Fraction including parentheses in MathmL - parentheses

How can I make the fraction like the second formula?
my sample formula
<math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>D</mi><mi>e</mi></msub><mo>=</mo><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow><mi>·</mi><mfrac><mfenced><msup><mrow><mi>a</mi><mo>·</mo><mi>b</mi></mrow><mn>0,625</mn></msup></mfenced><msup><mfenced><mrow><mi>a</mi><mo mathsize="small">+</mo><mi>b</mi></mrow></mfenced><mn>0,25</mn></msup></mfrac><mtext> [m]</mtext><mtext mathcolor="DodgerBlue"> Formel 1.3</mtext>
</math>

<math display="block" xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<msub><mi>D</mi><mi>e</mi></msub>
<mo>=</mo>
<mn>1,3</mn>
<mo>.</mo>
<mfrac>
<mrow><mo stretchy="false" form="prefix">(</mo><mi>a</mi><mo>.</mo><mi>b</mi><msup><mo stretchy="false" form="postfix">)</mo><mn>0,625</mn></msup></mrow>
<mrow><mo stretchy="false" form="prefix">(</mo><mi>a</mi><mo>+</mo><mi>b</mi><msup><mo stretchy="false" form="postfix">)</mo><mn>0,25</mn></msup></mrow>
</mfrac>
</mrow>
</math>

Related

For loop is "stucked" inside a pgfplot

I am trying to produce some plots in latex using pgfplots; because of the fact that I have several different plots to produce, I am trying to use a for loop. Unfortunately, without success. Indeed, the code is executed three times but the value of the variable of the for loop it is always equal to the first value of the list that defines the loop.
For example, the following minimal code
\documentclass[a4paper, 11pt]{article}
\usepackage{pgfplots}
\pgfplotsset{compat=1.13}
\usepgfplotslibrary{groupplots}
\begin{document}
\makeatletter
\begin{tikzpicture}
\begin{groupplot}[group style={group size= 2 by 3}]
\#for\refin:={1,2,3}\do{%
\nextgroupplot[ylabel={$h = \frac{1}{\refin}$}]
\addplot {exp(x)};
\nextgroupplot
\addplot{2 * x};
}
\end{groupplot}
\end{tikzpicture}
\makeatother
\end{document}
Produces a figure with 6 plots (as expected) but the label is always 1/1 and never 1/2 or 1/3. Why?
You can use the same trick as https://tex.stackexchange.com/a/539754/36296 :
\documentclass[a4paper, 11pt]{article}
\usepackage{pgffor}
\usepackage{pgfplots}
\pgfplotsset{compat=1.13}
\usepgfplotslibrary{groupplots}
\begin{document}
\begin{tikzpicture}
\begin{groupplot}[group style={group size= 2 by 3}]
\pgfplotsforeachungrouped \x in {1,2,3}{
\edef\tmp{
\noexpand\nextgroupplot[ylabel={$h = \frac{1}{\x}$}]
\noexpand\addplot {exp(x)};
}
\tmp
\nextgroupplot
\addplot{2 * x};
}
\end{groupplot}
\end{tikzpicture}
\end{document}

