2015-10-21 12:07:48 +02:00
|
|
|
#include <Python.h>
|
|
|
|
|
|
|
|
#define NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION
|
|
|
|
|
2015-10-21 13:42:40 +02:00
|
|
|
#include <numpy/arrayobject.h>
|
2015-10-21 12:07:48 +02:00
|
|
|
#include <complex.h>
|
|
|
|
//#include "tetra.h"
|
2015-10-21 13:42:40 +02:00
|
|
|
#include "argsort.h"
|
2015-10-21 12:07:48 +02:00
|
|
|
#include "dos_tetra3d.h"
|
|
|
|
|
|
|
|
/***************************************************
|
|
|
|
|
|
|
|
Analytical tetrahedron method as described in
|
|
|
|
Lambin et al., PRB 29, 6, 3430 (1984).
|
|
|
|
|
|
|
|
***************************************************/
|
|
|
|
|
|
|
|
static double F(double en, double e1, double e2, double e3, double e4);
|
|
|
|
static double K2(double en, double e1, double e2, double e3);
|
|
|
|
static double K1(double en, double e1, double e2);
|
|
|
|
|
|
|
|
static void fun_dos_case1(double en, double *eigs, double *ci);
|
|
|
|
static void fun_dos_case2(double en, double *eigs, double *ci);
|
|
|
|
static void fun_dos_case3(double en, double *eigs, double *ci);
|
|
|
|
|
2015-10-21 13:42:40 +02:00
|
|
|
int dos_corner_weights(double en, double *eigs, int *inds, double *ci);
|
|
|
|
int dos_tet_weights(double en, double *eigs, int *inds, double *ct);
|
|
|
|
|
|
|
|
const static int NUM_TET_CORNERS = 4;
|
|
|
|
|
|
|
|
static PyMethodDef c_tetraMethods[] = {
|
|
|
|
{"dos_weights_3d", tetra_DOS3D, METH_VARARGS,
|
|
|
|
"C-implementation of the tetrahedron method for calculating DOS"},
|
|
|
|
{NULL, NULL, 0, NULL}
|
|
|
|
};
|
|
|
|
|
|
|
|
PyMODINIT_FUNC
|
|
|
|
initc_tetra(void)
|
|
|
|
{
|
|
|
|
(void) Py_InitModule("c_atm_dos", c_tetraMethods);
|
|
|
|
import_array();
|
|
|
|
}
|
|
|
|
|
2015-10-21 12:07:48 +02:00
|
|
|
//
|
|
|
|
// Integration_Weights
|
|
|
|
//
|
|
|
|
static PyObject *
|
|
|
|
tetra_DOS3D(PyObject *self, PyObject *args)
|
|
|
|
{
|
|
|
|
|
|
|
|
PyArrayObject *py_eigk, *py_itt; // Input Numpy arrays
|
|
|
|
PyArrayObject *py_cti; // Output Numpy array
|
2015-10-21 13:42:40 +02:00
|
|
|
// npy_int64 *itt; // C-pointer to the 'itt' array
|
2015-10-21 12:07:48 +02:00
|
|
|
npy_intp *dims; // Dimensions of the output array 'rti'
|
2015-10-21 13:42:40 +02:00
|
|
|
double *cti; // C-pointer to 'eigk' and 'rti' arrays
|
|
|
|
double e;
|
|
|
|
