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#include "interaction.h"
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#include "math.h"
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#define raise2(x) (x)*(x)
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static float
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interaction_force_function
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( float r
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, float * coefficients)
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{
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float result = 0;
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int i;
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for(i = 0; i < 7; i++)
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{
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result += coefficients[i] * powf(r, i);
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}
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result *= coefficients[7] * expf(coefficients[8] * (r - coefficients[9]));
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result += coefficients[10] * expf(coefficients[11] * (r - coefficients[12]));
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result += coefficients[13] * expf(coefficients[14] * raise2(r - coefficients[15]));
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result += coefficients[16] * expf(coefficients[17] * raise2(r - coefficients[18]));
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return result;
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}
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static void
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interaction_ufunc_force
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( char ** args
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, npy_intp * dimensions
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, npy_intp * steps
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, void * data)
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{
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char * in = args[0]
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, * out = args[1]
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, * raw_coefficients = args[2];
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npy_intp n = dimensions[0];
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npy_intp in_step = steps[0]
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, out_step = steps[1]
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, raw_coefficients_steps = steps[2];
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npy_intp i;
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// Copy the coefficients to a safe array.
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// This is because NumPy arrays are not
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// necessarily cast-safe.
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float coefficients[19];
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for(i = 0; i < 19; i++)
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{
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coefficients[i] = *(float *)raw_coefficients;
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raw_coefficients += raw_coefficients_steps;
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}
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for(i = 0; i < n; i++)
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{
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*(float *)out = interaction_force_function(*(float *)in, coefficients);
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out += out_step;
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in += in_step;
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}
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}
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static void
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interaction_ufunc_float2D
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( char ** args
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, npy_intp * dimensions
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, npy_intp * steps
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, void * data)
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{
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npy_intp i;
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npy_intp j;
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npy_intp n = dimensions[0];
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char * x_old = args[0]
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, * y_old = args[1]
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, * p_x_old = args[2]
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, * p_y_old = args[3]
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, * raw_coefficients = args[4]
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, * p_x_new = args[5]
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, * p_y_new = args[6];
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npy_intp x_old_steps = steps[0]
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, y_old_steps = steps[1]
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, p_x_old_steps = steps[2]
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, p_y_old_steps = steps[3]
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, raw_coefficients_steps = steps[4]
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, p_x_new_steps = steps[5]
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, p_y_new_steps = steps[6];
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// Copy the coefficients to a safe array.
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// This is because NumPy arrays are not
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// necessarily cast-safe.
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float coefficients[19];
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for(i = 0; i < 19; i++)
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{
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coefficients[i] = *(float *)raw_coefficients;
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raw_coefficients += raw_coefficients_steps;
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}
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// Compute the new momenta:
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// Stuff we will need:
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float r; // Distance between interacting particles.
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float delta_x_e; // x-component of unit direction vector.
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float delty_y_e; // y-component of unit direction vector.
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float delta_p_x;
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float delta_p_y;
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// The current x_old[i], y_old[i] coordinates.
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float this_x_i;
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float this_y_i;
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// The current x_old[j], y_old[j] coordinates.
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float this_x_j;
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float this_y_j;
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for(i = 0; i < n; i++)
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{
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this_x_i = *(float *)(x_old + i*x_old_steps);
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this_y_i = *(float *)(y_old + i*y_old_steps);
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// copy current momenta
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*(float *)(p_x_new + i*p_x_new_steps) = *(float *)(p_x_old + i*p_x_old_steps);
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*(float *)(p_y_new + i*p_y_new_steps) = *(float *)(p_y_old + i*p_y_old_steps);
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// compute and add the momentum offset
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for(j = 0; j < i; j++)
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{
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this_x_j = *(float *)(x_old + j*x_old_steps);
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this_y_j = *(float *)(y_old + j*y_old_steps);
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// Compute distance and direction between particles i,j.
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r = sqrtf(raise2(this_x_i - this_x_j) + raise2(this_y_i - this_y_j));
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delta_x_e = (this_x_i - this_x_j) / r;
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delty_y_e = (this_y_i - this_y_j) / r;
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// Update the momenta.
