Example #1
0
static void DeleteEverythingVerySlowly(vector *numbers)
{
  long largestOriginalNumber;
  fprintf(stdout, "Erasing everything in the vector by repeatedly deleting the 100th-to-last remaining element (be patient).\n");
  fflush(stdout);
  largestOriginalNumber = *(long *)VectorNth(numbers, VectorLength(numbers) - 1);
  while (VectorLength(numbers) >= 100) {
    VectorDelete(numbers, VectorLength(numbers) - 100);
    assert(largestOriginalNumber == *(long *)VectorNth(numbers, VectorLength(numbers) -1));
  }
  fprintf(stdout, "\t[Okay, almost done... deleting the last 100 elements... ");
  fflush(stdout);
  while (VectorLength(numbers) > 0) VectorDelete(numbers, 0);
  fprintf(stdout, "and we're all done... whew!]\n");
  fflush(stdout);
}
Example #2
0
void HtResetContents(LPVECTOR *table, unsigned int tablelen) {
	unsigned int i;

	for (i = 0; i != tablelen; i++) {
		if (table[i]) {
			VectorDelete(table[i]);
			table[i] = NULL;
		}
	}
}
Example #3
0
File: main.c Project: lynnkse/sort
void MassiveRadixSortTest()
{
	int vectorSize, i, j;
	int num1, num2;
	Vector* vec;
	srand(time(NULL));
	
	for(j = 0; j < RUNS; j++)
	{
		
		vectorSize = rand() % MAX_VECTOR_SIZE;

		vec = VectorCreate(vectorSize, 100);

		for(i = 0; i < vectorSize; i++)
		{
			VectorAdd(vec, rand() % MAX_NUMBER);
		}

		RadixSort(vec, 3);

		
		VectorDelete(vec, &num1);

		for(i = 0; i < vectorSize - 1; i++)
		{
			VectorDelete(vec, &num2);
			if(num2 > num1)
			{
				printf("MassiveSortTest..................FAIL\n");
				VectorDestroy(vec);
				return;
			}
			num1 = num2;
		}

		VectorDestroy(vec);
	}

	printf("MassiveSortTest..................OK\n");
}
Example #4
0
File: main.c Project: lynnkse/sort
void MassiveGenericSortTestWithNegatives(ADTErr(*SortFunc)(Vector* _vec))
{
	int vectorSize, i, j;
	int num1, num2;
	Vector* vec;
	srand(time(NULL));
	
	for(j = 0; j < RUNS; j++)
	{
		
		vectorSize = rand() % MAX_VECTOR_SIZE;

		vec = VectorCreate(vectorSize, 100);
		

		for(i = 0; i < vectorSize; i++)
		{
			i % 2 == 0 ? VectorAdd(vec, rand() % MAX_NUMBER) : VectorAdd(vec, - rand() % MAX_NUMBER);
		}

		SortFunc(vec);

		VectorDelete(vec, &num1);

		for(i = 0; i < vectorSize - 1; i++)
		{
			VectorDelete(vec, &num2);
			if(num2 > num1)
			{
				printf("MassiveSortTestWithNegatives..................FAIL\n");
				VectorDestroy(vec);
				return;
			}
			num1 = num2;
		}

		VectorDestroy(vec);
	}

	printf("MassiveSortTestWithNegatives..................OK\n");
}
Example #5
0
static void TestInsertDelete(vector *alphabet)
{
  char ch = '-';
  int i;
  
  for (i = 3; i < VectorLength(alphabet); i += 4) // Insert dash every 4th char 
    VectorInsert(alphabet, &ch, i);
  fprintf(stdout, "\nAfter insert dashes: ");
  VectorMap(alphabet, PrintChar, stdout);
  
  for (i = 3; i < VectorLength(alphabet); i += 3) // Delete every 4th char 
    VectorDelete(alphabet, i);
  fprintf(stdout, "\nAfter deleting dashes: ");
  VectorMap(alphabet, PrintChar, stdout);
    
  ch = '!';
  VectorInsert(alphabet, &ch, VectorLength(alphabet));
  VectorDelete(alphabet, VectorLength(alphabet) - 1);
  fprintf(stdout, "\nAfter adding and deleting to very end: ");
  VectorMap(alphabet, PrintChar, stdout);
}
Example #6
0
File: main.c Project: lynnkse/sort
void SimpleRadixSort()
{
	Vector* vec; 
	int a;
	
	vec = VectorCreate(100, 100);
	
