MATLAB: Creating a specific lower rectangular matrix

Question

Hello Matlab experts!

I'm interested in creating a specific lower rectangular matrix while avoiding loops.

Step 1: I create the following column vector:

[ A1 A2 A3 . . . . An ]'

Where n is a predetermined integer (changes from one simulation to another).

Step 2: I create the following matrix:

A1 A1 A1 A1 . . . . A1

A2 A2 A2 A2 . . . . A2

A3 A3 A3 A3 . . . . A3

. . .

An An An An . . . . An

Step 3: I want to perform the following shifts: Shift the second column one step down, Shift the third column two steps down, etc. So eventually I'll get the following matrix:

A1 An An-1 An-2 . . . . A2

A2 A1 An An-1 . . . . A3

A3 A2 A1 An . . . . A4

A4 A3 A2 A1 . . . . A5

. . .

An An-1 An-2 An-3 . . . . A1

Step 4: I use the 'tril' function to get the matrix I'm interested in, which is:

A1 0 0 0 . . . . 0

A2 A1 0 0 . . . . 0

A3 A2 A1 0 . . . . 0

A4 A3 A2 A1 . . . . 0

. . .

An An-1 An-2 An-3 . . . . A1

I need assistance with performing step 3.

Maybe there are better ways to create this matrix, let me know.

Thanks, Amital

Answer 1

A = 1:5;
out = tril(toeplitz(A))