mike0609king opened a new pull request, #2559:
URL: https://github.com/apache/systemds/pull/2559
This PR introduces broadcasting ifelse as well as optimizations for certain
cases. The broadcasting is done such that the resulting values are the maximum
rows and columns of the inputs.
The following optimizations have been implemented
- the previous optimization for scalar values and certain non zero entries
have been extended to contain broadcasting behavior
- if the first input matrix block is a column vector, then the entire row of
either second or third input matrix block can be copied to the result matrix.
- if the first input matrix block is a row vector, then the entire column of
either second or third input matrix block can be copied to the resulting
matrix. The benchmarks also for larger matrices have shown, that this
optimization is effective although we are iterating column first. Note that
this seems to be effective although it is not good for caching.
**Measurements.** In the following benchmarks a row size of 2111 and column
size of 300 have been used. Note that multiple tests are run for each
optimization (around 30 for each); the median value is displayed to be more
robust to outliers.
- Scalar optimization. In this case we are testing all test cases involving
a scalar as first input and comparing them. Meaning we only test components
`**.functions.ternary.FullIfElseTest#testScalar*`
- Without optimization: 0.024s
- With optimization: 0.000s (mean was 0.003s)
- Row optimization. In this case we test the row vector optimization,
meaning we only run the tests `**.functions.ternary.FullIfElseTest#testRow*`
- Without optimization: 0.074s
- With optimization: 0.035s
- Column optimization. In this case we test the column vector optimization,
meaning we only run the tests `**.functions.ternary.FullIfElseTest#testCol*`
- Without optimization: 0.068s
- With optimization: 0.038s
- Overall. This executes all tests in `**.functions.ternary.FullIfElseTest`
with and without optimizations
- Without optimization: 0.069s
- With optimization: 0.027s
**Column optimization case.** Running larger matrices for all tests took
extremely long. This is why I only did this for the column case, which deserved
to be scrutinized more. The `testColMatrixMatrixDenseCP` test with a row size
of 4111 and column size of 3000 was executed out with and without optimization
the optimized version ran in 0.838s and the one without optimization required
1.547s. Other seeds for the matrix yielded similar results.
Additional comments
- The eps value in the tests were set to `1e-10` otherwise there are errors
with the matrix comparisons. This issue seems to be present in other tests such
as the `FullTransposeTest` as well. Maybe some exact values get lost while
matrices are stored in files due to compression.
- Tests have been implemented for every matrix, row vector, column vector
and scalar value combination. Those tests were of cause not generated by hand
by instead by a python script to avoid human error. Same for the aggregation of
the measurements above.
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