Solve matrix equation--documentation guide #23951
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Benchmark results from GitHub Actions Lower numbers are good, higher numbers are bad. A ratio less than 1 Significantly changed benchmark results (PR vs master) Significantly changed benchmark results (master vs previous release) before after ratio
[41d90958] [b1de2706]
<sympy-1.11.1^0>
- 1.26±0.03ms 837±20μs 0.66 solve.TimeSparseSystem.time_linear_eq_to_matrix(10)
- 3.65±0.1ms 1.59±0.05ms 0.44 solve.TimeSparseSystem.time_linear_eq_to_matrix(20)
- 7.23±0.3ms 2.25±0.1ms 0.31 solve.TimeSparseSystem.time_linear_eq_to_matrix(30)
Full benchmark results can be found as artifacts in GitHub Actions |
Remove inapplicable no-solution sections
Could not lex literal_block as "py".
Start Symbolic Matrix section
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Note to self: Just waiting on #23802 to be merged, then will link to |
Merge master into matrix.
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| ⎣c⋅e d ⎦ | ||
| >>> b = Matrix([2, 0]) | ||
| >>> A.LUsolve(b) |
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Have you introduced this above? Probably should explain the difference in .solve() somewhere before.
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Per your other comment about LUsolve, I now introduce LUsolve earlier.
Probably should explain the difference in
.solve()somewhere before.
I added a section Methods for Solving Matrix Equations, noting that Gauss-Jordan elimination is the default method, and another method is LU decomposition (via solve with method='LU', or LUsolve).
I think my earlier query to you, which method is best for a given kind of matrix (hermitian, symmetric, or triangular), will address this question?
that inverse can be much slower than LUsolve
| with the same number of unknowns as equations. If not, SymPy will give the error | ||
| ``ShapeError: `self` and `rhs` must have the same number of rows.`` | ||
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| The exception to the requirement that a matrix be square comes from SymPy's use |
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@moorepants If there's a concise explanation of what circumstances the Moore-Penrose pseudoinverse allows for a non-square matrix under, I would appreciate you sharing it. (That's beyond my math knowledge.) Thanks!
| - If matrix elements are zero, ensure that they are recognized as zero. You can | ||
| do this by either making them zero or by applying | ||
| [assumptions](assumptions_module). | ||
| - Selecting a solve method suited to the properties of the matrix, for example |
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@moorepants Are there specific solving functions, or flags for solving functions, that we should recommend to users who have those kinds of matrix (hermitian, symmetric, triangular, etc.)?
Add section Methods for Solving Matrix Equations
References to other Issues or PRs
Brief description of what is fixed or changed
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Release Notes