Class Model_DAE

• Defined in File model_dae.h

Inheritance Relationships

Base Type

• public amici::Model (Class Model)

Class Documentation

class Model_DAE : public amici::Model

The Model class represents an AMICI DAE model.

The model does not contain any data, but represents the state of the model at a specific time t. The states must not always be in sync, but may be updated asynchronously.

Public Functions

Model_DAE() = default

default constructor

inline Model_DAE(ModelDimensions const &model_dimensions, SimulationParameters simulation_parameters, SecondOrderMode const o2mode, std::vector<realtype> const &idlist, std::vector<int> const &z2event, bool const pythonGenerated = false, int const ndxdotdp_explicit = 0, int const ndxdotdx_explicit = 0, int const w_recursion_depth = 0, std::map<realtype, std::vector<int>> state_independent_events = {})

Constructor with model dimensions.

Parameters:

• model_dimensions – Model dimensions

• simulation_parameters – Simulation parameters

• o2mode – second order sensitivity mode

• idlist – indexes indicating algebraic components (DAE only)

• z2event – mapping of event outputs to events

• pythonGenerated – flag indicating matlab or python wrapping

• ndxdotdp_explicit – number of nonzero elements dxdotdp_explicit

• ndxdotdx_explicit – number of nonzero elements dxdotdx_explicit

• w_recursion_depth – Recursion depth of fw

• state_independent_events – Map of events with state-independent triggers functions, mapping trigger timepoints to event indices.

virtual void fJ(realtype t, realtype cj, AmiVector const &x, AmiVector const &dx, AmiVector const &xdot, SUNMatrix J) override

Dense Jacobian function.

Parameters:

• t – time

• cj – scaling factor (inverse of timestep, DAE only)

• x – state

• dx – time derivative of state (DAE only)

• xdot – values of residual function (unused)

• J – dense matrix to which values of the jacobian will be written

void fJ(realtype t, realtype cj, const_N_Vector x, const_N_Vector dx, const_N_Vector xdot, SUNMatrix J)

Jacobian of xdot with respect to states x.

Parameters:

• t – timepoint

• cj – scaling factor, inverse of the step size

• x – Vector with the states

• dx – Vector with the derivative states

• xdot – Vector with the right hand side

• J – Matrix to which the Jacobian will be written

virtual void fJB(realtype const t, realtype cj, AmiVector const &x, AmiVector const &dx, AmiVector const &xB, AmiVector const &dxB, AmiVector const &xBdot, SUNMatrix JB) override

Dense Jacobian function.

Parameters:

• t – time

• cj – scaling factor (inverse of timestep, DAE only)

• x – state

• dx – time derivative of state (DAE only)

• xB – Vector with the adjoint states

• dxB – Vector with the adjoint derivative states

• xBdot – Vector with the adjoint right hand side (unused)

• JB – dense matrix to which values of the jacobian will be written

void fJB(realtype t, realtype cj, const_N_Vector x, const_N_Vector dx, const_N_Vector xB, const_N_Vector dxB, SUNMatrix JB)

Jacobian of xBdot with respect to adjoint state xB.

Parameters:

• t – timepoint

• cj – scaling factor, inverse of the step size

• x – Vector with the states

• dx – Vector with the derivative states

• xB – Vector with the adjoint states

• dxB – Vector with the adjoint derivative states

• JB – Matrix to which the Jacobian will be written

virtual void fJSparse(realtype t, realtype cj, AmiVector const &x, AmiVector const &dx, AmiVector const &xdot, SUNMatrix J) override

Sparse Jacobian function.

Parameters:

• t – time

• cj – scaling factor (inverse of timestep, DAE only)

• x – state

• dx – time derivative of state (DAE only)

• xdot – values of residual function (unused)

• J – sparse matrix to which values of the Jacobian will be written

void fJSparse(realtype t, realtype cj, const_N_Vector x, const_N_Vector dx, SUNMatrix J)

J in sparse form (for sparse solvers from the SuiteSparse Package)

Parameters:

• t – timepoint

• cj – scalar in Jacobian (inverse stepsize)

• x – Vector with the states

• dx – Vector with the derivative states

• J – Matrix to which the Jacobian will be written

virtual void fJSparseB(realtype const t, realtype cj, AmiVector const &x, AmiVector const &dx, AmiVector const &xB, AmiVector const &dxB, AmiVector const &xBdot, SUNMatrix JB) override

Sparse Jacobian function.

