Skip to content

I
INMOST
Commit 7b6e4ef8 authored by Kirill Terekhov's avatar Kirill Terekhov
Browse files
Options

Synchronize 

Algorithms for removing rows and columns in dense matrices.

Update for MFD example.
parent 217fbf88
Hide whitespace changes
Inline Side-by-side
Showing with 190 additions and 19 deletions
Examples/ADMFD/main.cpp
View file @ 7b6e4ef8
......@@ -177,12 +177,12 @@ int main(int argc,char ** argv)
//K0.SVD(U,S,V);
//for(int k = 0; k < 3; ++k) S(k,k) = sqrt(S(k,k));
//rMatrix K = U*S*V;
rMatrix nKGRAD(NF,NF), NK(NF,3), R(NF,3); //big gradient matrix, co-normals, directions
rMatrix nKGRAD(NF,NF), NK(NF,3), R(NF,3), D(NF,NF), U(NF,NF), Areas(NF,1); //big gradient matrix, co-normals, directions
for(int k = 0; k < NF; ++k) //loop over faces
{
aF = faces[k]->Area();
faces[k]->Centroid(yF);
faces[k]->OrientedUnitNormal(cell->self(),nF);
aF = faces[k].Area();
faces[k].Centroid(yF);
faces[k].OrientedUnitNormal(cell->self(),nF);
// assemble matrix of directions
R(k,0) = (yF[0]-xP[0])*aF;
R(k,1) = (yF[1]-xP[1])*aF;
......@@ -193,10 +193,125 @@ int main(int argc,char ** argv)
NK(k,1) = nK(0,1);
NK(k,2) = nK(0,2);
} //end of loop over faces
rMatrix SU,SS,SV;
nKGRAD = NK*(NK.Transpose()*R).Invert(true).first*NK.Transpose(); //stability part
nKGRAD += (rMatrix::Unit(NF) - R*(R.Transpose()*R).Invert(true).first*R.Transpose())*(2.0/(static_cast<real>(NF)*vP)*(NK*K.Invert(true).first*NK.Transpose()).Trace());
//nKGRAD += (rMatrix::Unit(NF) - R*(R.Transpose()*R).Invert().first*R.Transpose())*(2.0/(static_cast<real>(NF))*nKGRAD.Trace());
real_array W = cell->RealArrayDV(tag_W); //access data structure for gradient matrix in mesh
/*
std::cout << "W" << std::endl;
nKGRAD.Print();
nKGRAD.SVD(SU,SS,SV);
std::cout << "U" << std::endl;
SU.Print();
std::cout << "S" << std::endl;
SS.Print();
std::cout << "V" << std::endl;
SV.Print();
std::cout << "Check " << (nKGRAD - SU*SS*SV.Transpose()).FrobeniusNorm() << std::endl;
*/
int rank = 0; //size of matrix U
{ //Retrive orthogonal to R matrix D
//Symmetric orthogonal matrix
rMatrix DUD = (rMatrix::Unit(NF) - R*(R.Transpose()*R).Invert(true).first*R.Transpose());
//perfrom singular value decomposition
//S should be unity matrix with rank NF-3
rMatrix DUD_U,DUD_S,DUD_V;
DUD.SVD(DUD_U,DUD_S,DUD_V);
//compute the rank
for(int q = 0; q < NF; ++q)
if( DUD_S(q,q) > 1.0e-2 )
rank++;
rank = NF-3;
if( rank != NF-3)
{
std::cout << "rank: " << rank << " expected " << NF-3 << std::endl;
DUD_S.Print();
}
//chop matrix to the full rank
DUD_S.RemoveSubset(rank,NF,rank,NF);
DUD_V.RemoveColumns(rank,NF);
