/**
* Performs a transposed mass evaluation
*
* @param storage GridStorage object that contains the grid's points information
* @param basis a reference to a class that implements a specific basis
* @param source the coefficients of the grid points
* @param x the d-dimensional vector with data points (row-wise)
* @param result the result vector of the matrix vector multiplication
*/
void mult_transpose(GridStorage* storage, BASIS& basis, DataVector& source,
DataMatrix& x, DataVector& result) {
result.setAll(0.0);
size_t source_size = source.getSize();
#pragma omp parallel
{
DataVector privateResult(result.getSize());
privateResult.setAll(0.0);
DataVector line(x.getNcols());
AlgorithmEvaluationTransposed<BASIS> AlgoEvalTrans(storage);
privateResult.setAll(0.0);
#pragma omp for schedule(static)
for (size_t i = 0; i < source_size; i++) {
x.getRow(i, line);
AlgoEvalTrans(basis, line, source[i], privateResult);
}
#pragma omp critical
{
result.add(privateResult);
}
}
}
void SolveEvolutionMatrix(
DataMatrix<double> & matM,
DataMatrix<double> & matB,
DataVector<double> & vecAlphaR,
DataVector<double> & vecAlphaI,
DataVector<double> & vecBeta,
DataMatrix<double> & matVR
) {
int iInfo = 0;
char jobvl = 'N';
char jobvr = 'V';
int n = matM.GetRows();
int lda = matM.GetRows();
int ldb = matM.GetRows();
int ldvl = 1;
int ldvr = matVR.GetRows();
DataVector<double> vecWork;
vecWork.Initialize(8 * n);
int lwork = vecWork.GetRows();
dggev_(
&jobvl,
&jobvr,
&n,
&(matM[0][0]),
&lda,
&(matB[0][0]),
&ldb,
&(vecAlphaR[0]),
&(vecAlphaI[0]),
&(vecBeta[0]),
NULL,
&ldvl,
&(matVR[0][0]),
&ldvr,
&(vecWork[0]),
&lwork,
&iInfo);
int nCount = 0;
for (int i = 0; i < n; i++) {
if (vecBeta[i] != 0.0) {
//printf("%i %1.5e %1.5e\n", i, vecAlphaR[i] / vecBeta[i], vecAlphaI[i] / vecBeta[i]);
nCount++;
}
}
/*
for (int i = 0; i < 40; i++) {
printf("%1.5e %1.5e\n", matVR[11][4*i+2], matVR[12][4*i+2]);
}
*/
Announce("%i total eigenvalues found", nCount);
}
int main(int, char**)
{
cout.precision(3);
typedef Matrix<float,Dynamic,2> DataMatrix;
// let's generate some samples on the 3D plane of equation z = 2x+3y (with some noise)
DataMatrix samples = DataMatrix::Random(12,2);
VectorXf elevations = 2*samples.col(0) + 3*samples.col(1) + VectorXf::Random(12)*0.1;
// and let's solve samples * [x y]^T = elevations in least square sense:
Matrix<float,2,1> xy
= (samples.adjoint() * samples).llt().solve((samples.adjoint()*elevations));
cout << xy << endl;
return 0;
}
/*! \brief save a DataMatrix as DMatrixPage */
inline static void Save(const char *fname_, const DataMatrix &mat, bool silent) {
std::string fname = fname_;
utils::FileStream fs(utils::FopenCheck(fname.c_str(), "wb"));
int magic = kMagic;
fs.Write(&magic, sizeof(magic));
mat.info.SaveBinary(fs);
fs.Close();
fname += ".row.blob";
utils::IIterator<RowBatch> *iter = mat.fmat()->RowIterator();
utils::FileStream fbin(utils::FopenCheck(fname.c_str(), "wb"));
SparsePage page;
iter->BeforeFirst();
while (iter->Next()) {
const RowBatch &batch = iter->Value();
for (size_t i = 0; i < batch.size; ++i) {
page.Push(batch[i]);
if (page.MemCostBytes() >= kPageSize) {
page.Save(&fbin); page.Clear();
}
}
}
if (page.data.size() != 0) page.Save(&fbin);
fbin.Close();
if (!silent) {
utils::Printf("DMatrixPage: %lux%lu is saved to %s\n",
static_cast<unsigned long>(mat.info.num_row()),
static_cast<unsigned long>(mat.info.num_col()), fname_);
}
}
inline void BoostOneIter(const DataMatrix &train,
float *grad, float *hess, bst_ulong len) {
this->gpair_.resize(len);
const bst_omp_uint ndata = static_cast<bst_omp_uint>(len);
#pragma omp parallel for schedule(static)
for (bst_omp_uint j = 0; j < ndata; ++j) {
gpair_[j] = bst_gpair(grad[j], hess[j]);
}
gbm_->DoBoost(train.fmat(), train.info.info, &gpair_);
}
/**
* Performs a mass evaluation
*
* @param storage GridStorage object that contains the grid's points information
* @param basis a reference to a class that implements a specific basis
