├── LICENSE
├── README.md
├── adiabatic_memory.py
├── adiabatic_process.py
├── bell_state_generator.tex
├── bifurcation_graph.tex
├── bloch_sphere.py
├── chimera.tex
├── cnot_gate.tex
├── common_graphics_settings.py
├── convex_loss_functions.py
├── feedforward.tex
├── fredkin_gate.tex
├── graphics_utils.py
├── grover_operator.tex
├── grover_search.tex
├── hadamard_gate.tex
├── hopfield.tex
├── meter.svg
├── nonconvex_loss_functions.py
├── perceptron.tex
├── quantum_annealing.py
├── quantum_neural_network.tex
├── quantum_parallelism.tex
├── quantum_swap.tex
├── quantum_swap_gate.tex
├── quantum_tunneling.py
├── supervised.py
├── support_vectors.py
├── swap_test.tex
├── toffoli_gate.tex
├── transductive.py
├── unsupervised.py
├── vc_dimension_line.py
├── vc_dimension_sine.py
└── xor_problem.py
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558 | License will continue to apply to the part which is the covered work,
559 | but the special requirements of the GNU Affero General Public License,
560 | section 13, concerning interaction through a network will apply to the
561 | combination as such.
562 |
563 | 14. Revised Versions of this License.
564 |
565 | The Free Software Foundation may publish revised and/or new versions of
566 | the GNU General Public License from time to time. Such new versions will
567 | be similar in spirit to the present version, but may differ in detail to
568 | address new problems or concerns.
569 |
570 | Each version is given a distinguishing version number. If the
571 | Program specifies that a certain numbered version of the GNU General
572 | Public License "or any later version" applies to it, you have the
573 | option of following the terms and conditions either of that numbered
574 | version or of any later version published by the Free Software
575 | Foundation. If the Program does not specify a version number of the
576 | GNU General Public License, you may choose any version ever published
577 | by the Free Software Foundation.
578 |
579 | If the Program specifies that a proxy can decide which future
580 | versions of the GNU General Public License can be used, that proxy's
581 | public statement of acceptance of a version permanently authorizes you
582 | to choose that version for the Program.
583 |
584 | Later license versions may give you additional or different
585 | permissions. However, no additional obligations are imposed on any
586 | author or copyright holder as a result of your choosing to follow a
587 | later version.
588 |
589 | 15. Disclaimer of Warranty.
590 |
591 | THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
592 | APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
593 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY
594 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,
595 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
596 | PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM
597 | IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
598 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
599 |
600 | 16. Limitation of Liability.
601 |
602 | IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
603 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
604 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
605 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
606 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
607 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
608 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
609 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
610 | SUCH DAMAGES.
611 |
612 | 17. Interpretation of Sections 15 and 16.
613 |
614 | If the disclaimer of warranty and limitation of liability provided
615 | above cannot be given local legal effect according to their terms,
616 | reviewing courts shall apply local law that most closely approximates
617 | an absolute waiver of all civil liability in connection with the
618 | Program, unless a warranty or assumption of liability accompanies a
619 | copy of the Program in return for a fee.
620 |
621 | END OF TERMS AND CONDITIONS
622 |
623 | How to Apply These Terms to Your New Programs
624 |
625 | If you develop a new program, and you want it to be of the greatest
626 | possible use to the public, the best way to achieve this is to make it
627 | free software which everyone can redistribute and change under these terms.
628 |
629 | To do so, attach the following notices to the program. It is safest
630 | to attach them to the start of each source file to most effectively
631 | state the exclusion of warranty; and each file should have at least
632 | the "copyright" line and a pointer to where the full notice is found.
633 |
634 | {one line to give the program's name and a brief idea of what it does.}
635 | Copyright (C) {year} {name of author}
636 |
637 | This program is free software: you can redistribute it and/or modify
638 | it under the terms of the GNU General Public License as published by
639 | the Free Software Foundation, either version 3 of the License, or
640 | (at your option) any later version.
641 |
642 | This program is distributed in the hope that it will be useful,
643 | but WITHOUT ANY WARRANTY; without even the implied warranty of
644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
645 | GNU General Public License for more details.
646 |
647 | You should have received a copy of the GNU General Public License
648 | along with this program. If not, see .
649 |
650 | Also add information on how to contact you by electronic and paper mail.
651 |
652 | If the program does terminal interaction, make it output a short
653 | notice like this when it starts in an interactive mode:
654 |
655 | {project} Copyright (C) {year} {fullname}
656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
657 | This is free software, and you are welcome to redistribute it
658 | under certain conditions; type `show c' for details.
659 |
660 | The hypothetical commands `show w' and `show c' should show the appropriate
661 | parts of the General Public License. Of course, your program's commands
662 | might be different; for a GUI interface, you would use an "about box".
663 |
664 | You should also get your employer (if you work as a programmer) or school,
665 | if any, to sign a "copyright disclaimer" for the program, if necessary.
666 | For more information on this, and how to apply and follow the GNU GPL, see
667 | .
668 |
669 | The GNU General Public License does not permit incorporating your program
670 | into proprietary programs. If your program is a subroutine library, you
671 | may consider it more useful to permit linking proprietary applications with
672 | the library. If this is what you want to do, use the GNU Lesser General
673 | Public License instead of this License. But first, please read
674 | .
--------------------------------------------------------------------------------
/README.md:
--------------------------------------------------------------------------------
1 | This repository stores the source code of the figures in the book Quantum Machine Learning: What Quantum Computing Means to Data Mining. More information on the book is here:
2 |
3 | [http://peterwittek.com/book](http://peterwittek.com/book)
4 |
5 | Dependencies
6 | ==
7 | The LaTeX files use tikz, which should be standard in most TeX distribution.
8 |
9 | The Python files use matplotlib, numpy, and seaborn. Furthermore, LaTeX is used for rendering text, hence a LaTeX compiler should be in the path. Plotting the Bloch sphere also requires the QuTIP toolbox.
10 |
--------------------------------------------------------------------------------
/adiabatic_memory.py:
--------------------------------------------------------------------------------
1 | # -*- coding: utf-8 -*-
2 | """
3 | Created on Sun Apr 27 09:23:32 2014
4 |
5 | @author: wittek
6 | """
7 |
8 | import matplotlib.pyplot as plt
9 | import numpy as np
10 | from common_graphics_settings import initialize_graphics
11 |
12 | #fig, axes = plt.subplots(2,2)
13 | #((ax1, ax2), (ax3, ax4)) = axes # unpack the axes
14 |
15 | colors = initialize_graphics()
16 | fig = plt.figure(1,figsize=(7,5))
17 | ax1 = fig.add_subplot(111, autoscale_on=False, xlim=(0,32), ylim=(-7.5,1.1))
18 |
19 | # Right side of the diagram
20 | domain = np.arange(0.0, 8*np.pi, 0.01)
21 | y1 = np.cos(domain)
22 | line, = ax1.plot(domain, y1, lw=3, color=colors[0])
23 | y2 = [ (np.log(x+4)-7*np.exp(-(x-15)*(x-15)/100))/3.5-3 for x in domain ]
24 | line, = ax1.plot(domain, y2, lw=3, color=colors[0])
25 | y3 = [ (np.cos(x)+np.log(x+4)-7*np.exp(-(x-15)*(x-15)/100))/3.5-6 for x in domain ]
26 | line, = ax1.plot(domain, y3, lw=3, color=colors[0])
27 | for i in range(1,9,2):
28 | ax1.plot(i*np.pi, -0.7, 'o', color=colors[2]) # Stable states in H_mem
29 | ax1.plot(14.7, -3.8, 'o', color=colors[2]) # Stable state in H_inp
30 | ax1.plot(1.06*np.pi, -5.9, 'o', color=colors[2]) # Stable states in the sum
31 | ax1.plot(3.1*np.pi, -6.74, 'o', color=colors[2])
32 | ax1.plot(4.95*np.pi, -7.1, 'o', color=colors[2])
33 | ax1.plot(6.85*np.pi, -6.3, 'o', color=colors[2])
34 |
35 | plt.text( 25, -1, '$H_{\mathrm{mem}}$',fontsize=20)
36 | plt.text( 25, -4, '$H_{\mathrm{inp}}$',fontsize=20)
37 | plt.text( 25, -7, '$H_{\mathrm{mem}}+H_{\mathrm{inp}}$',fontsize=20)
38 |
39 | plt.axis('off')
40 | plt.savefig('./adiabatic_memory.pdf',bbox_inches='tight')
--------------------------------------------------------------------------------
/adiabatic_process.py:
--------------------------------------------------------------------------------
1 | # -*- coding: utf-8 -*-
2 | """
3 | Created on Sun Apr 27 09:23:32 2014
4 |
5 | @author: wittek
6 | """
7 |
8 | import matplotlib.pyplot as plt
9 | import numpy as np
10 | from graphics_utils import initialize_graphics
11 |
12 | #fig, axes = plt.subplots(2,2)
13 | #((ax, ax2), (ax3, ax4)) = axes # unpack the axes
14 |
15 | colors=initialize_graphics()
16 | fig = plt.figure(1,figsize=(10,5))
17 | ax = fig.add_subplot(111, autoscale_on=False, xlim=(-33.3,26), ylim=(-7.43,1.1))
18 |
19 | # Right side of the diagram
20 | x = np.arange(0.0, 8*np.pi, 0.01)
21 | y = [ (3*np.cos(t)+np.log(t+4)-10*np.exp(-(t-15)*(t-15)/100))/3.5-4.5 for t in x ]
22 | ax.plot(x, y, lw=3, color=colors[0])
23 | ax.plot(4.98*np.pi, -6.95, 'o', color=colors[2])
24 |
25 | plt.text( 25, -7, '$H_1$',fontsize=20)
26 |
27 | # Left side of the diagram
28 | offset=25
29 |
30 | x = np.arange(-8-offset, 8-offset, 0.01)
31 | y4 = [ (t+offset)**2/20-2.5 for t in x]
32 | ax.plot(x, y4, lw=3, color=colors[0])
33 | y5 = [ (t+offset)**2/20-7.4 for t in x]
34 | ax.plot(x, y5, lw=3, color=colors[0])
35 |
36 | ax.plot(-31, 0, 'o', color=colors[2])
37 | ax.plot(-offset, -7, 'o', color=colors[2])
38 |
39 | #plt.text( -17, -2, '$H_1$',fontsize=20)
40 | plt.text( -17, -7, '$H_0$',fontsize=20)
41 |
42 | ax.annotate('', xy=(-offset, -4), xytext=(-offset, -2.7),
43 | arrowprops=dict(facecolor='black', shrink=0.05),
44 | )
45 |
46 | ax.annotate('', xy=(-3 ,-6), xytext=(-13, -6),
47 | arrowprops=dict(facecolor='black', shrink=0.05),
48 | )
49 |
50 | plt.axis('off')
51 | plt.savefig('./adiabatic_process.pdf',bbox_inches='tight')
--------------------------------------------------------------------------------
/bell_state_generator.tex:
--------------------------------------------------------------------------------
1 | % Based on the answer by qubyte at
2 | % http://tex.stackexchange.com/questions/9767/whats-a-good-package-for-typesetting-quantum-circuits
3 | \documentclass[12pt]{standalone}
4 | \usepackage{tikz}
5 |
6 | \usetikzlibrary{backgrounds}
7 | % Dirac Kets
8 | \newcommand{\ket}[1]{\ensuremath{\left|#1\right\rangle}}
9 |
10 | \begin{document}
11 | \begin{tikzpicture}[thick,cross/.style={path picture={
12 | \draw[black]
13 | (path picture bounding box.south) -- (path picture bounding box.north);
14 | }}]
15 |
16 | % `operator' will only be used by most gates.
