Evaluate array at specific subarray

Question

I warn in advance: I may be utterly confused at the moment. I tell a short story about what I actually try to achieve because that may clear things up. Say I have `f(a,b,c,d,e)`, and I want to find `arg max (d,e) f(a,b,c,d,e)`. Consider a (trivial example of a ) discretized grid `F` of `f`: ``` F = np.tile(np.arange(0,10,0.1)[newaxis,newaxis,:,newaxis,newaxis], [10, 10, 1, 10, 10]) maxE = F.max(axis=-1) argmaxD = maxE.argmax(axis=-1) maxD = F.max(axis=-2) argmaxE = maxD.argmax(axis=-1) ``` This is the case how I typically solve the discretized version. But now assume instead, that I want to solve `arg max d f(a,b,c,d,e=X)`: Instead of optimally chosen `e` for every other input, `e` is a fixed and given (of size AxBxCxD, which in this example would be `10x10x100x10`). I have troubles solving this. My naive approach was ``` X = np.tile(np.arange(0,10)[newaxis,newaxis,:,newaxis], [10,10,1,10]) maxX = F[X] argmaxD = maxX.argmax(axis=-1) ``` However, the huge surge of memory that crashes m…

Accepted Answer

I believe you can do it like this, but maybe there's a better way..

```
n = 10
F = np.tile(np.arange(0,n,0.1)[None,None,:,None,None], [n, n, 1, n, n])
X = np.tile(np.arange(0,n)[None,None,:,None], [n, n, 1, n])

a,b,c,d = np.ogrid[:n,:n,:n,:n]
argmaxD = F[a,b,c,d,X].argmax(axis=-1)
```

Above `X` doesn't occupy the whole space, as we discussed in the comments. If you would like to choose `e` for all `a`,`b`,`c` and `d` you could do e.g.:

```
X = np.tile(np.arange(0,n,0.1).astype(int)[None,None,:,None], [n, n, 1, n])
a,b,c,d = np.ogrid[:n,:n,:100,:n]
argmaxD = F[a,b,c,d,X].argmax(axis=-1)
```

Also, notice that instead of `tile` you could make use of broadcasting. But then `F[a,b,c,d,X]` has a singular dimension so you should provide something like `axis=3`:

```
X = np.arange(0,n,0.1).astype(int)[None,None,:,None]
a,b,c,d = np.ogrid[:n,:n,:100,:n]
argmaxD = F[a,b,c,d,X].argmax(axis=3)
```

Evaluate array at specific subarray

Solution

Problem