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Introduce Option for Custom Jacobian Function in physics.mechanics Linearizer
References to Other Issues or PRs
This PR is based on the modifications introduced in PR #26773.
Brief Description of What Is Fixed or Changed
This PR introduces an enhancement to the Linearizer class by allowing users to specify a custom function for Jacobian computation. Previously, the Jacobian was always computed using matrixbase's jacobian() method. With this update, users can now pass their own Jacobian function when calling the to_linearizer() method from Kane's or Lagrange's methods, providing greater flexibility and customization in the linearization process. By default the methods use the function _forward_jacobian().
Other Comments
I have doubts on the backward-compatibility as the jacobian() method is not anymore the default method used in the lineariser.
Release Notes
- physics.mechanics
- Added the ability to specify a custom Jacobian function in the
Linearizerclass. - Enhanced the
to_linearizer()method to accept a custom Jacobian function when invoked from Kane's or Lagrange's methods.
- Added the ability to specify a custom Jacobian function in the
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#### References to Other Issues or PRs
This PR is based on the modifications introduced in PR #26773.
#### Brief Description of What Is Fixed or Changed
This PR introduces an enhancement to the `Linearizer` class by allowing users to specify a custom function for Jacobian computation. Previously, the Jacobian was always computed using matrixbase's jacobian() method. With this update, users can now pass their own Jacobian function when calling the `to_linearizer()` method from Kane's or Lagrange's methods, providing greater flexibility and customization in the linearization process. By default the methods use the function _forward_jacobian().
#### Other Comments
I have doubts on the backward-compatibility as the jacobian() method is not anymore the default method used in the lineariser.
#### Release Notes
<!-- BEGIN RELEASE NOTES -->
* physics.mechanics
* Added the ability to specify a custom Jacobian function in the `Linearizer` class.
* Enhanced the `to_linearizer()` method to accept a custom Jacobian function when invoked from Kane's or Lagrange's methods.
<!-- END RELEASE NOTES -->
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Considerations about bicycle_example.rst
As can be observed from the automatic tests, there is a discrepancy between the expected values and the obtained values for the bicycle example in doc/src/tutorials/physics/mechanics/.
The expected values used in the test are taken from the paper Meijaard 2007.
To understand whether the discrepancy observed when running the test using the new forward_jacobian function inside the linearizer represents a problem, I summarize the findings in the following table:
| Source | v | Complex Eigenvalue (Real) | Complex Eigenvalue (Imaginary) | Real Eigenvalue 1 | Real Eigenvalue 2 |
|---|---|---|---|---|---|
| norm_jac | 1 | 3.52696170990069 | -0.807740275199311 | -3.13423125066578 | -7.11008014637441 |
| meijaard | 1 | 3.52696170990070 | -0.80774027519930 | -3.13423125066578 | -7.11008014637442 |
| new_jac | 1 | 3.52696170990069 | -0.807740275199311 | -3.13423125066578 | -7.11008014637441 |
| norm_jac | 2 | 2.68234517512745 | -1.68066296590676 | -3.07158645641514 | -8.67387984831737 |
| meijaard | 2 | 2.68234517512745 | -1.68066296590675 | -3.07158645641514 | -8.67387984831735 |
| norm_jac | 3 | 1.70675605663973 | -2.31582447384324 | -2.63366137253665 | -10.3510146724592 |
| meijaard | 3 | 1.70675605663975 | -2.31582447384325 | -2.63366137253667 | -10.35101467245920 |
| norm_jac | 4 | 0.413253315211239 | -3.07910818603205 | -1.42944427361326 | -12.1586142657644 |
| meijaard | 4 | 0.41325331521125 | -3.07910818603206 | -1.42944427361326 | -12.15861426576447 |
| new_jac | 4 | 0.413253315211238 | -3.07910818603205 | -1.42944427361326 | -12.1586142657644 |
| norm_jac | 5 | -0.775341882195845 | -4.46486771378823 | -0.322866429004087 | -14.0783896927982 |
| meijaard | 5 | -0.77534188219585 | -4.46486771378823 | -0.32286642900409 | -14.07838969279822 |
| new_jac | 5 | -0.775341882195846 | -4.46486771378823 | -0.322866429004085 | -14.0783896927982 |
In the table the current expected values are identified by: norm_jac, the values from the paper are identified as: meijaard, and the values that I obtained are identified by: new_jac.
There is also another discrepancy, regarding values of matrix A:
- The first two rows are identical in both matrices.
- In the third row, the discrepancy is in the first element:
- Expected: 9.48977444677355
- Got: 9.48977444677356
- The fourth row is identical in both matrices.
Note: I am not considering the obtained discrepancies between very low values (1e-64) becasue I don’t think they are relevant
It seems that by truncating just after the 13th decimal digit all the results should match. What are your thought on this? @tjstienstra @moorepants
You can merge in master into this branch to remove all the commits from the first PR.
Make a unit test that shows the new options work in the three locations.