I feel your pain… You sometimes end up storing several times the size of your array in values you will later discard. When processing one item in your array at a time, this is irrelevant, but can kill you when vectorizing.
I’ll use an example from work for illustration purposes. I recently coded the algorithm described here using numpy. It is a color map algorithm, which takes an RGB image, and converts it into a CMYK image. The process, which is repeated for every pixel, is as follows:
- Use the most significant 4 bits of every RGB value, as indices into a three-dimensional look up table. This determines the CMYK values for the 8 vertices of a cube within the LUT.
- Use the least significant 4 bits of every RGB value to interpolate within that cube, based on the vertex values from the previous step. The most efficient way of doing this requires computing 16 arrays of uint8s the size of the image being processed. For a 24bit RGB image that is equivalent to needing storage of x6 times that of the image to process it.
A couple of things you can do to handle this:
1. Divide and conquer
Maybe you cannot process a 1,000×1,000 array in a single pass. But if you can do it with a python for loop iterating over 10 arrays of 100×1,000, it is still going to beat by a very far margin a python iterator over 1,000,000 items! It´s going to be slower, yes, but not as much.
2. Cache expensive computations
This relates directly to my interpolation example above, and is harder to come across, although worth keeping an eye open for it. Because I am interpolating on a three-dimensional cube with 4 bits in each dimension, there are only 16x16x16 possible outcomes, which can be stored in 16 arrays of 16x16x16 bytes. So I can precompute them and store them using 64KB of memory, and look-up the values one by one for the whole image, rather than redoing the same operations for every pixel at huge memory cost. This already pays-off for images as small as 64×64 pixels, and basically allows processing images with x6 times the amount of pixels without having to subdivide the array.
3. Use your dtypes wisely
If your intermediate values can fit in a single uint8, don’t use an array of int32s! This can turn into a nightmare of mysterious errors due to silent overflows, but if you are careful, it can provide a big saving of resources.