substitute each element of a vector into a matrix without using loop

2013 11 19
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更新时间：2013 11 20
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Hi I want to substitute each element of vector1 into 'x' in matrix1 and store each matrix in an array without using a loop. Please tell me how.
vector1=[1:1:10];
matrix1=[4*x 5*x ; 4*x 2*x];
Thanks in advance.

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Jan
Jan 2013-11-19

0 个投票

Like this?
vector = 1:1:10;
vector = reshape( vector, [1, 1, numel(vector)] );
one_vector = ones( 1, 1, numel(vector) );
matrix = [4 * vector, 5 * one_vector; 4 * one_vector, 2 * vector ];

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Thank you that looks very good. But I don't understand what this line does
vector = reshape( vector, [1, 1, numel(vector)] );
can you explain it please?
Jan
Jan 2013-11-19
It forces vector to have the dimension [1, 1, numel(vector)]. I.e. if you will, the result is a 3D matrix with exactly one row, one column and numel(vector) elements in the third dimension.
Another question, I want to find the determinant of each matrix. So when I try det(matrix) it doesn't work, but with det(matrix(:,:,10)) for example it does. Can I apply 'det' to all elements of 'matrix'?
Jan
Jan 2013-11-20
Not as far as I can see. You will probably have to iterate over the third dimension.

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更多回答（3 个）

Sean de Wolski
Sean de Wolski 2013-11-19

0 个投票

So:
vector1=[1:1:10];
x = vector1;
matrix1=[4*x 5*x ; 4*x 2*x];
Or is x symbolic?
clear x;
syms x
matrix1=[4*x 5*x ; 4*x 2*x];
matrix1 = subs(matrix1,x,vector1)

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x is symbolic so my example should really be something like
matrix1=[4*x 5 ; 4 2*x];
Sean de Wolski
Sean de Wolski 2013-11-19
编辑：Sean de Wolski 2013-11-19
i.e. the second half of what I have...
Yes but if I want the matrix for vector1(4) how do I display it?
Yeh but I want all of the matrices to be stored in an array so that I can call on them when I need them.

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Jan
Jan 2013-11-19

0 个投票

Maybe something like the following?
matrix = [4, 5; 4, 2];
[p, q] = size( matrix );
vector = 1:1:10;
matrix = repmat( matrix(:), 1, numel( vector ) );
matrix = matrix .* repmat( vector, p*q, 1 );
matrix = reshape( matrix, p, q, numel( vector ) );
This gives you a 3d matrix, where each layer contains the specified matrix, mulitplied by one entry in vector

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This is almost there! in my example I have each element multiplied by x, but this was probably misleading as each element will not be multiplied by x. So more like
matrix1 = [4*x 5 ; 4 2*x];

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0 个投票

perhaps something like:
f = @(x)[4*x 5 ; 4 2*x]; % Matrix in functional form
vector = 1:10; % Your vector of values for 'x'
matrix = arrayfun(f,vector,'uni',0); % A cell array of matrices
values = cellfun(@det,matrix); % Determinant of each of those matrices

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