Matlab Mode in Euler

These examples are from the web page "A very short introduction in Matlab", and from some other sources.

Let us switch to Matlab mode. Matlab uses a very short display by default.

>matlab on; shortestformat;

Matrices can now have blanks between elements. Note: For negative elements, use the comma, since [1 -1 1] would yield [0 1] in Euler.

>A=[16 3 2 13; 5 10 11 8; 9 6 7 12; 4 15 14 1]

     16       3       2      13 
      5      10      11       8 
      9       6       7      12 
      4      15      14       1

Matrix elements can be accessed with round brackets.

>A(1,1)+A(2,1)+A(3,1)+A(4,1)

The sum operator now works columns vectors differently.

>sum(A(1:4,1)) // use sum(A[1:4,1]') in Euler

>sum(A) //

[34, 34, 34, 34]

>diag(A,0)

fliplr works like flipx, and flipud like flipy.

>sum(diag(fliplr(A)))

Another function which is available in EMT and Matlab is rot().

>rot(A,2)

      1      14      15       4 
     12       7       6       9 
      8      11      10       5 
     13       2       3      16

Euler does also have an algorithm for magic triangles.

>magic(4)

     16       2       3      13 
      5      11      10       8 
      9       7       6      12 
      4      14      15       1

Euler used the matrix language consistently for all operators. Matlab uses .* for the elementwise multiplication.

>v=1:10; v.*v

[1, 4, 9, 16, 25, 36, 49, 64, 81, 100]

And it uses * for the matrix product.

>v*v'

The power operator now uses the matrix power function.

>A=[1,2;3,4]; A^2

      7      10 
     15      22

This works for the inverse too.

>A^-1*A

      1       0 
      0       1

The division uses "divide into" now. I.e.

b/A = (A'\b')'

>sum(A)/A

[1, 1]

The \ operator now uses fit.

>A=[1,2;3,4;5,6]; b=[1;2;3]; A\b

      0 
    0.5

The same in Euler.

>fit(A,b)

      0 
    0.5

In Matlab mode, you can use Matlab's syntax for functions. A proper "return y" statement will be added. If the function is the last or the only function in a file, "endfunction" can be omitted.

>function y=f(x)
 y=x^2;
 endfunction

>f(5)

Examples