// double et[4]; // Real part of eigenvalues
|
|
|
|
// int strd_itt[2], strd_eigk, strd_cti[2], it_cti; // Strides
|
|
|
|
int ntet; // Indices of sorted 'eigs'; number of tetrahedra
|
2015-10-21 12:07:48 +02:00
|
|
|
// Auxiliary variables and loop indices
|
2015-10-21 13:42:40 +02:00
|
|
|
int nd;
|
2015-10-21 12:07:48 +02:00
|
|
|
|
|
|
|
// Data-preparation part
|
|
|
|
if (!PyArg_ParseTuple(args, "O!dO!",
|
|
|
|
&PyArray_Type, &py_eigk, &e, &PyArray_Type, &py_itt))
|
|
|
|
return NULL;
|
|
|
|
|
|
|
|
// Sanity tests (the types are assumed to be checked in the python wrapper)
|
2015-10-21 13:42:40 +02:00
|
|
|
// nd = py_eigk->nd;
|
|
|
|
nd = PyArray_NDIM(py_eigk);
|
2015-10-21 12:07:48 +02:00
|
|
|
if (nd != 1)
|
|
|
|
{
|
|
|
|
PyErr_SetString(PyExc_ValueError, " Array 'eigk' must be 1D");
|
|
|
|
return NULL;
|
|
|
|
}
|
|
|
|
|
2015-10-21 13:42:40 +02:00
|
|
|
// nd = py_itt->nd;
|
|
|
|
nd = PyArray_NDIM(py_itt);
|
2015-10-21 12:07:48 +02:00
|
|
|
if (nd != 2)
|
|
|
|
{
|
|
|
|
PyErr_SetString(PyExc_ValueError, " Array 'itt' must be 2D");
|
|
|
|
return NULL;
|
|
|
|
}
|
|
|
|
|
2015-10-21 13:42:40 +02:00
|
|
|
// nd = py_itt->dimensions[0];
|
|
|
|
dims = PyArray_DIMS(py_itt);
|
|
|
|
if (dims[0] != 5)
|
2015-10-21 12:07:48 +02:00
|
|
|
{
|
|
|
|
PyErr_SetString(PyExc_ValueError,
|
|
|
|
" The first dimension of 'itt' must be equal to 5");
|
|
|
|
return NULL;
|
|
|
|
}
|
|
|
|
|
2015-10-21 13:42:40 +02:00
|
|
|
// ntet = (int) py_itt->dimensions[1];
|
|
|
|
ntet = dims[1];
|
2015-10-21 12:07:48 +02:00
|
|
|
|
2015-10-21 13:42:40 +02:00
|
|
|
// eigk = (double *)py_eigk->data;
|
|
|
|
// strd_eigk = py_eigk->strides[0] / sizeof(npy_float64);
|
2015-10-21 12:07:48 +02:00
|
|
|
|
2015-10-21 13:42:40 +02:00
|
|
|
// itt = (npy_int64 *)py_itt->data;
|
|
|
|
// strd_itt[0] = py_itt->strides[0] / sizeof(npy_int64);
|
|
|
|
// strd_itt[1] = py_itt->strides[1] / sizeof(npy_int64);
|
2015-10-21 12:07:48 +02:00
|
|
|
|
|
|
|
// Resulting array (the question is whether dims is copied or not?)
|
2015-10-21 13:42:40 +02:00
|
|
|
cti = (double *)malloc(NUM_TET_CORNERS * ntet * sizeof(double));
|
2015-10-21 12:07:48 +02:00
|
|
|
dims = (npy_intp *)malloc(2 * sizeof(npy_intp));
|
|
|
|
|
2015-10-21 13:42:40 +02:00
|
|
|
dims[0] = NUM_TET_CORNERS;
|
2015-10-21 12:07:48 +02:00
|
|
|
dims[1] = ntet;
|
|
