void LatticeImageAndKernel
( const Matrix<Field>& B,
Matrix<Field>& M,
Matrix<Field>& K,
const LLLCtrl<Base<Field>>& ctrl )
{
EL_DEBUG_CSE
Matrix<Field> BCopy( B );
Matrix<Field> U, R;
auto info = LLL( BCopy, U, R, ctrl );
const Int rank = info.rank;
const Int n = B.Width();
M = BCopy(ALL,IR(0,rank));
K = U(ALL,IR(rank,n));
// Reduce the columns of U that corresponded to the kernel
LLL( K, ctrl );
// Rather than explicitly inverting the Gram matrix of the kernel basis
// as suggested by Cohen, we can simply solve a least squares problem
//
// NOTE: 'R' is reused for the least squares solution
// TODO(poulson): Support other options than just "Babai rounding", e.g.,
// Nulling and Cancelling (with optimal ordering)
LeastSquares( NORMAL, K, M, R );
Round( R );
Gemm( NORMAL, NORMAL, Field(-1), K, R, Field(1), M );
}
int main(int argc, char *argv[]){
char filename[256];
int verbose = 0;
// process command line args
if ((argc > 1 && strcmp(argv[2],"-help") == 0) || argc == 1){ // display help message if either no arguments passed or "-help" passed
printf("\n\nThis program calculates the least squares fit of a set of data. \nSupported file format is .csv. \nCurrently only supports comma as delimiter.\n\nDefault usage is: leastsquares.exe \"filename\" [-v]\n\n\t-help \tDisplays this help message\n\t-v\tVerbose mode: displays errors/status, prints the\n\t\tdata that it reads for verification purposes.\n\n");
return 0;
}
else if(argc > 1){
strcpy(filename,argv[1]);
if (strcmp(argv[2],"-v") == 0){
verbose = 1;
}
}
int choice;
// command line args processed, now go ~do shit~
dataset input;
graph output;
input = GetInput(filename,verbose); // go open the file
output = LeastSquares(input.length,input.x,input.y,input.yerr);
if(isnan(output.m) == 0 && isnan(output.merr) == 0 && isnan(output.c) == 0 && isnan(output.cerr) == 0){
printf("The least squares fit of this data is: y = (%.2f \361 %.2f)x + (%.2f \361 %.2f) \n",output.m,output.merr,output.c,output.cerr);
}
return 0;
}
bool LeastSquares(const vector<Vector>& data,int dependentVariable,
Vector& coeffs)
{
assert(!data.empty());
int n=data[0].n;
assert((int)data.size() >= n);
assert(dependentVariable >= 0 && dependentVariable < n);
Matrix mdata((int)data.size(),n-1);
Vector vdep((int)data.size());
for(size_t i=0;i<data.size();i++) {
assert(data[i].n == n);
for(int j=0;j<n;j++) {
if(j < dependentVariable)
mdata(i,j) = data[i](j);
else if(j > dependentVariable)
mdata(i,j-1) = data[i](j);
else
vdep(i) = data[i](j);
}
}
Vector tempcoeffs; Real offset;
if(!LeastSquares(mdata,vdep,tempcoeffs,offset)) return false;
coeffs.resize(n);
for(int j=0;j<n;j++) {
if(j < dependentVariable)
coeffs(j) = tempcoeffs(j);
else if(j > dependentVariable)
coeffs(j) = tempcoeffs(j-1);
else
coeffs(j) = offset;
}
return true;
}
bool LeastSquaresPickDependent(const vector<Vector>& data,
int& dependentVariable,Vector& coeffs)
{
//pick the dimension with the smallest standard deviation
Vector stddev;
StdDev_Robust(data,stddev);
Real minstddev = stddev.minElement(&dependentVariable);
return LeastSquares(data,dependentVariable,coeffs);
}
void Tikhonov
( Orientation orientation,
const SparseMatrix<F>& A,
const Matrix<F>& B,
