mat addPadding(mat x, int ksize) {
int offset = ksize/2;
x.insert_rows(0, offset);
x.insert_rows(x.n_rows, offset);
x.insert_cols(0, offset);
x.insert_cols(x.n_cols, offset);
return(x);
}
void SolveX(mat& C,mat& D,mat& G,mat& B,mat& A,mat& X,vec& Z){//Solve vector of unknowns
A.zeros(0,0);
C = trans(B);
A.insert_rows(0,G);
A.insert_cols(A.n_cols,B);
C.insert_cols(C.n_cols,D);
A.insert_rows(A.n_rows,C);
X = solve( A, Z );
}
//' C++ Wrapper to Check Stability of Two-sided Matching
//'
//' This function checks if a given matching is stable for a particular set of
//' preferences. This function provides an R wrapper for the C++ backend. Users
//' should not call this function directly and instead use
//' \code{\link{galeShapley.checkStability}}.
//'
//' @param proposerUtils is a matrix with cardinal utilities of the proposing
//' side of the market. If there are \code{n} proposers and \code{m} reviewers,
//' then this matrix will be of dimension \code{m} by \code{n}. The
//' \code{i,j}th element refers to the payoff that individual \code{j} receives
//' from being matched to individual \code{i}.
//' @param reviewerUtils is a matrix with cardinal utilities of the courted side
//' of the market. If there are \code{n} proposers and \code{m} reviewers, then
//' this matrix will be of dimension \code{n} by \code{m}. The \code{i,j}th
//' element refers to the payoff that individual \code{j} receives from being
//' matched to individual \code{i}.
//' @param proposals is a matrix that contains the number of the reviewer that a
//' given proposer is matched to: the first row contains the number of the
//' reviewer that is matched with the first proposer (using C++ indexing), the
//' second row contains the id of the reviewer that is matched with the second
//' proposer, etc. The column dimension accommodates proposers with multiple
//' slots.
//' @param engagements is a matrix that contains the number of the proposer that
//' a given reviewer is matched to (using C++ indexing). The column dimension
//' accommodates reviewers with multiple slots.
//' @return true if the matching is stable, false otherwise
// [[Rcpp::export]]
bool cpp_wrapper_galeshapley_check_stability(mat proposerUtils, mat reviewerUtils, umat proposals, umat engagements) {
// number of workers
const int M = proposerUtils.n_cols;
// number of firms
const int N = proposerUtils.n_rows;
// number of slots per firm
const int slotsReviewers = engagements.n_cols;
// number of slots per worker
const int slotsProposers = proposals.n_cols;
// more jobs than workers (add utility from being unmatched to firms' preferences)
if(N*slotsReviewers>M*slotsProposers) {
reviewerUtils.insert_rows(M, 1);
reviewerUtils.row(M).fill(-1e10);
}
// more workers than jobs (add utility from being unmatched to workers' preferences)
if(M*slotsProposers>N*slotsReviewers) {
proposerUtils.insert_rows(N, 1);
proposerUtils.row(N).fill(-1e10);
}
// loop over workers
for(int wX=0; wX<M; wX++) {
