add optimised "chaos" benchmark

Demos/benchmarks/chaos.pxd

+
+cimport cython
+
+cdef extern from "math.h":
+    cpdef double sqrt(double x)
+
+@cython.final
+cdef class GVector:
+    cdef public double x, y, z
+
+    cpdef double Mag(self)
+    cpdef double dist(self, GVector other)
+
+
+cpdef list GetKnots(list points, long degree)
+
+
+@cython.final
+cdef class Spline:
+    cdef list knots
+    cdef list points
+    cdef long degree
+
+    cpdef (long, long) GetDomain(self)
+    cpdef long GetIndex(self, u)
+
+
+@cython.final
+cdef class Chaosgame:
+    cdef list splines
+    cdef double thickness
+    cdef double minx, miny, maxx, maxy, height, width
+    cdef list num_trafos
+    cdef double num_total
+
+    cpdef tuple get_random_trafo(self)
+    cpdef GVector transform_point(self, GVector point, trafo=*)
+    cpdef truncate(self, GVector point)
+    cpdef create_image_chaos(self, timer, long w, long h, long n)

Demos/benchmarks/chaos.py

+#   Copyright (C) 2005 Carl Friedrich Bolz
+
+"""create chaosgame-like fractals
+"""
+
+from __future__ import division, print_function
+
+import cython
+
+import time
+import operator
+import optparse
+import random
+random.seed(1234)
+
+from functools import reduce
+
+if not cython.compiled:
+    from math import sqrt
+
+
+class GVector(object):
+    def __init__(self, x = 0, y = 0, z = 0):
+        self.x = x
+        self.y = y
+        self.z = z
+
+    def Mag(self):
+        return sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
+
+    def dist(self, other):
+        return sqrt((self.x - other.x) ** 2 +
+                    (self.y - other.y) ** 2 +
+                    (self.z - other.z) ** 2)
+
+    @cython.locals(self="GVector", other="GVector")
+    def __add__(self, other):
+        if not isinstance(other, GVector):
+            raise ValueError("Can't add GVector to " + str(type(other)))
+        v = GVector(self.x + other.x, self.y + other.y, self.z + other.z)
+        return v
+
+    @cython.locals(self="GVector", other="GVector")
+    def __sub__(self, other):
+        return self + other * -1
+
+    @cython.locals(self="GVector", other=cython.double)
+    def __mul__(self, other):
+        v = GVector(self.x * other, self.y * other, self.z * other)
+        return v
+    __rmul__ = __mul__
+
+    @cython.locals(other="GVector", l1=cython.double, l2_=cython.double)
+    def linear_combination(self, other, l1, l2=None):
+        l2_ = 1 - l1 if l2 is None else l2
+        v = GVector(self.x * l1 + other.x * l2_,
+                    self.y * l1 + other.y * l2_,
+                    self.z * l1 + other.z * l2_)
+        return v
+
+    def __str__(self):
+        return "<%f, %f, %f>" % (self.x, self.y, self.z)
+
+    def __repr__(self):
+        return "GVector(%f, %f, %f)" % (self.x, self.y, self.z)
+
+
+def GetKnots(points, degree):
+    knots = [0] * degree + range(1, len(points) - degree)
+    knots += [len(points) - degree] * degree
+    return knots
+
+
+class Spline(object):
+    """Class for representing B-Splines and NURBS of arbitrary degree"""
+    def __init__(self, points, degree = 3, knots = None):
+        """Creates a Spline. points is a list of GVector, degree is the degree of the Spline."""
+        if knots is None:
+            self.knots = GetKnots(points, degree)
+        else:
+            if len(points) > len(knots) - degree + 1:
+                raise ValueError("too many control points")
+            elif len(points) < len(knots) - degree + 1:
+                raise ValueError("not enough control points")
+            last = knots[0]
+            for cur in knots[1:]:
+                if cur < last:
+                    raise ValueError("knots not strictly increasing")
+                last = cur
+            self.knots = knots
+        self.points = points
+        self.degree = degree
+
+    def GetDomain(self):
+        """Returns the domain of the B-Spline"""
+        return (self.knots[self.degree - 1],
+                self.knots[len(self.knots) - self.degree])
+
+    @cython.locals(ik=cython.long, ii=cython.long, I=cython.long,
+                   ua=cython.long, ub=cython.long, u=cython.double)
+    def __call__(self, u):
+        """Calculates a point of the B-Spline using de Boors Algorithm"""
+        dom = self.GetDomain()
+        if u < dom[0] or u > dom[1]:
+            raise ValueError("Function value not in domain")
+        if u == dom[0]:
+            return self.points[0]
+        if u == dom[1]:
+            return self.points[-1]
+        I = self.GetIndex(u)
+        d = [self.points[I - self.degree + 1 + ii]
+             for ii in range(self.degree + 1)]
+        U = self.knots
+        for ik in range(1, self.degree + 1):
+            for ii in range(I - self.degree + ik + 1, I + 2):
+                ua = U[ii + self.degree - ik]
+                ub = U[ii - 1]
+                co1 = (ua - u) / (ua - ub)
+                co2 = (u - ub) / (ua - ub)
+                index = ii - I + self.degree - ik - 1
+                d[index] = d[index].linear_combination(d[index + 1], co1, co2)
+        return d[0]
+
+    @cython.locals(ii=cython.long, I=cython.long)
+    def GetIndex(self, u):
+        dom = self.GetDomain()
+        for ii in range(self.degree - 1, len(self.knots) - self.degree):
+            if self.knots[ii] <= u < self.knots[ii + 1]:
+                I = ii
+                break
+        else:
+             I = dom[1] - 1
+        return I
+
+    def __len__(self):
+        return len(self.points)
+
