FX * createExternalFunction( const char * const objname ){
FX * extFun = new ExternalFunction("./" + string(objname));
extFun->init();
return extFun;
}
void generateCodeAndCompile(FX fcn, const std::string& name, bool expand){
cout << "Generating code for " << name << endl;
// Convert to an SXFunction (may or may not improve efficiency)
if(expand && is_a<MXFunction>(fcn)){
fcn = SXFunction(shared_cast<MXFunction>(fcn));
fcn.init();
}
// Generate C code
fcn.generateCode(name + ".c");
// Compilation command
string compile_command = "gcc -fPIC -shared -O3 " + name + ".c -o " + name + ".so";
// Compile the c-code
int flag = system(compile_command.c_str());
casadi_assert_message(flag==0, "Compilation failed");
}
void NLPSolverInternal::init(){
// Read options
verbose_ = getOption("verbose");
gauss_newton_ = getOption("gauss_newton");
// Initialize the functions
casadi_assert_message(!F_.isNull(),"No objective function");
if(!F_.isInit()){
F_.init();
log("Objective function initialized");
}
if(!G_.isNull() && !G_.isInit()){
G_.init();
log("Constraint function initialized");
}
// Get dimensions
n_ = F_.input(0).numel();
m_ = G_.isNull() ? 0 : G_.output(0).numel();
parametric_ = getOption("parametric");
if (parametric_) {
casadi_assert_message(F_.getNumInputs()==2, "Wrong number of input arguments to F for parametric NLP. Must be 2, but got " << F_.getNumInputs());
} else {
casadi_assert_message(F_.getNumInputs()==1, "Wrong number of input arguments to F for non-parametric NLP. Must be 1, but got " << F_.getNumInputs() << " instead. Do you perhaps intend to use fixed parameters? Then use the 'parametric' option.");
}
// Basic sanity checks
casadi_assert_message(F_.getNumInputs()==1 || F_.getNumInputs()==2, "Wrong number of input arguments to F. Must be 1 or 2");
if (F_.getNumInputs()==2) parametric_=true;
casadi_assert_message(getOption("ignore_check_vec") || gauss_newton_ || F_.input().size2()==1,
"To avoid confusion, the input argument to F must be vector. You supplied " << F_.input().dimString() << endl <<
" We suggest you make the following changes:" << endl <<
" - F is an SXFunction: SXFunction([X],[rhs]) -> SXFunction([vec(X)],[rhs])" << endl <<
" or F - -> F = vec(F) " <<
" - F is an MXFunction: MXFunction([X],[rhs]) -> " << endl <<
" X_vec = MX(\"X\",vec(X.sparsity())) " << endl <<
" F_vec = MXFunction([X_flat],[F.call([X_flat.reshape(X.sparsity())])[0]]) " << endl <<
" or F - -> F = vec(F) " <<
" You may ignore this warning by setting the 'ignore_check_vec' option to true." << endl
);
casadi_assert_message(F_.getNumOutputs()>=1, "Wrong number of output arguments to F");
casadi_assert_message(gauss_newton_ || F_.output().scalar(), "Output argument of F not scalar.");
casadi_assert_message(F_.output().dense(), "Output argument of F not dense.");
casadi_assert_message(F_.input().dense(), "Input argument of F must be dense. You supplied " << F_.input().dimString());
if(!G_.isNull()) {
if (parametric_) {
casadi_assert_message(G_.getNumInputs()==2, "Wrong number of input arguments to G for parametric NLP. Must be 2, but got " << G_.getNumInputs());
} else {
casadi_assert_message(G_.getNumInputs()==1, "Wrong number of input arguments to G for non-parametric NLP. Must be 1, but got " << G_.getNumInputs() << " instead. Do you perhaps intend to use fixed parameters? Then use the 'parametric' option.");
}
casadi_assert_message(G_.getNumOutputs()>=1, "Wrong number of output arguments to G");
casadi_assert_message(G_.input().numel()==n_, "Inconsistent dimensions");
casadi_assert_message(G_.input().sparsity()==F_.input().sparsity(), "F and G input dimension must match. F " << F_.input().dimString() << ". G " << G_.input().dimString());
}
// Find out if we are to expand the objective function in terms of scalar operations
bool expand_f = getOption("expand_f");
if(expand_f){
log("Expanding objective function");
// Cast to MXFunction
