5.9. Math

Utilities and functions for math.

Functions not explicitly defined here fall back to the appropriate numpy-like math function for the provided inputs (if one exists), through __getattr__(). The inputs can be numpy arrays, arraycontext arrays, or pymbolic expressions.

example::

With numpy input data:

import mirgecom.math as mm

x_np = np.array([0, np.pi/2, np.pi])
s_np = mm.sin(x_np)  # Calls np.sin

or arraycontext input data:

x_device = actx.from_numpy(x_np)
s_device = mm.sin(x_device)  # Calls actx.np.sin

or pymbolic input expression:

x_sym = pmbl.var("x")
s_sym = mm.sin(x_sym)  # Creates an expression pmbl.var("sin")(x_sym)

mirgecom.math.harmonic_mean(x, y)

Return the harmonic mean of x and y.

The harmonic mean is defined as

\[\frac{2 x y}{x + y}.\]

Parameters:

• x – A number, array type, or symbolic expression.

• y – A number, array type, or symbolic expression.

mirgecom.math.__getattr__(name)

Return a function that calls an appropriate math function based on its inputs.

Returns a function that inspects the types of its input arguments and dispatches to the appropriate math function. If any of the arguments are symbolic, the function returns a pymbolic.primitives.ExpressionNode representing the call to name. If not, it next checks whether any of the arguments have array contexts. If so, it calls name from the array context’s numpy workalike. And if none of the arguments have array contexts, it calls numpy’s version of name.