I often have to manipulate a lot of matrices row by row using MATLAB.
Instead of having to type:
m(x, :);
every time I want to reference a particular row, I created an anonymous MATLAB function:
row = #(x) m(x, :);
allowing me to call row(x) and get the correct row back.
But it seems that this anonymous function is actually not the same as calling m(x, :) directly, as the reference to the matrix is lost. So when I call something like:
row(2) = 2 * row(2);
MATLAB returns the error:
error: can't perform indexed assignment for function handle type
error: assignment failed, or no method for 'function handle = matrix'
Is there a way to define a function handle to get around this problem, or am I better off just typing out m(x, :) when I want to reference a row?
Thanks so much!
By defining an anonymous function, you make every row immutable (at least through row). Reassigning the value of a function handle is simply not possible.
Imagine that you define the function handle mySquare(x) = #(x) x.^2 ;. If reassigning the output of a function handle would be possible, you could change the value of mySquare(2) (e.g., mySquare(2)=2) and basically states that 4=2!
On the positive side, your anonymous function "protects" your initial input m from unexpected modifications. If you want to use your function row, you should simply define another matrix m_prime, whose rows are initialized with the function handle row (avoid using m again since it would probably mix everything up).
reference through a handle only work for Matlab object/class inherited from the handle class.
If as you said in comment "elementary row operations is the end application for this", then David's answer is a good simple way to go (or simply keep using m(x,:) which is still the shortest syntax after all).
If you really want to venture into handles and true reference values, then you can create a class rowClass which you specialise in row operations. An example with a few row operations would be:
classdef rowClass < handle
properties
m = [] ;
end
methods
%// constructor
function obj = rowClass(matrix)
obj.m = matrix ;
end
%// row operations on a single row ----------------------------
function obj = rowinc(obj,irow,val)
%// increment values of row "irow" by scalar (or vector) "val"
obj.m(irow,:) = obj.m(irow,:) + val ;
end
function obj = rowmult(obj,irow,val)
%// multiply by a scalar or by a vector element wise
obj.m(irow,:) = obj.m(irow,:) .* val ;
end
function obj = rowsquare(obj,irow)
%// multiply the row by itself
obj.m(irow,:) = obj.m(irow,:).^2 ;
end
%// row operations between two rows ---------------------------
function obj = addrows(obj,irow,jrow)
%// add values of row "jrow" to row "irow"
obj.m(irow,:) = obj.m(irow,:) + obj.m(jrow,:) ;
end
function obj = swaprows(obj,irow,jrow)
%// swap rows
obj.m([irow,jrow],:) = obj.m([jrow,irow],:) ;
end
end
end
Of course you could add all the operations you frequently do to your rows, or even to the full matrix (or a subset).
Example usage:
%% // sample data
A = (1:5).' * ones(1,5) ; %'// initial matrix
B = rowClass( A ) ; %// make an object out of it
B =
rowClass with properties:
m: [5x5 double]
B.m %// display the matrix
ans =
1 1 1 1 1
2 2 2 2 2
3 3 3 3 3
4 4 4 4 4
5 5 5 5 5
Add a value (12) to all elements of the row(1):
%% // add a value (scalar or vector) to a row
rowinc(B,1,12) ;
B.m
ans =
13 13 13 13 13
2 2 2 2 2
3 3 3 3 3
4 4 4 4 4
5 5 5 5 5
Square the row(3):
%% // Square row 3
rowsquare(B,3) ;
B.m
ans =
13 13 13 13 13
2 2 2 2 2
9 9 9 9 9
4 4 4 4 4
5 5 5 5 5
Last one for the road, swap row(3) and row(5):
%% // swap rows
swaprows(B,5,3) ;
B.m
ans =
13 13 13 13 13
2 2 2 2 2
5 5 5 5 5
4 4 4 4 4
9 9 9 9 9
I think you'll be best off typing m(x,:)! It's not much quicker than doing row(x). Another issue with the anonymous function row is that it will keep the original matrix m, which wont change.
Here is an anonymous function that does what you want, I think it's a reasonable way of doing things. row(a,b,c) multiplies the b'th row of the matrix (not necessarily square) a by c.
x=rand(5)
row=#(x,i,k) (diag([ones(1,i-1) k ones(1,size(x,1)-(i))]))*x
x=row(x,2,20)
Ultimately, I think the simplest method is to make a standalone function to do each type of row operation. For example,
function x=scalarmult(x,i,k)
x(i,:)=k*x(i,:);
and
function x=addrows(x,i,j)
x(i,:)=x(i,:)+x(j,:);
and
function x=swaprows(x,i,j)
x([i,j],:)=x([j,i],:);
Related
I have a main matlab file. The main file accesses several functions. There is a loop in one of the functions and I want to see each part of the loop even though those variables aren't being stored. I am new to matlab and I don't understand whether the inputs are matrices, vectors or elements. How do I do that?
matrix1 = [1 2 3 4; 4 5 6 5; 7 8 1 0;3 5 7 6]
list1 = [1;3;5;4]
i=0
for a=1:1:4 %no. of rows
for b=2:1:4 % no. of col
x=matrix1(a,b);
s=1
n3=list1(a,1); %vector
mult=(s.*sin(i)./n3);
end
end
This is a part of a function that the main file calls. x, n3, mult are all being used but none of them are being saved. How can I see what these values are?
