bool fullMatrix<double>::invert(fullMatrix<double> &result) const
{
int M = size1(), N = size2(), lda = size1(), info;
int *ipiv = new int[std::min(M, N)];
if (result.size2() != M || result.size1() != N) {
if (result._own_data || !result._data)
result.resize(M,N,false);
else
Msg::Fatal("FullMatrix: Bad dimension, I cannot write in proxy");
}
result.setAll(*this);
F77NAME(dgetrf)(&M, &N, result._data, &lda, ipiv, &info);
if(info == 0){
int lwork = M * 4;
double *work = new double[lwork];
F77NAME(dgetri)(&M, result._data, &lda, ipiv, work, &lwork, &info);
delete [] work;
}
delete [] ipiv;
if(info == 0) return true;
else if(info > 0)
Msg::Error("U(%d,%d)=0 in matrix inversion", info, info);
else
Msg::Error("Wrong %d-th argument in matrix inversion", -info);
return false;
}
void LagMultTerm::get(MElement *ele, int npts, IntPt *GP,
fullMatrix<double> &m) const
{
int nbFF1 = BilinearTerm<SVector3, SVector3>::space1.getNumKeys(
ele); // nbVertices*nbcomp of parent
int nbFF2 = BilinearTerm<SVector3, SVector3>::space2.getNumKeys(
ele); // nbVertices of boundary
double jac[3][3];
m.resize(nbFF1, nbFF2);
m.setAll(0.);
for(int i = 0; i < npts; i++) {
double u = GP[i].pt[0];
double v = GP[i].pt[1];
double w = GP[i].pt[2];
const double weight = GP[i].weight;
const double detJ = ele->getJacobian(u, v, w, jac);
std::vector<TensorialTraits<SVector3>::ValType> Vals;
std::vector<TensorialTraits<SVector3>::ValType> ValsT;
BilinearTerm<SVector3, SVector3>::space1.f(ele, u, v, w, Vals);
BilinearTerm<SVector3, SVector3>::space2.f(ele, u, v, w, ValsT);
for(int j = 0; j < nbFF1; j++) {
for(int k = 0; k < nbFF2; k++) {
m(j, k) += _eqfac * dot(Vals[j], ValsT[k]) * weight * detJ;
}
}
}
}
void fullMatrix<double>::multOnBlock(const fullMatrix<double> &b, const int ncol, const int fcol, const int alpha_, const int beta_, fullVector<double> &c) const
{
int M = 1, N = ncol, K = b.size1() ;
int LDA = _r, LDB = b.size1(), LDC = 1;
double alpha = alpha_, beta = beta_;
F77NAME(dgemm)("N", "N", &M, &N, &K, &alpha, _data, &LDA, &(b._data[fcol*K]), &LDB,
&beta, &(c._data[fcol]), &LDC);
}
void fullMatrix<double>::mult(const fullMatrix<double> &b, fullMatrix<double> &c) const
{
int M = c.size1(), N = c.size2(), K = _c;
int LDA = _r, LDB = b.size1(), LDC = c.size1();
double alpha = 1., beta = 0.;
F77NAME(dgemm)("N", "N", &M, &N, &K, &alpha, _data, &LDA, b._data, &LDB,
&beta, c._data, &LDC);
}
void fullMatrix<double>::gemm(const fullMatrix<double> &a, const fullMatrix<double> &b,
double alpha, double beta, bool transposeA, bool transposeB)
{
int M = size1(), N = size2(), K = transposeA ? a.size1() : a.size2();
int LDA = a.size1(), LDB = b.size1(), LDC = size1();
F77NAME(dgemm)(transposeA ? "T" : "N", transposeB ? "T" :"N", &M, &N, &K, &alpha, a._data, &LDA, b._data, &LDB,
&beta, _data, &LDC);
}
void PViewFactory::setEntry (int id, const fullMatrix<double> &val)
{
std::vector<double> &vv = _values[id];
vv.resize(val.size1()*val.size2());
int k=0;
for (int i=0;i<val.size1(); i++) {
for (int j=0;j<val.size2(); j++) {
vv[k++] = val(i,j);
}
}
}
template<class T2> void BilinearTermContract<T2>::get(MElement *ele, int npts, IntPt *GP, fullMatrix<double> &m) const
{
fullVector<T2> va;
fullVector<T2> vb;
a->get(ele,npts,GP,va);
b->get(ele,npts,GP,vb);
m.resize(va.size(), vb.size());
m.setAll(0.);
for (int i=0;i<va.size();++i)
for (int j=0;j<vb.size();++j)
m(i,j)=dot(va(i),vb(j));
}
bool fullMatrix<double>::svd(fullMatrix<double> &V, fullVector<double> &S)
{
fullMatrix<double> VT(V.size2(), V.size1());
int M = size1(), N = size2(), LDA = size1(), LDVT = VT.size1(), info;
int lwork = std::max(3 * std::min(M, N) + std::max(M, N), 5 * std::min(M, N));
fullVector<double> WORK(lwork);
