From db7fa0ce13071ab1bce990797d45632ecaa272b8 Mon Sep 17 00:00:00 2001 From: caes Date: Mon, 29 Aug 2016 02:33:52 -0400 Subject: [PATCH 1/3] added some images for errors report --- plot.sh | 4 +-- press/errors/errors.tex | 37 ++++++++++++++++++++++++++ press/img/psd_atlas_err0.pdf | Bin 0 -> 35889 bytes press/img/psd_atlas_err2.pdf | Bin 0 -> 35411 bytes press/img/timelag_atlas_err0.pdf | Bin 0 -> 36688 bytes press/img/timelag_atlas_err2.pdf | Bin 0 -> 35558 bytes scripts/plot_MC_against_CM.sh | 38 ++++++++++++++------------- scripts/templates/timelag_compare.gp | 10 +++---- 8 files changed, 64 insertions(+), 25 deletions(-) create mode 100644 press/errors/errors.tex create mode 100644 press/img/psd_atlas_err0.pdf create mode 100644 press/img/psd_atlas_err2.pdf create mode 100644 press/img/timelag_atlas_err0.pdf create mode 100644 press/img/timelag_atlas_err2.pdf diff --git a/plot.sh b/plot.sh index 9e85488..cb4ee1a 100755 --- a/plot.sh +++ b/plot.sh @@ -4,7 +4,7 @@ # document-rady plots. # Only analyses with this error type will be represented in the atlas -errtype="CM" +errtype="LF" ref_band="1367Å" case $1 in @@ -54,4 +54,4 @@ case $1 in *) echo "Did not understand plot type." ;; -esac \ No newline at end of file +esac diff --git a/press/errors/errors.tex b/press/errors/errors.tex new file mode 100644 index 0000000..c3345cf --- /dev/null +++ b/press/errors/errors.tex @@ -0,0 +1,37 @@ +\documentclass[11pt,letterpaper]{article} + +\usepackage{natbib} +%\usepackage{cite} +\usepackage{graphicx} +\usepackage[margin=1.in,centering]{geometry} +\usepackage{hyperref} +\usepackage{caption} +\usepackage[export]{adjustbox} +\usepackage{float} + +\begin{document} + +\title{Computational Anomalies in Error Estimation} + +\date{August 25, 2016} + +\maketitle + +I'll print grids of results for each error type. Errors extracted from the covariance matrix (error code 0) + +Psdlag includes three methods for computing errors. These are designated by their error codes: + * 0 - Extracting from the covariance matrix + * 1 - Scanning the likelihood function + * 2 - Monte Carlo + +The covariance matrix method, i.e. the "quick" method, is the method we had our early successes with. Here are the grids of PSD and timelags. We do see some possible issues with errors here, with those that are too small + +\includegraphics{../img/timelag_atlas_err0.pdf} +\includegraphics{../img/timelag_atlas_err1.pdf} +\includegraphics{../img/timelag_atlas_err2.pdf} + +\includegraphics{../img/psd_atlas_err0.pdf} +\includegraphics{../img/psd_atlas_err1.pdf} +\includegraphics{../img/psd_atlas_err2.pdf} + +\end{document} diff --git a/press/img/psd_atlas_err0.pdf b/press/img/psd_atlas_err0.pdf new file mode 100644 index 0000000000000000000000000000000000000000..cc5af9a20b5545b37a4a4e1b0d623daf22d00472 GIT binary patch literal 35889 zcmZtu1yoyKus(pcXmOW7DHNx;2W@eR6?YH8-CbK;i$k#D?(R~Y;98vG?oMCY-@X5L z-&!w=m6O?fW`A?Cn0>x8XEHR3;*!klEZnFx^~V*DsGJmR6n4gzsDgqNta4ymGiP%O zF4&MVDg^}vtE7dsGuRP!v^H`Ei-SRSCSX)yVN@q)N3f9%syig#N3Zgz#c}!Zf#C3b zXM;&LfnMoTEHV}OC;wLt-fQR|iGR%_p`QXfB(d+-%mz;mY#rw^f9$NoxmBLzDo1hQ zhm_IE{&}eOp8NA$`RC@I$gk1+WvkPN$$-J{r8DO0evSOkewOgdj@`%P%I(Y3j}4U< z_aBA-Tszqe{89h27`=TtFdkFxZ8P$adRuvMx4XOB;a%<}@-&|1_k6EGzP2&9y%%s; 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#QW#VtbhQteU(33ks6>d!