SPSS: Syntax for Calculating FSCORE from rotated factors

I found the proper syntax to import my centriod factor extraction into SPSS and rotate it. (The semi-bumbling tale is here.
The next issue is this: because of limitations in SPSS on what subcommands can be used when reading a matrix in (only /ROTATE and /EXTRACTION are permitted), I can't get the factor scores. SPSS displays this error:
"Factor scores cannot be computed with matrix input."
I still need to find a way to get the FSCORE of the newly rotated factors of each factor for all cases by running a regression using the newly rotated factors and saving the regression values as a new variable (/SAVE REG(ALL).
Ideas are welcome. Thank you for your expertise!
Assets: Dataset A of 36 cases and 74 variables (the basis of the centriod factor extraction); centriod factor extraction matrix
Here's the SPSS syntax that almost does what I need - except it uses PCA extraction instead of centroid.
FACTOR
/VARIABLES VAR00001 VAR00002 VAR00003 VAR00004 VAR00005 VAR00006 VAR00007 VAR00008 VAR00009 VAR00010 VAR00011 VAR00012 VAR00013 VAR00014 VAR00015 VAR00016 VAR00017 VAR00018 VAR00019 VAR00020 VAR00021 VAR00022 VAR00023 VAR00024 VAR00025 VAR00026 VAR00027 VAR00028 VAR00029 VAR00030 VAR00031 VAR00032 VAR00033 VAR00034 VAR00035 VAR00036 VAR00037 VAR00038 VAR00039 VAR00040 VAR00041 VAR00042 VAR00043 VAR00044 VAR00045 VAR00046 VAR00047 VAR00048 VAR00049 VAR00050 VAR00051 VAR00052 VAR00053 VAR00054 VAR00055 VAR00056 VAR00057 VAR00058 VAR00059 VAR00060 VAR00061 VAR00062 VAR00063 VAR00064 VAR00065 VAR00066 VAR00067 VAR00068 VAR00069 VAR00070 VAR00071 VAR00072 VAR00073 VAR00074
/MISSING LISTWISE
/ANALYSIS VAR00001 VAR00002 VAR00003 VAR00004 VAR00005 VAR00006 VAR00007 VAR00008 VAR00009 VAR00010 VAR00011 VAR00012 VAR00013 VAR00014 VAR00015 VAR00016 VAR00017 VAR00018 VAR00019 VAR00020 VAR00021 VAR00022 VAR00023 VAR00024 VAR00025 VAR00026 VAR00027 VAR00028 VAR00029 VAR00030 VAR00031 VAR00032 VAR00033 VAR00034 VAR00035 VAR00036 VAR00037 VAR00038 VAR00039 VAR00040 VAR00041 VAR00042 VAR00043 VAR00044 VAR00045 VAR00046 VAR00047 VAR00048 VAR00049 VAR00050 VAR00051 VAR00052 VAR00053 VAR00054 VAR00055 VAR00056 VAR00057 VAR00058 VAR00059 VAR00060 VAR00061 VAR00062 VAR00063 VAR00064 VAR00065 VAR00066 VAR00067 VAR00068 VAR00069 VAR00070 VAR00071 VAR00072 VAR00073 VAR00074
/PRINT INITIAL CORRELATION SIG DET INV REPR AIC EXTRACTION ROTATION FSCORE
/FORMAT BLANK(.544)
/CRITERIA FACTORS(6) ITERATE(80)
/EXTRACTION PC <---Here's the rub.
/CRITERIA ITERATE(80) DELTA(0)
/ROTATION OBLIMIN
/SAVE REG(ALL)
/METHOD=CORRELATION.
I referred to the MATRIX command in my reply to your other post (Rotations). You will need to research the appropriate equations for performing this calculation and set up the matrix algebra within a MATRIX END - MATRIX code block. Easy once you have the math right. I'm too busy/lazy to research and write it but this should provide a fertile lead.

What do the four digit sequences in a JPEG mean?

So when I open a JPEG file in sublime or a text editor, i get a very long list of four digit sequences, such as:
84ac b7ac 5b2a ccda 5557 5541 af6a c5ae
17a8 d11c ec18 da5e c4c7 6b7a 9f25 896c
44b4 cf7b 52af 8ac9 4179 ec95 858c 0756
7395 3b36 71d7 99b3 d21e 2ae5 dbbe 72de
37d0 b2f3 b3d6 d352 cb46 7c3d c6de 7c47
0be9 a7ab 3f8b a7d7 a744 7cab d2fa d56f
c873 f49e bcb1 7469 d856 51af 743f 3fc8
f59e 4b58 5d79 f669 37d1 73e5 4d7f 5ecc
6f8b caf4 3c6e 8ad9 b69b e74e 6df5 823a
7cde a3f2 be27 b2e2 eeda d79d beea c785
b3b3 4e9c fcb1 b69e 9c73 871a c643 a29b
5880 6d15 f126 57a7 2af0 f93a 7a7d 1e47
522a d2c7 3d30 0bf3 ba4b aa69 a8b6 679a
fa47 3bbb c5d3 a466 e8a9 5ce3 a6d5 7c64
f4dc c34e 71dc c699 b4db 4ac6 fb39 41ae
8d7c dd0a 771d 1dae 5e7e 3f47 78f3 a6c3
52f3 162a 88a2 8e90 0578 c40e 010c 8c64
2ccc d5ed 96b3 55b2 a040 ed4b 3f9a f519
375e 3317 bb3d b979 4b7d 0e0d 12fb 4e37
63cd db07 cabe b3e4 749f 0bb7 b3de f4f1
f29a 7d4f 439e fc97 a7e9 dbc3 a60a fa73
What do these sequences of 4 digits mean? I tried googling this but haven't got an answer. Does each one relate to a pixel? or the color of a pixel?
It's the text editor's representation of the binary code that makes up the image file. Each set does not necessarily have to relate to one pixel or one detail of a pixel.

