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ChebyshevDistance[u,v]

给出向量 u 和 v 之间的切比雪夫模或上确界范数距离.

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范例  
基本范例  
范围  
应用  
属性和关系  
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ChebyshevDistance

自版本 7.0，ChebyshevDistance 已被 ChessboardDistance 取代.

ChebyshevDistance[u,v]

给出向量 u 和 v 之间的切比雪夫模或上确界范数距离.

更多信息

  • ChebyshevDistance[u,v] 相当于 Max[Abs[u-v]]. »

范例

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基本范例  (2)

两个向量之间的切比雪夫距离：

Wolfram Language code: ChebyshevDistance[{a, b, c}, {x, y, z}]

数字向量之间的切比雪夫距离：

Wolfram Language code: ChebyshevDistance[{1, 2, 3}, {2, 4, 6}]

范围  (2)

计算等长度任意向量之间的距离：

Wolfram Language code: ChebyshevDistance[RandomReal[5, 100], RandomReal[5, 100]]

计算任意精度的向量之间的距离：

Wolfram Language code: ChebyshevDistance[N[{1, 5, 2, 3, 10}, 50], N[{4, 15, 20, 5, 5}, 50]]

应用  (2)

用切比雪夫距离聚类数据：

Wolfram Language code: FindClusters[{{2, 3}, {5, 10}, {4, 5}, {2, 2}}, DistanceFunction -> ChebyshevDistance]

证明三角不等式：

Wolfram Language code: d1 = ChebyshevDistance[{a, b}, {a, c}]
Wolfram Language code: d2 = ChebyshevDistance[{a, c}, {d, c}]
Wolfram Language code: d3 = ChebyshevDistance[{a, b}, {d, c}]
Wolfram Language code: Simplify[d3 <= d1 + d2]

属性和关系  (4)

切比雪夫距离是最大绝对差：

Wolfram Language code: ChebyshevDistance[{a, b, c}, {x, y, z}]
Wolfram Language code: Max[Abs[{a, b, c} - {x, y, z}]]

ChebyshevDistance 相当于差的 Norm：

Wolfram Language code: ChebyshevDistance[{a, b, c}, {x, y, z}]
Wolfram Language code: Norm[{a, b, c} - {x, y, z}, Infinity]

ChebyshevDistance 小于或等于 ManhattanDistance：

Wolfram Language code: u = {a, b, c}; v = {x, y, z};
Wolfram Language code: Simplify[ChebyshevDistance[u, v] ≤ ManhattanDistance[u, v]]

ChebyshevDistance 小于或等于 EuclideanDistance：

Wolfram Language code: u = {a, b, c}; v = {x, y, z};
Wolfram Language code: Simplify[ChebyshevDistance[u, v] ≤ EuclideanDistance[u, v]]
Wolfram Research (2007)，ChebyshevDistance，Wolfram 语言函数，https://reference.wolfram.com/language/ref/ChebyshevDistance.html.

文本

Wolfram Research (2007)，ChebyshevDistance，Wolfram 语言函数，https://reference.wolfram.com/language/ref/ChebyshevDistance.html.

CMS

Wolfram 语言. 2007. "ChebyshevDistance." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/ChebyshevDistance.html.

APA

Wolfram 语言. (2007). ChebyshevDistance. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/ChebyshevDistance.html 年

BibTeX

@misc{reference.wolfram_2026_chebyshevdistance, author="Wolfram Research", title="{ChebyshevDistance}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/ChebyshevDistance.html}", note=[Accessed: 15-September-2026]}

BibLaTeX

@online{reference.wolfram_2026_chebyshevdistance, organization={Wolfram Research}, title={ChebyshevDistance}, year={2007}, url={https://reference.wolfram.com/language/ref/ChebyshevDistance.html}, note=[Accessed: 15-September-2026]}