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 int nx_rdata, const int nxtrue_rdata, const int nx_solver, const int nxtrue_solver, const int nx_solver_reinit, const int ny, const int nytrue, const int nz, const int nztrue, const int ne, const int nJ, const int nw, const int ndwdx, const int ndwdp, const int ndwdw, const int ndxdotdw, std::vector<int> ndJydy, const int nnz, const int ubw, const int lbw, const SecondOrderMode o2mode, std::vector<realtype> const &p, std::vector<realtype> const &k, std::vector<int> const &plist, std::vector<realtype> const &idlist, std::vector<int> const &z2event, const bool pythonGenerated = false, const int ndxdotdp_explicit = 0)

Constructor with model dimensions.

Parameters

  • nx_rdata: number of state variables

  • nxtrue_rdata: number of state variables of the non-augmented model

  • nx_solver: number of state variables with conservation laws applied

  • nxtrue_solver: number of state variables of the non-augmented model with conservation laws applied

  • nx_solver_reinit: number of state variables with conservation laws subject to reinitialization

  • ny: number of observables

  • nytrue: number of observables of the non-augmented model

  • nz: number of event observables

  • nztrue: number of event observables of the non-augmented model

  • ne: number of events

  • nJ: number of objective functions

  • nw: number of repeating elements

  • ndwdx: number of nonzero elements in the x derivative of the repeating elements

  • ndwdp: number of nonzero elements in the p derivative of the repeating elements

  • ndwdw: number of nonzero elements in the w derivative of the repeating elements

  • ndxdotdw: number of nonzero elements dxdotdw

  • ndJydy: number of nonzero elements dJydy

  • nnz: number of nonzero elements in Jacobian

  • ubw: upper matrix bandwidth in the Jacobian

  • lbw: lower matrix bandwidth in the Jacobian

  • o2mode: second order sensitivity mode

  • p: parameters

  • k: constants

  • plist: indexes wrt to which sensitivities are to be computed

  • 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, N_Vector x, N_Vector dx, 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, N_Vector x, N_Vector dx, N_Vector xB, 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, N_Vector x, 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, N_Vector x, N_Vector dx, N_Vector xB, 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, N_Vector x, N_Vector dx, 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, N_Vector x, N_Vector dx, N_Vector xB, N_Vector dxB, 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, N_Vector x, 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, N_Vector x, 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, N_Vector x, N_Vector dx, N_Vector xB, 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, N_Vector x, N_Vector dx, N_Vector xB, 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, N_Vector xB, 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, N_Vector xB, 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 N_Vector x, 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, N_Vector x, N_Vector dx, int ip, N_Vector sx, 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