virtual void test() {
std::vector<std::pair<boost::numeric::ublas::vector<double>, boost::numeric::ublas::vector<double> > > train = DataSetMNIST::get_train();
train.resize(100);
png::image<png::rgb_pixel> image(28 * train.size(), 28);
for (int z = 0; z < train.size(); z++) {
boost::numeric::ublas::vector<double> f = f_shallow(train[z].first);
for (std::size_t y = 0; y < 28; ++y) {
for (std::size_t x = 0; x < 28; ++x) {
double c = f[y * 28 + x] + 1;
c *= 127.5;
char b = c;
image[y][x + z * 28] = png::rgb_pixel(b, b, b);
}
}
}
image.write("badass.png");
for (std::size_t i = 0; i < train.size(); i++) {
boost::numeric::ublas::vector<double> t0 = m_network->f(train[i].first);
boost::numeric::ublas::vector<double> t1 = f_shallow(train[i].first);
std::cout << "final diff " << norm_1(t0 - t1) << std::endl;
for (int i = 0; i < t0.size(); i++) {
// std::cout << train[i].first[i] << " " << t0[i] << " " << t1[i] << std::endl;
}
}
}
bool operator==(const Vector& lhs, const Vector& rhs)
{
bool result = false;
if (lhs.size() == rhs.size()){
result = (norm_1(lhs-rhs) == 0);
}
return result;
}
matrix exp(matrix x, double ap, double rp,int ns)
{
matrix t = my_identity(x.cols);
matrix s = my_identity(x.cols);
for (int k=0; k<ns; k++)
{
t = t*x/k; // next term
s = s + t; // add next term
if (norm_1(t)<max(ap,norm_1(s)*rp))
{
return s;
}
}
cout << "error! exp: no convergence!\n";
exit(-1);
}
c_vector<double, SPACE_DIM+1> Element<ELEMENT_DIM, SPACE_DIM>::CalculateInterpolationWeightsWithProjection(const ChastePoint<SPACE_DIM>& rTestPoint)
{
//Can only test if it's a tetrahedral mesh in 3d, triangles in 2d...
assert(ELEMENT_DIM == SPACE_DIM);
c_vector<double, SPACE_DIM+1> weights = CalculateInterpolationWeights(rTestPoint);
// Check for negative weights and set them to zero.
bool negative_weight = false;
for (unsigned i=0; i<=SPACE_DIM; i++)
{
if (weights[i] < 0.0)
{
weights[i] = 0.0;
negative_weight = true;
}
}
if (negative_weight == false)
{
// If there are no negative weights, there is nothing to do.
return weights;
}
// Renormalise so that all weights add to 1.0.
// Note that all elements of weights are now non-negative and so the l1-norm (sum of magnitudes) is equivalent to the sum of the elements of the vector
double sum = norm_1 (weights);
//l1-norm ought to be above 1 (because we scrubbed negative weights)
//However, if we scrubbed weights that were the size of the machine precision then we might be close to one (even less than 1).
assert( sum + DBL_EPSILON >= 1.0);
//We might skip this division when sum ~= 1
weights = weights/sum;
return weights;
}
int main() {
Vec<3,double> v0;
std::cout << v0 << std::endl;
Vec<3,double> v1 = Vec<3,double>(0.,1.,2);
Vec<3,double> v2 = Vec<3,double>(3,4,5);
Vec<3,double> v3 = v1 * (v2 + v2);
std::cout << v3 << std::endl;
std::cout << norm(v3) << std::endl;
std::cout << norm_2(v3) << std::endl;
Vec<4, double> v = Vec<4,double>(1, 2.1f, 3.14, 2u);
std::cout << norm_1(v) << std::endl;
std::cout << norm_2(v) << std::endl;
std::cout << norm_inf(v) << std::endl;
std::cout << v << std::endl;
return 0;
}
dgematrix expm(const dgematrix &A)
{
int m_vals[5] = {3,5,7,9,13};
long double theta[5] = {1.495585217958292e-002,
2.539398330063230e-001,
9.504178996162932e-001,
2.097847961257068e+000,
5.371920351148152e+000};
double normA = norm_1(A);
int i;