17 | % `cnot' will refer to CNOT gates.
18 | % `phase' is used for controlled gates.
19 | \tikzstyle{operator} = [draw,fill=white,minimum size=1.5em]
20 | \tikzstyle{cnot} = [draw,cross,circle,minimum size=5pt]
21 | \tikzstyle{phase} = [draw,fill,shape=circle,minimum size=5pt,inner sep=0pt]
22 | %
23 | \matrix[row sep=0.4cm, column sep=0.8cm] (circuit) {
24 |
25 | % First row.
26 | \coordinate (start1); &[-0.5cm]
27 | \node[operator] (O11) {H}; &
28 | \node[phase] (P12) {}; &
29 | \coordinate (end1);\\
30 |
31 | \coordinate (start2); &[-0.5cm]
32 | &
33 | \node[cnot] (O22) {}; &
34 | \coordinate (end2);\\
35 | };
36 |
37 | \begin{pgfonlayer}{background}
38 | % Draw lines.
39 | \draw[thick] (start1) -- (end1) (start2) -- (end2) (P12) -- (O22);
40 | \end{pgfonlayer}
41 | %
42 | \end{tikzpicture}
43 | \end{document}
44 |
--------------------------------------------------------------------------------
/bifurcation_graph.tex:
--------------------------------------------------------------------------------
1 | % Based on
2 | % http://www.texample.net/tikz/examples/red-black-tree/
3 |
4 | \documentclass[12pt]{standalone}
5 | \usepackage{tikz}
6 | \usetikzlibrary{arrows}
7 | \definecolor{color1}{RGB}{0,114,178}
8 | \definecolor{color2}{RGB}{0,158,115}
9 | \definecolor{color3}{RGB}{213,94,0}
10 |
11 |
12 | \tikzset{
13 | treenode/.style = {align=center, inner sep=0pt, text centered,
14 | font=\sffamily},
15 | vertex/.style = {treenode, circle, black, font=\sffamily\bfseries, draw=color3,
16 | fill=color3, text width=0.3em},
17 | }
18 |
19 | \begin{document}
20 | \begin{tikzpicture}[-,>=stealth',thick,draw=color1,level/.style={sibling distance = 7cm/#1,
21 | level distance = 1.5cm}]
22 | \node [vertex] {}
23 | child{ node [vertex] {}
24 | child{ node [vertex] {}
25 | child{ node [vertex] {}
26 | }
27 | child{ node [vertex] {}
28 | }
29 | }
30 | child{ node [vertex] {}
31 | child{ node [vertex] {}
32 | }
33 | child{ node [vertex] {}
34 | }
35 | }
36 | }
37 | child{ node [vertex] {}
38 | child{ node [vertex] {}
39 | child{ node [vertex] {}}
40 | child{ node [vertex] {}}
41 | }
42 | child{ node [vertex] {}
43 | child{ node [vertex] {}}
44 | child{ node [vertex] {}}
45 | }
46 | }
47 | ;
48 | \end{tikzpicture}
49 | \end{document}
50 |
--------------------------------------------------------------------------------
/bloch_sphere.py:
--------------------------------------------------------------------------------
1 | # -*- coding: utf-8 -*-
2 | """
3 | Created on Mon May 5 14:15:02 2014
4 |
5 | @author: wittek
6 | """
7 | from mpl_toolkits.mplot3d import Axes3D
8 | import matplotlib.pyplot as plt
9 | from qutip import Bloch
10 | from graphics_utils import initialize_graphics
11 |
12 | colors = initialize_graphics()
13 |
14 | fig = plt.figure()
15 | axes = Axes3D(fig)
16 | axes.grid = True
17 | axes.axis("off")
18 | axes.set_axis_off()
19 |
20 | b=Bloch()
21 |
22 | b.fig = fig
23 | b.axes = axes
24 | #b.fig = fig
25 | #b.frame_width=1
26 | b.sphere_color = 'white'
27 | b.sphere_alpha = 0.1
28 | #b.size = [10, 10]
29 | b.make_sphere()
30 |
31 | plt.savefig('./bloch_sphere.svg',bbox_inches='tight')
32 | #b.show()
33 | #b.save('bloch_sphere.pdf',format='pdf')
34 |
--------------------------------------------------------------------------------
/chimera.tex:
--------------------------------------------------------------------------------
1 | % Based on
2 | % http://tex.stackexchange.com/questions/15088/bipartite-graphs
3 |
4 | \documentclass[12pt]{standalone}
5 | \usepackage[rgb]{xcolor}
6 | \definecolor{color1}{RGB}{0,114,178}
7 | \definecolor{color2}{RGB}{0,158,115}
8 | \definecolor{color3}{RGB}{213,94,0}
9 |
10 | \usepackage{tikz}
11 | \usetikzlibrary{chains,arrows}
12 |
13 | \begin{document}
14 |
15 | \begin{tikzpicture}[thick,
16 | leftnode/.style={circle,draw=color3,fill=color3},
17 | rightnode/.style={circle,draw=color3,fill=color3},
18 | blindnode/.style={draw=white,circle,fill=white}
19 | ]
20 |
21 | % blind nodes
22 | \begin{scope}[xshift=-1cm, yshift=4mm, start chain=going below,node distance=7mm]
23 | \foreach \i in {1,2,...,5}
24 | \node[blindnode,on chain] (bl\i) [] {};
25 | \end{scope}
26 | \begin{scope}[xshift=5cm, yshift=4mm, start chain=going below,node distance=7mm]
27 | \foreach \i in {1,2,...,5}
28 | \node[blindnode,on chain] (br\i) [] {};
29 | \end{scope}
30 |
31 |
32 | % the vertices of U
33 | \begin{scope}[start chain=going below,node distance=7mm]
34 | \foreach \i in {1,2,...,4}
35 | \node[leftnode,on chain] (l\i) [] {};
36 | \end{scope}
37 |
38 | % the vertices of V
39 | \begin{scope}[xshift=4cm,start chain=going below,node distance=7mm]
40 | \foreach \i in {1,2,...,4}
41 | \node[rightnode,on chain] (r\i) [] {};
42 | \end{scope}
43 |
44 | % the internal edges
45 | \foreach \i in {1,2,...,4}
46 | \foreach \j in {1,2,...,4}
47 | \draw[color1] (l\i) -- (r\j);
48 |
49 | % the external edges
50 | \foreach \i in {1,2,...,4} {
51 | \path[color1] (l\i) edge [bend left] node {} (bl\i) ;
52 | \pgfmathtruncatemacro{\j}{\i + 1}%
53 | \path[color1] (l\i) edge [bend right] node {} (bl\j) ;
54 | }
55 | \foreach \i in {1,2,...,4} {
56 | \path[color1] (r\i) edge [bend right] node {} (br\i) ;
57 | \pgfmathtruncatemacro{\j}{\i + 1}%
58 | \path[color1] (r\i) edge [bend left] node {} (br\j) ;
59 | }
60 |
61 | \end{tikzpicture}
62 | \end{document}
63 |
--------------------------------------------------------------------------------
/cnot_gate.tex:
--------------------------------------------------------------------------------
1 | % Based on the answer by qubyte at
2 | % http://tex.stackexchange.com/questions/9767/whats-a-good-package-for-typesetting-quantum-circuits
3 | \documentclass[12pt]{standalone}
4 | \usepackage{tikz}
5 |
6 | \usetikzlibrary{backgrounds}
7 | % Dirac Kets
8 | \newcommand{\ket}[1]{\ensuremath{\left|#1\right\rangle}}
9 |
10 | \begin{document}
11 | \begin{tikzpicture}[thick,cross/.style={path picture={
12 | \draw[black]
13 | (path picture bounding box.south) -- (path picture bounding box.north);
14 | }}]
15 |
16 | % `operator' will only be used by most gates.