F77NAME(dgesvd)("O", "A", &M, &N, _data, &LDA, S._data, _data, &LDA,
VT._data, &LDVT, WORK._data, &lwork, &info);
V = VT.transpose();
if(info == 0) return true;
if(info > 0)
Msg::Error("SVD did not converge");
else
Msg::Error("Wrong %d-th argument in SVD decomposition", -info);
return false;
}
void polynomialBasis::df(const fullMatrix<double> &coord,
fullMatrix<double> &dfm) const
{
double dfv[1256][3];
dfm.resize(coord.size1() * 3, coefficients.size1(), false);
int dimCoord = coord.size2();
for(int iPoint = 0; iPoint < coord.size1(); iPoint++) {
df(coord(iPoint, 0), dimCoord > 1 ? coord(iPoint, 1) : 0.,
dimCoord > 2 ? coord(iPoint, 2) : 0., dfv);
for(int i = 0; i < coefficients.size1(); i++) {
dfm(iPoint * 3 + 0, i) = dfv[i][0];
dfm(iPoint * 3 + 1, i) = dfv[i][1];
dfm(iPoint * 3 + 2, i) = dfv[i][2];
}
}
}
void polynomialBasis::f(const fullMatrix<double> &coord,
fullMatrix<double> &sf) const
{
double p[1256];
sf.resize(coord.size1(), coefficients.size1());
for(int iPoint = 0; iPoint < coord.size1(); iPoint++) {
evaluateMonomials(coord(iPoint, 0),
coord.size2() > 1 ? coord(iPoint, 1) : 0,
coord.size2() > 2 ? coord(iPoint, 2) : 0, p);
for(int i = 0; i < coefficients.size1(); i++) {
sf(iPoint, i) = 0.;
for(int j = 0; j < coefficients.size2(); j++)
sf(iPoint, i) += coefficients(i, j) * p[j];
}
}
}
void epsRRod(fullVector<double>& xyz, fullMatrix<Complex>& epsR){
epsR.scale(0);
epsR(0, 0) = Complex(epsRRodRe, epsRRodIm);
epsR(1, 1) = Complex(epsRRodRe, epsRRodIm);
epsR(2, 2) = Complex(epsRRodRe, epsRRodIm);
}
void nuRRod(fullVector<double>& xyz, fullMatrix<Complex>& nuR){
nuR.scale(0);
nuR(0, 0) = 1;
nuR(1, 1) = 1;
nuR(2, 2) = 1;
}
void BilinearTermBase::get(MElement *ele, int npts, IntPt *GP, fullMatrix<double> &m) const
{
std::vector<fullMatrix<double> > mv(npts);
get(ele,npts,GP,mv);
m.resize(mv[0].size1(), mv[0].size2());
m.setAll(0.);
double jac[3][3];
for (int k=0;k<npts;k++)
{
const double u = GP[k].pt[0]; const double v = GP[k].pt[1]; const double w = GP[k].pt[2];
const double weight = GP[k].weight; const double detJ = ele->getJacobian(u, v, w, jac);
const double coeff=weight*detJ;
for (int i=0;i<mv[k].size1();++i)
for (int j=0;j<mv[k].size2();++j)
m(i,j)+=mv[k](i,j)*coeff;
}
}
void ana(double (*f)(fullVector<double>& xyz),
const fullMatrix<double>& point,
fullMatrix<double>& eval){
// Alloc eval for Scalar Values //
const size_t nPoint = point.size1();
eval.resize(nPoint, 1);
// Loop on point and evaluate f //
fullVector<double> xyz(3);
for(size_t i = 0; i < nPoint; i++){
xyz(0) = point(i, 0);
xyz(1) = point(i, 1);
xyz(2) = point(i, 2);
eval(i, 0) = f(xyz);
}
}
double l2Norm(const fullMatrix<double>& valA, const fullMatrix<double>& valB){
const size_t nPoint = valA.size1();
const size_t dim = valA.size2();
double norm = 0;
double modSquare = 0;
for(size_t i = 0; i < nPoint; i++){
modSquare = 0;
for(size_t j = 0; j < dim; j++)
modSquare += (valA(i, j) - valB(i, j)) * (valA(i, j) - valB(i, j));
norm += modSquare;
}
return norm = sqrt(norm);
}
void pyramidalBasis::f(const fullMatrix<double> &coord, fullMatrix<double> &sf) const
{
const int N = bergot->size(), NPts = coord.size1();
sf.resize(NPts, N);
double *fval = new double[N];
for (int iPt=0; iPt<NPts; iPt++) {
bergot->f(coord(iPt,0), coord(iPt,1), coord(iPt,2), fval);
for (int i = 0; i < N; i++) {
sf(iPt,i) = 0.;
for (int j = 0; j < N; j++) sf(iPt,i) += coefficients(i,j)*fval[j];
}
}
delete[] fval;
}
void Quadrature::point(fullMatrix<double>& gC,
fullVector<double>& gW){
gW.resize(1);
gC.resize(1, 1);
gW(0) = 1;
gC(0, 0) = 0;
gC(0, 1) = 0;
gC(0, 2) = 0;
}
void solve( const fullMatrix & A,
fullMatrix& X,
const fullMatrix& Y )
