"Matthias Troyer" <troyer@itp.phys.ethz.ch> wrote
Andy Little wrote <...>
For matrices my tests have been limited to homogeneous transformation matrices. In this case the matrix elements for a *simple/obvious* implementation of a matrix for a physical quantity are comprised of various types, comprising of the quantity type, the reciprocal of the quantity and numeric types. It may be possible to somehow 'tag' a numeric matrix as a quantity matrix, but I havent invetigated that.
Just use a quantity as value type? What's the problem with that?
Assume a 2D homogeneous transform matrix intended to transform 2d points. With 9 elements it is possible for the matrix to contain up to 9 separate types T0 - T9 ( T1 , T2, T3) ( T4, T5, T6 ) ( T7, T8, T9) In the transform matrix T1, T2, T4 and T5 are concerned with rotation. IOW to rotate a point through an angle alpha (cos(alpha), sin(alpha), T3 (-sin(alpha), cos(alpha), T6) ( T7, T8, T9) Therefore T1, T2, T4, T5 must be numeric. T7 and T8 represent translation. To translate a homogeneous point [ X Y h], assuming h is a numeric and X and Y are some quantity, T7 and T8 must have the dimensionally equivalent quantity type ( but not necesarily same unit) as X and Y. (In fact in this case T3 and T6 have the reciprocal quantity type of X and Y and T9 is always a numeric representing scaling) Concatenating two matrices of the above type yields another matrix of the same type and multiplying by the point yields a point of the same type. Other matrix operations that I have tried also work from the point of view of dimensional analysis too. Another alternative is to make all the elements of the matrix numeric. In this case h in the homogeneous coordinate [X Y h] would have the same type as X and Y. That isnt as neat though as you have then lost the unit information in T7 and T8 regarding the translation and applying the matrix to a point in different units would give different results.
I havent looked into other use cases for linear algebra in association with Quan however. It may be that in the general case ( for large matrices) that it is impractical ( IOW the costs outweigh any possible benefits) to use non-numeric types as the elements, but that remains to be investigated.
Why? What should be the problem? Your quantity is just a number, and the rest is compile time type information? Or is a quantity heavier than just a floating point number?
I hope I have demonstrated some of the issues in the above example. However I have only limited my experiments to transform matrices. I should probably look at other matrix calculations to see what happens in other cases too. regards Andy Little