|
|
|
|
|
|
py_cti = (PyArrayObject *)PyArray_SimpleNewFromData(2, dims, NPY_DOUBLE, cti);
|
|
|
|
|
2015-10-21 13:42:40 +02:00
|
|
|
// strd_cti[0] = py_cti->strides[0] / sizeof(double);
|
|
|
|
// strd_cti[1] = py_cti->strides[1] / sizeof(double);
|
2015-10-21 12:07:48 +02:00
|
|
|
|
|
|
|
// Main part: now we can fill the 'cti' array and it will be returned
|
|
|
|
// by 'py_cti' as a numpy array
|
|
|
|
|
|
|
|
//
|
|
|
|
// Main function
|
|
|
|
//
|
2015-10-21 13:42:40 +02:00
|
|
|
// tet_dos3d(e, eigk, strd_eigk, itt, ntet, strd_itt, cti, strd_cti);
|
|
|
|
tet_dos3d(e, py_eigk, py_itt, ntet, py_cti);
|
2015-10-21 12:07:48 +02:00
|
|
|
|
|
|
|
return PyArray_Return(py_cti);
|
|
|
|
}
|
|
|
|
|
2015-10-21 13:42:40 +02:00
|
|
|
//void tet_dos3d(double en, double *eigk, int strd_eigk,
|
|
|
|
// npy_int64 *itt, int ntet, int *strd_itt,
|
|
|
|
// double *cti, int *strd_cti)
|
|
|
|
void tet_dos3d(double en, PyArrayObject *py_eigk,
|
|
|
|
PyArrayObject *py_itt, int ntet,
|
|
|
|
PyArrayObject *py_cti)
|
2015-10-21 12:07:48 +02:00
|
|
|
{
|
|
|
|
double eigs[4], ci[4];
|
2015-10-21 13:42:40 +02:00
|
|
|
int i, it, ik, inds[4], flag;
|
2015-10-21 12:07:48 +02:00
|
|
|
// **** DEBUG
|
|
|
|
double ct, ci_sum;
|
|
|
|
|
|
|
|
// Loop over tetrahedra (triangles)
|
|
|
|
for (it = 0; it < ntet; it++)
|
|
|
|
{
|
2015-10-21 13:42:40 +02:00
|
|
|
// it_cti = it * strd_cti[1];
|
2015-10-21 12:07:48 +02:00
|
|
|
// Sort eigenvalues and obtain indices of the sorted array
|
|
|
|
// eigs: sorted eigenvalues
|
|
|
|
// inds: index map
|
|
|
|
for (i = 1; i < 5; i++)
|
|
|
|
{
|
2015-10-21 13:42:40 +02:00
|
|
|
// ik = itt[i * strd_itt[0] + it * strd_itt[1]];
|
|
|
|
ik = ((int *)PyArray_GETPTR2(py_itt, i, it))[0];
|
|
|
|
// eigs[i - 1] = eigk[ik * strd_eigk];
|
|
|
|
eigs[i - 1] = ((double *)PyArray_GETPTR1(py_eigk, ik))[0];
|
2015-10-21 12:07:48 +02:00
|
|
|
}
|
|
|
|
|
|
|
|
// corner weights for a single tetrahedron
|
|
|
|
dos_corner_weights(en, eigs, inds, ci);
|
|
|
|
for(i = 0, ci_sum = 0.0; i < 4; i++)
|
|
|
|
ci_sum += ci[i];
|
|
|
|
|
2015-10-21 13:42:40 +02:00
|
|
|
flag = dos_tet_weights(en, eigs, inds, &ct);
|
2015-10-21 12:07:48 +02:00
|
|
|
if(fabs(ct - ci_sum) > tol)
|
|
|
|
{
|
2015-10-21 13:42:40 +02:00
|
|
|
printf(" *** Error in weights: it = %d, flag = %d, en = %lf", it, flag, en);