{ // find X s.t. A X = Y using Gausian Elimination with
// row pivoting -- no scaling this version
if( A.row != A.col ){
std::cerr << "solve only works for square matrices\n";
return;
}
int i, j, k, n = A.col, m=Y.col;
double s, pa;
// initialize X to Y and copy A
X = Y;
fullMatrix B(A);
// could scale here
// next do forward elimination and forward solution
for( i=0; i<n; i++ ){ // clean up the i-th column
// find the pivot
k = i; // row with the pivot
pa = std::abs(B(i,i));
for( j=i+1; j<n; j++ )
if( std::abs(B(j,i)) > pa ){
pa = std::abs(B(j,i));
k = j;
}
if( pa == 0.0 )
error( "solve: singular matrix");
B.swapRows(i,k);
X.swapRows(i,k); // the pivot is now in B(i,i)
for( j=i+1; j<n; j++ ){ // for each row below row i
s = B(j,i)/B(i,i);
for( k=i+1; k<n; k++ ) // modifications that make B(j,i) zero
B(j,k) -= s*B(i,k);
for( k=0; k<m; k++ ) // change the rhs too
X(j,k) -= s*X(i,k);
}
}
// now B is upper triangular
for( i=n-1; i>=0; i-- ){ // do back solution
for(j = i+1; j<n; j++ ){
for( k=0; k<m; k++ )
X(i,k) -= B(i,j)*X(j,k);
}
for( k=0; k<m; k++ )
X(i,k) /= B(i,i);
}
}
void pyramidalBasis::df(const fullMatrix<double> &coord, fullMatrix<double> &dfm) const
{
const int N = bergot->size(), NPts = coord.size1();
double (*dfv)[3] = new double[N][3];
dfm.resize (N, 3*NPts, false);
for (int iPt=0; iPt<NPts; iPt++) {
df(coord(iPt,0), coord(iPt,1), coord(iPt,2), dfv);
for (int i = 0; i < N; i++) {
dfm(i, 3*iPt) = dfv[i][0];
dfm(i, 3*iPt+1) = dfv[i][1];
dfm(i, 3*iPt+2) = dfv[i][2];
}
}
delete[] dfv;
}
template<class T1> void LaplaceTerm<T1, T1>::get(MElement *ele, int npts, IntPt *GP, fullMatrix<double> &m) const
{
int nbFF = BilinearTerm<T1, T1>::space1.getNumKeys(ele);
double jac[3][3];
m.resize(nbFF, nbFF);
m.setAll(0.);
for(int i = 0; i < npts; i++){
const double u = GP[i].pt[0]; const double v = GP[i].pt[1]; const double w = GP[i].pt[2];
const double weight = GP[i].weight; const double detJ = ele->getJacobian(u, v, w, jac);
std::vector<typename TensorialTraits<T1>::GradType> Grads;
BilinearTerm<T1, T1>::space1.gradf(ele, u, v, w, Grads);
for(int j = 0; j < nbFF; j++)
{
for(int k = j; k < nbFF; k++)
{
double contrib = weight * detJ * dot(Grads[j], Grads[k]) * diffusivity;
m(j, k) += contrib;
if(j != k) m(k, j) += contrib;
}
}
}
}
double taylorDistanceSq1D(const GradientBasis *gb, const fullMatrix<double> &nodesXYZ,
const std::vector<SVector3> &tanCAD)
{
const int nV = nodesXYZ.size1();
fullMatrix<double> dxyzdX(nV, 3);
gb->getGradientsFromNodes(nodesXYZ, &dxyzdX, 0, 0);
// const double dx = nodesXYZ(1, 0) - nodesXYZ(0, 0), dy = nodesXYZ(1, 1) - nodesXYZ(0, 1),
// dz = nodesXYZ(1, 2) - nodesXYZ(0, 2), h = 0.5*sqrt(dx*dx+dy*dy+dz*dz)/double(nV-1);
double distSq = 0.;
for (int i=0; i<nV; i++) {
SVector3 tanMesh(dxyzdX(i, 0), dxyzdX(i, 1), dxyzdX(i, 2));
const double h = 0.25*tanMesh.normalize(); // Half of "local edge length"
SVector3 diff = (dot(tanCAD[i], tanMesh) > 0) ?
tanCAD[i] - tanMesh : tanCAD[i] + tanMesh;
distSq += h*h*diff.normSq();
}
return distSq;
}
double taylorDistanceSq2D(const GradientBasis *gb, const fullMatrix<double> &nodesXYZ,
const std::vector<SVector3> &normCAD)
{
const int nV = nodesXYZ.size1();
fullMatrix<double> dxyzdX(nV, 3), dxyzdY(nV, 3);
gb->getGradientsFromNodes(nodesXYZ, &dxyzdX, &dxyzdY, 0);
double distSq = 0.;
for (int i=0; i<nV; i++) {
const double nz = dxyzdX(i, 0) * dxyzdY(i, 1) - dxyzdX(i, 1) * dxyzdY(i, 0);
const double ny = -dxyzdX(i, 0) * dxyzdY(i, 2) + dxyzdX(i, 2) * dxyzdY(i, 0);
const double nx = dxyzdX(i, 1) * dxyzdY(i, 2) - dxyzdX(i, 2) * dxyzdY(i, 1);
SVector3 normMesh(nx, ny, nz);
const double h = 0.25*sqrt(normMesh.normalize()); // Half of sqrt of "local area", to be adjusted w.r.t. el. type?
