Matrix<N, M, Container> Matrix<M, N, Container>::invert() const
{
Matrix<N, M, Container> result;
gsl_matrix* Z1 = gsl_matrix_alloc(M, M);
gsl_matrix* Z = gsl_matrix_alloc(M, M);
gsl_permutation* perm = gsl_permutation_alloc(M);
int k;
for (uint i = 0; i < M; i++)
for (uint j = 0; j < M; j++)
gsl_matrix_set(Z1, i, j, (*this)(i, j));
if (gsl_linalg_LU_decomp(Z1, perm, &k))
THROW_INVALID_ARG("gsl_linalg_LU_decomp failed");
if (gsl_linalg_LU_invert(Z1, perm, Z))
THROW_INVALID_ARG("gsl_linalg_LU_invert failed");
for (uint i = 0; i < M; i++)
for (uint j = 0; j < M; j++)
result(i, j) = gsl_matrix_get(Z, i, j);
gsl_permutation_free(perm);
gsl_matrix_free(Z);
gsl_matrix_free(Z1);
return result;
}
std::string xml::Node::getAttributeByName(const std::string& name) const
{
auto attrs = getAttributes();
auto iter = attrs.find(name);
if (iter != attrs.end())
return iter->second;
THROW_INVALID_ARG("Attribute \"" + name + "\" not found in list and default value is not provided");
}
xml::Node xml::Node::getChildByName(const std::string& name) const
{
NodeList nodes = getChildrenByName(name);
auto l = nodes.size();
if (l != 1) {
LOG_ERROR("Expected one node with name " << name << " but found " << l);
THROW_INVALID_ARG("Child not found");
}
return nodes[0];
}
/**
* Given with 6 point-value pairs, determine among them tetrahedron that
* contains the query point inside and perform linear interpolation in it
* @param c_i and v_i - points and values
* @param q point to interpolate
*/
static TValue interpolateInOwner(const Real3& c0, const TValue v0,
const Real3& c1, const TValue v1,
const Real3& c2, const TValue v2,
const Real3& c3, const TValue v3,
const Real3& c4, const TValue v4,
const Real3& c5, const TValue v5,
const Real3& q) {
Real4 lambda;
#define TRY_TETRAHEDRON(a, b, d, e) \
if (linal::volume(c##a, c##b, c##d, c##e) != 0) { \
lambda = linal::barycentricCoordinates(c##a, c##b, c##d, c##e, q); \
if (isInterpolation(lambda)) { \
return lambda(0) * v##a + lambda(1) * v##b + \
lambda(2) * v##d + lambda(3) * v##e; \
} \
}
TRY_TETRAHEDRON(0, 1, 2, 3)
TRY_TETRAHEDRON(0, 1, 2, 4)
TRY_TETRAHEDRON(0, 1, 2, 5)
TRY_TETRAHEDRON(0, 1, 3, 4)
TRY_TETRAHEDRON(0, 1, 3, 5)
TRY_TETRAHEDRON(0, 1, 4, 5)
TRY_TETRAHEDRON(0, 2, 3, 4)
TRY_TETRAHEDRON(0, 2, 3, 5)
TRY_TETRAHEDRON(0, 2, 4, 5)
TRY_TETRAHEDRON(0, 3, 4, 5)
TRY_TETRAHEDRON(1, 2, 3, 4)
TRY_TETRAHEDRON(1, 2, 3, 5)
TRY_TETRAHEDRON(1, 2, 4, 5)
TRY_TETRAHEDRON(1, 3, 4, 5)
TRY_TETRAHEDRON(2, 3, 4, 5)
#undef TRY_TETRAHEDRON
THROW_INVALID_ARG("Containing tetrahedron is not found");
}
void gcm::AnisotropicMatrix3DAnalytical::findEigenVec (double *eigenVec1,
double *eigenVec2, double l, float rho, const IAnisotropicElasticMaterial::RheologyParameters &C, int stage)
{
// Analitycal search eigenvectors
// M * x = 0, x = (x1, x2, x3)
// then x[4-9] <= x[1-3]
double** M = new double* [3];
for (int i = 0; i < 3; i++)
M[i] = new double [3];