* @param source the coefficients of the grid points
* @param x the d-dimensional vector with data points (row-wise)
* @param result the result vector of the matrix vector multiplication
*/
void mult(GridStorage* storage, BASIS& basis, DataVector& source, DataMatrix& x,
DataVector& result) {
result.setAll(0.0);
size_t result_size = result.getSize();
#pragma omp parallel
{
DataVector line(x.getNcols());
AlgorithmEvaluation<BASIS> AlgoEval(storage);
#pragma omp for schedule(static)
for (size_t i = 0; i < result_size; i++) {
x.getRow(i, line);
result[i] = AlgoEval(basis, line, source);
}
}
}
typedef Matrix<float,Dynamic,2> DataMatrix; // let's generate some samples on the 3D plane of equation z = 2x+3y (with some noise) DataMatrix samples = DataMatrix::Random(12,2); VectorXf elevations = 2*samples.col(0) + 3*samples.col(1) + VectorXf::Random(12)*0.1; // and let's solve samples * [x y]^T = elevations in least square sense: Matrix<float,2,1> xy = (samples.adjoint() * samples).llt().solve((samples.adjoint()*elevations)); cout << xy << endl;
void ActiveConnect(ArgListType &arg) //AT_FUN
{
// process the function arguments
static string FunctionName = "ActiveConnect";
static IntArg StartNeuron("-Nstart", "start neuron", 1);
static IntArg EndNeuron("-Nend", "end neuron{-1 gives last neuron}", -1);
static IntArg StartPat("-Pstart", "start pattern(or vector)", 1);
static IntArg EndPat("-Pend", "end pattern(or vector) {-1 gives end time}",
-1);
static StrArg SeqName("-name", "sequence name");
static StrArg ResetSeq("-reset", "reset sequence", "{zeros}");
static StrArg External("-ext", "external sequence", "{zeros}");
static FlagArg DoSummary("-sum", "-nosum", "print a summary", 1);
static int argunset = true;
static CommandLine ComL(FunctionName);
if (argunset) {
ComL.HelpSet("@ActiveConnect() \n"
"\tGenerates the data about conditional probabilities of firing\n"
"\tand saves the results into the ActiveConBuffer.\n"
"\tThe reset sequence is used for the 0 time step and\n"
"\tif externals are given then they are ignored.\n"
"\tActiveConBuffer is a matrix with 6 Vectors:\n"
"\t\t1: TimeStep(Pattern Number)\n"
"\t\t2: Absolute Activity Last Time\n"
"\t\t3: Absolute Activity This Time - Externals\n"
"\t\t4: # of Conns between CoActive Neurons\n"
"\t\t5: 4/3 = Ave # of Active Conns for Active Neurons\n"
"\t\t6: 4/(2*3) = Prob cij=1 given zi=1,zj=1\n"
"\tActiveConnect also updates the variable Pczz which\n"
"\tholds the Prob(cij=1 | zi=1,zj=1) for the whole sequence\n");
ComL.IntSet(4, &StartNeuron, &EndNeuron, &StartPat, &EndPat);
ComL.StrSet(3, &SeqName, &ResetSeq, &External);
ComL.FlagSet(1, &DoSummary);
argunset = false;
}
ComL.Process(arg, Output::Err());
if (!program::Main().getNetworkCreated()) {
CALL_ERROR << "Error: You must call @CreateNetwork() before you can "
"call @ActiveConnect." << ERR_WHERE;
exit(EXIT_FAILURE);
}
UIPtnSequence Seq = SystemVar::getSequence(SeqName, FunctionName, ComL);
int SeqSize = Seq.size();
UIPtnSequence ReSeq;
if (ResetSeq.getValue() != "{zeros}") {
ReSeq = SystemVar::getSequence(ResetSeq, FunctionName, ComL);
} else {
ReSeq.resize(SeqSize, UIVector(0));
}
int lastNeuron = 0;
for (UIPtnSequenceCIt it = Seq.begin(); it != Seq.end(); it++) {
updateMax(lastNeuron, it->back());
}
if (EndNeuron.getValue() == -1) {
EndNeuron.setValue(lastNeuron);
}
if (EndPat.getValue() == -1) {
EndPat.setValue(SeqSize);
}
if (StartNeuron.getValue() < 1 ||
StartNeuron.getValue() > EndNeuron.getValue() ||
EndNeuron.getValue() > static_cast<int>(ni)) {
CALL_ERROR << "Error in " << FunctionName << ": Neuron range of "
<< StartNeuron.getValue() << "..." << EndNeuron.getValue()
<< " is invalid." << ERR_WHERE;
ComL.DisplayHelp(Output::Err());
}
if (EndPat.getValue() < 1 || EndPat.getValue() > SeqSize ||
StartPat.getValue() < 1 || StartPat.getValue() > EndPat.getValue()) {
CALL_ERROR << "Error in " << FunctionName << ": Pattern range of "
<< StartPat.getValue() << "..." << EndPat.getValue() << " is invalid."