int s;
int p;
dgematrix F;
if (normA <= theta[4])
{
for (i=0;i<5;i++)
if(normA <= theta[i])
{
F = PadeApproximantOfDegree(A,m_vals[i]);
break;
}
}
else
{
s = (int)(log2(normA/theta[4])) + 1;
p = (int)pow(2.,s);
F = PadeApproximantOfDegree(A/p,m_vals[4]);
for( i=0 ; i < s ; i++)
F*=F;
}
return F;
}
typename type_traits<typename V::value_type>::real_type
asum (const V &v) {
return norm_1 (v);
}
double condition_number(const matrix& A)
{
return norm_1(A)/norm_1(inv(A));
}
bool operator==(const matrix& A, const matrix& B)
{
return (norm_1(A-B)<PRECISION);
}
void SQPInternal::evaluate(int nfdir, int nadir){
casadi_assert(nfdir==0 && nadir==0);
checkInitialBounds();
// Get problem data
const vector<double>& x_init = input(NLP_X_INIT).data();
const vector<double>& lbx = input(NLP_LBX).data();
const vector<double>& ubx = input(NLP_UBX).data();
const vector<double>& lbg = input(NLP_LBG).data();
const vector<double>& ubg = input(NLP_UBG).data();
// Set the static parameter
if (parametric_) {
const vector<double>& p = input(NLP_P).data();
if (!F_.isNull()) F_.setInput(p,F_.getNumInputs()-1);
if (!G_.isNull()) G_.setInput(p,G_.getNumInputs()-1);
if (!H_.isNull()) H_.setInput(p,H_.getNumInputs()-1);
if (!J_.isNull()) J_.setInput(p,J_.getNumInputs()-1);
}
// Set linearization point to initial guess
copy(x_init.begin(),x_init.end(),x_.begin());
// Lagrange multipliers of the NLP
fill(mu_.begin(),mu_.end(),0);
fill(mu_x_.begin(),mu_x_.end(),0);
// Initial constraint Jacobian
eval_jac_g(x_,gk_,Jk_);
// Initial objective gradient
eval_grad_f(x_,fk_,gf_);
// Initialize or reset the Hessian or Hessian approximation
reg_ = 0;
if( hess_mode_ == HESS_BFGS){
reset_h();
} else {
eval_h(x_,mu_,1.0,Bk_);
}
// Evaluate the initial gradient of the Lagrangian
copy(gf_.begin(),gf_.end(),gLag_.begin());
if(m_>0) DMatrix::mul_no_alloc_tn(Jk_,mu_,gLag_);
// gLag += mu_x_;
transform(gLag_.begin(),gLag_.end(),mu_x_.begin(),gLag_.begin(),plus<double>());
// Number of SQP iterations
int iter = 0;
// Number of line-search iterations
int ls_iter = 0;
// Last linesearch successfull
bool ls_success = true;
// Reset
merit_mem_.clear();
sigma_ = 0.; // NOTE: Move this into the main optimization loop
// Default stepsize
double t = 0;
// MAIN OPTIMIZATION LOOP
while(true){
// Primal infeasability
double pr_inf = primalInfeasibility(x_, lbx, ubx, gk_, lbg, ubg);
// 1-norm of lagrange gradient
double gLag_norm1 = norm_1(gLag_);
// 1-norm of step
double dx_norm1 = norm_1(dx_);
// Print header occasionally
if(iter % 10 == 0) printIteration(cout);
// Printing information about the actual iterate
printIteration(cout,iter,fk_,pr_inf,gLag_norm1,dx_norm1,reg_,ls_iter,ls_success);
// Call callback function if present
if (!callback_.isNull()) {
callback_.input(NLP_COST).set(fk_);
callback_.input(NLP_X_OPT).set(x_);
callback_.input(NLP_LAMBDA_G).set(mu_);
callback_.input(NLP_LAMBDA_X).set(mu_x_);
callback_.input(NLP_G).set(gk_);
callback_.evaluate();
if (callback_.output(0).at(0)) {
cout << endl;
cout << "CasADi::SQPMethod: aborted by callback..." << endl;
break;
}
}
// Checking convergence criteria
if (pr_inf < tol_pr_ && gLag_norm1 < tol_du_){
cout << endl;
cout << "CasADi::SQPMethod: Convergence achieved after " << iter << " iterations." << endl;
break;
}
if (iter >= maxiter_){
cout << endl;