Let say we have the vector v=[1,2,3] and we want to build the matrix of all the combinations of the numbers contained in v, i.e.
1 2 3
1 3 2
2 1 3
2 3 1
3 1 2
3 2 1
Since I'm not good in recursion, firstly I tried to write the code to build such a matrix by using for loops
makeLoop([1,2,3])
function A = makeLoop(v)
loops=length(v);
for i = 1:loops
dummy=v;
m=factorial(loops)/loops;
A((1+m*(i-1)):m*i,1)=v(i);
v(i)=[];
loops2=length(v);
for j = 1:loops2
dummy2=v;
m2=factorial(loops2)/loops2;
A(((1+m2*(j-1))+m*(i-1)):(m2*j+m*(i-1)),2)=v(j);
v(j)=[];
loops3=length(v);
for k = 1:loops3
m3=factorial(loops3)/loops3;
A(((1+m2*(j-1))+m*(i-1)):(m2*j+m*(i-1)),3)=v(k);
end
v=dummy2;
end
v=dummy;
end
end
it seems like it work, but obviously write it all for a bigger v would be like hell. Anyway I don't understand how to properly write the recursion, I think the recursive structure will be something like this
function A = makeLoop(v)
if length(v)==1
"do the last for loop"
else
"do a regular loop and call makeLoop(v) (v shrink at each loop)"
end
but I don't get which parts should I remove from the original code, and which to keep.
You were very close! The overall structure that you proposed is sound and your loopy-code can be inserted into it with practically no changes:
function A = makeLoop(v)
% number of (remaining) elements in the vector
loops = length(v);
if loops==1 %"do the last for loop"
A = v; %Obviously, if you input only a single number, the output has to be that number
else %"do a regular loop and call makeLoop(v) (v shrink at each loop)"
%preallocate matrix to store results
A = zeros(factorial(loops),loops);
%number of results per vector element
m = factorial(loops)/loops;
for i = 1:loops
%For each element of the vector, call the function again with that element missing.
dummy = v;
dummy(i) = [];
AOut = makeLoop(dummy);
%Then add that element back to the beginning of the output and store it.
A((1+m*(i-1)):m*i,:) = [bsxfun(#times,v(i),ones(m,1)) AOut];
end
end
Explanation bsxfun() line:
First, read the bsxfun documentation, it explains how it works way better than I could. But long story short, with bsxfun() we can replicate a scalar easily by multiplying it with a column vector of ones. E.g. bsxfun(#times,5,[1;1;1]) will result in the vector [5;5;5]. Note that since Matlab 2016b, bsxfun(#times,5,[1;1;1]) can written shorter as 5.*[1;1;1]
To the task at hand, we want to add v(i) in front (as the first column) of all permutations that may occur after it. Therefore we need to replicate the v(i) into the 1. dimension to match the number of rows of AOut, which is done with bsxfun(#times,v(i),ones(m,1)). Then we just horizontally concatenate this with AOut.
You can simply use the perms function to achieve this:
v = [1 2 3];
perms(v)
ans =
3 2 1
3 1 2
2 3 1
2 1 3
1 3 2
1 2 3
If you want them sorted using the same criterion you applied in the desired output, use the following code (refer to this page for an official documentation of the sortrows functon):
v = [1 2 3];
p = perms(v);
p = sortrows(p)
p =
1 2 3
1 3 2
2 1 3
2 3 1
3 1 2
3 2 1
I've two matrix a and b and I'd like to combine the rows in a way that in the first row I got no duplicate value and in the second value, columns in a and b which have the same row value get the maximum value in new matrix. i.e.
a = 1 2 3
8 2 5
b = 1 2 5 7
2 4 6 1
Desired output
c = 1 2 3 5 7
8 4 5 6 1
Any help is welcomed,please.( the case for accumulation is asked here)
Accumarray accepts functions both anonymous as well as built-in functions. It uses sum function as default. But you could change this to any in-built or anonymous functions like this:
In this case you could use max function.
in = horzcat(a,b).';
[uVal,~,idx] = unique(in(:,1));
out = [uVal,accumarray(idx,in(:,2),[],#max)].'
