We have a MxN matrix and a constrain cstrn = 100;.
The constrain is the summarize limit of column's elements (per column):
sum(matrix(:,:))<=cstrn.
For a given example as the following:
Columns 1 to 5:
15 18 -5 22 19
50 98 -15 39 -8
70 -15 80 45 38
31 52 9 80 72
-2 63 52 71 6
7 99 32 58 41
I want to find the max number of element per column who fulfill this constrain.
How can i summarize every column element with the others elements in same column and find which sum combinations uses the max number of elements per column?
In the given example solution is:
4 3 5 2 5
where
column 1: 15 + 50 + 31 +7 +(-2)
column 2: 18 +(-15) + 52 or 63 etc.
Thank you in advance.
Since it is always easier to fit small elements into a sum, you can do a sort, followed by the cumulative sum:
m= [
15 18 -5 22 19
50 98 -15 39 -8
70 -15 80 45 38
31 52 9 80 72
-2 63 52 71 6
7 99 32 58 41];
cs = cumsum(sort(m))
cs =
-2 -15 -15 22 -8
5 3 -20 61 -2
20 55 -11 106 17
51 118 21 164 55
101 216 73 235 96
171 315 153 315 168
Now you easily identify at which element you cross the threshold cnstrn (thanks, #sevenless)!
out = sum(cs <= cnstrn)
out =
4 3 5 2 5
I'd add to Jonas's answer, that you can impose your constraint in a way that outputs a logical matrix then sum over the 1's and 0's of that matrix like so:
cstrn = 100
m= [
15 18 -5 22 19
50 98 -15 39 -8
70 -15 80 45 38
31 52 9 80 72
-2 63 52 71 6
7 99 32 58 41];
val_matrix = cumsum(sort(m))
logical_matrix = val_matrix<=cstrn
output = sum(logical_matrix)
Giving output:
cstrn =
100
val_matrix =
-2 -15 -15 22 -8
5 3 -20 61 -2
20 55 -11 106 17
51 118 21 164 55
101 216 73 235 96
171 315 153 315 168
logical_matrix =
1 1 1 1 1
1 1 1 1 1
1 1 1 0 1
1 0 1 0 1
0 0 1 0 1
0 0 0 0 0
output =
4 3 5 2 5
Here is a logic, on mobile so can't give a code.
Check this out. Go to a column, sort it ascending order, loop to sum, break when hits <=100. Get counter. Refer back to original column, get the indices of elements matching the elements you just summed up :-)
Related
I want to change the base of a multiplication table to another base.
If I use
disp(dec2base((1:10).*(1:10)',7))
the numbers come flowing out individually. However I want them to stay in the exact position in the given matrix.
The numerical base is a display issue, numbers are always stored and manipulated in base 2 internally. So all you need to do is write a loop that displays the numbers in they way you want to. For example:
for ii=1:10
for jj=1:10
fprintf('%6s',dec2base(ii*jj,7));
end
fprintf('\n');
end
Output:
1 2 3 4 5 6 10 11 12 13
2 4 6 11 13 15 20 22 24 26
3 6 12 15 21 24 30 33 36 42
4 11 15 22 26 33 40 44 51 55
5 13 21 26 34 42 50 55 63 101
6 15 24 33 42 51 60 66 105 114
10 20 30 40 50 60 100 110 120 130
11 22 33 44 55 66 110 121 132 143
12 24 36 51 63 105 120 132 144 156
13 26 42 55 101 114 130 143 156 202
Storing base-7 representation of numbers as string array:
M = (1:10).*(1:10)';
out = strings(size(M));
for jj = 1:size(M,2)
for ii = 1:size(M,1)
out(ii,jj) = dec2base(M(ii,jj) ,7);
end
end
I have used the unique command to get the unique pixel intensities from my image. Then I tried to make a histogram using them, but it doesn't use all of the intensity values
I = imread('pout.tif');
[rows, columns] = size(I);
UniquePixels=unique(I);
hist=histogram(UniquePixels)
An alternative approach would be to use accumarray combined with unique. I would specifically use the third output of unique to transform your data into a consecutive sequence of 1 up to N where N is the total number of unique intensities, then leverage the first output of unique that will give you the list of unique intensities. Therefore, if the first output of unique is A and the output of accumarray is B, the effect is that at location B(i), this gives the total number of intensities of A(i).
Therefore:
[UniquePixels, ~, id] = unique(I);
histo = accumarray(id, 1);
UniquePixels gives you all unique pixels while histo gives you the counts of each unique pixel corresponding to each element in UniquePixels.
