I have a table contain height and frequency.I want to calculate the variance of it.
Height 140 150 160 170 180 190
Frequency 3 5 57 63 30 2
I have tried the below code:
height=[140 150 160 170 180 190;3 5 57 63 30 2]
height=height(:)
V = var(height) %Calculate Variance
**This give an answer of 5.7316e+03**
while with formula it give an answer of 81.8594. Now please tell me how can i do this?
Use weighted variance:
h=height;
var(h(1,:),h(2,:))
Related
I need to write a code to display the location of the highest and lowest tx value. Nothing appears to be working. Here is my code:
%times
tx=[tf-to];
tx=[130 103 152 163 218 278 82 195 221 154 94 159 214 185];
s=(130+103+52+163+218+278+82+195+221+154+94+159+214+185);
%minimum and maximum times
minvalue=min(tx);
maxvalue=max(tx);
How do I edit this code to show the max and min values of tx only??
[minvalue,idx_min]=min(tx);
[maxvalue,idx_max]=max(tx);
This uses the second output of both min and max, which returns the index of the min/max value respectively.
Adding two inline functions to return the min and max is a possibility.
min_index = #(vector) find(vector==min(vector))
max_index = #(vector) find(vector==max(vector))
idx_min = min_index(tx);
idx_max = max_index(tx);
I have a histogram that I want conditional coloring in it with this rule :
Values that are upper than 50 have red bars and values lower than 50 have blue bars.
Suppose that we have this input matrix:
X = [32 64 32 12 56 76 65 44 89 87 78 56 96 90 86 95 100 65];
I want default bins of MATLAB and applying this coloring on X-axes (bins). I'm using GUIDE to design my GUI and this histogram is an axes in my GUI.
This is our normal graph. Bars with upper values than 50 should be red and bars with lower values than 50 should be green (X-axes). Bars with upper values than 50 should be red and ?
I think this does what you want (as per comments). The bar around 50 is split into the two colors. This is done by using a patch to change the color of part of that bar.
%// Data:
X = [32 64 32 12 56 76 65 44 89 87 78 56 96 90 86 95 100 65]; %// data values
D = 50; %// where to divide into two colors
%// Histogram plot:
[y n] = hist(X); %// y: values; n: bin centers
ind = n>50; %// bin centers: greater or smaller than D?
bar(n(ind), y(ind), 1, 'r'); %// for greater: use red
hold on %// keep graph, Or use hold(your_axis_handle, 'on')
bar(n(~ind), y(~ind), 1, 'b'); %// for smaller: use blue
[~, nd] = min(abs(n-D)); %// locate bar around D: it needs the two colors
patch([(n(nd-1)+n(nd))/2 D D (n(nd-1)+n(nd))/2], [0 0 y(nd) y(nd)], 'b');
%// take care of that bar with a suitable patch
X = [32 64 32 12 56 76 65 44 89 87 78 56 96 90 86 95 100 65];
then you create an histogram, but you are only going to use this to get the numbers of bins, the numbers of elements and positions:
[N,XX]=hist(X);
close all
and finally here is the code where you use the Number of elements (N) and the position (XX) of the previous hist and color them
figure;
hold on;
width=8;
for i=1:length(N)
h = bar(XX(i), N(i),8);
if XX(i)>50
col = 'r';
else
col = 'b';
end
set(h, 'FaceColor', col)
end
here you can consider using more than one if and then you can set multiple colors
cheers
First sort X:
X = [32 64 32 12 56 76 65 44 89 87 78 56 96 90 86 95 100 65];
sorted_X = sort(X)
sorted_X :
sorted_X =
Columns 1 through 14
12 32 32 44 56 56 64 65 65 76 78 86 87 89
Columns 15 through 18
90 95 96 100
Then split the data based on 50:
idx1 = find(sorted_X<=50,1,'last');
A = sorted_X(1:idx1);
B = sorted_X(idx1+1:end);
Display it as two different histograms.
hist(A);
hold on;
hist(B);
h = findobj(gca,’Type’,’patch’);
display(h)
set(h(1),’FaceColor’,’g’,’EdgeColor’,’k’);
set(h(2),’FaceColor’,’r’,’EdgeColor’,’k’);
I have two arrays,
X = uint8 ([ 255 0 75; 44 225 100]);
Y = uint8 ([ 50 50 50; 50 50 50]);
When I perform X-Y, I get the result as
205 0 25
0 175 50
What I expect is
205 -50 25
-6 175 50
How to achieve this. Kindly help.
uint8 is can only contain values between 0 and 255 - it can't contain negative values. Use a signed data type (one without a u as its first letter).
