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    <p>In the bivariate case, <code>p</code> is a two-dimensional array. This means that C vs fortran ordering of arrays are different. By default numpy functions give C ordering, and obviously fortran routines use fortran ordering.</p> <p>f2py is smart enough to deal with this, and automatically converts between C and fortran format arrays. However, this results in some overhead, which is one of the possible reasons for reduced performance. You can check if this is the cause by manually converting <code>p</code> to fortran type using <code>numpy.asfortranarray</code> outside your timing routine. Of course, for this to be meaningful, in your real use case you want to make sure that your input arrays are in fortran order.</p> <p>f2py has an option <code>-DF2PY_REPORT_ON_ARRAY_COPY</code> which can warn you any time an array is copied.</p> <p>If this is not the cause, then you need to consider more in-depth details, such as which fortran compiler you are using, and what sort of optimisations it is applying. Examples of things which could slow you down include allocation of arrays on the heap instead of the stack (with expensive calls to <code>malloc</code>), although I would expect such effects to become less significant for larger array.</p> <p>Finally, you should consider the possibility that for bivariate fitting, for large <code>N</code>, that the numpy routines are already essentially at optimum efficiency. In such cases, the numpy routine may be spending most of its time running optimised C routines, and the overhead of the python code becomes negligible in comparison. In this case, you would not expect your fortran code to show any significant speedup.</p>
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    1. POWhy is univariate Horner in Fortran faster than NumPy counterpart while bivariate Horner is not
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    1. COThank you DaveP I got a 5x speedup by using `numpy.asfortranarray` for the bivariate case when p is of size 1000x1000
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