cout << "CasADi::SQPMethod: Maximum number of iterations reached." << endl;
break;
}
// Start a new iteration
iter++;
// Formulate the QP
transform(lbx.begin(),lbx.end(),x_.begin(),qp_LBX_.begin(),minus<double>());
transform(ubx.begin(),ubx.end(),x_.begin(),qp_UBX_.begin(),minus<double>());
transform(lbg.begin(),lbg.end(),gk_.begin(),qp_LBA_.begin(),minus<double>());
transform(ubg.begin(),ubg.end(),gk_.begin(),qp_UBA_.begin(),minus<double>());
// Solve the QP
solve_QP(Bk_,gf_,qp_LBX_,qp_UBX_,Jk_,qp_LBA_,qp_UBA_,dx_,qp_DUAL_X_,qp_DUAL_A_);
log("QP solved");
// Detecting indefiniteness
double gain = quad_form(dx_,Bk_);
if (gain < 0){
casadi_warning("Indefinite Hessian detected...");
}
// Calculate penalty parameter of merit function
sigma_ = std::max(sigma_,1.01*norm_inf(qp_DUAL_X_));
sigma_ = std::max(sigma_,1.01*norm_inf(qp_DUAL_A_));
// Calculate L1-merit function in the actual iterate
double l1_infeas = primalInfeasibility(x_, lbx, ubx, gk_, lbg, ubg);
// Right-hand side of Armijo condition
double F_sens = inner_prod(dx_, gf_);
double L1dir = F_sens - sigma_ * l1_infeas;
double L1merit = fk_ + sigma_ * l1_infeas;
// Storing the actual merit function value in a list
merit_mem_.push_back(L1merit);
if (merit_mem_.size() > merit_memsize_){
merit_mem_.pop_front();
}
// Stepsize
t = 1.0;
double fk_cand;
// Merit function value in candidate
double L1merit_cand = 0;
// Reset line-search counter, success marker
ls_iter = 0;
ls_success = true;
// Line-search
log("Starting line-search");
if(maxiter_ls_>0){ // maxiter_ls_== 0 disables line-search
// Line-search loop
while (true){
for(int i=0; i<n_; ++i) x_cand_[i] = x_[i] + t * dx_[i];
// Evaluating objective and constraints
eval_f(x_cand_,fk_cand);
eval_g(x_cand_,gk_cand_);
ls_iter++;
// Calculating merit-function in candidate
l1_infeas = primalInfeasibility(x_cand_, lbx, ubx, gk_cand_, lbg, ubg);
L1merit_cand = fk_cand + sigma_ * l1_infeas;
// Calculating maximal merit function value so far
double meritmax = *max_element(merit_mem_.begin(), merit_mem_.end());
if (L1merit_cand <= meritmax + t * c1_ * L1dir){
// Accepting candidate
log("Line-search completed, candidate accepted");
break;
}
// Line-search not successful, but we accept it.
if(ls_iter == maxiter_ls_){
ls_success = false;
log("Line-search completed, maximum number of iterations");
break;
}
// Backtracking
t = beta_ * t;
}
}
// Candidate accepted, update dual variables
for(int i=0; i<m_; ++i) mu_[i] = t * qp_DUAL_A_[i] + (1 - t) * mu_[i];
for(int i=0; i<n_; ++i) mu_x_[i] = t * qp_DUAL_X_[i] + (1 - t) * mu_x_[i];
if( hess_mode_ == HESS_BFGS){
// Evaluate the gradient of the Lagrangian with the old x but new mu (for BFGS)
copy(gf_.begin(),gf_.end(),gLag_old_.begin());
if(m_>0) DMatrix::mul_no_alloc_tn(Jk_,mu_,gLag_old_);
// gLag_old += mu_x_;
transform(gLag_old_.begin(),gLag_old_.end(),mu_x_.begin(),gLag_old_.begin(),plus<double>());
}
// Candidate accepted, update the primal variable
copy(x_.begin(),x_.end(),x_old_.begin());
copy(x_cand_.begin(),x_cand_.end(),x_.begin());
// Evaluate the constraint Jacobian
log("Evaluating jac_g");
eval_jac_g(x_,gk_,Jk_);
// Evaluate the gradient of the objective function
log("Evaluating grad_f");
eval_grad_f(x_,fk_,gf_);
// Evaluate the gradient of the Lagrangian with the new x and new mu
copy(gf_.begin(),gf_.end(),gLag_.begin());
