void GridPatchCartesianGLL::InterpolateData(
const DataVector<double> & dAlpha,
const DataVector<double> & dBeta,
const DataVector<int> & iPatch,
DataType eDataType,
DataLocation eDataLocation,
bool fInterpAllVariables,
DataMatrix3D<double> & dInterpData,
bool fIncludeReferenceState,
bool fConvertToPrimitive
) {
if (dAlpha.GetRows() != dBeta.GetRows()) {
_EXCEPTIONT("Point vectors must have equivalent length.");
}
// Vector for storage interpolated points
DataVector<double> dAInterpCoeffs;
dAInterpCoeffs.Initialize(m_nHorizontalOrder);
DataVector<double> dBInterpCoeffs;
dBInterpCoeffs.Initialize(m_nHorizontalOrder);
DataVector<double> dADiffCoeffs;
dADiffCoeffs.Initialize(m_nHorizontalOrder);
DataVector<double> dBDiffCoeffs;
dBDiffCoeffs.Initialize(m_nHorizontalOrder);
DataVector<double> dAInterpPt;
dAInterpPt.Initialize(m_nHorizontalOrder);
// Element-wise grid spacing
double dDeltaA = GetElementDeltaA();
double dDeltaB = GetElementDeltaB();
// Physical constants
const PhysicalConstants & phys = m_grid.GetModel().GetPhysicalConstants();
// Loop throught all points
for (int i = 0; i < dAlpha.GetRows(); i++) {
// Element index
if (iPatch[i] != GetPatchIndex()) {
continue;
}
// Verify point lies within domain of patch
const double Eps = 1.0e-10;
if ((dAlpha[i] < m_box.GetAEdge(m_box.GetAInteriorBegin()) - Eps) ||
(dAlpha[i] > m_box.GetAEdge(m_box.GetAInteriorEnd()) + Eps) ||
(dBeta[i] < m_box.GetBEdge(m_box.GetBInteriorBegin()) - Eps) ||
(dBeta[i] > m_box.GetBEdge(m_box.GetBInteriorEnd()) + Eps)
) {
_EXCEPTIONT("Point out of range");
}
// Determine finite element index
int iA =
(dAlpha[i] - m_box.GetAEdge(m_box.GetAInteriorBegin())) / dDeltaA;
int iB =
(dBeta[i] - m_box.GetBEdge(m_box.GetBInteriorBegin())) / dDeltaB;
// Bound the index within the element
if (iA < 0) {
iA = 0;
}
if (iA >= (m_box.GetAInteriorWidth() / m_nHorizontalOrder)) {
iA = m_box.GetAInteriorWidth() / m_nHorizontalOrder - 1;
}
if (iB < 0) {
iB = 0;
}
if (iB >= (m_box.GetBInteriorWidth() / m_nHorizontalOrder)) {
iB = m_box.GetBInteriorWidth() / m_nHorizontalOrder - 1;
}
iA = m_box.GetHaloElements() + iA * m_nHorizontalOrder;
iB = m_box.GetHaloElements() + iB * m_nHorizontalOrder;
// Compute interpolation coefficients
PolynomialInterp::LagrangianPolynomialCoeffs(
m_nHorizontalOrder,
&(m_box.GetAEdges()[iA]),
dAInterpCoeffs,
dAlpha[i]);
PolynomialInterp::LagrangianPolynomialCoeffs(
m_nHorizontalOrder,
&(m_box.GetBEdges()[iB]),
dBInterpCoeffs,
dBeta[i]);
int nComponents;
int nRElements = m_grid.GetRElements();
double ** pData2D;
// State Data: Perform interpolation on all variables
if (eDataType == DataType_State) {
if (eDataLocation == DataLocation_Node) {
nComponents = m_datavecStateNode[0].GetComponents();
} else {
nComponents = m_datavecStateREdge[0].GetComponents();
nRElements = m_grid.GetRElements() + 1;
}
// Tracer Data: Perform interpolation on all variables
} else if (eDataType == DataType_Tracers) {
nComponents = m_datavecTracers[0].GetComponents();
// Topography Data: Special handling due to 2D nature of data
} else if (eDataType == DataType_Topography) {
nComponents = 1;
pData2D = (double**)(m_dataTopography);
// Vorticity Data
} else if (eDataType == DataType_Vorticity) {
nComponents = 1;
// Divergence Data
} else if (eDataType == DataType_Divergence) {
nComponents = 1;
// Temperature Data
} else if (eDataType == DataType_Temperature) {
nComponents = 1;
} else {
_EXCEPTIONT("Invalid DataType");
}
