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10 Commits
Author | SHA1 | Date | |
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a9450179be | |||
be0e67e954 | |||
26acc9802d | |||
609c9c3d1a | |||
1e9bc3209c | |||
fd6e4d6bc4 | |||
48b8ce8c88 | |||
da2fd89946 | |||
9580818204 | |||
1a9ddddc6d |
@@ -113,17 +113,13 @@ interaction_ufunc_float2D
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char * x_old = args[0]
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char * x_old = args[0]
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, * y_old = args[1]
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, * y_old = args[1]
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, * p_x_old = args[2]
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, * p_x_new = args[2]
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, * p_y_old = args[3]
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, * p_y_new = args[3];
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, * p_x_new = args[4]
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, * p_y_new = args[5];
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npy_intp x_old_steps = steps[0]
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npy_intp x_old_steps = steps[0]
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, y_old_steps = steps[1]
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, y_old_steps = steps[1]
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, p_x_old_steps = steps[2]
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, p_x_new_steps = steps[2]
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, p_y_old_steps = steps[3]
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, p_y_new_steps = steps[3];
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, p_x_new_steps = steps[4]
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, p_y_new_steps = steps[5];
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float * coefficients = (float *) data;
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float * coefficients = (float *) data;
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float dt = coefficients[19];
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float dt = coefficients[19];
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@@ -133,7 +129,7 @@ interaction_ufunc_float2D
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// Stuff we will need:
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// Stuff we will need:
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float r; // Distance between interacting particles.
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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 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_y_e; // y-component of unit direction vector.
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float delta_p_x;
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float delta_p_x;
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float delta_p_y;
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float delta_p_y;
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@@ -151,10 +147,8 @@ interaction_ufunc_float2D
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this_x_i = *(float *)(x_old + i*x_old_steps);
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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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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) = 0;
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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) = 0;
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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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// compute and add the momentum offset
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for(j = 0; j < i; j++)
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for(j = 0; j < i; j++)
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{
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{
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@@ -168,7 +162,7 @@ interaction_ufunc_float2D
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if(r > 0)
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if(r > 0)
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{
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{
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delta_x_e = (this_x_i - this_x_j) / r;
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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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delta_y_e = (this_y_i - this_y_j) / r;
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}
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}
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else
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else
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{
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{
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@@ -178,13 +172,13 @@ interaction_ufunc_float2D
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printf("Warning: corrected r = 0 with random angle pi*%f\n", random_angle / M_PI);
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printf("Warning: corrected r = 0 with random angle pi*%f\n", random_angle / M_PI);
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#endif
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#endif
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delta_x_e = cosf(random_angle);
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delta_x_e = cosf(random_angle);
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delty_y_e = sinf(random_angle);
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delta_y_e = sinf(random_angle);
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}
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}
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// Update the momenta.
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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_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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delta_p_y = delta_y_e * interaction_force_function(r, coefficients);
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#ifdef WARN_NAN_OCCUR
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#ifdef WARN_NAN_OCCUR
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if(isnan(delta_p_x))
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if(isnan(delta_p_x))
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{
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{
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@@ -205,7 +199,7 @@ interaction_ufunc_float2D
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//NPY_END_THREADS;
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//NPY_END_THREADS;
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}
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}
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static char interaction_types[] =
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static char interaction_types[] =
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{ NPY_FLOAT, NPY_FLOAT, NPY_FLOAT, NPY_FLOAT, NPY_FLOAT, NPY_FLOAT};
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{ NPY_FLOAT, NPY_FLOAT, NPY_FLOAT, NPY_FLOAT};
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static char force_types[] =
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static char force_types[] =
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{ NPY_FLOAT, NPY_FLOAT};
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{ NPY_FLOAT, NPY_FLOAT};
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static char potential_types[] =
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static char potential_types[] =
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@@ -298,9 +292,9 @@ interaction_UFuncWrapper_init
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interaction_funcs
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interaction_funcs
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, self->data
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, self->data
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, interaction_types
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, interaction_types
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, 1
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, 1 // ntypes
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, 4
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, 2 // nin
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, 2
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, 2 // nout
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, PyUFunc_None
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, PyUFunc_None
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, "interaction2D"
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, "interaction2D"
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, "Update the momenta according to the given coefficients and positions"
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, "Update the momenta according to the given coefficients and positions"
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@@ -10,7 +10,7 @@ c = np.array(
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, 1 # *c*exp(
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, 1 # *c*exp(
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, -0.7 # c
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, -0.7 # c
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, 0 # (r - c))
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, 0 # (r - c))
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, 0 # + c*exp(
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, +5 # + c*exp(
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, -.1 # c
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, -.1 # c
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, 2 # (r - c))
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, 2 # (r - c))
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, -0 # + c*exp(
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, -0 # + c*exp(
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3
force.py
3
force.py
@@ -4,9 +4,12 @@ import matplotlib.pyplot as plt
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from coefficients import c
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from coefficients import c
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# This is the quite unreadable way to create
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# UFuncs with given parameters. FIXME: add this to another module.
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force_function = UFuncWrapper(0, c)
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force_function = UFuncWrapper(0, c)
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potential_function = UFuncWrapper(2, c)
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potential_function = UFuncWrapper(2, c)
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# Plot the force and potential.