~Yf_d>jH0HXt zRE05;5F4VYW7qO2MtZg8Kfr&{oAwy0#MVH;QqD5DY+XI3&AhdqDBSn#F4bMA?q#6| zOiuLJ3tm;G&`0R>(IG%sy^wB?PMO}oNwsZi(-wKAIPytQ+eS*&N)qIRYRjsN&x;?H zCSf&zLvT`BDrM1IADZbLKNQY?)NbSPKJ&`YXW0hzBhO86`eyAJoiv=XgOJtkTrocN z81p(0D$PMsF6|LF6|6yhP(7oWbQ@%$Lww9C@qCHm+R zJ%paD-&lGnaetQxZmmg$V%=*~g@~SWXNbKg^@(Y7C7s5WCW1xt(}!(1xC-;Trl2fS z7pd-&ZkXN@XFv-g&+K_Tt5@l!h;jxFeRvHGZ0bcfofl&FFD_Q(K1$mD9!gBDs7;3{ z3Ta3{<02V^|D6?ATkgiPA#2_6XK7QHgFHg5p zexzlh-=Ea^usy3ZuxD+4Rw`hB*g7W&XFcxOL=sbidz#?OWi{x`MhYzszvKH1ueAZ` zw!PIscH6G=@$qD#;?lErNhP!uG*_=8$d^kFKo{lOiL$c5TTQs&j(J~)LQVLWEZPB&<^vrcxnXUw_VFFk5-o@m#_Ei6&SZo6T| zKPDK^S2c|$%f4}RHjnJfyOJgzw}cmR2=`87vM=T4=%e6#SX)CwIgzU^X`v2b`dPb6 zqX#H;(oYOhhNGq&77PzcG;|RcQ0xwK^Y|P^%EUOIBi3yPr;XP;&&b$UITJ|QW#Y0z zg1P0g5=1;}28YX}YYQ8GN#B!0bl9Z|B}C=0RRT{H6RF3?Y_`WCWQo2zPo~#~%rr|P zm-|hPDZ~s}5p-sToB7gJY-A^2?^HiUVdta$q1;V~oMMw~{-sDnQK?PH5E+HhvQQvs z&B30u%_24OPTR3+knvbS|=awG>DT(+0C5(c9wWg1n+1AhOd0ELlZBiWgrq z-1}45Kw<9K&cJjaFDDg~gxscCqiYpBd74~5%RjfZf8XN$q4d8=F#O&( zyubASpNJ)<)2y2gHt5U?8mC#nHr^g8;x*K^o`2C=KE|ImCV! z75x%7}jgoZCtII%Yms$2;nb ziC`wb;%lsh11qV1EL>z!TD&4mWU?7*++*R{%*M&8jjhU7d5Ig@sb`z*GO2dsp#xxZ;!jIfnoHAo-u8{|jbdVP?apW?*D~n>QA= zH#r76w*MP6{1I&U7ieH$`rXC9K*M`8zfJ!)YIu`?_@ip^FWn5l-z6sgH{c*3CitF_ z_rrf+z`yXr|B|1#8VauVZ^%W=%Ef`P*dtW6Az2z;_W7``?Ye5mVn=dSAZs|CB0me9H^qZzBZ!^>)X53j%hA zx^HL~pG;rZ)Xo|oKm%Z)0pOFFI5^m_)4mC?ycvz{bZtyb_3de_?TpF)tX)|!!{~p8d(fmV*d-(*+-&~*R2;WINaF)-m9 z;s3EQFtXCUCF}i$Z}krwfQ63b4Q>9L?X3X#FMf<~i~QgG7y$IFZ=wFXjgk2s=KY%u zz(W5H^Zvue_>RQ>&Bj2-#PGJd{?qm*D)S#U0Np!6{&&B(HxT|aW(EKY tmp.gp + sed "s|%TITLE%|Error Fit Comparison for Time Lag of $echo_band|"| + sed "s|%SUBTITLE%|referred to ${ref_band}, as reported by Fausnaugh et. al, STORM III, 2016|"| + sed "s|%FILE1%|$table|"| + sed "s|%LABEL1%|${echo_band} Delay with Monte Carlo Fit|"| + sed "s|%FILE2%|$CMtable|"| + sed "s|%LABEL2%|${echo_band} Delay with Covariance Matrix Fit|"| + sed "s|%YMIN%|$ymin|"|sed "s|%YMAX|$ymax|"| + sed "s|%OUTPUTFILE%|$plotfile|" > tmp.gp gnuplot tmp.gp done @@ -53,7 +55,7 @@ do echo Plotting PSD error fit comparison for $echo_band. - plotfile=analyses/plots/PSD_${echo_band}_error_compare.png + plotfile=analyses/plots/PSD_${echo_band}_error_compare.pdf echo_band_noUTF=$(echo $echo_band| sed 's|𝛌|λ|g'| @@ -70,14 +72,14 @@ do sed 's|Å|A|g') cat scripts/templates/psd.gp| - sed "s|%TITLE|Error Fit Comparison for PSD of $echo_band|"| - sed "s|%SUBTITLE|as reported by Fausnaugh et. al, STORM III, 2016|"| - sed "s|%FILE1|$table|"| - sed "s|%LABEL1|${echo_band} PSD with Monte Carlo Fit|"| - sed "s|%FILE2|$CMtable|"| - sed "s|%LABEL2|${echo_band} PSD with Covariance Matrix Fit|"| - sed "s|%YMIN|$ymin|"|sed "s|%YMAX|$ymax|"| - sed "s|%OUTPUTFILE|$plotfile|" > tmp.gp + sed "s|%TITLE%|Error Fit Comparison for PSD of $echo_band|"| + sed "s|%SUBTITLE%|as reported by Fausnaugh et. al, STORM III, 2016|"| + sed "s|%FILE1%|$table|"| + sed "s|%LABEL1%|${echo_band}|"| + sed "s|%FILE2%|$CMtable|"| + sed "s|%LABEL2%|${echo_band} PSD with Covariance Matrix Fit|"| + sed "s|%YMIN%|$ymin|"|sed "s|%YMAX|$ymax|"| + sed "s|%OUTPUTFILE%|$plotfile|" > tmp.gp gnuplot tmp.gp done \ No newline at end of file diff --git a/scripts/templates/timelag_compare.gp b/scripts/templates/timelag_compare.gp index e682c4c..dc04b07 100644 --- a/scripts/templates/timelag_compare.gp +++ b/scripts/templates/timelag_compare.gp @@ -1,9 +1,9 @@ -set terminal pngcairo +set terminal pdf set termoption dash set termopt enhanced -set output "%OUTPUTFILE" +set output "%OUTPUTFILE%" -set title "%TITLE\n{/*0.7 %SUBTITLE}" +set title "%TITLE%\n{/*0.7 %SUBTITLE%}" set xlabel "Temporal Frequency [days^{-1}]" set xrange [0.005:0.620] set logscale x @@ -17,5 +17,5 @@ set key center bottom # Draw line at origin set arrow from 0.005,0 to 0.620,0 nohead lt 3 lc rgb 'black' set pointsize 0 -plot '%FILE1' using 1:2:3:4 with xyerrorbars title "%LABEL1", \ -"%FILE2" using 1:2:3:4 with xyerrorbars title 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ze@Vc9+L)OCIc9nmCf0w>jh>Z(?w|7j0vH(nd5#ww^FPl41TZuIXItj~7$1qRVUWo3`|EB?PP#McWS?^izl a!nJnxI=1$|A`PTx1^^+6i3OwtA^#sxld!4) literal 0 HcmV?d00001 From e89b3f470184293d7e8870586d210c8982d75425 Mon Sep 17 00:00:00 2001 From: caes Date: Tue, 6 Dec 2016 00:15:03 -0500 Subject: [PATCH 3/3] began script to accomodate new clag model --- press/errors/errors.tex | 126 ++++++++++++++++++++++++++++++---- scripts/analyze_lightcurve.py | 124 +++++++++++++++++++++++++++++++++ scripts/plot_MC_against_CM.sh | 2 +- 3 files changed, 237 insertions(+), 15 deletions(-) create mode 100644 scripts/analyze_lightcurve.py diff --git a/press/errors/errors.tex b/press/errors/errors.tex index c3345cf..85f3d97 100644 --- a/press/errors/errors.tex +++ b/press/errors/errors.tex @@ -12,26 +12,124 @@ \begin{document} \title{Computational Anomalies in Error Estimation} - \date{August 25, 2016} -\maketitle +Dear Dr. Cackett,\\ -I'll print grids of results for each error type. Errors extracted from the covariance matrix (error code 0) -Psdlag includes three methods for computing errors. These are designated by their error codes: - * 0 - Extracting from the covariance matrix - * 1 - Scanning the likelihood function - * 2 - Monte Carlo +Here are some musings on the computational anomalies seen in the results of the psdlag program. I cover some things about the input script, some calculations that didn't converge, and the error modes and results. I did my best to create grids of the error results, but compiling a grid from the error mode "1" results produces some pretty whacky results, and this is probably a problem with my graphing routines not working properly without a complete set of analyses -- that is, psdlag output files. -The covariance matrix method, i.e. the "quick" method, is the method we had our early successes with. Here are the grids of PSD and timelags. We do see some possible issues with errors here, with those that are too small +\section{Input Script} +I've included a psdlag input script which is made from the template I use, but each wavelength has its own initial parameters extracted from the err0 results. In the template, I use 0:0 0 to designate the basis light curve; however, this does differ from the original document you gave to me at the beginning of the summer. I don't remember the specifics of why I changed from the original to this form, but I came to that conclusion after some explorations and discussion with you. I'm confident I could reconstruct that, but perhaps this is where a mistake was made. This script and the files needs to run it are included in the .tar.gz file. -\includegraphics{../img/timelag_atlas_err0.pdf} -\includegraphics{../img/timelag_atlas_err1.pdf} -\includegraphics{../img/timelag_atlas_err2.pdf} +Example input script: \\ +2\\ +1367A.lc 0\\ +1479A.lc 0\\ +8 0.0049999999 0.018619375 0.044733049 0.069336227 0.10747115 0.16658029 0.25819945 0.40020915 0.62032418\\ +0\\ +6.533e-02 -9.694e-02 -1.175e+00 -1.525e+00 -2.166e+00 -2.492e+00 -3.258e+00 -9.328e+00 0.2e+00 -0.2e+00 -1.0e+00 -1.500e+00 -2.0e+00 -2.6e+00 -3.4e+00 -6e+00 9.340e-02 -8.842e-02 -1.173e+00 -1.512e+00 -2.113e+00 -2.547e+00 -3.178e+00 -7.000e+00 -6.035e-02 2.044e-02 1.258e-01 5.764e-02 2.580e-02 -4.737e-02 9.579e-02 6.411e-01\\ +0:0 0\\ +2\\ +0\\ +1000 50 400 mcmc\_1479A.dat\\ + +\section{Outputs of Each Error Mode} +I'll print grids of results for each error type. I will also include the psdlag output files for each analysis. It will be important for me to explain the filename format if you want to read the correct files. The first number in the filename is the wavelength of the reference band, which is succeeded by the wavelength of the reverberated band. In brackets, the timestep is given (should be 0.01 days) and finally the error type: $\sigma \in CM/LF/MC$. This allows one to know which error mode was used when running psdlag to produce the output. + +Psdlag includes three methods for computing errors, or error modes. These are designated by an integer from 0-2:\\ +- 0: Extracting from the covariance matrix (CM)\\ +- 1: Scanning the likelihood function (LF) \\ +- 2: Monte Carlo (MC)\\ + +\subsection{Error Mode 0 - Covariance Matrix (CM)} +The covariance matrix method, i.e. the "quick" method, is the method we had our early successes with. Here are the grids of PSD and timelags. We do see some possible issues with errors here, with those that are too small and one that is extremely large. Very small errors may be expected here since this method doesn't account for error dependencies across bins. I'm not sure what's going on with the very large errors in the 3465\AA$ $ time lags; the solution to the cross spectrum converges very quickly: within 11 steps, compared to often closer to 100 or 150 steps. It may need some different initial parameters, so I'll try that, but the convergence can be seen starting at a somewhat lower value (371), with a nice grade toward the likelihood value of 430, so I'm not terribly hopeful. These are both higher than the typical output: usually the program stops solving as the likelihood settles to 300-350. + +\begin{figure} + \label{fig:psd_err0} + \centering + \includegraphics{../img/psd_atlas_err0.pdf} + \caption{PSD from psdlag using error mode 0 (CM).} +\end{figure} + +\begin{figure} + \label{fig:lag_err0} + \centering + \includegraphics{../img/timelag_atlas_err0.pdf} + \caption{Time lag for psdlag run using error mode 0 (CM). These are the results included in my final report. } +\end{figure} + +\subsection{Error Mode 1 - Scanning Likelihood Function (LF)} +This is probably the preferred way of computing the variance of the PSD and time lags. Many of analyses in this group did not finish due to either the convergence routine not starting or not stepping the parameters. For example, in 1928\AA, under parameter 1 (the second parameter), the output shows:\\ + +******* par 1 *******\\ +1 7.01525e-05 36.107 0.0736126 -0.197534 -1.18167 -1.52074 -2.14419 -2.50319 -3.58007 -12.328 \\ +1 7.01525e-05 36.107 0.0736126 -0.197534 -1.18167 -1.52074 -2.14419 -2.50319 -3.58007 -12.328 \\ +1 7.01525e-05 36.107 0.0736126 -0.197534 -1.18167 -1.52074 -2.14419 -2.50319 -3.58007 -12.328 \\ + +and these lines are repeated ad infinitum, so there is clearly no convergence happening here. I have attempted other