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operations on Matrix MathObjects with dimension(s) 1

operations on Matrix MathObjects with dimension(s) 1

by Gavin LaRose -
Number of replies: 1
Hi all,

In the context of partitioned matrices I'm trying to do the following: 

    $a11 = Matrix( [ 1 ] );
    $a12 = Matrix( [ 2, 3, 4 ] );
    $a21 = Matrix( [ 5 ], [ 6 ], [ 7 ] );
    $a22 = Matrix( [ 8, 9, 10 ], [ 11, 12, 13 ], [ 14, 15, 16 ] );
    $b11 = Matrix( [ 21 ] );
    $b12 = Matrix( [ 22, 23, 24 ] );
    $b21 = Matrix( [ 25 ], [ 26 ], [ 27 ] );
    $b22 = Matrix( [ 28, 29, 30 ], [ 31, 32, 33 ], [ 34, 35, 36 ] );

    $c11 = $a11 * $b11 + $a12 * $b21;
    $c12 = $a11 * $b12 + $a12 * $b22;
    $c21 = $a21 * $b11 + $a22 * $b21;
    $c22 = $a21 * $b12 + $a22 * $b22;

but this fails: I'm accused of trying to add or multiply matrices of different dimensions. I tried building the matrices by explicitly indicating the full structure, e.g., 

    $a11 = Matrix( [ [ 1 ] ] );
    $a12 = Matrix( [ [  2, 3, 4 ] ] );
    $a21 = Matrix( [ [ 5 ], [ 6 ], [ 7 ] ] );
    $a22 = Matrix( [ [ 8, 9, 10 ], [ 11, 12, 13 ], [ 14, 15, 16 ] ] );

in which case the problem displays fine, but the answers solicited by $c11->ans_array() and $c12->ans_array() are marked wrong with the message "Matrix dimension is not correct."

Any suggestions are welcome.

Thanks,
Gavin

In reply to Gavin LaRose

Re: operations on Matrix MathObjects with dimension(s) 1

by Davide Cervone -
There are two things going on here, one a bug in MathObject (for which I have submitted a patch) and one a misunderstanding of the handling of the arguments for Matrix (no doubt aggravated by bad documentation).

Taking the second issue first, the Matrix object is more general than just a 2D array of numbers. It actually will handle arbitrary dimensions. For example, you can do a 3D matrix, or a 1D matrix (which is essentially a vector). Because of this, however, you do have to be a little careful about how you enter a matrix that has only one row.

The Matrix() macro treats multiple inputs as though they were enclosed in brackets. So 

   Matrix([1,2,3],[4,5,6])
is the same as 
  Matrix([[1,2,3],[4,5,6]])
which is a 2x3 matrix. This is meant for convenience, and it works well most of the time, but there is one ambiguity: 
  Matrix([1,2,3])
is not a 1x3 matrix, it is a 1-dimensional matrix of length 3 (i.e., essentially a vector). To get a 1x3 matrix, you must use the double brackets explicitly: 
  Matrix([[1,2,3]]);
That is why when you added the brackets, your multiplications worked out OK.

[Note that this also means Matrix(1,2,3) is the same as Matrix([1,2,3]), so this is a 1D matrix of length 3).]

So that is the misunderstanding of what Matrix arguments mean. It is really best to include the extra brackets for a 2D matrix, but they are not necessary except for 1 x n matrices.

As for the bug, it turns out that there was a problem with ans_array for 1 x n matrices which caused the dimension mismatch error that you were getting. I have submitted a patch for it, and that should take care of it in the future. If you want a work-around for now, I can give you one, but it's not pretty.

Davide