[GSOC] Constant coefficient non-homogeneous system of ODEs solver #19341

mijo2 · 2020-05-17T07:51:00Z

References to other Issues or PRs

Fixes #9244
Fixes #8859
Fixes #8567
Fixes #19150

Brief description of what is fixed or changed

Added linear first-order constant-coefficient non-homogeneous system of ODEs solver.

Other comments

The SymPy's ode module will be able to solve a number of linear first-order constant coefficient non-homogenous systems of ODEs

For example:

>>> from sympy import *
>>> from sympy.abc import *
>>> f, g = symbols("f g", cls=Function)
>>> eqs = [Eq(f(t).diff(t), f(t) + 2*g(t) + t), Eq(g(t).diff(t), 7*g(t) + t**2)]
>>> dsolve(eqs)
[Eq(f(t), C1*exp(t) + C2*exp(7*t)/3 + 2*t**2/7 - 17*t/49 - 115/343), Eq(g(t), C2*exp(7*t) - t**2/7 - 2*t/49 - 2/343)]

Release Notes

solvers
- In dsolve there is no a general solver that can solve systems of constant coefficient non-homogeneous first order ODEs of any size in terms of integrals.

Added the constant coefficient non-homogeneous solver.

sympy-bot · 2020-05-17T07:51:01Z

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solvers
- In dsolve there is no a general solver that can solve systems of constant coefficient non-homogeneous first order ODEs of any size in terms of integrals. (#19341 by @mijo2)

This will be added to https://github.com/sympy/sympy/wiki/Release-Notes-for-1.7.

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<!-- Your title above should be a short description of what
was changed. Do not include the issue number in the title. -->

#### References to other Issues or PRs
Fixes #9244
Fixes #8859
Fixes #8567
Fixes #19150


#### Brief description of what is fixed or changed
Added linear first-order constant-coefficient non-homogeneous system of ODEs solver.

#### Other comments

The SymPy's ode module will be able to solve a number of linear first-order constant coefficient non-homogenous systems of ODEs

For example:
```
>>> from sympy import *
>>> from sympy.abc import *
>>> f, g = symbols("f g", cls=Function)
>>> eqs = [Eq(f(t).diff(t), f(t) + 2*g(t) + t), Eq(g(t).diff(t), 7*g(t) + t**2)]
>>> dsolve(eqs)
[Eq(f(t), C1*exp(t) + C2*exp(7*t)/3 + 2*t**2/7 - 17*t/49 - 115/343), Eq(g(t), C2*exp(7*t) - t**2/7 - 2*t/49 - 2/343)]
```

#### Release Notes

<!-- Write the release notes for this release below. See
https://github.com/sympy/sympy/wiki/Writing-Release-Notes for more information
on how to write release notes. The bot will check your ease notes
automatically to see if they are formatted correctly. -->

<!-- BEGIN RELEASE NOTES -->
* solvers
  * In `dsolve` there is no a general solver that can solve systems of constant coefficient non-homogeneous first order ODEs of any size in terms of integrals.
<!-- END RELEASE NOTES -->

Update

The release notes on the wiki have been updated.

Updated the matching function to classify constant coefficient non-homogeneous functions as type2 and dsolve uses the new solver.

Moved the test cases from test_ode.py to test_systems.py

Some of the test cases from type1 were moved from test_ode.py to test_systems.py

The matching code for the removed solvers was deleted.

mijo2 · 2020-05-20T08:01:19Z

@oscarbenjamin @moorepants Except the final travis CI build and adding of few more test cases, the PR is almost completed. Please review and have a look. @namannimmo10 I hope this helps for your gsoc project.

This commit may be squashed later.

Some of the matching function code was incorrectly removed and it was rectified in this PR.

sympy/solvers/ode/tests/test_systems.py

mijo2 · 2020-05-21T06:29:27Z

@oscarbenjamin I don't know for what reason but the latex build is failing and I wasn't able to find out whats the problem.

oscarbenjamin · 2020-05-21T10:13:39Z

Have you tried building the latex docs yourself?

This is the end of the build log:

LaTeX Warning: Citation `modules/solvers/ode:r694' on page 1202 undefined on in
put line 90359.
! Missing } inserted.
<inserted text> 
                }
l.90406 ... e^{- A t} b\, dt\right + C)\end{split}

Searching for that in the diff here I find:

sympy/sympy/solvers/ode/systems.py

Lines 434 to 435 in f93d88d

    
               .. math:: 
        
                   X = e^{A t} (\int e^{- A t} b\, dt\right + C)

I don't think that the \right should be there. The way to use \right is like \left( \cos{x} \right).

mijo2 · 2020-05-21T10:28:27Z

Have you tried building the latex docs yourself?

