engine_RawArrayIntPairOrNull rawLQUPFactorizationInPlace(MutableMatrix *A, M2_bool transpose)
{
#ifdef HAVE_FFLAS_FFPACK
// Suppose A is m x n
// then we get A = LQUP = LSP, see e.g. http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2006/RR2006-28.pdf
// P and Q are permutation info using LAPACK's convention:, see
// http://www.netlib.org/lapack/explore-html/d0/d39/_v_a_r_i_a_n_t_s_2lu_2_r_e_c_2dgetrf_8f.html
// P is n element permutation on column: size(P)=min(m,n);
// for 1 <= i <= min(m,n), col i of the matrix was interchanged with col P(i).
// Qt is m element permutation on rows (inverse permutation)
// for 1 <= i <= min(m,n), col i of the matrix was interchanged with col P(i).
A->transpose();
DMat<M2::ARingZZpFFPACK> *mat = A->coerce< DMat<M2::ARingZZpFFPACK> >();
if (mat == 0)
{
throw exc::engine_error("LUDivine not defined for this ring");
// ERROR("LUDivine not defined for this ring");
// return 0;
}
size_t nelems = mat->numColumns();
if (mat->numRows() < mat->numColumns()) nelems = mat->numRows();
std::vector<size_t> P(nelems, -1);
std::vector<size_t> Qt(nelems, -1);
// ignore return value (rank) of:
LUdivine(mat->ring().field(),
FFLAS::FflasNonUnit,
(transpose ? FFLAS::FflasTrans : FFLAS::FflasNoTrans),
mat->numRows(),
mat->numColumns(),
mat->array(),
mat->numColumns(),
&P[0],
&Qt[0]);
engine_RawArrayIntPairOrNull result = new engine_RawArrayIntPair_struct;
result->a = stdvector_to_M2_arrayint(Qt);
result->b = stdvector_to_M2_arrayint(P);
return result;
#endif
return 0;
}
void AnisotropicElasticityTensor::calculateEntries(unsigned int /*qp*/)
{
//form_r_matrix();
//Form rotation matrix from Euler angles
const Real phi1 = _euler_angle[0] * (M_PI/180.0);
const Real phi = _euler_angle[1] * (M_PI/180.0);
const Real phi2 = _euler_angle[2] * (M_PI/180.0);
Real cp1 = cos(phi1);
Real cp2 = cos(phi2);
Real cp = cos(phi);
Real sp1 = sin(phi1);
Real sp2 = sin(phi2);
Real sp = sin(phi);
DenseMatrix<Real> R; // Rotational Matrix
R(0,0) = cp1 * cp2 - sp1 * sp2 * cp;
R(0,1) = sp1 * cp2 + cp1 * sp2 * cp;
R(0,2) = sp2 * sp;
R(1,0) = -cp1 * sp2 - sp1 * cp2 * cp;
R(1,1) = -sp1 * sp2 + cp1 * cp2 * cp;
R(1,2) = cp2 * sp;
R(2,0) = sp1 * sp;
R(2,1) = -cp1 * sp;
R(2,2) = cp;
//Initialize material Dt matrix
DenseMatrix<Real> Dt; // 6 x 6 Material Matrix
Dt(0,0) = Dt(1,1) = Dt(2,2) = _c11;
Dt(0,1) = Dt(0,2) = Dt(1,0) = Dt(2,0) = Dt(1,2) = Dt(2,1) = _c12;
Dt(3,3) = Dt(4,4) = Dt(5,5) = 2 * _c44;
//Form Q = R dyadic R and Q transpose
DenseMatrix<Real> Q, Qt; // Q = R (dyadic) R and Q transpose
for (unsigned int i = 0; i < 3; i++)
for (unsigned int j = 0; j < 3; j++)
for (unsigned int k = 0; k < 3; k++)
for (unsigned int l = 0; l < 3; l++)
Q(((i*3)+k),((j*3)+l)) = R(i,j) * R(k,l);
for (unsigned int p = 0; p < 9; p++)
for (unsigned int q = 0; q < 9; q++)
Qt(q,p) = Q(p,q);
// Form two kinds of transformation matrix
// TransD6toD9 transfroms Dt[6][6] to Dmat[9][9]
// TransD9toD6 transforms Dmat[9][9] to Dt[6][6]
DenseMatrix<Real> trans_d6_to_d9, transpose_trans_d6_to_d9;
DenseMatrix<Real> trans_d9_to_d6, transpose_trans_d9_to_d6;
Real sqrt2 = std::sqrt(2.0);
Real a = 1/sqrt2;
trans_d6_to_d9(0,0) = trans_d6_to_d9(4,1) = trans_d6_to_d9(8,2) = 1.0;
trans_d6_to_d9(1,3) = trans_d6_to_d9(3,3) = a;
trans_d6_to_d9(2,4) = trans_d6_to_d9(6,4) = a;
trans_d6_to_d9(5,5) = trans_d6_to_d9(7,5) = a;
for (unsigned int i = 0; i < 9; i++)
for (unsigned int j = 0; j < 6; j++)
transpose_trans_d6_to_d9(j,i) = trans_d6_to_d9(i,j);
trans_d9_to_d6(0,0) = trans_d9_to_d6(1,4) = trans_d9_to_d6(2,8) = 1.0;
trans_d9_to_d6(3,3) = trans_d9_to_d6(4,6) = trans_d9_to_d6(5,7) = sqrt2;
for (unsigned int i = 0; i < 6; i++)
for (unsigned int j = 0; j < 9; j++)
transpose_trans_d9_to_d6(j,i) = trans_d9_to_d6(i,j);
// The function makes use of TransD6toD9 matrix to transfrom Dt[6][6] to Dmat[9][9]
// Dmat = T * Dt * TT
DenseMatrix<Real> outputMatrix(9,6);
outputMatrix = trans_d6_to_d9;
outputMatrix.right_multiply(Dt);
DenseMatrix<Real> Dmat; // 9 x 9 Material Matrix
Dmat = outputMatrix;
Dmat.right_multiply(transpose_trans_d6_to_d9);
// The function makes use of Q matrix to rotate Dmat[9][9] to QDmat[9][9]
// QDmat = QT * Dmat * Q
DenseMatrix<Real> outputMatrix99(9,9);
outputMatrix99 = Qt;
outputMatrix99.right_multiply(Dmat);
DenseMatrix<Real> QDmat; // Rotated Material Matrix
QDmat = outputMatrix99;
QDmat.right_multiply(Q);
//Convert 9X9 matrix QDmat to 81 vector
unsigned int count = 0;
for (unsigned int j = 0; j < 9; j++)
for (unsigned int i = 0; i < 9; i++)
{
_values[count] = QDmat(i,j);
count = count + 1;
}
}