+    def __repr__(self):
+        return "Spline(%r, %r, %r)" % (self.points, self.degree, self.knots)
+
+
+class Chaosgame(object):
+    @cython.locals(splines=list, thickness=cython.double, maxlength=cython.double, length=cython.double,
+                   curr=GVector, last=GVector, p=GVector, spl=Spline, t=cython.double, i=int)
+    def __init__(self, splines, thickness=0.1):
+        self.splines = splines
+        self.thickness = thickness
+        self.minx = min([p.x for spl in splines for p in spl.points])
+        self.miny = min([p.y for spl in splines for p in spl.points])
+        self.maxx = max([p.x for spl in splines for p in spl.points])
+        self.maxy = max([p.y for spl in splines for p in spl.points])
+        self.height = self.maxy - self.miny
+        self.width = self.maxx - self.minx
+        self.num_trafos = []
+        maxlength = thickness * self.width / self.height
+        for spl in splines:
+            length = 0
+            curr = spl(0)
+            for i in range(1, 1000):
+                last = curr
+                t = 1 / 999 * i
+                curr = spl(t)
+                length += curr.dist(last)
+            self.num_trafos.append(max(1, int(length / maxlength * 1.5)))
+        self.num_total = reduce(operator.add, self.num_trafos, 0)
+
+    def get_random_trafo(self):
+        r = random.randrange(int(self.num_total) + 1)
+        l = 0
+        for i in range(len(self.num_trafos)):
+            if l <= r < l + self.num_trafos[i]:
+                return i, random.randrange(self.num_trafos[i])
+            l += self.num_trafos[i]
+        return len(self.num_trafos) - 1, random.randrange(self.num_trafos[-1])
+
+    @cython.locals(neighbour="GVector", basepoint="GVector", derivative="GVector",
+                   seg_length=cython.double, start=cython.double, end=cython.double,
+                   t=cython.double)
+    def transform_point(self, point, trafo=None):
+        x = (point.x - self.minx) / self.width
+        y = (point.y - self.miny) / self.height
+        if trafo is None:
+            trafo = self.get_random_trafo()
+        start, end = self.splines[trafo[0]].GetDomain()
+        length = end - start
+        seg_length = length / self.num_trafos[trafo[0]]
+        t = start + seg_length * trafo[1] + seg_length * x
+        basepoint = self.splines[trafo[0]](t)
+        if t + 1/50000 > end:
+            neighbour = self.splines[trafo[0]](t - 1/50000)
+            derivative = neighbour - basepoint
+        else:
+            neighbour = self.splines[trafo[0]](t + 1/50000)
+            derivative = basepoint - neighbour
+        if derivative.Mag() != 0:
+            basepoint.x += derivative.y / derivative.Mag() * (y - 0.5) * \
+                           self.thickness
+            basepoint.y += -derivative.x / derivative.Mag() * (y - 0.5) * \
+                           self.thickness
+        else:
+            print("r", end='')
+        self.truncate(basepoint)
+        return basepoint
+
+    def truncate(self, point):
+        if point.x >= self.maxx:
+            point.x = self.maxx
+        if point.y >= self.maxy:
+            point.y = self.maxy
+        if point.x < self.minx:
+            point.x = self.minx
+        if point.y < self.miny:
+            point.y = self.miny
+
+    def create_image_chaos(self, timer, w, h, n):
+        im = [[1] * h for i in range(w)]
+        point = GVector((self.maxx + self.minx) / 2,
+                        (self.maxy + self.miny) / 2, 0)
+        times = []
+        for _ in range(n):
+            t1 = timer()
+            for i in range(5000):
+                point = self.transform_point(point)
+                x = (point.x - self.minx) / self.width * w
+                y = (point.y - self.miny) / self.height * h
+                x = int(x)
+                y = int(y)
+                if x == w:
+                    x -= 1
+                if y == h:
+                    y -= 1
+                im[x][h - y - 1] = 0
+            t2 = timer()
+            times.append(t2 - t1)
+        return times
+
+
+def main(n, timer=time.time):
+    splines = [
+        Spline([
+            GVector(1.597350, 3.304460, 0.000000),
+            GVector(1.575810, 4.123260, 0.000000),
+            GVector(1.313210, 5.288350, 0.000000),
+            GVector(1.618900, 5.329910, 0.000000),
+            GVector(2.889940, 5.502700, 0.000000),
+            GVector(2.373060, 4.381830, 0.000000),
+            GVector(1.662000, 4.360280, 0.000000)],
+            3, [0, 0, 0, 1, 1, 1, 2, 2, 2]),
+        Spline([
+            GVector(2.804500, 4.017350, 0.000000),
+            GVector(2.550500, 3.525230, 0.000000),
+            GVector(1.979010, 2.620360, 0.000000),
+            GVector(1.979010, 2.620360, 0.000000)],
+            3, [0, 0, 0, 1, 1, 1]),
+        Spline([
+            GVector(2.001670, 4.011320, 0.000000),
+            GVector(2.335040, 3.312830, 0.000000),
+            GVector(2.366800, 3.233460, 0.000000),
+            GVector(2.366800, 3.233460, 0.000000)],
+            3, [0, 0, 0, 1, 1, 1])
+        ]
+    c = Chaosgame(splines, 0.25)
+    return c.create_image_chaos(timer, 1000, 1200, n)
+
+
+if __name__ == "__main__":
+    import util
+    parser = optparse.OptionParser(
+        usage="%prog [options]",
+        description="Test the performance of the Chaos benchmark")
+    util.add_standard_options_to(parser)
+    options, args = parser.parse_args()
+
+    util.run_benchmark(options, options.num_runs, main)