I did but I wasn't able to figure the error out.

I don't think that the \right should be there. The way to use \right is like \left( \cos{x} \right).

I see, when I separately generated the equation, it worked and gave the right answer. Thanks for this help.

oscarbenjamin · 2020-06-16T15:54:47Z

sympy/solvers/ode/tests/test_systems.py

+
+    e1, e2, e3 = symbols("e1:4", real=True)
+    b1, b2, b3 = symbols("b1:4", real=True)
+    v1, v2, v3 = symbols("v1:4", cls=Function, real=True)


Rather than duplicating this code here and above I think that it would be better to make a function that returns the system and expected solution and then call that in each of the two test functions here.

oscarbenjamin · 2020-06-16T15:55:54Z

sympy/solvers/ode/tests/test_systems.py

+    eq1 = r1*c1*Derivative(x1(t), t) + x1(t) - x2(t) - r1*i
+    eq2 = r2*c1*Derivative(x1(t), t) + r2*c2*Derivative(x2(t), t) + x2(t) - r2*i
+    eq = [eq1, eq2]
+    sol = [Eq(x1(t), -2*C1*c2*r2*exp(-t/(2*c2*r2) - t/(2*c2*r1) - t/(2*c1*r1) - t*sqrt(c1**2*r1**2 +


This can be simplified using the script.

Some of the test cases used repeated code, this was rectified in this commit.

The big test cases were updated with smaller representations of their solutions.

oscarbenjamin · 2020-06-17T10:31:13Z

sympy/solvers/ode/tests/test_systems.py

+    I = Function("I")
+    system = [Eq(V(t).diff(t), -1 / RC * V(t) + I(t) / C), Eq(I(t).diff(t), -R1 / L * I(t) - 1 / L * V(t) + Vs / L)]
+
+    return system, dsolve(system), [RC, t, C, Vs, L, R1, V0, I0, V, I]


It would be better to define the expected solution here and return system, funcs, sol and let the caller call dsolve. The way this is set up dsolve gets called twice because of the two tests that call this function.

oscarbenjamin · 2020-06-17T10:35:20Z

sympy/solvers/ode/tests/test_systems.py

+
+    eqs, dsolve_sol, symbols = _de_lorentz_solution()
+    m, q, t, e1, e2, e3, b1, b2, b3, v1, v2, v3 = symbols
+    x_1 = Integral(b1**3*b2*e2*q*exp(q*t*sqrt(-b1**2 - b2**2 - b3**2)/m)/(2*b1**3*b3*m +


This long expression for x_1 can be simplified further by running printsol on it.

oscarbenjamin · 2020-06-17T10:40:09Z

sympy/solvers/ode/tests/test_systems.py

@@ -795,16 +1120,23 @@ def test_linear_3eq_order1_type4_skip():
                Eq(diff(y(t), t), 2 * f * x(t) + (f + g) * y(t) - 2 * f * z(t)), Eq(diff(z(t), t), 5 * f * x(t) + f * y(


This function shouldn't be called _skip if it's not being skipped.

Updated one of the big test cases so that we call the dsolve method less number of times.

oscarbenjamin · 2020-06-17T16:32:03Z

sympy/solvers/ode/tests/test_systems.py

+    x_3 = exp(-t / (2 * c2 * r2) - t / (2 * c2 * r1) - t / (2 * c1 * r1) + t * sqrt(x_1) / (2 * c1 * c2 * r1 * r2))
+    x_4 = Integral(-i * r2 * exp(
+        t / (2 * c2 * r2) + t / (2 * c2 * r1) + t / (2 * c1 * r1) + t * sqrt(x_1) / (2 * c1 * c2 * r1 * r2)) / sqrt(
+        x_1), t)


Some of these lines are too long. They wouldn't need to be so long though if you didn't put all the spaces in:

x_4 = Integral(-i*r2*exp(t/(2*c2*r2) + t/(2*c2*r1) + t/(2*c1*r1) + t*sqrt(x_1)/(2*c1*c2*r1*r2))/sqrt(x_1), t)

