标签归档：epsilon

知识问答

python numpy机器epsilon

问题：python numpy机器epsilon

我试图了解什么是机器epsilon。根据维基百科，可以如下计算：

def machineEpsilon(func=float):
    machine_epsilon = func(1)
    while func(1)+func(machine_epsilon) != func(1):
        machine_epsilon_last = machine_epsilon
        machine_epsilon = func(machine_epsilon) / func(2)
    return machine_epsilon_last

但是，它仅适用于双精度数字。我有兴趣修改它以支持单精度数字。我读到可以使用numpy，尤其是numpy.float32类。有人可以帮助您修改功能吗？

点击查看英文原文

I am trying to understand what is machine epsilon. According to the Wikipedia, it can be calculated as follows:

def machineEpsilon(func=float):
    machine_epsilon = func(1)
    while func(1)+func(machine_epsilon) != func(1):
        machine_epsilon_last = machine_epsilon
        machine_epsilon = func(machine_epsilon) / func(2)
    return machine_epsilon_last

However, it is suitable only for double precision numbers. I am interested in modifying it to support also single precision numbers. I read that numpy can be used, particularly numpy.float32 class. Can anybody help with modifying the function?

回答 0

对于给定的float类型，获取机器epsilon的更简单方法是使用np.finfo()：

print(np.finfo(float).eps)
# 2.22044604925e-16

print(np.finfo(np.float32).eps)
# 1.19209e-07
点击查看英文原文

An easier way to get the machine epsilon for a given float type is to use np.finfo():

print(np.finfo(float).eps)
# 2.22044604925e-16

print(np.finfo(np.float32).eps)
# 1.19209e-07

回答 1

获得epsilon的另一种简单方法是：

In [1]: 7./3 - 4./3 -1
Out[1]: 2.220446049250313e-16
点击查看英文原文

Another easy way to get epsilon is:

In [1]: 7./3 - 4./3 -1
Out[1]: 2.220446049250313e-16

回答 2

正如David指出的那样，它已经可以工作了！

>>> def machineEpsilon(func=float):
...     machine_epsilon = func(1)
...     while func(1)+func(machine_epsilon) != func(1):
...         machine_epsilon_last = machine_epsilon
...         machine_epsilon = func(machine_epsilon) / func(2)
...     return machine_epsilon_last
... 
>>> machineEpsilon(float)
2.220446049250313e-16
>>> import numpy
>>> machineEpsilon(numpy.float64)
2.2204460492503131e-16
>>> machineEpsilon(numpy.float32)
1.1920929e-07
点击查看英文原文

It will already work, as David pointed out!

>>> def machineEpsilon(func=float):
...     machine_epsilon = func(1)
...     while func(1)+func(machine_epsilon) != func(1):
...         machine_epsilon_last = machine_epsilon
...         machine_epsilon = func(machine_epsilon) / func(2)
...     return machine_epsilon_last
... 
>>> machineEpsilon(float)
2.220446049250313e-16
>>> import numpy
>>> machineEpsilon(numpy.float64)
2.2204460492503131e-16
>>> machineEpsilon(numpy.float32)
1.1920929e-07