switch ( stage ) {
case 0 :
{
M[0][0] = -C.c11 + rho*l*l;
M[1][2] = -C.c55 + rho*l*l;
M[2][1] = -C.c66 + rho*l*l;
M[0][1] = M[2][0] = -C.c16;
M[0][2] = M[1][0] = -C.c15;
M[1][1] = M[2][2] = -C.c56;
break;
}
case 1 :
{
M[0][1] = -C.c22 + rho*l*l;
M[1][2] = -C.c44 + rho*l*l;
M[2][0] = -C.c66 + rho*l*l;
M[0][0] = M[2][1] = -C.c26;
M[1][0] = M[2][2] = -C.c46;
M[1][1] = M[0][2] = -C.c24;
break;
}
case 2 :
{
M[0][2] = -C.c33 + rho*l*l;
M[1][1] = -C.c44 + rho*l*l;
M[2][0] = -C.c55 + rho*l*l;
M[0][0] = M[2][2] = -C.c35;
M[2][1] = M[1][0] = -C.c45;
M[0][1] = M[1][2] = -C.c34;
break;
}
default:
THROW_INVALID_ARG("Wrong stage number (from findEigenVec)");
}
findNonZeroSolution(M, eigenVec1, eigenVec2);
switch ( stage ) {
case 0 :
{
eigenVec1[3] = -rho*l*eigenVec1[0];
eigenVec1[8] = -rho*l*eigenVec1[1];
eigenVec1[7] = -rho*l*eigenVec1[2];
eigenVec1[4] = -(C.c12*eigenVec1[0] + C.c26*eigenVec1[1] + C.c25*eigenVec1[2])/l;
eigenVec1[5] = -(C.c13*eigenVec1[0] + C.c36*eigenVec1[1] + C.c35*eigenVec1[2])/l;
eigenVec1[6] = -(C.c14*eigenVec1[0] + C.c46*eigenVec1[1] + C.c45*eigenVec1[2])/l;
eigenVec2[3] = -rho*l*eigenVec2[0];
eigenVec2[8] = -rho*l*eigenVec2[1];
eigenVec2[7] = -rho*l*eigenVec2[2];
eigenVec2[4] = -(C.c12*eigenVec2[0] + C.c26*eigenVec2[1] + C.c25*eigenVec2[2])/l;
eigenVec2[5] = -(C.c13*eigenVec2[0] + C.c36*eigenVec2[1] + C.c35*eigenVec2[2])/l;
eigenVec2[6] = -(C.c14*eigenVec2[0] + C.c46*eigenVec2[1] + C.c45*eigenVec2[2])/l;
break;
}
case 1 :
{
eigenVec1[4] = -rho*l*eigenVec1[1];
eigenVec1[8] = -rho*l*eigenVec1[0];
eigenVec1[6] = -rho*l*eigenVec1[2];
eigenVec1[3] = -(C.c16*eigenVec1[0] + C.c12*eigenVec1[1] + C.c14*eigenVec1[2])/l;
eigenVec1[5] = -(C.c36*eigenVec1[0] + C.c23*eigenVec1[1] + C.c34*eigenVec1[2])/l;
eigenVec1[7] = -(C.c56*eigenVec1[0] + C.c25*eigenVec1[1] + C.c45*eigenVec1[2])/l;
eigenVec2[4] = -rho*l*eigenVec2[1];
eigenVec2[8] = -rho*l*eigenVec2[0];
eigenVec2[6] = -rho*l*eigenVec2[2];
eigenVec2[3] = -(C.c16*eigenVec2[0] + C.c12*eigenVec2[1] + C.c14*eigenVec2[2])/l;
eigenVec2[5] = -(C.c36*eigenVec2[0] + C.c23*eigenVec2[1] + C.c34*eigenVec2[2])/l;
eigenVec2[7] = -(C.c56*eigenVec2[0] + C.c25*eigenVec2[1] + C.c45*eigenVec2[2])/l;
break;
}
case 2 :
{
eigenVec1[7] = -rho*l*eigenVec1[0];
eigenVec1[6] = -rho*l*eigenVec1[1];
eigenVec1[5] = -rho*l*eigenVec1[2];
eigenVec1[3] = -(C.c15*eigenVec1[0] + C.c14*eigenVec1[1] + C.c13*eigenVec1[2])/l;
eigenVec1[4] = -(C.c25*eigenVec1[0] + C.c24*eigenVec1[1] + C.c23*eigenVec1[2])/l;
eigenVec1[8] = -(C.c56*eigenVec1[0] + C.c46*eigenVec1[1] + C.c36*eigenVec1[2])/l;
eigenVec2[7] = -rho*l*eigenVec2[0];
eigenVec2[6] = -rho*l*eigenVec2[1];
eigenVec2[5] = -rho*l*eigenVec2[2];
eigenVec2[3] = -(C.c15*eigenVec2[0] + C.c14*eigenVec2[1] + C.c13*eigenVec2[2])/l;
eigenVec2[4] = -(C.c25*eigenVec2[0] + C.c24*eigenVec2[1] + C.c23*eigenVec2[2])/l;
eigenVec2[8] = -(C.c56*eigenVec2[0] + C.c46*eigenVec2[1] + C.c36*eigenVec2[2])/l;
break;
}
}
};
