:orphan:

diff
----


Solving The 2D Diffusion Equation

.. raw:: html

  <video width="558" height="558" controls autoplay>
    <source src="../_static/examples/diff.mov" type="video/mp4">
    <source src="../_static/examples/diff.ogg" type="video/ogg">
  </video>

----

.. code-block:: python
    
    
    
    import numpy
    import gr
    from numba.core.decorators import jit
    
    try:
        from time import perf_counter
    except ImportError:
        from time import clock as perf_counter
    
    dx = 0.005
    dy = 0.005
    a = 0.5
    dt = dx*dx*dy*dy/(2*a*(dx*dx+dy*dy))
    timesteps = 150
    
    nx = int(1/dx)
    ny = int(1/dy)
    ui = numpy.zeros([nx,ny])
    u = numpy.zeros([nx,ny])
    
    for i in range(nx):
        for j in range(ny):
            if ((i*dx-0.5)**2+(j*dy-0.5)**2 <= 0.1) and ((i*dx-0.5)**2+(j*dy-0.5)**2 >= 0.05):
                ui[i,j] = 1
    
    
    def diff_step(u, ui):
        for i in range(1, nx-1):
            for j in range(1, ny-1):
                uxx = (ui[i+1,j] - 2*ui[i,j] + ui[i-1, j]) / (dx*dx)
                uyy = (ui[i,j+1] - 2*ui[i,j] + ui[i, j-1]) / (dy*dy)
                u[i,j] = ui[i,j]+dt*a*(uxx+uyy)
    
    diff_step_numba = jit('void(f8[:,:], f8[:,:])')(diff_step)
    
    now = perf_counter()
    
    t = 0
    worker = 'CPython'
    
    for m in range(timesteps):
        gr.clearws()
    
        start = now
        if t > 5:
            diff_step_numba(u, ui)
            worker = 'Numba'
        else:
            diff_step(u, ui)
        ui = numpy.copy(u)
        now = perf_counter()
        t = t + now - start
    
        c = 1000 + 255 * u.ravel()
        gr.setviewport(0, 1, 0, 1)
        gr.setcolormap(-32)
        gr.cellarray(0, 1, 0, 1, nx, ny, c)
        gr.text(0.01, 0.95, '%10s: %7.2f fps' % (worker, 1.0 / (now - start)))
        gr.updatews()