if(m_>0) DMatrix::mul_no_alloc_tn(Jk_,mu_,gLag_);
// gLag += mu_x_;
transform(gLag_.begin(),gLag_.end(),mu_x_.begin(),gLag_.begin(),plus<double>());
// Updating Lagrange Hessian
if( hess_mode_ == HESS_BFGS){
log("Updating Hessian (BFGS)");
// BFGS with careful updates and restarts
if (iter % lbfgs_memory_ == 0){
// Reset Hessian approximation by dropping all off-diagonal entries
const vector<int>& rowind = Bk_.rowind(); // Access sparsity (row offset)
const vector<int>& col = Bk_.col(); // Access sparsity (column)
vector<double>& data = Bk_.data(); // Access nonzero elements
for(int i=0; i<rowind.size()-1; ++i){ // Loop over the rows of the Hessian
for(int el=rowind[i]; el<rowind[i+1]; ++el){ // Loop over the nonzero elements of the row
if(i!=col[el]) data[el] = 0; // Remove if off-diagonal entries
}
}
}
// Pass to BFGS update function
bfgs_.setInput(Bk_,BFGS_BK);
bfgs_.setInput(x_,BFGS_X);
bfgs_.setInput(x_old_,BFGS_X_OLD);
bfgs_.setInput(gLag_,BFGS_GLAG);
bfgs_.setInput(gLag_old_,BFGS_GLAG_OLD);
// Update the Hessian approximation
bfgs_.evaluate();
// Get the updated Hessian
bfgs_.getOutput(Bk_);
} else {
// Exact Hessian
log("Evaluating hessian");
eval_h(x_,mu_,1.0,Bk_);
}
}
// Save results to outputs
output(NLP_COST).set(fk_);
output(NLP_X_OPT).set(x_);
output(NLP_LAMBDA_G).set(mu_);
output(NLP_LAMBDA_X).set(mu_x_);
output(NLP_G).set(gk_);
// Save statistics
stats_["iter_count"] = iter;
}
void TestDistancesToCorner() throw (Exception)
{
TrianglesMeshReader<3,3> mesh_reader("mesh/test/data/cube_21_nodes_side/Cube21"); // 5x5x5mm cube (internode distance = 0.25mm)
TetrahedralMesh<3,3> mesh;
mesh.ConstructFromMeshReader(mesh_reader);
unsigned num_nodes=9261u;
TS_ASSERT_EQUALS(mesh.GetNumNodes(), num_nodes); // 21x21x21 nodes
TS_ASSERT_EQUALS(mesh.GetNumElements(), 48000u);
TS_ASSERT_EQUALS(mesh.GetNumBoundaryElements(), 4800u);
DistributedTetrahedralMesh<3,3> parallel_mesh(DistributedTetrahedralMeshPartitionType::DUMB); // No reordering;
parallel_mesh.ConstructFromMeshReader(mesh_reader);
TS_ASSERT_EQUALS(parallel_mesh.GetNumNodes(), num_nodes); // 21x21x21 nodes
TS_ASSERT_EQUALS(parallel_mesh.GetNumElements(), 48000u);
TS_ASSERT_EQUALS(parallel_mesh.GetNumBoundaryElements(), 4800u);
unsigned far_index=9260u;
c_vector<double,3> far_corner=mesh.GetNode(far_index)->rGetLocation();
TS_ASSERT_DELTA( far_corner[0], 0.25, 1e-11);
TS_ASSERT_DELTA( far_corner[1], 0.25, 1e-11);
TS_ASSERT_DELTA( far_corner[2], 0.25, 1e-11);
try
{
c_vector<double,3> parallel_far_corner=parallel_mesh.GetNode(far_index)->rGetLocation();
TS_ASSERT_DELTA( parallel_far_corner[0], 0.25, 1e-11);
TS_ASSERT_DELTA( parallel_far_corner[1], 0.25, 1e-11);
TS_ASSERT_DELTA( parallel_far_corner[2], 0.25, 1e-11);
}
catch (Exception&)
{
}
std::vector<unsigned> map_far_corner;
map_far_corner.push_back(far_index);
DistanceMapCalculator<3,3> distance_calculator(mesh);
std::vector<double> distances;
distance_calculator.ComputeDistanceMap(map_far_corner, distances);
DistanceMapCalculator<3,3> parallel_distance_calculator(parallel_mesh);
std::vector<double> parallel_distances;
parallel_distance_calculator.ComputeDistanceMap(map_far_corner, parallel_distances);
TS_ASSERT_EQUALS(distance_calculator.mRoundCounter, 1u);
//Nodes in mesh are order such that a dumb partitioning will give a sequential handover from proc0 to proc1...