SVector3 diff = (dot(normCAD[i], normMesh) > 0) ?
normCAD[i] - normMesh : normCAD[i] + normMesh;
distSq += h*h*diff.normSq();
}
return distSq;
}
void linearSystemPETSc<fullMatrix<double> >::addToMatrix(int row, int col,
const fullMatrix<double> &val)
{
if (!_entriesPreAllocated)
preAllocateEntries();
#ifdef PETSC_USE_COMPLEX
fullMatrix<std::complex<double> > modval(val.size1(), val.size2());
for (int ii = 0; ii < val.size1(); ii++) {
for (int jj = 0; jj < val.size1(); jj++) {
modval(ii, jj) = val (jj, ii);
modval(jj, ii) = val (ii, jj);
}
}
#else
fullMatrix<double> &modval = *const_cast<fullMatrix<double> *>(&val);
for (int ii = 0; ii < val.size1(); ii++) {
for (int jj = 0; jj < ii; jj++) {
PetscScalar buff = modval(ii, jj);
modval(ii, jj) = modval (jj, ii);
modval(jj, ii) = buff;
}
}
#endif
PetscInt i = row, j = col;
MatSetValuesBlocked(_a, 1, &i, 1, &j, &modval(0,0), ADD_VALUES);
//transpose back so that the original matrix is not modified
#ifndef PETSC_USE_COMPLEX
for (int ii = 0; ii < val.size1(); ii++)
for (int jj = 0; jj < ii; jj++) {
PetscScalar buff = modval(ii,jj);
modval(ii, jj) = modval (jj,ii);
modval(jj, ii) = buff;
}
#endif
_valuesNotAssembled = true;
}
// Calculate (signed) Jacobian and its gradients for one element, with normal vectors to straight element
// for regularization. Evaluation points depend on the given matrices for shape function gradients.
void JacobianBasis::getSignedJacAndGradientsGeneral(int nJacNodes, const fullMatrix<double> &gSMatX,
const fullMatrix<double> &gSMatY,
const fullMatrix<double> &gSMatZ,
const fullMatrix<double> &nodesXYZ,
const fullMatrix<double> &normals,
fullMatrix<double> &JDJ) const
{
switch (_dim) {
case 0 : {
for (int i = 0; i < nJacNodes; i++) {
for (int j = 0; j < numMapNodes; j++) {
JDJ (i,j) = 0.;
JDJ (i,j+1*numMapNodes) = 0.;
JDJ (i,j+2*numMapNodes) = 0.;
}
JDJ(i,3*numMapNodes) = 1.;
}
break;
}
case 1 : {
fullMatrix<double> dxyzdX(nJacNodes,3), dxyzdY(nJacNodes,3);
gSMatX.mult(nodesXYZ, dxyzdX);
for (int i = 0; i < nJacNodes; i++) {
const double &dxdX = dxyzdX(i,0), &dydX = dxyzdX(i,1), &dzdX = dxyzdX(i,2);
const double &dxdY = normals(0,0), &dydY = normals(0,1), &dzdY = normals(0,2);
const double &dxdZ = normals(1,0), &dydZ = normals(1,1), &dzdZ = normals(1,2);
for (int j = 0; j < numMapNodes; j++) {
const double &dPhidX = gSMatX(i,j);
JDJ (i,j) = dPhidX * dydY * dzdZ + dPhidX * dzdY * dydZ;
JDJ (i,j+1*numMapNodes) = dPhidX * dzdY * dxdZ - dPhidX * dxdY * dzdZ;
JDJ (i,j+2*numMapNodes) = dPhidX * dxdY * dydZ - dPhidX * dydY * dxdZ;
}
JDJ(i,3*numMapNodes) = calcDet3D(dxdX,dydX,dzdX,dxdY,dydY,dzdY,dxdZ,dydZ,dzdZ);
}
break;
}
case 2 : {
fullMatrix<double> dxyzdX(nJacNodes,3), dxyzdY(nJacNodes,3);
gSMatX.mult(nodesXYZ, dxyzdX);
gSMatY.mult(nodesXYZ, dxyzdY);
for (int i = 0; i < nJacNodes; i++) {
const double &dxdX = dxyzdX(i,0), &dydX = dxyzdX(i,1), &dzdX = dxyzdX(i,2);
const double &dxdY = dxyzdY(i,0), &dydY = dxyzdY(i,1), &dzdY = dxyzdY(i,2);
const double &dxdZ = normals(0,0), &dydZ = normals(0,1), &dzdZ = normals(0,2);
for (int j = 0; j < numMapNodes; j++) {
const double &dPhidX = gSMatX(i,j);
const double &dPhidY = gSMatY(i,j);
JDJ (i,j) =
dPhidX * dydY * dzdZ + dzdX * dPhidY * dydZ +
dPhidX * dzdY * dydZ - dydX * dPhidY * dzdZ;
JDJ (i,j+1*numMapNodes) =
dxdX * dPhidY * dzdZ +
dPhidX * dzdY * dxdZ - dzdX * dPhidY * dxdZ
- dPhidX * dxdY * dzdZ;