	VectorAdd(vec, 46);
	VectorAdd(vec, 2);
	VectorAdd(vec, 83);
	VectorAdd(vec, 41);
	VectorAdd(vec, 102);
	VectorAdd(vec, 5);
	VectorAdd(vec, 17);
	VectorAdd(vec, 31);
	VectorAdd(vec, 64);
	VectorAdd(vec, 49);
	VectorAdd(vec, 18);

	RadixSort(vec, 3);
	


	VectorDelete(vec, &a);
	VectorDelete(vec, &a);
	VectorDelete(vec, &a);
	
	if(a == 64)
	{
		printf("SimpleSort..................OK\n");
	}	
	else
	{
		printf("SimpleSort..................FAIL\n");
	}
	
	VectorDestroy(vec);
}
void DetachParent(GameObject* gameObject){
	if(gameObject->parent != NULL){
		int i;
		for(i = 0; i< VectorTotal(&gameObject->parent->childs); i++){
			if(gameObject == VectorGet(&gameObject->parent->childs, i)){
				VectorDelete(&gameObject->parent->childs, i);
			}
		}
		float PI = 3.14159265;
		float rad = gameObject->parent->rotation * PI / 180.0f;
		Point localPosition = gameObject->position;
		gameObject->position.x = gameObject->parent->position.x + (int)((float)localPosition.x * cos(rad) - (float)localPosition.y * sin(rad)); 
		gameObject->position.y = gameObject->parent->position.y + (int)((float)localPosition.x * sin(rad) + (float)localPosition.y * cos(rad)); 
		gameObject->scale = gameObject->parent->scale * gameObject->scale;
		gameObject->rotation = fmod(gameObject->parent->rotation + gameObject->rotation, 360);
		gameObject->parent = NULL;
	} 
}
Example #8
0
File: main.c Project: lynnkse/sort
void SimpleGenericSort(ADTErr(*SortFunc)(Vector* _vec))
{
	Vector* vec; 
	int a;
	
	vec = VectorCreate(100, 100);
	
	VectorAdd(vec, 46);
	VectorAdd(vec, 2);
	VectorAdd(vec, 83);
	VectorAdd(vec, 41);
	VectorAdd(vec, 102);
	VectorAdd(vec, 5);
	VectorAdd(vec, 17);
	VectorAdd(vec, 31);
	VectorAdd(vec, 64);
	VectorAdd(vec, 49);
	VectorAdd(vec, 18);

	/*VectorPrint(vec);*/

	SortFunc(vec);
	
	/*VectorPrint(vec);*/
	
	VectorDelete(vec, &a);
	
	if(a == 102)
	{
		printf("SimpleSort..................OK\n");
	}	
	else
	{
		printf("SimpleSort..................FAIL\n");
	}
	
	VectorDestroy(vec);
}
Example #9
0
File: main.c Project: lynnkse/sort
void SimpleRadixSortForSingleMember()
{
	Vector* vec; 
	int a;
	
	vec = VectorCreate(100, 100);
	
	VectorAdd(vec, 5);

	RadixSort(vec, 1);
	
	VectorDelete(vec, &a);
	
	if(a == 5)
	{
		printf("SimpleSortForSingleMember..................OK\n");
	}	
	else
	{
		printf("SimpleSortForSingleMember..................FAIL\n");
	}
	
	VectorDestroy(vec);
}
Example #10
0
File: main.c Project: lynnkse/sort
void SimpleGenericSortForSingleMember(ADTErr(*SortFunc)(Vector* _vec))
{
	Vector* vec; 
	int a;
	
	vec = VectorCreate(100, 100);
	
	VectorAdd(vec, 5);

	SortFunc(vec);
	
	VectorDelete(vec, &a);
	
	if(a == 5)
	{
		printf("SimpleSortForSingleMember..................OK\n");
	}	
	else
	{
		printf("SimpleSortForSingleMember..................FAIL\n");
	}
	
	VectorDestroy(vec);
}
Example #11
0
File: qr.c Project: r-barnes/ocp
void _householder(double **Q, double **R, double **B, int n, int m) {
    int i, j, k;
    Vector Beta = VectorNew(m);
    Vector W = VectorNew(n);
    Matrix V = MatrixNew(n, n);
    double *beta = Beta->e;