17 | % `cnot' will refer to CNOT gates.
18 | % `phase' is used for controlled gates.
19 | \tikzstyle{operator} = [draw,fill=white,minimum size=1.5em]
20 | \tikzstyle{cnot} = [draw,cross,circle,minimum size=5pt]
21 | \tikzstyle{phase} = [draw,fill,shape=circle,minimum size=5pt,inner sep=0pt]
22 | %
23 | \matrix[row sep=0.4cm, column sep=0.8cm] (circuit) {
24 |
25 | % First row.
26 | \coordinate (start1); &
27 | \node[phase] (P11) {}; &
28 | \coordinate (end1);\\
29 |
30 | \coordinate (start2); &
31 | \node[cnot] (O21) {}; &
32 | \coordinate (end2);\\
33 | };
34 |
35 | \begin{pgfonlayer}{background}
36 | % Draw lines.
37 | \draw[thick] (start1) -- (end1) (start2) -- (end2) (P11) -- (O21);
38 | \end{pgfonlayer}
39 | %
40 | \end{tikzpicture}
41 | \end{document}
42 |
--------------------------------------------------------------------------------
/common_graphics_settings.py:
--------------------------------------------------------------------------------
1 | # -*- coding: utf-8 -*-
2 | """
3 | Created on Thu Apr 10 14:48:01 2014
4 |
5 | @author: wittek
6 | """
7 |
8 | import seaborn as sns
9 | import matplotlib.pyplot as plt
10 | from matplotlib import rcParams
11 | from matplotlib import rc
12 |
13 | FONT_SIZE=27.5
14 | MP_LINEWIDTH = 2.4
15 | MP_TICKSIZE = 20.
16 |
17 | def initialize_graphics():
18 | rcParams.update({'figure.autolayout': True})
19 | rc('text', usetex=True)
20 | # Configure palette and plotting to pgf/tikz
21 | sns.set(style="nogrid")
22 | return sns.color_palette("colorblind")
23 |
24 | def setup_figure(ax):
25 |
26 | # Setting up font sizes
27 | for item in ([ax.title, ax.xaxis.label, ax.yaxis.label] ):
28 | item.set_fontsize(FONT_SIZE)
29 |
30 | for tick in plt.gca().xaxis.get_major_ticks():
31 | tick.label1.set_fontsize(0.85*FONT_SIZE)
32 | tick.tick1line.set_markeredgewidth(MP_LINEWIDTH)
33 | tick.tick1line.set_markersize(0.5*MP_TICKSIZE)
34 | for tick in plt.gca().yaxis.get_major_ticks():
35 | tick.label1.set_fontsize(0.85*FONT_SIZE)
36 | tick.tick1line.set_markeredgewidth(MP_LINEWIDTH)
37 | tick.tick1line.set_markersize(0.5*MP_TICKSIZE)
38 | legend = ax.legend(loc='upper left', shadow=False, handlelength=5)
39 |
40 | # Set the fontsize in legend
41 | for label in legend.get_texts():
42 | label.set_fontsize(FONT_SIZE)
43 |
--------------------------------------------------------------------------------
/convex_loss_functions.py:
--------------------------------------------------------------------------------
1 | import matplotlib.pyplot as plt
2 | import numpy as np
3 | from numpy.random import rand
4 |
5 | from graphics_utils import initialize_graphics, cm2inch
6 |
7 | def hinge_loss(x):
8 | if x>1:
9 | return 0
10 | else:
11 | return 1-x
12 |
13 | def zero_one(x):
14 | if x<0:
15 | return 1
16 | else:
17 | return 0
18 |
19 | x = np.arange(-5,8,0.01)
20 | y_least_square = (1-x)**2
21 | y_hinge_loss = [hinge_loss(t) for t in x]
22 | y_boosting = [np.exp(-t) for t in x]
23 | y_zero_one = [zero_one(t) for t in x]
24 |
25 | colors = initialize_graphics()
26 |
27 | fig, ax = plt.subplots()
28 | fig.set_size_inches(cm2inch([10,7]))
29 | plt.plot(x, y_zero_one, color='black', linewidth=3, label='Zero-one')
30 | plt.plot(x, y_boosting, color=colors[0], linewidth=2, label='Exponential')
31 | plt.plot(x, y_hinge_loss, '--', color=colors[1], linewidth=2, label='Hinge loss')
32 | plt.plot(x, y_least_square, ':', color=colors[2], linewidth=3, label='Least square')
33 |
34 | handles, labels = ax.get_legend_handles_labels()
35 | ax.legend(handles, labels, loc=4)
36 |
37 | #plt.axis('off')
38 | ax.set_xlim([-5, 8])
39 | ax.set_ylim([0, 5])
40 |
41 | plt.savefig('./convex_loss_functions.pdf',bbox_inches='tight')
42 |
--------------------------------------------------------------------------------
/feedforward.tex:
--------------------------------------------------------------------------------
1 | \documentclass[12pt]{standalone}
2 | % Based on http://www.texample.net/tikz/examples/neural-network/
3 |
4 | \usepackage{tikz}
5 |
6 | \begin{document}
7 |
8 | \def\layersep{2.5cm}
9 |
10 | \begin{tikzpicture}[shorten >=1pt,->,draw=black!80, node distance=\layersep]
11 | \tikzstyle{every pin edge}=[<-,shorten <=1pt]
12 | \tikzstyle{neuron}=[circle,fill=black!25,minimum size=17pt,inner sep=0pt]
13 | \tikzstyle{annot} = [text width=4em, text centered]
14 |
15 | % Draw the input layer nodes
16 | \foreach \name / \y in {1/1,2/2,$d$/4}
17 | % This is the same as writing \foreach \name / \y in {1/1,2/2,3/3,4/4}
18 | \node[neuron] (I-\name) at (0,-\y) {\name};
19 | \node (I-3) at (0,-3) {\vdots};
20 |
21 | % Draw the hidden layer nodes
22 | \foreach \name / \y in {1/1,2/2,$K$/5}
23 | \path[yshift=0.5cm]
24 | node[neuron] (H-\name) at (\layersep,-\y cm) {\name};
25 | \node (H-3) at (\layersep,-3) {\vdots};
26 |
27 | \foreach \name / \y in {1/1.5,2/2.5,$M$/4.5}
28 | \path[yshift=0.5cm]
29 | node[neuron] (O-\name) at (2*\layersep,-\y cm) {\name};
30 | \node (O-3) at (2*\layersep,-3) {\vdots};
31 |
32 | % Connect every node in the input layer with every node in the
33 | % hidden layer.
34 | \foreach \source in {1,2,$d$}
35 | \foreach \dest in {1,2,$K$}
36 | \path (I-\source) edge (H-\dest);
37 |
38 |
39 | % Connect every node in the hidden layer with the output layer
40 | \foreach \source in {1,2,$K$}
41 | \foreach \dest in {1,2,$M$}
42 | \path (H-\source) edge (O-\dest);
43 |
44 | % Annotate the layers
45 | \node[annot,above of=H-1, node distance=1cm] (hl) {Hidden layer};
46 | \node[annot,left of=hl] {Input layer};
47 | \node[annot,right of=hl] {Output layer};
48 | \end{tikzpicture}
49 | % End of code
50 | \end{document}
51 |
--------------------------------------------------------------------------------
/fredkin_gate.tex:
--------------------------------------------------------------------------------
1 | % Based on the answer by qubyte at
2 | % http://tex.stackexchange.com/questions/9767/whats-a-good-package-for-typesetting-quantum-circuits
3 | \documentclass[12pt]{standalone}
4 | \usepackage{tikz}
5 |
6 | \usetikzlibrary{backgrounds}
7 | % Dirac Kets
8 | \newcommand{\ket}[1]{\ensuremath{\left|#1\right\rangle}}
9 |
10 | \begin{document}
11 | \begin{tikzpicture}[thick,cross/.style={path picture={
12 | \draw[black]
13 | (path picture bounding box.south) -- (path picture bounding box.north);
14 | }},swap/.style={path picture={
15 | \draw[black]
16 | (path picture bounding box.south west) -- (path picture bounding box.north east) (path picture bounding box.south east) -- (path picture bounding box.north west);
17 | }}]
18 |
19 | % `operator' will only be used by most gates.
20 | % `cnot' will refer to CNOT gates.
21 | % `phase' is used for controlled gates.
22 | \tikzstyle{operator} = [draw,fill=white,minimum size=1.5em]
23 | \tikzstyle{cnot} = [draw,cross,circle,minimum size=5pt]
24 | \tikzstyle{phase} = [draw,fill,shape=circle,minimum size=5pt,inner sep=0pt]
25 | %
26 | \matrix[row sep=0.4cm, column sep=0.8cm] (circuit) {
27 |
28 | % First row.
29 | \coordinate (start1); &
30 | \node[phase] (P11) {}; &
31 | \coordinate (end1);\\
32 |
33 | % Second row.
34 | \coordinate (start2); &
35 | \coordinate (swap21);
36 | \node[swap] (O21) {}; &
37 | \coordinate (end2);\\
38 |
39 | % Third row
40 | \coordinate (start3); &
41 | \coordinate (swap31);
42 | \node[swap] (O31) {}; &
43 | \coordinate (end3);\\
44 | };
45 |
46 | \begin{pgfonlayer}{background}
47 | % Draw lines.
