static void calc_coefficients(AVFilterContext *ctx)
{
ColorMatrixContext *color = ctx->priv;
double rgb_coeffd[4][3][3];
double yuv_convertd[16][3][3];
int v = 0;
int i, j, k;
for (i = 0; i < 4; i++)
inverse3x3(rgb_coeffd[i], yuv_coeff[i]);
for (i = 0; i < 4; i++) {
for (j = 0; j < 4; j++) {
solve_coefficients(yuv_convertd[v], rgb_coeffd[i], yuv_coeff[j]);
for (k = 0; k < 3; k++) {
color->yuv_convert[v][k][0] = NS(yuv_convertd[v][k][0]);
color->yuv_convert[v][k][1] = NS(yuv_convertd[v][k][1]);
color->yuv_convert[v][k][2] = NS(yuv_convertd[v][k][2]);
}
if (color->yuv_convert[v][0][0] != 65536 || color->yuv_convert[v][1][0] != 0 ||
color->yuv_convert[v][2][0] != 0) {
av_log(ctx, AV_LOG_ERROR, "error calculating conversion coefficients\n");
}
v++;
}
}
}
/*
* generic matrix inverse code
*
* @param x, input nxn matrix
* @param y, Output inverted nxn matrix
* @param n, dimension of square matrix
* @returns false = matrix is Singular, true = matrix inversion successful
*/
bool inverse(float x[], float y[], uint16_t dim)
{
switch(dim){
case 3: return inverse3x3(x,y);
case 4: return inverse4x4(x,y);
default: return inversenxn(x,y,dim);
}
}
Matrix4 Matrix4::InverseFast() const
{
// assert: only rotation and translation
// First calculate the inverse of the rotation section by transposing
Matrix3 inverse3x3(*this);
inverse3x3.Transpose();
// Next caculate the translation inverse
Vector3 translation = -GetTranslation();
translation = translation.Transform(inverse3x3);
// Next generate the 4x4 inverse by combining the rotation with the translation
return Matrix4(inverse3x3, translation);
}
inline std::pair<typename SteadyStateUpscaler<Traits>::permtensor_t,
typename SteadyStateUpscaler<Traits>::permtensor_t>
SteadyStateUpscaler<Traits>::
upscaleSteadyState(const int flow_direction,
const std::vector<double>& initial_saturation,
const double boundary_saturation,
const double pressure_drop,
const permtensor_t& upscaled_perm)
{
static int count = 0;
++count;
int num_cells = this->ginterf_.numberOfCells();
// No source or sink.
std::vector<double> src(num_cells, 0.0);
Opm::SparseVector<double> injection(num_cells);
// Gravity.
Dune::FieldVector<double, 3> gravity(0.0);
if (use_gravity_) {
gravity[2] = Opm::unit::gravity;
}
if (gravity.two_norm() > 0.0) {
OPM_MESSAGE("Warning: Gravity is experimental for flow solver.");
}
// Set up initial saturation profile.
std::vector<double> saturation = initial_saturation;
// Set up boundary conditions.
setupUpscalingConditions(this->ginterf_, this->bctype_, flow_direction,
pressure_drop, boundary_saturation, this->twodim_hack_, this->bcond_);
// Set up solvers.
if (flow_direction == 0) {
this->flow_solver_.init(this->ginterf_, this->res_prop_, gravity, this->bcond_);
}
transport_solver_.initObj(this->ginterf_, this->res_prop_, this->bcond_);
// Run pressure solver.
this->flow_solver_.solve(this->res_prop_, saturation, this->bcond_, src,
this->residual_tolerance_, this->linsolver_verbosity_,
this->linsolver_type_, false,
this->linsolver_maxit_, this->linsolver_prolongate_factor_,
this->linsolver_smooth_steps_);
double max_mod = this->flow_solver_.postProcessFluxes();
std::cout << "Max mod = " << max_mod << std::endl;
// Do a run till steady state. For now, we just do some pressure and transport steps...
std::vector<double> saturation_old = saturation;
for (int iter = 0; iter < simulation_steps_; ++iter) {
// Run transport solver.
transport_solver_.transportSolve(saturation, stepsize_, gravity, this->flow_solver_.getSolution(), injection);
// Run pressure solver.