TS_ASSERT_EQUALS(parallel_distance_calculator.mRoundCounter, PetscTools::GetNumProcs());
//Note unsigned division is okay here
TS_ASSERT_DELTA(parallel_distance_calculator.mPopCounter, num_nodes/PetscTools::GetNumProcs(), 1u);
TS_ASSERT_DELTA(distance_calculator.mPopCounter, num_nodes, 1u);
for (unsigned index=0; index<distances.size(); index++)
{
c_vector<double, 3> node = mesh.GetNode(index)->rGetLocation();
//Straightline distance
double euclidean_distance = norm_2(far_corner - node);
// x + y + z distance
double manhattan_distance = norm_1(far_corner - node);
//If they differ, then allow the in-mesh distance to be in between
double error_bound = (manhattan_distance - euclidean_distance)/2.0;
//If they don't differ, then we expect the in-mesh distance to be similar
if (error_bound < 1e-15)
{
error_bound = 1e-15;
}
TS_ASSERT_LESS_THAN_EQUALS(distances[index], manhattan_distance+DBL_EPSILON);
TS_ASSERT_LESS_THAN_EQUALS(euclidean_distance, distances[index]+DBL_EPSILON);
TS_ASSERT_DELTA(distances[index], euclidean_distance, error_bound);
TS_ASSERT_DELTA(distances[index], parallel_distances[index], 1e-15);
}
// Test some point-to-point distances
RandomNumberGenerator::Instance()->Reseed(1);
unsigned trials=25;
unsigned pops=0;
unsigned sequential_pops=0;
for (unsigned i=0; i<trials; i++)
{
unsigned index=RandomNumberGenerator::Instance()->randMod(parallel_distances.size());
TS_ASSERT_DELTA(parallel_distance_calculator.SingleDistance(9260u, index), parallel_distances[index], 1e-15);
TS_ASSERT_DELTA(distance_calculator.SingleDistance(9260u, index), parallel_distances[index], 1e-15);
pops += parallel_distance_calculator.mPopCounter;
sequential_pops += distance_calculator.mPopCounter;
TS_ASSERT_LESS_THAN_EQUALS(parallel_distance_calculator.mRoundCounter, PetscTools::GetNumProcs()+2);
}
// Without A*: TS_ASSERT_DELTA(sequential_pops/(double)trials, num_nodes/2, 300);
TS_ASSERT_LESS_THAN(sequential_pops/(double)trials, num_nodes/20.0);
if (PetscTools::IsSequential())
{
//Early termination
TS_ASSERT_EQUALS(pops, sequential_pops);
}
else
{
//Early termination on remote processes is not yet possible
//This may lead to multiple updates from remote
//A* Leads to even more updates on average
// Without A*: TS_ASSERT_DELTA(pops/(double)trials, num_nodes/PetscTools::GetNumProcs(), 700.0);
TS_ASSERT_LESS_THAN(pops/(double)trials, num_nodes/10.0 );
}
//Reverse - to check that cached information is flushed.