48 | \draw[thick] (start1) -- (end1) (start2) -- (end2) (start3) -- (end3) (P11) -- (swap21) (swap21) -- (swap31);
49 | \end{pgfonlayer}
50 | %
51 | \end{tikzpicture}
52 | \end{document}
53 |
--------------------------------------------------------------------------------
/graphics_utils.py:
--------------------------------------------------------------------------------
1 | # -*- coding: utf-8 -*-
2 | """
3 | Created on Thu Apr 10 14:48:01 2014
4 |
5 | @author: wittek
6 | """
7 |
8 | import matplotlib.pyplot as plt
9 | from matplotlib import rcParams
10 | from matplotlib import rc
11 | from matplotlib.transforms import Affine2D
12 | import mpl_toolkits.axisartist.floating_axes as floating_axes
13 | import seaborn as sns
14 |
15 | FONT_SIZE=12
16 | MP_LINEWIDTH = 2.4
17 | MP_TICKSIZE = 20.
18 |
19 | def initialize_graphics():
20 | rcParams.update({'figure.autolayout': True})
21 | rc('text', usetex=True)
22 | # Configure palette and plotting to pgf/tikz
23 | sns.set(style="nogrid")
24 | return sns.color_palette("colorblind")
25 |
26 | def setup_figure(ax):
27 |
28 | # Setting up font sizes
29 | for item in ([ax.title, ax.xaxis.label, ax.yaxis.label] ):
30 | item.set_fontsize(FONT_SIZE)
31 |
32 | for tick in plt.gca().xaxis.get_major_ticks():
33 | tick.label1.set_fontsize(FONT_SIZE)
34 | tick.tick1line.set_markeredgewidth(MP_LINEWIDTH)
35 | tick.tick1line.set_markersize(0.5*MP_TICKSIZE)
36 | for tick in plt.gca().yaxis.get_major_ticks():
37 | tick.label1.set_fontsize(FONT_SIZE)
38 | tick.tick1line.set_markeredgewidth(MP_LINEWIDTH)
39 | tick.tick1line.set_markersize(0.5*MP_TICKSIZE)
40 | legend = ax.legend(loc='upper left', shadow=False, handlelength=5)
41 |
42 | # Set the fontsize in legend
43 | for label in legend.get_texts():
44 | label.set_fontsize(FONT_SIZE)
45 |
46 |
47 | def rotate(fig, degree):
48 | """Rotation of plot with impossible-to-remove, rotated frame.
49 | """
50 | plot_extents = 0, 1, 0, 1
51 | transform = Affine2D().rotate_deg(degree)
52 | helper = floating_axes.GridHelperCurveLinear(transform, plot_extents)
53 | ax = floating_axes.FloatingSubplot(fig, 111, grid_helper=helper)
54 | fig.add_subplot(ax)
55 | aux_ax = ax.get_aux_axes(transform)
56 | return aux_ax
57 |
58 |
59 | def cm2inch(tupl):
60 | """Helper function to convert centimeters to inches.
61 | """
62 | return tuple(i/2.54 for i in tupl)
63 |
--------------------------------------------------------------------------------
/grover_operator.tex:
--------------------------------------------------------------------------------
1 | % Based on the answer by qubyte at
2 | % http://tex.stackexchange.com/questions/9767/whats-a-good-package-for-typesetting-quantum-circuits
3 | \documentclass[12pt]{standalone}
4 | \usepackage{tikz}
5 |
6 | \usetikzlibrary{backgrounds}
7 | % Dirac Kets
8 | \newcommand{\ket}[1]{\ensuremath{\left|#1\right\rangle}}
9 |
10 | \begin{document}
11 | \begin{tikzpicture}[thick,
12 | cross/.style={path picture={
13 | \draw[black]
14 | (path picture bounding box.south) -- (path picture bounding box.north);
15 | }},
16 | swap/.style={path picture={
17 | \draw[black]
18 | (path picture bounding box.south west) -- (path picture bounding box.north east)
19 | (path picture bounding box.south east) -- (path picture bounding box.north west);
20 | }},
21 | bundle/.style={path picture={
22 | \draw[black]
23 | (path picture bounding box.south west) -- (path picture bounding box.north east);
24 | }}]
25 |
26 | % `operator' will only be used by most gates.
27 | % `cnot' will refer to CNOT gates.
28 | % `phase' is used for controlled gates.
29 | \tikzstyle{operator} = [draw,fill=white,minimum size=1.5em]
30 | \tikzstyle{cnot} = [draw,cross,circle,minimum size=5pt]
31 | \tikzstyle{phase} = [draw,fill,shape=circle,minimum size=5pt,inner sep=0pt]
32 | %
33 | \matrix[row sep=0.4cm, column sep=0.8cm] (circuit) {
34 |
35 | % First row.
36 | \coordinate (start1); &[-0.5cm]
37 | \node[bundle] (B0) {};
38 | \node[above right] (B0) {$n$}; &
39 | &
40 | \node[operator] (O12) {$H^{\otimes n}$};
41 | &
42 | \node[operator] (O13) {$2|0\rangle\langle 0| - I$};
43 | &
44 | \node[operator] (O14) {$H^{\otimes n}$};
45 | &[-0.5cm]
46 | \coordinate (end1);\\
47 |
48 | % Second row.
49 | \coordinate (start2); &[-0.5cm]
50 | &
51 | &
52 | &
53 | &
54 | &[-0.5cm]
55 | \coordinate (end2);\\
56 | };
57 | \draw [thick,black,fill=white] (-3.5,-2.3em) rectangle (-2.5,1.7em);
58 | \node at (-3,-0.15) (O) {$O$};
59 |
60 | \begin{pgfonlayer}{background}
61 | % Draw lines.
62 | \draw[thick] (start1) -- (end1) (start2) -- (end2)
63 | ;
64 | \end{pgfonlayer}
65 | %
66 | \end{tikzpicture}
67 | \end{document}
68 |
--------------------------------------------------------------------------------
/grover_search.tex:
--------------------------------------------------------------------------------
1 | % Based on the answer by qubyte at
2 | % http://tex.stackexchange.com/questions/9767/whats-a-good-package-for-typesetting-quantum-circuits
3 | \documentclass[12pt]{standalone}
4 | \usepackage{tikz}
5 | \pgfdeclareimage[height=1.5em]{meter}{meter}
6 |
7 | \usetikzlibrary{backgrounds}
8 | % Dirac Kets
9 | \newcommand{\ket}[1]{\ensuremath{\left|#1\right\rangle}}
10 |
11 | \begin{document}
12 | \begin{tikzpicture}[thick,
13 | cross/.style={path picture={
14 | \draw[black]
15 | (path picture bounding box.south) -- (path picture bounding box.north);
16 | }},
17 | swap/.style={path picture={
18 | \draw[black]
19 | (path picture bounding box.south west) -- (path picture bounding box.north east)
20 | (path picture bounding box.south east) -- (path picture bounding box.north west);
21 | }},
22 | bundle/.style={path picture={
23 | \draw[black]
24 | (path picture bounding box.south west) -- (path picture bounding box.north east);
25 | }}]
26 |
27 | % `operator' will only be used by most gates.
28 | % `cnot' will refer to CNOT gates.
29 | % `phase' is used for controlled gates.
30 | \tikzstyle{operator} = [draw,fill=white,minimum size=1.5em]
31 | \tikzstyle{cnot} = [draw,cross,circle,minimum size=5pt]
32 | \tikzstyle{meter} = [draw,color=white,fill=white,minimum size=1.7em]
33 | \tikzstyle{phase} = [draw,fill,shape=circle,minimum size=5pt,inner sep=0pt]
34 | %
35 | \matrix[row sep=0.4cm, column sep=0.8cm] (circuit) {
36 |
37 | % First row.
38 | \node (S0) {$|0\rangle$};&[-0.5cm]
39 | \node[bundle] (B0) {};
40 | \node[above right] (B0) {$n$}; &[-0.5cm]
41 | \node[operator] (O12) {$H^{\otimes n}$};
42 | &
43 | &
44 | &
45 | \node (O14) {\ldots};
46 | &
47 | &
48 | &
49 | \node[meter] (M11) {\pgfbox[center,center]{\pgfuseimage{meter}}};
50 | \coordinate (end1);\\
51 |
52 | % Second row.
53 | \node (S1) {$|1\rangle$};&[-0.5cm]
54 | &
55 | \node[operator] (O22) {$H$};&
56 | &
57 | &
58 | \node (O24) {\ldots};
59 | &
60 | &
61 | &
62 | \coordinate (end2);\\
63 | };
64 | \draw [thick,black,fill=white] (-0.7,-2.2em) rectangle (0.3,1.8em);
65 | \node at (-0.2,-0.14) (O) {$G$};
66 | \draw [thick,black,fill=white] (2.1,-2.2em) rectangle (3.1,1.8em);
67 | \node at (2.6,-0.14) (O) {$G$};
68 |
69 | \begin{pgfonlayer}{background}
70 | % Draw lines.
71 | \draw[thick] (S0) -- (O14) (O14) -- (end1) (S1) -- (O24) (O24) -- (end2)
72 | ;
73 | \end{pgfonlayer}
74 | %
75 | \end{tikzpicture}
76 | \end{document}
77 |
--------------------------------------------------------------------------------
/hadamard_gate.tex:
--------------------------------------------------------------------------------
1 | % Based on the answer by qubyte at
2 | % http://tex.stackexchange.com/questions/9767/whats-a-good-package-for-typesetting-quantum-circuits
3 | \documentclass[12pt]{standalone}
4 | \usepackage{tikz}
5 |
6 | \usetikzlibrary{backgrounds}
7 | % Dirac Kets
8 | \newcommand{\ket}[1]{\ensuremath{\left|#1\right\rangle}}
9 |
10 | \begin{document}
11 | \begin{tikzpicture}[thick,cross/.style={path picture={
12 | \draw[black]
13 | (path picture bounding box.south) -- (path picture bounding box.north);
14 | }}]
15 |
16 | % `operator' will only be used by most gates.
