I am solving the following linear programming problem, I am guiding myself on the documentation
Documentation Matlab
Every time I execute I get the following error
Dimensions of matrices being concatenated are not consistent.
I have the objective function and restrictions as follows
%F.O
f=[0.669 0.654 0.503 0.683 0.670 0.673 0.749 0.655 0.660 0.583 1.243 0.639 2.024 2.156 1.672 0.473 0.139 0.687];
%Restrictions
Aeq=[0.1 0.12 0.335 0.15 0.18 0.19 0.12 0.15 0.15 0.15 0.15 0.11 0.13 0.46;
0.3 0.24 0.03 0.05 0.04 0.27 0.03 0.24 0.15 0.52 0.52;
0.1 0.12 0.31 0.15 0.19 0.08 0.2 0.12 0.15 0.50 0.34 0.44;
0.26 0.50;
0.06 0.17];
b=[285.71; 305.33; 450; 262.50; 41.50];
and I execute it with the following command
x=linprog(f,Aeq,b)
The restrictions take them out of the following exercise
Exercise
This should be the result of z
Result
A matrix must have the same number of columns in each row. Aeq in your case has different number of columns.
How to fix it?
The variables missing in the equations of constraints have zero coefficients. So:
%Objective Function
%X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18
f = [0.669 0.654 0.503 0.683 0.670 0.673 0.749 0.655 0.660 0.583 1.243 0.639 2.024 2.156 1.672 0.473 0.139 0.687];
A = []; b = []; %No inequality constraints
%Equality Constraints are:
%X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18
Aeq=[0.1 0.12 0.335 0.15 0.18 0.19 0.12 0.15 0.15 0.15 0 0.15 0.11 0 0.13 0 0 0.46; %Nitrogeno
0.3 0.24 0 0.03 0.05 0.04 0.27 0.03 0.24 0.15 0 0 0.52 0.52 0 0 0 0 ; %Fosforo
0.1 0.12 0 0.31 0.15 0.19 0.08 0.2 0.12 0.15 0.50 0 0 0.34 0.44 0 0 0 ; %Potasio
0 0 0 0 0 0 0 0 0 0 0 0.26 0 0 0 0 0.50 0 ; %Calcio
0 0 0 0 0.06 0 0 0 0 0 0 0 0 0 0 0.17 0 0]; %Magnesio
beq = [285.71; 305.33; 450; 262.50; 41.50]; %What you defined as 'b' is actually `beq`
lb = zeros(18,1); ub = inf(18,1); %Bounds
[x, Optimal_sol] = linprog(f, A, b, Aeq, beq, lb, ub);
>> x
x =
1.0e+03 *
0.7142
0
0
1.0268
0
0
0
0
0
0.4018
0
0
0
0
0
0.2441
0.5250
0
>> Optimal_sol
Optimal_sol =
1.6018e+03
Related
I am trying to optimise the running time of my code by getting rid of some for loops. However, I have a variable that is incremented in each iteration in which sometimes the index is repeated. I provide here a minimal example:
a = [1 4 2 2 1 3 4 2 3 1]
b = [0.5 0.2 0.3 0.4 0.1 0.05 0.7 0.3 0.55 0.8]
c = [3 5 7 9]
for i = 1:10
c(a(i)) = c(a(i)) + b(i)
end
Ideally, I would like to compute it by writting:
c(a) = c(a) + b
but obviously it would not give me the same results since I have to recalculate the value for the same index several times so this way to vectorise it would not work.
Also, I am working in Matlab or Octave in case that this is important.
Thank you very much for any help, I am not sure that it is possible to be vectorise.
Edit: thank you very much for your answers so far. I have discovered accumarray, which I did not know before and also understood why changing the for loop between Matlab and Octave was giving me such different times. I also understood my problem better. I gave a too simple example which I thought I could extend, however, what if b was a matrix?