<< ERR_WHERE;
ComL.DisplayHelp(Output::Err());
}
// get externals
UIMatrix ExtSeq;
if (External.getValue() != "{zeros}") {
ExtSeq = SystemVar::getSequence(External, FunctionName, ComL);
} else {
ExtSeq.resize(SeqSize, UIVector(0));
}
// Do the loops
int NumPats = EndPat.getValue() - StartPat.getValue() + 1;
DataList Ave(NumPats);
DataList Sum(NumPats);
DataList Pats(NumPats);
DataList jNumFired(NumPats);
DataList iNumFired(NumPats);
DataList PczzV(NumPats);
int index = 0;
UIPtnSequenceCIt SeqConstIterator = Seq.begin();
UIPtnSequenceCIt ExtConstIterator = ExtSeq.begin();
UIVector pat_b4;
if (StartPat.getValue() == 1) {
pat_b4 = ReSeq.front();
} else {
for (int inc = 0; inc < StartPat.getValue() - 2; ++inc) ++SeqConstIterator;
pat_b4 = *(SeqConstIterator++);
}
for (int t = StartPat.getValue(); t <= EndPat.getValue(); ++t, ++index, ++SeqConstIterator, ++ExtConstIterator) {
Pats.at(index) = static_cast<float>(t);
Pattern pat = UIVectorToPtn(*SeqConstIterator, lastNeuron);
Pattern pat_ext = UIVectorToPtn(*ExtConstIterator, lastNeuron);
for (int j = StartNeuron.getValue(); j <= EndNeuron.getValue(); j++) {
// count the number on
if (pat_b4.at(j-1)) ++iNumFired.at(index);
// do the calculation for non-externals and active
if (pat.at(j-1) && (!(pat_ext.at(j-1)))) {
++jNumFired.at(index);
for (unsigned int c = 0; c < FanInCon.at(j-1); c++) {
if (pat_b4.at(inMatrix[j-1][c].getSrcNeuron()))
++Sum.at(index);
}
}
}
pat_b4 = pat;
}
// Output the data
Output::Out() << "\nSummed Active Connections in sequence " << SeqName.getValue()
<< " using neurons " << StartNeuron.getValue() << "..."
<< EndNeuron.getValue() << " and patterns " << StartPat.getValue()
<< "..." << EndPat.getValue() << "\n\tignoring externals given by "
<< External.getValue();
if (DoSummary.getValue()) {
Output::Out() << "\n" << std::setw(11) << "1:TimeStep"
<< std::setw(9) << "2:#z(t-1)"
<< std::setw(9) << "3:#z(t)"
<< std::setw(15) << "4:#cz(t-1)z(t)"
<< std::setw(9) << "4/3" << std::setw(9) << "4/(2*3)" << "\n";
}
float TotalSumC = 0.0f;
float TotalSumZ = 0.0f;
for (int i = 0; i < index; i++) {
if (fabs(Sum.at(i)) < verySmallFloat) {
Ave.at(i) = 0.0f;
PczzV.at(i) = 0.0f;
} else {
Ave.at(i) = Sum.at(i) / jNumFired.at(i);
PczzV.at(i) = Ave.at(i) / iNumFired.at(i);
}
TotalSumC += Sum.at(i);
TotalSumZ += iNumFired.at(i) * jNumFired.at(i);
if (DoSummary.getValue()) {
Output::Out() << "\n" << std::setw(11) << static_cast<int>(Pats.at(i))
<< std::setw(9) << static_cast<int>(iNumFired.at(i))
<< std::setw(9) << static_cast<int>(jNumFired.at(i))
<< std::setw(15) << static_cast<int>(Sum.at(i))
<< std::setw(9) << Ave.at(i)
<< std::setw(9) << PczzV.at(i);
}
}
Output::Out() << "\n";
float Pczz;
if (fabs(TotalSumC) < verySmallFloat) {
Pczz = 0.0f;
} else {
Pczz = TotalSumC / TotalSumZ;
}
SystemVar::SetFloatVar("Pczz", Pczz);
if (DoSummary.getValue()) {
Output::Out() << "Average: " << Pczz << "\n";
}
// Save the vector to the ActiveConBuffer
DataMatrix ActiveConMat;
ActiveConMat.push_back(Pats);
ActiveConMat.push_back(iNumFired);
ActiveConMat.push_back(jNumFired);
ActiveConMat.push_back(Sum);
ActiveConMat.push_back(Ave);
ActiveConMat.push_back(PczzV);
SystemVar::insertData("ActiveConBuffer", ActiveConMat, DLT_matrix);
return;
}
int main(int argc, char ** argv) {
MPI_Init(&argc, &argv);
try {
// Number of latitudes
int nLat;
// Number of longitudes
int nLon;
// Zonal wavenumber
int nK;
// Meridional power
int nLpow;
// Output file
std::string strOutputFile;
// Parse the command line
BeginCommandLine()
CommandLineInt(nLat, "lat", 40);
CommandLineInt(nLon, "lon", 80);
CommandLineString(strOutputFile, "out", "topo.nc");
ParseCommandLine(argc, argv);
EndCommandLine(argv)
// Generate longitude and latitude arrays
AnnounceBanner();
AnnounceStartBlock("Generating longitude and latitude arrays");
DataVector<double> dLon;
dLon.Initialize(nLon);
Parameters param;
param.GenerateLatituteArray(nLat);
std::vector<double> & dLat = param.vecNode;
double dDeltaLon = 2.0 * M_PI / static_cast<double>(nLon);
for (int i = 0; i < nLon; i++) {