MXFunction F_mx = shared_cast<MXFunction>(F_);
if(F_mx.isNull()){
casadi_warning("Cannot expand objective function as it is not an MXFunction");
} else {
// Take use the input scheme of G if possible (it might be an SXFunction)
vector<SXMatrix> inputv;
if(!G_.isNull() && F_.getNumInputs()==G_.getNumInputs()){
inputv = G_.symbolicInputSX();
} else {
inputv = F_.symbolicInputSX();
}
// Try to expand the MXFunction
F_ = F_mx.expand(inputv);
F_.setOption("number_of_fwd_dir",F_mx.getOption("number_of_fwd_dir"));
F_.setOption("number_of_adj_dir",F_mx.getOption("number_of_adj_dir"));
F_.init();
}
}
// Find out if we are to expand the constraint function in terms of scalar operations
bool expand_g = getOption("expand_g");
if(expand_g){
log("Expanding constraint function");
// Cast to MXFunction
MXFunction G_mx = shared_cast<MXFunction>(G_);
if(G_mx.isNull()){
casadi_warning("Cannot expand constraint function as it is not an MXFunction");
} else {
// Take use the input scheme of F if possible (it might be an SXFunction)
vector<SXMatrix> inputv;
if(F_.getNumInputs()==G_.getNumInputs()){
inputv = F_.symbolicInputSX();
} else {
inputv = G_.symbolicInputSX();
}
// Try to expand the MXFunction
G_ = G_mx.expand(inputv);
G_.setOption("number_of_fwd_dir",G_mx.getOption("number_of_fwd_dir"));
G_.setOption("number_of_adj_dir",G_mx.getOption("number_of_adj_dir"));
G_.init();
}
}
// Find out if we are to expand the constraint function in terms of scalar operations
bool generate_hessian = getOption("generate_hessian");
if(generate_hessian && H_.isNull()){
casadi_assert_message(!gauss_newton_,"Automatic generation of Gauss-Newton Hessian not yet supported");
log("generating hessian");
// Simple if unconstrained
if(G_.isNull()){
// Create Hessian of the objective function
FX HF = F_.hessian();
HF.init();
// Symbolic inputs of HF
vector<MX> HF_in = F_.symbolicInput();
// Lagrange multipliers
MX lam("lam",0);
// Objective function scaling
MX sigma("sigma");
// Inputs of the Hessian function
vector<MX> H_in = HF_in;
H_in.insert(H_in.begin()+1, lam);
H_in.insert(H_in.begin()+2, sigma);
// Get an expression for the Hessian of F
MX hf = HF.call(HF_in).at(0);
// Create the scaled Hessian function
H_ = MXFunction(H_in, sigma*hf);
log("Unconstrained Hessian function generated");
} else { // G_.isNull()
// Check if the functions are SXFunctions
SXFunction F_sx = shared_cast<SXFunction>(F_);
SXFunction G_sx = shared_cast<SXFunction>(G_);
// Efficient if both functions are SXFunction
if(!F_sx.isNull() && !G_sx.isNull()){
// Expression for f and g
SXMatrix f = F_sx.outputSX();
SXMatrix g = G_sx.outputSX();
// Numeric hessian
bool f_num_hess = F_sx.getOption("numeric_hessian");
bool g_num_hess = G_sx.getOption("numeric_hessian");
// Number of derivative directions
int f_num_fwd = F_sx.getOption("number_of_fwd_dir");
int g_num_fwd = G_sx.getOption("number_of_fwd_dir");
int f_num_adj = F_sx.getOption("number_of_adj_dir");
int g_num_adj = G_sx.getOption("number_of_adj_dir");
// Substitute symbolic variables in f if different input variables from g
if(!isEqual(F_sx.inputSX(),G_sx.inputSX())){
f = substitute(f,F_sx.inputSX(),G_sx.inputSX());
}
// Lagrange multipliers
SXMatrix lam = ssym("lambda",g.size1());
// Objective function scaling
SXMatrix sigma = ssym("sigma");
// Lagrangian function
vector<SXMatrix> lfcn_in(parametric_? 4: 3);
lfcn_in[0] = G_sx.inputSX();
lfcn_in[1] = lam;
lfcn_in[2] = sigma;
if (parametric_) lfcn_in[3] = G_sx.inputSX(1);
SXFunction lfcn(lfcn_in, sigma*f + inner_prod(lam,g));
lfcn.setOption("verbose",getOption("verbose"));
lfcn.setOption("numeric_hessian",f_num_hess || g_num_hess);
lfcn.setOption("number_of_fwd_dir",std::min(f_num_fwd,g_num_fwd));
lfcn.setOption("number_of_adj_dir",std::min(f_num_adj,g_num_adj));
lfcn.init();
// Hessian of the Lagrangian
H_ = static_cast<FX&>(lfcn).hessian();
H_.setOption("verbose",getOption("verbose"));
log("SX Hessian function generated");