for (unsigned i=0; i<3; i++)
{
unsigned index=RandomNumberGenerator::Instance()->randMod(parallel_distances.size());
TS_ASSERT_DELTA(parallel_distance_calculator.SingleDistance(index, 9260u), parallel_distances[index], 1e-15);
}
}
const matrix<T, D, A_>
expm( const matrix<T, D, A_>& A )
{
typedef matrix<T, D, A_> matrix_type;
typedef typename matrix_type::value_type value_type_;
typedef typename expm_private::fix_complex_value_type<value_type_>::value_type value_type;
typedef typename matrix_type::size_type size_type;
assert( A.row() == A.col() );
static const value_type theta[] = { 0.000000000000000e+000, //0
3.650024139523051e-008, //1
5.317232856892575e-004, //2
1.495585217958292e-002, //3
8.536352760102745e-002, //4
2.539398330063230e-001, //5
5.414660951208968e-001, //6
9.504178996162932e-001, //7
1.473163964234804e+000, //8
2.097847961257068e+000, //9
2.811644121620263e+000, //10
3.602330066265032e+000, //11
4.458935413036850e+000, //12
5.371920351148152e+000 //13
};
value_type const norm_A = norm_1( A );
//value_type const ratio = theta[13] / norm_A;
value_type const ratio = norm_A / theta[13];
size_type const s = ratio < value_type(1) ? 0 : static_cast<size_type>( std::ceil( std::log2( ratio ) ) );
value_type const s__2 = s ? value_type(1 << s) : value_type(1);
/*
std::cerr << "Matrix expm starting with S__2 is " << s__2 << "\n";
if ( std::abs( s__2 - 1.0 ) < 0.1 )
std::cerr << "\tencountering matrix \n" << A << "\n";
*/
matrix_type const& _A = A / s__2;
size_type const n = _A.row();
static value_type const c [] = { 0.000000000000000, // 0
//64764752532480000, // 1
6.4764752532480000e+16, // 1
//32382376266240000, // 2
3.2382376266240000e+16, // 2
//7771770303897600, // 3
7.771770303897600e+15, // 3
//1187353796428800, // 4
1.187353796428800e+15, // 4
//129060195264000, // 5
1.29060195264000e+14, // 5
//10559470521600, // 6
1.0559470521600e+13, // 6
//670442572800, // 7
6.70442572800e+11, // 7
//33522128640, // 8
3.3522128640e+10, // 8
//1323241920, // 9
1.323241920e+9, // 9
//40840800, // 10
4.0840800e+7, // 10
//960960, // 11
9.60960e+5, // 11
//16380, // 12
1.6380e+4, // 12
//182, // 13
1.82e+2, // 13
1 // 14
};
matrix_type const& _A2 = _A * _A;
matrix_type const& _A4 = _A2 * _A2;
matrix_type const& _A6 = _A2 * _A4;
matrix_type const& U = _A * ( _A6 * ( c[14] * _A6 + c[12] * _A4 + c[10] * _A2 ) + c[8] * _A6 + c[6] * _A4 + c[4] * _A2 + c[2] * eye<value_type>( n, n ) );
matrix_type const& V = _A6 * ( c[13] * _A6 + c[11] * _A4 + c[9] * _A2 ) + c[7] * _A6 + c[5] * _A4 + c[3] * _A2 + c[1] * eye<value_type>( n, n );
matrix_type const& VU = V + U;
matrix_type const& UV = V - U;
matrix_type F = VU / UV;
//matrix_type F = ( V + U ) / ( V - U );
////!!!!!!!!!!!!!!!!
/*
matrix_type const& _A = A / s__2;
matrix_type _a = _A;
size_type const n = _A.row();
auto F = eye<value_type_>( n, n );
const unsigned long loops = 10;
value_type factor = value_type(1);
for ( unsigned long i = 0; i != loops; ++i )
{
factor /= i;
F = F + _a * factor;
if ( i + 1 == loops ) break;
_a *= _A;
}
*/
////!!!!!!!!!!!!!!!!