|
2015-10-21 12:07:48 +02:00
|
|
|
for(i = 0; i < 4; i++)
|
|
|
|
printf(", e[%d] = %lf", i, eigs[i]);
|
|
|
|
printf(", c_diff = %le\n", fabs(ct - ci_sum));
|
|
|
|
return;
|
|
|
|
}
|
|
|
|
// printf(" it = %d, flag = %d", it, j);
|
|
|
|
// for(i = 0; i < 4; i++)
|
|
|
|
// printf(", e[%d] = %lf", i, eigs[i]);
|
|
|
|
// printf(", c_diff = %le\n", fabs(ct - ci_sum));
|
|
|
|
|
|
|
|
// if(j < 4)
|
|
|
|
// {
|
|
|
|
// printf(" flag = %d, e = %lf", j, en);
|
|
|
|
// for(i = 0; i < 4; i++)
|
|
|
|
// printf(", eigs[%d] = %lf", i, eigs[i]);
|
|
|
|
// printf("\n");
|
|
|
|
// printf(" ci = ");
|
|
|
|
// for(i = 0; i < 4; i++)
|
|
|
|
// printf(", %lf", ci[i]);
|
|
|
|
// printf("\n");
|
|
|
|
// }
|
|
|
|
|
|
|
|
for(i = 0; i < 4; i++)
|
|
|
|
{
|
2015-10-21 13:42:40 +02:00
|
|
|
// j = inds[i] * strd_cti[0] + it_cti;
|
|
|
|
// cti[j] = ci[i];
|
|
|
|
((double *)PyArray_GETPTR2(py_cti, inds[i], it))[0] = ci[i];
|
2015-10-21 12:07:48 +02:00
|
|
|
}
|
|
|
|
|
|
|
|
} // it = 1, ntet
|
|
|
|
}
|
|
|
|
|
|
|
|
int dos_corner_weights(double en, double *eigs, int *inds,
|
|
|
|
double *ci)
|
|
|
|
{
|
|
|
|
int flag, i;
|
|
|
|
flag = dos_reorder(en, eigs, inds);
|
|
|
|
|
|
|
|
switch(flag)
|
|
|
|
{
|
|
|
|
// E1 <= E <= E2
|
|
|
|
case 1:
|
|
|
|
fun_dos_case1(en, eigs, ci);
|
|
|
|
break;
|
|
|
|
|
|
|
|
// E2 <= E <= E3
|
|
|
|
case 2:
|
|
|
|
fun_dos_case2(en, eigs, ci);
|
|
|
|
break;
|
|
|
|
|
|
|
|
// E3 <= E <= E4
|
|
|
|
case 3:
|
|
|
|
fun_dos_case3(en, eigs, ci);
|
|
|
|
break;
|
|
|
|
|
|
|
|
// E < E1 || E4 < E
|
|
|
|
case 4:
|
|
|
|
case 5:
|
|
|
|
for(i = 0; i < 4; i++) ci[i] = 0.0;
|
|
|
|
break;
|
|
|
|
|
|
|
|
// E1 == E4 == E
|
|
|
|
case 6:
|
|
|
|
for(i = 0; i < 4; i++) ci[i] = 0.25;
|
|
|
|
break;
|
|
|
|
}
|
|
|
|
|
|
|
|
return flag;
|
|
|
|
}
|
|
|
|
|
|
|
|
int dos_tet_weights(double en, double *eigs, int *inds,
|
|
|
|
double *ct)
|
|
|
|
{
|
|
|
|
double e1, e2, e3, e4;
|
|
|
|
double complex s;
|
2015-10-21 13:42:40 +02:00
|
|
|
int flag;
|
2015-10-21 12:07:48 +02:00
|
|
|
flag = dos_reorder(en, eigs, inds);
|
|
|
|
|
|
|
|
e1 = eigs[0];
|
|
|
|
e2 = eigs[1];
|
|
|
|
e3 = eigs[2];
|
|
|
|
e4 = eigs[3];
|
|
|
|
|
|
|
|
switch(flag)
|
|
|
|
{
|
|
|
|
// E1 <= E <= E2
|
|
|
|
case 1:
|
|
|
|
if(fabs(e2 - e1) > tol && fabs(e3 - e1) > tol && fabs(e4 - e1) > tol)