this->flow_solver_.solve(this->res_prop_, saturation, this->bcond_, src,
this->residual_tolerance_, this->linsolver_verbosity_,
this->linsolver_type_, false,
this->linsolver_maxit_, this->linsolver_prolongate_factor_,
this->linsolver_smooth_steps_);
max_mod = this->flow_solver_.postProcessFluxes();
std::cout << "Max mod = " << max_mod << std::endl;
// Print in-out flows if requested.
if (print_inoutflows_) {
std::pair<double, double> w_io, o_io;
computeInOutFlows(w_io, o_io, this->flow_solver_.getSolution(), saturation);
std::cout << "Pressure step " << iter
<< "\nWater flow [in] " << w_io.first
<< " [out] " << w_io.second
<< "\nOil flow [in] " << o_io.first
<< " [out] " << o_io.second
<< std::endl;
}
// Output.
if (output_vtk_) {
writeVtkOutput(this->ginterf_,
this->res_prop_,
this->flow_solver_.getSolution(),
saturation,
std::string("output-steadystate")
+ '-' + boost::lexical_cast<std::string>(count)
+ '-' + boost::lexical_cast<std::string>(flow_direction)
+ '-' + boost::lexical_cast<std::string>(iter));
}
// Comparing old to new.
int num_cells = saturation.size();
double maxdiff = 0.0;
for (int i = 0; i < num_cells; ++i) {
maxdiff = std::max(maxdiff, std::fabs(saturation[i] - saturation_old[i]));
}
#ifdef VERBOSE
std::cout << "Maximum saturation change: " << maxdiff << std::endl;
#endif
if (maxdiff < sat_change_threshold_) {
#ifdef VERBOSE
std::cout << "Maximum saturation change is under steady state threshold." << std::endl;
#endif
break;
}
// Copy to old.
saturation_old = saturation;
}
// Compute phase mobilities.
// First: compute maximal mobilities.
typedef typename Super::ResProp::Mobility Mob;
Mob m;
double m1max = 0;
double m2max = 0;
for (int c = 0; c < num_cells; ++c) {
this->res_prop_.phaseMobility(0, c, saturation[c], m.mob);
m1max = maxMobility(m1max, m.mob);
this->res_prop_.phaseMobility(1, c, saturation[c], m.mob);
m2max = maxMobility(m2max, m.mob);
}
// Second: set thresholds.
const double mob1_abs_thres = relperm_threshold_ / this->res_prop_.viscosityFirstPhase();
const double mob1_rel_thres = m1max / maximum_mobility_contrast_;
const double mob1_threshold = std::max(mob1_abs_thres, mob1_rel_thres);
const double mob2_abs_thres = relperm_threshold_ / this->res_prop_.viscositySecondPhase();
const double mob2_rel_thres = m2max / maximum_mobility_contrast_;
const double mob2_threshold = std::max(mob2_abs_thres, mob2_rel_thres);
// Third: extract and threshold.
std::vector<Mob> mob1(num_cells);
std::vector<Mob> mob2(num_cells);
for (int c = 0; c < num_cells; ++c) {
this->res_prop_.phaseMobility(0, c, saturation[c], mob1[c].mob);
thresholdMobility(mob1[c].mob, mob1_threshold);
this->res_prop_.phaseMobility(1, c, saturation[c], mob2[c].mob);
thresholdMobility(mob2[c].mob, mob2_threshold);
}
// Compute upscaled relperm for each phase.
ReservoirPropertyFixedMobility<Mob> fluid_first(mob1);
permtensor_t eff_Kw = Super::upscaleEffectivePerm(fluid_first);
ReservoirPropertyFixedMobility<Mob> fluid_second(mob2);
permtensor_t eff_Ko = Super::upscaleEffectivePerm(fluid_second);
// Set the steady state saturation fields for eventual outside access.
last_saturation_state_.swap(saturation);
// Compute the (anisotropic) upscaled mobilities.
// eff_Kw := lambda_w*K
// => lambda_w = eff_Kw*inv(K);
permtensor_t lambda_w(matprod(eff_Kw, inverse3x3(upscaled_perm)));
permtensor_t lambda_o(matprod(eff_Ko, inverse3x3(upscaled_perm)));
// Compute (anisotropic) upscaled relative permeabilities.