for ( size_type i = 0; i != s; ++i )
F *= F;
//std::cerr << "EXPM ends.\n";
return F;
}
void Newton::solveNonLinear() {
casadi_msg("Newton::solveNonLinear:begin");
// Set up timers for profiling
double time_zero=0;
double time_start=0;
double time_stop=0;
if (CasadiOptions::profiling && !CasadiOptions::profilingBinary) {
time_zero = getRealTime();
CasadiOptions::profilingLog << "start " << this << ":" <<getOption("name") << std::endl;
}
// Pass the inputs to J
for (int i=0; i<nIn(); ++i) {
if (i!=iin_) jac_.setInput(input(i), i);
}
// Aliases
DMatrix &u = output(iout_);
DMatrix &J = jac_.output(0);
DMatrix &F = jac_.output(1+iout_);
// Perform the Newton iterations
int iter=0;
bool success = true;
while (true) {
// Break if maximum number of iterations already reached
if (iter >= max_iter_) {
log("evaluate", "Max. iterations reached.");
stats_["return_status"] = "max_iteration_reached";
success = false;
break;
}
// Start a new iteration
iter++;
// Print progress
if (monitored("step") || monitored("stepsize")) {
userOut() << "Step " << iter << "." << std::endl;
}
if (monitored("step")) {
userOut() << " u = " << u << std::endl;
}
// Use u to evaluate J
jac_.setInput(u, iin_);
for (int i=0; i<nIn(); ++i)
if (i!=iin_) jac_.setInput(input(i), i);
if (CasadiOptions::profiling) {
time_start = getRealTime(); // Start timer
}
jac_.evaluate();
// Write out profiling information
if (CasadiOptions::profiling && !CasadiOptions::profilingBinary) {
time_stop = getRealTime(); // Stop timer
CasadiOptions::profilingLog
<< (time_stop-time_start)*1e6 << " ns | "
<< (time_stop-time_zero)*1e3 << " ms | "
<< this << ":" << getOption("name") << ":0|" << jac_.get() << ":"
<< jac_.getOption("name") << "|evaluate jacobian" << std::endl;
}
if (monitored("F")) userOut() << " F = " << F << std::endl;
if (monitored("normF"))
userOut() << " F (min, max, 1-norm, 2-norm) = "
<< (*std::min_element(F.data().begin(), F.data().end()))
<< ", " << (*std::max_element(F.data().begin(), F.data().end()))
<< ", " << norm_1(F) << ", " << norm_F(F) << std::endl;
if (monitored("J")) userOut() << " J = " << J << std::endl;
double abstol = 0;
if (numeric_limits<double>::infinity() != abstol_) {
abstol = std::max((*std::max_element(F.data().begin(),
F.data().end())),
-(*std::min_element(F.data().begin(),
F.data().end())));
if (abstol <= abstol_) {
casadi_msg("Converged to acceptable tolerance - abstol: " << abstol_);
break;
}
}
// Prepare the linear solver with J
linsol_.setInput(J, LINSOL_A);
if (CasadiOptions::profiling) {
time_start = getRealTime(); // Start timer
}
linsol_.prepare();
// Write out profiling information
if (CasadiOptions::profiling && !CasadiOptions::profilingBinary) {
time_stop = getRealTime(); // Stop timer
CasadiOptions::profilingLog
<< (time_stop-time_start)*1e6 << " ns | "
<< (time_stop-time_zero)*1e3 << " ms | "
<< this << ":" << getOption("name")
<< ":1||prepare linear system" << std::endl;
}
if (CasadiOptions::profiling) {
time_start = getRealTime(); // Start timer
}
// Solve against F
linsol_.solve(&F.front(), 1, false);
if (CasadiOptions::profiling && !CasadiOptions::profilingBinary) {
time_stop = getRealTime(); // Stop timer
CasadiOptions::profilingLog
<< (time_stop-time_start)*1e6 << " ns | "
<< (time_stop-time_zero)*1e3 << " ms | "
<< this << ":" << getOption("name") << ":2||solve linear system" << std::endl;
}
if (monitored("step")) {
userOut() << " step = " << F << std::endl;
}
double abstolStep=0;
if (numeric_limits<double>::infinity() != abstolStep_) {
abstolStep = std::max((*std::max_element(F.data().begin(),
F.data().end())),
-(*std::min_element(F.data().begin(),
F.data().end())));
if (monitored("stepsize")) {
userOut() << " stepsize = " << abstolStep << std::endl;
}
if (abstolStep <= abstolStep_) {
casadi_msg("Converged to acceptable tolerance - abstolStep: " << abstolStep_);
break;
}
}
if (print_iteration_) {
// Only print iteration header once in a while
if (iter % 10==0) {
printIteration(userOut());
}
// Print iteration information
printIteration(userOut(), iter, abstol, abstolStep);
}
// Update Xk+1 = Xk - J^(-1) F
std::transform(u.begin(), u.end(), F.begin(), u.begin(), std::minus<double>());
}
// Get auxiliary outputs
for (int i=0; i<nOut(); ++i) {
if (i!=iout_) jac_.getOutput(output(i), 1+i);
}
// Store the iteration count
if (gather_stats_) stats_["iter"] = iter;
if (success) stats_["return_status"] = "success";
// Factorization up-to-date
fact_up_to_date_ = true;
casadi_msg("Newton::solveNonLinear():end after " << iter << " steps");
}