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 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());
}
}