Here's a quick example:
>> I = randi(255, 10, 10)
I =
42 115 28 111 218 107 199 60 140 237
203 22 246 233 159 13 100 91 76 198
80 59 2 47 90 231 62 210 190 125
135 233 198 68 131 241 103 4 49 112
43 39 209 38 103 126 25 11 176 114
154 211 222 35 20 125 34 44 47 79
68 138 22 222 62 87 241 166 94 130
167 255 102 148 32 230 244 187 160 131
176 20 67 141 47 95 147 166 199 209
191 113 205 37 62 29 16 115 21 203
>> [UniquePixels, ~, id] = unique(I);
>> histo = accumarray(id, 1);
>> [UniquePixels histo]
ans =
2 1
4 1
11 1
13 1
16 1
20 2
21 1
22 2
25 1
28 1
29 1
32 1
34 1
35 1
37 1
38 1
39 1
42 1
43 1
44 1
47 3
49 1
59 1
60 1
62 3
67 1
68 2
76 1
79 1
80 1
87 1
90 1
91 1
94 1
95 1
100 1
102 1
103 2
107 1
111 1
112 1
113 1
114 1
115 2
125 2
126 1
130 1
131 2
135 1
138 1
140 1
141 1
147 1
148 1
154 1
159 1
160 1
166 2
167 1
176 2
187 1
190 1
191 1
198 2
199 2
203 2
205 1
209 2
210 1
211 1
218 1
222 2
230 1
231 1
233 2
237 1
241 2
244 1
246 1
255 1
If you double check the input example and the final output, you will see that only the unique pixels are shown combined with their counts. Any bins that were zero in count are not shown.
I have created graphs using filledcurves. Now, the graphs looks bad because long range of data.
This is my data:
a b c d e f g h i
201312 49 26 34 30 14 25 9 4 1
201311 38 22 47 30 9 9 4 3 1
201310 44 24 43 38 9 14 5 7 0
201309 65 18 33 39 15 12 4 5 1
201308 42 31 44 30 5 11 0 2 2
201307 58 27 35 29 8 4 2 4 2
201306 30 22 15 17 2 6 3 4 0
201305 61 52 20 16 11 12 2 3 0
201304 62 60 33 18 13 9 5 6 0
201303 43 53 49 27 9 11 7 0 0
201302 31 30 42 27 10 8 4 2 0
201301 42 30 20 47 9 13 3 2 1
201212 26 19 39 24 9 11 0 0 0
201211 26 26 30 28 1 2 0 2 1
201210 55 46 34 30 13 5 0 2 1
201209 56 31 27 28 27 13 2 4 1
201208 48 75 38 46 22 10 0 1 0
201207 60 56 37 47 19 11 2 1 0
201206 60 41 37 28 17 12 5 1 0
201205 49 43 38 46 15 16 2 2 0
201204 43 50 36 33 4 7 3 0 2
201203 49 63 35 43 16 7 1 2 0
201202 43 59 59 52 16 13 3 4 1
201201 51 44 30 37 20 9 4 1 0
201112 50 38 36 36 8 2 3 1 1
201111 75 35 30 36 16 7 3 3 1
201110 68 53 41 27 11 15 1 2 1
201109 68 46 48 47 16 19 4 0 1
201108 45 41 20 36 17 10 1 0 0
201107 48 34 30 24 13 7 3 3 1
201106 49 29 24 25 5 6 0 3 0
201105 45 35 21 37 1 7 2 1 0
201104 53 35 23 18 4 6 1 5 1
201103 58 42 20 18 6 4 1 0 4
201102 54 32 19 20 4 10 0 2 0
201101 42 41 21 28 3 6 1 2 1
and this is my gnuplot file:
set terminal postscript eps color font 20
set xtics 1 out
set tics front
#set style fill transparent solid 0.5 noborder
set key below autotitle columnheader
set ylabel "Count"
set xlabel "across time"
set output 't1.eps'
set title "t1-Across time of Aspects"
set xtics 1
plot for [i=10:2:-1] \
"< awk 'NR==1 {print \"year\",$".(i-1)."} NR>=2 {for (i=2; i<=".i."; i++) \
{sum+= $i} {print $1, sum; sum=0} }' data.dat" \
using (column(2)):xtic(1) with filledcurves x1 t column(2)
When I add time in xdata:
set xdata time
set timefmt "%Y%m"
set xtics format "%b"
Erros message:
Need full using spec for x time data
Is the Errors because of my date format? I have googling this and do not have any answer about it. Please give me suggestion about this.