17 | % `cnot' will refer to CNOT gates.
18 | % `phase' is used for controlled gates.
19 | \tikzstyle{operator} = [draw,fill=white,minimum size=1.5em]
20 | \tikzstyle{cnot} = [draw,cross,circle,minimum size=5pt]
21 | \tikzstyle{phase} = [draw,fill,shape=circle,minimum size=5pt,inner sep=0pt]
22 | %
23 | \matrix[row sep=0.4cm, column sep=0.8cm] (circuit) {
24 |
25 | % First row.
26 | \coordinate (start1); &
27 | \node[operator] (O11) {H}; &
28 | \coordinate (end1);\\
29 | };
30 |
31 | \begin{pgfonlayer}{background}
32 | % Draw lines.
33 | \draw[thick] (start1) -- (end1);
34 | \end{pgfonlayer}
35 | %
36 | \end{tikzpicture}
37 | \end{document}
38 |
--------------------------------------------------------------------------------
/hopfield.tex:
--------------------------------------------------------------------------------
1 | \documentclass[12pt]{standalone}
2 | % Based on http://www.texample.net/tikz/examples/neural-network/
3 |
4 | \usepackage[rgb]{xcolor}
5 | \definecolor{color1}{RGB}{0,114,178}
6 | \definecolor{color2}{RGB}{0,158,115}
7 | \definecolor{color3}{RGB}{213,94,0}
8 |
9 | \usepackage{tikz}
10 |
11 | \begin{document}
12 |
13 | \def\layersep{2.5cm}
14 |
15 | \begin{tikzpicture}[shorten >=1pt,->,draw=black!80, node distance=\layersep]
16 | \tikzstyle{every pin edge}=[<-,shorten <=1pt]
17 | \tikzstyle{neuron}=[circle,fill=black!25,minimum size=17pt,inner sep=0pt]
18 | \tikzstyle{phantomneuron}=[circle,fill=black!0,minimum size=17pt,inner sep=0pt]
19 | \tikzstyle{annot} = [text width=4em, text centered]
20 |
21 | % Draw the input layer nodes
22 | \foreach \name / \y in {1/1,2/2,$d$/4}
23 | \node[phantomneuron] (I-\y) at (0,-\y) {\name};
24 | \node (I-3) at (0,-3) {\vdots};
25 |
26 | % Draw the hidden layer nodes
27 | \foreach \name / \y in {1/1,2/2,$K$/4}
28 | \node[neuron] (H-\y) at (\layersep,-\y) {\name};
29 | \node (H-3) at (\layersep,-3) {\vdots};
30 |
31 | \foreach \name / \y in {1/1,2/2,$d$/4}
32 | \node[phantomneuron] (O-\y) at (2*\layersep,-\y) {};
33 |
34 | % Connect every node in the input layer with every node in the
35 | % hidden layer.
36 | \foreach \source in {1,2,4}
37 | \path[very thick] (I-\source) edge (H-\source);
38 |
39 | % Connect every node in the hidden layer with the output layer
40 | \foreach \source in {1,2,4}
41 | \path[very thick] (H-\source) edge (O-\source);
42 |
43 | \foreach \dest / \y in {1/1, 2/2, $d$/4}
44 | \draw[thick,color=color1] (H-1) -- + (0.5, 0.5) -- + (0.5, 1.1) --+ (-1.1, 1.1) -- + (-1.1, -\y+1.3) -- + (H-\y);
45 |
46 | \foreach \dest / \y in {1/1, 2/2, $d$/4}
47 | \draw[thick,color=color2] (H-2) -- + (0.7, 0.5) -- + (0.7, 1.9) -- + (-0.9, 1.9) -- + (-0.9, -\y+2.5) -- + (H-\y);
48 |
49 | \foreach \dest / \y in {1/1, 2/2, $d$/4}
50 | \draw[thick,color=color3] (H-4) -- + (0.9, 0.5) -- + (0.9,3.7) -- + (-0.7, 3.7) -- + (-0.7, -\y+4.7) -- + (H-\y);
51 |
52 |
53 | \end{tikzpicture}
54 | % End of code
55 | \end{document}
56 |
--------------------------------------------------------------------------------
/meter.svg:
--------------------------------------------------------------------------------
1 |
2 |
3 |
4 |
124 |
--------------------------------------------------------------------------------
/nonconvex_loss_functions.py:
--------------------------------------------------------------------------------
1 | import matplotlib.pyplot as plt
2 | import numpy as np
3 | from numpy.random import rand
4 |
5 | from graphics_utils import initialize_graphics, cm2inch
6 |
7 | def zero_one(x):
8 | if x<0:
9 | return 1
10 | else:
11 | return 0
12 |
13 | def savage_loss(x):
14 | return 4/(1+np.exp(2*x))**2
15 |
16 | def tangent_loss(x):
17 | return (2*np.arctan(x)-1)**2
18 |
19 | x = np.arange(-6,8,0.01)
20 | y_zero_one = [zero_one(t) for t in x]
21 | y_savage_loss = [savage_loss(t) for t in x]
22 | y_tangent_loss = [tangent_loss(t) for t in x]
23 | colors = initialize_graphics()
24 |
25 | fig, ax = plt.subplots()
26 | fig.set_size_inches(cm2inch([10,7]))
27 | plt.plot(x, y_zero_one, color='black', linewidth=3, label='Zero-one')
28 | plt.plot(x, y_savage_loss, color=colors[0], linewidth=2, label='Savage loss')
29 | plt.plot(x, y_tangent_loss, '--', color=colors[1], linewidth=2, label='Tangent loss')
30 |
31 | handles, labels = ax.get_legend_handles_labels()
32 | ax.legend(handles, labels, loc=1)
33 |
34 | #plt.axis('off')
35 | ax.set_xlim([-5, 8])
36 | ax.set_ylim([0, 15])
37 |
38 | plt.savefig('./nonconvex_loss_functions.pdf',bbox_inches='tight')
39 |
--------------------------------------------------------------------------------
/perceptron.tex:
--------------------------------------------------------------------------------
1 | \documentclass[12pt]{standalone}
2 | % Based on http://www.texample.net/tikz/examples/neural-network/
3 |
4 | \usepackage{tikz}
5 |
6 | \begin{document}
7 |
8 | \def\layersep{2.5cm}
9 |
10 | \begin{tikzpicture}[shorten >=1pt,->,draw=black!80, node distance=\layersep]
11 | \tikzstyle{every pin edge}=[<-,shorten <=1pt]
12 | \tikzstyle{neuron}=[circle,fill=black!25,minimum size=17pt,inner sep=0pt]
13 | \tikzstyle{phantomneuron}=[circle,fill=black!0,minimum size=17pt,inner sep=0pt]
14 | \tikzstyle{annot} = [text width=4em, text centered]
15 |
16 | % Draw the input layer nodes
17 | \foreach \name / \y in {1/1,2/2,$d$/4}
18 | % This is the same as writing \foreach \name / \y in {1/1,2/2,3/3,4/4}
19 | \node[phantomneuron] (I-\name) at (0,-\y) {\name};
20 | \node (I-3) at (0, -3) {\vdots};
21 |
22 | \node[neuron] (P) at (\layersep, -2 cm) {};
23 |
24 | \node[phantomneuron] (O) at (2*\layersep,-2 cm) {$f(\mathbf{x})$};
25 | % Connect every node in the input layer with every node in the
26 | % hidden layer.