// Number of radial elements
for (int c = 0; c < nComponents; c++) {
const double *** pData;
if (eDataType == DataType_State) {
if (eDataLocation == DataLocation_Node) {
pData = (const double ***)(m_datavecStateNode[0][c]);
} else {
pData = (const double ***)(m_datavecStateREdge[0][c]);
}
} else if (eDataType == DataType_Topography) {
pData = (const double ***)(&pData2D);
nRElements = 1;
} else if (eDataType == DataType_Tracers) {
pData = (const double ***)(m_datavecTracers[0][c]);
} else if (eDataType == DataType_Vorticity) {
pData = (const double ***)(double ***)(m_dataVorticity);
} else if (eDataType == DataType_Divergence) {
pData = (const double ***)(double ***)(m_dataDivergence);
} else if (eDataType == DataType_Temperature) {
pData = (const double ***)(double ***)(m_dataTemperature);
}
// Perform interpolation on all levels
for (int k = 0; k < nRElements; k++) {
dInterpData[c][k][i] = 0.0;
for (int m = 0; m < m_nHorizontalOrder; m++) {
for (int n = 0; n < m_nHorizontalOrder; n++) {
dInterpData[c][k][i] +=
dAInterpCoeffs[m]
* dBInterpCoeffs[n]
* pData[k][iA+m][iB+n];
}
}
// Do not include the reference state
if ((eDataType == DataType_State) &&
(!fIncludeReferenceState)
) {
if (eDataLocation == DataLocation_Node) {
for (int m = 0; m < m_nHorizontalOrder; m++) {
for (int n = 0; n < m_nHorizontalOrder; n++) {
dInterpData[c][k][i] -=
dAInterpCoeffs[m]
* dBInterpCoeffs[n]
* m_dataRefStateNode[c][k][iA+m][iB+n];
}
}
} else {
for (int m = 0; m < m_nHorizontalOrder; m++) {
for (int n = 0; n < m_nHorizontalOrder; n++) {
dInterpData[c][k][i] -=
dAInterpCoeffs[m]
* dBInterpCoeffs[n]
* m_dataRefStateREdge[c][k][iA+m][iB+n];
}
}
}
}
}
}
}
}
void GridPatchCSGLL::InterpolateData(
DataType eDataType,
const DataArray1D<double> & dREta,
const DataArray1D<double> & dAlpha,
const DataArray1D<double> & dBeta,
const DataArray1D<int> & iPatch,
DataArray3D<double> & dInterpData,
DataLocation eOnlyVariablesAt,
bool fIncludeReferenceState,
bool fConvertToPrimitive
) {
if ((dAlpha.GetRows() != dBeta.GetRows()) ||
(dAlpha.GetRows() != iPatch.GetRows())
) {
_EXCEPTIONT("Point vectors must have equivalent length.");
}
// Vector for storage interpolated points
DataArray1D<double> dAInterpCoeffs(m_nHorizontalOrder);
DataArray1D<double> dBInterpCoeffs(m_nHorizontalOrder);
DataArray1D<double> dADiffCoeffs(m_nHorizontalOrder);
DataArray1D<double> dBDiffCoeffs(m_nHorizontalOrder);
DataArray1D<double> dAInterpPt(m_nHorizontalOrder);
// Physical constants
const PhysicalConstants & phys = m_grid.GetModel().GetPhysicalConstants();
// Perform interpolation on all variables
int nComponents = 0;
int nRElements = m_grid.GetRElements();
// Discretization type
Grid::VerticalDiscretization eVerticalDiscType =
m_grid.GetVerticalDiscretization();
// State Data: Perform interpolation on all variables
if (eDataType == DataType_State) {
nComponents = m_datavecStateNode[0].GetSize(0);
nRElements = m_grid.GetRElements() + 1;
// Tracer Data: Perform interpolation on all variables
} else if (eDataType == DataType_Tracers) {
nComponents = m_datavecTracers[0].GetSize(0);
// Topography Data
} else if (eDataType == DataType_Topography) {
nComponents = 1;
nRElements = 1;
// Vorticity Data
} else if (eDataType == DataType_Vorticity) {
nComponents = 1;
// Divergence Data
} else if (eDataType == DataType_Divergence) {
nComponents = 1;
// Temperature Data
} else if (eDataType == DataType_Temperature) {
nComponents = 1;
// Surface Pressure Data
