DevMatrix (FlatMatrix<T> a2)
{
h = a2.Height();
w = a2.Width();
cudaMalloc((T**)&dev_data, h*w*sizeof(T));
cudaMemcpy (dev_data, &a2(0,0), sizeof(T)*h*w, cudaMemcpyHostToDevice);
}
void CalcSchurComplement (const FlatMatrix<double> a,
FlatMatrix<double> s,
const BitArray & used,
LocalHeap & lh)
{
if (s.Height() == 0) return;
if (s.Height() == a.Height())
{
s = a;
return;
}
HeapReset hr(lh);
int n = a.Height();
Array<int> used_dofs(n, lh);
Array<int> unused_dofs(n, lh);
used_dofs.SetSize(0);
unused_dofs.SetSize(0);
for (int i = 0; i < n; i++)
if (used[i])
used_dofs.Append(i);
else
unused_dofs.Append(i);
s = a.Rows(used_dofs).Cols(used_dofs);
FlatMatrix<> b1 = a.Rows(unused_dofs).Cols(used_dofs) | lh;
FlatMatrix<> b2 = a.Rows(used_dofs).Cols(unused_dofs) | lh;
FlatMatrix<> c = a.Rows(unused_dofs).Cols(unused_dofs) | lh;
FlatMatrix<> hb1 (b1.Height(), b1.Width(), lh);
if (n > 10)
{
LapackInverse (c);
hb1 = c * b1 | Lapack;
s -= b2 * hb1 | Lapack;
}
else
{
CalcInverse (c);
hb1 = c * b1;
s -= b2 * hb1;
}
}
extern NGS_DLL_HEADER void CalcInverse (FlatMatrix<double> inv, INVERSE_LIB il)
{
#ifdef LAPACK
if (il == INVERSE_LIB::INV_LAPACK)
LapackInverse(inv);
else if (il == INVERSE_LIB::INV_CHOOSE && inv.Height() >= 20)
LapackInverse(inv);
else
#endif
T_CalcInverse (inv);
}
void DGFiniteElement<D>::
CalcTraceMatrix (int facet, FlatMatrix<> trace) const
{
ELEMENT_TYPE ftype = ElementTopology::GetFacetType (this->ElementType(), facet);
Facet2ElementTrafo f2el(this->ElementType(), FlatArray<int> (8, const_cast<int*> (vnums)) );
const IntegrationRule & ir = SelectIntegrationRule (ftype, 2*order);
ScalarFiniteElement<0> * facetfe0 = NULL;
ScalarFiniteElement<1> * facetfe1 = NULL;
ScalarFiniteElement<2> * facetfe2 = NULL;
switch (ftype)
{
case ET_POINT : facetfe0 = new FE_Point; break;
case ET_SEGM : facetfe1 = new L2HighOrderFE<ET_SEGM> (order); break;
case ET_TRIG : facetfe2 = new L2HighOrderFE<ET_TRIG> (order); break;
case ET_QUAD : facetfe2 = new L2HighOrderFE<ET_QUAD> (order); break;
default:
;
}
int ndof_facet = trace.Height();
Vector<> shape(ndof);
Vector<> fshape(ndof_facet);
Vector<> norms(ndof_facet);
trace = 0.0;
norms = 0.0;
for (int i = 0; i < ir.Size(); i++)
{
if (D == 1)
facetfe0 -> CalcShape (ir[i], fshape);
else if (D == 2)
facetfe1 -> CalcShape (ir[i], fshape);
else
facetfe2 -> CalcShape (ir[i], fshape);
this -> CalcShape (f2el (facet, ir[i]), shape);
trace += ir[i].Weight() * fshape * Trans (shape);
for (int j = 0; j < norms.Size(); j++)
norms(j) += ir[i].Weight() * sqr (fshape(j));
}
for (int j = 0; j < fshape.Size(); j++)
trace.Row(j) /= norms(j);
delete facetfe0;
delete facetfe1;
delete facetfe2;
}
void T_CalcInverse (FlatMatrix<T2> inv)
{
// static Timer t("CalcInverse");
// RegionTimer reg(t);
// Gauss - Jordan - algorithm
// Algorithm of Stoer, Einf. i. d. Num. Math, S 145
// int n = m.Height();
int n = inv.Height();
ngstd::ArrayMem<int,100> p(n); // pivot-permutation
for (int j = 0; j < n; j++) p[j] = j;
for (int j = 0; j < n; j++)
{
// pivot search
double maxval = abs(inv(j,j));
int r = j;
for (int i = j+1; i < n; i++)
if (abs (inv(j, i)) > maxval)
{
r = i;
maxval = abs (inv(j, i));
}
double rest = 0.0;
