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I have the data of error, firstly I need to transform the range of data between -pi and pi
then using code hist(error)
my question is how I can transform this data using code in R, if there exists code please tell me?
error<- c( 5.71444784 ,5.55435896 ,5.60671884, 5.19927462 ,4.81470000 ,5.53028500,
0.87085808 ,5.37982604, 5.43760222 ,5.77523327, 5.68796681 ,5.54533123,
5.27149485 ,5.75717780 ,0.53623627 ,5.29496664 ,5.33288247 ,5.49297135,
5.51343389 ,4.87307837 ,4.87849468 ,5.78305665, 0.13721761 ,5.91185037,
5.50741540 ,5.72588264, 5.03918574, 4.14846564 ,5.25644862 ,0.57956841,
0.37614739, 0.40864692, 5.92087811, 5.92689660, 5.72889189 ,5.64643955,
5.96902437, 5.91666449, 6.18508456 ,5.86249974 ,5.17279359, 5.37982604,
5.25163450, 5.43098155, 5.73912232, 5.80592625 ,5.43940710, 4.84659734,
5.76078923, 5.76379847, 5.76078923 ,5.78606589, 5.68977169 ,5.68375320,
0.42790509 ,6.08939254, 4.89955940 ,5.53389643, 5.67954126 ,5.71324348,
5.66930915 ,5.54111761 ,5.87273017, 5.86791605 ,5.50199909, 5.50199909,
5.69699455 ,5.29737370 ,4.97117745, 5.62838408 ,5.77402891, 5.30640144,
5.85106494 ,5.58926555 ,5.58926555 ,4.62271379 ,3.36547454, 6.19892642,
0.28888093 ,6.09541103, 5.89499926 ,5.87453672, 5.67954126 ,5.46408326,
1.44982681 ,0.24193736 ,0.77516606 ,5.88055521, 5.55435896, 5.58926555,
5.58926555 ,5.39126084, 4.47466189, 0.06800662, 5.75777998, 5.44963921)
I try this problem by transforming the data handly .... and hist ... but the residual doesn't about zero.
To compute the range from -pi to pi just subtract pi from the radian measurement since radians range from 0 to 2*pi:
error - pi
hist(error - pi)
But that does not give you what you want. You really need to use circular statistics to see what is going on:
install.packages("circular")
library(circular)
plot.circular(error, stack=TRUE)
You can ignore the warning message. Notice that the data are not around zero. To plot a histogram we need to cut the data at pi and flip the values greater than pi:
errortrans <- ifelse(error<pi, error, error-2*pi)
# Alternate transform
# errortrans <- ifelse(error<pi, -error, 2*pi-error)
hist(errortrans, xlim=c(-pi, pi))
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This is a follow-up question to this question.
Taking the following image as an example:
What I know:
x and y coordinates of points D, E, and P.
Therefore, I also know slope and intercept of D-E line
What I want to know:
x and y coordinates of point Q. (This is the point which crosses the D-E line).
Notation P=[px,py], D=[dx,dy], E=[ex,ey], Q=[qx,qy]
First:
R=P-D=[px-dx, py-dy]=[rx,ry]
K=E-D=[ex-dx, ey-dy]=[kx, ky]
Then
z=dot(R,K)/dot(K,K)=(rx*kx+ry*ky) / (kx*kx+ky*ky)
Finally
Q=D+z*K=[dx+z*kx, dy+z*ky]
The R is vector which start on point D and ends on point K, the K is vector which start on point D and ends on point E. Using this we made scalar projection to calculate result Q. More info about concept here
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I have this question :
Unfortunately, my book didn't provide definition and how to draw/read a logic venn diagram, i have to look at the internet but couldn't find any understandable explanation
From what i understand, the logics for the three diagrams are :
X AND NOT (Y OR Z)
NOT X AND (Y OR Z)
Y AND NOT (X OR Z)
Am i right ? Please correct me if i'm wrong
By the ways, does the question mean to combine all three diagrams with OR operation, like :
1 OR 2 OR 3
Any help is greatly appreciated !
I could not understand the question correctly. Here's the logic for the three Venn Diagrams:
1. Your logic for the first Venn Diagram is correct: X AND NOT (Y OR Z)
2. Your logic for the second Venn Diagram is slightly incorrect, if you look at the Venn Diagram: It is simply NOT (X) (Everything except X).
3. In this case as well, the logic is simply Y.
Now if we perform OR operation on these three:
(X AND NOT (Y OR Z)) + NOT(X) + Y
= X AND NOT(Y) AND NOT(Z) OR NOT(X) OR Y [By de Morgan's law]
which matches option c.
NOTE: Your second and third logics would have been correct if X, Y and Z were the only three regions in the diagram. However there is also a region outside all of them - bounded by the box. You might want to look up on the internet about basics of Venn Diagram, it's one of the easiest things to learn IMO!
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Given (x,y) that is (3,4) , velocity is 1 m/sec and given angle is 15 degree. what will be next coordinate (x', y') after 1 sec ?
Anyone please help!
Assuming the angle is measure w.r.t. the x-axis, then:
the total distance is v*t = 1m
displacement in x-direction: cos(15)*1m=.97m
displacement in y-direction: sin(15)*1m=.25m
So the new location is (3.97, 4.25).
#Alexander-Vogt's answer is close but I think it is missing a conversion from angles to radians. Here is matlab code that provides the answer:
pi=3.1415926535897932384626433832795028841971;
x=3;y=4;
t=1; % time
s=1*t; % speed * time
a=15; % angle of movement
a=a/360 * pi*2; % convert to radians
x=cos(a)*s+x;
y=sin(a)*s+y;
fprintf("%f %f\n",x,y);
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I want to rotate a plane represented by the equation z = 6 , by n degrees along y axis and find the new equation of the plane. how can this be done?
Thanks
Base point (0,0,6) after rotation will lie in XZ plane with coordinates
(x0, y0, z0) = (-6*sin(Fi), 0, 6*cos(Fi))
normal vector
n = (A,B,C) = (-sin(Fi), 0, cos(Fi))
so new plane equation is (for explanation see beginning of the article)
A*(x-x0)+B*(y-y0)+C*(z-z0)=0
or
-sin(Fi)*x + cos(Fi)*z - 6 = 0