Vector to Matrix syntax in MATLAB

Question

Is there a way to combine 2 vectors in MATLAB such that:

mat = zeros(length(C),length(S));
for j=1:length(C)
    mat(j,:)=C(j)*S;
end

Using normal MATLAB syntax similar to:

mat = C * S(1:length(S))

This gives a "Inner matrix dimensions must agree error" because it's trying to do normal matrix operations. This is not a standard Linear Algebra operation so I'm not sure how to correctly express it in MATLAB, but it seems like it should be possible without requiring a loop, which is excessively slow in MATLAB.

Solution 1

From your description, it sounds like a simple matrix operation. You just have to make sure you have the right dimensions for C and S. C should be a column vector (length(C)-by-1) and S should be a row vector (1-by-length(S)). Assuming they are the right dimensions, just do the following:

mat = C*S;

If you're not sure of their dimensions, this should work:

mat = (C(:))*(S(:)');

EDIT: Actually, I went a little crazy with the parentheses. Some of them are unnecessary, since there are no order-of-operation concerns. Here's a cleaner version:

mat = C(:)*S(:)';

---

EXPLANATION:

The matrix multiplication operator in MATLAB will produce either an inner product (resulting in a scalar value) or an outer product (resulting in a matrix) depending on the dimensions of the vectors it is applied to.

The last equation above produces an outer product because of the use of the colon operator to reshape the dimensions of the vector arguments. The syntax C(:) reshapes the contents of C into a single column vector. The syntax S(:)' reshapes the contents of S into a column vector, then transposes it into a row vector. When multiplied, this results in a matrix of size (length(C)-by-length(S)).

Note: This use of the colon operator is applicable to vectors and matrices of any dimension, allowing you to reshape their contents into a single column vector (which makes some operations easier, as shown by this other SO question).

Solution 2

Try executing this in MATLAB:

mat = C*S'

As In:

C = [1; 2; 3];
S = [2; 2; 9; 1];

mat = zeros(length(C),length(S));
for j=1:length(C)
    mat(j,:)=C(j)*S;
end

% Equivalent code:
mat2 = C*S';

myDiff = mat - mat2

Solution 3

Do you mean the following?

mat = zeros(length(C),length(S));
for j=1:length(C)
    mat(j,:)=C(j)*S;
end

If so, it's simply matrix multiplication:

C' * S    % if C and S are row vectors
C * S'    % if C and S are column vectors

If you don't know whether C and S are row vectors or column vectors, you can use a trick to turn them into column vectors, then transpose S before multiplying them:

C(:) * S(:)'

Solution 4

I'm not entirely clear on what you're doing - it looks like your resulting matrix will consist of length(C) rows, where the ith row is the vector S scaled by the ith entry of C (since subscripting a vector gives a scalar). In this case, you can do something like

mat = repmat(C,[1 length(S)]) .* repmat(S, [length(C) 1])

where you tile C across columns, and S down rows.

Solution 5

Try this:

C = 1:3 S = 1:5 mat1 = C'*S

mat2 = bsxfun(@times, C',S)

(esp. good when the function you need isn't simpler MATLAB notation)

--Loren

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