Linspace

Linspace is a numerical utility used to generate a sequence of evenly spaced numbers over a specified interval. It is a common function in scientific computing libraries and is found in environments such as MATLAB and NumPy. The function helps create grids for plotting, integration, and numerical methods by providing a predictable, evenly distributed set of sample points.

In MATLAB, linspace(a, b, n) returns a row vector of n evenly spaced values starting at a and ending at b, inclusive. If n is omitted, a default of 100 points is generated. The values are computed so that the distance between consecutive elements is constant, and the endpoints are included.

In NumPy, the equivalent is numpy.linspace(start, stop, num=50, endpoint=True, retstep=False, dtype=None, axis=0). It returns a one-dimensional array of num evenly spaced samples over the interval [start, stop] by default. The endpoint parameter controls whether stop is included. The retstep option can also return the spacing between samples. The dtype parameter allows for a specific numeric type, and axis determines the axis along which samples are generated.

The spacing is determined as follows: when endpoint is True, step = (stop - start) / (num - 1); when endpoint is False, step = (stop - start) / num. Floating point rounding can cause small deviations from exact endpoints.

Linspace is commonly used for plotting, numerical integration grids, and tests that require evenly distributed samples across an interval.