element-wise operator to scale rows of matrix with entries of a vector

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SA-W le 17 Jan 2023
Modifié(e) : Matt J le 17 Jan 2023
Given a matrix and a vector
A = [2 3 4 5;5 4 3 2;1 2 3 4;4 3 2 1];
d = [1 2 3 4];
I want to scale the rows of A with the corresponding entries of d to obtain
res = [2 3 4 5;10 8 6 4;3 6 9 12;16 12 8 4];
I figured out that
res=A.*d(:); --> correct
res2=A.*d; --> wrong, results in column-wise scaling
I know that .* indicates element-wise operations and d(:) re-shapes d into a column-vector, but my question is how to systematically read the expression A.*d(:) . Also, applies the element-wise operator .* to its left argument (here, A) or to its right argument (here, d)?
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Matt J le 17 Jan 2023
Modifié(e) : Matt J le 17 Jan 2023
Also, applies the element-wise operator .* to its left argument (here, A) or to its right argument (here, d)?
.* has two operands A and d, so it applies to both of them. It is also commutative (as you would expect), so you could have also done,
res=d(:).*A
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SA-W le 17 Jan 2023
Modifié(e) : SA-W le 17 Jan 2023
Nice to know these properties.
If the element-wise operator .* has two operands, the elements of the left and right operand are somehow defined. Here, the elements of d are simply the entries, but an element of A could be a row, a column, or a individual entry...I think my question boils down to the following: Given the expression
res=d(:).*A
, how do I know that this expression scales the rows of A?
Matt J le 17 Jan 2023
Modifié(e) : Matt J le 17 Jan 2023
how do I know that this expression scales the rows of A?
Because of Matlab's implicit expansion rules:
So, because d(:) has 1 column and A has N columns, the elements of d(:) get duplicated to form multiple columns before the multiplication is done.

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