Incidentally, do you have a good reason to specify the data type at all?
I have a matrix of measured angles between M planes
0 52 77 79
52 0 10 14
77 10 0 3
79 14 3 0
I have a list of known angles between planes, which is an N-by-N matrix which I name rho. Here's is a subset of it (it's too large to display):
0 51 68 75 78 81 82
51 0 17 24 28 30 32
68 17 0 7 11 13 15
75 24 7 0 4 6 8
78 28 11 4 0 2 4
81 30 13 6 2 0 2
82 32 15 8 4 2 0
My mission is to find the set of M planes whose angles in rho are nearest to the measured angles.
For example, the measured angles for the planes shown above are relatively close to the known angles between planes 1, 2, 4 and 6.
Put differently, I need to find a set of points in a distance matrix (which uses cosine-related distances) which matches a set of distances I measured. This can also be thought of as matching a pattern to a mold.
In my problem, I have M=5 and N=415.
I really tried to get my head around it but have run out of time. So currently I'm using the simplest method: iterating over every possible combination of 3 planes but this is slow and currently written only for M=3. I then return a list of matching planes sorted by a matching score:
function [scores] = which_zones(rho, angles)
N = size(rho,1);
scores = zeros(N^3, 4);
index = 1;
for i=1:N-2
for j=(i+1):N-1
for k=(j+1):N
found_angles = [rho(i,j) rho(i,k) rho(j,k)];
score = sqrt(sum((found_angles-angles).^2));
scores(index,:)=[score i j k];
index = index + 1;
end
end;
end
scores=scores(1:(index-1),:); % was too lazy to pre-calculate #
scores=sortrows(scores, 1);
end
I have a feeling pdist2 might help but not sure how. I would appreciate any help in figuring this out.
There is http://www.mathworks.nl/help/matlab/ref/dsearchn.html for closest point search, but that requires same dimensionality. I think you have to bruteforce find it anyway because it's just a special problem.
Here's a way to bruteforce iterate over all unique combinations of the second matrix and calculate the score, after that you can find the one with the minimum score.
A=[ 0 52 77 79;
52 0 10 14;
77 10 0 3;
79 14 3 0];
B=[ 0 51 68 75 78 81 82;
51 0 17 24 28 30 32;
68 17 0 7 11 13 15;
75 24 7 0 4 6 8;
78 28 11 4 0 2 4;
81 30 13 6 2 0 2;
82 32 15 8 4 2 0];
M = size(A,1);
N = size(B,1);
% find all unique permutations of `1:M`
idx = nchoosek(1:N,M);
K = size(idx,1); % number of combinations = valid candidates for matching A
score = NaN(K,1);
idx_triu = triu(true(M,M),1);
Atriu = A(idx_triu);
for ii=1:K
partB = B(idx(ii,:),idx(ii,:));
partB_triu = partB(idx_triu);
score = norm(Atriu-partB_triu,2);
end
[~, best_match_idx] = min(score);
best_match = idx(best_match_idx,:);
The solution of your example actually is [1 2 3 4], so the upperleft part of B and not [1 2 4 6].
This would theoretically solve your problem, and I don't know how to make this algorithm any faster. But it will still be slow for large numbers. For example for your case of M=5 and N=415, there are 100 128 170 583 combinations of B which are a possible solution; just generating the selector indices is impossible in 32-bit because you can't address them all.
I think the real optimization here lies in cutting away some of the planes in the NxN matrix in a preceding filtering part.
I have two vectors which are paired values
size(X)=1e4 x 1; size(Y)=1e4 x 1
Is it possible to plot a contour plot of some sort making the contours by the highest density of points? Ie highest clustering=red, and then gradient colour elsewhere?
