allow rhs in rref #25687

smichr · 2023-09-16T02:25:28Z

References to other Issues or PRs

#25661 related

Brief description of what is fixed or changed

Other comments

see issue page and the questions I raise there

Release Notes

matrices
- A.rref_rhs(b) will return rref of A and resulting form of b without reducing b; pivots are returned as 3rd arg

sympy-bot · 2023-09-16T02:25:34Z

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matrices
- A.rref_rhs(b) will return rref of A and resulting form of b without reducing b; pivots are returned as 3rd arg (#25687 by @smichr)

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#25661 related

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see issue page and the questions I raise there

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* matrices
  * `A.rref_rhs(b)` will return rref of A and resulting form of b without reducing b; pivots are returned as 3rd arg
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Update

The release notes on the wiki have been updated.

sympy/matrices/tests/test_reductions.py

sympy/matrices/reductions.py

github-actions · 2023-09-16T20:52:27Z

Benchmark results from GitHub Actions

Lower numbers are good, higher numbers are bad. A ratio less than 1
means a speed up and greater than 1 means a slowdown. Green lines
beginning with + are slowdowns (the PR is slower then master or
master is slower than the previous release). Red lines beginning
with - are speedups.

Significantly changed benchmark results (PR vs master)

Significantly changed benchmark results (master vs previous release)

| Change   | Before [8059df73] <sympy-1.12^0>   | After [781442f7]    |   Ratio | Benchmark (Parameter)                                                |
|----------|------------------------------------|---------------------|---------|----------------------------------------------------------------------|
| -        | 85.6±1ms                           | 56.9±0.2ms          |    0.67 | integrate.TimeIntegrationRisch02.time_doit(10)                       |
| -        | 85.8±1ms                           | 55.7±0.2ms          |    0.65 | integrate.TimeIntegrationRisch02.time_doit_risch(10)                 |
| +        | 22.6±0.07μs                        | 39.0±0.09μs         |    1.73 | integrate.TimeIntegrationRisch03.time_doit(1)                        |
| -        | 6.97±0.01ms                        | 3.74±0.01ms         |    0.54 | logic.LogicSuite.time_load_file                                      |
| -        | 4.25±1ms                           | 2.25±0ms            |    0.53 | polys.TimeGCD_LinearDenseQuadraticGCD.time_op(2, 'dense')            |
| -        | 2.11±0.01ms                        | 660±2μs             |    0.31 | polys.TimePREM_LinearDenseQuadraticGCD.time_op(3, 'sparse')          |
| -        | 10.3±0.02ms                        | 1.96±0.01ms         |    0.19 | polys.TimePREM_LinearDenseQuadraticGCD.time_op(5, 'sparse')          |
| -        | 367±0.8μs                          | 81.9±0.1μs          |    0.22 | polys.TimePREM_QuadraticNonMonicGCD.time_op(1, 'sparse')             |
| -        | 4.84±0.01ms                        | 364±0.8μs           |    0.08 | polys.TimePREM_QuadraticNonMonicGCD.time_op(3, 'sparse')             |
| -        | 10.6±0.02ms                        | 1.10±0ms            |    0.1  | polys.TimePREM_QuadraticNonMonicGCD.time_op(5, 'sparse')             |
| -        | 6.23±0.02ms                        | 3.95±0.01ms         |    0.63 | polys.TimeSUBRESULTANTS_LinearDenseQuadraticGCD.time_op(2, 'sparse') |
| -        | 27.1±0.05ms                        | 12.1±0.02ms         |    0.44 | polys.TimeSUBRESULTANTS_LinearDenseQuadraticGCD.time_op(3, 'sparse') |
| -        | 6.95±0.02ms                        | 1.18±0ms            |    0.17 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(1, 'sparse')    |
| -        | 16.2±0.02ms                        | 9.22±0.02ms         |    0.57 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(2, 'sparse')    |
| -        | 211±0.3ms                          | 70.7±0.2ms          |    0.33 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(3, 'sparse')    |
| -        | 6.38±0.01ms                        | 535±1μs             |    0.08 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(3, 'sparse')     |
| -        | 27.7±0.05ms                        | 857±2μs             |    0.03 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(5, 'sparse')     |
| -        | 613±2μs                            | 199±1μs             |    0.32 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(1, 'sparse') |
| -        | 6.48±0.01ms                        | 201±0.9μs           |    0.03 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(3, 'sparse') |
| -        | 17.1±0.04ms                        | 205±0.9μs           |    0.01 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(5, 'sparse') |
| -        | 164±0.1μs                          | 89.0±0.2μs          |    0.54 | solve.TimeMatrixOperations.time_rref(3, 0)                           |
| -        | 316±0.4μs                          | 107±0.7μs           |    0.34 | solve.TimeMatrixOperations.time_rref(4, 0)                           |
| -        | 31.6±0.06ms                        | 13.5±0.03ms         |    0.43 | solve.TimeSolveLinSys189x49.time_solve_lin_sys                       |