trying to parse specific data using xpath

I have a small xml file that I'm trying to grab the away_team first and then the home_team second.
/game/team/statistics/#goals gives me the data I want but I need to reverse the order. So I'm trying to understand how to get the away_team goals first, followed by the home_team.
Below is the file
<game id="f24275a9-4f30-4a81-abdf-d16a9aeda087" status="closed" coverage="full" home_team="4416d559-0f24-11e2-8525-18a905767e44" away_team="44167db4-0f24-11e2-8525-18a905767e44" scheduled="2013-10-10T23:00:00+00:00" attendance="18210" start_time="2013-10-10T23:08:00+00:00" end_time="2013-10-11T01:32:00+00:00" clock="00:00" period="3" xmlns="http://feed.elasticstats.com/schema/hockey/game-v2.0.xsd">
<venue id="bd7b42fa-19bb-4b91-8615-214ccc3ff987" name="First Niagara Center" capacity="18690" address="One Seymour H. Knox III Plaza" city="Buffalo" state="NY" zip="14203" country="USA"/>
<team name="Sabres" market="Buffalo" id="4416d559-0f24-11e2-8525-18a905767e44" points="1">
<scoring>
<period number="1" sequence="1" points="1"/>
<period number="2" sequence="2" points="0"/>
<period number="3" sequence="3" points="0"/>
</scoring>
<statistics goals="1" assists="2" penalties="7" penalty_minutes="23" team_penalties="0" team_penalty_minutes="0" shots="27" blocked_att="14" missed_shots="8" hits="25" giveaways="5" takeaways="10" blocked_shots="7" faceoffs_won="22" faceoffs_lost="28" powerplays="1" faceoffs="50" faceoff_win_pct="44.0" shooting_pct="3.7" points="3">
<powerplay faceoffs_won="2" faceoffs_lost="0" shots="0" goals="0" missed_shots="1" assists="0" faceoff_win_pct="100.0" faceoffs="2"/>
<shorthanded faceoffs_won="3" faceoffs_lost="3" shots="1" goals="0" missed_shots="0" assists="0" faceoffs="6" faceoff_win_pct="50.0"/>
<evenstrength faceoff_win_pct="40.5" missed_shots="7" goals="1" faceoffs_won="17" shots="26" faceoffs="42" faceoffs_lost="25" assists="2"/>
<penalty shots="0" goals="0" missed_shots="0"/>
</statistics>
<shootout shots="0" missed_shots="0" goals="0" shots_against="0" goals_against="0" saves="0" saves_pct="0"/>
<goaltending shots_against="33" goals_against="4" saves="29" saves_pct="0.879" total_shots_against="33" total_goals_against="4">
<powerplay shots_against="0" goals_against="0" saves="0" saves_pct="0"/>
<shorthanded shots_against="7" goals_against="0" saves="7" saves_pct="1.0"/>
<evenstrength goals_against="4" saves_pct="0.846" shots_against="26" saves="22"/>
<penalty shots_against="0" goals_against="0" saves="0" saves_pct="0"/>
<emptynet goals_against="0" shots_against="0">
<powerplay goals_against="0"/>
<shorthanded goals_against="0"/>
<evenstrength goals_against="0"/>
</emptynet>
</goaltending>
Here's an XPath 2.0 expression that should do what you asked, yielding a sequence of two elements:
(/game/team[#id = /game/#home_team]/statistics/#goals,
/game/team[#id = /game/#away_team]/statistics/#goals)
Credit to #Ian for sleuthing out the details of the question.
In XPath 1.0, you could concatenate string data from the two teams in whatever order you want:
concat(/game/team[#id = /game/#home_team]/statistics/#goals, ' ',
/game/team[#id = /game/#away_team]/statistics/#goals)
But as Ian said, you can't produce a nodeset with an order different from document order. (I don't think a nodeset has any intrinsic order at all... it's how it's processed that imposes an order.)
Update:
As Ian pointed out, your XML data is in a namespace, thanks to the default namespace declaration on <game>. Since you said that "/game/team/statistics/#goals gives me the data", I'm assuming that you've already taken care of this aspect of the problem, perhaps by declaring the default namespace in your XPath execution environment.

