On Fri, 10 Nov 2006, Jason Hise wrote:
On 11/10/06, François Duranleau <duranlef@iro.umontreal.ca> wrote:
On Fri, 10 Nov 2006, Jason Hise wrote:
I agree on your stand about matrix vs vector types as being distinct, but I don't agree that a matrix is just composed of rows of elements. It could also be columns of elements. Which is it? A matrix should be left as a two dimensional array (conceptually), either row-major or column-major or the exact layout could be a parameter, as for boost::multi_array, except this time maybe as a template parameter.
Maybe. I have to wonder though if this flexibility adds functionality, or just room for confusion. I've heard of doing elementary row opeerations, but I have not heard of doing elementary column operations. I would think that a standardized means of storage and accesss would make code clearer, but I will concede this point if you can show me use cases where this flexibility comes in handy for client code.
I can think of a few. One is when you do graphics with OpenGL (I don't know how it is with other APIs). The latter uses column-major format for matrices. Thus if you need to often interface with OpenGL, it's better (faster) if you're internal representation is in the same order (as a result, I often see matrix implementations in column-major order instead of standard C ordering in the graphics community). Another one, still in graphics (or actually, any applications dealing with geometry), concerns rotation matrices. If you have a basis of three orthonormal vectors (assuming 3D here), you can get a rotation matrix by assign two vectors as the columns or rows of a 3x3 matrix, depending on the direction of the transformation (local coordinates to world or vice-versa). It is also often useful to extract back those vectors (columns or rows). Also, when you do some linear solving, if you want to implement a scheme with full pivoting (rows and columns), you have more than row operations. Concerning the cost of that flexibility, well, after posting my previous reply, I went back to my matrix implementation and see what I had to change to had a choice of ordering as a template parameter. I was surprised that I had only a few changes to do. The only thing that poses some problem is when applying an operator on two matrices of different ordering: what should be the returned ordering type? -- François Duranleau LIGUM, Université de Montréal