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delta_p_x = delta_x_e * interaction_force_function(r, coefficients);
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delta_p_y = delty_y_e * interaction_force_function(r, coefficients);
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*(float *)(p_x_new + i*p_x_new_steps) -= delta_p_x;
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*(float *)(p_y_new + i*p_y_new_steps) -= delta_p_y;
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*(float *)(p_x_new + j*p_x_new_steps) += delta_p_x;
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*(float *)(p_y_new + j*p_y_new_steps) += delta_p_y;
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}
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}
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}
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static PyMethodDef InteractionMethods[] = {
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{NULL, NULL, 0, NULL}
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};
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PyUFuncGenericFunction interaction_funcs[] =
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{ &interaction_ufunc_float2D};
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PyUFuncGenericFunction force_funcs[] =
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{ &interaction_ufunc_force};
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static char interaction_types[] =
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{ NPY_FLOAT, NPY_FLOAT, NPY_FLOAT, NPY_FLOAT, NPY_FLOAT, NPY_FLOAT, NPY_FLOAT};
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static char force_types[] =
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{ NPY_FLOAT, NPY_FLOAT, NPY_FLOAT};
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static void *interaction_data[] = {NULL};
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static void *force_data[] = {NULL};
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static struct PyModuleDef moduledef = {
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PyModuleDef_HEAD_INIT
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, "brown.interaction"
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, NULL
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, -1
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, InteractionMethods
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, NULL
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, NULL
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, NULL
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, NULL
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};
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PyMODINIT_FUNC
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PyInit_interaction(void)
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{
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PyObject * module
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, * ufunc_interaction
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, * ufunc_force
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, * dct;
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module = PyModule_Create(&moduledef);
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if(!module)
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{
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return NULL;
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}
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import_array();
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import_umath();
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ufunc_interaction = PyUFunc_FromFuncAndDataAndSignature(
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interaction_funcs
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, interaction_data
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, interaction_types
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, 1
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, 5
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, 2
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, PyUFunc_None
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, "interaction2D"
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, "Update the momenta according to the given coefficients and positions"
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, 0
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, "(n),(n),(n),(n),(19)->(n),(n)");
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ufunc_force = PyUFunc_FromFuncAndDataAndSignature(
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force_funcs
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, force_data
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, force_types
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, 1
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, 2
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, 1
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, PyUFunc_None
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, "force_function"
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, "computes the scalar force between two particles with given coefficients"
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, 0
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, "(n),(19)->(n)");
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dct = PyModule_GetDict(module);
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PyDict_SetItemString(dct, "interaction2D", ufunc_interaction);
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PyDict_SetItemString(dct, "force_function", ufunc_force);
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Py_DECREF(ufunc_interaction);
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Py_DECREF(ufunc_force);
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return module;
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}
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#ifndef interaction_h
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#define interaction_h
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#include <Python.h>
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#include <numpy/ndarraytypes.h>
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#include <numpy/ufuncobject.h>
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/*
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* This is a quite generic force function mapping a
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* distance to the magnitude of a force. The coefficients
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* are an array of length 19 and the force function
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* is given as:
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*
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* (c0 + c1*r + c2*r^2 + ... + c6*r^6) * c7 * exp(c8*(r - c9))
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* + c10 * exp(c11 * (r - c12))
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* + c13 * exp(c14 * (r - c15)^2)
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* + c16 * exp(c17 * (r - c18)^2)
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* */
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static float
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interaction_force_function
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( float r
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, float * coefficients);
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static void
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interaction_ufunc_float2D
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( char ** args
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, npy_intp * dimensions
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, npy_intp * steps
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, void * data);
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#endif
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#from distutils.core import setup, Extension
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#
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#
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#interaction = Extension("brown.interaction",
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# sources = ["c/interaction/interaction.c"])
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#
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#setup(name = "brown",
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# version = "0.0.1",
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# description = "Me playing around with single-atom classical gases",
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# ext_modules = [interaction],
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# packages = [
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# "brown"
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# ],
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# package_dir = {"brown": "py/brown"},
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# #url="https://github.com/daknuett/python3-nf",
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# author = "Daniel Knüttel",
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# author_email = "daniel.knuettel@daknuett.eu")
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def configuration(parent_package='', top_path=None):
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from numpy.distutils.misc_util import Configuration
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config = Configuration('brown'
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, parent_package
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, top_path)
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config.add_extension('interaction', ['c/interaction/interaction.c'])
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return config
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if __name__ == "__main__":
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from numpy.distutils.core import setup
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setup(configuration=configuration)
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from brown.interaction import interaction2D,force_function
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import numpy as np
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from collections import deque
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from copy import copy
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import matplotlib.pyplot as plt
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c = np.array([5, 10, 20, 0, 0, 0, 0, 1, -2, 0, -2, -0.1, 2, 0, 0, 0, 0, 0, 0], dtype=np.float16)
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x_coords = np.array([0, 1], dtype=np.float16)
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y_coords = np.array([0, 0], dtype=np.float16)
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x_momenta = np.array([0, 0], dtype=np.float16)
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y_momenta = np.array([0, 0], dtype=np.float16)
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time = np.arange(0, 5, 1, dtype=np.float16)
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time_evolution = deque()
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for t in time:
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x_momenta, y_momenta = interaction2D(x_coords, y_coords, x_momenta, y_momenta, c)
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x_coords += x_momenta
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y_coords += y_momenta
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time_evolution.append(copy(x_coords))
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time_evolution = np.array(time_evolution)
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particle_one_evolution = time_evolution[:, 0]
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particle_two_evolution = time_evolution[:, 1]
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#plt.subplot(2, 1, 1)
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r = np.arange(0, 0.5, 0.01, dtype=np.float16)
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plt.title("Force")
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plt.xlabel("particle distance")
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plt.ylabel("scalar force")
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plt.plot(r, force_function(r, c))
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#plt.subplot(2, 1, 2)
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#plt.title("Particle x-positions over time")
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#plt.xlabel("time")
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#plt.ylabel("particle x-position")
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#h0, = plt.plot(time, particle_one_evolution, label="particle 1")
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#h1, = plt.plot(time, particle_two_evolution, label="particle 2")
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#plt.legend(handles=[h0, h1])
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plt.show()
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