(Let's forget about c at the moment):
a = [1 4 2 2 1 3 4 2 3 1]
b =[0.69 -0.41 -0.13 -0.13 -0.42 -0.14 -0.23 -0.17 0.22 -0.24;
0.34 -0.39 -0.36 0.68 -0.66 -0.19 -0.58 0.78 -0.23 0.25;
-0.68 -0.54 0.76 -0.58 0.24 -0.23 -0.44 0.09 0.69 -0.41;
0.11 -0.14 0.32 0.65 0.26 0.82 0.32 0.29 -0.21 -0.13;
-0.94 -0.15 -0.41 -0.56 0.15 0.09 0.38 0.58 0.72 0.45;
0.22 -0.59 -0.11 -0.17 0.52 0.13 -0.51 0.28 0.15 0.19;
0.18 -0.15 0.38 -0.29 -0.87 0.14 -0.13 0.23 -0.92 -0.21;
0.79 -0.35 0.45 -0.28 -0.13 0.95 -0.45 0.35 -0.25 -0.61;
-0.42 0.76 0.15 0.99 -0.84 -0.03 0.27 0.09 0.57 0.64;
0.59 0.82 -0.39 0.13 -0.15 -0.71 -0.84 -0.43 0.93 -0.74]
I understood now that what I would be doing is rowSum per group, and given that I am using Octave I cannot use "splitapply". I tried to generalise your answers, but accumarray would not work for matrices and also I could not generalise #rahnema1 solution. The desired output would be:
[0.34 0.26 -0.93 -0.56 -0.42 -0.76 -0.69 -0.02 1.87 -0.53;
0.22 -1.03 1.53 -0.21 0.37 1.54 -0.57 0.73 0.23 -1.15;
-0.20 0.17 0.04 0.82 -0.32 0.10 -0.24 0.37 0.72 0.83;
0.52 -0.54 0.02 0.39 -1.53 -0.05 -0.71 1.01 -1.15 0.04]
that is "equivalent" to
[sum(b([1 5 10],:))
sum(b([3 4 8],:))
sum(b([6 9],:))
sum(b([2 7],:))]
Thank you very much, If you think I should include this in another question instead of adding the edit I will do so.
Original question
It can be done with accumarray:
a = [1 4 2 2 1 3 4 2 3 1];
b = [0.5 0.2 0.3 0.4 0.1 0.05 0.7 0.3 0.55 0.8];
c = [3 5 7 9];
c(:) = c(:) + accumarray(a(:), b(:));
This sums the values from b in groups defined by a, and adds that to the original c.
Edited question
If b is a matrix, you can use
full(sparse(repmat(a, 1, size(b,1)), repelem(1:size(b,2), size(b,1)), b))
or
accumarray([repmat(a, 1, size(b,1)).' repelem(1:size(b,2), size(b,1)).'], b(:))
Matrix multiplication and implicit expansion and can be used (Octave):
nc = numel(c);
c += b * (1:nc == a.');
For input of large size it may be more memory efficient to use sparse matrix:
nc = numel(c);
nb = numel(b);
c += b * sparse(1:nb, a, 1, nb, nc);
Edit: When b is a matrix you can extend this solution as:
nc = numel(c);
na = numel(a);
out = sparse(a, 1:na, 1, nc, na) * b;
I have this matrix in MATLAB:
x = [NaN -2 -1 0 1 2;
1 0.21 0.15 0.34 0.11 0.32;
2 0.14 0.10 0.16 0.31 0.11];
The first row represents the location of the values following X coordinates.
I shift the first row by -0.63, so x becomes:
New_x = [NaN -2.63 -1.63 -0.63 0.37 1.37;
1 0.21 0.15 0.34 0.11 0.32;
2 0.14 0.10 0.16 0.31 0.11];
How can I use interpolation to get the values at specific coordinates of the New_x matrix that we have in the x matrix? ([-2 -1 0 1 2] points)
New_xInterp = [NaN -2.63 .. -2 .. -1.63 .. -1 .. -0.63 .. 0 .. 0.37 .. 1 .. 1.37 .. 2;
1 0.21 .. ? .. 0.15 .. ? .. 0.34 .. ? .. 0.11 .. ? .. 0.32 .. ?;
2 0.14 .. ? .. 0.10 .. ? .. 0.16 .. ? .. 0.31 .. ? .. 0.11 .. ?];
I want to get the '?' values. I tried to use interp2 function but I don't know which step or 2^k-1 interpolated points between coordinates values I have to have in order to get the points like -2, -1, 0, 1, 2.
Thanks !
Since you do not have 2D data, you are only interpolating on one dimension, you only need the function interp1.
This function can work on vector or matrices if necessary, but it require a slight reorganisation of your data.