initial parameters. The following analyses showed such a situation:\\ + - 1746\AA\\ + - 1928\AA\\ + - 2246\AA\\ + - 2600\AA\\ + - 3465\AA\\ + - 4368\AA\\ + +The analyses that did not finish because the optimization routine didn't start show as a last line in the output file something like:\\ +******* par 7 *******\\ + +with no succeeding lines. This includes:\\ +- 1497\AA\\ +- 4382\AA\\ +- 5468\AA\\ +- 8560\AA\\ + +When I learned that these optimizations were not working, I stopped the other models, so some models did not finish. I then moved on to the Monte Carlo method. + +\begin{figure} + \label{fig:psd_err1} + \centering + \includegraphics{../img/psd_atlas_err1.pdf} + \caption{PSD from psdlag using error mode 1 (LF). Most of these models did not finish, so the grid is very sparse and may be misreporting values due to a lack of proper scraping logic.} +\end{figure} + +\begin{figure} + \label{fig:lag_err1} + \centering + \includegraphics{../img/timelag_atlas_err1.pdf} + \caption{Time lag for psdlag run using error mode 1 (LF). Most of these models did not finish, so the grid is very sparse and may be misreporting values due to a lack of proper scraping logic.} +\end{figure} + + + +\subsection{Error Mode 2 - Monte Carlo (MC)} +This is the method we ultimately tried to get working for my final presentation, but were unsuccessful. Chia-ying told me that she has used this method for analyses in the past, and chose to do so because she was unable to get LF to work. 4392\AA$ $ and 5404\AA$ $ did not finish, so they're meaningless: that means they took over 48 hours to run on a computation node on our cluster at WMU. That might indicate a problem unto itself. 1756\AA$ $ did finish, with those results. Ultimately, we decided that the errors on the timelags didn't make much sense, which is why I never went back to complete the remaining two models. + +I tried to look through the output files for clues, but in the end, I could find no apparently pattern indicated why any models showed strange results, with either strong or weak variance. I may not be keen enough to notice the important values popping up in the optimization readouts in the output files, but I did notice that 1928\AA$ $ and 4368\AA$ $ oscillate to the final 400$^{th}$ step rather than converge. Many of these models take close to or more than 24 hours to run on cores at the WMU cluster, which are not top-of-the-line, but are reasonably modern and fast machines. + + +\begin{figure} + \label{fig:psd_err2} + \centering + \includegraphics{../img/psd_atlas_err2.pdf} + \caption{PSD from psdlag using error mode 2 (MC).} +\end{figure} + + +\begin{figure} + \label{fig:lag_err2} + \centering + \includegraphics{../img/timelag_atlas_err2.pdf} + \caption{Time lag for psdlag run using error mode 2 (MC).} +\end{figure} + + +\section{Closing} +That's all I have for now. I will keep changing things and trying new runs. I'll let you know if I find out anything new of importance. Hopefully some good can come from this.