Symbolic differentiation

[gkronber]

Sometimes it can be helpful to look at derivatives of a model. It is rather straightforward to implement symbolic differentiation using our tree representation of expressions.

[gkronber]

r16206: added first implementation of symbolic differentiation as well as a test case (to be checked manually)

[gkronber]

r16207: added new unit test class to project (combine with previous commit)

[gkronber]

r16213: changed unit test cases to assert results of derivative calculations. Fixed bug in deriving sqrt(x)

[gkronber]

r16216: removed string interpolation

[mkommend]

Review Comments

Derivative Calculator

• Method Derive (line 29) - Although ADFs are virtually never used at least a check that they are not present should be included before accessing tree.Root.GetSubtree(0).GetSubtree(0).
• Static symbol variables (line 38-42) - Should be static readonly to avoid reassignment.
• Should a shortcut for deriving f(x1, ... x10) / dy be included ( f'(x1,...,x10)/dy = 0) or is this automatically handled by simplification of a constant expression regardless of its length?
• Method Derive (line 74) - Is there a specific reason why unary multiplication is not handled?
• Method Derive (line 90) - Is there a specific reason why divisions with more than 2 arguments are not handled?
• Method Derive (line 136) - What about the tangent symbol that can be expressed as sin() / cos()?
• Method IsCompatible (line 172) - This method is never used!

DeriveTest

• Reviewed unit tests
  • Some of them look overly complicated (due to our simplifier) and I had to use wolfram alpha for verification.

[gkronber]

r16294: worked on review comments.

[gkronber]

implemented the following review comments with r16294:

Replying to mkommend:

• Method Derive (line 29) - Although ADFs are virtually never used at least a check that they are not present should be included before accessing tree.Root.GetSubtree(0).GetSubtree(0).
• Static symbol variables (line 38-42) - Should be static readonly to avoid reassignment.
• Method Derive (line 74) - Is there a specific reason why unary multiplication is not handled?
• Method Derive (line 90) - Is there a specific reason why divisions with more than 2 arguments are not handled?
• Method Derive (line 136) - What about the tangent symbol that can be expressed as sin() / cos()?

Still open:

• Should a shortcut for deriving f(x1, ... x10) / dy be included ( f'(x1,...,x10)/dy = 0) or is this automatically handled by simplification of a constant expression regardless of its length?

• Method IsCompatible (line 172) - This method is never used!

It can be used by classes working with DerivativeCalculator. The pattern is the same for the AutoDiffConverter.

[gkronber]

r16358: adapted expected results for derivative calculator unit tests because the TreeSimplifier has been changed within ticket #2915.

-> #2915 must be merged to stable together with this ticket

[gkronber]

Replying to mkommend:

Review Comments

Derivative Calculator

• Should a shortcut for deriving f(x1, ... x10) / dy be included ( f'(x1,...,x10)/dy = 0) or is this automatically handled by simplification of a constant expression regardless of its length?

Checking whether the variable is used in ISymbolicExpressionTree would necessitate an iteration over all tree nodes. If Derive(ISymbolicExpressionTree tree, string variableName) is called for a variableName which does not occur in the tree the result is automatically a constant zero tree. I added a unit test with r16494 to assert this.

[gkronber]

Thanks for the review comments, I have considered all of them. Please review r16294, r16358, and r16494

[gkronber]

Not supported:

• Factor variables
• Abs
• AQ, Cube, CubeRoot
• time series symbols
• Boolean operators and conditionals
• Power, root (with rounding)
• all special functions

[gkronber]

r16543: added support for deriving cube, cuberoot, abs, analytic-quotient

[gkronber]

r16737: fixed a bug for products with >2 factors

[mkommend]

Reviewed all changesets of this ticket and the code looks good. However, I haven't tested it.

[mkommend]

r17066: Merged 16206, 16207, 16213, 16216, 16294 to stable.

[mkommend]

r17102: Merged 16358, 16494, 16543, 16737 into stable.

[gkronber]

Hyperbolic tangent is not supported.

[gkronber]

r17125: added support for tanh and a unit test case

[gkronber]

Please review / release r17125

[mkommend]

Reviewed r17125.

[gkronber]

r17155: merged r17125 from trunk to stable