Class Model_DAE

Inheritance Relationships

Base Type

Class Documentation

class amici::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

Model_DAE(const ModelDimensions &model_dimensions, SimulationParameters simulation_parameters, const SecondOrderMode o2mode, std::vector<realtype> const &idlist, std::vector<int> const &z2event, const bool pythonGenerated = false, const int ndxdotdp_explicit = 0)

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

void fJ(realtype t, realtype cj, const AmiVector &x, const AmiVector &dx, const AmiVector &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

void fJB(const realtype t, realtype cj, const AmiVector &x, const AmiVector &dx, const AmiVector &xB, const AmiVector &dxB, const AmiVector &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

void fJSparse(realtype t, realtype cj, const AmiVector &x, const AmiVector &dx, const AmiVector &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

void fJSparseB(const realtype t, realtype cj, const AmiVector &x, const AmiVector &dx, const AmiVector &xB, const AmiVector &dxB, const AmiVector &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

void fJDiag(realtype t, AmiVector &JDiag, realtype cj, const AmiVector &x, const AmiVector &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

void fJv(realtype t, const AmiVector &x, const AmiVector &dx, const AmiVector &xdot, const AmiVector &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)

void froot(realtype t, const AmiVector &x, const AmiVector &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

void fxdot(realtype t, const AmiVector &x, const AmiVector &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

void fxBdot_ss(const realtype t, const AmiVector &xB, const AmiVector &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

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

void writeSteadystateJB(const realtype t, realtype cj, const AmiVector &x, const AmiVector &dx, const AmiVector &xB, const AmiVector &dxB, const AmiVector &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 const_N_Vector x, const const_N_Vector dx)

Sensitivity of dx/dt wrt model parameters p.

Parameters

  • t: timepoint

  • x: Vector with the states

  • dx: Vector with the derivative states

void fdxdotdp(const realtype t, const AmiVector &x, const AmiVector &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)

void fsxdot(realtype t, const AmiVector &x, const AmiVector &dx, int ip, const AmiVector &sx, const AmiVector &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

std::unique_ptr<Solver> getSolver() override

Retrieves the solver object.

Return

The Solver instance

Protected Functions

void fJSparse(SUNMatrixContent_Sparse JSparse, realtype t, const realtype *x, const double *p, const double *k, const realtype *h, realtype cj, const realtype *dx, const realtype *w, const realtype *dwdx) = 0

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

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

void fxdot(realtype *xdot, realtype t, const realtype *x, const double *p, const double *k, const realtype *h, const realtype *dx, const realtype *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

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

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

Model specific implementation of fM.

Parameters

  • M: mass matrix

  • t: timepoint

  • x: Vector with the states

  • p: parameter vector

  • k: constants vector