Efficient array creation in numpy

Question

I am trying to create a three dimensional array, Tusing numpy defined as follows:

T_{i, j, k} = \delta_{i, k} - \delta{j, k}

where \delta_{i, j} is the Kronecker delta function (1 when i=j and 0 otherwise). I am wondering what the most efficient way to do this using numpy. I can create two three dimensional arrays using for loops and subtract them. But I suspect there is a quicker and more idiomatic method. Any help would be most appreciated.

Daniel · Accepted Answer · 2017-02-26 07:54:28Z

6

The equivalent to delta is eye in numpy:

delta = numpy.eye(5)
T = delta[:,None,:] - delta[None,:,:]

The None creates a ‹virtual› dimension (doesn't take any additional memory) used for broadcasting in numpy.

edited Feb 26, 2017 at 7:54

answered Feb 26, 2017 at 7:44

Daniel

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2 Comments

stableMatch Over a year ago

Awesome! Just so I can better understand this. Suppose I just wanted to create a three dimensional array X defined by X_{i, j, k} = X_{i, k} for all j. The first term in the above does not seem to do that as the first dimension must have length. How would I do that?

stableMatch Over a year ago

@gzc yes I think there is a typo. What we want is delta[:, None, :] - delta[None, :, :]

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