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Linear Algebra Levels

Functions using linear algebra are divided into two levels:

For purely "1d" functions we use the C-style arguments (double *, stride, size) so that it is simpler to use the functions in a normal C program, without needing to invoke all the gsl_vector machinery.

The philosophy here is to minimize the learning curve. If someone only needs to use one function, like an fft, they can do so without having to learn about gsl_vector.

This leads to the question of why we don't do the same for matrices. In that case the argument list gets too long and confusing, with (size1, size2, tda) for each matrix and potential ambiguities over row vs column ordering. In this case, it makes sense to use gsl_vector and gsl_matrix, which take care of this for the user.

So really the library has two levels -- a lower level based on C types for 1d operations, and a higher level based on gsl_matrix and gsl_vector for general linear algebra.

Of course, it would be possible to define a vector version of the lower level functions too. So far we have not done that because it was not essential -- it could be done but it is easy enough to get by using the C arguments, by typing v->data, v->stride, v->size instead. A gsl_vector version of low-level functions would mainly be a convenience.

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