Paul Godfrey

The package is generally excellent.
My only complaint is that the accuracy of the zeta function deterioriates rapidly for |z|>80.
For example, the script returns
0.541674252238781 - 0.348243845696725i
for the 29-th non-trivial zero, which is approximately 0.5+98.8311i.
 
If you ever have time for an upgrade it would be much appreciated!

Great job, and good examples.

A couple of modifications that could be implemented.

Let there be one input, the order of the denominator, and accept an array. Calculate rms error and return that for the array. Could either set the numerator to the denominator, or sweep the numerator from 2 to the order of the denominator.

Incorporate a lag term, including raising the exponent to a power.

In your examples, you may want to include extracting the polynomial from a psd, generating a time history from a filter on rand, and replotting the resulting psd for comparison.

Very helpful and useful (rating and comments based only on gamma and gammaln functions). Suggestions:

1. The code to allocate storage:

 f = 0.*z; % reserve space in advance

is not needed (indeed is wasteful), as preallocation is only useful ahead of a loop or to set up an array of a specific shape.

2. It might be worth switching to logical indexing rather than linear indexing - this would avoid the use of find() and the reshape at the end.

3. gammaln(z) returns infinities for abs(imag(z)) greater than about 226 and real(z) < 0. This is due to overflow of sin() in the reflection formula, but it is an unnecessary restriction as log(sin(z)) can be computed without overflow over a larger set of values than can sin(z). For example, we can use log(sin(x + iy)) (x and y real) is approximately equal to y + log(0.5i * exp(-1i * x)) for large positive y, and the approximation is good to machine accuracy if y > 18 or thereabouts. (For negative y the approximation is -y + log(-0.5i * exp(1i * x)).) Replacing log(sin()) by a call to a logsin() function that uses these approximations greatly extends the set of valid arguments.