dLon[i] = (static_cast<double>(i) + 0.5) * dDeltaLon;
}
AnnounceEndBlock("Done");
// Open NetCDF output file
AnnounceStartBlock("Writing to file");
NcFile ncdf_out(strOutputFile.c_str(), NcFile::Replace);
// Output coordinates
NcDim * dimLat = ncdf_out.add_dim("lat", nLat);
NcDim * dimLon = ncdf_out.add_dim("lon", nLon);
NcVar * varLat = ncdf_out.add_var("lat", ncDouble, dimLat);
varLat->set_cur((long)0);
varLat->put(&(param.vecNode[0]), nLat);
NcVar * varLon = ncdf_out.add_var("lon", ncDouble, dimLon);
varLon->set_cur((long)0);
varLon->put(&(dLon[0]), nLon);
// Generate topography
DataMatrix<double> dTopo;
dTopo.Initialize(nLat, nLon);
double dK = static_cast<double>(nK);
double dLpow = static_cast<double>(nLpow);
double dA = 6.37122e6;
double dX = 500.0;
double dLatM = 0.0;
double dLonM = M_PI / 4.0;
double dD = 5000.0;
double dH0 = 1.0;
double dXiM = 4000.0;
for (int j = 0; j < nLat; j++) {
for (int i = 0; i < nLon; i++) {
// Great circle distance
double dR = dA / dX * acos(sin(dLatM) * sin(dLat[j])
+ cos(dLatM) * cos(dLat[j]) * cos(dLon[i] - dLonM));
double dCosXi = 1.0; //cos(M_PI * dR / dXiM);
dTopo[j][i] = dH0 * exp(- dR * dR / (dD * dD))
* dCosXi * dCosXi;
}
}
// Write topography
NcVar * varZs = ncdf_out.add_var("Zs", ncDouble, dimLat, dimLon);
varZs->set_cur(0, 0);
varZs->put(&(dTopo[0][0]), nLat, nLon);
AnnounceEndBlock("Done");
Announce("Completed successfully!");
AnnounceBanner();
} catch(Exception & e) {
Announce(e.ToString().c_str());
}
MPI_Finalize();
}
void GenerateEvolutionMatrix(
int nK,
const Parameters & param,
DataMatrix<double> & matM,
DataMatrix<double> & matB
) {
int nMatrixSize = 5 * param.nPhiElements - 1;
matM.Initialize(nMatrixSize, nMatrixSize);
matB.Initialize(nMatrixSize, nMatrixSize);
// Radius of the Earth
const double ParamEarthRadius = 6.37122e6;
// Ideal gas constant
const double ParamRd = 287.0;
// Inverse Rossby number
double dInvRo =
2.0 * ParamEarthRadius * param.dOmega * param.dXscale / param.dU0;
// Scale height
double dH = ParamRd * param.dT0 / param.dG;
// Froude number
double dFr = param.dU0 / sqrt(param.dG * dH);
// Squared Froude number
double dFr2 = dFr * dFr;
// Aspect ratio
double dAs = dH / (ParamEarthRadius / param.dXscale);
// Velocity ratio
double dAv = dAs;
// Wave number
double dK2 = static_cast<double>(nK * nK);
// Gamma
double dInvGamma = 1.0 / param.dGamma;
// Grid spacing
double dDeltaPhi = param.vecNode[1] - param.vecNode[0];
// Loop through all elements
for (int j = 0; j < param.nPhiElements; j++) {
// Index of the start of this block
int ix = 4 * j;
int ixU = ix;
int ixP = ix + 1;
int ixW = ix + 2;
int ixR = ix + 3;
int ixVL = 4 * param.nPhiElements + j - 1;
int ixVR = 4 * param.nPhiElements + j;
// Phi at this node
double dPhi = param.vecNode[j];
// Cosine Phi
double dCosPhi = cos(dPhi);
// Sin Phi
double dSinPhi = sin(dPhi);
// Tan Phi
double dTanPhi = tan(dPhi);
// U evolution equations
matM[ixU][ixU] = dFr2 * dCosPhi * dCosPhi;
matM[ixP][ixU] = 1.0;
if (j != 0) {
matM[ixVL][ixU] = - 0.5 * dFr2 * (2.0 + dInvRo) * dSinPhi * dCosPhi;
}
if (j != param.nPhiElements - 1) {
matM[ixVR][ixU] = - 0.5 * dFr2 * (2.0 + dInvRo) * dSinPhi * dCosPhi;
}
// V evolution equations
if (j != 0) {
int ixV = ixVL;
int ixUL = ix - 4;
int ixPL = ix - 3;
int ixRL = ix - 1;
int ixUR = ix;
int ixPR = ix + 1;
int ixRR = ix + 3;
double dPhiS = param.vecEdge[j];
double dSinPhiS = sin(dPhiS);
double dCosPhiS = cos(dPhiS);
matM[ixUL][ixV] = 0.5 * dFr2 * (2.0 + dInvRo) * dSinPhiS * dCosPhiS;
matM[ixUR][ixV] = 0.5 * dFr2 * (2.0 + dInvRo) * dSinPhiS * dCosPhiS;
matM[ixV][ixV] = - dK2 * dFr2;
matM[ixPL][ixV] =
- 0.5 * dFr2 * (1.0 + dInvRo) * dSinPhiS * dCosPhiS
- 1.0 / dDeltaPhi;
matM[ixPR][ixV] =
- 0.5 * dFr2 * (1.0 + dInvRo) * dSinPhiS * dCosPhiS
+ 1.0 / dDeltaPhi;
matM[ixRL][ixV] = 0.5 * dFr2 * (1.0 + dInvRo) * dSinPhiS * dCosPhiS;
matM[ixRR][ixV] = 0.5 * dFr2 * (1.0 + dInvRo) * dSinPhiS * dCosPhiS;
}
// P evolution equations
matM[ixU][ixP] = 1.0;
matM[ixR][ixP] = 1.0;
if (j != 0) {
matM[ixVL][ixP] =
- 0.5 * dFr2 * (1.0 + dInvRo) * dSinPhi * dCosPhi