// lambda = k_r/mu
permtensor_t k_rw(lambda_w);
k_rw *= this->res_prop_.viscosityFirstPhase();
permtensor_t k_ro(lambda_o);
k_ro *= this->res_prop_.viscositySecondPhase();
return std::make_pair(k_rw, k_ro);
}
void CorotationalLinearFEM::ComputeForceAndStiffnessMatrixOfSubmesh(double * u, double * f, SparseMatrix * stiffnessMatrix, int warp, int elementLo, int elementHi)
{
// clear f to zero
if (f != NULL)
memset(f, 0, sizeof(double) * 3 * numVertices);
// clear stiffness matrix to zero
if (stiffnessMatrix != NULL)
stiffnessMatrix->ResetToZero();
for (int el=elementLo; el < elementHi; el++)
{
int vtxIndex[4];
for (int vtx=0; vtx<4; vtx++)
vtxIndex[vtx] = tetMesh->getVertexIndex(el, vtx);
double KElement[144]; // element stiffness matrix, to be computed below; row-major
if (warp > 0)
{
double P[16]; // the current world-coordinate positions (row-major)
/*
P = [ v0 v1 v2 v3 ]
[ 1 1 1 1 ]
*/
// rows 1,2,3
for(int i=0; i<3; i++)
for(int j=0; j<4; j++)
P[4 * i + j] = undeformedPositions[3 * vtxIndex[j] + i] + u[3 * vtxIndex[j] + i];
// row 4
for(int j=0; j<4; j++)
P[12 + j] = 1;
// F = P * Inverse(M)
double F[9]; // upper-left 3x3 block
for(int i=0; i<3; i++)
for(int j=0; j<3; j++)
{
F[3 * i + j] = 0;
for(int k=0; k<4; k++)
F[3 * i + j] += P[4 * i + k] * MInverse[el][4 * k + j];
}
double R[9]; // rotation (row-major)
double S[9]; // symmetric (row-major)
double tolerance = 1E-6;
int forceRotation = 1;
PolarDecomposition::Compute(F, R, S, tolerance, forceRotation);
// RK = R * K
// KElement = R * K * R^T
double RK[144]; // row-major
WarpMatrix(KElementUndeformed[el], R, RK, KElement);
// f = RK (RT x - x0)
double fElement[12];
for(int i=0; i<12; i++)
{
fElement[i] = 0;
for(int j=0; j<4; j++)
for(int l=0; l<3; l++)
fElement[i] += KElement[12 * i + 3 * j + l] * P[4 * l + j] - RK[12 * i + 3 * j + l] * undeformedPositions[3 * vtxIndex[j] + l];
}
// add fElement into the global f
if (f != NULL)
{
for(int j=0; j<4; j++)
for(int l=0; l<3; l++)
f[3 * vtxIndex[j] + l] += fElement[3 * j + l];
}
// compute exact stiffness matrix
if (warp == 2)
{
// compute G = (tr(S) I - S) R^T
double G[9];
double tr = S[0] + S[4] + S[8];
double temp[9];
for(int i=0; i<9; i++)
temp[i] = -S[i];
temp[0] += tr;
temp[4] += tr;
temp[8] += tr;
// G = temp * R^T
MATRIX_MULTIPLY3X3ABT(temp, R, G);
double invG[9]; // invG = G^{-1}
inverse3x3(G, invG);
double rhs[27]; // 3 x 9 matrix (column-major)
for(int i=0; i<3; i++)
for(int j=0; j<3; j++)
{
double temp[9];
for(int k=0; k<9; k++)
temp[k] = 0.0;
// copy i-th row of R into column j of temp
for(int k=0; k<3; k++)
temp[3 * k + j] = R[3 * i + k];
// extract the skew-symmetric part
SKEW_PART(temp, &rhs[3 * (3 * i + j)]);
}
// must undo division by 2 from inside the SKEW_PART macro
for(int i=0; i<27; i++)
rhs[i] *= 2.0;
// solve G * omega = rhs
double omega[27]; // column-major
for(int i=0; i<9; i++)
{
MATRIX_VECTOR_MULTIPLY3X3(invG, &rhs[3 * i], &omega[3 * i]);
}
double dRdF[81]; // each column is skew(omega) * R ; column-major
for(int i=0; i<9; i++)
{
double skew[9];
SKEW_MATRIX(&omega[3 * i], skew);
MATRIX_MULTIPLY3X3(skew, R, &dRdF[9 * i]);
}
double B[3][3][9];
// re-arrange dRdF into B, for easier dRdF * dFdx multiplication (to exploit sparsity of dFdx)