|
|
|
|
*ct = 3.0 * (en - e1) * (en - e1) / ((e2 - e1) * (e3 - e1) * (e4 - e1));
|
|
|
|
else
|
|
|
|
{
|
|
|
|
s = fmin(fabs(e1 - e2), fabs(e3 - e1));
|
|
|
|
s = fmin(fabs(s), fabs(e4 - e1));
|
|
|
|
s /= 100.0;
|
|
|
|
s = fmax(s, 1.0e-20) * I;
|
|
|
|
|
|
|
|
*ct = 3.0 * creal((en - e1 + s) * (en - e1 + s) / ((e2 - e1 + s) * (e3 - e1 + s) * (e4 - e1 + s)));
|
|
|
|
}
|
|
|
|
|
|
|
|
break;
|
|
|
|
|
|
|
|
// E2 <= E <= E3
|
|
|
|
case 2:
|
|
|
|
if(fabs(e4 - e2) > tol && fabs(e3 - e2) > tol && fabs(e4 - e1) > tol && fabs(e3 - e1) > tol)
|
|
|
|
*ct = 3.0 * (
|
|
|
|
(e3 - en) * (en - e2) / ((e4 - e2) * (e3 - e2) * (e3 - e1)) +
|
|
|
|
(e4 - en) * (en - e1) / ((e4 - e1) * (e4 - e2) * (e3 - e1)));
|
|
|
|
else
|
|
|
|
{
|
|
|
|
s = fmin(fabs(e3 - e2), fabs(e3 - e1));
|
|
|
|
s = fmin(fabs(s), fabs(e4 - e1));
|
|
|
|
s = fmin(fabs(s), fabs(e4 - e2));
|
|
|
|
s /= 100.0;
|
|
|
|
s = fmax(s, 1.0e-20) * I;
|
|
|
|
|
|
|
|
*ct = 3.0 * creal((
|
|
|
|
(e3 - en + s) * (en - e2 + s) / ((e4 - e2 + s) * (e3 - e2 + s) * (e3 - e1 + s)) +
|
|
|
|
(e4 - en + s) * (en - e1 + s) / ((e4 - e1 + s) * (e4 - e2 + s) * (e3 - e1 + s))));
|
|
|
|
}
|
|
|
|
break;
|
|
|
|
|
|
|
|
// E3 <= E <= E4
|
|
|
|
case 3:
|
|
|
|
if(fabs(e4 - e2) > tol && fabs(e4 - e3) > tol && fabs(e4 - e1) > tol)
|
|
|
|
*ct = 3.0 * (e4 - en) * (e4 - en) / ((e4 - e1) * (e4 - e2) * (e4 - e3));
|
|
|
|
else
|
|
|
|
{
|
|
|
|
s = fmin(fabs(e4 - e2), fabs(e4 - e1));
|
|
|
|
s = fmin(fabs(s), fabs(e4 - e3));
|
|
|
|
s /= 100.0;
|
|
|
|
s = fmax(s, 1.0e-20) * I;
|
|
|
|
|
|
|
|
*ct = 3.0 * creal((e4 - en + s) * (e4 - en + s) / ((e4 - e1 + s) * (e4 - e2 + s) * (e4 - e3 + s)));
|
|
|
|
}
|
|
|
|
|
|
|
|
break;
|
|
|
|
|
|
|
|
// E < E1 || E4 < E
|
|
|
|
case 4:
|
|
|
|
case 5:
|
|
|
|
*ct = 0.0;
|
|
|
|
break;
|
|
|
|
|
|
|
|
// E1 == E4 == E
|
|
|
|
case 6:
|
|
|
|
*ct = 1.0;
|
|
|
|
break;
|
|
|
|
}
|
|
|
|
|
|
|
|
return flag;
|
|
|
|
}
|
|
|
|
|
|
|
|
int dos_reorder(double en, double *e, int *inds)
|
|
|
|
{
|
|
|
|
double *ptrs[4], e_tmp[4];
|
|
|
|
int i;
|
|
|
|
|
|
|
|
for(i = 0; i < 4; i++)
|
|
|
|
e_tmp[i] = e[i];
|
|
|
|
|
|
|
|
argsort(e_tmp, inds, ptrs, 4);
|
|
|
|
|
|
|
|
for(i = 0; i < 4; i++)
|
|
|
|
e[i] = e_tmp[inds[i]];
|
|
|
|
|
|
|
|
if((e[0] <= en && en <= e[3]) && fabs(e[3] - e[0]) < tol) return 6;
|
|
|
|