If you need more clarification please ask.
Regards,
EXAMPLE DATA:
X=[53 58 62 56 72 63 65 57 52 56 52 70 54 54 59 58 71 66 55 56];
Y=[40 33 35 37 33 36 32 36 35 33 41 35 37 31 40 41 34 33 34 37 ];
scatter(X,Y,'ro');
Thank you for everyone's help. Also remembered we can use hist3:
x={0:0.38/4:0.38}; % # How many bins in x direction
y={0:0.65/7:0.65}; % # How many bins in y direction
ncount=hist3([X Y],'Edges',[x y]);
pcolor(ncount./sum(sum(ncount)));
colorbar
Anyone know why edges in hist3 have to be cells?
This is basically a question about estimating the probability density function generating your data and then visualizing it in a good and meaningful way I'd say. To that end, I would recommend using a more smooth estimate than the histogram, for instance Parzen windowing (a generalization of the histogram method).
In my code below, I have used your example dataset, and estimated the probability density in a grid set up by the range of your data. You here have 3 variables you need to adjust to use on your original data; Borders, Sigma and stepSize.
Border = 5;
Sigma = 5;
stepSize = 1;
X=[53 58 62 56 72 63 65 57 52 56 52 70 54 54 59 58 71 66 55 56];
Y=[40 33 35 37 33 36 32 36 35 33 41 35 37 31 40 41 34 33 34 37 ];
D = [X' Y'];
N = length(X);
Xrange = [min(X)-Border max(X)+Border];
Yrange = [min(Y)-Border max(Y)+Border];
%Setup coordinate grid
[XX YY] = meshgrid(Xrange(1):stepSize:Xrange(2), Yrange(1):stepSize:Yrange(2));
YY = flipud(YY);
%Parzen parameters and function handle
pf1 = #(C1,C2) (1/N)*(1/((2*pi)*Sigma^2)).*...
exp(-( (C1(1)-C2(1))^2+ (C1(2)-C2(2))^2)/(2*Sigma^2));
PPDF1 = zeros(size(XX));
%Populate coordinate surface
[R C] = size(PPDF1);
NN = length(D);
for c=1:C
for r=1:R
for d=1:N
PPDF1(r,c) = PPDF1(r,c) + ...
pf1([XX(1,c) YY(r,1)],[D(d,1) D(d,2)]);
end
end
end
%Normalize data
m1 = max(PPDF1(:));
PPDF1 = PPDF1 / m1;
%Set up visualization
set(0,'defaulttextinterpreter','latex','DefaultAxesFontSize',20)
fig = figure(1);clf
stem3(D(:,1),D(:,2),zeros(N,1),'b.');
hold on;
%Add PDF estimates to figure
s1 = surfc(XX,YY,PPDF1);shading interp;alpha(s1,'color');
sub1=gca;
view(2)
axis([Xrange(1) Xrange(2) Yrange(1) Yrange(2)])
Note, this visualization is actually 3-dimensional:
See this 4 minute video on the mathworks site:
http://blogs.mathworks.com/videos/2010/01/22/advanced-making-a-2d-or-3d-histogram-to-visualize-data-density/
I believe this should provide very close to exactly the functionality you require.
I would divide the area the plot covers into a grid and then count the number of points in each square of the grid. Here's an example of how that could be done.
% Get random data with high density
X=randn(1e4,1);
Y=randn(1e4,1);
Xmin=min(X);
Xmax=max(X);
Ymin=min(Y);
Ymax=max(Y);
% guess of grid size, could be divided into nx and ny
n=floor((length(X))^0.25);
% Create x and y-axis
x=linspace(Xmin,Xmax,n);
y=linspace(Ymin,Ymax,n);
dx=x(2)-x(1);
dy=y(2)-y(1);
griddata=zeros(n);
for i=1:length(X)
% Calculate which bin the point is positioned in
indexX=floor((X(i)-Xmin)/dx)+1;
indexY=floor((Y(i)-Ymin)/dy)+1;
griddata(indexX,indexY)=griddata(indexX,indexY)+1;
end
contourf(x,y,griddata)
Edit: The video in the answer by Marm0t uses the same technique but probably explains it in a better way.