    // Q = I
    for (i = 0; i < n; i++) {
        for (j = 0; j < n; j++) {
            if (i == j) {
                Q[i][j] = 1.0;
            } else {
                Q[i][j] = 0.0;
            }
        }
    }
    
    // R = B
    for (i = 0; i < n; i++) {
        double *Ri = R[i];
        double *Bi = B[i];
        for (k = 0; k < m; k++) {
            Ri[k] = Bi[k];
        }
    }

    // find the Householder vectors for each column of R
    for (k = 0; k < m; k++) {
        double xi;
        double norm_x = 0.0;
        double *w = W->e;
        double *v = V->e[k];
        for (i = k; i < n; i++) {
            xi = R[i][k];
            norm_x += xi * xi;
            v[i] = xi;
        }
        norm_x = sqrt(norm_x);
        double x1 = v[k];
        double sign_x1 = sign(x1);
        double gamma = -1.0 * sign_x1 * norm_x;
        double v_dot_v = 2.0 * norm_x * (norm_x + sign_x1 * x1);

        if (v_dot_v < DBL_EPSILON) {
            for (i = k; i < m; i++) {
                R[i][i] = 0.0;
            }
            VectorDelete(Beta);
            VectorDelete(W);
            MatrixDelete(V);
            return;
        }
        v[k] -= gamma;
        beta[k] = -2.0 / v_dot_v;
      
        // w(k:m) = R(k:n, k:m)^T * v(k:n)
        for (i = k; i < m; i++) {
            double s = 0.0;
            for (j = k; j < n; j++) { // FIX: make this row-wise
                s += R[j][i] * v[j];
            }
            w[i] = s;
        }

        // R(k:n, k:m) += beta * v(k:n) * w(k:m)^T
        //a[k : n, k : m] = a[k : n, k : m] + beta * (v * wT)
        for (i = k; i < n; i++) {
            for (j = k; j < m; j++) {
                R[i][j] += beta[k] * v[i] * w[j];
            }
        }
    }

    for (k = m-1; k >= 0; k--) {
        double *v = V->e[k];
        double *u = W->e;
        //uT = v.transpose() * Q[k : n, k : n]
        for (i = k; i < n; i++) {
            double s = 0.0;
            for (j = k; j < n; j++) {
                s += Q[j][i] * v[j];
            }
            u[i] = s;
        }
        //Q[k : n, k : n] = Q[k : n, k : n] + Beta[k] * (v * uT)
        for (i = k; i < n; i++) {
            for (j = k; j < n; j++) {
                Q[i][j] += beta[k] * v[i] * u[j];
            }
        }
    }
    VectorDelete(Beta);
    VectorDelete(W);
    MatrixDelete(V);
}
Example #12
0
double _RKOCPfhgE(Vector nlp_x, Vector nlp_h, Vector nlp_g) {
    RKOCP r = thisRKOCP;
    double phi = 0;
    double t;
    int i_node, l;
    int i, j;
    int m = r->nlp_m;
    int p = r->nlp_p;
    int n_nodes = r->n_nodes;
    int n_parameters = r->n_parameters;
    int n_states = r->n_states;
    int n_controls = r->n_controls;
    int n_inequality = r->ocp->n_inequality;
    int n_initial = r->ocp->n_initial;
    int n_terminal = r->ocp->n_terminal;

    int rk_stages = r->rk_stages;
    double **rk_a = r->rk_a->e;
    double *rk_b = r->rk_b->e;
    double *rk_c = r->rk_c->e;
    double *rk_e = r->rk_e->e;

    Vector T = r->T;
    Matrix Yw = r->Yw;
    Vector yc = r->yc;
    Vector uc = r->uc;
    Vector pc = r->pc;
    Vector local_error = r->local_error;
    Vector lte = r->lte;

    Vector Gamma = r->Gamma;
    Vector G = r->G;
    Vector Psi = r->Psi;

