int CFeasibilityMap::s_to_tau_fn( ColumnVector &s_i ){
int tau_i=0;
for (int i_var = 0; i_var<s_i.nrows(); i_var++){
if (s_i(i_var+1)==1) tau_i += 1 << i_var;
}
return tau_i;
}
// Multiply X by n-1 x n matrix to give n-1 contrasts
// Return a ColumnVector
ReturnMatrix Helmert(const ColumnVector& X, bool full)
{
REPORT
Tracer et("Helmert * CV");
int n = X.nrows();
if (n == 0) Throw(ProgramException("X Vector of length 0", X));
Real sum = 0.0; ColumnVector Y;
if (full) Y.resize(n); else Y.resize(n-1);
for (int i = 1; i < n; ++i)
{ sum += X(i); Y(i) = (i * X(i+1) - sum) / sqrt((Real)i * (i+1)); }
if (full) { sum += X(n); Y(n) = sum / sqrt((Real)n); }
Y.release(); return Y.for_return();
}
// same as above but want only j-th element
Real Helmert_transpose(const ColumnVector& Y, int j, bool full)
{
REPORT
Tracer et("Helmert_transpose:single element ");
int n = Y.nrows(); Real sum;
if (full) sum = Y(n) / sqrt((Real)n); else { sum = 0.0; ++n; }
if (j > n || j <= 0) Throw(IndexException(j, Y));
for (int i = n-1; i > 0; --i)
{
Real Yi = Y(i) / sqrt((Real)i * (i+1));
if (i+1 == j) return i * Yi + sum;
sum -= Yi;
}
return sum;
}
ReturnMatrix Helmert_transpose(const ColumnVector& Y, bool full)
{
REPORT
Tracer et("Helmert_transpose * CV ");
int n = Y.nrows(); Real sum;
if (full) sum = Y(n) / sqrt((Real)n); else { sum = 0.0; ++n; }
ColumnVector X(n);
for (int i = n-1; i > 0; --i)
{
Real Yi = Y(i) / sqrt((Real)i * (i+1));
X(i+1) = i * Yi + sum; sum -= Yi;
}
X(1) = sum;
X.release(); return X.for_return();
}
int CFeasibilityMap::test_feasible_test_fn(CData &Data, ColumnVector &x_tilde_i, ColumnVector &s_i){
int is_feasible = 0 ;
int n_var = x_tilde_i.nrows() ;
int n_EditVec = Data.EditVec.nrows() ;
int sum_s_1 = s_i.sum() ; int sum_s_0 = n_var - sum_s_1 ;
ColumnVector x_0(sum_s_0); x_0 = 0;
Matrix A_0(n_EditVec,sum_s_0) ; A_0 = 0;
Matrix A_1(n_EditVec,sum_s_1) ; A_1 = 0;
int count0 = 0;
int count1 = 0;
for (int j_var=1; j_var<=n_var; j_var++){
if ((int)s_i(j_var)==0){
count0++;
x_0(count0) = x_tilde_i(j_var) ;
A_0.column(count0) = Data.EditMat.column(j_var) ;
} else {
count1++;
A_1.column(count1) = Data.EditMat.column(j_var) ;
}
}
ColumnVector which_rows(n_EditVec); which_rows = 0 ;
for (int i_row=1; i_row<=n_EditVec; i_row++){
int n_zero = 0 ;
for (int j=1; j<=sum_s_1; j++){
if (A_1(i_row,j)==0) n_zero++;
}
if (n_zero<sum_s_1) which_rows(i_row) = 1 ;
}
Matrix A_1_red(which_rows.sum(),sum_s_1);
ColumnVector b_1_red(which_rows.sum());
Matrix A_0_red(which_rows.sum(),sum_s_0);
for (int i_row=1, count_row = 0; i_row<=n_EditVec; i_row++){
if (which_rows(i_row)==1){
count_row++;
A_1_red.row(count_row) = A_1.row(i_row) ; // Constraints
b_1_red.row(count_row) = Data.EditVec.row(i_row) ;
A_0_red.row(count_row) = A_0.row(i_row) ;
}
}
ColumnVector EditVec_shr = b_1_red - A_0_red * x_0 ;
is_feasible = SolveLP(A_1_red, EditVec_shr);
return is_feasible?1:0;
}
int CFeasibilityMap::feasible_test_fn(CData &Data, ColumnVector &x_tilde_i,
ColumnVector &s_i, int i_original, bool initD_S, float epsilon, ColumnVector &x){
int is_feasible = 0 ;
if (initD_S) {
if (!Data.PassStep0_for_init(x_tilde_i,s_i,epsilon)) { return is_feasible;}
} else {
// Step 0 - check balance edits hold, but only one s_ij has the value 1.
if (!Data.PassStep0(s_i,i_original)) { return is_feasible;}
}
// Step 1
int n_var = x_tilde_i.nrows() ;
int n_EditVec = Data.EditVec.nrows() ;
int sum_s_1 = s_i.sum() ; int sum_s_0 = n_var - sum_s_1 ;
ColumnVector x_0(sum_s_0); x_0 = 0;
Matrix A_0(n_EditVec,sum_s_0) ; A_0 = 0;
Matrix A_1(n_EditVec,sum_s_1) ; A_1 = 0;
int count0 = 0;
int count1 = 0;
for (int j_var=1; j_var<=n_var; j_var++){
if ((int)s_i(j_var)==0){
count0++;
x_0(count0) = x_tilde_i(j_var) ;
A_0.column(count0) = Data.EditMat.column(j_var) ;
} else {
count1++;
A_1.column(count1) = Data.EditMat.column(j_var) ;
}
}
Data.Debug = Debug;
if (!Data.PassStep1(s_i, A_0, x_0)) { return is_feasible;}
// Step 2: lpSolve to check whether s_i has a feasible solution of x_i
ColumnVector which_rows(n_EditVec); which_rows = 0 ;
for (int i_row=1; i_row<=n_EditVec; i_row++){
int n_zero = 0 ;
for (int j=1; j<=sum_s_1; j++){
if (A_1(i_row,j)==0) n_zero++;
}
if (n_zero<sum_s_1) which_rows(i_row) = 1 ;
}
Matrix A_1_red(which_rows.sum(),sum_s_1);
ColumnVector b_1_red(which_rows.sum());
Matrix A_0_red(which_rows.sum(),sum_s_0);
for (int i_row=1, count_row = 0; i_row<=n_EditVec; i_row++){
if (which_rows(i_row)==1){
count_row++;
A_1_red.row(count_row) = A_1.row(i_row) ; // Constraints
b_1_red.row(count_row) = Data.EditVec.row(i_row) ;
A_0_red.row(count_row) = A_0.row(i_row) ;
}
}
ColumnVector EditVec_shr = b_1_red - A_0_red * x_0 ;
if (initD_S) {
is_feasible = SolveLP(A_1_red, EditVec_shr,x);
} else {
is_feasible = SolveLP(A_1_red, EditVec_shr);
}
return is_feasible?1:0;
}