Smoothing measured data in MATLAB?

I have measured data from MATLAB and I'm wondering how to best smooth the data?
Example data (1st colum=x-data / second-colum=y-data):
33400 209.11
34066 210.07
34732 212.3
35398 214.07
36064 215.61
36730 216.95
37396 218.27
38062 219.52
38728 220.11
39394 221.13
40060 221.4
40726 222.5
41392 222.16
42058 223.29
42724 222.77
43390 223.97
44056 224.42
44722 225.4
45388 225.32
46054 225.98
46720 226.7
47386 226.53
48052 226.61
48718 227.43
49384 227.84
50050 228.41
50716 228.57
51382 228.92
52048 229.67
52714 230.02
53380 229.54
54046 231.19
54712 231.00
55378 231.5
56044 231.5
56710 231.79
57376 232.26
58042 233.12
58708 232.65
59374 233.51
60040 234.16
60706 234.21
The data in the second column should be monoton but it isn't. How to make it smooth?
I could probably invent a short algorithm myself but I think it's a better way to use an established and proven one... do you know a good way to somehow integrate the outliners to make it a monoton curve!?
Thanks in advance
Monotone in your case is always increasing!
See the options below (1. Cobb-Douglas; 2. Quadratic; 3. Cubic)
clear all
close all
load needSmooth.dat % Your data
x=needSmooth(:,1);
y=needSmooth(:,2);
n=length(x);
% Figure 1
logX=log(x);
logY=log(y);
Y=logY;
X=[ones(n,1),logX];
B=regress(Y,X);
a=exp(B(1,1));
b=B(2,1);
figure(1)
plot(x,y,'k*')
hold
for i=1:n-1
plot([x(i,1);x(i+1,1)],[a*x(i,1)^b;a*x(i+1,1)^b],'k-')
end
%Figure 2
X=[ones(n,1),x,x.*x];
Y=y;
B=regress(Y,X);
c=B(1,1);
b=B(2,1);
a=B(3,1);
figure(2)
plot(x,y,'k*')
hold
for i=1:n-1
plot([x(i,1);x(i+1,1)],[c+b*x(i,1)+a*x(i,1)^2; c+b*x(i+1,1)+a*x(i+1,1)^2],'k-')
end
%Figure 3
X=[ones(n,1),x,x.*x,x.*x.*x];
Y=y;
B=regress(Y,X);
d=B(1,1);
c=B(2,1);
b=B(3,1);
a=B(4,1);
figure(3)
plot(x,y,'k*')
hold
for i=1:n-1
plot([x(i,1);x(i+1,1)],[d+c*x(i,1)+b*x(i,1)^2+a*x(i,1)^3; d+c*x(i+1,1)+b*x(i+1,1)^2+a*x(i+1,1)^3],'k-')
end
There are also some cooked functions in Matlab such as "smooth" and "spline" that should also work in your case since your data is almost monotone.

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