Ufuncs

ufuncs, short for universal functions, are a NumPy concept that provides fast elementwise operations on arrays. They are implemented in C and designed to replace explicit Python loops with efficient vectorized computation. A ufunc takes one or more input arrays and applies a scalar operation to each corresponding element, producing an output array of the same shape after broadcasting inputs as needed.

Key properties include broadcasting, which aligns arrays of different shapes, and dtype handling, where the result's data type is determined by the inputs and the ufunc's type resolution rules. Ufuncs are designed to work without Python-level loops, enabling performance close to native code for large arrays.

Ufuncs expose additional functionality through methods and parameters: out to specify the destination array, where to selectively apply computation, and dtype to control the result's data type. They also provide reduction and accumulation operations (for example, reducing across an axis or computing a cumulative sum), as well as outer operations that combine two arrays in a pairwise fashion.

Common examples include arithmetic and trigonometric operations such as add, subtract, multiply, divide, sin, cos, exp, and log, as well as comparisons like greater and equal. In practice, Python expressions like a + b or np.sin(x) dispatch to the corresponding ufuncs, enabling fast, vectorized computation on large datasets.

While ufuncs are highly optimized for array inputs, there is also a Python-level wrapper called vectorize, which can apply a regular Python function elementwise but loses the performance advantages of true ufuncs.