// ----------------------------------------------------------------------------- bool Algorithms::Test_QuickSort() { bool pass = true; { int a[] = {}; std::vector<int> v = vec_transform(a, sizeof(a) / sizeof(int)); QuickSort(v); pass = pass && vec_equal(v, a, sizeof(a) / sizeof(int)); } { int a[] = {1}; std::vector<int> v = vec_transform(a, sizeof(a) / sizeof(int)); QuickSort(v); pass = pass && vec_equal(v, a, sizeof(a) / sizeof(int)); } { int a[] = {1, 2}; std::vector<int> v = vec_transform(a, sizeof(a) / sizeof(int)); QuickSort(v); pass = pass && vec_equal(v, a, sizeof(a) / sizeof(int)); } { int a[] = {2, 1}; std::vector<int> v = vec_transform(a, sizeof(a) / sizeof(int)); QuickSort(v); int b[] = {1, 2}; pass = pass && vec_equal(v, b, sizeof(b) / sizeof(int)); } { int a[] = {9, 8, 7, 6, 5}; std::vector<int> v = vec_transform(a, sizeof(a) / sizeof(int)); QuickSort(v); int b[] = {5, 6, 7, 8, 9}; pass = pass && vec_equal(v, b, sizeof(b) / sizeof(int)); } return pass; }
// ----------------------------------------------------------------------------- //virtual bool Solution::Test() { bool pass = true; { int a[] = {1, 2, 3, 4, 5, 5, 4, 3, 2, 1}; std::vector<int> v = vec_transform(a, sizeof(a) / sizeof(int)); int new_size = removeElement(v, 1); int r[] = {2, 3, 4, 5, 5, 4, 3, 2}; pass = pass && (8 == new_size) && vec_equal(v,r, sizeof(r) / sizeof(int)); } { int a[] = {1, 2, 3, 4, 5, 5, 4, 3, 2, 1}; std::vector<int> v = vec_transform(a, sizeof(a) / sizeof(int)); int new_size = removeElement(v, 10); pass = pass && (10 == new_size) && vec_equal(v,a, sizeof(a) / sizeof(int)); } return pass; }
vprop_t vprop_animate(vprop_t vp, float dt){ vec_t s; if (!(vp.speed == 0.0 || vec_equal(vp.val,vp.target))){ s = vec_scale(vec_normalize(vec_diff(vp.val,vp.target)),vp.speed); if(vec_dist(vp.val,vp.target) < vec_len(s)){ vp.val = vp.target; }else{ vp.val = vec_add(vp.val,s); } } return vp; }
bool operator==(vec<N,S> const& u, vec<N,S> const& v) { return vec_equal(u, v); }
/*!***************************************************************************** ******************************************************************************* \note parm_opt \date 10/20/91 \remarks this is the major optimzation program ******************************************************************************* Function Parameters: [in]=input,[out]=output \param[in] tol : error tolernance to be achieved \param[in] n_parm : number of parameters to be optimzed \param[in] n_con : number of contraints to be taken into account \param[in] f_dLda : function which calculates the derivative of the optimziation criterion with respect to the parameters; must return vector \param[in] f_dMda : function which calculates the derivate of the constraints with respect to parameters must return matrix \param[in] f_M : constraints function, must always be formulted to return 0 for properly fulfilled constraints \param[in] f_L : function to calculate simple cost (i.e., constraint cost NOT included), the constraint costs are added by this program automatically, the function returns a double scalar \param[in] f_dLdada : second derivative of L with respect to the parameters, must be a matrix of dim n_parm x n_parm \param[in] f_dMdada : second derivative of M with respect to parameters, must be a matrix n_con*n_parm x n_parm \param[in] use_newton: TRUE or FALSE to indicate that second derivatives are given and can be used for Newton algorithm \param[in,out] a : initial setting of parameters and also return of optimal value (must be a vector, even if scalar) \param[out] final_cost: the final cost \param[out] err : the sqrt of the squared error of all constraints NOTE: - program returns TRUE if everything correct, otherwise FALSE - always minimizes the cost!!! - algorithms come from Dyer McReynolds NOTE: besides the possiblity of a bug, the Newton method seems to sacrifice the validity of the constraint a little up to quite a bit and should be used prudently ******************************************************************************/ int parm_opt(double *a,int n_parm, int n_con, double *tol, void (*f_dLda)(), void (*f_dMda)(), void (*f_M)(), double (*f_L)(), void (*f_dMdada)(), void (*f_dLdada)(), int use_newton, double *final_cost, double *err) { register int i,j,n; double cost= 999.e30; double last_cost = 0.0; double *mult=NULL, *new_mult=NULL; /* this is the vector of Lagrange mulitplier */ double **dMda=NULL, **dMda_t=NULL; double *dLda; double *K=NULL; /* the error in the constraints */ double eps = 0.025; /* the learning rate */ double **aux_mat=NULL; /* needed for inversion of matrix */ double *aux_vec=NULL; double *new_a; double **dMdada=NULL; double **dLdada=NULL; double **A=NULL; /* big matrix, a combination of several other matrices */ double *B=NULL; /* a big vector */ double **A_inv=NULL; int rc=TRUE; long count = 0; int last_sign = 1; int pending1 = FALSE, pending2 = FALSE; int firsttime = TRUE; int newton_active = FALSE; dLda = my_vector(1,n_parm); new_a = my_vector(1,n_parm); if (n_con > 0) { mult = my_vector(1,n_con); dMda = my_matrix(1,n_con,1,n_parm); dMda_t = my_matrix(1,n_parm,1,n_con); K = my_vector(1,n_con); aux_mat = my_matrix(1,n_con,1,n_con); aux_vec = my_vector(1,n_con); } if (use_newton) { dLdada = my_matrix(1,n_parm,1,n_parm); A = my_matrix(1,n_parm+n_con,1,n_parm+n_con); A_inv = my_matrix(1,n_parm+n_con,1,n_parm+n_con); B = my_vector(1,n_parm+n_con); if (n_con > 0) { dMdada = my_matrix(1,n_con*n_parm,1,n_parm); new_mult = my_vector(1,n_con); } for (i=1+n_parm; i<=n_con+n_parm; ++i) { for (j=1+n_parm; j<=n_con+n_parm; ++j) { A[i][j] = 0.0; } } } while (fabs(cost-last_cost) > *tol) { ++count; pending1 = FALSE; pending2 = FALSE; AGAIN: /* calculate the current Lagrange multipliers */ if (n_con > 0) { (*f_M)(a,K); /* takes the parameters, returns residuals */ (*f_dMda)(a,dMda); /* takes the parameters, returns the Jacobian */ } (*f_dLda)(a,dLda); /* takes the parameters, returns the gradient */ if (n_con > 0) { mat_trans(dMda,dMda_t); } if (newton_active) { if (n_con > 0) { (*f_dMdada)(a,dMdada); } (*f_dLdada)(a,dLdada); } /* the first step is always a gradient step */ if (newton_active) { if (firsttime) { firsttime = FALSE; eps = 0.1; } /* build the A matrix */ for (i=1; i<=n_parm; ++i) { for (j=1; j<=n_parm; ++j) { A[i][j] = dLdada[i][j]; for (n=1; n<=n_con; ++n) { A[i][j] += mult[n]*dMdada[n+(i-1)*n_con][j]; } } } for (i=1+n_parm; i<=n_con+n_parm; ++i) { for (j=1; j<=n_parm; ++j) { A[j][i] = A[i][j] = dMda[i-n_parm][j]; } } /* build the B vector */ if (n_con > 0) { mat_vec_mult(dMda_t,mult,B); } for (i=1; i<=n_con; ++i) { B[i+n_parm] = K[i]; } /* invert the A matrix */ if (!my_inv_ludcmp(A, n_con+n_parm, A_inv)) { rc = FALSE; break; } mat_vec_mult(A_inv,B,B); vec_mult_scalar(B,eps,B); for (i=1; i<=n_parm; ++i) { new_a[i] = a[i] + B[i]; } for (i=1; i<=n_con; ++i) { new_mult[i] = mult[i] + B[n_parm+i]; } } else { if (n_con > 0) { /* the mulitpliers are updated according: mult = (dMda dMda_t)^(-1) (K/esp - dMda dLda_t) */ mat_mult(dMda,dMda_t,aux_mat); if (!my_inv_ludcmp(aux_mat, n_con, aux_mat)) { rc = FALSE; break; } mat_vec_mult(dMda,dLda,aux_vec); vec_mult_scalar(K,1./eps,K); vec_sub(K,aux_vec,aux_vec); mat_vec_mult(aux_mat,aux_vec,mult); } /* the update step looks the following: a_new = a - eps * (dLda + mult_t * dMda)_t */ if (n_con > 0) { vec_mat_mult(mult,dMda,new_a); vec_add(dLda,new_a,new_a); } else { vec_equal(dLda,new_a); } vec_mult_scalar(new_a,eps,new_a); vec_sub(a,new_a,new_a); } if (count == 1 && !pending1) { last_cost = (*f_L)(a); if (n_con > 0) { (*f_M)(a,K); last_cost += vec_mult_inner(K,mult); } } else { last_cost = cost; } /* calculate the updated cost */ cost = (*f_L)(new_a); /*printf(" %f\n",cost);*/ if (n_con > 0) { (*f_M)(new_a,K); if (newton_active) { cost += vec_mult_inner(K,new_mult); } else { cost += vec_mult_inner(K,mult); } } /* printf("last=%f new=%f\n",last_cost,cost); */ /* check out whether we reduced the cost */ if (cost > last_cost && fabs(cost-last_cost) > *tol) { /* reduce the gradient climbing rate: sometimes a reduction of eps causes an increase in cost, thus leave an option to increase eps */ cost = last_cost; /* reset last_cost */ if (pending1 && pending2) { /* this means that either increase nor decrease of eps helps, ==> leave the program */ rc = TRUE; break; } else if (pending1) { eps *= 4.0; /* the last cutting by half did not help, thus multiply by 2 to get to previous value, and one more time by 2 to get new value */ pending2 = TRUE; } else { eps /= 2.0; pending1 = TRUE; } goto AGAIN; } else { vec_equal(new_a,a); if (newton_active && n_con > 0) { vec_equal(new_mult,mult); } if (use_newton && fabs(cost-last_cost) < NEWTON_THRESHOLD) newton_active = TRUE; } } my_free_vector(dLda,1,n_parm); my_free_vector(new_a,1,n_parm); if (n_con > 0) { my_free_vector(mult,1,n_con); my_free_matrix(dMda,1,n_con,1,n_parm); my_free_matrix(dMda_t,1,n_parm,1,n_con); my_free_vector(K,1,n_con); my_free_matrix(aux_mat,1,n_con,1,n_con); my_free_vector(aux_vec,1,n_con); } if (use_newton) { my_free_matrix(dLdada,1,n_parm,1,n_parm); my_free_matrix(A,1,n_parm+n_con,1,n_parm+n_con); my_free_matrix(A_inv,1,n_parm+n_con,1,n_parm+n_con); my_free_vector(B,1,n_parm+n_con); if (n_con > 0) { my_free_matrix(dMdada,1,n_con*n_parm,1,n_parm); my_free_vector(new_mult,1,n_con); } } *final_cost = cost; *tol = fabs(cost-last_cost); if (n_con > 0) { *err = sqrt(vec_mult_inner(K,K)); } else { *err = 0.0; } /* printf("count=%ld rc=%d\n",count,rc); */ return rc; }
// ----------------------------------------------------------------------------- //virtual bool Algorithms::Test() { bool pass = true; BTNode nodes[9]; create_tree(nodes, 9); { std::vector<int> result; Traverse_Pre_order(&nodes[_('F')], result); int r[] = { 'F', 'B', 'A', 'D', 'C', 'E', 'G', 'I', 'H' }; pass = pass && (vec_equal(result, r, sizeof(r) / sizeof(int))); } { std::vector<int> result; Traverse_In_order(&nodes[_('F')], result); int r[] = { 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I' }; pass = pass && (vec_equal(result, r, sizeof(r) / sizeof(int))); } { std::vector<int> result; Traverse_In_order(&nodes[_('F')], result, 0); int r[] = { 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I' }; pass = pass && (vec_equal(result, r, sizeof(r) / sizeof(int))); } { std::vector<int> result; Traverse_Post_order(&nodes[_('F')], result); int r[] = { 'A', 'C', 'E', 'D', 'B', 'H', 'I', 'G', 'F' }; pass = pass && (vec_equal(result, r, sizeof(r) / sizeof(int))); } { std::vector<int> result; Traverse_Level_order(&nodes[_('F')], result); int r[] = { 'F', 'B', 'G', 'A', 'D', 'I', 'C', 'E', 'H' }; pass = pass && (vec_equal(result, r, sizeof(r) / sizeof(int))); } { int pre[] = { 'F', 'B', 'A', 'D', 'C', 'E', 'G', 'I', 'H' }; int in[] = { 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I' }; std::vector<int> preorder = vec_transform(pre, sizeof(pre) / sizeof(int)); std::vector<int> inorder = vec_transform(in, sizeof(in) / sizeof(int)); BTNode * root = Reconstruct_InPre(inorder, preorder); std::vector<int> result_pre, result_in; Traverse_In_order(root, result_in); Traverse_Pre_order(root, result_pre); pass = pass && vec_equal(result_pre, pre, sizeof(pre) / sizeof(int)) && vec_equal(result_in, in, sizeof(in) / sizeof(int)) ; } { int post[] = { 'A', 'C', 'E', 'D', 'B', 'H', 'I', 'G', 'F' }; int in[] = { 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I' }; std::vector<int> postorder = vec_transform(post, sizeof(post) / sizeof(int)); std::vector<int> inorder = vec_transform(in, sizeof(in) / sizeof(int)); BTNode * root = Reconstruct_InPost(inorder, postorder); std::vector<int> result_post, result_in; Traverse_In_order(root, result_in); Traverse_Post_order(root, result_post); pass = pass && vec_equal(result_post, post, sizeof(post) / sizeof(int)) && vec_equal(result_in, in, sizeof(in) / sizeof(int)) ; } return pass; }