Norm of group of elements whose position is reported on a cell array

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jason beckell 2018-4-15

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编辑： jason beckell 2018-4-16

Dear all,

I have a vector x containing 4095 unknowns. I know that these unknowns have been already clustered into 115 classes, whose positions are reported in a cell array of length 115 (i.e. at position i of the cell array, there are the indexes of all the elements in the vector x belonging to class i). My questions is the following. Is there a way to get a vector with the 2-norm of the elements of x which belongs to each clusters (hence, a vector of length 115) WITHOUT using any loop? My problem arises since I have to pass such norms as a variable to be optimized by a numerical solver (cvx). Hence, since it will be part of the objective function to be optimized, I cannot put any cycle inside of it. Moreover, my objective function also contains a linear combinations of such unknowns, hence it is not so evident to me if there exist any bounds which may satisfy my request as a work-around. If required, I can pre-transform the cell array into another structure.

Many thanks for the attention and my best regards.

Jason.

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Answer 1

Akira Agata 2018-4-15

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https://ww2.mathworks.cn/matlabcentral/answers/394965-norm-of-group-of-elements-whose-position-is-reported-on-a-cell-array#answer_315165

编辑：Akira Agata 2018-4-15

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Like this?

% Sample data x and class info cell array g
x = rand(10,1);
g = {[1 3 5 7 9],[2 4 6 8 10]};
% Calculate 2-norm for each class
func = @(idx) norm(x(idx));
d = cellfun(func,g);

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jason beckell 2018-4-16

编辑：jason beckell 2018-4-16

在 MATLAB Online 中打开

Dear Akira,

many thanks for your answer. I have finally discovered that the expression within a cxvblock must be declared by means of the keyword "expression". Hence, in our instance, the required code turns out to be something like this:

% Sample data x and class info cell array g
n = 10;
x = rand(n,1);
g = {[1 3 5 7 9],[2 4 6 8 10]};
% cvx block
cvx_begin
variable x(n)
expression l(length(g))
func = @(idx) norm(x(idx));
l = cellfun(func,g);
minimize((norm(A*x+b))+l(1))
cvx_end