change code so KanesMethod will find nonlinearities in speed constraints

[Peter230655]

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• physics.mechanics
  • KanesMethod allows for linear speed constraints, however it does not check whether they really are linear. It does test the kinematic differential equations for linearity. So, I simply copied the few lines of code there and added them around line 320

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• physics.mechanics
  • KanesMethod requires linear speed constraints, but it does not check whether they indeed are linear. Using linear_eq_to_matrix instead of the Jacobian serves two purposes: 1) it makes solving the constraints faster and 2) it will raise an error in the speed constraints are not linear. (#26900 by @Peter230655)

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* physics.mechanics
  * KanesMethod requires linear speed constraints, but it does not check whether they indeed are linear. Using _linear_eq_to_matrix_ instead of the Jacobian serves two purposes: 1) it makes solving the constraints faster and 2) it will raise an error in the speed constraints are not linear.

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[smichr]

A test that catches this error should be added.

[Peter230655]

I checked the speeds with my 40 link closed pendulum, as suggested: ( since the code for checking the linearity of the kinematic DEs is part of KanesMethod, and since I simply copied this code, I was hoping the time consumed would be similar - which it was in this example)

• checking for linearity of the kinematic DEs: 0.0 sec
• checking for linearity of the velocity constraints: 0.0sec to 0.01sec

It takes about 35 sec to set up KanesEquations in this example. I tested like this:

zeit = time.time()
code to be checked
......
......
duration = time.time() - zeit

[Peter230655]

A test that catches this error should be added.

You added the label PR: author's turn. I am unclear what changes I should submit. Thanks!

[moorepants]

Doesn't the 40 link pendulum not have any speed constraints? What are you checking in that case?

[Peter230655]

I used the version where the other end is also attached to a point. Sorry, should hsve mentioned it.

[moorepants]

I am unclear what changes I should submit.

@smichr wrote "A test that catches this error should be added."

[Peter230655]

I am unclear what changes I should submit.

@smichr wrote "A test that catches this error should be added."

I did make a test, it is PR # 26901, maybe this is why I did not understand what was meant. Is this o.k.?

[moorepants]

The test needs to be in the same PR as the change, i.e. this PR.

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The following commits add new files:

• e2f3773b7be23a97703713602ece473a253e8ca6:
  • sympy/physics/mechanics/tests/test_linearity_of_velocity_constraints.py

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[Peter230655]

I added the test for nonlinearity of velocity constraints to this PR, I will close the other PR, which only held the test

[Peter230655]

I checked the time needed to check the velocity constrains for nonlinearity again, using an old simulation of mine. Basically the skateboard of your lecture, modified a bit. It has 6 velocity constraints. Checking for nonlinearity took between 0.0 sec and 0.002 sec, total time to get kanes eoms took 1.3 sec. I used the same method mentioned abvoe to check for the time:

zeit = time.time()
code to check for nonlinearity
.....
....
time_needed = time.tim() - zeit

I also made the velocity constraints nonlinear, and as I hoped, it caught it.

[Peter230655]

I managed the linear_eq_to_matrix part. But it seems, that the method must be change at other places. On the other had, it seems to cut the time needed by around 50% from 0.36 sec to 0.17sec. Worth pursuing? If yes, I guess this would be a new PR, as the idea has changed: speed up calculating the velocity constraints.

[moorepants]

It doesn't need a new pr, but you can change the title to reflect what it has become.

[Peter230655]

It doesn't need a new pr, but you can change the title to reflect what it has become.

I will do so, if I get it going. :-)

[Peter230655]

It seems to work, and definitely 50% to 80% faster, but I am running in this problem: linear_eq_to_matrix raises a PolyNonlinearError and a NonlinearError, but neither one seems 'defined': When I write

try:
    code
    ......
except NonlinearError as e:
    raise NonlineaeError('message')

I get the message NonlinearError is not defined or similar. Same with

with pytest.raises(NonlinearError):

So, I do not know how to write the test, which does not stop if the speed constraints are nonlinear. Thanks for any help!

[tjstienstra]

I get the message NonlinearError is not defined or similar.

Did you forget to import NonlinearError?

import sympy as sm
from sympy.solvers.solveset import NonlinearError

x = sm.Matrix(sm.symbols("x1:3"))
A = sm.Matrix([[1, 2], [3, 4]])
b = sm.Matrix([5, 6])
sm.linear_eq_to_matrix(A * x - b, x[:])  # Works fine

try:
    sm.linear_eq_to_matrix(A * x * x[0] - b, x[:])
except NonlinearError as e:
    msg = "Some custom message."
    print("here")
    raise NonlinearError(msg) from e

This raises the following error:

Traceback (most recent call last):
  File "...\sympy\solvers\solveset.py", line 2874, in linear_eq_to_matrix
    eq, c = _linear_eq_to_dict(equations, symbols)
  File "...\sympy\polys\matrices\linsolve.py", line 171, in _linear_eq_to_dict
    c, d = _lin_eq2dict(e, symset)
  File "...\sympy\polys\matrices\linsolve.py", line 199, in _lin_eq2dict
    ci, ti = _lin_eq2dict(ai, symset)
  File "...\sympy\polys\matrices\linsolve.py", line 219, in _lin_eq2dict
    raise PolyNonlinearError(filldedent('''
sympy.polys.solvers.PolyNonlinearError:
nonlinear cross-term: x1*(x1 + 2*x2)

During handling of the above exception, another exception occurred:

Traceback (most recent call last):
  File "...\temp.py", line 10, in <module>
    sm.linear_eq_to_matrix(A * x * x[0] - b, x[:])
  File "...\sympy\solvers\solveset.py", line 2876, in linear_eq_to_matrix
    raise NonlinearError(str(err))
sympy.solvers.solveset.NonlinearError:
nonlinear cross-term: x1*(x1 + 2*x2)

The above exception was the direct cause of the following exception:

Traceback (most recent call last):
  File "...\temp.py", line 14, in <module>
    raise NonlinearError(msg) from e
sympy.solvers.solveset.NonlinearError: Some custom message.

