// abs(x'*y)/\sqrt(x'*x)/sqrt(y'*y)
double dvec_dcos_abs(int n, const double *x, const double *y){
double norm_x,norm_y,dcos,dot;
norm_x=dvec_norm2(n,x);
norm_y=dvec_norm2(n,y);
dot=dvec_dot(n,x,y);
dcos=fabs(dot)/(norm_x*norm_y);
return dcos;
}
static void add_ref_l_p_a(double **PXX, int *i1, double **AXX, double **BXX, double *CXX, double **DXX, double **R23, double *S32, double **R12_a, double **T12_a, double *S12_a, double **R21_a, double **T21_a, double *S21_a, double *S32_a, double **R13_a, double *S31_a, int n, double atran, double *atran_a, double *v1, double *v2, double **w1, double **w2, work_data work) {
/*
double **w3;
*/
double **EXX_a;
/*
w3 = get_work1(&work, WORK_DXX);
*/
EXX_a = get_work1(&work, WORK_DXX);
dmat_add(R12_a, R13_a, R12_a, n, n);
/*
dmat_trans(BXX, w1, n, n);
dmat_mul(R13_a, w1, n, n, n, EXX_a);
*/
dmat_gxgxmx(0, R13_a, 1, BXX, 1., EXX_a, 0., n, n, n);
/*
dmat_trans(DXX, w1, n, n);
dmat_mul(w1, R13_a, n, n, n, w2);
dmat_add(T12_a, w2, T12_a, n, n);
*/
dmat_gxgxmx(1, DXX, 0, R13_a, 1., T12_a, 1., n, n, n);
dvec_add(S21_a, S31_a, S21_a, n);
dmat_vxvtmx(S31_a, CXX, 1., EXX_a, 1., n, n);
/*
dmat_trans(AXX, w1, n, n);
dm_v_mul(w1, S31_a, n, n, v1);
*/
dmat_gxvxmx(1, AXX, S31_a, 1., v1, 0., n, n);
dvec_scale(atran, v1, v2, n);
dvec_add(S32_a, v2, S32_a, n);
*atran_a += dvec_dot(S32, v1, n);
/*
dmat_trans(R23, w1, n, n);
dm_v_mul(w1, v1, n, n, v2);
dvec_add(S12_a, v2, S12_a, n);
*/
dmat_gxvxmx(1, R23, v1, 1., S12_a, 1., n, n);
dmat_copy(w1, EXX_a, n, n);
dmat_getrs2('t', PXX, w1, n, n, i1);
dmat_add(T21_a, w1, T21_a, n, n);
/*
dmat_trans(DXX, w2, n, n);
dmat_mul(w2, w1, n, n, n, w3);
dmat_add(R21_a, w3, R21_a, n, n);
*/
dmat_gxgxmx(1, DXX, 0, w1, 1., R21_a, 1., n, n, n);
dmat_zero(R13_a, n, n);
dvec_zero(S31_a, n);
}
void build_global_source_a2(int n_quad_v, double atran, double *atran_a,
double **R_p, double **T_p, double **R_m, double **T_m,
double *F_p, double *F_m, double *S_p, double *S_m,
double **R_p_a, double **T_p_a, double **R_m_a, double **T_m_a,
double *F_p_a, double *F_m_a, double *S_p_a, double *S_m_a,
work_data work) {
double *v1;
double *v2;
v1 = get_work1(&work, WORK_DX);
v2 = get_work1(&work, WORK_DX);
dvec_scale(atran, S_m_a, v1, n_quad_v);
dvec_add(F_m_a, v1, F_m_a, n_quad_v);
*atran_a += dvec_dot(F_m, S_m_a, n_quad_v);
dmat_vxvtmx(S_m_a, F_m, -1., T_m_a, 1., n_quad_v, n_quad_v);
dmat_gxvxmx(1, T_m, S_m_a, -1., F_m_a, 1., n_quad_v, n_quad_v);
dmat_vxvtmx(S_m_a, F_p, -atran, R_p_a, 1., n_quad_v, n_quad_v);
dmat_gxvxmx(1, R_p, S_m_a, -1., v1, 0., n_quad_v, n_quad_v);
dvec_add(F_p_a, S_p_a, F_p_a, n_quad_v);
dmat_vxvtmx(S_p_a, F_p, -atran, T_p_a, 1., n_quad_v, n_quad_v);
dmat_gxvxmx(1, T_p, S_p_a, -1., v1, 1., n_quad_v, n_quad_v);
dmat_vxvtmx(S_p_a, F_m, -1., R_m_a, 1., n_quad_v, n_quad_v);
dmat_gxvxmx(1, R_m, S_p_a, -1., F_m_a, 1., n_quad_v, n_quad_v);
dvec_scale(atran, v1, v2, n_quad_v);
dvec_add(F_p_a, v2, F_p_a, n_quad_v);
*atran_a += dvec_dot(F_p, v1, n_quad_v);
dvec_zero(S_p_a, n_quad_v);
dvec_zero(S_m_a, n_quad_v);
}
void scale_source_vectors_a(int n_quad_v,
double btran, double *btran_a,
double *F_p1, double *F_m1,
double *F_p2, double *F_m2,
double *F_p_a1, double *F_m_a1,
double *F_p_a2, double *F_m_a2, work_data work) {
double *v1;
v1 = get_work1(&work, WORK_DX);
*btran_a += dvec_dot(F_p1, F_p_a2, n_quad_v);
dvec_scale(btran, F_p_a2, v1, n_quad_v);
dvec_add(F_p_a1, v1, F_p_a1, n_quad_v);