- 0.5 * dTanPhi
- 1.0 / dDeltaPhi;
}
if (j != param.nPhiElements - 1) {
matM[ixVR][ixP] =
- 0.5 * dFr2 * (1.0 + dInvRo) * dSinPhi * dCosPhi
- 0.5 * dTanPhi
+ 1.0 / dDeltaPhi;
}
// W evolution equation
matM[ixW][ixW] = - dK2 * dAs * dAv * dFr2;
matM[ixR][ixW] = 1.0;
// R evolution equation
matM[ixP][ixR] = dInvGamma / (1.0 - dInvGamma);
matM[ixW][ixR] = dAv / dAs;
matM[ixR][ixR] = - 1.0 / (1.0 - dInvGamma);
if (j != 0) {
matM[ixVL][ixR] = 0.5 * dFr2 * (1.0 + dInvRo) * dSinPhi * dCosPhi;
}
if (j != param.nPhiElements - 1) {
matM[ixVR][ixR] = 0.5 * dFr2 * (1.0 + dInvRo) * dSinPhi * dCosPhi;
}
// B matrix coefficients
matB[ixP][ixW] = -1.0;
matB[ixW][ixP] = -1.0;
}
}
int main(int argc, char ** argv) {
try {
// Parameters
Parameters param;
// Output filename
std::string strOutputFile;
// Horizontal minimum wave number
int nKmin;
// Horizontal maximum wave number
int nKmax;
// Parse the command line
BeginCommandLine()
CommandLineInt(param.nPhiElements, "n", 40);
CommandLineInt(nKmin, "kmin", 1);
CommandLineInt(nKmax, "kmax", 20);
CommandLineDouble(param.dXscale, "X", 1.0);
CommandLineDouble(param.dT0, "T0", 300.0);
CommandLineDouble(param.dU0, "U0", 20.0);
CommandLineDouble(param.dG, "G", 9.80616);
CommandLineDouble(param.dOmega, "omega", 7.29212e-5);
CommandLineDouble(param.dGamma, "gamma", 1.4);
CommandLineString(strOutputFile, "out", "wave.nc");
ParseCommandLine(argc, argv);
EndCommandLine(argv)
AnnounceBanner();
// Generate latitude values
param.GenerateLatituteArray(param.nPhiElements);
// Open NetCDF file
NcFile ncdf_out(strOutputFile.c_str(), NcFile::Replace);
NcDim *dimK = ncdf_out.add_dim("k", nKmax - nKmin + 1);
NcDim *dimLat = ncdf_out.add_dim("lat", param.nPhiElements);
NcDim *dimEig = ncdf_out.add_dim("eig", param.nPhiElements);
// Write parameters and latitudes to file
param.WriteToNcFile(ncdf_out, dimLat, dimLatS);
// Wave numbers
NcVar *varK = ncdf_out.add_var("k", ncInt, dimK);
DataVector<int> vecK;
vecK.Initialize(nKmax - nKmin + 1);
for (int nK = nKmin; nK <= nKmax; nK++) {
vecK[nK - nKmin] = nK;
}
varK->set_cur((long)0);
varK->put(vecK, nKmax - nKmin + 1);
// Eigenvalues
NcVar *varMR = ncdf_out.add_var("mR", ncDouble, dimK, dimEig);
NcVar *varMI = ncdf_out.add_var("mI", ncDouble, dimK, dimEig);
NcVar *varUR = ncdf_out.add_var("uR", ncDouble, dimK, dimEig, dimLat);
NcVar *varUI = ncdf_out.add_var("uI", ncDouble, dimK, dimEig, dimLat);
NcVar *varVR = ncdf_out.add_var("vR", ncDouble, dimK, dimEig, dimLatS);
NcVar *varVI = ncdf_out.add_var("vI", ncDouble, dimK, dimEig, dimLatS);
NcVar *varPR = ncdf_out.add_var("pR", ncDouble, dimK, dimEig, dimLat);
NcVar *varPI = ncdf_out.add_var("pI", ncDouble, dimK, dimEig, dimLat);
NcVar *varWR = ncdf_out.add_var("wR", ncDouble, dimK, dimEig, dimLat);
NcVar *varWI = ncdf_out.add_var("wI", ncDouble, dimK, dimEig, dimLat);
NcVar *varRhoR = ncdf_out.add_var("rhoR", ncDouble, dimK, dimEig, dimLat);
NcVar *varRhoI = ncdf_out.add_var("rhoI", ncDouble, dimK, dimEig, dimLat);
// Allocate temporary arrays
DataVector<double> dUR;
dUR.Initialize(param.nPhiElements);
DataVector<double> dUI;
dUI.Initialize(param.nPhiElements);
DataVector<double> dVR;
dVR.Initialize(param.nPhiElements-1);
DataVector<double> dVI;
dVI.Initialize(param.nPhiElements-1);
DataVector<double> dPR;
dPR.Initialize(param.nPhiElements);
DataVector<double> dPI;
dPI.Initialize(param.nPhiElements);
DataVector<double> dWR;
dWR.Initialize(param.nPhiElements);
DataVector<double> dWI;
dWI.Initialize(param.nPhiElements);
DataVector<double> dRhoR;
dRhoR.Initialize(param.nPhiElements);
DataVector<double> dRhoI;
dRhoI.Initialize(param.nPhiElements);
// Loop over all horizontal wave numbers
for (int nK = nKmin; nK <= nKmax; nK++) {
// Build matrices
char szMessage[100];
sprintf(szMessage, "Building evolution matrices (k = %i)", nK);
AnnounceStartBlock(szMessage);
DataMatrix<double> matM;
DataMatrix<double> matB;
GenerateEvolutionMatrix(nK, param, matM, matB);
AnnounceEndBlock("Done");
// Solve the matrices
AnnounceStartBlock("Solving evolution matrices");