JDJ (i,j+2*numMapNodes) =
dPhidX * dxdY * dydZ +
dydX * dPhidY * dxdZ - dPhidX * dydY * dxdZ -
dxdX * dPhidY * dydZ;
}
JDJ(i,3*numMapNodes) = calcDet3D(dxdX,dydX,dzdX,dxdY,dydY,dzdY,dxdZ,dydZ,dzdZ);
}
break;
}
case 3 : {
fullMatrix<double> dxyzdX(nJacNodes,3), dxyzdY(nJacNodes,3), dxyzdZ(nJacNodes,3);
gSMatX.mult(nodesXYZ, dxyzdX);
gSMatY.mult(nodesXYZ, dxyzdY);
gSMatZ.mult(nodesXYZ, dxyzdZ);
for (int i = 0; i < nJacNodes; i++) {
const double &dxdX = dxyzdX(i,0), &dydX = dxyzdX(i,1), &dzdX = dxyzdX(i,2);
const double &dxdY = dxyzdY(i,0), &dydY = dxyzdY(i,1), &dzdY = dxyzdY(i,2);
const double &dxdZ = dxyzdZ(i,0), &dydZ = dxyzdZ(i,1), &dzdZ = dxyzdZ(i,2);
for (int j = 0; j < numMapNodes; j++) {
const double &dPhidX = gSMatX(i,j);
const double &dPhidY = gSMatY(i,j);
const double &dPhidZ = gSMatZ(i,j);
JDJ (i,j) =
dPhidX * dydY * dzdZ + dzdX * dPhidY * dydZ +
dydX * dzdY * dPhidZ - dzdX * dydY * dPhidZ -
dPhidX * dzdY * dydZ - dydX * dPhidY * dzdZ;
JDJ (i,j+1*numMapNodes) =
dxdX * dPhidY * dzdZ + dzdX * dxdY * dPhidZ +
dPhidX * dzdY * dxdZ - dzdX * dPhidY * dxdZ -
dxdX * dzdY * dPhidZ - dPhidX * dxdY * dzdZ;
JDJ (i,j+2*numMapNodes) =
dxdX * dydY * dPhidZ + dPhidX * dxdY * dydZ +
dydX * dPhidY * dxdZ - dPhidX * dydY * dxdZ -
dxdX * dPhidY * dydZ - dydX * dxdY * dPhidZ;
}
JDJ(i,3*numMapNodes) = calcDet3D(dxdX,dydX,dzdX,dxdY,dydY,dzdY,dxdZ,dydZ,dzdZ);
}
break;
}
}
}
bool fullMatrix<double>::invert(fullMatrix<double> &result) const
{
if(_r != _c) return false;
// Copy the matrix
result.resize(_r,_c);
// to find out Determinant
double det = this->determinant();
if(det == 0)
return false;
// Matrix of cofactor put this in a function?
fullMatrix<double> cofactor(_r,_c);
if(_r == 2)
{
cofactor(0,0) = (*this)(1,1);
cofactor(0,1) = -(*this)(1,0);
cofactor(1,0) = -(*this)(0,1);
cofactor(1,1) = (*this)(0,0);
}
else if(_r >= 3)
{
std::vector<std::vector<fullMatrix<double> > > temp(_r,std::vector<fullMatrix<double> >(_r,fullMatrix<double>(_r-1,_r-1)));
for(int k1 = 0; k1 < _r; k1++)
{
for(int k2 = 0; k2 < _r; k2++)
{
int i1 = 0;
for(int i = 0; i < _r; i++)
{
int j1 = 0;
for(int j = 0; j < _r; j++)
{
if(k1 != i && k2 != j)
temp[k1][k2](i1,j1++) = (*this)(i,j);
}
if(k1 != i)
i1++;
}
}
}
bool flagPositive;
for(int k1 = 0; k1 < _r; k1++)
{
flagPositive = (k1 % 2) == 0 ? true : false;
for(int k2 = 0; k2 < _r; k2++)
{
if(flagPositive)
{
cofactor(k1,k2) = temp[k1][k2].determinant();
flagPositive = false;
}
else
{
cofactor(k1,k2) = -temp[k1][k2].determinant();
flagPositive = true;
}
}
}
}
// end cofactor
// inv = transpose of cofactor / Determinant
for(int i = 0; i < _r; i++)
{
for(int j = 0; j < _c; j++)
{
result(j,i) = cofactor(i,j) / det;
}
}
return true;
}
void fMaterial(fullVector<double>& xyz, fullMatrix<double>& tensor){
tensor.scale(0);
tensor(0, 0) = 1;
tensor(1, 1) = 2;
tensor(2, 2) = 1;
}
void write(bool isScalar, const fullMatrix<double>& l2, string name){
// Stream
ofstream stream;
string fileName;
if(isScalar)
fileName = name + "Node.m";
else
fileName = name + "Edge.m";
stream.open(fileName.c_str());
// Matrix data
const size_t l2Row = l2.size1();
const size_t l2ColMinus = l2.size2() - 1;
// Clean Octave
stream << "close all;" << endl
<< "clear all;" << endl
<< endl;
// Mesh (Assuming uniform refinement)
stream << "h = [1, ";
for(size_t i = 1; i < l2ColMinus; i++)
stream << 1 / pow(2, i) << ", ";