if(e[0] <= en && en <= e[1]) return 1;
|
|
|
|
if(e[1] <= en && en <= e[2]) return 2;
|
|
|
|
if(e[2] <= en && en <= e[3]) return 3;
|
|
|
|
if(en < e[0]) return 4;
|
|
|
|
if(e[3] < en) return 5;
|
|
|
|
return -1;
|
|
|
|
}
|
|
|
|
|
|
|
|
static void fun_dos_case1(double en, double *eigs, double *ci)
|
|
|
|
{
|
|
|
|
double e1, e2, e3, e4;
|
2015-10-21 13:42:40 +02:00
|
|
|
// int i;
|
2015-10-21 12:07:48 +02:00
|
|
|
|
|
|
|
// if(fabs(eigs[1] - eigs[0]) < tol)
|
|
|
|
// {
|
|
|
|
// for(i = 0; i < 4; i++) ci[i] = 0.0;
|
|
|
|
// return;
|
|
|
|
// }
|
|
|
|
|
|
|
|
e1 = eigs[0];
|
|
|
|
e2 = eigs[1];
|
|
|
|
e3 = eigs[2];
|
|
|
|
e4 = eigs[3];
|
|
|
|
|
|
|
|
ci[0] = K2(en, e1, e2, e4) * F(en, e2, e1, e1, e3) +
|
|
|
|
K2(en, e1, e2, e3) * F(en, e3, e1, e1, e4) +
|
|
|
|
K2(en, e1, e3, e4) * F(en, e4, e1, e1, e2);
|
|
|
|
|
|
|
|
ci[1] = -K1(en, e1, e2) * F(en, e1, e1, e3, e4);
|
|
|
|
|
|
|
|
ci[2] = -K1(en, e1, e3) * F(en, e1, e1, e2, e4);
|
|
|
|
|
|
|
|
ci[3] = -K1(en, e1, e4) * F(en, e1, e1, e2, e3);
|
|
|
|
}
|
|
|
|
|
|
|
|
static void fun_dos_case2(double en, double *eigs, double *ci)
|
|
|
|
{
|
|
|
|
double e1, e2, e3, e4;
|
|
|
|
|
|
|
|
// if(fabs(eigs[2] - eigs[1]) < tol)
|
|
|
|
// {
|
|
|
|
// for(i = 0; i < 4; i++) ci[i] = 0.0;
|
|
|
|
// return;
|
|
|
|
// }
|
|
|
|
|
|
|
|
e1 = eigs[0];
|
|
|
|
e2 = eigs[1];
|
|
|
|
e3 = eigs[2];
|
|
|
|
e4 = eigs[3];
|
|
|
|
|
|
|
|
ci[0] = 0.5 * (K1(en, e3, e1) * (
|
|
|
|
F(en, e3, e2, e2, e4) +
|
|
|
|
F(en, e4, e1, e2, e4) +
|
|
|
|
F(en, e3, e1, e2, e4)) +
|
|
|
|
K1(en, e4, e1) * (
|
|
|
|
F(en, e4, e1, e2, e3) +
|
|
|
|
F(en, e4, e2, e2, e3) +
|
|
|
|
F(en, e3, e1, e2, e3)));
|
|
|
|
|
|
|
|
ci[1] = 0.5 * (K1(en, e3, e2) * (
|
|
|
|
F(en, e3, e2, e1, e4) +
|
|
|
|
F(en, e4, e2, e1, e4) +
|
|
|
|
F(en, e3, e1, e1, e4)) +
|
|
|
|
K1(en, e4, e2) * (
|
|
|
|
F(en, e3, e2, e1, e3) +
|
|
|
|
F(en, e4, e1, e1, e3) +
|
|
|
|
F(en, e4, e2, e1, e3)));
|
|
|
|
|
|
|
|
ci[2] = 0.5 * (-K1(en, e2, e3) * (
|
|
|
|
F(en, e3, e2, e1, e4) +
|
|
|
|
F(en, e4, e2, e1, e4) +
|
|
|
|
F(en, e3, e1, e1, e4)) -
|
|
|
|
K1(en, e1, e3) * (
|
|
|
|
F(en, e3, e2, e2, e4) +
|
|
|
|
F(en, e4, e1, e2, e4) +
|
|
|
|
F(en, e3, e1, e2, e4)));
|
|
|
|
|
|
|
|
ci[3] = 0.5 * (-K1(en, e2, e4) * (
|
|
|
|
F(en, e3, e2, e1, e3) +
|
|
|
|
F(en, e4, e1, e1, e3) +
|
|
|
|