27 | \foreach \source in {1,2,$d$}
28 | \path (I-\source) edge (P);
29 | \path (P) edge (O);
30 |
31 | % Connect every node in the hidden layer with the output layer
32 | %\foreach \source in {1,2,$K$}
33 | % \foreach \dest in {1,2,$M$}
34 | % \path (H-\source) edge (O-\dest);
35 |
36 | \end{tikzpicture}
37 | % End of code
38 | \end{document}
39 |
--------------------------------------------------------------------------------
/quantum_annealing.py:
--------------------------------------------------------------------------------
1 | # -*- coding: utf-8 -*-
2 | """
3 | Created on Sun Apr 27 09:23:32 2014
4 |
5 | @author: wittek
6 | """
7 |
8 | import matplotlib.pyplot as plt
9 | import numpy as np
10 | from common_graphics_settings import initialize_graphics
11 |
12 | colors = initialize_graphics()
13 | fig = plt.figure(1,figsize=(5,5))
14 | ax1 = fig.add_subplot(111)
15 |
16 | # Right side of the diagram
17 | domain = np.arange(0.0, 8*np.pi, 0.01)
18 | y3 = [ 10*((2*np.cos(x)+np.log(x+4)-7*np.exp(-(x-15)*(x-15)/100))/3.5) for x in domain ]
19 | line, = ax1.plot(domain, y3, lw=3, color=colors[0])
20 | ax1.annotate('', xy=(11.6, -4), xytext=(9.7, -12.1),
21 | arrowprops=dict(facecolor=colors[1], shrink=0.05),
22 | )
23 | plt.text( 11.5, -3.3, 'Thermal\n annealing',fontsize=14)
24 | ax1.annotate('', xy=(14.8, -13.1), xytext=(9.5, -13.1),
25 | arrowprops=dict(facecolor=colors[2], shrink=0.05),
26 | )
27 | plt.text( 8.3, -16.5, 'Quantum\n tunneling',fontsize=14)
28 |
29 | plt.axis('off')
30 | plt.savefig('./quantum_annealing.pdf',bbox_inches='tight')
--------------------------------------------------------------------------------
/quantum_neural_network.tex:
--------------------------------------------------------------------------------
1 | \documentclass[12pt]{standalone}
2 | % Based on http://www.texample.net/tikz/examples/neural-network/
3 |
4 | \usepackage{tikz}
5 |
6 | \begin{document}
7 |
8 | \def\layersep{2.5cm}
9 |
10 | \begin{tikzpicture}[shorten >=1pt,->,draw=black!80, node distance=\layersep]
11 | \tikzstyle{every pin edge}=[<-,shorten <=1pt]
12 | \tikzstyle{neuron}=[circle,fill=black!25,minimum size=17pt,inner sep=0pt]
13 | \tikzstyle{annot} = [text width=4em, text centered]
14 |
15 | % Draw the input layer nodes
16 | \foreach \name / \y in {1/1,2/2,$d$/4}
17 | % This is the same as writing \foreach \name / \y in {1/1,2/2,3/3,4/4}
18 | \node[neuron] (I-\name) at (0,-\y) {};
19 | \node (I-3) at (0,-3) {\vdots};
20 |
21 | % Draw the hidden layer nodes
22 | \foreach \name / \y in {1/1,2/2,$K$/4}
23 | \node[neuron] (H-\name) at (\layersep,-\y cm) {};
24 | \node (H-3) at (\layersep,-3) {\vdots};
25 |
26 | \foreach \name / \y in {1/1,2/2,$M$/4}
27 | \node[neuron] (O-\name) at (2*\layersep,-\y cm) {};
28 | \node (O-3) at (2*\layersep,-3) {\vdots};
29 |
30 | \foreach \source in {-1,-2,-4}{
31 | \draw [black,-,dotted,thick,domain=-80:80] plot ({0.3+0.3*cos(\x)}, {\source+0.3*sin(\x)});
32 | \draw [black,-,dotted,thick,domain=-80:80] plot ({0.6+0.6*cos(\x)}, {\source+0.6*sin(\x)});
33 | \draw [black,-,dotted,thick,domain=-80:80] plot ({0.9+0.9*cos(\x)}, {\source+0.9*sin(\x)});
34 | }
35 |
36 | % Connect every node in the hidden layer with the output layer
37 | \foreach \source in {1,2,$K$}
38 | \foreach \dest in {1,2,$M$}
39 | \path (H-\source) edge (O-\dest);
40 |
41 | \end{tikzpicture}
42 | % End of code
43 | \end{document}
44 |
--------------------------------------------------------------------------------
/quantum_parallelism.tex:
--------------------------------------------------------------------------------
1 | % Based on the answer by qubyte at
2 | % http://tex.stackexchange.com/questions/9767/whats-a-good-package-for-typesetting-quantum-circuits
3 | \documentclass[12pt]{standalone}
4 | \usepackage{tikz}
5 |
6 | \usetikzlibrary{backgrounds,calc,decorations.pathreplacing}
7 | % Dirac Kets
8 | \newcommand{\ket}[1]{\ensuremath{\left|#1\right\rangle}}
9 |
10 | \begin{document}
11 | \begin{tikzpicture}[thick,cross/.style={path picture={
12 | \draw[black]
13 | (path picture bounding box.south) -- (path picture bounding box.north);
14 | }}]
15 |
16 | % `operator' will only be used by most gates.
17 | % `cnot' will refer to CNOT gates.
18 | % `phase' is used for controlled gates.
19 | \tikzstyle{operator} = [draw,fill=white,minimum size=1.5em]
20 | \tikzstyle{cnot} = [draw,cross,circle,minimum size=5pt]
21 | \tikzstyle{phase} = [draw,fill,shape=circle,minimum size=5pt,inner sep=0pt]
22 | %
23 | \matrix[row sep=0.4cm, column sep=0.8cm] (circuit) {
24 |
25 | % First row.
26 | \node (q1) {\ket{0}};
27 | \coordinate (start1); &[-0.5cm]
28 | \node[operator] (O11) {H}; &
29 | &
30 | &[-0.5cm]
31 | \coordinate (end1);\\
32 |
33 | \node (q2) {\ket{0}};
34 | \coordinate (start2); &[-0.5cm]
35 | &
36 | &
37 | &[-0.5cm]
38 | \coordinate (end2);\\
39 | };
40 | \draw [thick,black,fill=white] (0.3,-2em) rectangle (1.3,2em);
41 | \node at (0.8,0) (Uf) {$U_f$};
42 |
43 |
44 | \draw[decorate,decoration={brace},thick]
45 | ($(circuit.north east)-(0cm,0.3cm)$)
46 | to node[midway,right] (bracket) {$\displaystyle\frac{\ket{0,f(0)}+\ket{1,f(1)}}{\sqrt{2}}$}
47 | ($(circuit.south east)+(0cm,0.3cm)$);
48 | \begin{pgfonlayer}{background}
49 | % Draw lines.
50 | \draw[thick] (q1) -- (end1) (q2) -- (end2);
51 | \end{pgfonlayer}
52 | %
53 | \end{tikzpicture}
54 | \end{document}
55 |
--------------------------------------------------------------------------------
/quantum_swap.tex:
--------------------------------------------------------------------------------
1 | % Based on the answer by qubyte at
2 | % http://tex.stackexchange.com/questions/9767/whats-a-good-package-for-typesetting-quantum-circuits
3 | \documentclass[12pt]{standalone}
4 | \usepackage{tikz}
5 |
6 | \usetikzlibrary{backgrounds}
7 | % Dirac Kets
8 | \newcommand{\ket}[1]{\ensuremath{\left|#1\right\rangle}}
9 |
10 | \begin{document}
11 | \begin{tikzpicture}[thick,cross/.style={path picture={
12 | \draw[black]
13 | (path picture bounding box.south) -- (path picture bounding box.north);
14 | }}]
15 |
16 | % `operator' will only be used by most gates.
17 | % `cnot' will refer to CNOT gates.
18 | % `phase' is used for controlled gates.
19 | \tikzstyle{operator} = [draw,fill=white,minimum size=1.5em]
20 | \tikzstyle{cnot} = [draw,cross,circle,minimum size=5pt]
21 | \tikzstyle{phase} = [draw,fill,shape=circle,minimum size=5pt,inner sep=0pt]
22 | %
23 | \matrix[row sep=0.4cm, column sep=0.8cm] (circuit) {
24 |
25 | % First row.
26 | \node (q1) {\ket{A}}; &[-0.5cm]
27 | \node[phase] (P11) {}; &
28 | \node[cnot] (C12) {}; &
29 | \node[phase] (P13) {}; &[-0.3cm]
30 | \node (q1end) {\ket{B}};\\
31 |
32 | % Second row.
33 | \node (q2) {\ket{B}}; &
34 | \node[cnot] (C21) {}; &
35 | \node[phase] (P22) {}; &
36 | \node[cnot] (C23) {}; &[-0.3cm]
37 | \node (q2end) {\ket{A}}; \\
38 | };
39 |
40 | \begin{pgfonlayer}{background}
41 | % Draw lines.
42 | \draw[thick] (q1) -- (q1end) (q2) -- (q2end) (P11) -- (C21) (C12) -- (P22) (P13) -- (C23);
43 | \end{pgfonlayer}
44 | %
45 | \end{tikzpicture}
46 | \end{document}
47 |
--------------------------------------------------------------------------------
/quantum_swap_gate.tex:
--------------------------------------------------------------------------------
1 | % Based on the answer by qubyte at
2 | % http://tex.stackexchange.com/questions/9767/whats-a-good-package-for-typesetting-quantum-circuits
3 | \documentclass[12pt]{standalone}
4 | \usepackage{tikz}
5 |
6 | \usetikzlibrary{backgrounds}
7 | % Dirac Kets
8 | \newcommand{\ket}[1]{\ensuremath{\left|#1\right\rangle}}
9 |
10 | \begin{document}
11 | \begin{tikzpicture}[thick,cross/.style={path picture={
12 | \draw[black]
13 | (path picture bounding box.south) -- (path picture bounding box.north);
14 | }},swap/.style={path picture={
15 | \draw[black]
16 | (path picture bounding box.south west) -- (path picture bounding box.north east) (path picture bounding box.south east) -- (path picture bounding box.north west);
17 | }}]
18 |
19 | % `operator' will only be used by most gates.
20 | % `cnot' will refer to CNOT gates.
21 | % `phase' is used for controlled gates.
22 | \tikzstyle{operator} = [draw,fill=white,minimum size=1.5em]
23 | \tikzstyle{cnot} = [draw,cross,circle,minimum size=5pt]
24 | \tikzstyle{phase} = [draw,fill,shape=circle,minimum size=5pt,inner sep=0pt]
25 | %
26 | \draw [white] (-2,0.5) rectangle (2,0.5);
27 | \matrix[row sep=0.4cm, column sep=0.8cm] (circuit) {
28 |
29 | % First row.
30 | \coordinate (start1); &
31 | \coordinate (swap11);
32 | \node[swap] (O11) {}; &
33 | \coordinate (end1);\\
34 |
35 | \coordinate (start2); &
36 | \coordinate (swap21);
37 | \node[swap] (O21) {}; &
38 | \coordinate (end2);\\
39 | };
40 |
41 | \begin{pgfonlayer}{background}
42 | % Draw lines.
