2018-02-27 23:58

4 files changed, 0 insertions, 182 deletions

diff --git a/software/PyCMDS/ideal axis positions/delay steps.pdf b/software/PyCMDS/ideal axis positions/delay steps.pdf
deleted file mode 100644
index 1472e0c..0000000
--- a/software/PyCMDS/ideal axis positions/delay steps.pdf
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diff --git a/software/PyCMDS/ideal axis positions/delay steps.tex b/software/PyCMDS/ideal axis positions/delay steps.tex
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--- a/software/PyCMDS/ideal axis positions/delay steps.tex
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-% document

-\documentclass[11 pt]{report}

-\usepackage[letterpaper, margin=0.75in]{geometry}  % 1 inch margins required

-\usepackage{setspace}

-\usepackage{afterpage}

-\usepackage{color}

-\usepackage{soul}

-\usepackage{array}

-

-% text

-\usepackage[utf8]{inputenc}

-\setlength\parindent{0pt}

-\setlength{\parskip}{1em}

-\usepackage{enumitem}

-\renewcommand{\familydefault}{\sfdefault}

-\newcommand{\RomanNumeral}[1]{\textrm{\uppercase\expandafter{\romannumeral #1\relax}}}

-\usepackage{etoolbox}

-\AtBeginEnvironment{verse}{\singlespacing}

-\AtBeginEnvironment{tabular}{\singlespacing}

-

-% graphics

-\usepackage{graphics}

-\usepackage{graphicx}

-\usepackage{epsfig}

-\usepackage{epstopdf}

-\usepackage{etoc}

-\usepackage{tikz}

-

-% math

-\usepackage{amssymb}

-\usepackage{amsmath}

-\usepackage[cm]{sfmath}

-\DeclareMathOperator{\me}{e}

-

-% hyperref

-\usepackage[colorlinks=true, linkcolor=black, urlcolor=blue, citecolor=black, anchorcolor=black]{hyperref}

-\usepackage[all]{hypcap}  % helps hyperref work properly

-

-% date (http://tex.stackexchange.com/a/237251)

-\def\twodigits#1{\ifnum#1<10 0\fi\the#1}

-\def\mydate{\leavevmode\hbox{\the\year-\twodigits\month-\twodigits\day}}

-

-\begin{document}

-

-{\Huge{delay space stepping strategy}}

-

-Blaise Thompson \hfill last modified \mydate

-

-\dotfill

-

-Linear stepping is more expensive than it needs to be.

-

-Want to capture the dynamic range of the data as quickly as possible.

-

-Typically have exponential decay dynamics (perhaps multi-exponential)\dots we can capitalize on this. We want to take high resolution data at early delays and low resolution data at late delays.

-

-Of course, we don't want to throw away any information we would otherwise be entitled to.

-

-Conceptually we want to 'linearize' the data, so that each subsequent delay step accounts for the same change in signal.

-

-Signal goes exponentially...

-

-\begin{eqnarray}

-S &=& \me^{-\frac{t}{\tau}} \\

-\log{(S)} &=& -\frac{t}{\tau} \\

-t &=& -\tau\log{(S)}

-\end{eqnarray}

-

-So to step linearly in $t$, my step size has to go as $-\tau\log{(S)}$.

-

-We want to go linearly in signal, meaning that we want to divide $S$ into even sections. If $S$ goes from 0 to 1 and we choose to acquire $N$ points,

-

-\begin{eqnarray}

-t_n &=& -\tau\log{\left(\frac{n}{N}\right)}.

-\end{eqnarray}

-

-Note that $t_n$ starts at long times and approaches zero delay. So the first $t_1$ is the smallest signal and $t_N$ is the largest.

-

-Now we can start to consider realistic cases, like where $\tau$ is not quite known and where some other longer dynamics persist (manifested as a static offset). Since these values are not separable in a general system, I'll keep $S$ normalized between 0 and 1.

