Numpy Utilities

Some extended utility functions for ‘numpy’ module.

numpy_utils.meshgrid_nd(*arrs)

Multi-dimensional meshgrid.

Parameters:

x, y, z, ...: ndarray

Multiple 1-D arrays representing the coordinates of the grid.

Returns:

X, Y, Z, ... : ndarray

Multi-dimensional arrays of shape (len(x), len(y), len(z), ...). Note that there is a discrepancy to the original 2D meshgrid, where the output array shape is swapped, i.e. (len(y), len(x)). Specifically, if:

X, Y = meshgrid(x, y)
X2, Y2 = meshgrid_nd(x, y)

then we have X == X2.T and Y == Y2.T.

Examples

>>> X, Y, Z = np.meshgrid([1,2,3], [10,20], [-2,-3,-4,-5])
>>> X
array([[[1, 1, 1, 1],
        [1, 1, 1, 1]],
       [[2, 2, 2, 2],
        [2, 2, 2, 2]],
       [[3, 3, 3, 3],
        [3, 3, 3, 3]]])
>>> Y
array([[[10, 10, 10, 10],
        [20, 20, 20, 20]],
       [[10, 10, 10, 10],
        [20, 20, 20, 20]],
       [[10, 10, 10, 10],
        [20, 20, 20, 20]]])
>>> Z
array([[[-2, -3, -4, -5],
        [-2, -3, -4, -5]],
       [[-2, -3, -4, -5],
        [-2, -3, -4, -5]],
       [[-2, -3, -4, -5],
        [-2, -3, -4, -5]]])

numpy_utils.null(A, tol=1e-12)

Return the null space of matrix or vector A, such that:

dot(A, null(A)) == eps(M, N)

Each column r of null(A) is a unit vector, and ||dot(A, r)|| < tol.