43 | \draw[thick] (start1) -- (end1) (start2) -- (end2) (swap11) -- (swap21);
44 | \end{pgfonlayer}
45 | %
46 | \end{tikzpicture}
47 | \end{document}
48 |
--------------------------------------------------------------------------------
/quantum_tunneling.py:
--------------------------------------------------------------------------------
1 | # -*- coding: utf-8 -*-
2 | """
3 | Created on Sun May 4 15:56:25 2014
4 |
5 | @author: wittek
6 | """
7 | from mpl_toolkits.axes_grid.axislines import SubplotZero
8 | import matplotlib.pyplot as plt
9 | import numpy as np
10 | from graphics_utils import initialize_graphics, cm2inch
11 |
12 | def potential_barrier(x,x1,x2,V0):
13 | if x>x1 and xx2:
22 | return amplitude2*np.sin(2*np.pi*omega*x)
23 | else:
24 | return 0
25 |
26 | x1 = 6.5
27 | x2 = 8.5
28 | V0 = 2
29 | omega = 0.5
30 | amplitude1 = 1
31 | amplitude2 = 0.2
32 |
33 | full_range = np.arange(0, 5*np.pi, 0.01)
34 | potential = [ potential_barrier(x, x1, x2, V0) for x in full_range]
35 |
36 | until_x1 = np.arange(0.0, x1, 0.01)
37 | wave_until_x1 = [tunneling_wave(t, x1, x2, omega, amplitude1, amplitude2) for t in until_x1]
38 | from_x2 = np.arange(x2+0.01, 5*np.pi, 0.01)
39 | wave_from_x2 = [tunneling_wave(t, x1, x2, omega, amplitude1, amplitude2) for t in from_x2]
40 |
41 |
42 | colors=initialize_graphics()
43 |
44 | fig = plt.figure(1)
45 | ax = SubplotZero(fig, 111)
46 | fig.add_subplot(ax)
47 | #fig, ax = plt.subplots()
48 | fig.set_size_inches(cm2inch([10,5]))
49 |
50 | ax.plot(full_range, potential, lw=2, color=colors[2])
51 | ax.plot(until_x1, wave_until_x1, lw=2, color=colors[0])
52 | ax.plot(from_x2, wave_from_x2, lw=2, color=colors[0])
53 |
54 | ax.annotate('$U(x)$', xy=(x2, V0), xytext=(x2+0.3, V0-0.2))
55 |
56 | ax.set_frame_on(False)
57 | #ax.axes.get_yaxis().set_visible(False)
58 | ax.axes.get_xaxis().set_ticks([x1, x2, 5*np.pi+0.5])
59 | ax.axes.get_xaxis().set_ticklabels(['$x_1$','$x_2$', '$x$'])
60 | ax.axis["xzero"].set_axisline_style("-|>")
61 | ax.axis["xzero"].set_visible(True)
62 | ax.axis["yzero"].set_visible(False)
63 |
64 | for direction in ["left", "right", "bottom", "top"]:
65 | ax.axis[direction].set_visible(False)
66 |
67 | ax.set_xlim([-0.5, 5*np.pi+0.5])
68 |
69 | plt.savefig('./quantum_tunneling.pdf')
70 |
--------------------------------------------------------------------------------
/supervised.py:
--------------------------------------------------------------------------------
1 | import matplotlib.pyplot as plt
2 | import numpy as np
3 | from numpy.random import rand
4 |
5 | from graphics_utils import initialize_graphics, cm2inch
6 |
7 | x = rand(40)-0.5
8 | z = x*x+0.4
9 | y = z+rand(40)/3
10 | w = z-rand(40)/3
11 |
12 | xx = np.arange(-0.55,0.55,0.01)
13 | yy = xx*xx+0.4
14 |
15 | colors = initialize_graphics()
16 |
17 | fig, ax = plt.subplots()
18 | fig.set_size_inches(cm2inch([10,10]))
19 | plt.plot(x, y, 'D' , color=colors[0], label='Class 1')
20 | plt.plot(x, w, 's', color=colors[1], label='Class 2')
21 | plt.plot(xx, yy, color=colors[2], linewidth=4, label='Decision\n surface')
22 |
23 | handles, labels = ax.get_legend_handles_labels()
24 | ax.legend(handles, labels, loc=4)
25 |
26 | plt.axis('off')
27 | ax.set_ylim([-0.2, 0.9])
28 |
29 | plt.savefig('./supervised.pdf',bbox_inches='tight')
30 |
--------------------------------------------------------------------------------
/support_vectors.py:
--------------------------------------------------------------------------------
1 | import matplotlib.pyplot as plt
2 | from matplotlib.patches import Circle
3 | import numpy as np
4 | from numpy.random import rand
5 |
6 | from graphics_utils import initialize_graphics, cm2inch
7 |
8 | x = rand(40)-0.5
9 | z = x+0.4
10 | y = z+rand(40)/2+0.3
11 | w = z-rand(40)/2-0.3
12 |
13 | xx = np.arange(-0.8,0.8,0.01)
14 | yy = xx+0.4
15 |
16 | margin_one = xx+0.4+0.2
17 | margin_two = xx+0.4-0.2
18 |
19 | colors = initialize_graphics()
20 |
21 | fig, ax = plt.subplots()
22 | fig.set_size_inches(cm2inch([10,10]))
23 | plt.plot(x, y, 'D' , color=colors[0], label='Class 1')
24 | plt.plot(x, w, 's', color=colors[1], label='Class 2')
25 | plt.plot(xx, yy, color=colors[2], linewidth=4, label='Decision\n surface')
26 | plt.plot(xx, margin_one, '--', color=colors[2], linewidth=2, label='Margin')
27 | plt.plot(xx, margin_two, '--', color=colors[2], linewidth=2)
28 |
29 | support_vectors_x1 = [-0.4, 0.3]
30 | support_vectors_y1 = [-0.4+0.6, 0.3+0.6]
31 | plt.plot(support_vectors_x1, support_vectors_y1, 'D' , color=colors[0])
32 | for x1, y1 in zip(support_vectors_x1, support_vectors_y1):
33 | circle1 = Circle((x1, y1), 0.06, facecolor='none', edgecolor=colors[0], linewidth=1)
34 | ax.add_patch(circle1)
35 |
36 | support_vectors_x2 = [-0.1, 0.5]
37 | support_vectors_y2 = [-0.1+0.2, 0.5+0.2]
38 | plt.plot(support_vectors_x2, support_vectors_y2, 's' , color=colors[1])
39 | for x2, y2 in zip(support_vectors_x2, support_vectors_y2):
40 | circle2 = Circle((x2, y2), 0.06, facecolor='none', edgecolor=colors[1], linewidth=1)
41 | ax.add_patch(circle2)
42 |
43 |
44 | handles, labels = ax.get_legend_handles_labels()
45 | ax.legend(handles, labels, loc=4)
46 |
47 | plt.axis('off')
48 | ax.set_xlim([-1.1,1.1])
49 | ax.set_ylim([-0.7, 1.5])
50 |
51 | plt.savefig('./support_vectors.pdf',bbox_inches='tight')
52 |
--------------------------------------------------------------------------------
/swap_test.tex:
--------------------------------------------------------------------------------
1 | % Based on the answer by qubyte at
2 | % http://tex.stackexchange.com/questions/9767/whats-a-good-package-for-typesetting-quantum-circuits
3 | \documentclass[12pt]{standalone}
4 | \usepackage{tikz}
5 |
6 | \usetikzlibrary{backgrounds}
7 | % Dirac Kets
8 | \newcommand{\ket}[1]{\ensuremath{\left|#1\right\rangle}}
9 | \pgfdeclareimage[height=1.5em]{meter}{meter}
10 |
11 | \begin{document}
12 | \begin{tikzpicture}[thick,cross/.style={path picture={
13 | \draw[black]
14 | (path picture bounding box.south) -- (path picture bounding box.north);
15 | }},swap/.style={path picture={
16 | \draw[black]
17 | (path picture bounding box.south west) -- (path picture bounding box.north east) (path picture bounding box.south east) -- (path picture bounding box.north west);
18 | }}]
19 |
20 | % `operator' will only be used by most gates.
21 | % `cnot' will refer to CNOT gates.
22 | % `phase' is used for controlled gates.
23 | \tikzstyle{operator} = [draw,fill=white,minimum size=1.5em]
24 | \tikzstyle{meter} = [draw,color=white,fill=white,minimum size=1.7em]
25 | \tikzstyle{cnot} = [draw,cross,circle,minimum size=5pt]
26 | \tikzstyle{phase} = [draw,fill,shape=circle,minimum size=5pt,inner sep=0pt]
27 | %
28 | \matrix[row sep=0.4cm, column sep=0.8cm] (circuit) {
29 |
30 | % First row.
31 | \node (q1) {\ket{0}}; &[-0.5cm]
32 | \node[operator] (O11) {H}; &
33 | \node[phase] (P12) {}; &
34 | \node[operator] (O13) {H}; &
35 | \node[meter] (M11) {\pgfbox[center,center]{\pgfuseimage{meter}}};\\
36 |
37 | % Second row.
38 | \node (q2) {\ket{\psi}}; &
39 | &
40 | \coordinate (swap22);
41 | \node[swap] (O22) {}; &
42 | &
43 | \coordinate (end2); \\
44 |
45 | % Third row.
46 | \node (q3) {\ket{\phi}}; &
47 | &
48 | \coordinate (swap32);
49 | \node[swap] (O32) {}; &
50 | &
51 | \coordinate (end3); \\
52 | };
53 |
54 | \begin{pgfonlayer}{background}
55 | % Draw lines.
56 | \draw[thick] (q1) -- (M11) (q2) -- (end2) (q3) -- (end3) (P12) -- (swap22) (swap22) -- (swap32);
57 | \end{pgfonlayer}
58 | %
59 | \end{tikzpicture}
60 | \end{document}
61 |
--------------------------------------------------------------------------------
/toffoli_gate.tex:
--------------------------------------------------------------------------------
1 | % Based on the answer by qubyte at
2 | % http://tex.stackexchange.com/questions/9767/whats-a-good-package-for-typesetting-quantum-circuits
3 | \documentclass[12pt]{standalone}
4 | \usepackage{tikz}
5 |
6 | \usetikzlibrary{backgrounds}
7 | % Dirac Kets
8 | \newcommand{\ket}[1]{\ensuremath{\left|#1\right\rangle}}
9 |
10 | \begin{document}
11 | \begin{tikzpicture}[thick,cross/.style={path picture={
12 | \draw[black]
13 | (path picture bounding box.south) -- (path picture bounding box.north);
14 | }}]
15 |
16 | % `operator' will only be used by most gates.
