from pyspark import SparkContext
sc = SparkContext('local', 'pyspark')
牛顿法求平方根
我们知道牛顿法求 n−−√ (达到eps准确度)的算法是这样的：**
* 给定一个初始值 x=1.0.
* 求x和n/x的平均(x+n/x)/2
* 根据(x+n/x)/2和n−−√的大小比较，确定下一步迭代的2个端点，同时不断迭代直至x∗x与n之间的差值小于eps.
在Spark中完成上述算法
给定0-9 10个数的作为输入，计算它们的平方根，初始值都设为1.0
initial_sqrt=[(n,1.0) for n in range(10)]
initial_sqrt
[(0, 1.0),
(1, 1.0),
(2, 1.0),
(3, 1.0),
(4, 1.0),
(5, 1.0),
(6, 1.0),
(7, 1.0),
(8, 1.0),
(9, 1.0)]
设置误差eps和最大迭代次数max_iter
并执行牛顿法求平方根
eps=0.0001
max_iter=10 //注明：迭代10次，每次均进行n:(n[0],(n[1]+n[0]/n[1])/2) 计算。
ns=sc.parallelize(initial_sqrt)
while max_iter!=0:
ns=ns.map(lambda n:(n[0],(n[1]+n[0]/n[1])/2) if abs(n[1]**2-n[0])>eps else n)
ns.cache()
max_iter-=1
ns.collect()
[(0, 0.0078125),
(1, 1.0),
(2, 1.4142156862745097),
(3, 1.7320508100147274),
(4, 2.0000000929222947),
(5, 2.2360688956433634),
(6, 2.4494943716069653),
(7, 2.64576704419029),
(8, 2.8284271250498643),
(9, 3.000000001396984)]
在Spark里使用reduce()计算10!
rdd = sc.parallelize(range(1,10+1))
rdd.reduce(lambda x, y: x * y)
3628800
from pyspark import SparkContext
sc1 = SparkContext('local', 'pyspark')
In [4]:
initial_sqrt=[(n,1.0) for n in range(10)]
initial_sqrt
Out[4]:
[(0, 1.0),
(1, 1.0),
(2, 1.0),
(3, 1.0),
(4, 1.0),
(5, 1.0),
(6, 1.0),
(7, 1.0),
(8, 1.0),
(9, 1.0)]
In [6]:
eps=0.0001
max_iter=10
ns=sc1.parallelize(initial_sqrt)
while max_iter!=0:
ns=ns.map(lambda n:(n[0],(n[1]+n[0]/n[1])/2) if abs(n[1]**2-n[0])>eps else n)
ns.cache()
max_iter-=1
print(ns.collect())
print("")
ns.collect()
[(0, 0.5), (1, 1.0), (2, 1.5), (3, 2.0), (4, 2.5), (5, 3.0), (6, 3.5), (7, 4.0), (8, 4.5), (9, 5.0)]
[(0, 0.25), (1, 1.0), (2, 1.4166666666666665), (3, 1.75), (4, 2.05), (5, 2.3333333333333335), (6, 2.607142857142857), (7, 2.875), (8, 3.138888888888889), (9, 3.4)]
[(0, 0.125), (1, 1.0), (2, 1.4142156862745097), (3, 1.7321428571428572), (4, 2.000609756097561), (5, 2.238095238095238), (6, 2.454256360078278), (7, 2.654891304347826), (8, 2.843780727630285), (9, 3.023529411764706)]
[(0, 0.0625), (1, 1.0), (2, 1.4142156862745097), (3, 1.7320508100147274), (4, 2.0000000929222947), (5, 2.2360688956433634), (6, 2.4494943716069653), (7, 2.64576704419029), (8, 2.8284685718801468), (9, 3.00009155413138)]
[(0, 0.03125), (1, 1.0), (2, 1.4142156862745097), (3, 1.7320508100147274), (4, 2.0000000929222947), (5, 2.2360688956433634), (6, 2.4494943716069653), (7, 2.64576704419029), (8, 2.8284271250498643), (9, 3.000000001396984)]
[(0, 0.015625), (1, 1.0), (2, 1.4142156862745097), (3, 1.7320508100147274), (4, 2.0000000929222947), (5, 2.2360688956433634), (6, 2.4494943716069653), (7, 2.64576704419029), (8, 2.8284271250498643), (9, 3.000000001396984)]
[(0, 0.0078125), (1, 1.0), (2, 1.4142156862745097), (3, 1.7320508100147274), (4, 2.0000000929222947), (5, 2.2360688956433634), (6, 2.4494943716069653), (7, 2.64576704419029), (8, 2.8284271250498643), (9, 3.000000001396984)]
[(0, 0.0078125), (1, 1.0), (2, 1.4142156862745097), (3, 1.7320508100147274), (4, 2.0000000929222947), (5, 2.2360688956433634), (6, 2.4494943716069653), (7, 2.64576704419029), (8, 2.8284271250498643), (9, 3.000000001396984)]
[(0, 0.0078125), (1, 1.0), (2, 1.4142156862745097), (3, 1.7320508100147274), (4, 2.0000000929222947), (5, 2.2360688956433634), (6, 2.4494943716069653), (7, 2.64576704419029), (8, 2.8284271250498643), (9, 3.000000001396984)]
[(0, 0.0078125), (1, 1.0), (2, 1.4142156862745097), (3, 1.7320508100147274), (4, 2.0000000929222947), (5, 2.2360688956433634), (6, 2.4494943716069653), (7, 2.64576704419029), (8, 2.8284271250498643), (9, 3.000000001396984)]
Out[6]:
[(0, 0.0078125),
(1, 1.0),
(2, 1.4142156862745097),
(3, 1.7320508100147274),
(4, 2.0000000929222947),
(5, 2.2360688956433634),
(6, 2.4494943716069653),
(7, 2.64576704419029),
(8, 2.8284271250498643),
(9, 3.000000001396984)]