stream << 1 / pow(2, l2ColMinus) << "];" << endl;
// Order (Assuming uniform refinement)
stream << "p = [1:" << l2Row << "];" << endl
<< endl;
// Matrix of l2 error (l2[Order][Mesh])
stream << "l2 = ..." << endl
<< " [..." << endl;
for(size_t i = 0; i < l2Row; i++){
stream << " ";
for(size_t j = 0; j < l2ColMinus; j++)
stream << scientific << showpos
<< l2(i, j) << " , ";
stream << scientific << showpos
<< l2(i, l2ColMinus) << " ; ..." << endl;
}
stream << " ];" << endl
<< endl;
// Delta
stream << "P = size(p, 2);" << endl
<< "H = size(h, 2);" << endl
<< endl
<< "delta = zeros(P, H - 1);" << endl
<< endl
<< "for i = 1:H-1" << endl
<< " delta(:, i) = ..." << endl
<< " (log10(l2(:, i + 1)) - log10(l2(:, i))) / ..." << endl
<< " (log10(1/h(i + 1)) - log10(1/h(i)));" << endl
<< "end" << endl
<< endl
<< "delta" << endl
<< endl;
// Plot
stream << "figure;" << endl
<< "loglog(1./h, l2', '-*');" << endl
<< "grid;"
<< endl;
// Title
stream << "title(" << "'" << name << ": ";
if(isScalar)
stream << "Nodal";
else
stream << "Edge";
stream << "');" << endl
<< endl;
// Axis
stream << "xlabel('1/h [-]');" << endl
<< "ylabel('L2 Error [-]');" << endl;
// Close
stream.close();
}
inline void JacobianBasis::getJacobianGeneral(int nJacNodes, const fullMatrix<double> &gSMatX,
const fullMatrix<double> &gSMatY, const fullMatrix<double> &gSMatZ,
const fullMatrix<double> &nodesX, const fullMatrix<double> &nodesY,
const fullMatrix<double> &nodesZ, fullMatrix<double> &jacobian) const
{
switch (_dim) {
case 0 : {
const int numEl = nodesX.size2();
for (int iEl = 0; iEl < numEl; iEl++)
for (int i = 0; i < nJacNodes; i++) jacobian(i,iEl) = 1.;
break;
}
case 1 : {
const int numEl = nodesX.size2();
fullMatrix<double> dxdX(nJacNodes,numEl), dydX(nJacNodes,numEl), dzdX(nJacNodes,numEl);
gSMatX.mult(nodesX, dxdX); gSMatX.mult(nodesY, dydX); gSMatX.mult(nodesZ, dzdX);
for (int iEl = 0; iEl < numEl; iEl++) {
fullMatrix<double> nodesXYZ(numPrimMapNodes,3);
for (int i = 0; i < numPrimMapNodes; i++) {
nodesXYZ(i,0) = nodesX(i,iEl);
nodesXYZ(i,1) = nodesY(i,iEl);
nodesXYZ(i,2) = nodesZ(i,iEl);
}
fullMatrix<double> normals(2,3);
const double invScale = getPrimNormals1D(nodesXYZ,normals);
if (scaling) {
const double scale = 1./invScale;
normals(0,0) *= scale; normals(0,1) *= scale; normals(0,2) *= scale; // Faster to scale 1 normal than afterwards
}
const double &dxdY = normals(0,0), &dydY = normals(0,1), &dzdY = normals(0,2);
const double &dxdZ = normals(1,0), &dydZ = normals(1,1), &dzdZ = normals(1,2);
for (int i = 0; i < nJacNodes; i++)
jacobian(i,iEl) = calcDet3D(dxdX(i,iEl),dydX(i,iEl),dzdX(i,iEl),
dxdY,dydY,dzdY,
dxdZ,dydZ,dzdZ);
}
break;
}
case 2 : {
const int numEl = nodesX.size2();
fullMatrix<double> dxdX(nJacNodes,numEl), dydX(nJacNodes,numEl), dzdX(nJacNodes,numEl);
fullMatrix<double> dxdY(nJacNodes,numEl), dydY(nJacNodes,numEl), dzdY(nJacNodes,numEl);
gSMatX.mult(nodesX, dxdX); gSMatX.mult(nodesY, dydX); gSMatX.mult(nodesZ, dzdX);
gSMatY.mult(nodesX, dxdY); gSMatY.mult(nodesY, dydY); gSMatY.mult(nodesZ, dzdY);
for (int iEl = 0; iEl < numEl; iEl++) {
fullMatrix<double> nodesXYZ(numPrimMapNodes,3);
for (int i = 0; i < numPrimMapNodes; i++) {
nodesXYZ(i,0) = nodesX(i,iEl);
nodesXYZ(i,1) = nodesY(i,iEl);
nodesXYZ(i,2) = nodesZ(i,iEl);
}
fullMatrix<double> normal(1,3);
const double invScale = getPrimNormal2D(nodesXYZ,normal);
if (scaling) {