Parameters:

• t – time

• cj – scaling factor (inverse of timestep, DAE only)

• x – state

• dx – time derivative of state (DAE only)

• xB – Vector with the adjoint states

• dxB – Vector with the adjoint derivative states

• xBdot – Vector with the adjoint right hand side (unused)

• JB – dense matrix to which values of the jacobian will be written

void fJSparseB(realtype t, realtype cj, const_N_Vector x, const_N_Vector dx, const_N_Vector xB, const_N_Vector dxB, SUNMatrix JB)

JB in sparse form (for sparse solvers from the SuiteSparse Package)

Parameters:

• t – timepoint

• cj – scalar in Jacobian

• x – Vector with the states

• dx – Vector with the derivative states

• xB – Vector with the adjoint states

• dxB – Vector with the adjoint derivative states

• JB – Matrix to which the Jacobian will be written

virtual void fJDiag(realtype t, AmiVector &JDiag, realtype cj, AmiVector const &x, AmiVector const &dx) override

Diagonal of the Jacobian (for preconditioning)

Parameters:

• t – timepoint

• JDiag – Vector to which the Jacobian diagonal will be written

• cj – scaling factor, inverse of the step size

• x – Vector with the states

• dx – Vector with the derivative states

virtual void fJv(realtype t, AmiVector const &x, AmiVector const &dx, AmiVector const &xdot, AmiVector const &v, AmiVector &nJv, realtype cj) override

Jacobian multiply function.

Parameters:

• t – time

• x – state

• dx – time derivative of state (DAE only)

• xdot – values of residual function (unused)

• v – multiplication vector (unused)

• nJv – array to which result of multiplication will be written

• cj – scaling factor (inverse of timestep, DAE only)

void fJv(realtype t, const_N_Vector x, const_N_Vector dx, const_N_Vector v, N_Vector Jv, realtype cj)

Matrix vector product of J with a vector v (for iterative solvers)

Parameters:

• t – timepoint

• cj – scaling factor, inverse of the step size

• x – Vector with the states

• dx – Vector with the derivative states

• v – Vector with which the Jacobian is multiplied

• Jv – Vector to which the Jacobian vector product will be written

void fJvB(realtype t, const_N_Vector x, const_N_Vector dx, const_N_Vector xB, const_N_Vector dxB, const_N_Vector vB, N_Vector JvB, realtype cj)

Matrix vector product of JB with a vector v (for iterative solvers)

Parameters:

• t – timepoint

• x – Vector with the states

• dx – Vector with the derivative states

• xB – Vector with the adjoint states

• dxB – Vector with the adjoint derivative states

• vB – Vector with which the Jacobian is multiplied

• JvB – Vector to which the Jacobian vector product will be written

• cj – scalar in Jacobian (inverse stepsize)

virtual void froot(realtype t, AmiVector const &x, AmiVector const &dx, gsl::span<realtype> root) override

Root function.

Parameters:

• t – time

• x – state

• dx – time derivative of state (DAE only)

• root – array to which values of the root function will be written

void froot(realtype t, const_N_Vector x, const_N_Vector dx, gsl::span<realtype> root)

Event trigger function for events.

Parameters:

• t – timepoint

• x – Vector with the states

• dx – Vector with the derivative states

• root – array with root function values

virtual void fxdot(realtype t, AmiVector const &x, AmiVector const &dx, AmiVector &xdot) override

Residual function.

Parameters:

• t – time

• x – state

• dx – time derivative of state (DAE only)

• xdot – array to which values of the residual function will be written

void fxdot(realtype t, const_N_Vector x, const_N_Vector dx, N_Vector xdot)

Residual function of the DAE.

Parameters:

• t – timepoint

• x – Vector with the states

• dx – Vector with the derivative states

• xdot – Vector with the right hand side

void fxBdot(realtype t, const_N_Vector x, const_N_Vector dx, const_N_Vector xB, const_N_Vector dxB, N_Vector xBdot)

Right hand side of differential equation for adjoint state xB.

Parameters:

• t – timepoint

• x – Vector with the states

• dx – Vector with the derivative states

• xB – Vector with the adjoint states

• dxB – Vector with the adjoint derivative states

• xBdot – Vector with the adjoint right hand side

void fqBdot(realtype t, const_N_Vector x, const_N_Vector dx, const_N_Vector xB, const_N_Vector dxB, N_Vector qBdot)

Right hand side of integral equation for quadrature states qB.