[Peter230655]

I get the message NonlinearError is not defined or similar.

Did you forget to import NonlinearError?

import sympy as sm
from sympy.solvers.solveset import NonlinearError

x = sm.Matrix(sm.symbols("x1:3"))
A = sm.Matrix([[1, 2], [3, 4]])
b = sm.Matrix([5, 6])
sm.linear_eq_to_matrix(A * x - b, x[:])  # Works fine

try:
    sm.linear_eq_to_matrix(A * x * x[0] - b, x[:])
except NonlinearError as e:
    msg = "Some custom message."
    print("here")
    raise NonlinearError(msg) from e

This raises the following error:

Traceback (most recent call last):
  File "...\sympy\solvers\solveset.py", line 2874, in linear_eq_to_matrix
    eq, c = _linear_eq_to_dict(equations, symbols)
  File "...\sympy\polys\matrices\linsolve.py", line 171, in _linear_eq_to_dict
    c, d = _lin_eq2dict(e, symset)
  File "...\sympy\polys\matrices\linsolve.py", line 199, in _lin_eq2dict
    ci, ti = _lin_eq2dict(ai, symset)
  File "...\sympy\polys\matrices\linsolve.py", line 219, in _lin_eq2dict
    raise PolyNonlinearError(filldedent('''
sympy.polys.solvers.PolyNonlinearError:
nonlinear cross-term: x1*(x1 + 2*x2)

During handling of the above exception, another exception occurred:

Traceback (most recent call last):
  File "...\temp.py", line 10, in <module>
    sm.linear_eq_to_matrix(A * x * x[0] - b, x[:])
  File "...\sympy\solvers\solveset.py", line 2876, in linear_eq_to_matrix
    raise NonlinearError(str(err))
sympy.solvers.solveset.NonlinearError:
nonlinear cross-term: x1*(x1 + 2*x2)

The above exception was the direct cause of the following exception:

Traceback (most recent call last):
  File "...\temp.py", line 14, in <module>
    raise NonlinearError(msg) from e
sympy.solvers.solveset.NonlinearError: Some custom message.

I did not forget - I did not know! :-) Same with PolyNonlinearError? Thanks!!

[tjstienstra]

Same with PolyNonlinearError?

from sympy.polys.solvers import PolyNonlinearError

I wouldn't expect that you get a PolyNonlinearError as I guess that linear_eq_to_matrix actually catches those and changes them to NonlinearErrors.

[Peter230655]

Same with PolyNonlinearError?

from sympy.polys.solvers import PolyNonlinearError

I wouldn't expect that you get a PolyNonlinearError as I guess that linear_eq_to_matrix actually catches those and changes them to NonlinearErrors.

I seem to get both:

PolyNonlinearError: nonlinear term: ux(t)**2

During handling of the above exception, another exception occurred:

NonlinearError                            Traceback (most recent call last)
File Untitled-1:306
    [305](untitled-1:305)     u_test = list(self.u)
--> [306](untitled-1:306)     self._k_nh, self._f_nh = linear_eq_to_matrix(vel_test, u_test)
    [308](untitled-1:308) # If no acceleration constraints given, calculate them.

[tjstienstra]

I seem to get both:

No, what happens is that PolyNonlinearError is catched using try except and a NonlinearError is raised, which is what you get. However, to give users more insight Python also shows the original error, i.e. the PolyNonlinearError, in the traceback.

[Peter230655]

I seem to get both:

No, what happens is that PolyNonlinearError is catched using try except and a NonlinearError is raised, which is what you get. However, to give users more insight Python also shows the original error, i.e. the PolyNonlinearError, in the traceback.

Thanks! So should I skip the try.....except(NonlinearError) part, as you suggested originally?

[tjstienstra]

So should I skip the try.....except(NonlinearError) part, as you suggested originally?

No, I would just use self._k_nh, self._f_nh = linear_eq_to_matrix(...) directly without wrapping it in a try except statement. The error raised by linear_eq_to_matrix is already quite clear.

[Peter230655]

Finally I got it to work, even with the try.....except! Thanks al lot - I did learn something today!!

The increase in speed is leally substantial as per my inaccurate measurements!

[Peter230655]

I used Timo's idea of linear_eq_to_matrix function to speed things up considerably. Raise error if nonlinear.

[Peter230655]

I just copied Timo's version, hopefully correctly so.

[Peter230655]

I copied correctly! :-) To be very clear: That this finally worked was ONLY Timo's skill!

[moorepants]

KanesMethod allows for linear speed constraints, however it does not check whether they really are linear. It does test the kinematic differential equations for linearity. So, I simply copied the few lines of code there and added them around line 320

needs to be improved. State what is changes: "KanesMethod will now raise a NonLinearError if nonlinear velocity constraints are passed in."

[Peter230655]

KanesMethod allows for linear speed constraints, however it does not check whether they really are linear. It does test the kinematic differential equations for linearity. So, I simply copied the few lines of code there and added them around line 320

needs to be improved. State what is changes: "KanesMethod will now raise a NonLinearError if nonlinear velocity constraints are passed in."

I changed the description. It was NOT my idea, but Timo's. Can I mention it there?