} else { // !F_sx.isNull() && !G_sx.isNull()
// Check if the functions are SXFunctions
MXFunction F_mx = shared_cast<MXFunction>(F_);
MXFunction G_mx = shared_cast<MXFunction>(G_);
// If they are, check if the arguments are the same
if(!F_mx.isNull() && !G_mx.isNull() && isEqual(F_mx.inputMX(),G_mx.inputMX())){
casadi_warning("Exact Hessian calculation for MX is still experimental");
// Expression for f and g
MX f = F_mx.outputMX();
MX g = G_mx.outputMX();
// Lagrange multipliers
MX lam("lam",g.size1());
// Objective function scaling
MX sigma("sigma");
// Inputs of the Lagrangian function
vector<MX> lfcn_in(parametric_? 4:3);
lfcn_in[0] = G_mx.inputMX();
lfcn_in[1] = lam;
lfcn_in[2] = sigma;
if (parametric_) lfcn_in[3] = G_mx.inputMX(1);
// Lagrangian function
MXFunction lfcn(lfcn_in,sigma*f+ inner_prod(lam,g));
lfcn.init();
log("SX Lagrangian function generated");
/* cout << "countNodes(lfcn.outputMX()) = " << countNodes(lfcn.outputMX()) << endl;*/
bool adjoint_mode = true;
if(adjoint_mode){
// Gradient of the lagrangian
MX gL = lfcn.grad();
log("MX Lagrangian gradient generated");
MXFunction glfcn(lfcn_in,gL);
glfcn.init();
log("MX Lagrangian gradient function initialized");
// cout << "countNodes(glfcn.outputMX()) = " << countNodes(glfcn.outputMX()) << endl;
// Get Hessian sparsity
CRSSparsity H_sp = glfcn.jacSparsity();
log("MX Lagrangian Hessian sparsity determined");
// Uni-directional coloring (note, the hessian is symmetric)
CRSSparsity coloring = H_sp.unidirectionalColoring(H_sp);
log("MX Lagrangian Hessian coloring determined");
// Number of colors needed is the number of rows
int nfwd_glfcn = coloring.size1();
log("MX Lagrangian gradient function number of sensitivity directions determined");
glfcn.setOption("number_of_fwd_dir",nfwd_glfcn);
glfcn.updateNumSens();
log("MX Lagrangian gradient function number of sensitivity directions updated");
// Hessian of the Lagrangian
H_ = glfcn.jacobian();
} else {
// Hessian of the Lagrangian
H_ = lfcn.hessian();
}
log("MX Lagrangian Hessian function generated");
} else {
casadi_assert_message(0, "Automatic calculation of exact Hessian currently only for F and G both SXFunction or MXFunction ");
}
} // !F_sx.isNull() && !G_sx.isNull()
} // G_.isNull()
} // generate_hessian && H_.isNull()
if(!H_.isNull() && !H_.isInit()) {
H_.init();
log("Hessian function initialized");
}
// Create a Jacobian if it does not already exists
bool generate_jacobian = getOption("generate_jacobian");
if(generate_jacobian && !G_.isNull() && J_.isNull()){
log("Generating Jacobian");
J_ = G_.jacobian();
// Use live variables if SXFunction
if(!shared_cast<SXFunction>(J_).isNull()){
J_.setOption("live_variables",true);
}
log("Jacobian function generated");
}
if(!J_.isNull() && !J_.isInit()){
J_.init();
log("Jacobian function initialized");
}
if(!H_.isNull()) {
if (parametric_) {
casadi_assert_message(H_.getNumInputs()>=2, "Wrong number of input arguments to H for parametric NLP. Must be at least 2, but got " << G_.getNumInputs());
} else {
casadi_assert_message(H_.getNumInputs()>=1, "Wrong number of input arguments to H for non-parametric NLP. Must be at least 1, but got " << G_.getNumInputs() << " instead. Do you perhaps intend to use fixed parameters? Then use the 'parametric' option.");
}
casadi_assert_message(H_.getNumOutputs()>=1, "Wrong number of output arguments to H");
casadi_assert_message(H_.input(0).numel()==n_,"Inconsistent dimensions");
casadi_assert_message(H_.output().size1()==n_,"Inconsistent dimensions");
casadi_assert_message(H_.output().size2()==n_,"Inconsistent dimensions");
}
if(!J_.isNull()){
if (parametric_) {
casadi_assert_message(J_.getNumInputs()==2, "Wrong number of input arguments to J for parametric NLP. Must be at least 2, but got " << G_.getNumInputs());
} else {
casadi_assert_message(J_.getNumInputs()==1, "Wrong number of input arguments to J for non-parametric NLP. Must be at least 1, but got " << G_.getNumInputs() << " instead. Do you perhaps intend to use fixed parameters? Then use the 'parametric' option.");