-

-\begin{eqnarray}

-S &=& (1-c)\me^{-\frac{t}{\tau_{\mathrm{actual}}}} + c \\

-S_n &=& (1-c)\me^{-\frac{-\tau_{\mathrm{step}}\log{\left(\frac{n}{N}\right)}}{\tau_{\mathrm{actual}}}} + c \\

-S_n &=& (1-c)\me^{-\frac{\tau_{\mathrm{step}}}{\tau_{\mathrm{actual}}} \log{\left(\frac{N}{n}\right)}} + c \\

-S_n &=& (1-c)\left(\frac{N}{n}\right)^{-\frac{\tau_{\mathrm{step}}}{\tau_{\mathrm{actual}}}} + c \\

-S_n &=& (1-c)\left(\frac{n}{N}\right)^{\frac{\tau_{\mathrm{step}}}{\tau_{\mathrm{actual}}}} + c

-\end{eqnarray}

-

-

-

-\begin{figure}[!htb]

-	\centering

-	\includegraphics[scale=0.5]{"out"}

-	\caption{}

-\end{figure}

-

-

-

-\end{document}
\ No newline at end of file
diff --git a/software/PyCMDS/ideal axis positions/exponential.png b/software/PyCMDS/ideal axis positions/exponential.png
deleted file mode 100644
index 7ad27f3..0000000
--- a/software/PyCMDS/ideal axis positions/exponential.png
+++ /dev/null
diff --git a/software/PyCMDS/ideal axis positions/steps.py b/software/PyCMDS/ideal axis positions/steps.py
deleted file mode 100644
index 13419c3..0000000
--- a/software/PyCMDS/ideal axis positions/steps.py
+++ /dev/null
@@ -1,83 +0,0 @@
-### import ####################################################################

-

-

-import matplotlib.pyplot as plt

-plt.close('all')

-

-import numpy as np

-

-import WrightTools as wt

-

-

-### define ####################################################################

-

-

-def get_signal(d, tau, pulsewidth=10, offset=0):

-    # pulse

-    pulse = np.exp((-d**2)/(pulsewidth**2))

-    # signal

-    sig = np.zeros(d.shape)

-    sig[d<=0] = np.exp(d[d<=0]/tau)

-    sig[d<=0] += offset

-    sig /= sig.max()

-    # finish

-    #sig = np.convolve(sig, pulse, mode='same')

-    return sig

-

-

-def logarithmic_stepping(p_tau, p_npts, n_tau, n_npts):

-    # positive

-    p_xi = np.arange(0, p_npts)

-    p_delays = p_tau * np.log((p_xi.size+1)/(p_xi+1))

-    # negative

-    n_xi = np.arange(0, n_npts)

-    n_delays = -n_tau * np.log((n_xi.size+1)/(n_xi+1))

-    return np.hstack((n_delays, [0], p_delays))

-

-

-tau = 200

-

-

-d = logarithmic_stepping(50, 3, 200, 15)

-

-

-### workspace #################################################################

-

-

-if True:

-    fig, gs = wt.artists.create_figure(width=13, cols=[1, 1], nrows=1)

-    # delay space

-    ax = plt.subplot(gs[0, 0]) 

-    ds = np.linspace(-1500, 1500, 1000)

-    sig = get_signal(ds, tau)

-    plt.plot(ds, sig, c='b', lw=2, alpha=0.5)

-    sig = get_signal(ds, tau, offset=0.5)

-    plt.plot(ds, sig, c='r', lw=2, alpha=0.5)

-    sig = get_signal(ds, tau*2, offset=0)

-    plt.plot(ds, sig, c='g', lw=2, alpha=0.5)

-    plt.xlim(-1250, 100)

-    plt.ylim(-0.1, 1.1)

-    for x in d:

-        plt.axvline(x, c='k', zorder=0)

-    plt.axvline(0, lw=3, c='k')

-    ax.set_xlabel('delay', fontsize=18)

-    ax.set_ylabel('signal', fontsize=18)

-    plt.grid(ls=':')

-    # index space

-    ax = plt.subplot(gs[0, 1])

-    d = logarithmic_stepping(50, 3, 200, 15)

-    sig = get_signal(d, tau)

-    plt.scatter(np.arange(sig.size), sig, c='b', edgecolor='none', s=50, alpha=0.5)

-    sig = get_signal(d, tau, offset=0.5)

-    plt.scatter(np.arange(sig.size), sig, c='r', edgecolor='none', s=50, alpha=0.5)

-    sig = get_signal(d, tau*2, offset=0)

-    plt.scatter(np.arange(sig.size), sig, c='g', edgecolor='none', s=50, alpha=0.5) 

-    i = np.argmin(np.abs(d))

-    plt.axvline(i, lw=3, c='k')

-    plt.grid(ls=':')

-    plt.ylim(-0.1, 1.1)

-    plt.setp(ax.get_yticklabels(), visible=False)

-    ax.set_xlim(0-1, sig.size)

-    ax.set_xlabel('index', fontsize=18)

-    # finish

-    wt.artists.savefig('exponential.png')