//assign the matrix
D = DUD_V;
U = DUD_S;
}
//std::cout << "D" << std::endl;
//D.Print();
//std::cout << "U" << std::endl;
//U.Print();
//std::cout << "DtR" << std::endl;
//(D.Transpose()*R).Print();
U *=(2.0/(static_cast<real>(NF)*vP)*(NK*K.Invert(true).first*NK.Transpose()).Trace());
{ //Make W a Z-matrix
vMatrix vU(rank,rank), vW(NF,NF);
int unk = 0;
for(int i = 0; i < rank; ++i)
vU(i,i) = unknown(U(i,i),unk++);
for(int i = 0; i < rank; ++i)
for(int j = i+1; j < rank; ++j)
{
vU(i,j) = unknown(0.0,unk);
vU(j,i) = unknown(0.0,unk);
unk++;
}
//std::cout << "unknowns: " << unk << std::endl;
variable phi,s;
int iter = 0;
do
{ //Optimize U matrix
vW = nKGRAD + D*vU*D.Transpose();
//construct minimization functional phi(W)
phi = 0.0;
for(int i = 0; i < NF; ++i)
{
phi += 1.0 / (vW(i,i)*vW(i,i));
s = vW(i,i)*faces[i].Area();
for(int j = 0; j < NF; ++j) if( i != j )
{
s += vW(i,j)*faces[j].Area();
phi += (vW(i,j)+abs(vW(i,j)))*(vW(i,j)+abs(vW(i,j)));
}
phi += (s - abs(s))*(s - abs(s));
}
//std::cout << "[" << iter << "] phi: " << get_value(phi) << "\r" << std::endl;
Sparse::Row & der = phi.GetRow(); //row of derivatives
//std::sort(der.Begin(),der.End());
//for(int i = 0; i < der.Size(); ++i)
// std::cout << "(" << der.GetIndex(i) << "," << der.GetValue(i) << ") ";
//std::cout<<std::endl;
int q = 0;
real a = 0.05;
for(int i = 0; i < rank; ++i)
vU(i,i) -= a*der[q++];
for(int i = 0; i < rank; ++i)
for(int j = i+1; j < rank; ++j)
{
real d = a*der[q++];
vU(i,j) -= d;
vU(j,i) -= d;
}
iter++;
}
while(iter < 6 && phi > 1.0e-3);
for(int i = 0; i < rank; ++i)
for(int j = 0; j < rank; ++j)
U(i,j) = get_value(vU(i,j));
//std::cout << "U: " << std::endl;
//U.Print();
}
//std::cout << "UDtR" << std::endl;
//(U*D.Transpose()*R).Print();
nKGRAD += D*U*D.Transpose();
//std::cout << "W: " << std::endl;
//nKGRAD.Print();
real_array W = cell->RealArrayDV(tag_W); //access data structure for gradient matrix in mesh
W.resize(NF*NF); //resize the structure
std::copy(nKGRAD.data(),nKGRAD.data()+NF*NF,W.data()); //write down the gradient matrix
} //end of loop over cells
......@@ -301,11 +416,11 @@ int main(int argc,char ** argv)
if( R.Norm() < 1.0e-4 ) break;
Solver S(Solver::INNER_MPTILUC);
Solver S(Solver::INNER_ILU2);
S.SetMatrix(R.GetJacobian());
S.SetParameterReal("relative_tolerance", 1.0e-14);
S.SetParameterReal("absolute_tolerance", 1.0e-12);
S.SetParameterReal("drop_tolerance", 1.0e-2);
S.SetParameterReal("drop_tolerance", 1.0e-3);
S.SetParameterReal("reuse_tolerance", 1.0e-4);
//std::fill(Update.Begin(),Update.End(),0.0);
if( S.Solve(R.GetResidual(),Update) )
......