    Matrix *Ydata = r->Ydata;
    Matrix *Udata = r->Udata;
    Vector *Kstage = r->Kstage;

    double _y;

    double fac0 = 0.2, fac1 = 5.0, beta = 0.9;
    int step, max_steps = 100;
    Vector Y0, Y1;
    double T0, h = 1.0e-8;
    Y0 = VectorNew(n_states+1);
    Y1 = VectorNew(n_states+1);

    
    if (m > 0) {
        VectorSetAllTo(nlp_h, 0.0);
    }
    
    if (p > 0) {
        VectorSetAllTo(nlp_g, 0.0);
    }
    
    for (i = 0; i < n_parameters; i++) {
        pc->e[i] = nlp_x->e[i];
    }
    
    for (j = 0; j < n_states; j++) {
        Yw->e[0][j] = nlp_x->e[n_parameters+j];
    }
    Yw->e[0][n_states] = 0;

    if (n_controls > 0) {
        _setUdata(r, nlp_x);
    }

    // integrate the ODEs using an explicit Runge-Kutta method

    Matrix Ystage;
    double delta, ti;

    for (i_node = 0; i_node < n_nodes-1; i_node++) {
        Ystage = Ydata[i_node]; // save the stage values for use in Dfhg

        ti = T->e[i_node];
        delta = T->e[i_node+1] - ti;
        t = ti;

        //- save the control values for use in Dfhg
        //- getControl(i_node, t, Udata[i_node][0]);
        for (i = 0; i < n_controls; i++) 
            uc->e[i] = Udata[i_node]->e[0][i];

        for (i = 0; i < n_states+1; i++) {
            _y = Yw->e[i_node][i];
            Ystage->e[0][i] = _y;
            yc->e[i] = _y;
            Y0->e[i] = _y;
        }

        // form Gamma(y(t_initial), p)
        if ((i_node == 0) && (n_initial > 0)) {
            r->ocp->initial_constraints(yc, pc, Gamma);
            for (i = 0; i < n_initial; i++) {
                nlp_h->e[i] = Gamma->e[i];
            }
        }
        // form g(y,u,p,t)
        if (n_inequality > 0) {
            r->ocp->inequality_constraints(yc, uc, pc, t, G);
            for (i = 0; i < n_inequality; i++) {
                nlp_g->e[i + i_node * n_inequality] = G->e[i];
            }
        }
        
        // K = F(y,u,p,t)
        Kstage[0]->e[n_states] = r->ocp->differential_equations(yc, uc, pc, t, Kstage[0]);
        
        T0 = t;
        if (i_node == 0)
            h = delta;
                
        for (step = 0; step <= max_steps; step++) {
            
            for (l = 1; l < rk_stages; l++) {
                t = T0 + rk_c[l]*h;
                //getControl(i_node, t, Udata[i_node][l]);
                //for (i = 0; i < n_controls; i++) 
                //    uc->e[i] = Udata[i_node]->e[0][i]; // constant control
    
                //Y_l = yc + h * sum_{j=0 to j=l-1} rk_a[l][j] * K_j
                for (i = 0; i < n_states + 1; i++) 
                    Ystage->e[l][i] = Y0->e[i];//Yw->e[i_node][i];
                for (j = 0; j < l; j++) {
                    for (i = 0; i < n_states+1; i++) {
                        Ystage->e[l][i] += h*rk_a[l][j]*Kstage[j]->e[i];
                    }
                }
    
                for (i = 0; i < n_states+1; i++) 
                    yc->e[i] = Ystage->e[l][i];
                    
                Kstage[l]->e[n_states] = r->ocp->differential_equations(yc, uc, pc, t, Kstage[l]);
            }
    
            // Y1 = Y0 + h * sum_{l=0 to stages-1} b[l] * K[l]
            for (i = 0; i < n_states+1; i++) {
                Y1->e[i] = Y0->e[i];
                local_error->e[i] = 0;
            }
            for (l = 0; l < rk_stages; l++) {
                for (i = 0; i < n_states+1; i++) {
                    Y1->e[i] += h*rk_b[l]*Kstage[l]->e[i];
                    local_error->e[i] += h*rk_e[l]*Kstage[l]->e[i];
                }
            }
            lte->e[i_node+1] = _compute_LTE(r, local_error->e, Y0->e, Y1->e);
            
            double sigma = pow(lte->e[i_node+1], -1.0/r->rk_order);
            double hnew = h * fmin(fac1, fmax(fac0, beta*sigma));
            //double _dt = fabs(T0 + h - T->e[i_node+1]);
            if (lte->e[i_node+1] < 1.0) {
                T0 = T0 + h;
                if (fabs(T0-T->e[i_node+1]) <= 100.0*DBL_EPSILON) {
                    for (i = 0; i < n_states+1; i++)
                        Yw->e[i_node+1][i] = Y1->e[i];
                    break;
                }
                for (i = 0; i < n_states+1; i++) {
                    Y0->e[i] = Y1->e[i];
                    yc->e[i] = Y1->e[i];
                }
                Kstage[0]->e[n_states] = r->ocp->differential_equations(yc, uc, pc, T0, Kstage[0]);
            }

