python image函数_python shuffle函数

①imageset()函数与ImageSet()函数的区别

两个函数都是用于表达集合变换后的形式，其区别在于：

1. 用途不同
   ①imageset()函数主要用于需要计算出具体值的情况
   ②ImageSet()函数主要用于无需计算出具体值的情况
2. 参数设置形式上的不同（详见后文）
3. 一般情况下不直接使用ImageSet()函数而是使用imageset()函数

②imageset()函数的官方介绍

sympy.sets.sets.imageset(*args)

Return an image of the set under transformation f.

Explanation

If this function cannot compute the image, it returns an unevaluated
ImageSet object.
{ f ( x ) ∣ x ∈ s e l f } \left\{ f\left( x\right) \mid x\in self\right\} {
f(x)∣x∈self}
Examples

>>>from sympy import S, Interval, imageset, sin, Lambda
>>>from sympy.abc import x

>>>imageset(x, 2*x, Interval(0, 2))
Interval(0, 4)

>>>imageset(lambda x: 2*x, Interval(0, 2))
Interval(0, 4)

>>>imageset(Lambda(x, sin(x)), Interval(-2, 1))
ImageSet(Lambda(x, sin(x)), Interval(-2, 1))

>>>imageset(sin, Interval(-2, 1))
ImageSet(Lambda(x, sin(x)), Interval(-2, 1))
>>>imageset(lambda y: x + y, Interval(-2, 1))
ImageSet(Lambda(y, x + y), Interval(-2, 1))

Expressions applied to the set of Integers are simplified to show as
few negatives as possible and linear expressions are converted to a
canonical form. If this is not desirable then the unevaluated ImageSet
should be used.

>>>imageset(x, -2*x + 5, S.Integers)
ImageSet(Lambda(x, 2*x + 1), Integers)

③ImageSet()函数的官方介绍

class sympy.sets.fancysets.ImageSet(lambda, *sets)

Image of a set under a mathematical function. The transformation must
be given as a Lambda function which has as many arguments as the
elements of the set upon which it operates, e.g. 1 argument when
acting on the set of integers or 2 arguments when acting on a complex
region.

This function is not normally called directly, but is called from
imageset.

Examples

>>>from sympy import Symbol, S, pi, Dummy, Lambda
>>>from sympy import FiniteSet, ImageSet, Interval

>>>x = Symbol('x')
>>>N = S.Naturals
>>>squares = ImageSet(Lambda(x, x**2), N) # {x**2 for x in N}
>>>4 in squares
True
>>>5 in squares
False

>>>FiniteSet(0, 1, 2, 3, 4, 5, 6, 7, 9, 10).intersect(squares)
{ 
   1, 4, 9}

>>>square_iterable = iter(squares)
>>>for i in range(4):
       next(square_iterable)
1
4
9
16

If you want to get value for x=2, 1/2 etc. (Please check whether the x value is in base_set or not before passing it as args)

>>>squares.lamda(2)
4
>>>squares.lamda(S(1)/2)
1/4

>>>n = Dummy('n')
>>>solutions = ImageSet(Lambda(n, n*pi), S.Integers) # solutions of sin(x) = 0
>>>dom = Interval(-1, 1)
>>>dom.intersect(solutions)
{ 
   0}

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