}
casadi_assert_message(J_.getNumOutputs()>=1, "Wrong number of output arguments to J");
casadi_assert_message(J_.input().numel()==n_,"Inconsistent dimensions");
casadi_assert_message(J_.output().size2()==n_,"Inconsistent dimensions");
}
if (parametric_) {
sp_p = F_->input(1).sparsity();
if (!G_.isNull()) casadi_assert_message(sp_p == G_->input(G_->getNumInputs()-1).sparsity(),"Parametric NLP has inconsistent parameter dimensions. F has got " << sp_p.dimString() << " as dimensions, while G has got " << G_->input(G_->getNumInputs()-1).dimString());
if (!H_.isNull()) casadi_assert_message(sp_p == H_->input(H_->getNumInputs()-1).sparsity(),"Parametric NLP has inconsistent parameter dimensions. F has got " << sp_p.dimString() << " as dimensions, while H has got " << H_->input(H_->getNumInputs()-1).dimString());
if (!J_.isNull()) casadi_assert_message(sp_p == J_->input(J_->getNumInputs()-1).sparsity(),"Parametric NLP has inconsistent parameter dimensions. F has got " << sp_p.dimString() << " as dimensions, while J has got " << J_->input(J_->getNumInputs()-1).dimString());
}
// Infinity
double inf = numeric_limits<double>::infinity();
// Allocate space for inputs
input_.resize(NLP_NUM_IN - (parametric_? 0 : 1));
input(NLP_X_INIT) = DMatrix(n_,1,0);
input(NLP_LBX) = DMatrix(n_,1,-inf);
input(NLP_UBX) = DMatrix(n_,1, inf);
input(NLP_LBG) = DMatrix(m_,1,-inf);
input(NLP_UBG) = DMatrix(m_,1, inf);
input(NLP_LAMBDA_INIT) = DMatrix(m_,1,0);
if (parametric_) input(NLP_P) = DMatrix(sp_p,0);
// Allocate space for outputs
output_.resize(NLP_NUM_OUT);
output(NLP_X_OPT) = DMatrix(n_,1,0);
output(NLP_COST) = DMatrix(1,1,0);
output(NLP_LAMBDA_X) = DMatrix(n_,1,0);
output(NLP_LAMBDA_G) = DMatrix(m_,1,0);
output(NLP_G) = DMatrix(m_,1,0);
if (hasSetOption("iteration_callback")) {
callback_ = getOption("iteration_callback");
if (!callback_.isNull()) {
if (!callback_.isInit()) callback_.init();
casadi_assert_message(callback_.getNumOutputs()==1, "Callback function should have one output, a scalar that indicates wether to break. 0 = continue");
casadi_assert_message(callback_.output(0).size()==1, "Callback function should have one output, a scalar that indicates wether to break. 0 = continue");
casadi_assert_message(callback_.getNumInputs()==NLP_NUM_OUT, "Callback function should have the output scheme of NLPSolver as input scheme. i.e. " <<NLP_NUM_OUT << " inputs instead of the " << callback_.getNumInputs() << " you provided." );
for (int i=0;i<NLP_NUM_OUT;i++) {
casadi_assert_message(callback_.input(i).sparsity()==output(i).sparsity(),
"Callback function should have the output scheme of NLPSolver as input scheme. " <<
"Input #" << i << " (" << getSchemeEntryEnumName(SCHEME_NLPOutput,i) << " aka '" << getSchemeEntryName(SCHEME_NLPOutput,i) << "') was found to be " << callback_.input(i).dimString() << " instead of expected " << output(i).dimString() << "."
);
callback_.input(i).setAll(0);
}
}
}
callback_step_ = getOption("iteration_callback_step");
// Call the initialization method of the base class
FXInternal::init();
}
void CollocationIntegratorInternal::init(){
// Call the base class init
IntegratorInternal::init();
// Legendre collocation points
double legendre_points[][6] = {
{0},
{0,0.500000},
{0,0.211325,0.788675},
{0,0.112702,0.500000,0.887298},
{0,0.069432,0.330009,0.669991,0.930568},
{0,0.046910,0.230765,0.500000,0.769235,0.953090}};
// Radau collocation points
double radau_points[][6] = {
{0},
{0,1.000000},
{0,0.333333,1.000000},
{0,0.155051,0.644949,1.000000},
{0,0.088588,0.409467,0.787659,1.000000},
{0,0.057104,0.276843,0.583590,0.860240,1.000000}};
// Read options
bool use_radau;
if(getOption("collocation_scheme")=="radau"){
use_radau = true;
} else if(getOption("collocation_scheme")=="legendre"){
use_radau = false;
}
// Hotstart?
