How to create linearly spaced values with NumPy

Evenly spaced coordinates keep plots, interpolation points, and simulation inputs tied to a fixed sample count. NumPy np.linspace() creates those values from interval endpoints, so the result can include the right boundary without calculating the step by hand.

Unlike np.arange(), which advances by a step size, np.linspace() starts from the number of samples to return. The default output is floating point, and retstep=True exposes the spacing NumPy used for the interval.

Choose endpoint=False for half-open intervals such as periodic bins where the stop value would duplicate the next cycle. Checking the size, spacing, and adjacent differences before reusing the array catches off-by-one mistakes while the sample grid is still small.

1. Create a Python script that builds a closed interval, a half-open interval, and a calculation that uses the generated samples.

   linear-spacing-create.py

   import numpy as np
    
   samples, spacing = np.linspace(-1.0, 1.0, num=5, retstep=True)
   half_open = np.linspace(-1.0, 1.0, num=5, endpoint=False)
   curve = samples**2
    
   print("samples:", samples)
   print("count:", samples.size)
   print("spacing:", spacing)
   print("dtype:", samples.dtype)
   print("diffs:", np.diff(samples))
   print("half-open:", half_open)
   print("curve:", curve)

   retstep=True returns the generated array and the spacing between adjacent samples.

2. Run the script.

   $ python linear-spacing-create.py
   samples: [-1.  -0.5  0.   0.5  1. ]
   count: 5
   spacing: 0.5
   dtype: float64
   diffs: [0.5 0.5 0.5 0.5]
   half-open: [-1.  -0.6 -0.2  0.2  0.6]
   curve: [1.   0.25 0.   0.25 1.  ]

3. Check the closed interval output.

   The samples row has five values, reaches both -1.0 and 1.0, and the diffs row confirms the same 0.5 spacing between adjacent values.

4. Compare the half-open interval output before using endpoint=False.

   The half-open row still has five values, but 1.0 is excluded and the spacing changes to 0.4 across the half-open interval.

5. Keep the default floating dtype unless integer rounding is intended.

   Supplying an integer dtype rounds generated values. Keep a floating array for plotting, interpolation, and simulations that need fractional coordinates.

6. Verify that the generated samples feed the next calculation.

   The curve row is samples**2 calculated from the same linearly spaced coordinates.