CasADi S-Function: Getting Correct Output In Simulink

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CasADi S-Function: Getting Correct Output in Simulink

Hey guys! 👋 Having trouble getting your CasADi S-functions to play nice with Simulink, especially when it comes to Jacobian calculations? You're not alone! Many developers face challenges integrating the sparse output of CasADi functions into Simulink models. Let's dive into a common issue and explore some cleaner solutions to ensure your S-functions return the correct results.

The Challenge: Sparse Output and Simulink

When working with CasADi, you might find yourself leveraging its powerful symbolic computation capabilities to calculate Jacobians. These Jacobians, representing the derivatives of your functions, are crucial for various Simulink applications. However, CasADi often represents these Jacobians in a sparse format, which can cause headaches when directly used in Simulink.

The user in the initial discussion highlighted this exact problem. They were using CasADi to compute a Jacobian and integrate it into a Simulink model via an S-function. Following a helpful blog post (https://web.casadi.org/blog/s-function/), they successfully created the S-function but encountered incorrect results in Simulink. The culprit? The sparse output of the CasAdi function.

The workaround they devised – adding a matrix of ones in CasAdi, generating the S-function, and then subtracting a one-matrix in Simulink – is a clever but admittedly "dirty" fix. It underscores the need for a more robust and elegant solution. The core of the issue lies in how to obtain a dense output from the CasAdi function, which is where the documentation seems to fall short, leaving users in the dark about the options struct and its potential parameters like .sparsity_out.

Why Sparse Matrices Matter

Before we delve into solutions, let's quickly recap why sparse matrices are important and why they cause problems. Sparse matrices are efficient representations of matrices where most elements are zero. Instead of storing every element, sparse formats only store the non-zero values and their indices, saving significant memory and computation time, especially for large matrices. CasADi intelligently uses sparse matrices to represent Jacobians, which are often sparse in many engineering and scientific problems.

However, Simulink, or rather the specific S-function implementation, might not always handle sparse matrices seamlessly. This is because Simulink's default matrix operations often assume dense matrices, leading to incorrect results or compatibility issues when a sparse matrix is unexpectedly encountered. Therefore, we need to find a way to convert the sparse output from CasADi into a dense format suitable for Simulink.

Exploring Solutions for Dense Output

So, how can we get CasADi to generate a dense output for our S-function? Let's explore some potential avenues, building on the user's initial attempts and expanding with further strategies.

1. Understanding CasADi Function Options

The user's attempt to use the options struct with parameters like .sparsity_out is on the right track. CasADi functions can be configured with various options to control their behavior, including output sparsity. However, the documentation's lack of clarity on these options is a common pain point.

To effectively use the options struct, we need to understand which parameters are relevant and how they should be set. While .sparsity_out might seem intuitive, it's crucial to know the expected input format and whether it's the correct option for forcing dense output. This often involves digging into CasADi's source code or experimenting with different options to see their effect.

Another potentially relevant option might be related to the function's internal representation of the Jacobian. CasADi might have options to control whether the Jacobian is computed and stored in sparse or dense format internally. If we can force a dense internal representation, the output might also be dense.

Key Takeaway: Explore the CasADi function options meticulously. Experiment with different settings, and don't hesitate to consult CasADi's source code or community forums for insights.

2. Compiler Flags: A Deeper Dive

The user also tried using compiler flags -DCASASI_MEX_ALWAYS_DENSE and -DCASASI_MEX_ALLOW_DENSE. These flags are intended to influence how CasADi's MEX (MATLAB Executable) functions handle sparsity. However, the user's experience suggests that these flags alone might not be sufficient.

It's important to understand the nuances of these flags:

  • -DCASASI_MEX_ALWAYS_DENSE: This flag, as the name suggests, should ideally force all MEX functions generated by CasADi to use dense matrices. If it's not working as expected, there might be an issue with how the flag is being passed to the compiler or an underlying bug in CasADi.
  • -DCASASI_MEX_ALLOW_DENSE: This flag might be a more permissive option, allowing dense matrices where possible but not necessarily forcing them. It might be less effective if the default behavior is still to use sparse matrices.

To ensure these flags are effective, double-check the compilation process. Verify that the flags are correctly passed to the compiler when generating the S-function. You might need to modify your build scripts or MATLAB's MEX configuration to include these flags.

Key Takeaway: Compiler flags can be powerful, but their effectiveness depends on correct usage and underlying CasADi behavior. Verify the compilation process and consider potential bugs.

3. Explicitly Converting to Dense Matrix

If options and compiler flags don't yield the desired result, a more direct approach is to explicitly convert the sparse output to a dense matrix within the CasAdi function definition. CasADi provides functions for manipulating sparse matrices, including conversion to dense format.

Within your CasAdi function, after computing the Jacobian, you can use a function like full() (if it exists in CasAdi, similar to MATLAB) or an equivalent to convert the sparse matrix to a dense one. This ensures that the output passed to the S-function is in the correct format for Simulink.

Here's a conceptual example (assuming a full() function exists):

import casadi as ca

# Define your CasAdi function
x = ca.SX.sym('x', n)
y = your_function(x)
J = ca.jacobian(y, x)

# Explicitly convert to dense
J_dense = ca.full(J)

# Create CasAdi function for S-function
F = ca.Function('F', [x], [J_dense], ...)

This approach guarantees a dense output, regardless of CasADi's internal sparsity handling. However, it might introduce some performance overhead if the Jacobian is very large and mostly sparse. In such cases, consider whether the performance trade-off is acceptable for the sake of Simulink compatibility.

Key Takeaway: Explicitly converting to a dense matrix within the CasAdi function provides the most control over the output format.

4. S-Function Implementation Details

Sometimes, the issue might not be with CasAdi itself but with how the S-function is implemented. S-functions have different output ports, and it's crucial to ensure that the output port handling the Jacobian is correctly configured to accept dense matrices.

Review your S-function code (likely in C/C++) and check how the output data is being handled. Ensure that the output port's data type and dimensions are correctly defined to accommodate a dense matrix. If the S-function is inadvertently treating the output as sparse, it might lead to incorrect results even if CasAdi is generating a dense matrix.

Key Takeaway: Scrutinize your S-function implementation to ensure it correctly handles dense matrix outputs.

5. Leveraging CasADi's Documentation and Community

As the user pointed out, CasAdi's documentation can sometimes be lacking in specific details, especially regarding function options. However, CasAdi has an active community forum and mailing list where you can ask questions and seek guidance from experienced users and developers.

When facing a problem like this, don't hesitate to reach out to the CasAdi community. Describe your problem clearly, including the steps you've taken, the results you're seeing, and any relevant code snippets. The community can often provide valuable insights and help you troubleshoot your issue.

Key Takeaway: The CasAdi community is a valuable resource for troubleshooting and learning best practices.

Conclusion: Taming CasADi's Sparsity for Simulink

Integrating CasAdi with Simulink via S-functions offers a powerful way to leverage symbolic computation within your models. However, dealing with sparse outputs can be tricky. By understanding the nuances of CasAdi's function options, compiler flags, and explicit conversion methods, you can overcome these challenges and ensure accurate results.

Remember, the key is to be methodical in your approach. Start by exploring CasAdi's options and compiler flags. If those don't suffice, explicitly convert the sparse matrix to a dense one within your CasAdi function. Finally, review your S-function implementation to ensure it correctly handles dense outputs. And of course, don't hesitate to tap into the knowledge of the CasAdi community!

By following these strategies, you can seamlessly integrate CasAdi's powerful capabilities into your Simulink workflows, guys. Good luck! 👍 🚀