hotstart_ = getOption("hotstart");
// Number of finite elements
int nk = getOption("number_of_finite_elements");
// Interpolation order
int deg = getOption("interpolation_order");
// Assume explicit ODE
bool explicit_ode = f_.input(DAE_XDOT).size()==0;
// All collocation time points
double* tau_root = use_radau ? radau_points[deg] : legendre_points[deg];
// Size of the finite elements
double h = (tf_-t0_)/nk;
// MX version of the same
MX h_mx = h;
// Coefficients of the collocation equation
vector<vector<MX> > C(deg+1,vector<MX>(deg+1));
// Coefficients of the continuity equation
vector<MX> D(deg+1);
// Collocation point
SXMatrix tau = ssym("tau");
// For all collocation points
for(int j=0; j<deg+1; ++j){
// Construct Lagrange polynomials to get the polynomial basis at the collocation point
SXMatrix L = 1;
for(int j2=0; j2<deg+1; ++j2){
if(j2 != j){
L *= (tau-tau_root[j2])/(tau_root[j]-tau_root[j2]);
}
}
SXFunction lfcn(tau,L);
lfcn.init();
// Evaluate the polynomial at the final time to get the coefficients of the continuity equation
lfcn.setInput(1.0);
lfcn.evaluate();
D[j] = lfcn.output();
// Evaluate the time derivative of the polynomial at all collocation points to get the coefficients of the continuity equation
for(int j2=0; j2<deg+1; ++j2){
lfcn.setInput(tau_root[j2]);
lfcn.setFwdSeed(1.0);
lfcn.evaluate(1,0);
C[j][j2] = lfcn.fwdSens();
}
}
// Initial state
MX X0("X0",nx_);
// Parameters
MX P("P",np_);
// Backward state
MX RX0("RX0",nrx_);
// Backward parameters
MX RP("RP",nrp_);
// Collocated differential states and algebraic variables
int nX = (nk*(deg+1)+1)*(nx_+nrx_);
int nZ = nk*deg*(nz_+nrz_);
// Unknowns
MX V("V",nX+nZ);
int offset = 0;
// Get collocated states, algebraic variables and times
vector<vector<MX> > X(nk+1);
vector<vector<MX> > RX(nk+1);
vector<vector<MX> > Z(nk);
vector<vector<MX> > RZ(nk);
coll_time_.resize(nk+1);
for(int k=0; k<nk+1; ++k){
// Number of time points
int nj = k==nk ? 1 : deg+1;
// Allocate differential states expressions at the time points
X[k].resize(nj);
RX[k].resize(nj);
coll_time_[k].resize(nj);
// Allocate algebraic variable expressions at the collocation points
if(k!=nk){
Z[k].resize(nj-1);
RZ[k].resize(nj-1);
}
// For all time points
for(int j=0; j<nj; ++j){
// Get expressions for the differential state
X[k][j] = V[range(offset,offset+nx_)];
offset += nx_;
RX[k][j] = V[range(offset,offset+nrx_)];
offset += nrx_;
// Get the local time
coll_time_[k][j] = h*(k + tau_root[j]);
// Get expressions for the algebraic variables
if(j>0){
Z[k][j-1] = V[range(offset,offset+nz_)];
offset += nz_;
RZ[k][j-1] = V[range(offset,offset+nrz_)];
offset += nrz_;
}
}
}
// Check offset for consistency
casadi_assert(offset==V.size());
// Constraints
vector<MX> g;
g.reserve(2*(nk+1));
// Quadrature expressions
MX QF = MX::zeros(nq_);
MX RQF = MX::zeros(nrq_);
// Counter
int jk = 0;
// Add initial condition
g.push_back(X[0][0]-X0);
// For all finite elements
for(int k=0; k<nk; ++k, ++jk){
