How can I create a matrix from a vector with the vector indices given in a matrix, without using a loop?

Dear all,

I have a (1x6) vector v and would like to create a (5x5) matrix A from the vector entries of v. Another (5x5) matrix B demonstrates the pattern. I would like to create A such that A(i,j)=v(1,B(i,j)) if B(i,j)>0 and A(i,j)=0 if B(i,j)=0.

B=[2 3 4 5 6; 3 4 5 6 0; 4 5 6 0 0; 5 6 0 0 0; 6 0 0 0 0]

I know how to do that in a loop, but since I have to do this operation on a large scale, I am looking for an efficient way to do this in vectorized form. It might be related to a more efficient (generalized) way of defining B, but I can't find the solution.

I would very much appreciate any help, thanks in advance!

Answer 1

[Distelfink]

The easiest way to go is the command hankel(v(2:6)). See the answer I received in this thread

Answer 2

[Benjamin Thompson]

If you can add an entry to v to handle the creating of the zero entries in A, it can be pretty elegant. First make A as a vector and then call reshape to convert to 5x5:

>> B=[2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 7; 5 6 7 7 7; 6 7 7 7 7]

B =

2 3 4 5 6

3 4 5 6 7

4 5 6 7 7

5 6 7 7 7

6 7 7 7 7

>> v = [1 2 3 4 5 6 0]'

v =

1

2

3

4

5

6

0

>> A = v(B(:))

A =

2

3

4

5

6

3

4

5

6

0

4

5

6

0

0

5

6

0

0

0

6

0

0

0

0

>> A = reshape(A,5,5)'

A =

2 3 4 5 6

3 4 5 6 0

4 5 6 0 0

5 6 0 0 0

6 0 0 0 0

[Distelfink]

That works well, Benjamin, thank you very much! Just one thing, you have the line A = reshape(A,5,5)' twice in your answer; the first should be deleted.

[Benjamin Thompson]

I have corrected that, and thanks for accepting the answer!