            if (step >= max_steps) {
                for (i = 0; i < n_states+1; i++)
                        Yw->e[i_node+1][i] = Y1->e[i];
/*printf("local error:\n");
VectorPrint(local_error);
printf("Y1:\n");
VectorPrint(Y1);
printf("step: %d, lte: %e, T0: %e, T1: %e, h: %e, hnew: %e, sigma: %e, _dt: %e\n", step, lte->e[i_node+1], T0, T->e[i_node+1], h, hnew, sigma, _dt);
pause();*/
                break;
            }

/*printf("control:\n");
VectorPrint(uc);
printf("local error:\n");
VectorPrint(local_error);
printf("step: %d, lte: %e, T0: %e, T1: %e, h: %e, hnew: %e, sigma: %e, _dt: %e\n", step, lte->e[i_node+1], T0, T->e[i_node+1], h, hnew, sigma, _dt);
pause();*/
          
            h = hnew;

            if (T0+h > T->e[i_node+1])
                h = T->e[i_node+1] - T0;
//
        }
//pause();
    }

    // form g at time t_final
    t = T->e[n_nodes-1];
    if (n_controls > 0) {
        //getControl(n_nodes - 2, t, Udata[n_nodes - 1][0]);
        for (i = 0; i < n_controls; i++) 
            uc->e[i] = Udata[n_nodes-2]->e[rk_stages-1][i];
    }

    for (i = 0; i < n_states; i++) 
        yc->e[i] = Yw->e[n_nodes-1][i];
    
    if (n_inequality > 0) {
        r->ocp->inequality_constraints(yc, uc, pc, t, G);
        for (i = 0; i < n_inequality; i++) {
            nlp_g->e[i + (n_nodes-1)*n_inequality] = G->e[i];
        }
    }
    
    // form phi, Psi
    phi = r->ocp->terminal_constraints(yc, pc, Psi);
    for (i = 0; i < n_terminal; i++) {
        nlp_h->e[i + n_initial] = Psi->e[i];
    }

    VectorDelete(Y0);
    VectorDelete(Y1);
    
    return phi + Yw->e[n_nodes-1][n_states];
}
Example #13
0
double _RKOCPfhg_implicitZ(Vector nlp_x, Vector nlp_h, Vector nlp_g) {
    RKOCP r = thisRKOCP;
    double phi = 0;
    int i_node;
    int i, j, k;
    int m = r->nlp_m;
    int p = r->nlp_p;
    int n_nodes = r->n_nodes;
    int n_parameters = r->n_parameters;
    int n_states = r->n_states;
    int n_controls = r->n_controls;
    int n_inequality = r->ocp->n_inequality;
    int n_initial = r->ocp->n_initial;
    int n_terminal = r->ocp->n_terminal;
    int only_compute_lte = r->only_compute_lte;

    int rk_stages = r->rk_stages;
    double **W = r->rk_w->e;
    //double **rk_a = r->rk_a->e;
    //double *rk_b = r->rk_b->e;
    double *rk_c = r->rk_c->e;
    //double *rk_e = r->rk_e->e;

    Vector T = r->T;
    Matrix Yw = r->Yw;
    Vector yc = r->yc;
    Vector uc = r->uc;
    Vector pc = r->pc;
    //Vector local_error = r->local_error;
    //Vector lte = r->lte;

    Vector Gamma = r->Gamma;
    Vector G = r->G;
    Vector Psi = r->Psi;

    Matrix *Ydata = r->Ydata;  // Ydata[i] => Ystage
    Matrix *Udata = r->Udata;
    Vector *Zstage = r->Kstage;
    Matrix Ystage;
    double ti;