Based upon your previous question and looking at the help file for accumarray, which has this exact example.
[ii, ~, kk] = unique([a(1,:) b(1,:)]);
result = [ ii; accumarray(kk(:), [a(2,:) b(2,:)], [], #max).'];
The only difference is the anonymous function.
I want to show 2dim. Surface plots for different combinations of 2 parameters of a 3- or higher-dimensional array in matlab. The data for the non-shown dimensions are integrated (i.e. summed in the remaining dimensions). I am using surf(), and for parameter combinations other than (1,2) (eg. (1,3), (2,3) ...) I have to rearrange the data matrices in order to make it work.
I am looking for an alternative command (or shorter code) which does this work.
Here's the code:
a=zeros(3,3,2);
a(:,:,1) = [1 2 3 ;4 5 6; 7 8 9; 10 11 12]; % // data matrix
a(:,:,2) = -[1 2 3 ;4 5 6; 7 8 9; 10 11 12]*2; % // data matrix
ai=[[1 2 3 4]' [5 6 7 0]' [8 9 0 0]']; % // parameter vector
mat12 = sum(a,3);
surf(ai(1:3,2),ai(1:4,1),mat12)
aux13 = sum(a,2);
for i = 1:2; mat13(:,i) = aux13(:,:,i);
surf(ai(1:2,3),ai(1:4,1),mat13)
aux23 = sum(a,1);
for i = 1:2; mat23(i,:) = aux23(:,:,i);
surf(ai(1:3,2),ai(1:2,3),mat23)
In other words, I am looking for a way to use surf for matrices mat13 and mat23 without the aux13, aux23 variables and the for loop.
First your example doesn't run because you declare a=zeros(3,3,2); as a matrix [3x3x2] but you immediately try to populate it as a [4x3x2] matrix, so I had to adjust your first line to: a=zeros(4,3,2);
If I run your code with that adjustment, your auxiliary variable and for loops are to reform/reshape a matrix stripped of it's singleton dimension. Matlab provide a handy function for that : squeeze.
For example, your variable aux13 is of dimension [4x1x2], then mat13=squeeze(aux13); achieve the same thing than your for loop. Your matrix mat13 is now of dimension [4x2].
Since no for loop is needed, you can completely bypass your auxiliary variable by calling squeeze directly on the result of your summation: mat13=squeeze( sum(a,2) );
Full example, the code below does exactly the same than your code sample:
mat12 = sum(a,3);
surf(ai(1:3,2),ai(1:4,1),mat12)
mat13 = squeeze( sum(a,2) ) ;
surf(ai(1:2,3),ai(1:4,1),mat13)
mat23 = squeeze( sum(a,1) ) ;
mat23 = mat23.' ; %'// <= note the "transpose" operation here
surf(ai(1:3,2),ai(1:2,3),mat23)
Note that I had to transpose mat23 to make it match the one in your example.
sum(a,1) is [1x3x2] => squeeze that and you obtain a [3x2] matrix but your code arrange the same values in a [2x3] matrix, so the use of the transpose. The transpose operator has a shorthand notation .'.
I used it in the example in a separate line just to highlight it. Once understood you can simply write the full operation in one line:
mat23 = squeeze(sum(a,1)).' ;
The way you write your loops isn't exactly MATLAB syntax. Below is the correct loop syntax shown.
On line 2 and 3, you are trying to load (4x3)-matrices into (3x3)-matrices. That is why you get a subscript error. You could resolve it by making the zeros-matrix bigger. Here's some Syntax fixed:
a=zeros(4,3,2);
a(:,:,1) = [1 2 3 ;4 5 6; 7 8 9; 10 11 12]; % // data matrix
a(:,:,2) = -[1 2 3 ;4 5 6; 7 8 9; 10 11 12]*2; % // data matrix
ai=[[1 2 3 4]' [5 6 7 0]' [8 9 0 0]']; % // parameter vector
mat12 = sum(a,3);
surf(ai(1:3,2),ai(1:4,1),mat12)
aux13 = sum(a,2);
for i = 1:2 mat13(:,i) = aux13(:,:,i);
surf(ai(1:2,3),ai(1:4,1),mat13)
end
aux23 = sum(a,1);
for i = 1:2 mat23(i,:) = aux23(:,:,i);
surf(ai(1:3,2),ai(1:2,3),mat23)
end
Now, what are you exactly trying to do inside those loops?
As an example, I have a matrix [1,2,3,4,5]'. This matrix contains one column and 5 rows, and I have to generate a pair of points like (1,2),(1,3)(1,4)(1,5),(2,3)(2,4)(2,5),(3,4)(3,5)(4,5).