const double scale = 1./invScale;
normal(0,0) *= scale; normal(0,1) *= scale; normal(0,2) *= scale; // Faster to scale normal than afterwards
}
const double &dxdZ = normal(0,0), &dydZ = normal(0,1), &dzdZ = normal(0,2);
for (int i = 0; i < nJacNodes; i++)
jacobian(i,iEl) = calcDet3D(dxdX(i,iEl),dydX(i,iEl),dzdX(i,iEl),
dxdY(i,iEl),dydY(i,iEl),dzdY(i,iEl),
dxdZ,dydZ,dzdZ);
}
break;
}
case 3 : {
const int numEl = nodesX.size2();
fullMatrix<double> dxdX(nJacNodes,numEl), dydX(nJacNodes,numEl), dzdX(nJacNodes,numEl);
fullMatrix<double> dxdY(nJacNodes,numEl), dydY(nJacNodes,numEl), dzdY(nJacNodes,numEl);
fullMatrix<double> dxdZ(nJacNodes,numEl), dydZ(nJacNodes,numEl), dzdZ(nJacNodes,numEl);
gSMatX.mult(nodesX, dxdX); gSMatX.mult(nodesY, dydX); gSMatX.mult(nodesZ, dzdX);
gSMatY.mult(nodesX, dxdY); gSMatY.mult(nodesY, dydY); gSMatY.mult(nodesZ, dzdY);
gSMatZ.mult(nodesX, dxdZ); gSMatZ.mult(nodesY, dydZ); gSMatZ.mult(nodesZ, dzdZ);
for (int iEl = 0; iEl < numEl; iEl++) {
for (int i = 0; i < nJacNodes; i++)
jacobian(i,iEl) = calcDet3D(dxdX(i,iEl),dydX(i,iEl),dzdX(i,iEl),
dxdY(i,iEl),dydY(i,iEl),dzdY(i,iEl),
dxdZ(i,iEl),dydZ(i,iEl),dzdZ(i,iEl));
if (scaling) {
fullMatrix<double> nodesXYZ(numPrimMapNodes,3);
for (int i = 0; i < numPrimMapNodes; i++) {
nodesXYZ(i,0) = nodesX(i,iEl);
nodesXYZ(i,1) = nodesY(i,iEl);
nodesXYZ(i,2) = nodesZ(i,iEl);
}
const double scale = 1./getPrimJac3D(nodesXYZ);
for (int i = 0; i < nJacNodes; i++) jacobian(i,iEl) *= scale;
}
}
break;
}
}
}
void IsotropicElasticTerm::get(MElement *ele, int npts, IntPt *GP,
fullMatrix<double> &m) const
{
if(ele->getParent()) ele = ele->getParent();
if(sym) {
int nbFF = BilinearTerm<SVector3, SVector3>::space1.getNumKeys(ele);
double jac[3][3];
fullMatrix<double> B(6, nbFF);
fullMatrix<double> BTH(nbFF, 6);
fullMatrix<double> BT(nbFF, 6);
m.resize(nbFF, nbFF);
m.setAll(0.);
// std::cout << m.size1() << " " << m.size2() << std::endl;
for(int i = 0; i < npts; i++) {
const double u = GP[i].pt[0];
const double v = GP[i].pt[1];
const double w = GP[i].pt[2];
const double weight = GP[i].weight;
const double detJ = ele->getJacobian(u, v, w, jac);
std::vector<TensorialTraits<SVector3>::GradType> Grads;
BilinearTerm<SVector3, SVector3>::space1.gradf(ele, u, v, w,
Grads); // a optimiser ??
for(int j = 0; j < nbFF; j++) {
BT(j, 0) = B(0, j) = Grads[j](0, 0);
BT(j, 1) = B(1, j) = Grads[j](1, 1);
BT(j, 2) = B(2, j) = Grads[j](2, 2);
BT(j, 3) = B(3, j) = Grads[j](0, 1) + Grads[j](1, 0);
BT(j, 4) = B(4, j) = Grads[j](1, 2) + Grads[j](2, 1);
BT(j, 5) = B(5, j) = Grads[j](0, 2) + Grads[j](2, 0);
}
BTH.setAll(0.);
BTH.gemm(BT, H);
m.gemm(BTH, B, weight * detJ, 1.); // m = m + w*detJ*BT*H*B
}
}
else {
int nbFF1 = BilinearTerm<SVector3, SVector3>::space1.getNumKeys(ele);
int nbFF2 = BilinearTerm<SVector3, SVector3>::space2.getNumKeys(ele);
double jac[3][3];
fullMatrix<double> B(6, nbFF2);
fullMatrix<double> BTH(nbFF2, 6);
fullMatrix<double> BT(nbFF1, 6);
m.resize(nbFF1, nbFF2);
m.setAll(0.);
// Sum on Gauss Points i
for(int i = 0; i < npts; i++) {
const double u = GP[i].pt[0];
const double v = GP[i].pt[1];
const double w = GP[i].pt[2];
const double weight = GP[i].weight;
const double detJ = ele->getJacobian(u, v, w, jac);
std::vector<TensorialTraits<SVector3>::GradType>
Grads; // tableau de matrices...
std::vector<TensorialTraits<SVector3>::GradType>
GradsT; // tableau de matrices...