17 | % `cnot' will refer to CNOT gates.
18 | % `phase' is used for controlled gates.
19 | \tikzstyle{operator} = [draw,fill=white,minimum size=1.5em]
20 | \tikzstyle{cnot} = [draw,cross,circle,minimum size=5pt]
21 | \tikzstyle{phase} = [draw,fill,shape=circle,minimum size=5pt,inner sep=0pt]
22 | %
23 | \matrix[row sep=0.4cm, column sep=0.8cm] (circuit) {
24 |
25 | % First row.
26 | \coordinate (start1); &
27 | \node[phase] (P11) {}; &
28 | \coordinate (end1);\\
29 |
30 | % Second row.
31 | \coordinate (start2); &
32 | \node[phase] (P21) {}; &
33 | \coordinate (end2);\\
34 |
35 | % Third row
36 | \coordinate (start3); &
37 | \node[cnot] (O31) {}; &
38 | \coordinate (end3);\\
39 | };
40 |
41 | \begin{pgfonlayer}{background}
42 | % Draw lines.
43 | \draw[thick] (start1) -- (end1) (start2) -- (end2) (start3) -- (end3) (P11) -- (P21) (P21) -- (O31);
44 | \end{pgfonlayer}
45 | %
46 | \end{tikzpicture}
47 | \end{document}
48 |
--------------------------------------------------------------------------------
/transductive.py:
--------------------------------------------------------------------------------
1 | import matplotlib.pyplot as plt
2 | import numpy as np
3 | from numpy.random import rand
4 |
5 | from graphics_utils import initialize_graphics, cm2inch
6 |
7 | r = rand(8)/5
8 | t = rand(8)
9 | x = r/2 * np.cos(2*np.pi*t) - 0.2
10 | y = r * np.sin(2*np.pi*t) - 0.2
11 | r = rand(40)/5
12 | t = rand(40)
13 | xz = r/2 * np.cos(2*np.pi*t) - 0.2
14 | z = r * np.sin(2*np.pi*t) - 0.2
15 |
16 | r = rand(8)/5
17 | t = rand(8)
18 | xx = r * np.cos(2*np.pi*t) + 0.2
19 | yy = r/3 * np.sin(2*np.pi*t)
20 | r = rand(40)/5
21 | t = rand(40)
22 | xzz = r * np.cos(2*np.pi*t) + 0.2
23 | zz = r/3 * np.sin(2*np.pi*t)
24 |
25 | colors = initialize_graphics()
26 |
27 | fig, ax = plt.subplots()
28 | fig.set_size_inches(cm2inch([10,10]))
29 | ax.plot(xz, z, 'o',color=colors[0], label='Unlabeled instances')
30 | ax.plot(x, y, 'D', color=colors[1], label='Class 1')
31 | ax.plot(xzz, zz, 'o',color=colors[0])
32 | ax.plot(xx, yy, 's', color=colors[2], label='Class 2')
33 |
34 | handles, labels = ax.get_legend_handles_labels()
35 | ax.legend(handles, labels, loc=4)
36 |
37 | plt.axes().set_aspect('equal')
38 | plt.axis('off')
39 |
40 | plt.savefig('./transductive.pdf',bbox_inches='tight')
41 |
--------------------------------------------------------------------------------
/unsupervised.py:
--------------------------------------------------------------------------------
1 | import matplotlib.pyplot as plt
2 | from matplotlib.patches import Ellipse
3 | import numpy as np
4 | from numpy.random import rand
5 |
6 | from graphics_utils import initialize_graphics, cm2inch
7 |
8 | r = rand(40)/5
9 | t = rand(40)
10 | x = r * np.cos(2*np.pi*t) - 0.3
11 | y = r * np.sin(2*np.pi*t) - 0.3
12 |
13 | r = rand(40)/5
14 | t = rand(40)
15 | xx = r * np.cos(2*np.pi*t) + 0.3
16 | yy = r/3 * np.sin(2*np.pi*t) + 0.3
17 |
18 |
19 | r = rand(40)/5
20 | t = rand(40)
21 | xxx = r/2 * np.cos(2*np.pi*t) - 0.15
22 | yyy = r * np.sin(2*np.pi*t) + 0.15
23 |
24 | colors = initialize_graphics()
25 | circle1 = Ellipse((-0.3, -0.3), 0.42, 0.42, facecolor='none', edgecolor=colors[1], linewidth=4, label='Decision boundary')
26 | circle2 = Ellipse((0.3, 0.3), 0.42, 0.22, facecolor='none', edgecolor=colors[1], linewidth=4)
27 | circle3 = Ellipse((-0.15, +0.15), 0.22, 0.42, facecolor='none', edgecolor=colors[1], linewidth=4)
28 |
29 | fig, ax = plt.subplots()
30 | fig.set_size_inches(cm2inch([10,10]))
31 | plt.plot(x, y, 'o', color=colors[0], label='Unlabeled instances')
32 | plt.plot(xx, yy, 'o', color=colors[0])
33 | plt.plot(xxx, yyy, 'o', color=colors[0])
34 |
35 | ax.add_patch(circle1)
36 | ax.add_patch(circle2)
37 | ax.add_patch(circle3)
38 |
39 | handles, labels = ax.get_legend_handles_labels()
40 | ax.legend(handles, labels, loc=4)
41 |
42 | plt.axes().set_aspect('equal')
43 | plt.axis('off')
44 | ax.set_xlim([-0.52, 0.52])
45 | ax.set_ylim([-0.52, 0.52])
46 |
47 | plt.savefig('./unsupervised.pdf',bbox_inches='tight')
48 |
--------------------------------------------------------------------------------
/vc_dimension_line.py:
--------------------------------------------------------------------------------
1 | # -*- coding: utf-8 -*-
2 | """
3 | Created on Sun Apr 27 09:23:32 2014
4 |
5 | @author: wittek
6 | """
7 |
8 | import matplotlib.pyplot as plt
9 | import numpy as np
10 | from numpy.random import rand
11 | from graphics_utils import initialize_graphics, cm2inch
12 |
13 | x = np.arange(0.0, 10, 0.01)
14 | y = x
15 |
16 | colors=initialize_graphics()
17 |
18 | fig, ax = plt.subplots()
19 | fig.set_size_inches(cm2inch([10,10]))
20 |
21 | ax.plot(x, y, lw=3, color=colors[0])
22 |
23 | ax.plot(5, 6, 'o', color=colors[1])
24 | ax.plot(3, 7, 'o', color=colors[1])
25 | ax.plot(7, 4, 'D', color=colors[2])
26 |
27 | ax.set_xlim([-1, 11])
28 | ax.set_ylim([-2, 11])
29 |
30 | plt.axis('off')
31 |
32 | plt.savefig('./vc_dimension_line.pdf',bbox_inches='tight')
33 |
--------------------------------------------------------------------------------
/vc_dimension_sine.py:
--------------------------------------------------------------------------------
1 | # -*- coding: utf-8 -*-
2 | """
3 | Created on Sun Apr 27 09:23:32 2014
4 |
5 | @author: wittek
6 | """
7 |
8 | import matplotlib.pyplot as plt
9 | import numpy as np
10 | from numpy.random import rand
11 | from graphics_utils import initialize_graphics, cm2inch
12 |
13 | x = np.arange(0.0, 10*np.pi, 0.01)
14 | y = np.cos(x)
15 |
16 | colors=initialize_graphics()
17 |
18 | fig, ax = plt.subplots()
19 | fig.set_size_inches(cm2inch([10,10]))
20 |
21 | ax.plot(x, y, lw=3, color=colors[0])
22 | for i in range(0,11,2):
23 | ax.plot(i*np.pi + 2*(rand(1)-0.5), -0.1, 'o', color=colors[1])
24 | for i in range(1,11,2):
25 | ax.plot(i*np.pi + 2*(rand(1)-0.5), -0.1, 'D', color=colors[2])
26 |
27 |
28 | ax.set_ylim([-1.5, 1.5])
29 |
30 | plt.axis('off')
31 |
32 | plt.savefig('./vc_dimension_sine.pdf',bbox_inches='tight')
--------------------------------------------------------------------------------
/xor_problem.py:
--------------------------------------------------------------------------------
1 | import matplotlib.pyplot as plt
2 | import numpy as np
3 |
4 | from graphics_utils import initialize_graphics, cm2inch
5 |
6 |
7 | xx = np.arange(-0.1, 1.1,0.01)
8 | yy = -xx+0.9
9 |
10 | x1 = [0, 1]
11 | y1 = [1, 0]
12 | x2 = [1 ,0]
13 | y2 = [1, 0]
14 |
15 | colors = initialize_graphics()
16 |
17 | fig, ax = plt.subplots()
18 | fig.set_size_inches(cm2inch([10,10]))
19 | plt.plot(x1, y1, 'D' , color=colors[0], label='Class 1')
20 | plt.plot(x2, y2, 's', color=colors[1], label='Class 2')
21 | plt.plot(xx, yy, color=colors[2], linewidth=4, label='Decision\n surface')
22 |
23 | handles, labels = ax.get_legend_handles_labels()
24 | ax.legend(handles, labels, loc=7)
25 |
26 | plt.axis('off')
27 | ax.set_ylim([-0.1, 1.1])
28 |
29 | plt.savefig('./xor_problem.pdf',bbox_inches='tight')
30 |
--------------------------------------------------------------------------------