Mandelbrot using GPU and two CPU variants

Calculate the Mandelbrot set, display it in a Tkinter window. You can choose to use the GPU (ElementwiseKernel) for the calculation or two numpy CPU solutions. Timing results are shown in the code. [[!table header="no" class="mointable" data=""" License of this example: | GPL Date: | July 2010 PyCUDA version: | 0.94 """]]

# Mandelbrot calculate using GPU, Serial numpy and faster numpy
# Use to show the speed difference between CPU and GPU calculations
# July 2010

# Based on vegaseat's TKinter/numpy example code from 2006
# with minor changes to move to numpy from the obsolete Numeric

import sys
import numpy as nm

import Tkinter as tk
import Image          # PIL
import ImageTk        # PIL

import pycuda.driver as drv
import pycuda.autoinit
from pycuda.compiler import SourceModule
import pycuda.gpuarray as gpuarray

# set width and height of window, more pixels take longer to calculate
w = 1000
h = 1000

from pycuda.elementwise import ElementwiseKernel
complex_gpu = ElementwiseKernel(
        "pycuda::complex<float> *z, pycuda::complex<float> *q, int *iteration, int maxiter",
            "for (int n=0; n < maxiter; n++) {z[i] = (z[i]*z[i])+q[i]; if (abs(z[i]) > 2.0f) {iteration[i]=n; z[i] = pycuda::complex<float>(); q[i] = pycuda::complex<float>();};}",
        preamble="#include <pycuda-complex.hpp>",)

def calculate_z_gpu(q, maxiter, z):
    output = nm.resize(nm.array(0,), q.shape)
    q_gpu = gpuarray.to_gpu(q.astype(nm.complex64))
    z_gpu = gpuarray.to_gpu(z.astype(nm.complex64))
    iterations_gpu = gpuarray.to_gpu(output)
    # the for loop and complex calculations are all done on the GPU
    # we bring the iterations_gpu array back to determine pixel colours later
    complex_gpu(z_gpu, q_gpu, iterations_gpu, maxiter)

    iterations = iterations_gpu.get()
    return iterations

def calculate_z_numpy_gpu(q, maxiter, z):
    """Calculate z using numpy on the GPU via gpuarray"""
    outputg = gpuarray.to_gpu(nm.resize(nm.array(0,), q.shape).astype(nm.int32))
    zg = gpuarray.to_gpu(z.astype(nm.complex64))
    qg = gpuarray.to_gpu(q.astype(nm.complex64))
    # 2.0 as an array
    twosg = gpuarray.to_gpu(nm.array([2.0]*zg.size).astype(nm.float32))
    # 0+0j as an array
    cmplx0sg = gpuarray.to_gpu(nm.array([0+0j]*zg.size).astype(nm.complex64))
    # for abs_zg > twosg result
    comparison_result = gpuarray.to_gpu(nm.array([False]*zg.size).astype(nm.bool))
    # we'll add 1 to iterg after each iteration
    iterg = gpuarray.to_gpu(nm.array([0]*zg.size).astype(nm.int32))

    for iter in range(maxiter):
        zg = zg*zg + qg

        # abs returns a complex (rather than a float) from the complex
        # input where the real component is the absolute value (which
        # looks like a bug) so I take the .real after abs()
        abs_zg = abs(zg).real

        comparison_result = abs_zg > twosg
        qg = gpuarray.if_positive(comparison_result, cmplx0sg, qg)
        zg = gpuarray.if_positive(comparison_result, cmplx0sg, zg)
        outputg = gpuarray.if_positive(comparison_result, iterg, outputg)
        iterg = iterg + 1
    output = outputg.get()
    return output

def calculate_z_numpy(q, maxiter, z):
    # calculate z using numpy, this is the original
    # routine from vegaseat's URL
    # NOTE this routine was faster using a default of double-precision complex nbrs
    # rather than the current single precision
    output = nm.resize(nm.array(0,), q.shape).astype(nm.int32)
    for iter in range(maxiter):
        z = z*z + q
        done = nm.greater(abs(z), 2.0)
        q = nm.where(done,0+0j, q)
        z = nm.where(done,0+0j, z)
        output = nm.where(done, iter, output)
    return output