DataVector<double> vecAlphaR;
DataVector<double> vecAlphaI;
DataVector<double> vecBeta;
DataMatrix<double> matVR;
vecAlphaR.Initialize(matM.GetRows());
vecAlphaI.Initialize(matM.GetRows());
vecBeta .Initialize(matM.GetRows());
matVR .Initialize(matM.GetRows(), matM.GetColumns());
SolveEvolutionMatrix(
matM,
matB,
vecAlphaR,
vecAlphaI,
vecBeta,
matVR);
// Sort eigenvalues
std::multimap<double, int> mapSortedRows;
for (int i = 0; i < vecBeta.GetRows(); i++) {
if (vecBeta[i] != 0.0) {
double dLambdaR = vecAlphaR[i] / vecBeta[i];
double dLambdaI = vecAlphaI[i] / vecBeta[i];
double dMR = dLambdaI;
double dMI = - dLambdaR - 1.0;
double dEvalMagnitude = fabs(dMR);
//printf("\n%1.5e %1.5e ", dMR, dMI);
// Purely imaginary eigenvalue
if (dMR == 0.0) {
// Wave must decay with height
if (dMI < 0.0) {
continue;
}
// Complex-conjugate pair of eigenvalues
} else {
// Phase propagation must be downward, and energy
// propagation upwards
if (dMR < 0.0) {
continue;
}
}
//printf("(OK)");
mapSortedRows.insert(
std::pair<double, int>(dEvalMagnitude, i));
// Only store one entry for complex-conjugate pairs
if (vecAlphaI[i] != 0.0) {
i++;
}
}
}
Announce("%i eigenmodes found to satisfy entropy condition",
mapSortedRows.size());
/*
if (mapSortedRows.size() != param.nPhiElements) {
_EXCEPTIONT("Mismatch between eigenmode count and latitude count");
}
*/
AnnounceEndBlock("Done");
// Write the matrices to a file
AnnounceStartBlock("Writing results");
int iKix = nK - nKmin;
int iWave = 0;
std::map<double, int>::const_iterator it;
for (it = mapSortedRows.begin(); it != mapSortedRows.end(); it++) {
int i = it->second;
double dLambdaR = vecAlphaR[i] / vecBeta[i];
double dLambdaI = vecAlphaI[i] / vecBeta[i];
double dMR = dLambdaI;
double dMI = - dLambdaR - 1.0;
// Dump eigenvalue to NetCDF file
varMR->set_cur(iKix, iWave);
varMR->put(&dMR, 1, 1);
varMI->set_cur(iKix, iWave);
varMI->put(&dMI, 1, 1);
// Store real part of eigenfunction
for (int j = 0; j < param.nPhiElements; j++) {
dUR [j] = matVR[i][4*j ];
dPR [j] = matVR[i][4*j+1];
dWR [j] = matVR[i][4*j+2];
dRhoR[j] = matVR[i][4*j+3];
}
for (int j = 0; j < param.nPhiElements-1; j++) {
dVR[j] = matVR[i][4 * param.nPhiElements + j];
}
// Complex eigenvalue / eigenfunction pair
if (dLambdaI != 0.0) {
// Eigenvalue Lambda is complex conjugate
dMR = -dMR;
// Dump eigenvalue to NetCDF file
varMR->set_cur(iKix, iWave+1);
varMR->put(&dMR, 1, 1);
varMI->set_cur(iKix, iWave+1);
varMI->put(&dMI, 1, 1);
// Store imaginary component of vector
for (int j = 0; j < param.nPhiElements; j++) {
dUI [j] = matVR[i+1][4*j ];
dPI [j] = matVR[i+1][4*j+1];
dWI [j] = matVR[i+1][4*j+2];
dRhoI[j] = matVR[i+1][4*j+3];
}
for (int j = 0; j < param.nPhiElements-1; j++) {
dVI[j] = matVR[i+1][4 * param.nPhiElements + j];
}
// Real eigenvalue / eigenvector pair
} else {
dUI.Zero();
dPI.Zero();
dWI.Zero();
dRhoI.Zero();
dVI.Zero();
}
// Dump the first eigenfunction to the file
varUR->set_cur(iKix, iWave, 0);
varUR->put(dUR, 1, 1, param.nPhiElements);
varVR->set_cur(iKix, iWave, 0);
varVR->put(dVR, 1, 1, param.nPhiElements-1);
varPR->set_cur(iKix, iWave, 0);
varPR->put(dPR, 1, 1, param.nPhiElements);
varWR->set_cur(iKix, iWave, 0);
varWR->put(dWR, 1, 1, param.nPhiElements);
varRhoR->set_cur(iKix, iWave, 0);
varRhoR->put(dRhoR, 1, 1, param.nPhiElements);
varUI->set_cur(iKix, iWave, 0);
varUI->put(dUI, 1, 1, param.nPhiElements);
varVI->set_cur(iKix, iWave, 0);
varVI->put(dVI, 1, 1, param.nPhiElements-1);
varPI->set_cur(iKix, iWave, 0);
varPI->put(dPI, 1, 1, param.nPhiElements);
varWI->set_cur(iKix, iWave, 0);
varWI->put(dWI, 1, 1, param.nPhiElements);
varRhoI->set_cur(iKix, iWave, 0);
varRhoI->put(dRhoI, 1, 1, param.nPhiElements);
// Complex eigenvalue / eigenvector pair
if (dLambdaI != 0.0) {
for (int j = 0; j < param.nPhiElements; j++) {
dUI [j] = - dUI [j];
dPI [j] = - dPI [j];
dWI [j] = - dWI [j];
dRhoI[j] = - dRhoI[j];
}
for (int j = 0; j < param.nPhiElements-1; j++) {
dVI[j] = - dVI[j];
}
varUR->set_cur(iKix, iWave+1, 0);
varUR->put(dUR, 1, 1, param.nPhiElements);