Parameters:

• t – timepoint

• x – Vector with the states

• dx – Vector with the derivative states

• xB – Vector with the adjoint states

• dxB – Vector with the adjoint derivative states

• qBdot – Vector with the adjoint quadrature right hand side

virtual void fxBdot_ss(realtype const t, AmiVector const &xB, AmiVector const &dxB, AmiVector &xBdot) override

Residual function backward when running in steady state mode.

Parameters:

• t – time

• xB – adjoint state

• dxB – time derivative of state (DAE only)

• xBdot – array to which values of the residual function will be written

void fxBdot_ss(realtype t, const_N_Vector xB, const_N_Vector dxB, N_Vector xBdot) const

Implementation of fxBdot for steady state case at the N_Vector level.

Parameters:

• t – timepoint

• xB – Vector with the adjoint state

• dxB – Vector with the adjoint derivative states

• xBdot – Vector with the adjoint right hand side

void fqBdot_ss(realtype t, const_N_Vector xB, const_N_Vector dxB, N_Vector qBdot) const

Implementation of fqBdot for steady state at the N_Vector level.

Parameters:

• t – timepoint

• xB – Vector with the adjoint states

• dxB – Vector with the adjoint derivative states

• qBdot – Vector with the adjoint quadrature right hand side

virtual void fJSparseB_ss(SUNMatrix JB) override

Sparse Jacobian function backward, steady state case.

Parameters:

JB – sparse matrix to which values of the Jacobian will be written

virtual void writeSteadystateJB(realtype const t, realtype cj, AmiVector const &x, AmiVector const &dx, AmiVector const &xB, AmiVector const &dxB, AmiVector const &xBdot) override

Computes the sparse backward Jacobian for steadystate integration and writes it to the model member.

Parameters:

• t – timepoint

• cj – scalar in Jacobian

• x – Vector with the states

• dx – Vector with the derivative states

• xB – Vector with the adjoint states

• dxB – Vector with the adjoint derivative states

• xBdot – Vector with the adjoint state right hand side

void fdxdotdp(realtype t, const_N_Vector const x, const_N_Vector const dx)

Sensitivity of dx/dt wrt model parameters p.

Parameters:

• t – timepoint

• x – Vector with the states

• dx – Vector with the derivative states

inline virtual void fdxdotdp(realtype const t, AmiVector const &x, AmiVector const &dx) override

Model-specific sparse implementation of explicit parameter derivative of right hand side.

Parameters:

• t – time

• x – state

• dx – time derivative of state (DAE only)

virtual void fsxdot(realtype t, AmiVector const &x, AmiVector const &dx, int ip, AmiVector const &sx, AmiVector const &sdx, AmiVector &sxdot) override

Sensitivity Residual function.

Parameters:

• t – time

• x – state

• dx – time derivative of state (DAE only)

• ip – parameter index

• sx – sensitivity state

• sdx – time derivative of sensitivity state (DAE only)

• sxdot – array to which values of the sensitivity residual function will be written

void fsxdot(realtype t, const_N_Vector x, const_N_Vector dx, int ip, const_N_Vector sx, const_N_Vector sdx, N_Vector sxdot)

Right hand side of differential equation for state sensitivities sx.

Parameters:

• t – timepoint

• x – Vector with the states

• dx – Vector with the derivative states

• ip – parameter index

• sx – Vector with the state sensitivities

• sdx – Vector with the derivative state sensitivities

• sxdot – Vector with the sensitivity right hand side

void fM(realtype t, const_N_Vector x)

Mass matrix for DAE systems.

Parameters:

• t – timepoint

• x – Vector with the states

virtual std::unique_ptr<Solver> getSolver() override

Retrieves the solver object.

Returns:

The Solver instance

Protected Functions

virtual void fJSparse(SUNMatrixContent_Sparse JSparse, realtype t, realtype const *x, double const *p, double const *k, realtype const *h, realtype cj, realtype const *dx, realtype const *w, realtype const *dwdx)

Model specific implementation for fJSparse.

Parameters:

• JSparse – Matrix to which the Jacobian will be written

• t – timepoint

• x – Vector with the states

• p – parameter vector

• k – constants vector

• h – Heaviside vector

• cj – scaling factor, inverse of the step size

• dx – Vector with the derivative states

• w – vector with helper variables

• dwdx – derivative of w wrt x

virtual void froot(realtype *root, realtype t, realtype const *x, double const *p, double const *k, realtype const *h, realtype const *dx)

Model specific implementation for froot.

