A= [1 1
2 2
3 3
. .
. .
. .
N N]
I have an [N,2] matrix and I need to split it row-wise into some number of [N/4,2] submatrices. Then for each submatrix I need to find linear regression where the first column of each submatrix is my x data and the second column is my y data. The output should be a struct with fields a,b,c,d.... and values of linear regression for each submatrix
First I tried splitting the matrix with mat2cell where k = length(N)/4 and mat = mat2cell(A, [k k k k], [1 1]).
Next I tried converting mat into struct with out = cell2struct(mat,fields,1) where fields = {'col1','col2'} and use
new = structfun(#(x)polyfit(x.col1, x.col2,1), out,'UniformOutput', false)
But I get the error:
Inputs to STRUCTFUN must be scalar structures.
Does anyone know how to do it? Many thanks
The most straightforawrd way (and probably the fastest) to do this is with a good old for loop:
A = [1:64;1:64]'; % Demo data
m = 4;
N = size(A,1);
k = N/m; % Assumes that length is evenly divisible by 4
c = zeros(m,2); % Coefficients
for i = 1:m
c(i,:) = polyfit(A((i-1)*k+1:i*k,1),A(i-1)*k+1:i*k,2),1);
end
Or rather than using cell2struct and structfun you can use cellfun:
A = [1:64;1:64]'; % Demo data
m = 4;
N = size(A,1);
k = N/m; % Assumes that length is evenly divisible by 4
c = cellfun(#(x)polyfit(x(:,1),x(:,2),1).',mat2cell(A,k+zeros(1,m),2),'UniformOutput',false)
or alternatively
Ac = mat2cell(A,k+zeros(1,m),[1 1])
c = cellfun(#(x1,x2)polyfit(x1,x2,1).',Ac(:,1),Ac(:,2),'UniformOutput',false)
You can convert the output of cellfun to a matrix with:
c = [c{:}].'
As for why you're getting the error, your variable out is a 4-by-1 struct array (array of structures) rather than a simple (scalar) structure of arrays. The documentation for structfun points out this requirement in the description of the short function: "Apply function to each field of scalar structure." This video from The MathWorks tries to explain the difference.
Related
I want to generalise to any n the Matlab code below.
Let A be an n-dimensional array:
clear
rng default
n=4;
A=randn(n,n,n,n);
n=5;
A=randn(n,n,n,n,n);
Note that A is composed of n^(n-2) 2-dimensional matrices, each of size nxn.
For example, when n=4 these matrices are A(:,:,1,1),...,A(:,:,4,1),A(:,:,1,2),...,A(:,:,4,4).
Suppose I'm interested in a code which:
1) deletes the last column and row in each of the n^(n-2) 2-dimensional matrices
%when n=4
A(n,:,:,:)=[];
A(:,n,:,:)=[];
%when n=5
A(n,:,:,:,:)=[];
A(:,n,:,:,:)=[];
2) deletes the 2-dimensional matrices with the 3-th,4-th,5-th,n-th index equal to n.
%when n=4
A(:,:,n,:)=[];
A(:,:,:,n)=[];
%when n=5
A(:,:,n,:,:)=[];
A(:,:,:,n,:)=[];
A(:,:,:,:,n)=[];
Question: could you help me to generalise the code above to any n? I cannot see how to proceed.
You can index your matrix with a cell containing multiple elements. Each element will be interpreted as a new index (more information here):
%Example 1: A(:,:,1:3,1:3,1:3}
%elements per dimension
n = 4;
%number of dimension
d = 5;
%random matrix
repdim = repmat({n},d,1)
A = rand(repdim{:});
%We want A(:,:,1:3,1:3,1:3}, so we create c = {1:3,1:3,1:3}
c = repmat({1:n-1},d-2,1);
%Get the new matrix
A = A(:,:,c{:});
%Example 2: A(1:3,1:3,:,:,:}
%elements per dimension
n = 4;
%number of dimension
d = 5;
%random matrix
repdim = repmat({n},d,1)
A = rand(repdim{:});
%We want A(1:3,1:3,:,:,:}, so we create c1 = {1:3,1:3} and c2 = {':',':',':'}
c1 = repmat({1:n-1},2,1);
c2 = repmat({':'},d-2,1); %thanks to #LuisMendo for the suggestion.
%Get the new matrix
A = A(c1{:},c2{:});
In Matlab I am trying to create a cell of size 16 x1 where each entry of this cell is a matrix. I have the following equation
$$W_g = exp^{\frac{j{2\pi m}{N}(n+\frac{g}{G}))} \,\,\,\,\,\,\, m,n=0,1,.....(N-1)$$
for this work assume $N=4$ and the index $g$ is the index that refers to the cell element i.e g=0:1:15
W=cell(16,1);
for g=1:16
for m=1:3
for n=1:3
W{g,m,n}= exp((2*pi*j*m/4)* n+(g-1)/16));
end
end
end
How can I make this work? I have two problems with this, you see g starts from 0 and MATLAB doesnt accept index of zero and how to actually define the matrices within the cell.
Thanks
So if I understand you have this equation:
And you just want the following code:
W=cell(16,1);
n = 1:3;
m = 1:3;
N = 4;
for g=1:16
W{g}= exp((2*pi*j.*m/4*N).*n+(g-1)/16);
end
%or the 1 line version:
W = cellfun(#(g) exp((2*pi*j.*m/4*N).*n+(g-1)/16),num2cell([1:16]),'UniformOutput',0);
With matlab you can use the Element-wise multiplication symbol .*
For example:
%A matrix multiplication
A = [2,3]
B = [1,3]';
result = A * B %result = 11
%An element wise multiplication
A = [2,3]
B = [1,3];
result = A .* B %result = [2,9]
First of all, i is the complex number in matlab (sqrt(-1)) not j, and you are correct, matlab is indexed in 1, so simply start counting g at 1, until 16.