varVR->set_cur(iKix, iWave+1, 0);
varVR->put(dVR, 1, 1, param.nPhiElements-1);
varPR->set_cur(iKix, iWave+1, 0);
varPR->put(dPR, 1, 1, param.nPhiElements);
varWR->set_cur(iKix, iWave+1, 0);
varWR->put(dWR, 1, 1, param.nPhiElements);
varRhoR->set_cur(iKix, iWave+1, 0);
varRhoR->put(dRhoR, 1, 1, param.nPhiElements);
varUI->set_cur(iKix, iWave+1, 0);
varUI->put(dUI, 1, 1, param.nPhiElements);
varVI->set_cur(iKix, iWave+1, 0);
varVI->put(dVI, 1, 1, param.nPhiElements-1);
varPI->set_cur(iKix, iWave+1, 0);
varPI->put(dPI, 1, 1, param.nPhiElements);
varWI->set_cur(iKix, iWave+1, 0);
varWI->put(dWI, 1, 1, param.nPhiElements);
varRhoI->set_cur(iKix, iWave+1, 0);
varRhoI->put(dRhoI, 1, 1, param.nPhiElements);
}
// Increment wave index
iWave++;
if (dLambdaI != 0.0) {
iWave++;
}
}
AnnounceEndBlock("Done");
AnnounceBanner();
}
} catch(Exception & e) {
Announce(e.ToString().c_str());
}
}
LogisticRegression::LogisticRegression(DataMatrix<double> ddata, std::vector<double> iinit, double aalpha):
data(ddata), init(iinit), alpha(aalpha), nrows(ddata.getRows()), ncols(ddata.getCols()){
if(init.size() != (ncols-1))
std::cerr<<"Error!"<<std::endl;
}
float_t OperationNaiveEvalHessianModFundamentalSpline::evalHessian(
const DataVector& alpha, const DataVector& point,
DataVector& gradient, DataMatrix& hessian) {
const size_t n = storage->size();
const size_t d = storage->dim();
float_t result = 0.0;
gradient.resize(storage->dim());
gradient.setAll(0.0);
hessian = DataMatrix(d, d);
hessian.setAll(0.0);
DataVector curGradient(d);
DataMatrix curHessian(d, d);
for (size_t i = 0; i < n; i++) {
const GridIndex& gp = *(*storage)[i];
float_t curValue = 1.0;
curGradient.setAll(alpha[i]);
curHessian.setAll(alpha[i]);
for (size_t t = 0; t < d; t++) {
const float_t val1d = base.eval(gp.getLevel(t), gp.getIndex(t), point[t]);
const float_t dx1d = base.evalDx(gp.getLevel(t), gp.getIndex(t),
point[t]);
const float_t dxdx1d = base.evalDxDx(gp.getLevel(t), gp.getIndex(t), point[t]);
curValue *= val1d;
for (size_t t2 = 0; t2 < d; t2++) {
if (t2 == t) {
curGradient[t2] *= dx1d;
for (size_t t3 = 0; t3 < d; t3++) {
if (t3 == t) {
curHessian(t2, t3) *= dxdx1d;
} else {
curHessian(t2, t3) *= dx1d;
}
}
} else {
curGradient[t2] *= val1d;
for (size_t t3 = 0; t3 < d; t3++) {
if (t3 == t) {
curHessian(t2, t3) *= dx1d;
} else {
curHessian(t2, t3) *= val1d;
}
}
}
}
}
result += alpha[i] * curValue;
gradient.add(curGradient);
hessian.add(curHessian);
}
return result;
}
int main(int argc, char** argv) {
NcError error(NcError::verbose_nonfatal);
try {
// Input file
std::string strInputFile;
// Input file list
std::string strInputFileList;
// Input file format
std::string strInputFormat;
// NetCDF file containing latitude and longitude arrays
std::string strLatLonFile;
// Output file (NetCDF)
std::string strOutputFile;
// Output variable name
std::string strOutputVariable;
// Column in which the longitude index appears
int iLonIxCol;
// Column in which the latitude index appears
int iLatIxCol;
// Begin latitude
double dLatBegin;
// End latitude
double dLatEnd;
// Begin longitude
double dLonBegin;
// End longitude
double dLonEnd;
// Number of latitudes in output
int nLat;
// Number of longitudes in output
int nLon;
// Parse the command line
BeginCommandLine()
CommandLineString(strInputFile, "in", "");
CommandLineString(strInputFileList, "inlist", "");
CommandLineStringD(strInputFormat, "in_format", "std", "(std|visit)");
CommandLineString(strOutputFile, "out", "");
CommandLineString(strOutputVariable, "outvar", "density");
CommandLineInt(iLonIxCol, "iloncol", 8);
CommandLineInt(iLatIxCol, "ilatcol", 9);
CommandLineDouble(dLatBegin, "lat_begin", -90.0);
CommandLineDouble(dLatEnd, "lat_end", 90.0);
CommandLineDouble(dLonBegin, "lon_begin", 0.0);
CommandLineDouble(dLonEnd, "lon_end", 360.0);
CommandLineInt(nLat, "nlat", 180);
CommandLineInt(nLon, "nlon", 360);
ParseCommandLine(argc, argv);
EndCommandLine(argv)
AnnounceBanner();
// Check input
if ((strInputFile == "") && (strInputFileList == "")) {
_EXCEPTIONT("No input file (--in) or (--inlist) specified");