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r = np.arange(0, 100, 0.02, dtype=np.float16)
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r = np.arange(0, 100, 0.02, dtype=np.float16)
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f, = plt.plot(r, force_function(r), label="force")
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f, = plt.plot(r, force_function(r), label="force")
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p, = plt.plot(r, potential_function(r), label="potential")
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p, = plt.plot(r, potential_function(r), label="potential")
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19
particles.py
19
particles.py
@@ -11,23 +11,34 @@ from coefficients import c
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#force_function = UFuncWrapper(0, c)
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#force_function = UFuncWrapper(0, c)
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#interaction2D = UFuncWrapper(1, c)
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#interaction2D = UFuncWrapper(1, c)
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# Borders for both the plot and the boundary condition
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# (the boundary condition might be deactivated, when creating
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# the BrownIterator).
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borders_x = [-100, 100]
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borders_x = [-100, 100]
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borders_y = [-100, 100]
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borders_y = [-100, 100]
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n_particles = 600
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n_particles = 600
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# Idk, seems to not do anyting.
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frames = 100
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frames = 100
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# Only spawn in 1/x of the borders.
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spawn_restriction = 3
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spawn_restriction = 3
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# Time resolution. Note that setting this to a too
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# high value (i.e. low resolution) will lead to
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# erratic behaviour, because potentials can be skipped.
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dt = 0.1
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dt = 0.1
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c[-1] = dt
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c[-1] = dt
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# Initial positions.
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x_coords = np.random.uniform(borders_x[0] / spawn_restriction, borders_x[1] / spawn_restriction, n_particles).astype(np.float16)
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x_coords = np.random.uniform(borders_x[0] / spawn_restriction, borders_x[1] / spawn_restriction, n_particles).astype(np.float16)
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y_coords = np.random.uniform(borders_y[0] / spawn_restriction, borders_y[1] / spawn_restriction, n_particles).astype(np.float16)
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y_coords = np.random.uniform(borders_y[0] / spawn_restriction, borders_y[1] / spawn_restriction, n_particles).astype(np.float16)
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# Initial momenta are 0.
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x_momenta = np.zeros(n_particles, dtype=np.float16)
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x_momenta = np.zeros(n_particles, dtype=np.float16)
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y_momenta = np.zeros(n_particles, dtype=np.float16)
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y_momenta = np.zeros(n_particles, dtype=np.float16)
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# Prepare the plot, remove axis & stuff.
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fig = plt.figure(figsize=(7, 7))
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fig = plt.figure(figsize=(7, 7))
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ax = fig.add_axes([0, 0, 1, 1], frameon=False)
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ax = fig.add_axes([0, 0, 1, 1], frameon=False)
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ax.set_xlim(*borders_x)
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ax.set_xlim(*borders_x)
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@@ -35,22 +46,28 @@ ax.set_xticks([])
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ax.set_ylim(*borders_y)
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ax.set_ylim(*borders_y)
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ax.set_yticks([])
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ax.set_yticks([])
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# Plot the initial values.
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plot, = ax.plot(x_coords, y_coords, "b.")
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plot, = ax.plot(x_coords, y_coords, "b.")
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center_of_mass, = ax.plot(x_coords.mean(), y_coords.mean(), "r-")
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center_of_mass, = ax.plot(x_coords.mean(), y_coords.mean(), "r-")
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# Keep track of the center of mass.
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center_of_mass_history_x = deque([x_coords.mean()])
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center_of_mass_history_x = deque([x_coords.mean()])
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center_of_mass_history_y = deque([y_coords.mean()])
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center_of_mass_history_y = deque([y_coords.mean()])
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brown = BrownIterator(-1, c
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brown = BrownIterator(-1, c # Max iterations, simulation parameters.
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, x_coords, y_coords
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, x_coords, y_coords
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, y_momenta, y_momenta
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, y_momenta, y_momenta
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# The boundary condition: reflect at the borders,
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, borders_x, borders_y
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, borders_x, borders_y
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# or just let propagate to infinity.
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#, [], []
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#, [], []
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# Let the border dampen the system, border_dampening < 1 => energy is absorbed.
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, border_dampening=1
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, border_dampening=1
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, dt=dt)
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, dt=dt)
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u = iter(brown)
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u = iter(brown)
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def update(i):
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def update(i):
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# Get the next set of positions.
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data = next(u)
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data = next(u)
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center_of_mass_history_x.append(x_coords.mean())
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center_of_mass_history_x.append(x_coords.mean())
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center_of_mass_history_y.append(y_coords.mean())
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center_of_mass_history_y.append(y_coords.mean())
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@@ -37,11 +37,15 @@ class BrownIterator(object):
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if(self._i == 1):
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if(self._i == 1):
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return self.x, self.y
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return self.x, self.y
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self.px, self.py = self._interaction(self.x, self.y, self.px, self.py)
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delta_px, delta_py = self._interaction(self.x, self.y)
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self.px = delta_px + self.px
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self.py = delta_py + self.py
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# XXX: We need the (-1)**i to make the problem
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# XXX: We need the (-1)**i to make the problem
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# symmetric.
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# symmetric.
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# FIXME: is this necessary?
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self.px[np.isnan(self.px)] = self.speed_of_light * (-1)**self._i
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self.px[np.isnan(self.px)] = self.speed_of_light * (-1)**self._i
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self.py[np.isnan(self.py)] = self.speed_of_light * (-1)**self._i
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self.py[np.isnan(self.py)] = self.speed_of_light * (-1)**self._i
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self._reflect_at_borders()
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self._reflect_at_borders()
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self.x += self.dt * self.px
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self.x += self.dt * self.px
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