This example can be written as

_x1 = c1**2*r1**2 + 2*c1**2*r1*r2 + c1**2*r2**2 - 2*c1*c2*r1*r2 + 2*c1*c2*r2**2 + c2**2*r2**2 _x2 = Integral(i*r2*exp(-sqrt(_x1)*t/(2*c1*c2*r1*r2) + t/(2*c2*r2) + t/(2*c2*r1) + t/(2*c1*r1))/sqrt(_x1), t) _x3 = Integral(-i*r2*exp(sqrt(_x1)*t/(2*c1*c2*r1*r2) + t/(2*c2*r2) + t/(2*c2*r1) + t/(2*c1*r1))/sqrt(_x1), t) _x4 = exp(sqrt(_x1)*t/(2*c1*c2*r1*r2) - t/(2*c2*r2) - t/(2*c2*r1) - t/(2*c1*r1)) _x5 = exp(-sqrt(_x1)*t/(2*c1*c2*r1*r2) - t/(2*c2*r2) - t/(2*c2*r1) - t/(2*c1*r1)) sol = [ Eq(x1(t), - 2*C1*_x5*c2*r2/(sqrt(_x1) + c1*r1 + c1*r2 - c2*r2) - 2*C2*_x4*c2*r2/(-sqrt(_x1) + c1*r1 + c1*r2 - c2*r2) - 2*_x2*_x4*c2*r2/(-sqrt(_x1) + c1*r1 + c1*r2 - c2*r2) - 2*_x3*_x5*c2*r2/(sqrt(_x1) + c1*r1 + c1*r2 - c2*r2)), Eq(x2(t), C1*_x5 + C2*_x4 + _x2*_x4 + _x3*_x5), ]

oscarbenjamin · 2020-06-17T18:26:15Z

sympy/solvers/ode/tests/test_systems.py

+    x_2 = 1/(2*b1**2*m*exp(q*t*sqrt(-b1**2 - b2**2 - b3**2)/m) + 2*b2**2*m*exp(q*t*sqrt(-b1**2 - b2**2 - b3**2)/m) +
+            2*b3**2*m*exp(q*t*sqrt(-b1**2 - b2**2 - b3**2)/m))
+    x_3 = exp(q*t*sqrt(-b1**2 - b2**2 - b3**2)/m)
+    x_4 = sqrt(b1**2 + b2**2 + b3**2)


This example can be written as

x1 = sqrt(b1**2 + b2**2 + b3**2) x2 = exp(q*t*sqrt(-b1**2 - b2**2 - b3**2)/m) x3 = 1/(b1**2*x1*x2 + b2**2*x1*x2) x4 = 1/(2*b1**2*m*x2 + 2*b2**2*m*x2 + 2*b3**2*m*x2) x5 = Integral( b1*b3*e1*q/(b1**2*m + b2**2*m + b3**2*m) + b2*b3*e2*q/(b1**2*m + b2**2*m + b3**2*m) + b3**2*e3*q/(b1**2*m + b2**2*m + b3**2*m), t) x6 = 1/(2*b1**3*b3*m + 2*I*b1**2*b2*m*x1 + 2*b1*b2**2*b3*m + 2*b1*b3**3*m + 2*I*b2**3*m*x1 + 2*I*b2*b3**2*m*x1) x7 = Integral( b1**2*e3*q*x4 - b1*b3*e1*q*x4 + I*b1*e2*q*x1*x4 + b2**2*e3*q*x4 - b2*b3*e2*q*x4 - I*b2*e1*q*x1*x4, t) x8 = Integral( b1**3*b2*e2*q*x2*x6 - b1**2*b2**2*e1*q*x2*x6 - b1**2*b3**2*e1*q*x2*x6 - I*b1**2*b3*e2*q*x1*x2*x6 + b1**2*e3*q*x2/(2*b1**2*m + 2*b2**2*m + 2*b3**2*m) + b1*b2**3*e2*q*x2*x6 - b2**4*e1*q*x2*x6 - b2**2*b3**2*e1*q*x2*x6 - I*b2**2*b3*e2*q*x1*x2*x6 + b2**2*e3*q*x2/(2*b1**2*m + 2*b2**2*m + 2*b3**2*m), t) sol = [ Eq(v1(t), C1*b1/b3 - I*C2*b1**2*b2*x3 - C2*b1*b3*x1*x3 - I*C2*b2**3*x3 - I*C2*b2*b3**2*x3 + I*C3*b1**2*b2*x2/(b1**2*x1 + b2**2*x1) - C3*b1*b3*x1*x2/(b1**2*x1 + b2**2*x1) + I*C3*b2**3*x2/(b1**2*x1 + b2**2*x1) + I*C3*b2*b3**2*x2/(b1**2*x1 + b2**2*x1) + I*b1**2*b2*x2*x7/(b1**2*x1 + b2**2*x1) - I*b1**2*b2*x3*x8 - b1*b3*x1*x2*x7/(b1**2*x1 + b2**2*x1) - b1*b3*x1*x3*x8 + b1*x5/b3 + I*b2**3*x2*x7/(b1**2*x1 + b2**2*x1) - I*b2**3*x3*x8 + I*b2*b3**2*x2*x7/(b1**2*x1 + b2**2*x1) - I*b2*b3**2*x3*x8), Eq(v2(t), C1*b2/b3 + C2*b1*sqrt(-b1**2 - b2**2 - b3**2)/(b1**2*x2 + b2**2*x2) - C2*b2*b3/(b1**2*x2 + b2**2*x2) - I*C3*b1*x1*x2/(b1**2 + b2**2) - C3*b2*b3*x2/(b1**2 + b2**2) - I*b1*x1*x2*x7/(b1**2 + b2**2) + b1*x8*sqrt(-b1**2 - b2**2 - b3**2)/(b1**2*x2 + b2**2*x2) - b2*b3*x2*x7/(b1**2 + b2**2) - b2*b3*x8/(b1**2*x2 + b2**2*x2) + b2*x5/b3), Eq(v3(t), C1 + C3*x2 + x2*x7 + x5 + (C2 + x8)*exp(-q*t*sqrt(-b1**2 - b2**2 - b3**2)/m)), ]