// loop over firms
for(int fX=0; fX<N; fX++) {
// loop over multiple "slots" at the same worker
for(int swX=0;swX<slotsProposers;swX++) {
// loop over multiple slots at the same firm
for(int sfX=0;sfX<slotsReviewers;sfX++) {
// check if wX and fX would rather be matched with each other than with their actual matches
if(reviewerUtils(wX, fX) > reviewerUtils(engagements(fX, sfX), fX) && proposerUtils(fX, wX) > proposerUtils(proposals(wX, swX), wX)) {
::Rf_warning("matching is not stable; worker %d would rather be matched to firm %d and vice versa.\n", wX, fX);
return false;
}
}
}
}
}
return true;
}
void addBias(mat &inputs)
{
mat inputBias = mat(1,1);
inputBias(0,0) = 1.0;
inputs.insert_rows(0, inputBias);
}
void initialize_Matrices () {
//assign matrices
mat A_d_triple = {{1, dT, 0}, {0,1,0}, {dT, dT*dT/2, 1}};
mat tmp;
blkdiag( A_d_triple, A_d_triple, tmp );
blkdiag( A_d_triple, tmp, A_d_all);
mat B_one_state;
B_one_state << dT*dT/2 <<endr
<< dT <<endr
<< dT*dT*dT/6 <<endr;
blkdiag( B_one_state, B_one_state, tmp );
blkdiag( B_one_state, tmp, B_d);
mat R(3,3);
R.eye();
R = R*0.001;
float a[] = {1,1,0.001,1,1,0.001,0.001,0.01,0.001};
mat Q_end, Q;
bldMatrixDiag(a, Q_end, sizeof(a)/sizeof(*a));
float b[] = {1, 0.05, 0.01, 1, 0.05, 0.01, 0.01, 0.01, 0.01};
bldMatrixDiag(b, Q, sizeof(b)/sizeof(*b));
H.reset();
C.reset();
mat zero_mat, eye_mat;
for (int i = 0; i < HORIZON; i ++) {
// cout<<"i: "<<i<<endl;
if(i != HORIZON - 1) {
blkdiag(H, R, H);
blkdiag(H, Q, H);
} else {
blkdiag(H, R, H);
blkdiag(H, Q_end, H);
}
if ( i == 0) {
// cout<<__LINE__<<endl;
tmp.reset();
pushMatrix_row(tmp, -B_d);
eye_mat.eye(9,9);
pushMatrix_row(tmp, eye_mat);
eye_mat.zeros(9, 12*(HORIZON - 1));
pushMatrix_row(tmp, eye_mat);
C.insert_rows(C.n_rows, tmp);
}
else if (i == HORIZON - 1) {
// cout<<__LINE__<<endl;
tmp.reset();
zero_mat.zeros(9,3);
pushMatrix_row(tmp, zero_mat);
zero_mat.zeros(9, 12*((i + 1) - 2));
pushMatrix_row(tmp, zero_mat);
pushMatrix_row(tmp, -A_d_all);
pushMatrix_row(tmp, -B_d);
// tmp.print("tmp at i = 1");
eye_mat.eye(9,9);
pushMatrix_row(tmp, eye_mat);
// tmp.print("tmp at i = 1");
C.insert_rows(C.n_rows, tmp);
// pushMatrix_col(C, tmp);
// C.print("C");
}
else if (i == 1) {
// cout<<__LINE__<<endl;
tmp.reset();
zero_mat.zeros(9, 3);
pushMatrix_row(tmp, zero_mat);
pushMatrix_row(tmp, -A_d_all);
pushMatrix_row(tmp, -B_d);
eye_mat.eye(9,9);
pushMatrix_row(tmp, eye_mat);
zero_mat.zeros(9, 12 * (HORIZON - 2));
pushMatrix_row(tmp, zero_mat);
// tmp.print("tmp at i = 1");
C.insert_rows(C.n_rows, tmp);
}
else {
// cout<<__LINE__<<endl;
tmp.reset();
zero_mat.zeros(9, 3);
pushMatrix_row(tmp, zero_mat);
zero_mat.zeros(9, ((i + 1) - 2)*12);
pushMatrix_row(tmp, zero_mat);
pushMatrix_row(tmp, -A_d_all);
pushMatrix_row(tmp, -B_d);
eye_mat.eye(9, 9);
pushMatrix_row(tmp, eye_mat);
zero_mat.zeros(9, 12*(HORIZON - (i + 1)));
pushMatrix_row(tmp, zero_mat);
C.insert_rows(C.n_rows, tmp);
}
}
// cout << "C: " << C.n_rows << ", " <<C.n_cols << endl;
}