} else if (eDataType == DataType_SurfacePressure) {
nComponents = 1;
nRElements = 1;
// 2D User Data
} else if (eDataType == DataType_Auxiliary2D) {
nComponents = m_dataUserData2D.GetSize(0);
nRElements = 1;
} else {
_EXCEPTIONT("Invalid DataType");
}
// Buffer storage in column
DataArray1D<double> dColumnDataOut(dREta.GetRows());
// Loop through all components
for (int c = 0; c < nComponents; c++) {
DataLocation eDataLocation = DataLocation_Node;
if (eDataType == DataType_State) {
eDataLocation = m_grid.GetVarLocation(c);
// Exclude variables not at the specified DataLocation
if ((eOnlyVariablesAt != DataLocation_None) &&
(eOnlyVariablesAt != eDataLocation)
) {
continue;
}
// Adjust RElements depending on state data location
if (eDataLocation == DataLocation_Node) {
nRElements = m_grid.GetRElements();
} else if (eDataLocation == DataLocation_REdge) {
nRElements = m_grid.GetRElements() + 1;
} else {
_EXCEPTIONT("Invalid DataLocation");
}
}
// Vertical interpolation operator
LinearColumnInterpFEM opInterp;
if (nRElements != 1) {
// Finite element interpolation
if (eVerticalDiscType ==
Grid::VerticalDiscretization_FiniteElement
) {
if (eDataLocation == DataLocation_Node) {
opInterp.Initialize(
LinearColumnInterpFEM::InterpSource_Levels,
m_nVerticalOrder,
m_grid.GetREtaLevels(),
m_grid.GetREtaInterfaces(),
dREta);
} else if (eDataLocation == DataLocation_REdge) {
opInterp.Initialize(
LinearColumnInterpFEM::InterpSource_Interfaces,
m_nVerticalOrder,
m_grid.GetREtaLevels(),
m_grid.GetREtaInterfaces(),
dREta);
} else {
_EXCEPTIONT("Invalid DataLocation");
}
// Finite volume interpolation
} else if (
eVerticalDiscType ==
Grid::VerticalDiscretization_FiniteVolume
) {
if (eDataLocation == DataLocation_Node) {
opInterp.Initialize(
LinearColumnInterpFEM::InterpSource_Levels,
1,
m_grid.GetREtaLevels(),
m_grid.GetREtaInterfaces(),
dREta);
} else if (eDataLocation == DataLocation_REdge) {
opInterp.Initialize(
LinearColumnInterpFEM::InterpSource_Interfaces,
1,
m_grid.GetREtaLevels(),
m_grid.GetREtaInterfaces(),
dREta);
} else {
_EXCEPTIONT("Invalid DataLocation");
}
// Invalid vertical discretization type
} else {
_EXCEPTIONT("Invalid VerticalDiscretization");
}
} else {
opInterp.InitializeIdentity(1);
}
// Buffer storage in column
DataArray1D<double> dColumnData(nRElements);
// Get a pointer to the 3D data structure
DataArray3D<double> pData;
DataArray3D<double> pDataRef;
pData.SetSize(
nRElements,
m_box.GetATotalWidth(),
m_box.GetBTotalWidth());
pDataRef.SetSize(
nRElements,
m_box.GetATotalWidth(),
m_box.GetBTotalWidth());
if (eDataType == DataType_State) {
if (eDataLocation == DataLocation_Node) {
pData.AttachToData(&(m_datavecStateNode[0][c][0][0][0]));
pDataRef.AttachToData(&(m_dataRefStateNode[c][0][0][0]));
} else if (eDataLocation == DataLocation_REdge) {
pData.AttachToData(&(m_datavecStateREdge[0][c][0][0][0]));
pDataRef.AttachToData(&(m_dataRefStateREdge[c][0][0][0]));
} else {
_EXCEPTIONT("Invalid DataLocation");
}
} else if (eDataType == DataType_Tracers) {
pData.AttachToData(&(m_datavecTracers[0][c][0][0][0]));
} else if (eDataType == DataType_Topography) {
pData.AttachToData(&(m_dataTopography[0][0]));
} else if (eDataType == DataType_Vorticity) {
pData.AttachToData(&(m_dataVorticity[0][0][0]));
} else if (eDataType == DataType_Divergence) {
pData.AttachToData(&(m_dataDivergence[0][0][0]));
} else if (eDataType == DataType_Temperature) {
pData.AttachToData(&(m_dataTemperature[0][0][0]));
