2046.sagews

%cython

print "Hi Math 480"

Hi Math 480

%cython

from math import sin

def f(x):
    return sin(x**2)

def integral(a, b, N):
    dx = (b-a)/N
    s = 0
    for i in range(N):
        s += f(a+dx*i)
    return s * dx

time integral(0.0, 1.0, 100000)

0.310264094377461 Time: CPU 1.50 s, Wall: 1.53 s

%cython

from math import sin

def f(x):
    return sin(x**2)

def integral(double a, double b, int N):
    cdef double dx = (b-a)/N
    cdef int i
    cdef double s = 0
    for i in range(N):
        s += f(a+dx*i)
    return s * dx

time integral(0.0, 1.0, 100000)

0.310264094377461 Time: CPU 0.06 s, Wall: 0.06 s

1.5 / .06

25.0000000000000

time integral(0.0, 1.0, 1000000)

0.31026788098798791 Time: CPU 0.58 s, Wall: 0.58 s

%cython

cdef extern from "math.h": # external library
    double sin(double)

cdef double f(double x):
    return sin(x**2)

def integral(double a, double b, int N):
    cdef double dx = (b-a)/N
    cdef int i
    cdef double s = 0
    for i in range(N):
        s += f(a+dx*i)
    return s * dx

time integral(0.0, 1.0, 100000000)

0.31026829751610591 Time: CPU 3.15 s, Wall: 3.17 s

(1.5 / 100000) / (3.15 / 100000000)

476.190476190476

numerical_integral(sin(x^2), 0, 1)

(0.31026830172338099, 3.444670123846427e-15)

%cython

def square(int i):
    return i*i

square(10^6)

-727379968

def square(i):
    return i*i

square(10^6)

1000000000000

%cython

cdef square_inplace(int* x):
    x[0] = x[0]**2

def call_square_inplace(int x):
    print "x is", x
    square_inplace(&x)
    print "x is", x

call_square_inplace(2)

x is 2 x is 4

class TwoNumbers:
    def __init__(self, a, b):
        self.a = a
        self.b = b
    def sum(self):
        return self.a + self.b
    def sum_a_lot(self, N):
        for i in range(N):
            self.sum()
    def __repr__(self):
        return "The numbers %s and %s" % (self.a, self.b)
    def __str__(self):
        return repr(self)

a = TwoNumbers(3, 5)
a

The numbers 3 and 5

a.sum()

8

time a.sum_a_lot(1000000)

Time: CPU 0.67 s, Wall: 0.68 s

%cython

cdef class TwoNumbers:
    cdef int a,b
    def __init__(self, a, b):
        self.a = a
        self.b = b
    def sum(self):
        return self.a + self.b
    def sum_a_lot(self, N):
        for i in range(N):
            self.sum()
    def __repr__(self):
        return "The numbers %s and %s" % (self.a, self.b)
    def __str__(self):
        return repr(self)

a = TwoNumbers(3, 5)
time a.sum_a_lot(1000000)

Time: CPU 0.18 s, Wall: 0.18 s

.67/.18

3.72222222222222

%cython

cdef class TwoNumbers:
    cdef int a, b
    def __init__(self, a, b):
        self.a = a
        self.b = b
    cpdef int sum(self):
        return self.a + self.b
    def sum_a_lot(self, int N):
        cdef int i
        for i in range(N):
            self.sum()
    def __repr__(self):
        return "The numbers %s and %s" % (self.a, self.b)
    def __str__(self):
        return repr(self)

a = TwoNumbers(3, 5)
time a.sum_a_lot(1000000)

Time: CPU 0.01 s, Wall: 0.01 s

a = TwoNumbers(3, 5)
time a.sum_a_lot(100000000)

Time: CPU 0.91 s, Wall: 0.92 s

.67 / .009

74.4444444444445

a = TwoNumbers(2^30, 2^30)

a.sum()

-2147483648

%cython

cimport cython
@cython.infer_types(True)
def f():
    x = 4
    print cython.typeof(x)
    y = 5.1
    print cython.typeof(y)
    z = 1
    z = "hi"
    print cython.typeof(z)

f()

long double Python object

%cython

print eval("[n**2 for n in range(10)]")

[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]