def calculate_z_serial(q, maxiter, z):
    # calculate z using pure python with numpy arrays
    # this routine unrolls calculate_z_numpy as an intermediate
    # step to the creation of calculate_z_gpu
    # it runs slower than calculate_z_numpy
    output = nm.resize(nm.array(0,), q.shape).astype(nm.int32)
    for i in range(len(q)):
        if i % 100 == 0:
            # print out some progress info since it is so slow...
            print "%0.2f%% complete" % (1.0/len(q) * i * 100)
        for iter in range(maxiter):
            z[i] = z[i]*z[i] + q[i]
            if abs(z[i]) > 2.0:
                q[i] = 0+0j
                z[i] = 0+0j
                output[i] = iter
    return output

show_instructions = False
if len(sys.argv) == 1:
    show_instructions = True

if len(sys.argv) > 1:
    if sys.argv[1] not in ['gpu', 'gpuarray', 'numpy', 'python']:
        show_instructions = True

if show_instructions:
    print "Usage: python [gpu|gpuarray|numpy|python]"
    print "Where:"
    print " gpu is a pure CUDA solution on the GPU"
    print " gpuarray uses a numpy-like CUDA wrapper in Python on the GPU"
    print " numpy is a pure Numpy (C-based) solution on the CPU"
    print " python is a pure Python solution on the CPU with numpy arrays"

routine = {'gpuarray':calculate_z_numpy_gpu,

calculate_z = routine[sys.argv[1]]
##if sys.argv[1] == 'python':
#    import psyco
#    psyco.full()

# Using a WinXP Intel Core2 Duo 2.66GHz CPU (1 CPU used)
# with a 9800GT GPU I get the following timings (smaller is better).
# With 200x200 problem with max iterations set at 300:
# calculate_z_gpu: 0.03s
# calculate_z_serial: 8.7s
# calculate_z_numpy: 0.3s
# Using WinXP Intel 2.9GHz CPU (1 CPU used)
# with a GTX 480 GPU I get the following using 1000x1000 plot with 1000 max iterations:
# gpu: 0.07s
# gpuarray: 3.4s
# numpy: 43.4s
# python (serial): 1605.6s

class Mandelbrot(object):
    def __init__(self):
        # create window
        self.root = tk.Tk()
        self.root.title("Mandelbrot Set")
        # start event loop

    def draw(self, x1, x2, y1, y2, maxiter=300):
        # draw the Mandelbrot set, from numpy example
        xx = nm.arange(x1, x2, (x2-x1)/w*2)
        yy = nm.arange(y2, y1, (y1-y2)/h*2) * 1j
        # force yy, q and z to use 32 bit floats rather than
        # the default 64 doubles for nm.complex for consistency with CUDA
        yy = yy.astype(nm.complex64)
        q = nm.ravel(xx+yy[:, nm.newaxis]).astype(nm.complex64)
        z = nm.zeros(q.shape, nm.complex64)

        start_main = drv.Event()
        end_main  = drv.Event()
        output = calculate_z(q, maxiter, z)

        secs = start_main.time_till(end_main)*1e-3
        print "Main took", secs

        output = (output + (256*output) + (256**2)*output) * 8
        # convert output to a string
        self.mandel = output.tostring()

    def create_image(self):
        create the image from the draw() string
        """ ="RGB", (w/2, h/2))
        # you can experiment with these x and y ranges
        self.draw(-2.13, 0.77, -1.3, 1.3, 1000), "raw", "RGBX", 0, -1)

    def create_label(self):
        # put the image on a label widget
        self.image = ImageTk.PhotoImage(
        self.label = tk.Label(self.root, image=self.image)

# test the class
if __name__ == '__main__':
    test = Mandelbrot()