Python 实用宝典

Question 1

使用numpy，如何执行以下操作：

ln(x)

它等效于：

np.log(x)

我这样一个看似微不足道的问题道歉，但我之间的差异的理解log和ln被认为ln是LOGSPACEè？

Question 2

Using numpy, how can I do the following:

ln(x)

Is it equivalent to:

np.log(x)

I apologise for such a seemingly trivial question, but my understanding of the difference between log and ln is that ln is logspace e?

Question 3

np.log是ln，而np.log10您是以10为基数的标准对数。

float → float `math.log2(x)`

import math

log2 = math.log(x, 2.0)
log2 = math.log2(x)   # python 3.3 or later

Thanks @akashchandrakar and @unutbu.

float → int `math.frexp(x)`

If all you need is the integer part of log base 2 of a floating point number, extracting the exponent is pretty efficient:

log2int_slow = int(math.floor(math.log(x, 2.0)))
log2int_fast = math.frexp(x)[1] - 1

Python frexp() calls the C function frexp() which just grabs and tweaks the exponent.
Python frexp() returns a tuple (mantissa, exponent). So [1] gets the exponent part.
For integral powers of 2 the exponent is one more than you might expect. For example 32 is stored as 0.5×2⁶. This explains the - 1 above. Also works for 1/32 which is stored as 0.5×2⁻⁴.
Floors toward negative infinity, so log₂31 computed this way is 4 not 5. log₂(1/17) is -5 not -4.

int → int `x.bit_length()`

If both input and output are integers, this native integer method could be very efficient:

log2int_faster = x.bit_length() - 1

- 1 because 2ⁿ requires n+1 bits. Works for very large integers, e.g. 2**10000.
Floors toward negative infinity, so log₂31 computed this way is 4 not 5.

Question 16

If you are on python 3.3 or above then it already has a built-in function for computing log2(x)

import math
'finds log base2 of x'
answer = math.log2(x)

If you are on older version of python then you can do like this

import math
'finds log base2 of x'
answer = math.log(x)/math.log(2)

Question 17

Using numpy:

In [1]: import numpy as np

In [2]: np.log2?
Type:           function
Base Class:     <type 'function'>
String Form:    <function log2 at 0x03049030>
Namespace:      Interactive
File:           c:\python26\lib\site-packages\numpy\lib\ufunclike.py
Definition:     np.log2(x, y=None)
Docstring:
    Return the base 2 logarithm of the input array, element-wise.

Parameters
----------
x : array_like
  Input array.
y : array_like
  Optional output array with the same shape as `x`.

Returns
-------
y : ndarray
  The logarithm to the base 2 of `x` element-wise.
  NaNs are returned where `x` is negative.

See Also
--------
log, log1p, log10

Examples
--------
>>> np.log2([-1, 2, 4])
array([ NaN,   1.,   2.])

In [3]: np.log2(8)
Out[3]: 3.0

Question 18

http://en.wikipedia.org/wiki/Binary_logarithm

def lg(x, tol=1e-13):
  res = 0.0

  # Integer part
  while x<1:
    res -= 1
    x *= 2
  while x>=2:
    res += 1
    x /= 2

  # Fractional part
  fp = 1.0
  while fp>=tol:
    fp /= 2
    x *= x
    if x >= 2:
        x /= 2
        res += fp

  return res

Question 19

>>> def log2( x ):
...     return math.log( x ) / math.log( 2 )
... 
>>> log2( 2 )
1.0
>>> log2( 4 )
2.0
>>> log2( 8 )
3.0
>>> log2( 2.4 )
1.2630344058337937
>>>

Question 20

Try this ,

import math
print(math.log(8,2))  # math.log(number,base)

Question 21

logbase2(x) = log(x)/log(2)

Question 22

In python 3 or above, math class has the fallowing functions

import math

math.log2(x)
math.log10(x)
math.log1p(x)

or you can generally use math.log(x, base) for any base you want.

Question 23

log_base_2(x) = log(x) / log(2)

Question 24

Don’t forget that log[base A] x = log[base B] x / log[base B] A.

So if you only have log (for natural log) and log10 (for base-10 log), you can use

myLog2Answer = log10(myInput) / log10(2)

Question 25

I was just testing an example from Numerical Methods in Engineering with Python.

from numpy import zeros, array
from math import sin, log
from newtonRaphson2 import *

def f(x):
    f = zeros(len(x))
    f[0] = sin(x[0]) + x[1]**2 + log(x[2]) - 7.0
    f[1] = 3.0*x[0] + 2.0**x[1] - x[2]**3 + 1.0
    f[2] = x[0] + x[1] + x[2] -5.0
    return f

x = array([1.0, 1.0, 1.0])
print newtonRaphson2(f,x)

When I run it, it shows the following error:

File "example NR2method.py", line 8, in f
    f[0] = sin(x[0]) + x[1]**2 + log(x[2]) - 7.0
ValueError: math domain error

I have narrowed it down to the log as when I remove log and add a different function, it works. I assume it is because of some sort of interference with the base, I can’t figure out how. Can anyone suggest a solution?

Question 26

Your code is doing a log of a number that is less than or equal to zero. That’s mathematically undefined, so Python’s log function raises an exception. Here’s an example:

>>> from math import log
>>> log(-1)
Traceback (most recent call last):
  File "<pyshell#59>", line 1, in <module>
    log(-1)
ValueError: math domain error

Without knowing what your newtonRaphson2 function does, I’m not sure I can guess where the invalid x[2] value is coming from, but hopefully this will lead you on the right track.