// For all collocation points
for(int j=1; j<deg+1; ++j, ++jk){
// Get the time
MX tkj = coll_time_[k][j];
// Get an expression for the state derivative at the collocation point
MX xp_jk = 0;
for(int j2=0; j2<deg+1; ++j2){
xp_jk += C[j2][j]*X[k][j2];
}
// Add collocation equations to the NLP
vector<MX> f_in(DAE_NUM_IN);
f_in[DAE_T] = tkj;
f_in[DAE_P] = P;
f_in[DAE_X] = X[k][j];
f_in[DAE_Z] = Z[k][j-1];
vector<MX> f_out;
if(explicit_ode){
// Assume equation of the form ydot = f(t,y,p)
f_out = f_.call(f_in);
g.push_back(h_mx*f_out[DAE_ODE] - xp_jk);
} else {
// Assume equation of the form 0 = f(t,y,ydot,p)
f_in[DAE_XDOT] = xp_jk/h_mx;
f_out = f_.call(f_in);
g.push_back(f_out[DAE_ODE]);
}
// Add the algebraic conditions
if(nz_>0){
g.push_back(f_out[DAE_ALG]);
}
// Add the quadrature
if(nq_>0){
QF += D[j]*h_mx*f_out[DAE_QUAD];
}
// Now for the backward problem
if(nrx_>0){
// Get an expression for the state derivative at the collocation point
MX rxp_jk = 0;
for(int j2=0; j2<deg+1; ++j2){
rxp_jk += C[j2][j]*RX[k][j2];
}
// Add collocation equations to the NLP
vector<MX> g_in(RDAE_NUM_IN);
g_in[RDAE_T] = tkj;
g_in[RDAE_X] = X[k][j];
g_in[RDAE_Z] = Z[k][j-1];
g_in[RDAE_P] = P;
g_in[RDAE_RP] = RP;
g_in[RDAE_RX] = RX[k][j];
g_in[RDAE_RZ] = RZ[k][j-1];
vector<MX> g_out;
if(explicit_ode){
// Assume equation of the form xdot = f(t,x,p)
g_out = g_.call(g_in);
g.push_back(h_mx*g_out[RDAE_ODE] - rxp_jk);
} else {
// Assume equation of the form 0 = f(t,x,xdot,p)
g_in[RDAE_XDOT] = xp_jk/h_mx;
g_in[RDAE_RXDOT] = rxp_jk/h_mx;
g_out = g_.call(g_in);
g.push_back(g_out[RDAE_ODE]);
}
// Add the algebraic conditions
if(nrz_>0){
g.push_back(g_out[RDAE_ALG]);
}
// Add the backward quadrature
if(nrq_>0){
RQF += D[j]*h_mx*g_out[RDAE_QUAD];
}
}
}
// Get an expression for the state at the end of the finite element
MX xf_k = 0;
for(int j=0; j<deg+1; ++j){
xf_k += D[j]*X[k][j];
}
// Add continuity equation to NLP
g.push_back(X[k+1][0] - xf_k);
if(nrx_>0){
// Get an expression for the state at the end of the finite element
MX rxf_k = 0;
for(int j=0; j<deg+1; ++j){
rxf_k += D[j]*RX[k][j];
}
// Add continuity equation to NLP
g.push_back(RX[k+1][0] - rxf_k);
}
}
// Add initial condition for the backward integration
if(nrx_>0){
g.push_back(RX[nk][0]-RX0);
}
// Constraint expression
MX gv = vertcat(g);
// Make sure that the dimension is consistent with the number of unknowns
casadi_assert_message(gv.size()==V.size(),"Implicit function unknowns and equations do not match");
// Nonlinear constraint function input
vector<MX> gfcn_in(1+INTEGRATOR_NUM_IN);
gfcn_in[0] = V;
gfcn_in[1+INTEGRATOR_X0] = X0;
gfcn_in[1+INTEGRATOR_P] = P;
gfcn_in[1+INTEGRATOR_RX0] = RX0;
gfcn_in[1+INTEGRATOR_RP] = RP;
vector<MX> gfcn_out(1+INTEGRATOR_NUM_OUT);
gfcn_out[0] = gv;
gfcn_out[1+INTEGRATOR_XF] = X[nk][0];
gfcn_out[1+INTEGRATOR_QF] = QF;
gfcn_out[1+INTEGRATOR_RXF] = RX[0][0];
gfcn_out[1+INTEGRATOR_RQF] = RQF;
// Nonlinear constraint function
FX gfcn = MXFunction(gfcn_in,gfcn_out);
// Expand f?
