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# numpy.meshgrid

numpy.meshgrid(*xi, copy=True, sparse=False, indexing='xy')

  Return a tuple of coordinate matrices from coordinate vectors.

  Make N-D coordinate arrays for vectorized evaluations of N-D scalar/vector fields over N-D grids, given one-dimensional coordinate arrays x1, x2,…, xn.

  Parameters:
    x1, x2,…, xn array_like

      1-D arrays representing the coordinates of a grid.

    indexing{‘xy’, ‘ij’}, optional

      Cartesian (‘xy’, default) or matrix (‘ij’) indexing of output. See Notes for more details.

    sparse bool, optional

      If True the shape of the returned coordinate array for dimension i is reduced from `(N1, ..., Ni, ... Nn)` to `(1, ..., 1, Ni, 1, ..., 1)`. These sparse coordinate grids are intended to be used with Broadcasting. When all coordinates are used in an expression, broadcasting still leads to a fully-dimensional result array.

      Default is False.

    copy bool, optional

      If False, a view into the original arrays are returned in order to conserve memory. Default is True. Please note that `sparse=False, copy=False` will likely return non-contiguous arrays. Furthermore, more than one element of a broadcast array may refer to a single memory location. If you need to write to the arrays, make copies first.

  Returns:
    X1, X2,…, XN tuple of ndarrays

      For vectors x1, x2,…, xn with lengths `Ni=len(xi)`, returns `(N1, N2, N3,..., Nn)` shaped arrays if indexing=’ij’ or `(N2, N1, N3,..., Nn)` shaped arrays if indexing=’xy’ with the elements of xi repeated to fill the matrix along the first dimension for x1, the second for x2 and so on.

  See also

  `mgrid`

    Construct a multi-dimensional “meshgrid” using indexing notation.

  `ogrid`

    Construct an open multi-dimensional “meshgrid” using indexing notation.

  How to index ndarrays

  Notes

  This function supports both indexing conventions through the indexing keyword argument. Giving the string ‘ij’ returns a meshgrid with matrix indexing, while ‘xy’ returns a meshgrid with Cartesian indexing. In the 2-D case with inputs of length M and N, the outputs are of shape (N, M) for ‘xy’ indexing and (M, N) for ‘ij’ indexing. In the 3-D case with inputs of length M, N and P, outputs are of shape (N, M, P) for ‘xy’ indexing and (M, N, P) for ‘ij’ indexing. The difference is illustrated by the following code snippet:

      xv, yv = np.meshgrid(x, y, indexing='ij')
      for i in range(nx):
          for j in range(ny):
              # treat xv[i,j], yv[i,j]

      xv, yv = np.meshgrid(x, y, indexing='xy')
      for i in range(nx):
          for j in range(ny):
              # treat xv[j,i], yv[j,i]

  In the 1-D and 0-D case, the indexing and sparse keywords have no effect.

  Examples

      >>> import numpy as np
      >>> nx, ny = (3, 2)
      >>> x = np.linspace(0, 1, nx)
      >>> y = np.linspace(0, 1, ny)
      >>> xv, yv = np.meshgrid(x, y)
      >>> xv
      array([[0. , 0.5, 1. ],
             [0. , 0.5, 1. ]])
      >>> yv
      array([[0.,  0.,  0.],
             [1.,  1.,  1.]])

  The result of `meshgrid` is a coordinate grid:

      >>> import matplotlib.pyplot as plt
      >>> plt.plot(xv, yv, marker='o', color='k', linestyle='none')
      >>> plt.show()

  You can create sparse output arrays to save memory and computation time.

      >>> xv, yv = np.meshgrid(x, y, sparse=True)
      >>> xv
      array([[0. ,  0.5,  1. ]])
      >>> yv
      array([[0.],
             [1.]])

  `meshgrid` is very useful to evaluate functions on a grid. If the function depends on all coordinates, both dense and sparse outputs can be used.

      >>> x = np.linspace(-5, 5, 101)
      >>> y = np.linspace(-5, 5, 101)
      >>> # full coordinate arrays
      >>> xx, yy = np.meshgrid(x, y)
      >>> zz = np.sqrt(xx**2 + yy**2)
      >>> xx.shape, yy.shape, zz.shape
      ((101, 101), (101, 101), (101, 101))
      >>> # sparse coordinate arrays
      >>> xs, ys = np.meshgrid(x, y, sparse=True)
      >>> zs = np.sqrt(xs**2 + ys**2)
      >>> xs.shape, ys.shape, zs.shape
      ((1, 101), (101, 1), (101, 101))
      >>> np.array_equal(zz, zs)
      True

      >>> h = plt.contourf(x, y, zs)
      >>> plt.axis('scaled')
      >>> plt.colorbar()
      >>> plt.show()