Dynamical systems of second order as often encountered in structural dynamics can be transformed in the state-space configuration, where the order is reduced to first, and dimension is doubled. The essence is that the state vector is extended to include not only the position state, but also the velocity state.
This formulation leads to a Jacobian matrix which contains large areas of "zeros" and "ones". Would it be possible to define an additional option in Matcont, where the user can define the pattern/sparsity of the Jacobian and Hessian? If the algorithm would take this into account, I could imagine that te continuation could be accelerated.
Best regards
Lysandros Anastasopoulos
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The continuer, using \ for the Newton iterations. But, unless you have really large systems (>200 variables) matlab will provide a proper direct solve. If your system is larger, then consider using the commandline package adapted for large systems; cl_MatContL, but not on this forum.
Setting up the Jacobian matrices. This is the part that is most time-consuming, especially for periodic orbits. We have no plans ourselves to improve this part, but we're open to suggestions.
Best regards, Hil
From: lanast lanast@users.sourceforge.net
Sent: Saturday, April 4, 2020 12:33 PM
To: [matcont:discussion]
Subject: [matcont:discussion] Suggestion related to the Jacobian and Hessian calculation
Hi
Dynamical systems of second order as often encountered in structural dynamics can be transformed in the state-space configuration, where the order is reduced to first, and dimension is doubled. The essence is that the state vector is extended to include not only the position state, but also the velocity state.
This formulation leads to a Jacobian matrix which contains large areas of "zeros" and "ones". Would it be possible to define an additional option in Matcont, where the user can define the pattern/sparsity of the Jacobian and Hessian? If the algorithm would take this into account, I could imagine that te continuation could be accelerated.
Dear professor,
thank you for these remarks on the continuation process.
I have attached a suggestion of how the code structure could be adapted. It would allow for finite difference calculation solely at the degrees of freedom affected by nonlinearities, while circumventing the sparse and/or constant columns of the Jacobian matrix.
Kind regards
Lysandros
When you define a system in the GUI, you can specify whether you want to have your derivatives numerically, symbolically, or "from window". Have you tried integrating your input with this option?
Best, Hil
From: lanast lanast@users.sourceforge.net
Sent: Tuesday, May 12, 2020 9:17 PM
To: [matcont:discussion]
Subject: [matcont:discussion] Suggestion related to the Jacobian and Hessian calculation
Dear professor,
thank you for these remarks on the continuation process.
I have attached a suggestion of how the code structure could be adapted. It would allow for finite difference calculation solely at the degrees of freedom affected by nonlinearities, while circumventing the sparse and/or constant columns of the Jacobian matrix.
Kind regards
Lysandros
Hi
Dynamical systems of second order as often encountered in structural dynamics can be transformed in the state-space configuration, where the order is reduced to first, and dimension is doubled. The essence is that the state vector is extended to include not only the position state, but also the velocity state.
This formulation leads to a Jacobian matrix which contains large areas of "zeros" and "ones". Would it be possible to define an additional option in Matcont, where the user can define the pattern/sparsity of the Jacobian and Hessian? If the algorithm would take this into account, I could imagine that te continuation could be accelerated.
Best regards
Lysandros Anastasopoulos
Dear Lysandros,
There are only two spots where this is relevant:
Best regards, Hil
From: lanast lanast@users.sourceforge.net
Sent: Saturday, April 4, 2020 12:33 PM
To: [matcont:discussion]
Subject: [matcont:discussion] Suggestion related to the Jacobian and Hessian calculation
Hi
Dynamical systems of second order as often encountered in structural dynamics can be transformed in the state-space configuration, where the order is reduced to first, and dimension is doubled. The essence is that the state vector is extended to include not only the position state, but also the velocity state.
This formulation leads to a Jacobian matrix which contains large areas of "zeros" and "ones". Would it be possible to define an additional option in Matcont, where the user can define the pattern/sparsity of the Jacobian and Hessian? If the algorithm would take this into account, I could imagine that te continuation could be accelerated.
Best regards
Lysandros Anastasopoulos
Suggestion related to the Jacobian and Hessian calculation
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Dear professor,
thank you for these remarks on the continuation process.
I have attached a suggestion of how the code structure could be adapted. It would allow for finite difference calculation solely at the degrees of freedom affected by nonlinearities, while circumventing the sparse and/or constant columns of the Jacobian matrix.
Kind regards
Lysandros
Dear Lysandros,
When you define a system in the GUI, you can specify whether you want to have your derivatives numerically, symbolically, or "from window". Have you tried integrating your input with this option?
Best, Hil
From: lanast lanast@users.sourceforge.net
Sent: Tuesday, May 12, 2020 9:17 PM
To: [matcont:discussion]
Subject: [matcont:discussion] Suggestion related to the Jacobian and Hessian calculation
Dear professor,
thank you for these remarks on the continuation process.
I have attached a suggestion of how the code structure could be adapted. It would allow for finite difference calculation solely at the degrees of freedom affected by nonlinearities, while circumventing the sparse and/or constant columns of the Jacobian matrix.
Kind regards
Lysandros
Attachments:
Suggestion related to the Jacobian and Hessian calculation
Sent from sourceforge.net because you indicated interest in https://sourceforge.net/p/matcont/discussion/762214/
To unsubscribe from further messages, please visit https://sourceforge.net/auth/subscriptions/
Dear Hil,
Thanks for the hint. I am aware of the fact, that the derivatives can be defined numerically, symbolically or from window.
Kind regards