How to create a meshgrid with NumPy

A coordinate grid turns separate x and y vectors into aligned arrays, so a formula can evaluate every coordinate pair with NumPy array operations. The np.meshgrid() function fits contour data, sampled surfaces, and other calculations where rows represent y positions and columns represent x positions.

The default indexing=“xy” convention returns two-dimensional arrays with shape (len(y), len(x)). Values from x repeat across rows, while values from y repeat down columns. Use indexing=“ij” when downstream code expects the first array axis to follow the first input vector instead.

Dense grids allocate a full array for every coordinate direction. With sparse=True, each coordinate keeps singleton dimensions and expands through broadcasting only when it participates in a calculation; the calculated surface is still a full two-dimensional array.

1. Create meshgrid-create.py with the x and y coordinate vectors.

   meshgrid-create.py

   import numpy as np
    
   x = np.array([0, 1, 2])
   y = np.array([10, 20])

2. Add the dense Cartesian grid and its output below the coordinate vectors.

   xx, yy = np.meshgrid(x, y, indexing="xy")
    
   print("xy grid shapes:", xx.shape, yy.shape)
   print("xx:")
   print(xx)
   print("yy:")
   print(yy)

3. Run the partial script to confirm the Cartesian grid orientation.

   $ python meshgrid-create.py
   xy grid shapes: (2, 3) (2, 3)
   xx:
   [[0 1 2]
    [0 1 2]]
   yy:
   [[10 10 10]
    [20 20 20]]

   The two y coordinates determine the rows, and the three x coordinates determine the columns under indexing=“xy”.

4. Complete meshgrid-create.py with the surface calculation, matrix-indexed grid, sparse grid, and assertions.

   meshgrid-create.py

   import numpy as np
    
   x = np.array([0, 1, 2])
   y = np.array([10, 20])
    
   xx, yy = np.meshgrid(x, y, indexing="xy")
   surface = xx + yy
    
   ii, jj = np.meshgrid(x, y, indexing="ij")
    
   xs, ys = np.meshgrid(x, y, indexing="xy", sparse=True)
   sparse_surface = xs + ys
    
   assert xx.shape == (2, 3)
   assert yy.shape == (2, 3)
   assert surface.shape == (2, 3)
   assert ii.shape == (3, 2)
   assert jj.shape == (3, 2)
   assert xs.shape == (1, 3)
   assert ys.shape == (2, 1)
   assert np.array_equal(surface, sparse_surface)
    
   print("xy grid shapes:", xx.shape, yy.shape)
   print("xx:")
   print(xx)
   print("yy:")
   print(yy)
   print("surface:")
   print(surface)
   print("ij grid shapes:", ii.shape, jj.shape)
   print("sparse grid shapes:", xs.shape, ys.shape)
   print("sparse matches dense:", np.array_equal(surface, sparse_surface))

   indexing=“ij” produces shape (3, 2) because its first axis follows x. The sparse arrays use shapes (1, 3) and (2, 1), which broadcast to the same (2, 3) surface.
   Related: Calculate with broadcasting

5. Run the completed script to execute the shape and equality assertions.

   $ python meshgrid-create.py
   xy grid shapes: (2, 3) (2, 3)
   xx:
   [[0 1 2]
    [0 1 2]]
   yy:
   [[10 10 10]
    [20 20 20]]
   surface:
   [[10 11 12]
    [20 21 22]]
   ij grid shapes: (3, 2) (3, 2)
   sparse grid shapes: (1, 3) (2, 1)
   sparse matches dense: True