Ok I will update this.

oscarbenjamin · 2020-06-17T18:39:03Z

I've put the simplifying script in #19574 and improved it a bit.

Updated those test case solutions with better and efficient substitutions.

mijo2 · 2020-06-18T16:18:59Z

@oscarbenjamin All checks have passed.

oscarbenjamin · 2020-06-18T16:54:56Z

sympy/solvers/ode/tests/test_systems.py

+              + 2 * b1 * b3 ** 3 * m + 2 * I * b2 ** 3 * m * x1 + 2 * I * b2 * b3 ** 2 * m * x1)
+    x7 = Integral(
+        b1 ** 2 * e3 * q * x4 - b1 * b3 * e1 * q * x4 + I * b1 * e2 * q * x1 * x4
+        + b2 ** 2 * e3 * q * x4 - b2 * b3 * e2 * q * x4 - I * b2 * e1 * q * x1 * x4, t)


I don't understand why you've added all of these spaces. Is that something that your editor does automatically? It's easier to read with the spacing from str and careful line breaks:

x7 = Integral(b1**2*e3*q*x4 - b1*b3*e1*q*x4 + I*b1*e2*q*x1*x4 + b2**2*e3*q*x4 - b2*b3*e2*q*x4 - I*b2*e1*q*x1*x4, t)

Most probably it's the problem with my editor, I would get it fixed.

oscarbenjamin · 2020-06-18T16:57:53Z

I would merge this but github won't let me. It hasn't updated since Travis passed the tests.

oscarbenjamin · 2020-06-18T21:11:09Z

I've edited the release note and closed/reopened to restart the tests. Hopefully github will detect when the tests are complete on Travis (#19589)

oscarbenjamin · 2020-06-18T23:08:40Z

I'm still unable to merge this even though the tests have passed (again)...

oscarbenjamin · 2020-06-18T23:10:41Z

Apparently commenting updated the PR and made it mergeable!

solvers.ode: Added the new type2 solver

b1ebae5

Added the constant coefficient non-homogeneous solver.

mijo2 mentioned this pull request May 17, 2020

Tracking changes and tasks in systems.py #19178

Open

9 tasks

czgdp1807 added solvers solvers.dsolve GSoC labels May 17, 2020

mijo2 added 2 commits May 18, 2020 13:20

solvers.ode: Updated the matching function and sysode neq function

f8f9673

Updated the matching function to classify constant coefficient non-homogeneous functions as type2 and dsolve uses the new solver.