for(int i=0; i<3; i++)
for(int j=0; j<3; j++)
for(int k=0; k<3; k++)
for(int l=0; l<3; l++)
{
int row = 3 * i + k;
int column = 3 * j + l;
B[i][j][3 * k + l] = dRdF[9 * column + row];
}
// four pointers to a 3-vector
double * minv[4] = { &MInverse[el][0], &MInverse[el][4], &MInverse[el][8], &MInverse[el][12] }; // the four rows of MInverse (last column ignored)
double dRdx[108]; // derivative of the element rotation matrix with respect to the positions of the tet vertices; column-major
for(int k=0; k<4; k++)
for(int i=0; i<3; i++)
for(int j=0; j<3; j++)
{
double temp[3];
MATRIX_VECTOR_MULTIPLY3X3(B[i][j], minv[k], temp);
int row = 3 * i;
int column = 3 * k + j;
VECTOR_SET3(&dRdx[9 * column + row], temp);
}
// add contribution of dRdx to KElement
// term 1: \hat{dR/dxl} K (R^T x - m)
// compute K (R^T x - m)
double tempVec[12]; // R^T x - m
for(int vtx=0; vtx<4; vtx++)
{
double pos[3];
for(int i=0; i<3; i++)
pos[i] = P[4 * i + vtx];
MATRIX_VECTOR_MULTIPLY3X3T(R, pos, &tempVec[3*vtx]);
// subtract m
for(int i=0; i<3; i++)
tempVec[3*vtx+i] -= undeformedPositions[3 * vtxIndex[vtx] + i];
}
double a[12]; // a = K * tempVec
for (int i=0; i<12; i++)
{
a[i] = 0.0;
for (int j=0; j<12; j++)
a[i] += KElementUndeformed[el][12 * i + j] * tempVec[j];
}
// add [\hat{dR/dxl} K R^T x]_l, l=1 to 12
for(int column=0; column<12; column++)
{
double b[12]; // b = \hat{dR/dxl} * a
for(int j=0; j<4; j++)
{
MATRIX_VECTOR_MULTIPLY3X3(&dRdx[9 * column], &a[3*j], &b[3*j]);
}
// write b into KElement (add b to i-th column)
for(int row=0; row<12; row++)
KElement[12 * row + column] += b[row]; // KElement is row-major
}
// term 2: (R K \hat{dRdxl}^T)x
// re-write positions into a
for(int vtx=0; vtx<4; vtx++)
{
for(int i=0; i<3; i++)
a[3 * vtx + i] = P[4 * i + vtx];
}
// compute [\hat{dRdxl}^T x)]_l, l=1 to 12
for(int column=0; column<12; column++)
{
double b[12]; // b = \hat{dRdxl}^T * a
for(int j=0; j<4; j++)
{
MATRIX_VECTOR_MULTIPLY3X3T(&dRdx[9 * column], &a[3*j], &b[3*j]);
}
// add RK * b to column of KElement
int rowStart = 0;
for (int row=0; row<12; row++)
{
double contrib = 0.0;
for (int j=0; j<12; j++)
contrib += RK[rowStart + j] * b[j];
KElement[rowStart + column] += contrib;
rowStart += 12;
}
}
}
}
else
{
// no warp
memcpy(KElement, KElementUndeformed[el], sizeof(double) * 144);
// f = K u
double fElement[12];
for(int i=0; i<12; i++)
{
fElement[i] = 0;
for(int j=0; j<4; j++)
{
fElement[i] +=
KElement[12 * i + 3 * j + 0] * u[3 * vtxIndex[j] + 0] +
KElement[12 * i + 3 * j + 1] * u[3 * vtxIndex[j] + 1] +
KElement[12 * i + 3 * j + 2] * u[3 * vtxIndex[j] + 2];
}
}
// add fElement into the global f
if (f != NULL)
{
for(int j=0; j<4; j++)
{
f[3 * vtxIndex[j] + 0] += fElement[3 * j + 0];
f[3 * vtxIndex[j] + 1] += fElement[3 * j + 1];
f[3 * vtxIndex[j] + 2] += fElement[3 * j + 2];
}
}
}
if (stiffnessMatrix != NULL)
{
int * rowIndex = rowIndices[el];
int * columnIndex = columnIndices[el];
// add KElement to the global stiffness matrix
for (int i=0; i<4; i++)
for (int j=0; j<4; j++)
for(int k=0; k<3; k++)
for(int l=0; l<3; l++)
stiffnessMatrix->AddEntry(3 * rowIndex[i] + k, 3 * columnIndex[4 * i + j] + l, KElement[12 * (3 * i + k) + 3 * j + l]);
}
}
}