BilinearTerm<SVector3, SVector3>::space1.gradf(ele, u, v, w, Grads);
BilinearTerm<SVector3, SVector3>::space2.gradf(ele, u, v, w, GradsT);
for(int j = 0; j < nbFF1; j++) {
BT(j, 0) = Grads[j](0, 0);
BT(j, 1) = Grads[j](1, 1);
BT(j, 2) = Grads[j](2, 2);
BT(j, 3) = Grads[j](0, 1) + Grads[j](1, 0);
BT(j, 4) = Grads[j](1, 2) + Grads[j](2, 1);
BT(j, 5) = Grads[j](0, 2) + Grads[j](2, 0);
}
for(int j = 0; j < nbFF2; j++) {
B(0, j) = GradsT[j](0, 0);
B(1, j) = GradsT[j](1, 1);
B(2, j) = GradsT[j](2, 2);
B(3, j) = GradsT[j](0, 1) + GradsT[j](1, 0);
B(4, j) = GradsT[j](1, 2) + GradsT[j](2, 1);
B(5, j) = GradsT[j](0, 2) + GradsT[j](2, 0);
}
BTH.setAll(0.);
BTH.gemm(BT, H);
// gemm add the product to m so there is a sum on gauss' points here
m.gemm(BTH, B, weight * detJ, 1.);
}
}
}
inline void JacobianBasis::getJacobianGeneral(int nJacNodes, const fullMatrix<double> &gSMatX,
const fullMatrix<double> &gSMatY, const fullMatrix<double> &gSMatZ,
const fullMatrix<double> &nodesXYZ, fullVector<double> &jacobian) const
{
switch (_dim) {
case 0 : {
for (int i = 0; i < nJacNodes; i++) jacobian(i) = 1.;
break;
}
case 1 : {
fullMatrix<double> normals(2,3);
const double invScale = getPrimNormals1D(nodesXYZ,normals);
if (scaling) {
const double scale = 1./invScale;
normals(0,0) *= scale; normals(0,1) *= scale; normals(0,2) *= scale; // Faster to scale 1 normal than afterwards
}
fullMatrix<double> dxyzdX(nJacNodes,3);
gSMatX.mult(nodesXYZ, dxyzdX);
for (int i = 0; i < nJacNodes; i++) {
const double &dxdX = dxyzdX(i,0), &dydX = dxyzdX(i,1), &dzdX = dxyzdX(i,2);
const double &dxdY = normals(0,0), &dydY = normals(0,1), &dzdY = normals(0,2);
const double &dxdZ = normals(1,0), &dydZ = normals(1,1), &dzdZ = normals(1,2);
jacobian(i) = calcDet3D(dxdX,dydX,dzdX,dxdY,dydY,dzdY,dxdZ,dydZ,dzdZ);
}
break;
}
case 2 : {
fullMatrix<double> normal(1,3);
const double invScale = getPrimNormal2D(nodesXYZ,normal);
if (scaling) {
const double scale = 1./invScale;
normal(0,0) *= scale; normal(0,1) *= scale; normal(0,2) *= scale; // Faster to scale normal than afterwards
}
fullMatrix<double> dxyzdX(nJacNodes,3), dxyzdY(nJacNodes,3);
gSMatX.mult(nodesXYZ, dxyzdX);
gSMatY.mult(nodesXYZ, dxyzdY);
for (int i = 0; i < nJacNodes; i++) {
const double &dxdX = dxyzdX(i,0), &dydX = dxyzdX(i,1), &dzdX = dxyzdX(i,2);
const double &dxdY = dxyzdY(i,0), &dydY = dxyzdY(i,1), &dzdY = dxyzdY(i,2);
const double &dxdZ = normal(0,0), &dydZ = normal(0,1), &dzdZ = normal(0,2);
jacobian(i) = calcDet3D(dxdX,dydX,dzdX,dxdY,dydY,dzdY,dxdZ,dydZ,dzdZ);
}
break;
}
case 3 : {
fullMatrix<double> dum;
fullMatrix<double> dxyzdX(nJacNodes,3), dxyzdY(nJacNodes,3), dxyzdZ(nJacNodes,3);
gSMatX.mult(nodesXYZ, dxyzdX);
gSMatY.mult(nodesXYZ, dxyzdY);
gSMatZ.mult(nodesXYZ, dxyzdZ);
for (int i = 0; i < nJacNodes; i++) {
const double &dxdX = dxyzdX(i,0), &dydX = dxyzdX(i,1), &dzdX = dxyzdX(i,2);
const double &dxdY = dxyzdY(i,0), &dydY = dxyzdY(i,1), &dzdY = dxyzdY(i,2);
const double &dxdZ = dxyzdZ(i,0), &dydZ = dxyzdZ(i,1), &dzdZ = dxyzdZ(i,2);
jacobian(i) = calcDet3D(dxdX,dydX,dzdX,dxdY,dydY,dzdY,dxdZ,dydZ,dzdZ);
}
if (scaling) {
const double scale = 1./getPrimJac3D(nodesXYZ);
jacobian.scale(scale);
}
break;
}
}
}