*btran_a += dvec_dot(F_m1, F_m_a2, n_quad_v);
dvec_scale(btran, F_m_a2, v1, n_quad_v);
dvec_add(F_m_a1, v1, F_m_a1, n_quad_v);
dvec_zero(F_p_a2, n_quad_v);
dvec_zero(F_m_a2, n_quad_v);
}
void build_source_vectors_1n_a(int n_quad, int n_stokes, double *qx_v,
double F_0, double omega, double *omega_a,
double as_0, double *as_0_a,
double *P_q0_mm, double *P_q0_pm,
double **tpr, double **tmr, double **gamma,
double *F_p, double *F_m,
double *P_q0_mm_a, double *P_q0_pm_a,
double **tpr_a, double **tmr_a, double **gamma_a,
double *F_p_a, double *F_m_a,
save_tree_data save_tree, work_data work) {
int i;
int n_quad_v;
double *v1;
double *a_a;
double *b_a;
double *c_a;
double *d_a;
double *e_a;
double *p_a;
double *h_a;
double **w1;
forward_save_build_source_vectors_1n_data *save;
n_quad_v = n_quad * n_stokes;
/*-------------------------------------------------------------------------
*
*-----------------------------------------------------------------------*/
save_tree_encode_s(&save_tree, "build_source_vectors_1n");
save_tree_retrieve_data(&save_tree, forward_save_build_source_vectors_1n_data, &save);
/*-------------------------------------------------------------------------
*
*-----------------------------------------------------------------------*/
v1 = get_work1(&work, WORK_DX);
a_a = get_work1(&work, WORK_DX);
b_a = get_work1(&work, WORK_DX);
c_a = get_work1(&work, WORK_DX);
d_a = get_work1(&work, WORK_DX);
e_a = get_work1(&work, WORK_DX);
p_a = get_work1(&work, WORK_DX);
h_a = get_work1(&work, WORK_DX);
w1 = get_work1(&work, WORK_DXX);
/*-------------------------------------------------------------------------
*
*-----------------------------------------------------------------------*/
dm_v_mul_D_A(n_quad, n_stokes, F_m_a, F_m_a);
dvec_add(F_p_a, F_m_a, F_p_a, n_quad_v);
dvec_scale(-1., F_m_a, p_a, n_quad_v);
*as_0_a += -dvec_dot(save->h, F_p_a, n_quad_v) / (2. * as_0 * as_0);
dvec_scale(1. / (2. * as_0), F_p_a, h_a, n_quad_v);
dvec_scale(1. / 2., F_p_a, v1, n_quad_v);
dvec_add(p_a, v1, p_a, n_quad_v);
dmat_vxvtmx(h_a, save->p, 1., tpr_a, 1., n_quad_v, n_quad_v);
dmat_gxvxmx(1, tpr, h_a, 1., p_a, 1., n_quad_v, n_quad_v);
dvec_copy(e_a, h_a, n_quad_v);
dvec_copy(v1, p_a, n_quad_v);
dmat_getrs2('t', save->f, &v1, n_quad_v, 1, save->ip);
dmat_vxvtmx(v1, save->p, -1., w1, 0., n_quad_v, n_quad_v);
dmat_add(gamma_a, w1, gamma_a, n_quad_v, n_quad_v);
for (i = 0; i < n_quad_v; ++i)
*as_0_a += -2. * as_0 * w1[i][i];
dmat_vxvtmx(v1, save->e, -1., tmr_a, 1., n_quad_v, n_quad_v);
dmat_gxvxmx(1, tmr, v1, -1., e_a, 1., n_quad_v, n_quad_v);
*as_0_a -= dvec_dot(v1, save->d, n_quad_v);
dvec_scale(-as_0, v1, d_a, n_quad_v);
dvec_copy(b_a, e_a, n_quad_v);
dvec_scale(-1., e_a, c_a, n_quad_v);
dvec_add(b_a, d_a, b_a, n_quad_v);
dvec_add(c_a, d_a, c_a, n_quad_v);
dm_v_mul_D_A(n_quad, n_stokes, c_a, c_a);
for (i = 0; i < n_quad_v; ++i)
a_a[i] = c_a[i] * P_q0_mm[i];
for (i = 0; i < n_quad_v; ++i)
P_q0_mm_a[i] += F_0 * omega / (4. * PI) / qx_v[i] * c_a[i];
for (i = 0; i < n_quad_v; ++i)
a_a[i] += b_a[i] * P_q0_pm[i];
for (i = 0; i < n_quad_v; ++i)
P_q0_pm_a[i] += F_0 * omega / (4. * PI) / qx_v[i] * b_a[i];
for (i = 0; i < n_quad_v; ++i)
*omega_a += F_0 / (4. * PI) / qx_v[i] * a_a[i];
dvec_zero(F_p_a, n_quad_v);
dvec_zero(F_m_a, n_quad_v);
}
// y=y-(x'*y)*x where x'*x=1
void dvec_orthogonalize(int n, double *y, const double *x)
{
double dot;
dot=dvec_dot(n,x,y);
dvec_sub_scaled(n,y,dot,x);
}