t_j-t_{j-1}} \;` for
+:math:`\;Z_j \sim \mathcal{N}(0,1)`
+
+Lattice Discrete Distribution: -
+:math:`\:\: x_j \overset{lds}{\sim} \mathcal{U}(0,1)`
+
+.. code:: ipython3
+
+    time_vec = [arange(1 / 64, 65 / 64, 1 / 64)]
+    dim = [len(tv) for tv in time_vec]
+    
+    discrete_distrib = Lattice(rng_seed=7)
+    true_measure = BrownianMotion(dim, time_vector=time_vec)
+    integrand = AsianCall(true_measure,
+                    volatility = .5,
+                    start_price = 30,
+                    strike_price = 25,
+                    interest_rate = .01,
+                    mean_type = 'geometric')
+    stopping_criterion = CLTRep(discrete_distrib, true_measure, abs_tol=.05)
+    _, data = integrate(integrand, true_measure, discrete_distrib, stopping_criterion)
+    print(data)
+
+
+.. parsed-literal::
+
+    Solution: 5.8356         
+    AsianCall (Integrand Object)
+    	volatility      0.500
+    	start_price     30
+    	strike_price    25
+    	interest_rate   0.010
+    	mean_type       geometric
+    	exercise_time   1
+    Lattice (Discrete Distribution Object)
+    	mimics          StdUniform
+    	rng_seed        7
+    BrownianMotion (True Measure Object)
+    	dimension       64
+    	time_vector     [ 0.016  0.031  0.047 ...  0.969  0.984  1.000]
+    CLTRep (Stopping Criterion Object)
+    	abs_tol         0.050
+    	rel_tol         0
+    	n_max           1073741824
+    	inflate         1.200
+    	alpha           0.010
+    MeanVarDataRep (AccumData Object)
+    	n               2048
+    	n_total         2048
+    	confid_int      [ 5.833  5.838]
+    	time_total      0.434
+    	r               16
+    
+
+
+Asian Option Pricing Example
+----------------------------
+
+Multi-Level
+~~~~~~~~~~~
+
+:math:`Y_0 = 0`
+
+:math:`Y_1` = Asian Option Monitored at
+:math:`t=[\frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1]`
+
+:math:`Y_2` = Asian Option Monitored at
+:math:`t=[\frac{1}{16}, \frac{1}{8}, ... , 1]`
+
+:math:`Y_3` = Asian Option Monitored at
+:math:`t=[\frac{1}{64}, \frac{1}{32}, ... , 1]`
+
+:math:`Z_1 = \mathbb{E}[Y_1-Y_0] + \mathbb{E}[Y_2-Y_1] + \mathbb{E}[Y_3-Y_2] = \mathbb{E}[Y_3]`
+
+.. code:: ipython3
+
+    time_vec = [arange(1 / 4, 5 / 4, 1 / 4),
+                     arange(1 / 16, 17 / 16, 1 / 16),
+                     arange(1 / 64, 65 / 64, 1 / 64)]
+    dim = [len(tv) for tv in time_vec]
+    
+    discrete_distrib = IIDStdGaussian(rng_seed=7)
+    true_measure = BrownianMotion(dim, time_vector=time_vec)
+    integrand = AsianCall(true_measure,
+                    volatility = .5,
+                    start_price = 30,
+                    strike_price = 25,
+                    interest_rate = .01,
+                    mean_type = 'geometric')
+    stopping_criterion = CLT(discrete_distrib, true_measure, abs_tol=.05, n_max = 1e10)
+    _, data = integrate(integrand, true_measure, discrete_distrib, stopping_criterion)
+    print(data)
+
+
+.. parsed-literal::
+
+    Solution: 5.8320         
+    AsianCall (Integrand Object)
+    	volatility      [ 0.500  0.500  0.500]
+    	start_price     [30 30 30]
+    	strike_price    [25 25 25]
+    	interest_rate   [ 0.010  0.010  0.010]
+    	mean_type       ['geometric' 'geometric' 'geometric']
+    	exercise_time   [ 1.000  1.000  1.000]
+    IIDStdGaussian (Discrete Distribution Object)
+    	mimics          StdGaussian
+    BrownianMotion (True Measure Object)
+    	dimension       [ 4 16 64]
+    	time_vector     [array([ 0.250,  0.500,  0.750,  1.000])
+    	                array([ 0.062,  0.125,  0.188, ...,  0.875,  0.938,  1.000])
+    	                array([ 0.016,  0.031,  0.047, ...,  0.969,  0.984,  1.000])]
+    CLT (Stopping Criterion Object)
+    	abs_tol         0.050
+    	rel_tol         0
+    	n_max           10000000000
+    	inflate         1.200
+    	alpha           0.010
+    MeanVarData (AccumData Object)
+    	n               [ 249322.000  31697.000  5429.000]
+    	n_total         289520
+    	confid_int      [ 5.783  5.881]
+    	time_total      0.119
+    
+
+