Source/Headers/inmost_dense.h
View file @ 7b6e4ef8
......@@ -63,17 +63,63 @@ namespace INMOST
space.resize((n-1)*m);
--n;
}
void RemoveRows(enumerator first, enumerator last)
{
enumerator shift = last-first;
for(enumerator k = last+1; k < n; ++k)
{
for(enumerator l = 0; l < m; ++l)
(*this)(k-shift-1,l) = (*this)(k,l);
}
space.resize((n-shift)*m);
n-=shift;
}
void RemoveColumn(enumerator col)
{
array<Var> tmp(n*(m-1));
Matrix<Var> tmp(n,m-1);
for(enumerator k = 0; k < n; ++k)
{
for(enumerator l = 0; l < col; ++l)
tmp(k,l) = (*this)(k,l);
for(enumerator l = col+1; l < m; ++l)
(*this)(k,l-1) = (*this)(k,l);
tmp(k,l-1) = (*this)(k,l);
}
space.swap(tmp);
--m;
this->Swap(tmp);
}
void RemoveColumns(enumerator first, enumerator last)
{
enumerator shift = last-first;
Matrix<Var> tmp(n,m-shift);
for(enumerator k = 0; k < n; ++k)
{
for(enumerator l = 0; l < first; ++l)
tmp(k,l) = (*this)(k,l);
for(enumerator l = last+1; l < m; ++l)
tmp(k,l-shift-1) = (*this)(k,l);
}
this->Swap(tmp);
}
void RemoveSubset(enumerator firstrow, enumerator lastrow, enumerator firstcol, enumerator lastcol)
{
enumerator shiftrow = lastrow-firstrow;
enumerator shiftcol = lastcol-firstcol;
Matrix<Var> tmp(n-shiftrow, m-shiftcol);
for(enumerator k = 0; k < firstrow; ++k)
{
for(enumerator l = 0; l < firstcol; ++l)
tmp(k,l) = (*this)(k,l);
for(enumerator l = lastcol+1; l < m; ++l)
tmp(k,l-shiftcol-1) = (*this)(k,l);
}
for(enumerator k = lastrow+1; k < n; ++k)
{
for(enumerator l = 0; l < firstcol; ++l)
tmp(k-shiftrow-1,l) = (*this)(k,l);
for(enumerator l = lastcol+1; l < m; ++l)
tmp(k-shiftrow-1,l-shiftcol-1) = (*this)(k,l);
}
this->Swap(tmp);
}
void Swap(Matrix & b)
{
space.swap(b.space);
......@@ -392,7 +438,7 @@ namespace INMOST
}
Matrix & operator =(Matrix const & other)
{
space.resize(other.n*other.m);
if( n*m != other.n*other.m ) space.resize(other.n*other.m);
for(enumerator i = 0; i < other.n*other.m; ++i)
space[i] = other.space[i];
n = other.n;
......@@ -427,7 +473,9 @@ namespace INMOST
assert(Rows() == other.Rows());
assert(Cols() == other.Cols());
Matrix<typename Promote<Var,typeB>::type> ret(n,m); //check RVO
for(enumerator k = 0; k < n*m; ++k) ret.space[k] = space[k]-other.space[k];
for(enumerator i = 0; i < Rows(); ++i)
for(enumerator j = 0; j < Cols(); ++j)
ret(i,j) = (*this)(i,j)-other(i,j);
return ret;
}
Matrix & operator-=(const Matrix & other)
......@@ -443,7 +491,9 @@ namespace INMOST
assert(Rows() == other.Rows());
assert(Cols() == other.Cols());
Matrix<typename Promote<Var,typeB>::type> ret(n,m); //check RVO
for(enumerator k = 0; k < n*m; ++k) ret.space[k] = space[k]+other.space[k];
for(enumerator i = 0; i < Rows(); ++i)
for(enumerator j = 0; j < Cols(); ++j)
ret(i,j) = (*this)(i,j)+other(i,j);
return ret;
}
Matrix & operator+=(const Matrix & other)
......@@ -457,7 +507,8 @@ namespace INMOST
Matrix<typename Promote<Var,typeB>::type> operator*(typeB coef) const
{
Matrix<typename Promote<Var,typeB>::type> ret(n,m); //check RVO
for(enumerator k = 0; k < n*m; ++k) ret.space[k] = space[k]*coef;
for(enumerator i = 0; i < Rows(); ++i)
for(enumerator j = 0; j < Cols(); ++j) ret(i,j) = (*this)(i,j)*coef;
return ret;
}
Matrix & operator*=(Var coef)
......@@ -469,7 +520,8 @@ namespace INMOST
Matrix<typename Promote<Var,typeB>::type> operator/(typeB coef) const
{
Matrix<typename Promote<Var,typeB>::type> ret(n,m); //check RVO
for(enumerator k = 0; k < n*m; ++k) ret.space[k] = space[k]/coef;
for(enumerator i = 0; i < Rows(); ++i)
for(enumerator j = 0; j < Cols(); ++j) ret(i,j) = (*this)(i,j)/coef;
return ret;
}
Matrix & operator/=(Var coef)
......@@ -661,8 +713,12 @@ namespace INMOST
for(enumerator l = 0; l < m; ++l)
{
if( fabs(get_value((*this)(k,l))) > threshold )
#if defined(USE_AUTODIFF)
std::cout << std::setw(10) << get_value((*this)(k,l));
else
#else
std::cout << std::setw(10) << (*this)(k,l);
#endif
else
std::cout << std::setw(10) << 0;
std::cout << " ";
}
......
Markdown is supported
0% or
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment