void expm(gsl_matrix_complex * L, gsl_complex t, gsl_matrix * m)
{
int i,j,s;
gsl_vector_complex *eval = gsl_vector_complex_alloc(4);
gsl_matrix_complex *evec = gsl_matrix_complex_alloc(4, 4);
gsl_eigen_nonsymmv_workspace * w = gsl_eigen_nonsymmv_alloc(4);
gsl_matrix_complex *evalmat = gsl_matrix_complex_alloc(4, 4);
gsl_matrix_complex *vd = gsl_matrix_complex_alloc(4, 4);
gsl_complex one = gsl_complex_rect(1, 0);
gsl_complex zero = gsl_complex_rect(0, 0);
gsl_matrix_complex *K = gsl_matrix_complex_alloc(4, 4);
gsl_permutation *p = gsl_permutation_alloc(4);
gsl_vector_complex *x = gsl_vector_complex_alloc(4);
gsl_vector_complex_view bp;
gsl_complex z;
gsl_eigen_nonsymmv(m, eval, evec, w);
gsl_eigen_nonsymmv_sort(eval, evec, GSL_EIGEN_SORT_ABS_DESC);
gsl_eigen_nonsymmv_free(w); // clear workspace
for (i = 0; i < 4; i++)
{
gsl_complex eval_i = gsl_vector_complex_get(eval, i);
gsl_complex expeval = gsl_complex_mul(eval_i,t);
expeval = gsl_complex_exp(expeval);
gsl_matrix_complex_set(evalmat, i, i, expeval);
}
gsl_vector_complex_free(eval); // clear vector for eigenvalues
// v'L'=De'v'
gsl_blas_zgemm(CblasTrans, CblasTrans, one, evalmat, evec, zero, vd);
gsl_matrix_complex_transpose(evec);//transpose v
gsl_matrix_complex_memcpy(K,evec);
for (i = 0; i < 4; i++)
{
bp = gsl_matrix_complex_column(vd, i);
gsl_linalg_complex_LU_decomp(evec, p, &s);
gsl_linalg_complex_LU_solve(evec, p, &bp.vector, x);
for (j = 0; j < 4; j++)
{
z = gsl_vector_complex_get(x, j);
gsl_matrix_complex_set(L,i,j,z); //'through the looking glass' transpose
}
gsl_matrix_complex_memcpy(evec,K);
}
gsl_permutation_free(p);
gsl_vector_complex_free(x);
gsl_matrix_complex_free(vd);
gsl_matrix_complex_free(evec);
gsl_matrix_complex_free(evalmat);
gsl_matrix_complex_free(K);
}
static int
mc_solve(lua_State *L)
{
mMatComplex *m = qlua_checkMatComplex(L, 1);
mVecComplex *v = qlua_checkVecComplex(L, 2);
mMatComplex *lu;
mVecComplex *x;
gsl_permutation *p;
/* XXX assume GSL and QLA_D_Complex use compatible layout */
gsl_vector_complex_view vb = gsl_vector_complex_view_array((void *)&v->val[0], v->size);
gsl_vector_complex_view vx;
int signum;
if (m->l_size != m->r_size)
return luaL_error(L, "square matrix expected");
if (m->l_size != v->size)
return luaL_error(L, "vector dim mismatch matrix size");
p = new_permutation(L, m->l_size);
lu = qlua_newMatComplex(L, m->l_size, m->l_size);
x = qlua_newVecComplex(L, m->l_size);
/* XXX assume GSL and QLA_D_Complex use compatible layout */
vx = gsl_vector_complex_view_array((void *)&x->val[0], x->size);
gsl_matrix_complex_memcpy(lu->m, m->m);
gsl_linalg_complex_LU_decomp(lu->m, p, &signum);
if (gsl_linalg_complex_LU_solve(lu->m, p, &vb.vector, &vx.vector))
luaL_error(L, "matrix:solve() failed");
gsl_permutation_free(p);
return 1;
}
Real DAESolver::solve()
{
if (the_system_size_ == 0)
{
return 0.0;
}
const VariableArray::size_type a_size(the_system_size_);
gsl_linalg_LU_solve(the_jacobian_matrix1_, the_permutation1_,
the_velocity_vector1_, the_solution_vector1_);
gsl_linalg_complex_LU_solve(the_jacobian_matrix2_, the_permutation2_,
the_velocity_vector2_, the_solution_vector2_);
Real a_norm(0.0);
Real delta_w(0.0);
gsl_complex comp;
VariableArray a_tmp_value_buffer = the_value_differential_buffer_;
a_tmp_value_buffer.insert(
a_tmp_value_buffer.end(), the_value_algebraic_buffer_.begin(),
the_value_algebraic_buffer_.end());
for (VariableArray::size_type c(0); c < a_size; ++c)
{
Real a_tolerance2(rtoler_ * fabs(a_tmp_value_buffer[c]) + atoler_);
a_tolerance2 = a_tolerance2 * a_tolerance2;
delta_w = gsl_vector_get(the_solution_vector1_, c);
the_w_[c] += delta_w;
a_norm += delta_w * delta_w / a_tolerance2;
comp = gsl_vector_complex_get(the_solution_vector2_, c);
delta_w = GSL_REAL(comp);
the_w_[c + a_size] += delta_w;
a_norm += delta_w * delta_w / a_tolerance2;
delta_w = GSL_IMAG(comp);
the_w_[c + a_size * 2] += delta_w;
a_norm += delta_w * delta_w / a_tolerance2;
}
return sqrt(a_norm / (3 * a_size));
}
static VALUE rb_gsl_linalg_complex_LU_solve(int argc, VALUE *argv, VALUE obj)
{
gsl_matrix_complex *m = NULL, *mtmp = NULL;
gsl_permutation *p = NULL;
gsl_vector_complex *b = NULL, *x = NULL;
int flagm = 0, flagx = 0, itmp, signum;
switch (TYPE(obj)) {
case T_MODULE:
case T_CLASS:
case T_OBJECT:
if (argc < 2 || argc > 4)
rb_raise(rb_eArgError, "Usage: solve(m, b), solve(m, b, x), solve(lu, p, b), solve(lu, p, b, x)");
CHECK_MATRIX(argv[0]);
Data_Get_Struct(argv[0], gsl_matrix_complex, m);
if (CLASS_OF(argv[0]) != cgsl_matrix_complex_LU) {
flagm = 1;
mtmp = gsl_matrix_complex_alloc(m->size1, m->size2);
gsl_matrix_complex_memcpy(mtmp, m);
} else {
mtmp = m;
}
itmp = 1;
break;
default:
if (argc < 1 || argc > 3)
rb_raise(rb_eArgError, "Usage: LU_solve(b), LU_solve(p, b), LU_solve(b, x), solve(p, b, x)");
Data_Get_Struct(obj, gsl_matrix_complex, m);
if (CLASS_OF(obj) != cgsl_matrix_complex_LU) {
flagm = 1;
mtmp = gsl_matrix_complex_alloc(m->size1, m->size2);
gsl_matrix_complex_memcpy(mtmp, m);
} else {
mtmp = m;
}
itmp = 0;
}
if (flagm == 1) {
if (itmp != argc-1) rb_raise(rb_eArgError, "Usage: m.LU_solve(b)");
Data_Get_Struct(argv[itmp], gsl_vector_complex, b);
x = gsl_vector_complex_alloc(b->size);
p = gsl_permutation_alloc(b->size);
gsl_linalg_complex_LU_decomp(mtmp, p, &signum);
} else {
Data_Get_Struct(argv[itmp], gsl_permutation, p);
itmp++;
Data_Get_Struct(argv[itmp], gsl_vector_complex, b);
itmp++;
if (itmp == argc-1) {
Data_Get_Struct(argv[itmp], gsl_vector_complex, x);
flagx = 1;
} else {
x = gsl_vector_complex_alloc(m->size1);
}
}
gsl_linalg_complex_LU_solve(mtmp, p, b, x);
if (flagm == 1) {
gsl_matrix_complex_free(mtmp);
gsl_permutation_free(p);
}
if (flagx == 0) return Data_Wrap_Struct(cgsl_vector_complex, 0, gsl_vector_complex_free, x);
else return argv[argc-1];
}
/**
* C++ version of gsl_linalg_complex_LU_solve().
* @param LU An LU decomposition matrix
* @param p A permutation
* @param b A vector
* @param x A vector
* @return Error code on failure
*/
inline int complex_LU_solve( matrix_complex const& LU, permutation const& p,
vector_complex const& b, vector_complex& x ){
return gsl_linalg_complex_LU_solve( LU.get(), p.get(), b.get(), x.get() ); }
double Calculator::getIntensity(double Q)
{
std::complex<double> cppf1, cppf2;
gsl_complex alpha, beta;
gsl_complex gslf1, gslf2;
int s;
double avFactor;
cppf1 = m_sf1->F(0.0, 0.0, Q, m_energy);
cppf2 = m_sf2->F(0.0, 0.0, Q, m_energy);
gslf1 = gsl_complex_rect(cppf1.real(), cppf1.imag());
gslf2 = gsl_complex_rect(cppf2.real(), cppf2.imag());
avFactor = exp(-2.0 / m_N);
alpha = gsl_complex_rect (1.0, 0.0);
beta = gsl_complex_rect (0.0, 0.0);
/*set vector F (scattering factors)*/
gsl_vector_complex_set(F, 0, gslf1);
gsl_vector_complex_set(F, 1, gslf2);
/*set vector conj(F) (scattering factors)*/
gsl_vector_complex_set(Fconj, 0, gsl_complex_conjugate(gslf1));
gsl_vector_complex_set(Fconj, 1, gsl_complex_conjugate(gslf2));
/*set exp matrix*/
setMatrixExp(m_Exp, Q);
/*find W = P * Exp * Ps * conj(F) vector:*/
/* (1) W = alpha * Ps * conj(F) + beta * W */
gsl_blas_zgemv (CblasNoTrans, alpha, m_Ps, Fconj, beta, W);
/*printf("W(1):\n");
gsl_vector_complex_fprintf (stdout, W, "%g");*/
/* (2) W = alpha * Exp * tmp_vec + beta * W */
gsl_blas_zgemv (CblasNoTrans, alpha, m_Exp, W, beta, tmp_vec);
/*printf("W(2):\n");
gsl_vector_complex_fprintf (stdout, tmp_vec, "%g");*/
/* (3) W = alpha * P * tmp_vec + beta * W */
gsl_blas_zgemv (CblasNoTrans, alpha, m_P, tmp_vec, beta, W);
/*Find J0 = F.(Ps * conj(F)) */
gsl_blas_zgemv (CblasNoTrans, alpha, m_Ps, Fconj, beta, tmp_vec);
gsl_blas_zdotu (F, tmp_vec, &J0);
/*alpha = exp(-2 / N)*/
alpha = gsl_complex_rect (avFactor, 0.0);
beta = gsl_complex_rect (0.0, 0.0);
/*find T matrix: T = alpha * P * exp + beta * T*/
gsl_blas_zgemm (CblasNoTrans, CblasNoTrans, alpha, m_P, m_Exp, beta, T);
/*printf("T:\n");
gsl_matrix_complex_fprintf (stdout, T, "%g");*/
/*Find Jns = F. (G * W) */
/*tmp_mat = I */
gsl_matrix_complex_set_identity (tmp_mat);
/*tmp_mat = I - T */
gsl_matrix_complex_sub (tmp_mat, T);
/*LU decomposition*/
gsl_linalg_complex_LU_decomp(tmp_mat, perm, &s);
/*calculate product G * W = (I - T)^(-1) W directly using LU decomposition*/
gsl_linalg_complex_LU_solve (tmp_mat, perm, W, tmp_vec);
/*calculate F.(G * W)*/
gsl_blas_zdotu (F, tmp_vec, &Jns);
/*Find Js = F.(G^2 * (I - T^N) * W) however, this term should be negligible*/
/*result = N *(2 * Jns + J0) - Js */
alpha = gsl_complex_mul_real (Jns, 2.0 * avFactor);
alpha = gsl_complex_add (alpha, J0);
return m_N * m_I0 * GSL_REAL(alpha) * getPLGfactor(getTheta(Q)) + m_Ibg;
}