bool expand_f = getOption("expand_f");
if(expand_f){
gfcn.init();
gfcn = SXFunction(shared_cast<MXFunction>(gfcn));
}
// Get the NLP creator function
implicitFunctionCreator implicit_function_creator = getOption("implicit_solver");
// Allocate an NLP solver
implicit_solver_ = implicit_function_creator(gfcn);
// Pass options
if(hasSetOption("implicit_solver_options")){
const Dictionary& implicit_solver_options = getOption("implicit_solver_options");
implicit_solver_.setOption(implicit_solver_options);
}
// Initialize the solver
implicit_solver_.init();
if(hasSetOption("startup_integrator")){
// Create the linear solver
integratorCreator startup_integrator_creator = getOption("startup_integrator");
// Allocate an NLP solver
startup_integrator_ = startup_integrator_creator(f_,g_);
// Pass options
startup_integrator_.setOption("number_of_fwd_dir",0); // not needed
startup_integrator_.setOption("number_of_adj_dir",0); // not needed
startup_integrator_.setOption("t0",coll_time_.front().front());
startup_integrator_.setOption("tf",coll_time_.back().back());
if(hasSetOption("startup_integrator_options")){
const Dictionary& startup_integrator_options = getOption("startup_integrator_options");
startup_integrator_.setOption(startup_integrator_options);
}
// Initialize the startup integrator
startup_integrator_.init();
}
// Mark the system not yet integrated
integrated_once_ = false;
}
int main(){
// Test both SX and MX
for(int test=0; test<2; ++test){
// Create a simple function
FX f;
if(test==0){
cout << "SXFunction:" << endl;
SXMatrix x = ssym("x",3);
SXMatrix z = x[0]*x[0]+x[2] + 3;
f = SXFunction(x,z);
} else {
cout << "MXFunction:" << endl;
MX x = msym("x",3);
MX z = x[0]*x[0]+x[2] + 3;
f = MXFunction(x,z);
}
f.init();
// Get arrays for the inputs and outputs, reinterpreting the vector of double as an array of unsigned integers
bvec_t* f_in = get_bvec_t(f.input().data());
bvec_t* f_out = get_bvec_t(f.output().data());
// Propagate from input to output (forward mode)
cout << "forward mode" << endl;
int fwd = true;
// Make sure that the class is able to support the dependency propagation
casadi_assert(f.spCanEvaluate(fwd));
// Pass seeds
f_in[0] = bvec_t(1) << 0; // seed in direction 0
f_in[1] = bvec_t(1) << 2; // seed in direction 2
f_in[2] = (bvec_t(1) << 4) | (bvec_t(1) << 63); // seed in direction 4 and 63
// Reset sensitivities
f_out[0] = 0;
// Propagate dependencies
f.spInit(fwd);
f.spEvaluate(fwd);
// Print the result
printBinary(f_out[0]);
// Propagate from output to input (adjoint/reverse/backward mode)
cout << "backward mode" << endl;
fwd = false;
// Make sure that the class is able to support the dependency propagation
casadi_assert(f.spCanEvaluate(fwd));
// Pass seeds
f_out[0] = (bvec_t(1) << 5) | (bvec_t(1) << 6); // seed in direction 5 and 6
// Reset sensitivities
f_in[0] = 0;
f_in[1] = 0;
f_in[2] = 0;
// Propagate dependencies
f.spInit(fwd);
f.spEvaluate(fwd);
// Print the result
printBinary(f_in[0]);
printBinary(f_in[1]);
printBinary(f_in[2]);
}
return 0;
}
int main(){
// Time horizon
double t0 = 0, tf = 10;
// Bounds on the control
double /*u_lb = -0.5, u_ub = 1.3,*/ u_init = 1;
// Initial conditions
vector<double> x0(3);
x0[0] = 0;
x0[1] = 0;
x0[2] = 1;
// Integrator
Integrator integrator = create_Sundials();
// Attach user-defined linear solver
if(user_defined_solver){
if(sparse_direct){
integrator.setOption("linear_solver_creator",CSparse::creator);
// integrator.setOption("linear_solver_creator",SuperLU::creator);
} else {
integrator.setOption("linear_solver_creator",LapackLUDense::creator);
integrator.setOption("linear_solver","user_defined");
}
// integrator.setOption("linear_solver","user_defined"); // FIXME: bug for second order
}
// Set common integrator options
integrator.setOption("fsens_err_con",true);
integrator.setOption("quad_err_con",true);
integrator.setOption("abstol",1e-12);
integrator.setOption("reltol",1e-12);
integrator.setOption("fsens_abstol",1e-6);
integrator.setOption("fsens_reltol",1e-6);
integrator.setOption("asens_abstol",1e-6);
integrator.setOption("asens_reltol",1e-6);
integrator.setOption("exact_jacobian",exact_jacobian);
integrator.setOption("finite_difference_fsens",finite_difference_fsens);
integrator.setOption("max_num_steps",100000);