Question 27

You are trying to do a logarithm of something that is not positive.

Logarithms figure out the base after being given a number and the power it was raised to. log(0) means that something raised to the power of 2 is 0. An exponent can never result in 0*, which means that log(0) has no answer, thus throwing the math domain error

*Note: 0^0 can result in 0, but can also result in 1 at the same time. This problem is heavily argued over.

Question 28

You may also use math.log1p.

According to the official documentation :

math.log1p(x)

Return the natural logarithm of 1+x (base e). The result is calculated in a way which is accurate for x near zero.

You may convert back to the original value using math.expm1 which returns e raised to the power x, minus 1.

Question 29

you are getting math domain error for either one of the reason : either you are trying to use a negative number inside log function or a zero value.

Question 30

In matplotlib, I can set the axis scaling using either pyplot.xscale() or Axes.set_xscale(). Both functions accept three different scales: 'linear' | 'log' | 'symlog'.

What is the difference between 'log' and 'symlog'? In a simple test I did, they both looked exactly the same.

I know the documentation says they accept different parameters, but I still don’t understand the difference between them. Can someone please explain it? The answer will be the best if it has some sample code and graphics! (also: where does the name ‘symlog’ come from?)

Question 31

I finally found some time to do some experiments in order to understand the difference between them. Here’s what I discovered:

log only allows positive values, and lets you choose how to handle negative ones (mask or clip).
symlog means symmetrical log, and allows positive and negative values.
symlog allows to set a range around zero within the plot will be linear instead of logarithmic.

I think everything will get a lot easier to understand with graphics and examples, so let’s try them:

import numpy
from matplotlib import pyplot

# Enable interactive mode
pyplot.ion()

# Draw the grid lines
pyplot.grid(True)

# Numbers from -50 to 50, with 0.1 as step
xdomain = numpy.arange(-50,50, 0.1)

# Plots a simple linear function 'f(x) = x'
pyplot.plot(xdomain, xdomain)
# Plots 'sin(x)'
pyplot.plot(xdomain, numpy.sin(xdomain))

# 'linear' is the default mode, so this next line is redundant:
pyplot.xscale('linear')

# How to treat negative values?
# 'mask' will treat negative values as invalid
# 'mask' is the default, so the next two lines are equivalent
pyplot.xscale('log')
pyplot.xscale('log', nonposx='mask')

# 'clip' will map all negative values a very small positive one
pyplot.xscale('log', nonposx='clip')

# 'symlog' scaling, however, handles negative values nicely
pyplot.xscale('symlog')

# And you can even set a linear range around zero
pyplot.xscale('symlog', linthreshx=20)

Just for completeness, I’ve used the following code to save each figure:

# Default dpi is 80
pyplot.savefig('matplotlib_xscale_linear.png', dpi=50, bbox_inches='tight')

Remember you can change the figure size using:

fig = pyplot.gcf()
fig.set_size_inches([4., 3.])
# Default size: [8., 6.]

(If you are unsure about me answering my own question, read this)

Question 32

symlog is like log but allows you to define a range of values near zero within which the plot is linear, to avoid having the plot go to infinity around zero.

From http://matplotlib.sourceforge.net/api/axes_api.html#matplotlib.axes.Axes.set_xscale

In a log graph, you can never have a zero value, and if you have a value that approaches zero, it will spike down way off the bottom off your graph (infinitely downward) because when you take “log(approaching zero)” you get “approaching negative infinity”.

symlog would help you out in situations where you want to have a log graph, but when the value may sometimes go down towards, or to, zero, but you still want to be able to show that on the graph in a meaningful way. If you need symlog, you’d know.

Question 33

Here’s an example of behaviour when symlog is necessary:

Initial plot, not scaled. Notice how many dots cluster at x~0

    ax = sns.scatterplot(x= 'Score', y ='Total Amount Deposited', data = df, hue = 'Predicted Category')

[ ‘

Log scaled plot. Everything collapsed.

    ax = sns.scatterplot(x= 'Score', y ='Total Amount Deposited', data = df, hue = 'Predicted Category')

    ax.set_xscale('log')
    ax.set_yscale('log')
    ax.set(xlabel='Score, log', ylabel='Total Amount Deposited, log')

‘

Why did it collapse? Because of some values on the x-axis being very close or equal to 0.

Symlog scaled plot. Everything is as it should be.

    ax = sns.scatterplot(x= 'Score', y ='Total Amount Deposited', data = df, hue = 'Predicted Category')

    ax.set_xscale('symlog')
    ax.set_yscale('symlog')
    ax.set(xlabel='Score, symlog', ylabel='Total Amount Deposited, symlog')

问题：在Python中如何用numpy处理自然日志（例如“ ln（）”）？

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问题：登录到以2为底的python

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回答 1

浮动→浮动 math.log2(x)

浮点数→整数 math.frexp(x)

整数→整数 x.bit_length()

float → float math.log2(x)

float → int math.frexp(x)

int → int x.bit_length()

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问题：ValueError：数学域错误

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问题：“ log”和“ symlog”有什么区别？

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问题：在python中使用matplotlib绘制对数轴

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有趣好用的Python教程

浮动→浮动 `math.log2(x)`

浮点数→整数 `math.frexp(x)`

整数→整数 `x.bit_length()`

float → float `math.log2(x)`

float → int `math.frexp(x)`

int → int `x.bit_length()`