Parameters:

• root – values of the trigger function

• t – timepoint

• x – Vector with the states

• p – parameter vector

• k – constants vector

• h – Heaviside vector

• dx – Vector with the derivative states

virtual void fxdot(realtype *xdot, realtype t, realtype const *x, double const *p, double const *k, realtype const *h, realtype const *dx, realtype const *w) = 0

Model specific implementation for fxdot.

Parameters:

• xdot – residual function

• t – timepoint

• x – Vector with the states

• p – parameter vector

• k – constants vector

• h – Heaviside vector

• w – vector with helper variables

• dx – Vector with the derivative states

virtual void fdxdotdp(realtype *dxdotdp, realtype t, realtype const *x, realtype const *p, realtype const *k, realtype const *h, int ip, realtype const *dx, realtype const *w, realtype const *dwdp)

Model specific implementation of fdxdotdp.

Parameters:

• dxdotdp – partial derivative xdot wrt p

• t – timepoint

• x – Vector with the states

• p – parameter vector

• k – constants vector

• h – Heaviside vector

• ip – parameter index

• dx – Vector with the derivative states

• w – vector with helper variables

• dwdp – derivative of w wrt p

virtual void fdxdotdp_explicit(realtype *dxdotdp_explicit, realtype t, realtype const *x, realtype const *p, realtype const *k, realtype const *h, realtype const *dx, realtype const *w)

Model specific implementation of fdxdotdp_explicit, no w chainrule (Py)

Parameters:

• dxdotdp_explicit – partial derivative xdot wrt p

• t – timepoint

• x – Vector with the states

• p – parameter vector

• k – constants vector

• h – Heaviside vector

• dx – Vector with the derivative states

• w – vector with helper variables

virtual void fdxdotdp_explicit_colptrs(SUNMatrixWrapper &dxdotdp)

Model specific implementation of fdxdotdp_explicit, colptrs part.

Parameters:

dxdotdp – sparse matrix to which colptrs will be written

virtual void fdxdotdp_explicit_rowvals(SUNMatrixWrapper &dxdotdp)

Model specific implementation of fdxdotdp_explicit, rowvals part.

Parameters:

dxdotdp – sparse matrix to which rowvals will be written

virtual void fdxdotdx_explicit(realtype *dxdotdx_explicit, realtype t, realtype const *x, realtype const *p, realtype const *k, realtype const *h, realtype const *dx, realtype const *w)

Model specific implementation of fdxdotdx_explicit, no w chainrule (Py)

Parameters:

• dxdotdx_explicit – partial derivative xdot wrt x

• t – timepoint

• x – Vector with the states

• p – parameter vector

• k – constants vector

• h – heavyside vector

• dx – Vector with the derivative states

• w – vector with helper variables

virtual void fdxdotdx_explicit_colptrs(SUNMatrixWrapper &dxdotdx)

Model specific implementation of fdxdotdx_explicit, colptrs part.

Parameters:

dxdotdx – sparse matrix to which colptrs will be written

virtual void fdxdotdx_explicit_rowvals(SUNMatrixWrapper &dxdotdx)

Model specific implementation of fdxdotdx_explicit, rowvals part.

Parameters:

dxdotdx – sparse matrix to which rowvals will be written

virtual void fdxdotdw(realtype *dxdotdw, realtype t, realtype const *x, realtype const *p, realtype const *k, realtype const *h, realtype const *dx, realtype const *w)

Model specific implementation of fdxdotdw, data part.

Parameters:

• dxdotdw – partial derivative xdot wrt w

• t – timepoint

• x – Vector with the states

• p – parameter vector

• k – constants vector

• h – Heaviside vector

• dx – Vector with the derivative states

• w – vector with helper variables

virtual void fdxdotdw_colptrs(SUNMatrixWrapper &dxdotdw)

Model specific implementation of fdxdotdw, colptrs part.

Parameters:

dxdotdw – sparse matrix to which colptrs will be written

virtual void fdxdotdw_rowvals(SUNMatrixWrapper &dxdotdw)

Model specific implementation of fdxdotdw, rowvals part.

Parameters:

dxdotdw – sparse matrix to which rowvals will be written

void fdxdotdw(realtype t, const_N_Vector x, const_N_Vector dx)

Sensitivity of dx/dt wrt model parameters w.

Parameters:

• t – timepoint

• x – Vector with the states

• dx – Vector with the derivative states

virtual void fM(realtype *M, realtype const t, realtype const *x, realtype const *p, realtype const *k)

Model specific implementation of fM.

Parameters:

• M – mass matrix

• t – timepoint

• x – Vector with the states

• p – parameter vector

• k – constants vector