    // FIX: preallocate the variables
    Vector y_old = VectorNew(n_states+1);
    Vector *Z_old = NULL;
    Z_old = VectorArrayNew(r->rk_stages, n_states+1);
    Vector f = VectorNew(n_states+1);
    Vector res = VectorNew(rk_stages*(n_states+1));
    Vector dZ = VectorNew(rk_stages*(n_states+1));
    Vector y = VectorNew(n_states+1);
    Matrix L;// = MatrixNew(rk_stages*(n_states+1), rk_stages*(n_states+1));
    Matrix U;// = MatrixNew(rk_stages*(n_states+1), rk_stages*(n_states+1));
    int *P;// = (int *)malloc(rk_stages*(n_states+1)*sizeof(int));
    
    if (only_compute_lte == NO) {
        if (m > 0) {
            VectorSetAllTo(nlp_h, 0.0);
        }
        if (p > 0) {
            VectorSetAllTo(nlp_g, 0.0);
        }
    }
    for (i = 0; i < n_parameters; i++) {
        pc->e[i] = nlp_x->e[i];
    }
    for (j = 0; j < n_states; j++) {
        Yw->e[0][j] = nlp_x->e[n_parameters+j];
        y->e[j] = Yw->e[0][j];
    }
    Yw->e[0][n_states] = 0;
    y->e[n_states] = 0;

    if (n_controls > 0) {
        _setUdata(r, nlp_x);
        for (i = 0; i < n_controls; i++) {
            uc->e[i] = nlp_x->e[n_parameters+n_states+i];
        }
    }

    if (only_compute_lte == NO) {
        // form Gamma(y(t_initial), p)
        if (n_initial > 0) {
            r->ocp->initial_constraints(y, pc, Gamma);
            for (i = 0; i < n_initial; i++) {
                nlp_h->e[i] = Gamma->e[i];
            }
        }
        // form g(y,u,p,t_initial)
        if (n_inequality > 0) {
            r->ocp->inequality_constraints(y, uc, pc, T->e[0], G);
            for (i = 0; i < n_inequality; i++) {
                nlp_g->e[i] = G->e[i];
            }
        }
    }
    
    // integrate the ODEs using an implicit Runge-Kutta method

    int MAX_NEWTON_ITER = 15;
    int iter;
    int err;
    
    for (i_node = 0; i_node < (n_nodes-1); i_node++) {
        L = r->Lnode[i_node];
        U = r->Unode[i_node];
        P = r->pLUnode[i_node];
        // form H = (1/h) W (x) I - I (x) J
        // get the L, U, p factors of H
        double h = T->e[i_node+1] - T->e[i_node];
        err = _formIRKmatrixZ(r, y, uc, pc, T->e[i_node], h, L, U, P);
        if (err != 0) {
printf("IRK factor error: t = %e\n", T->e[i_node]);
//pause();
            r->integration_fatal_error = YES;
            if (m > 0) VectorSetAllTo(nlp_h, 0);
            if (p > 0) VectorSetAllTo(nlp_g, 0);
            return 0;
        }
        // initialize Kstage
        // FIX: extrapolate previous result
        if (i_node == 0 ) {
            for (i = 0; i < rk_stages; i++) {
                for (j = 0; j < n_states+1; j++) {
                    Zstage[i]->e[j] = 0;
                }
            }
        } else {
            // given y0, Z0, y1, tau = h1/h0, estimate Z1
            // using a Lagrange interpolation formula
            double tau;
            tau = h / (T->e[i_node] - T->e[i_node-1]);
            _estimateZ(r, y_old, Z_old, y, tau, Zstage);
        }
        Ystage = Ydata[i_node];
        
        // Y_i = y + Z_i
        // Ydot_i = (1/h) sum_{j = 1, s} w_{i,j} * Z_j
        // set res_i = -Ydot_i
        for (i = 0; i < rk_stages; i++) {
            for (j = 0; j < n_states+1; j++) {
                Ystage->e[i][j] = y->e[j] + Zstage[i]->e[j];
            }
            for (k = 0; k < n_states+1; k++) {
                //Ydot[i]->e[k] = 0.0;
                res->e[i*(n_states+1) + k] = 0;
            }
            for (j = 0; j < rk_stages; j++) {
                for (k = 0; k < n_states+1; k++) {
                    //Ydot[i]->e[k] += W[i][j] * Zstage[j]->e[k] / h;
                    res->e[i*(n_states+1) + k] -= W[i][j] * Zstage[j]->e[k] / h;
                }
            }
        }