const SparseMatrix<F>& G,
Matrix<F>& X,
const LeastSquaresCtrl<Base<F>>& ctrl )
{
DEBUG_CSE
// Explicitly form W := op(A)
// ==========================
SparseMatrix<F> W;
if( orientation == NORMAL )
W = A;
else if( orientation == TRANSPOSE )
Transpose( A, W );
else
Adjoint( A, W );
const Int m = W.Height();
const Int n = W.Width();
const Int numRHS = B.Width();
// Embed into a higher-dimensional problem via appending regularization
// ====================================================================
SparseMatrix<F> WEmb;
if( m >= n )
VCat( W, G, WEmb );
else
HCat( W, G, WEmb );
Matrix<F> BEmb;
Zeros( BEmb, WEmb.Height(), numRHS );
if( m >= n )
{
auto BEmbT = BEmb( IR(0,m), IR(0,numRHS) );
BEmbT = B;
}
else
BEmb = B;
// Solve the higher-dimensional problem
// ====================================
Matrix<F> XEmb;
LeastSquares( NORMAL, WEmb, BEmb, XEmb, ctrl );
// Extract the solution
// ====================
if( m >= n )
X = XEmb;
else
X = XEmb( IR(0,n), IR(0,numRHS) );
}
HRESULT FrequencyOffset::Calibration()
{
HRESULT ret = -1;
LeastSquares(&slope, &intercept, &x[0], &y[0], x.size());
logger->Log(LOG_INFO, L"Calibration result:\r\ny = %fx + %f\r\n", slope, intercept);
Radio::Current()->SetCalibrationLineSlope(slope);
Radio::Current()->SetCalibrationLineIntercept(intercept);
//ret = AddCalibrationToRegistry(slope, intercept);
return ret;
}
void Ricatti( Matrix<F>& W, Matrix<F>& X, SignCtrl<Base<F>> ctrl )
{
DEBUG_ONLY(CallStackEntry cse("Ricatti"))
Sign( W, ctrl );
const Int n = W.Height()/2;
Matrix<F> WTL, WTR,
WBL, WBR;
PartitionDownDiagonal
( W, WTL, WTR,
WBL, WBR, n );
// (ML, MR) = sgn(W) - I
UpdateDiagonal( W, F(-1) );
// Solve for X in ML X = -MR
Matrix<F> ML, MR;
PartitionRight( W, ML, MR, n );
Scale( F(-1), MR );
LeastSquares( NORMAL, ML, MR, X );
}
void Tikhonov
( Orientation orientation,
const DistSparseMatrix<F>& A,
const DistMultiVec<F>& B,
const DistSparseMatrix<F>& G,
DistMultiVec<F>& X,
const LeastSquaresCtrl<Base<F>>& ctrl )
{
DEBUG_CSE
mpi::Comm comm = A.Comm();
// Explicitly form W := op(A)
// ==========================
DistSparseMatrix<F> W(comm);
if( orientation == NORMAL )
W = A;
else if( orientation == TRANSPOSE )
Transpose( A, W );
else
Adjoint( A, W );
const Int m = W.Height();
const Int n = W.Width();
const Int numRHS = B.Width();
// Embed into a higher-dimensional problem via appending regularization
// ====================================================================
DistSparseMatrix<F> WEmb(comm);
if( m >= n )
VCat( W, G, WEmb );
else
HCat( W, G, WEmb );
DistMultiVec<F> BEmb(comm);
Zeros( BEmb, WEmb.Height(), numRHS );
if( m >= n )
{
// BEmb := [B; 0]
// --------------
const Int mLocB = B.LocalHeight();
BEmb.Reserve( mLocB*numRHS );
for( Int iLoc=0; iLoc<mLocB; ++iLoc )
{
const Int i = B.GlobalRow(iLoc);
for( Int j=0; j<numRHS; ++j )
BEmb.QueueUpdate( i, j, B.GetLocal(iLoc,j) );
}
BEmb.ProcessQueues();
}
else
BEmb = B;
// Solve the higher-dimensional problem
// ====================================
DistMultiVec<F> XEmb(comm);
LeastSquares( NORMAL, WEmb, BEmb, XEmb, ctrl );
// Extract the solution
// ====================
if( m >= n )
X = XEmb;
else
GetSubmatrix( XEmb, IR(0,n), IR(0,numRHS), X );
}