Next, create a zero matrix, and calculate all indices accordingly. Something like this should work just fine :
clc
clear all
W=cell(16,1);
for g=1:16;
temp = zeros(3,3);
for m=1:3
for n=1:3
temp (m,n) = exp((2*pi*1i*m/4)* n+g/16);
end
end
W{g} = temp;
end
if you are considering doing much larger operations, consider using linspace to create your m and n indices and using matrix operations
I have many array (n*1 dimension), how can I do something like
matrix = [];
for i = 1:5
for j =1:5
matrix (i,j) = zeros(n,1); % store a given array to a cell of a matrix
end
end
I find Array of Matrices in MATLAB
But this is store matrices into array, not the otherwise.
Ying Xiong's suggestion is what you want if the vectors are of different lengths. But assuming the number of elements is constant (which they seem to be) you may also use a 3-dimensional array, where each (i,j) element contains a vector in the third dimension, like this:
rows = 5; cols = 5; n = 10; %// Dimensions
matrix = zeros(rows, cols, n); %// Initialize matrix
vector = 1:n; %// Just an example
for ii = 1:rows %// Bad practice to use i as a variable name
for jj = 1:cols %// Bad practice to use j as a variable name
matrix(ii,jj,:) = vector; %// Assignment
end
end
Now each index (i,j) contains the vectors you want, for instance:
squeeze(matrix(1,1,:))
ans =
1
2
3
4
5
6
7
8
9
10
Having all values in a single matrix can be a good thing if you want to do similar operations on all elements, as vectorized approaches are usually very fast in MATLAB. You might want to check out permute, reshape and functions like bsxfun.
Note that you might be able to vectorize the loops, but without knowing the specifics, that's impossible to know.
You need to use cell array.
n = 10;
matrix = cell(5,5);
for i = 1:5
for j = 1:5
matrix{i,j} = zeros(n,1);
end
end
I'd like to generate every boolean matrix in matlab as a 3-dimensional array.
For example:
mat(:,:,1) = [[1 0][0 1]]
mat(:,:,2) = [[1 1][0 1]]
...
My final goal is to generate every trinary matrix of a given size.
Keep in mind that I know that the number of matrices is exponential, but I'll use small numbers.
Not sure that the previous answer actually does what you want... With that method, I get multiple entries in array2D that are the same. Here is a vectorised and (I believe) correct solution:
clear all;
nRows = 2;
nCols = nRows; % Only works for square matrices
% Generate matrix of all binary numbers that fit in nCols
max2Pow = nCols;
maxNum = 2 ^ max2Pow - 1;
allBinCols = bsxfun(#bitand, (0:maxNum)', 2.^((max2Pow-1):-1:0)) > 0;
% Get the indices of the rows in this matrix required for each output
% binary matrix
N = size(allBinCols, 1);
A = repmat({1:N}, nCols, 1);
[B{1:nCols}] = ndgrid(A{:});
rowInds = reshape(cat(3, B{:}), [], nCols)';
% Get the appropriate rows and reshape to a 3D array of right size
nMats = size(rowInds, 2);
binMats = reshape(allBinCols(rowInds(:), :)', nRows, nCols, nMats)
Note that for anything other than small numbers of nRows you will run out of memory pretty quickly, because you're generating 2^(nRows*nRows) matrices of size nRows*nRows. ThatsAlottaNumbers.
Actually the answer is pretty straightforward. Each matrix being boolean, it can be indexed by the binary number obtained when reading all the values in any given order.
For a binary matrix: let n be the number of element in your matrix (n = rows * cols).
for d=0:(2^n-1)
%Convert binary to decimal string
str = dec2bin(d);
%Convert string to array
array1D = str - '0';
array1D = [array1D zeros(1, n-length(array1D))];
%Reshape
array2D(:,:,d+1) = reshape(array1D, rows, cols);
end
This can be very easily generalized to any base by changing dec2bin into dec2base and changing 2^n into (yourbase)^n.
I have two large matrices of row numbers and column numbers and a matrix of data. I want to create a matrix where:
output(i,j) = data(row(i,j),col(i,j))
How can I do this quickly?
Let [T, N] = size(Row), and let [DataT, DataN] = size(Data), then a one-line solution is:
Soln = reshape(Data(sub2ind([DataT DataN], Row(:), Col(:))), T, N);
This one-liner looks a bit complicated, so let's break it down step by step in an example case. I've included comments to indicate what is happening with each section:
%# Set fixed parameters for example matrices
T = 3; N = 2;
DataT = 5; DataN = 4;
%# Generate random Data matrix
Data = rand(DataT, DataN);
%# Generate some random subscript index matrices for indexing Data
Row = randi(DataT, T, N);
Col = randi(DataN, T, N);
%# Obtain the linear indices implied by treating Row and Col as subscript matrices
L = sub2ind([DataT DataN], Row(:), Col(:));
%# Use the linear indices to get the data we want
Soln = Data(L);
%# Reshape the data from a vector into matrix of size T by N
Soln = reshape(Soln, T, N);
The standard reference for solving these types of problems is Matrix-Indexing-in-MATLAB