        for (iter = 0; iter < MAX_NEWTON_ITER; iter++) {
            for (i = 0; i < rk_stages; i++) {
                ti = T->e[i_node] + h*rk_c[i];
                // get uc = u(t_i)
                for (j = 0; j < n_controls; j++) {
                    uc->e[j] = Udata[i_node]->e[i][j];
                }
                // get yc = Y_i
                for (j = 0; j < n_states+1; j++) {
                    yc->e[j] = Ystage->e[i][j];
                }
                // form f(Y_i, u_i, p, t_i)
                f->e[n_states] = r->ocp->differential_equations(yc, uc, pc, ti, f);
                // form res_i = Ydot_i - f(Y_i, u_i, p, t_i)
                for (j = 0; j < n_states+1; j++) {
                    res->e[i*(n_states+1) + j] += f->e[j];
                }
            }
            // solve H*dZ = -res = -(ydot - f(y,u,p,t))
            err = LUSolve(L, U, P, res, dZ);
            // Z = Z + dZ
            for (i = 0; i < rk_stages; i++) {
                for (j = 0; j < n_states+1; j++) {
                    Zstage[i]->e[j] += dZ->e[i*(n_states+1) + j];
                }
            }
            // Y_i = y + Z_i
            // Ydot_i = (1/h) sum_{j = 1, s} w_{i,j} * Z_j
            // set res_i = -Ydot_i
            for (i = 0; i < rk_stages; i++) {
                for (j = 0; j < n_states+1; j++) {
                    Ystage->e[i][j] = y->e[j] + Zstage[i]->e[j];
                }
                for (k = 0; k < n_states+1; k++) {
                    //Ydot[i]->e[k] = 0.0;
                     res->e[i*(n_states+1) + k] = 0;
                }
                for (j = 0; j < rk_stages; j++) {
                    for (k = 0; k < n_states+1; k++) {
                        //Ydot[i]->e[k] += W[i][j] * Zstage[j]->e[k] / h;
                        res->e[i*(n_states+1) + k] -= W[i][j] * Zstage[j]->e[k] / h;
                    }
                }
            }
            // test for convergence
            double norm_dZ = VectorNorm(dZ);
            if (norm_dZ <= 0.01*r->tolerance) {
                break;
            }
        }
//printf("i_node: %d, iter: %d\n", i_node, iter);
        // y_old = y
        // Z_old = Z
        for (j = 0; j < n_states+1; j++) {
            for (i = 0; i < rk_stages; i++) {
                Z_old[i]->e[j] = Zstage[i]->e[j];
            }
            y_old->e[j] = y->e[j];
        }
        
        // Assumes R-K methods with c[s] = 1
        // form Yw[i_node+1] = Ystage_s
        // update y = Yw[i_node+1]
        for (j = 0; j < n_states+1; j++) {
            Yw->e[i_node+1][j] = Ystage->e[rk_stages-1][j];
            y->e[j] = Yw->e[i_node+1][j];
        }
        
        // update u = u[i_node+1];
        int i_node1 = i_node+1;
        if ((r->c_type == CONSTANT) && (i_node1 == (r->n_nodes-1))) {
            i_node1 -= 1;
        }
        
        for (i = 0; i < n_controls; i++) {
            uc->e[i] = nlp_x->e[n_parameters + n_states + i_node1*n_controls + i];
        }
        
        // compute g(y(t+h),u(t+h),p,t+h)
        if (only_compute_lte == NO) {
            if (n_inequality > 0) {
                r->ocp->inequality_constraints(y, uc, pc, T->e[i_node+1], G);
                for (i = 0; i < n_inequality; i++) {
                    nlp_g->e[i + (i_node+1) * n_inequality] = G->e[i];
                }
            }
        }
        // FIX:  compute LTE 
    }

    if (only_compute_lte == YES) {
        return 0;
    }

    // form phi, Psi
    phi = r->ocp->terminal_constraints(yc, pc, Psi);
    for (i = 0; i < n_terminal; i++) {
        nlp_h->e[i + n_initial] = Psi->e[i];
    }

    VectorDelete(y_old);
    VectorArrayDelete(Z_old, r->rk_stages);
    VectorDelete(f);
    VectorDelete(res);
    VectorDelete(y);
    VectorDelete(dZ);
    //MatrixDelete(L);
    //MatrixDelete(U);
    //free(P);
//pause();
    return phi + Yw->e[n_nodes-1][n_states];
}