} else if (eDataType == DataType_SurfacePressure) {
pData.AttachToData(&(m_dataSurfacePressure[0][0]));
} else if (eDataType == DataType_Auxiliary2D) {
pData.AttachToData(&(m_dataUserData2D[c][0][0]));
}
// Loop throught all points
for (int i = 0; i < dAlpha.GetRows(); i++) {
// Element index
if (iPatch[i] != GetPatchIndex()) {
continue;
}
// Verify point lies within domain of patch
const double Eps = 1.0e-10;
if ((dAlpha[i] < m_dAEdge[m_box.GetAInteriorBegin()] - Eps) ||
(dAlpha[i] > m_dAEdge[m_box.GetAInteriorEnd()] + Eps) ||
(dBeta[i] < m_dBEdge[m_box.GetBInteriorBegin()] - Eps) ||
(dBeta[i] > m_dBEdge[m_box.GetBInteriorEnd()] + Eps)
) {
_EXCEPTIONT("Point out of range");
}
// Determine finite element index
int iA =
(dAlpha[i] - m_dAEdge[m_box.GetAInteriorBegin()])
/ GetElementDeltaA();
int iB =
(dBeta[i] - m_dBEdge[m_box.GetBInteriorBegin()])
/ GetElementDeltaB();
// Bound the index within the element
if (iA < 0) {
iA = 0;
}
if (iA >= (m_box.GetAInteriorWidth() / m_nHorizontalOrder)) {
iA = m_box.GetAInteriorWidth() / m_nHorizontalOrder - 1;
}
if (iB < 0) {
iB = 0;
}
if (iB >= (m_box.GetBInteriorWidth() / m_nHorizontalOrder)) {
iB = m_box.GetBInteriorWidth() / m_nHorizontalOrder - 1;
}
iA = m_box.GetHaloElements() + iA * m_nHorizontalOrder;
iB = m_box.GetHaloElements() + iB * m_nHorizontalOrder;
// Compute interpolation coefficients
PolynomialInterp::LagrangianPolynomialCoeffs(
m_nHorizontalOrder,
&(m_dAEdge[iA]),
dAInterpCoeffs,
dAlpha[i]);
PolynomialInterp::LagrangianPolynomialCoeffs(
m_nHorizontalOrder,
&(m_dBEdge[iB]),
dBInterpCoeffs,
dBeta[i]);
// Perform interpolation on all levels
for (int k = 0; k < nRElements; k++) {
dColumnData[k] = 0.0;
// Rescale vertical velocity
const int WIx = 3;
if ((c == WIx) && (fConvertToPrimitive)) {
if (m_grid.GetVarLocation(WIx) == DataLocation_REdge) {
for (int m = 0; m < m_nHorizontalOrder; m++) {
for (int n = 0; n < m_nHorizontalOrder; n++) {
dColumnData[k] +=
dAInterpCoeffs[m]
* dBInterpCoeffs[n]
* pData[k][iA+m][iB+n]
/ m_dataDerivRREdge[k][iA][iB][2];
}
}
} else {
for (int m = 0; m < m_nHorizontalOrder; m++) {
for (int n = 0; n < m_nHorizontalOrder; n++) {
dColumnData[k] +=
dAInterpCoeffs[m]
* dBInterpCoeffs[n]
* pData[k][iA+m][iB+n]
/ m_dataDerivRNode[k][iA][iB][2];
}
}
}
} else {
for (int m = 0; m < m_nHorizontalOrder; m++) {
for (int n = 0; n < m_nHorizontalOrder; n++) {
dColumnData[k] +=
dAInterpCoeffs[m]
* dBInterpCoeffs[n]
* pData[k][iA+m][iB+n];
}
}
}
// Do not include the reference state
if ((eDataType == DataType_State) &&
(!fIncludeReferenceState)
) {
for (int m = 0; m < m_nHorizontalOrder; m++) {
for (int n = 0; n < m_nHorizontalOrder; n++) {
dColumnData[k] -=
dAInterpCoeffs[m]
* dBInterpCoeffs[n]
* pDataRef[k][iA+m][iB+n];
}
}
}
}
// Interpolate vertically
opInterp.Apply(
&(dColumnData[0]),
&(dColumnDataOut[0]));
// Store data
for (int k = 0; k < dREta.GetRows(); k++) {
dInterpData[c][k][i] = dColumnDataOut[k];
}
}
}
// Convert to primitive variables
if ((eDataType == DataType_State) && (fConvertToPrimitive)) {
for (int i = 0; i < dAlpha.GetRows(); i++) {
if (iPatch[i] != GetPatchIndex()) {
continue;
}
for (int k = 0; k < dREta.GetRows(); k++) {
double dUalpha =
dInterpData[0][k][i] / phys.GetEarthRadius();
double dUbeta =
dInterpData[1][k][i] / phys.GetEarthRadius();
CubedSphereTrans::CoVecTransRLLFromABP(
tan(dAlpha[i]),
tan(dBeta[i]),
GetPatchBox().GetPanel(),
dUalpha,
dUbeta,
dInterpData[0][k][i],
dInterpData[1][k][i]);
}
}
}
}