}
if ((strInputFile != "") && (strInputFileList != "")) {
_EXCEPTIONT("Only one input file (--in) or (--inlist) allowed");
}
if (strInputFormat != "std") {
_EXCEPTIONT("UNIMPLEMENTED: Only \"--in_format std\" supported");
}
// Check output
if (strOutputFile == "") {
_EXCEPTIONT("No output file (--out) specified");
}
// Check output variable
if (strOutputVariable == "") {
_EXCEPTIONT("No output variable name (--outvar) specified");
}
// Number of latitudes and longitudes
if (nLat == 0) {
_EXCEPTIONT("UNIMPLEMENTED: --nlat must be specified currently");
}
if (nLon == 0) {
_EXCEPTIONT("UNIMPLEMENTED: --nlon must be specified currently");
}
// Input file list
std::vector<std::string> vecInputFiles;
if (strInputFile != "") {
vecInputFiles.push_back(strInputFile);
}
if (strInputFileList != "") {
GetInputFileList(strInputFileList, vecInputFiles);
}
int nFiles = vecInputFiles.size();
// Density
DataMatrix<int> nCounts;
nCounts.Initialize(nLat, nLon);
// Loop through all files in list
AnnounceStartBlock("Processing files");
std::string strBuffer;
strBuffer.reserve(1024);
for (int f = 0; f < nFiles; f++) {
Announce("File \"%s\"", vecInputFiles[f].c_str());
FILE * fp = fopen(vecInputFiles[f].c_str(), "r");
if (fp == NULL) {
_EXCEPTION1("Unable to open input file \"%s\"",
vecInputFiles[f].c_str());
}
for (;;) {
// Read in the next line
fgets(&(strBuffer[0]), 1024, fp);
int nLength = strlen(&(strBuffer[0]));
// Check for end of file
if (feof(fp)) {
break;
}
// Check for comment line
if (strBuffer[0] == '#') {
continue;
}
// Check for new storm
if (strncmp(&(strBuffer[0]), "start", 5) == 0) {
continue;
}
// Parse line
double dLon;
double dLat;
int iCol = 0;
int iLast = 0;
bool fWhitespace = true;
for (int i = 0; i <= nLength; i++) {
if ((strBuffer[i] == ' ') ||
(strBuffer[i] == ',') ||
(strBuffer[i] == '\t') ||
(strBuffer[i] == '\0')
) {
if (!fWhitespace) {
if (iCol == iLonIxCol) {
strBuffer[i] = '\0';
dLon = atof(&(strBuffer[iLast]));
}
if (iCol == iLatIxCol) {
strBuffer[i] = '\0';
dLat = atof(&(strBuffer[iLast]));
}
}
fWhitespace = true;
} else {
if (fWhitespace) {
iLast = i;
iCol++;
}
fWhitespace = false;
}
}
// Latitude and longitude index
int iLon =
static_cast<int>(static_cast<double>(nLon)
* (dLon - dLonBegin) / (dLonEnd - dLonBegin));
int iLat =
static_cast<int>(static_cast<double>(nLat)
* (dLat - dLatBegin) / (dLatEnd - dLatBegin));
if (iLon == (-1)) {
iLon = 0;
}
if (iLon == nLon) {
iLon = nLon - 1;
}
if (iLat == (-1)) {
iLat = 0;
}
if (iLat == nLat) {
iLat = nLat - 1;
}
if ((iLat < 0) || (iLat >= nLat)) {
_EXCEPTION1("Latitude index (%i) out of range", iLat);
}
if ((iLon < 0) || (iLon >= nLon)) {
_EXCEPTION1("Longitude index (%i) out of range", iLon);
}
nCounts[iLat][iLon]++;
}
fclose(fp);
}
AnnounceEndBlock("Done");
// Output results
AnnounceStartBlock("Output results");
// Load the netcdf output file
NcFile ncOutput(strOutputFile.c_str(), NcFile::Replace);
if (!ncOutput.is_valid()) {
_EXCEPTION1("Unable to open output file \"%s\"",
strOutputFile.c_str());
}
// Create output
NcDim * dimLat = ncOutput.add_dim("lat", nLat);
NcDim * dimLon = ncOutput.add_dim("lon", nLon);
NcVar * varLat = ncOutput.add_var("lat", ncDouble, dimLat);
NcVar * varLon = ncOutput.add_var("lon", ncDouble, dimLon);
varLat->add_att("units", "degrees_north");
varLon->add_att("units", "degrees_east");
DataVector<double> dLat(nLat);
DataVector<double> dLon(nLon);
for (int j = 0; j < nLat; j++) {
dLat[j] = dLatBegin
+ (dLatEnd - dLatBegin)
* (static_cast<double>(j) + 0.5)
/ static_cast<double>(nLat);
}
for (int i = 0; i < nLon; i++) {
dLon[i] = dLonBegin
+ (dLonEnd - dLonBegin)
* (static_cast<double>(i) + 0.5)
/ static_cast<double>(nLon);
}
varLat->put(&(dLat[0]), nLat);
varLon->put(&(dLon[0]), nLon);
// Output counts
NcVar * varCount =
ncOutput.add_var(
strOutputVariable.c_str(),
ncInt,
dimLat,
dimLon);
varCount->put(&(nCounts[0][0]), nLat, nLon);
ncOutput.close();
AnnounceEndBlock("Done");
AnnounceBanner();
} catch(Exception & e) {
Announce(e.ToString().c_str());
}
}