Full benchmark results can be found as artifacts in GitHub Actions
(click on checks at the top of the PR).

oscarbenjamin · 2023-09-16T22:02:16Z

What about having a separate function like rref_aug or rref_rhs or something?

sylee957 · 2023-09-16T22:03:28Z

I wanted to vote about the idea to have separate function, especially if the structure of return is dependent on some parameters.

donnaaboise · 2023-09-17T16:57:14Z

Thanks for SymPy developers for looking into this!

I haven't actually tested the PR, but do have the following questions/comments :

Does this PR handle the case that @smichr pointed out? That is, the case in the pivot rows are not the first r=A.rank() rows? A fix would be to allow row exchanges. It seems that A.rref() already does row exchanges and can handle, for example, Matrix([[0,0],[0,1]]). Can this PR get at the row permutations needed? (my original approach failed with this matrix).

sympy/matrices/matrices.py

smichr · 2023-09-17T18:57:21Z

Thanks for SymPy developers for looking into this!

I haven't actually tested the PR, but do have the following questions/comments :

Does this PR handle the case that @smichr pointed out? That is, the case in the pivot rows are not the first r=A.rank() rows? A fix would be to allow row exchanges. It seems that A.rref() already does row exchanges and can handle, for example, Matrix([[0,0],[0,1]]). Can this PR get at the row permutations needed? (my original approach failed with this matrix).

Yes, this case is handled and the rank calculation is omitted. @sylee957 pointed out that simply satcking a full identity matrix is a more robust aproach.

sylee957 · 2023-09-17T21:56:54Z

sympy/matrices/reductions.py

+    rhs : Matrix
+        If ``rhs`` is passed it must have the same number of rows as ``M``.
+        Reduction steps will not take place in this matrix, but
+        the elements will be included in the reduction steps. If a single
+        column matrix of symbols is passed, the expressions in each
+        row at the end of the reduction will indicate how rows were
+        combined to perform the reduction.


Unfortunately, I missed this point that this should move to the documentation in rref_rhs. This option should not be carried by rref.__doc__ = _rref.__doc__

I will make new pr. Sorry I missed that.

oscarbenjamin · 2023-09-17T22:05:32Z

Thanks everyone!

sylee957 reviewed Sep 16, 2023

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smichr force-pushed the rref branch from 6616481 to 3365dd4 Compare September 16, 2023 04:12

allow rhs in rref

6fedaa8

smichr force-pushed the rref branch from 3365dd4 to 6fedaa8 Compare September 16, 2023 04:20

sylee957 reviewed Sep 16, 2023

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sylee957 reviewed Sep 16, 2023

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review edits

25d5167

oscarbenjamin added the matrices label Sep 16, 2023

smichr marked this pull request as ready for review September 17, 2023 00:09

smichr force-pushed the rref branch from 7e41f58 to c1ed7b7 Compare September 17, 2023 00:13

introduce rref_rhs

0320e2e

smichr force-pushed the rref branch from c1ed7b7 to 0320e2e Compare September 17, 2023 00:14

smichr mentioned this pull request Sep 17, 2023

allow for rhs matrix to be passed to rref #25661

Open

oscarbenjamin reviewed Sep 17, 2023

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rref_rhs accepts only rhs as arg

a9a6d07

sylee957 merged commit 29c5514 into sympy:master Sep 17, 2023

sylee957 reviewed Sep 17, 2023

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smichr deleted the rref branch September 17, 2023 21:58

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