%% Input
M = [NaN -2 -1 0 1 2;
1 0.21 0.15 0.34 0.11 0.32;
2 0.14 0.10 0.16 0.31 0.11];
%% Demultiplex inputs
x = M(1,2:end).' ; % extract X values, reorder in column
y = M(2:end,2:end).' ; % extract Y values, reorder in columns
%% Interpolate
xn = sort( [x-0.63 ; x] ) ; % Generate the new_x target values
yn = interp1( x-0.63 , y , xn ,'linear','extrap') ; % Interpolate the full matrix in one go
At this point you have your new xn and yn values in columns:
xn= yn=
-2.63 0.21 0.14
-2 0.1722 0.1148
-1.63 0.15 0.1
-1 0.2697 0.1378
-0.63 0.34 0.16
0 0.1951 0.2545
0.37 0.11 0.31
1 0.2423 0.184
1.37 0.32 0.11
2 0.4523 -0.016
I would keep them like that if you have more operations to do on them later on. However, if you want it back into the format you had at the beginning, we can simply rebuild the new full matrix:
%% Rebuild global matrix
Mout = [ M(:,1) , [xn.' ; yn.'] ]
Mout =
NaN -2.63 -2 -1.63 -1 -0.63 0 0.37 1 1.37 2
1 0.21 0.1722 0.15 0.2697 0.34 0.1951 0.11 0.2423 0.32 0.4523
2 0.14 0.1148 0.1 0.1378 0.16 0.2545 0.31 0.184 0.11 -0.016
Maybe you can try interp1 + arrayfun like below
r = sort([x(1,2:end),New_x(1,2:end)]);
New_xInterp = [New_x(:,1),cell2mat(arrayfun(#(k) interp1(New_x(1,2:end),New_x(k,2:end),r),1:size(New_x,1),'UniformOutput',false).')];
which gives
New_xInterp =
NaN -2.63000 -2.00000 -1.63000 -1.00000 -0.63000 0.00000 0.37000 1.00000 1.37000 NA
1.00000 0.21000 0.17220 0.15000 0.26970 0.34000 0.19510 0.11000 0.24230 0.32000 NA
2.00000 0.14000 0.11480 0.10000 0.13780 0.16000 0.25450 0.31000 0.18400 0.11000 NA
The code above used linear interpolation. If you want other options, you can type help interp1 to see more.
I have a big matrix lets say 100000x13.
I need to sum specific columns of this matrix.
For example:
matrix = [0.70 0.30 0 0 0.15 0.21 0.58 0.06 0.00 1.00 0 0 1.00;
0.70 0.00 0 0 0.00 0.00 0.07 0.06 0.00 0.80 0 0 1.00;
0.70 0.00 0 0 0.00 0.00 0.58 0.06 0.00 1.00 0 0 0.94];
inputVect = [4 4 3 2];
idx2 = cumsum(inputVect);
idx1 = [1 idx2(1:end-1)+1];
result = (1-sum(matrix(:,idx1(1):idx2(1)),2)) + (1-sum(matrix(:,idx1(2):idx2(2)),2))+(1-sum(matrix(:,idx1(3):idx2(3)),2)) + (1-sum(matrix(:,idx1(4):idx2(4)),2));
The thing is inputVect needs to be a function argument that I don't allways know the size. And because of the size of the matrix I should also avoid for loops. Any help would be much appreciated.
I have a vector:
0.02
-0.02
0
-0.02
-0.08
-0.05
-0.04
-0.1
0
0.05
0.05
0.05
0.08
0.04
How do I normalize this with the first value starting at 100?
Simply divide by the first element and multiply by 100:
a = [0.02 -0.02 0 -0.02 -0.08 -0.05 -0.04 -0.1 0 0.05 0.05 0.05 0.08 0.04]
b = a ./ a(1) * 100
b =
100 -100 0 -100 -400 -250 -200 -500 0 250 250 250 400 200
myArr = [0.02 -0.02 0 -0.02 -0.08 -0.05 -0.04 ...
-0.1 0 0.05 0.05 0.05 0.08 0.04]
myArr = 100*myArr/myArr(1)
Let say I have
A = [0 0 0 0 1 1 1 1 1 0 0 1 1 1 1 0 0 0 1 1 1 1 1 ]
B = [0.01 0.02 0.01 0.03 0.04 0.05 0.07 0.04 0.03 0.01 0.01 0.03 0.04 0.03 0.02 0.01 0.011 0.02 0.03 0.04 0.05 0.04 0.01]
How can I rescale A follow maximum number of B.
The result should be
C = [0 0 0 0 0.07 0.07 0.07 0.07 0.07 0 0 0.04 0.04 0.04 0.04 0 0 0 0.05 0.05 0.05 0.05 0.05]
You can use accumarray like so:
subs = cumsum([diff(A) > 0, 0]).*A + 1; %//Similar to bwlabel if you have the image processing toolbox...
maximums = accumarray(subs(:), B(:), [], #max);
maximums(1) = 0;
C = maximums(subs)
Is it what you want to do?
C = A*max(B)/max(A)