// integrator.setOption("max_multistep_order",4);
integrator.setOption("t0",t0);
integrator.setOption("tf",tf);
// Initialize the integrator
integrator.init();
// Set parameters
integrator.setInput(u_init,INTEGRATOR_P);
// Set inital state
integrator.setInput(x0,INTEGRATOR_X0);
// Integrate
integrator.evaluate();
// Save the result
Matrix<double> res0_xf = integrator.output(INTEGRATOR_XF);
Matrix<double> res0_qf = integrator.output(INTEGRATOR_QF);
// Perturb in some direction
if(perturb_u){
double u_pert = u_init + 0.01;
integrator.setInput(u_pert,INTEGRATOR_P);
} else {
vector<double> x_pert = x0;
x_pert[1] += 0.01;
integrator.setInput(x_pert,INTEGRATOR_X0);
}
// Integrate again
integrator.evaluate();
// Print statistics
integrator.printStats();
// Calculate finite difference approximation
Matrix<double> fd_xf = (integrator.output(INTEGRATOR_XF) - res0_xf)/0.01;
Matrix<double> fd_qf = (integrator.output(INTEGRATOR_QF) - res0_qf)/0.01;
cout << "unperturbed " << res0_xf << "; " << res0_qf << endl;
cout << "perturbed " << integrator.output(INTEGRATOR_XF) << "; " << integrator.output(INTEGRATOR_QF) << endl;
cout << "finite_difference approximation " << fd_xf << "; " << fd_qf << endl;
if(perturb_u){
integrator.setFwdSeed(1.0,INTEGRATOR_P);
} else {
vector<double> x0_seed(x0.size(),0);
x0_seed[1] = 1;
integrator.setFwdSeed(x0_seed,INTEGRATOR_X0);
}
// Reset parameters
integrator.setInput(u_init,INTEGRATOR_P);
// Reset initial state
integrator.setInput(x0,INTEGRATOR_X0);
if(with_asens){
// backward seeds
vector<double> &bseed = integrator.adjSeed(INTEGRATOR_XF).data();
fill(bseed.begin(),bseed.end(),0);
bseed[1] = 1;
// evaluate with forward and adjoint sensitivities
integrator.evaluate(1,1);
} else {
// evaluate with only forward sensitivities
integrator.evaluate(1,0);
}
Matrix<double> fsens_xf = integrator.fwdSens(INTEGRATOR_XF);
Matrix<double> fsens_qf = integrator.fwdSens(INTEGRATOR_QF);
cout << "forward sensitivities " << fsens_xf << "; " << fsens_qf << endl;
if(with_asens){
cout << "adjoint sensitivities ";
cout << integrator.adjSens(INTEGRATOR_X0) << "; ";
cout << integrator.adjSens(INTEGRATOR_P) << "; ";
cout << endl;
}
if(second_order){
// Preturb the forward seeds
if(perturb_u){
double u_seed = 1.001;
integrator.setFwdSeed(u_seed,INTEGRATOR_P);
} else {
vector<double> x0_seed(x0.size(),0);
x0_seed[1] = 1.001;
integrator.setFwdSeed(x0_seed,INTEGRATOR_X0);
}
// evaluate again with forward sensitivities
integrator.evaluate(1,0);
vector<double> fsens_pret_xf = integrator.fwdSens(INTEGRATOR_XF).data();
vector<double> fsens_pret_qf = integrator.fwdSens(INTEGRATOR_QF).data();
cout << "forward sensitivities preturbed " << fsens_pret_xf << "; " << fsens_pret_qf << endl;
vector<double> fd2_xf(fsens_xf.size());
vector<double> fd2_qf(fsens_qf.size());
for(int i=0; i<fd2_xf.size(); ++i)
fd2_xf[i] = (fsens_pret_xf.at(i)-fsens_xf.at(i))/0.001;
for(int i=0; i<fd2_qf.size(); ++i)
fd2_qf[i] = (fsens_pret_qf.at(i)-fsens_qf.at(i))/0.001;
cout << "finite differences, 2nd order " << fd2_xf << "; " << fd2_qf << endl;
// Generate the jacobian by creating a new integrator for the sensitivity equations by source transformation
FX intjac = integrator.jacobian(INTEGRATOR_P,INTEGRATOR_XF);
// Set options
intjac.setOption("number_of_fwd_dir",0);
intjac.setOption("number_of_adj_dir",1);
// Initialize the integrator
intjac.init();
// Set inputs
intjac.setInput(u_init,INTEGRATOR_P);
intjac.setInput(x0,INTEGRATOR_X0);
// Set adjoint seed
vector<double> jacseed(3*1,0);
jacseed[0] = 1;
intjac.setAdjSeed(jacseed);
// Evaluate the Jacobian
intjac.evaluate(0,0);
cout << "jacobian " << intjac.output(0) << endl;
// Get the results
/* cout << "unperturbed via jacobian " << intjac.output(1+INTEGRATOR_XF) << endl;*/
cout << "second order (fwd-over-adj) " ;
cout << intjac.adjSens(INTEGRATOR_X0) << ", ";
cout << intjac.adjSens(INTEGRATOR_P) << endl;
// Save the unpreturbed value
Matrix<double> unpret = intjac.output();
// Perturb X0
intjac.setInput(u_init+0.01,INTEGRATOR_P);
intjac.evaluate();
Matrix<double> pret = intjac.output();
cout << "unperturbed fwd sens " << unpret << endl;
cout << "perturbed fwd sens " << pret << endl;
cout << "finite diff. (augmented dae) " << (pret-unpret)/0.01 << endl;
}
return 0;
}