In the script you show, you specify only a single column in the using statement (besides the xtic). That means, that this value is taken as y-value and the row number is implicitely used as x-value.
When using time data, you must explicitely specify all columns which are needed for the plotting style, there is no assumption about what might be the first column. Use:
set key below autotitle columnheader
set ylabel "Count"
set xlabel "across time"
set tics front
set xdata time
set timefmt "%Y%m"
set xtics format "%b'%y"
set autoscale xfix
plot for [i=10:2:-1] \
"< awk 'NR==1 {print \"year\",$".(i-1)."} NR>=2 {for (i=2; i<=".i."; i++) \
{sum+= $i} {print $1, sum; sum=0} }' data.dat" \
using 1:2 with filledcurves x1 t column(2)
Result with 4.6.4:
I guess you don't want xtic(1) if you have time data and specify the x format.
I have a vector of electrical power consumption data which consists of transient, steady and power off states. I would like to identify steady-state starting point by the following condition:
The 5 consecutive elements of the data have difference values between each adjacent element <= threshold value (for this case, let say =10 W)
The first element that meets the condition shows the starting point of steady-state.
Example:
data = [0 0 0 40 70 65 59 50 38 30 32 33 30 33 37 19 ...
0 0 0 41 73 58 43 34 25 39 33 38 34 31 35 38 19 0]
abs(diff(data)) = [0 0 40 30 15 7 9 12 8 3 2 1 3 4 18 19 ...
0 0 41 32 15 9 14 6 5 4 3 4 3 19 19 0]
The sequences of abs(diff(data)) that meet the condition are 8 3 2 1 3 and 6 5 4 3 4. Therefore, the output should show the 10th data element (=30) and 27th data element (=33) as starting point of steady-state (There are 2 times of steady-state detected).
How would I write MATLAB code for this scenario?
(PS: data = 0 shows power off state)
Here's one approach using nlfilter (if the function is not available, you can implement a sliding window yourself):
data = [0 0 0 40 70 65 59 50 38 30 32 33 30 33 37 19 0 0 0 41 73 58 43 34 25 39 33 38 34 31 35 38 19 0];
difs = abs(diff(data));
% Use sliding window to find windows of consecutive elements below threshold
steady = nlfilter(difs, [1, 5], #(x)all(x <= 10));
% Find where steady state starts (1) and ends (-1)
start = diff(steady);
% Return indices of starting steady state
ind = find(start == 1);
I have a matrix 'eff_tot' with dimension (m x n) which I want to rearrange according to a matrix called 'matches' (e.g. [n2 n3; n4 n5]) and put all the collumns not specified in 'matches' at the end.
That is, I want to have [eff_tot(:,n2) eff_tot(:,n3) ; eff_tot(:,n4) eff_tot(:,n5) ; eff_tot(:,n1)].
That's all folks!
Taking the example in the first answer, what I would like to have is:
eff_tot =
81 15 45 15 24
44 86 11 14 42
92 63 97 87 5
19 36 1 58 91
27 52 78 55 95
82 41 0 0 0
87 8 0 0 0
9 24 0 0 0
40 13 0 0 0
26 19 0 0 0
Regards.
Create a vector listing the indices of all the columns in eff_tot and then use SETDIFF to determine which columns do not occur in [n2 n3 n4 n5]. These columns are the unmatched ones. Now concatenate the matched and unmatched column indices to create your column-reordered eff_tot matrix.
>> eff_tot = randi(100, 5, 7)
eff_tot =
45 82 81 15 15 41 24
11 87 44 14 86 8 42
97 9 92 87 63 24 5
1 40 19 58 36 13 91
78 26 27 55 52 19 95
>> n2 = 3; n3 = 5; n4 = 2; n5 = 6;
>> missingColumn = setdiff(1:size(eff_tot, 2), [n2 n3 n4 n5])
missingColumn =
1 4 7
>> eff_tot = [eff_tot(:,n2) eff_tot(:,n3) eff_tot(:,missingIndex); eff_tot(:,n4) eff_tot(:,n5) zeros(size(eff_tot, 1), length(missingIndex))];
eff_tot =
81 15 45 15 24
44 86 11 14 42
92 63 97 87 5
19 36 1 58 91
27 52 78 55 95
82 41 0 0 0
87 8 0 0 0
9 24 0 0 0
40 13 0 0 0
26 19 0 0 0