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

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AllKindsofMath AllKinds 2013-11-19

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回答： Alfonso Nieto-Castanon 2013-11-20

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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Answer 1

Jan 2013-11-19

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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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AllKindsofMath AllKinds 2013-11-19

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 2013-11-20

Not as far as I can see. You will probably have to iterate over the third dimension.

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Answer 2

Sean de Wolski 2013-11-19

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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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Sean de Wolski 2013-11-19

在 MATLAB Online 中打开

subs(matrix1,x,vector1(4))

AllKindsofMath AllKinds 2013-11-19

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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Answer 3

Jan 2013-11-19

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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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AllKindsofMath AllKinds 2013-11-19

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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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Answer 4

Alfonso Nieto-Castanon 2013-11-20

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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