I have to store these values in 2 columns in a matrix. I have the following code, but it isn't quite giving me the right answer.
for s = 1:5;
for tb = (s+1):5;
if tb>s
in = sub2ind(size(pairpoints),(tb-1),1);
pairpoints(in) = s;
in = sub2ind(size(pairpoints),(tb-1),2);
pairpoints(in) = tb;
end
end
end
With this code, I got (1,2),(2,3),(3,4),(4,5). What should I do, and what is the general formula for the number of pairs?
One way, though is limited depending upon how many different elements there are to choose from, is to use nchoosek as follows
pairpoints = nchoosek([1:5],2)
pairpoints =
1 2
1 3
1 4
1 5
2 3
2 4
2 5
3 4
3 5
4 5
See the limitations of this function in the provided link.
An alternative is to just iterate over each element and combine it with the remaining elements in the list (assumes that all are distinct)
pairpoints = [];
data = [1:5]';
len = length(data);
for k=1:len
pairpoints = [pairpoints ; [repmat(data(k),len-k,1) data(k+1:end)]];
end
This method just concatenates each element in data with the remaining elements in the list to get the desired pairs.
Try either of the above and see what happens!
Another suggestion I can add to the mix if you don't want to rely on nchoosek is to generate an upper triangular matrix full of ones, disregarding the diagonal, and use find to generate the rows and columns of where the matrix is equal to 1. You can then concatenate both of these into a single matrix. By generating an upper triangular matrix this way, the locations of the matrix where they're equal to 1 exactly correspond to the row and column pairs that you are seeking. As such:
%// Highest value in your data
N = 5;
[rows,cols] = find(triu(ones(N),1));
pairpoints = [rows,cols]
pairPoints =
1 2
1 3
2 3
1 4
2 4
3 4
1 5
2 5
3 5
4 5
Bear in mind that this will be unsorted (i.e. not in the order that you specified in your question). If order matters to you, then use the sortrows command in MATLAB so that we can get this into the proper order that you're expecting:
pairPoints = sortrows(pairPoints)
pairPoints =
1 2
1 3
1 4
1 5
2 3
2 4
2 5
3 4
3 5
4 5
Take note that I specified an additional parameter to triu which denotes how much of an offset you want away from the diagonal. The default offset is 0, which includes the diagonal when you extract the upper triangular matrix. I specified 1 as the second parameter because I want to move away from the diagonal towards the right by 1 unit so I don't want to include the diagonal as part of the upper triangular decomposition.
for loop approach
If you truly desire the for loop approach, going with your model, you'll need two for loops and you need to keep track of the previous row we are at so that we can just skip over to the next column until the end using this. You can also use #GeoffHayes approach in using just a single for loop to generate your indices, but when you're new to a language, one key advice I will always give is to code for readability and not for efficiency. Once you get it working, if you have some way of measuring performance, you can then try and make the code faster and more efficient. This kind of programming is also endorsed by Jon Skeet, the resident StackOverflow ninja, and I got that from this post here.
As such, you can try this:
pairPoints = []; %// Initialize
N = 5; %// Highest value in your data
for row = 1 : N
for col = row + 1 : N
pairPoints = [pairPoints; [row col]]; %// Add row-column pair to matrix
end
end
We get the equivalent output:
pairPoints =
1 2
1 3
1 4
1 5
2 3
2 4
2 5
3 4
3 5
4 5
Small caveat
This method will only work if your data is enumerated from 1 to N.
Edit - August 20th, 2014
You wish to generalize this to any array of values. You also want to stick with the for loop approach. You can still keep the original for loop code there. You would simply have to add a couple more lines to index your new array. As such, supposing your data array was:
dat = [12, 45, 56, 44, 62];
You would use the pairPoints matrix and use each column to subset the data array to access your values. Also, you need to make sure your data is a column vector, or this won't work. If we didn't, we would be creating a 1D array and concatenating rows and that's not obviously what we're looking for. In other words:
dat = [12, 45, 56, 44, 62];
dat = dat(:); %// Make column vector - Important!
N = numel(dat); %// Total number of elements in your data array
pairPoints = []; %// Initialize
%// Skip if the array is empty
if (N ~= 0)
for row = 1 : N
for col = row + 1 : N
pairPoints = [pairPoints; [row col]]; %// Add row-column pair to matrix
end
end
vals = [dat(pairPoints(:,1)) dat(pairPoints(:,2))];
else
vals = [];
Take note that I have made a provision where if the array is empty, don't even bother doing any calculations. Just output an empty matrix.
We thus get:
vals =
12 45
12 56
12 44
12 62
45 56
45 44
45 62
56 44
56 62
44 62