Universal Functions (Ufuncs)

A universal function (ufunc) is a function that performs element-wise operations on data in ndarrays. Ufuncs act as fast, vectorized wrappers for simple functions that take one or more scalar values and produce one or more scalar results.

Ufuncs can be classified into two types:

• Unary ufuncs: These take a single input array and perform operations on each element (e.g., numpy.sqrt or numpy.exp).
• Binary ufuncs: These take two input arrays and perform operations element-wise between them (e.g., numpy.add or numpy.maximum).

Key Features of Ufuncs:

• Out Argument: Ufuncs accept an optional out argument that allows them to assign their results into an existing array rather than creating a new one.
• Continuous Updates: New ufuncs are regularly added to NumPy, so it’s best to consult the official documentation for a comprehensive list and stay up-to-date.

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Common Unary Ufuncs

Function	Description
abs, fabs	Compute the absolute value element-wise for integer, floating-point, or complex values.
sqrt	Compute the square root of each element (equivalent to arr ** 0.5).
square	Compute the square of each element (equivalent to arr ** 2).
exp	Compute the exponent e^x of each element.
log, log10, log2, log1p	Compute the natural logarithm (base e), log base 10, log base 2, and log(1 + x) respectively.
sign	Compute the sign of each element: 1 (positive), 0 (zero), or –1 (negative).
ceil	Compute the ceiling of each element (i.e., the smallest integer greater than or equal to the number).
floor	Compute the floor of each element (i.e., the largest integer less than or equal to the number).
rint	Round elements to the nearest integer, preserving the dtype.
modf	Return fractional and integral parts of an array as separate arrays.
isnan	Return a Boolean array indicating whether each value is NaN (Not a Number).
isfinite, isinf	Return a Boolean array indicating whether each element is finite (non-inf, non-NaN) or infinite, respectively.
cos, cosh, sin, sinh, tan, tanh	Regular and hyperbolic trigonometric functions.
arccos, arccosh, arcsin, arcsinh, arctan, arctanh	Inverse trigonometric functions.
logical_not	Compute the truth value of not x element-wise (equivalent to ~arr).

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Common Binary Ufuncs

Function	Description
add	Add corresponding elements in two arrays.
subtract	Subtract elements in the second array from the first array.
multiply	Multiply array elements element-wise.
divide, floor_divide	Divide or floor divide (truncating the remainder) element-wise.
power	Raise elements in the first array to powers indicated in the second array.
maximum, fmax	Element-wise maximum; fmax ignores NaN values.
minimum, fmin	Element-wise minimum; fmin ignores NaN values.
mod	Element-wise modulus (remainder of division).
copysign	Copy the sign of values in the second argument to values in the first argument.
greater, greater_equal, less, less_equal, equal, not_equal	Perform element-wise comparison, yielding a Boolean array (equivalent to infix operators: >, >=, <, <=, ==, !=).
logical_and	Compute the element-wise truth value of the AND (&) logical operation.
logical_or	Compute the element-wise truth value of the OR (`
logical_xor	Compute the element-wise truth value of the XOR (^) logical operation.

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These ufuncs provide powerful, efficient tools for performing element-wise operations on NumPy arrays.