solvers.ode: Moved the test cases of type2

c2aaf51

Moved the test cases from test_ode.py to test_systems.py

mijo2 added the solvers.dsolve.system label May 18, 2020

mijo2 added 11 commits May 19, 2020 12:36

solvers.ode: Added documentation for type2 solver

4b301a2

doc: Added type2 documentation in ode.rst

0eeb561

solvers.ode: Moved the test cases of type 1

48acac5

Some of the test cases from type1 were moved from test_ode.py to test_systems.py

solvers.ode: Updated some errors in test cases in test_systems.py

7eb4be0

solvers.ode: Removed 2eq type1 and type2 solvers.

c30e138

solvers.ode: Removed unused imports

b158705

doc: Removed documentation for the removed solvers

0c1c006

solvers.ode: Added regression test case for issue sympy#8859

adaff72

solvers.ode: Added regression test case for issue sympy#8567

a5dcaa1

solvers.ode: Added regression test case for issue sympy#19150

9a56c8b

solvers.ode: Removed some of the matching code

ebf2067

The matching code for the removed solvers was deleted.

mijo2 mentioned this pull request May 20, 2020

Cannot solve system of ODEs #16125

Open

mijo2 added 3 commits May 20, 2020 13:50

solvers.ode: Added some XFAIL test cases

4c137da

solvers.ode: Fixed some minor error

11ffbe6

This commit may be squashed later.

solvers.ode: Updated some of the matching function code

6df222a

Some of the matching function code was incorrectly removed and it was rectified in this PR.

oscarbenjamin reviewed May 20, 2020

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sympy/solvers/ode/tests/test_systems.py Outdated Show resolved Hide resolved

solvers.ode: Split one test case function into two.

f93d88d

oscarbenjamin reviewed Jun 16, 2020

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mijo2 added 3 commits June 17, 2020 12:41

solvers.ode: Removed some outdated comments and simplified tests

371c354

Some of the test cases used repeated code, this was rectified in this commit.

solvers.ode: Updated some new functions to private functions

5dbaa00

solvers.ode: Updated the test cases

c182a99

The big test cases were updated with smaller representations of their solutions.

oscarbenjamin reviewed Jun 17, 2020

View reviewed changes

mijo2 added 2 commits June 17, 2020 16:25

solvers.ode: Updated the test case

90044ac

Updated one of the big test cases so that we call the dsolve method less number of times.

solvers.ode: Simplified some of the substitutions in a test

8935785

oscarbenjamin reviewed Jun 17, 2020

View reviewed changes

mijo2 added 2 commits June 18, 2020 13:18

Merge branch 'master' into const_coeff_nonhomogeneous

d1b49ff

solvers.ode: Updated the big solutions for test cases

fac6758

Updated those test case solutions with better and efficient substitutions.

mijo2 force-pushed the const_coeff_nonhomogeneous branch from b76beb1 to fac6758 Compare June 18, 2020 09:56

doc: Updated the doc import nomenclature

bf482b2

oscarbenjamin reviewed Jun 18, 2020

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oscarbenjamin closed this Jun 18, 2020

oscarbenjamin reopened this Jun 18, 2020

oscarbenjamin merged commit 25e8a79 into sympy:master Jun 18, 2020

This was referenced Jun 21, 2020

TypeError with dsolve and a system of ODEs #14001

Closed

[GSoC] API change for the newly added system of ODEs solvers #19653

Merged

mijo2 deleted the const_coeff_nonhomogeneous branch June 27, 2020 08:11

mijo2 mentioned this pull request Jun 28, 2020

dsolve((eq1, eq2)) AttributeError: 'list' object has no attribute 'func' #19656

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[GSOC] Constant coefficient non-homogeneous system of ODEs solver #19341

[GSOC] Constant coefficient non-homogeneous system of ODEs solver #19341

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oscarbenjamin commented Jun 18, 2020

		@@ -795,16 +1120,23 @@ def test_linear_3eq_order1_type4_skip():
		Eq(diff(y(t), t), 2 * f * x(t) + (f + g) * y(t) - 2 * f * z(t)), Eq(diff(z(t), t), 5 * f * x(t) + f * y(

[GSOC] Constant coefficient non-homogeneous system of ODEs solver #19341

[GSOC] Constant coefficient non-homogeneous system of ODEs solver #19341

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mijo2 commented May 17, 2020 • edited by oscarbenjamin

References to other Issues or PRs

Brief description of what is fixed or changed

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Release Notes

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