F(en, e4, e2, e1, e3)) -
|
|
|
|
K1(en, e1, e4) * (
|
|
|
|
F(en, e4, e1, e2, e3) +
|
|
|
|
F(en, e4, e2, e2, e3) +
|
|
|
|
F(en, e3, e1, e2, e3)));
|
|
|
|
}
|
|
|
|
|
|
|
|
static void fun_dos_case3(double en, double *eigs, double *ci)
|
|
|
|
{
|
|
|
|
double e1, e2, e3, e4;
|
|
|
|
|
|
|
|
// if(fabs(eigs[3] - eigs[2]) < tol)
|
|
|
|
// {
|
|
|
|
// for(i = 0; i < 4; i++) ci[i] = 0.0;
|
|
|
|
// return;
|
|
|
|
// }
|
|
|
|
|
|
|
|
e1 = eigs[0];
|
|
|
|
e2 = eigs[1];
|
|
|
|
e3 = eigs[2];
|
|
|
|
e4 = eigs[3];
|
|
|
|
|
|
|
|
ci[0] = K1(en, e4, e1) * F(en, e4, e4, e2, e3);
|
|
|
|
|
|
|
|
ci[1] = K1(en, e4, e2) * F(en, e4, e4, e1, e3);
|
|
|
|
|
|
|
|
ci[2] = K1(en, e4, e3) * F(en, e4, e4, e1, e2);
|
|
|
|
|
|
|
|
ci[3] = -K2(en, e4, e3, e1) * F(en, e4, e3, e2, e4) -
|
|
|
|
K2(en, e4, e2, e3) * F(en, e4, e2, e1, e4) -
|
|
|
|
K2(en, e4, e1, e2) * F(en, e4, e1, e3, e4);
|
|
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
static double F(double en, double e1, double e2, double e3, double e4)
|
|
|
|
{
|
|
|
|
double complex s;
|
|
|
|
|
|
|
|
if(fabs(e1 - e3) > tol && fabs(e4 - e2) > tol)
|
|
|
|
return (e1 - en) * (en - e2) / ((e1 - e3) * (e4 - e2));
|
|
|
|
else
|
|
|
|
{
|
|
|
|
s = fmin(fabs(e3 - e1), fabs(e4 - e2));
|
|
|
|
s /= 100.0;
|
|
|
|
s = fmax(s, 1.0e-20) * I;
|
|
|
|
|
|
|
|
return creal((e1 - en + s) * (en - e2 + s) / ((e1 - e3 + s) * (e4 - e2 + s)));
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
static double K2(double en, double e1, double e2, double e3)
|
|
|
|
{
|
|
|
|
double complex s;
|
|
|
|
|
|
|
|
if(fabs(e1 - e3) > tol && fabs(e1 - e2) > tol)
|
|
|
|
return (en - e1) / ((e2 - e1) * (e3 - e1));
|
|
|
|
else
|
|
|
|
{
|
|
|
|
s = fmin(fabs(e3 - e1), fabs(e1 - e2));
|
|
|
|
s /= 100.0;
|
|
|
|
s = fmax(s, 1.0e-20) * I;
|
|
|
|
|
|
|
|
return creal((en - e1 + s) / ((e2 - e1 + s) * (e3 - e1 + s)));
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
static double K1(double en, double e1, double e2)
|
|
|
|
{
|
|
|
|
double complex s;
|
|
|
|
|
|
|
|
if(fabs(e1 - e2) > tol)
|
|
|
|
return (e1 - en) / ((e2 - e1) * (e2 - e1));
|
|
|
|
else
|
|
|
|
{
|
|
|
|
s = fabs(e1 - e2);
|
|
|
|
s /= 100.0;
|
|
|
|
s = fmax(s, 1.0e-20) * I;
|
|
|
|
|
|
|
|
return creal((e1 - en + s) / ((e2 - e1 + s) * (e2 - e1 + s)));
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|