how to multiply values between arrays columns to rows and generate a new vector form each of the multiplication?

given x= [ 1 1 1 ] and y=[ 1 2 3 ] how can I generate a code that will multiply each column value of x by each row of y and sote this values in a new array? How can I at the same time add a zero for every new array generated at the beginning (and end) of these vectors so that i can then add all of these vectors together?

ie:

x= [ 1 1 1 ] and y=[ 1 2 3 ]

x1=[1 2 3 0 0]

x2=[0 1 2 3 0]

x3=[0 0 1 2 3 ]

x4=x1+x2+x3

answer: x4=[1 3 6 5 3 ]

I hope my question is clear enough.

Thank you in advance!

Answer 1

[Star Strider]

The operation you are looking for is not actually multiplication, it is convolution.

Example:

x = [ 1 1 1 ];
y = [ 1 2 3 ];

z = conv(x, y)

producing:

z =
     1     3     6     5     3

as you describe yoiu want.

See the documentation on the conv function (and related links) for details.

[Seba.V]

That's great thank you!

May I ask if it possible to add zeros to either side of an array (end or start) without overwrite the array values? I mean just expand the vector and be able to shift a set of values between the zeros?

like

x=[1 2 3]

x1=[ 0 1 2 3 0 0 0]

x2= [ 0 0 1 2 3 0 0]

x3=[ 0 0 0 1 2 3 0]

[Star Strider]

My pleasure!

What you want to do is what the conv function does internally.

To do what you describe, try this:

x1 = zeros(1,6);
x2 = x1;
x3 = x1;
x1((1:3)+1) = y
x2((1:3)+2) = y
x3((1:3)+3) = y

producing:

x1 =
     0     1     2     3     0     0

x2 =
     0     0     1     2     3     0

x3 =
     0     0     0     1     2     3

You can then add them:

     z = x1 + x2 + x3 

to get:

z =
     0     1     3     6     5     3

Experiment to get the result you want.