for (int i = j+1; i < n; i++)
rest += abs(inv(r, i));
if (maxval < 1e-20*rest)
{
throw Exception ("Inverse matrix: Matrix singular");
}
// exchange rows
if (r > j)
{
for (int k = 0; k < n; k++)
swap (inv(k, j), inv(k, r));
swap (p[j], p[r]);
}
// transformation
T2 hr;
CalcInverse (inv(j,j), hr);
for (int i = 0; i < n; i++)
{
T2 h = hr * inv(j, i);
inv(j, i) = h;
}
inv(j,j) = hr;
for (int k = 0; k < n; k++)
if (k != j)
{
T2 help = inv(n*k+j);
T2 h = help * hr;
for (int i = 0; i < n; i++)
{
T2 h = help * inv(n*j+i);
inv(n*k+i) -= h;
}
inv(k,j) = -h;
}
}
// row exchange
VectorMem<100,T2> hv(n);
for (int i = 0; i < n; i++)
{
for (int k = 0; k < n; k++) hv(p[k]) = inv(k, i);
for (int k = 0; k < n; k++) inv(k, i) = hv(k);
}
}
void CalcEigenSystem (const FlatMatrix<double> & mat1,
FlatVector<double> & lami,
FlatMatrix<double> & eigenvecs)
{
int i, j, k, l;
int n = mat1.Height();
Matrix<double> mat(n, n);
mat = mat1;
eigenvecs = 0;
for (i = 0; i < n; i++)
eigenvecs(i,i) = 1;
for (l = 0; l < 100; l++)
for (i = 0; i < n; i++)
for (j = 0; j < i; j++)
{
// find eigensystem of a(i-j,i-j)
double a11 = mat(i,i);
double a12 = mat(i,j);
double a22 = mat(j,j);
if (a12*a12 <= 1e-32 * fabs(a11*a22)) continue;
/*
double lam1, lam2;
// y is EV from a y = lam y
// quadratic eq. for eigenvalues lam:
// c0 + c1 lam + c2 lam^2 = 0
double c0 = a11*a22-a12*a12;
double c1 = -a22 - a11;
double c2 = 1;
lam1 = -c1/(2*c2) + sqrt( sqr(c1/(2*c2)) - c0/c2);
lam2 = -c1/(2*c2) - sqrt( sqr(c1/(2*c2)) - c0/c2);
cout << "lam1,2 = " << lam1 << ", " << lam2 << endl;
lam1 = (a11+a22) / 2 + sqrt ( sqr(a11-a22)/4 + a12*a12);
lam2 = (a11+a22) / 2 - sqrt ( sqr(a11-a22)/4 + a12*a12);
// cout << "lam1,2 = " << lam1 << ", " << lam2 << endl;
*/
double p = (a22-a11)/2;
double q = a12;
// compute eigenvectors:
double y11, y12, y21, y22, y;
y11 = a12;
// y12 = lam1-a11;
y12 =
(p >= 0) ?
p + sqrt (p*p + q*q) :
-q*q / (p - sqrt (p*p+q*q));
y = sqrt (y11*y11+y12*y12);
y11 /= y;
y12 /= y;
y21 = a12;
// y22 = lam2-a11;
y22 =
(p <= 0) ?
p - sqrt (p*p + q*q) :
-q*q / (p + sqrt (p*p+q*q));
y = sqrt (y21*y21+y22*y22);
y21 /= y;
y22 /= y;
/*
(*testout) << "evecs = "
<< "(" << y11 << ", " << y12 << "), "
<< "(" << y21 << ", " << y22 << ")" << endl;
(*testout) << "Y Y = "
<< (y11*y11+y12*y12) << ", "
<< (y11*y21+y12*y22) << ", "
<< (y21*y21+y22*y22) << endl;
*/
// V^T A V = V^T G^{-1} (G^T A G) G^{-1} V
for (k = 0; k < n; k++)
{
double v1 = mat(k,i);
double v2 = mat(k,j);
mat(k,i) = v1 * y11 + v2 * y12;
mat(k,j) = v1 * y21 + v2 * y22;
}
for (k = 0; k < n; k++)
{
double v1 = mat(i,k);
double v2 = mat(j,k);
mat(i,k) = v1 * y11 + v2 * y12;
mat(j,k) = v1 * y21 + v2 * y22;
}
mat(i,j) = 0;
mat(j,i) = 0;
for (k = 0; k < n; k++)
{
double v1 = eigenvecs(i,k);
double v2 = eigenvecs(j,k);
eigenvecs(i,k) = v1 * y11 + v2 * y12;
eigenvecs(j,k) = v1 * y21 + v2 * y22;
}
}
for (i = 0; i < n; i++)
lami(i) = mat(i,i);
}
/// Factor the matrix A
FlatCholeskyFactors (const FlatMatrix<T> & a, LocalHeap & lh)
{
diag = (T*)lh.Alloc(sizeof(T)*RequiredMem(a.Height()));
Factor (a);
}
/// Factor the matrix A
CholeskyFactors (const FlatMatrix<T> & a)
: FlatCholeskyFactors<T> (a, new T[this->RequiredMem(a.Height())])
{ ; }
