mars.tensor.
meshgrid
Return 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 tensors x1, x2,…, xn.
x1 (array_like) – 1-D arrays representing the coordinates of a grid.
x2 (array_like) – 1-D arrays representing the coordinates of a grid.
.. (array_like) – 1-D arrays representing the coordinates of a grid.
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 a sparse grid is returned in order to conserve memory. Default is False.
X1, X2,…, XN – For vectors x1, x2,…, ‘xn’ with lengths Ni=len(xi) , return (N1, N2, N3,...Nn) shaped tensors if indexing=’ij’ or (N2, N1, N3,...Nn) shaped tensors 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.
Ni=len(xi)
(N1, N2, N3,...Nn)
(N2, N1, N3,...Nn)
Tensor
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 = mt.meshgrid(x, y, sparse=False, indexing='ij') for i in range(nx): for j in range(ny): # treat xv[i,j], yv[i,j] xv, yv = mt.meshgrid(x, y, sparse=False, 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 mars.tensor as mt
>>> nx, ny = (3, 2) >>> x = mt.linspace(0, 1, nx) >>> y = mt.linspace(0, 1, ny) >>> xv, yv = mt.meshgrid(x, y) >>> xv.execute() array([[ 0. , 0.5, 1. ], [ 0. , 0.5, 1. ]]) >>> yv.execute() array([[ 0., 0., 0.], [ 1., 1., 1.]]) >>> xv, yv = mt.meshgrid(x, y, sparse=True) # make sparse output arrays >>> xv.execute() array([[ 0. , 0.5, 1. ]]) >>> yv.execute() array([[ 0.], [ 1.]])
meshgrid is very useful to evaluate functions on a grid.
>>> import matplotlib.pyplot as plt >>> x = mt.arange(-5, 5, 0.1) >>> y = mt.arange(-5, 5, 0.1) >>> xx, yy = mt.meshgrid(x, y, sparse=True) >>> z = mt.sin(xx**2 + yy**2) / (xx**2 + yy**2) >>> h = plt.contourf(x,y,z)