\\ + +Best Regards, + +Otho Ulrich -\includegraphics{../img/psd_atlas_err0.pdf} -\includegraphics{../img/psd_atlas_err1.pdf} -\includegraphics{../img/psd_atlas_err2.pdf} \end{document} diff --git a/scripts/analyze_lightcurve.py b/scripts/analyze_lightcurve.py new file mode 100644 index 0000000..7300e9d --- /dev/null +++ b/scripts/analyze_lightcurve.py @@ -0,0 +1,124 @@ +# -*- coding: utf-8 -*- +from __future__ import unicode_literals +import numpy as np +import clag +import sys + + +# For jupyter notebook +# %pylab inline + +try: + opts,args = getopt.getopt(args, "") +except getopt.GetoptError: + print 'analyze_lightcure.py ' + sys.exit(2) + +## load the first light curve +lc1 = np.loadtxt(args[0]) + +# works if first two entries represent minimum spacing, from example +# dt = lc1[1,0] - lc1[0, 0] + +# Time resolution determined from inspection and testing. +dt = 0.01 + + +_ = plot(lc1[:,0], lc1[:,1]) +_ = plot(lc1[:,0], lc1[:,3]) + +# Split the light curve into segments # +seg_length = 256 +index = np.arange(len(lc1)).reshape((-1, seg_length)) + +lc1_time = [lc1[i, 0] for i in index] +lc1_strength = [lc1[i, 1] for i in index] +lc1_strength_err = [lc1[i, 2] for i in index] + +# This would work if both curves are in same file +# Lc2 = [lc1[i, 3] for i in index] +#Lc2e = [lc1[i, 4] for i in index] + + + +#### Get the psd for the first light curve #### + +# These bin values determined summer 2015 for STORM III optical/UV lightcurves +fqL = [0.0049999999, 0.018619375, 0.044733049, 0.069336227, 0.10747115, 0.16658029, 0.25819945, 0.40020915, 0.62032418] + +# using utilities to set up frequency bins # +# fqL = np.logspace(np.log10(1.1/seg_length),np.log10(.5/dt),7) +# fqL = np.concatenate(([0.5/seg_length], fqL)) + +nfq = len(fqL) - 1 + + + +## initialize the psd class for multiple light curves ## +P1 = clag.clag('psd', lc1_time, lc1_strength, lc1_strength_err, dt, fqL) + + + + + +## initial parameters, start with ones +inpars = np.ones(nfq) + +## print the loglikelihood for the input values ## +print P1.logLikelihood(inpars) + + + +## Now do the fitting and find the best fit psd values at the given frequency bins ## +psd1, psd1e = clag.optimize(P1, inpars) + + + + +## plot ## +fqd = 10**(np.log10( (fqL[:-1]*fqL[1:]) )/2.) + +loglog(fqd, 0.1*fqd**(-1.5), label='input psd') +errorbar(fqd[1:-1], psd1[1:-1], yerr=psd1e[1:-1], fmt='o', ms=10, label='fit') + + + + +## Now do the second light curve + +P2 = clag.clag('psd', lc1_time, Lc2, Lc2e, dt, fqL) + +psd2, psd2e = clag.optimize(P2, inpars) + + + + + + +### Now the cross spectrum ### +### We also give it the calculated psd values as input ### +Cx = clag.clag('cxd', + [list(i) for i in zip(lc1_time,lc1_time)], + [list(i) for i in zip(lc1_strength,Lc2)], + [list(i) for i in zip(lc1_strength_err,Lc2e)], + dt, fqL, psd1, psd2) + +inpars = np.concatenate( (0.3*(psd1*psd2)**0.5, psd1*0+1.) ) +p, pe = clag.optimize(Cx, inpars) +phi, phie = p[nfq:], pe[nfq:] +lag, lage = phi/(2*np.pi*fqd), phie/(2*np.pi*fqd) +cx, cxe = p[:nfq], pe[:nfq] + + + + + + + + +## plot ## + +semilogx(fqd, fqd*0+1.0, label='input phase lag') +ylim([0.8, 1.2]) +errorbar(fqd[1:-1], phi[1:-1], yerr=phie[1:-1], fmt='o', ms=10, label='fit') + diff --git a/scripts/plot_MC_against_CM.sh b/scripts/plot_MC_against_CM.sh index 714ee2c..fd00019 100755 --- a/scripts/plot_MC_against_CM.sh +++ b/scripts/plot_MC_against_CM.sh @@ -75,7 +75,7 @@ do sed "s|%TITLE%|Error Fit Comparison for PSD of $echo_band|"| sed "s|%SUBTITLE%|as reported by Fausnaugh et. al, STORM III, 2016|"| sed "s|%FILE1%|$table|"| - sed "s|%LABEL1%|${echo_band}|"| + sed "s|%LABEL1%|${echo_band} PSD with Monte Carlo Fit|"| sed "s|%FILE2%|$CMtable|"| sed "s|%LABEL2%|${echo_band} PSD with Covariance Matrix Fit|"| sed "s|%YMIN%|$ymin|"|sed "s|%YMAX|$ymax|"|