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CoolDiff is a C++ 17 library dedicated to compute both automatic as well as symbolic differentiation of mathematical expressions.
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CoolDiff APIs provide an easy and simple way of modeling and computing scalar mathematical expression values, forward/reverse (adjoint) mode derivatives and symbolic derivatives (objects).
By default, the numerical type for computation is complex numbers and this allows the tool to perform complex analysis as well.
Firstly, the CoolDiff library needs to be build. The following steps will build the library
- Clone the git repository -
git clone https://github.com/Kartz4code/CoolDiff.git
- Build the library using following steps -
cmake -S . -B buildcmake --build build -j16
- Run the Gaussian example to verify the success of the build -
./build/example/Gaussian
Link the generated CoolDiff library with your project and include the header CoolDiff.hpp to utilize the CoolDiff APIs. The example folder has few examples to exhibit the use case of the library.
The main classes/types involved in CoolDiff library are:
- Expression - Expression objects are used to model mathematical expressions.
- Variable - Variable objects are the optimization/decision/control variables that are of interest for computing the derivatives.
- Parameter - Parameter objects are used to model scalar variables that are either constant or vary over run-time (e.g. parameter varying system).
- Type - Type objects are used to model scalar variables, however, unlike Parameters, the value of Type objects cannot be changed over run-time.
The list of implemented binary operators in CoolDiff library are listed in the following table
| Function (Operator) | LHS operand type | RHS operand type |
|---|---|---|
| Addition (+) | Variable/Parameter/Expression | Variable/Parameter/Expression |
| Addition (+) | Type | Variable/Parameter/Expression |
| Addition (+) | Variable/Parameter/Expression | Type |
| Subtraction (-) | Variable/Parameter/Expression | Variable/Parameter/Expression |
| Subtraction (-) | Variable/Parameter/Expression | Type |
| Subtraction (-) | Type | Variable/Parameter/Expression |
| Multiplication (*) | Variable/Parameter/Expression | Variable/Parameter/Expression |
| Multiplication (*) | Type | Variable/Parameter/Expression |
| Multiplication (*) | Variable/Parameter/Expression | Type |
| Division (/) | Variable/Parameter/Expression | Variable/Parameter/Expression |
| Division (/) | Type | Variable/Parameter/Expression |
| Division (/) | Variable/Parameter/Expression | Type |
| Exponentiation (pow) | Variable/Parameter/Expression | Variable/Parameter/Expression |
| Exponentiation (pow) | Type | Variable/Parameter/Expression |
| Exponentiation (pow) | Variable/Parameter/Expression | Type |
The list of implemented unary operators in CoolDiff library are listed in the following table
| Function (Operator) | Operand type |
|---|---|
| Sin (sin) | Variable/Parameter/Expression |
| Cos (cos) | Variable/Parameter/Expression |
| Tan (tan) | Variable/Parameter/Expression |
| Asin (asin) | Variable/Parameter/Expression |
| Acos (acos) | Variable/Parameter/Expression |
| Atan (atan) | Variable/Parameter/Expression |
| Sinh (sinh) | Variable/Parameter/Expression |
| Cosh (cosh) | Variable/Parameter/Expression |
| Tanh (tanh) | Variable/Parameter/Expression |
| Asinh (asinh) | Variable/Parameter/Expression |
| Acosh (acosh) | Variable/Parameter/Expression |
| Atanh (atanh) | Variable/Parameter/Expression |
| Exp (exp) | Variable/Parameter/Expression |
| Log (log) | Variable/Parameter/Expression |
| Sqrt (sqrt) | Variable/Parameter/Expression |
The list of 8 important APIs and along with its description are listed in the following table.
| API | Description | 1st Argument type | 2nd Argument type | Output type |
|---|---|---|---|---|
| Eval | Evaluates the given expression | Expression& | - | Type |
| DevalF | Computes the forward AD derivative for the given expression and variable | Expression& | const Variable& | Type |
| PreComp | Precomputes all the reverse AD (adjoint) derivatives for the given expression | Expression& | - | - |
| DevalR | Returns the reverse AD derivative for the given expression and variable | Expression& | const Variable& | Type |
| SymDiff | Computes the symbolic derivative for the given expression and variable | Expression& | const Variable& | Expression& |
| CreateExpr | Factory method to create Expression object on heap | const Type& | - | Expression& |
| CreateVar | Factory method to create Variable object on heap | const Type& | - | Expression& |
| CreateParam | Factory method to create Parameter object on heap | const Type& | - | Expression& |
CoolDiff is currently in its nascent stage. I will constantly make contributions to make this library a better one. Kindly, feel free to try it and in case if you encounter any bugs, issues or errors let me know 😄. Your feedback would constanly motivate me to make this software a better one.