EuclideanDistance
EuclideanDistance[u,v]
给出向量 u 和 v 之间的欧几里得距离.
更多信息
- EuclideanDistance[u,v] 等价于 Norm[u-v]. »
- EuclideanDistance 可以与 GeometricScene 中的符号向量一起使用.
范例
打开所有单元 关闭所有单元基本范例 (2)
范围 (2)
应用 (2)
FindClusters[{{2, 3}, {5, 10}, {4, 5}, {2, 2}}, DistanceFunction -> EuclideanDistance]d1 = EuclideanDistance[{a, b}, {a, c}]d2 = EuclideanDistance[{a, c}, {d, c}]d3 = EuclideanDistance[{a, b}, {d, c}]Simplify[d3 <= d1 + d2]属性和关系 (7)
EuclideanDistance 等价于一个差的 Norm ：
EuclideanDistance[{a, b, c}, {x, y, z}]Norm[{a, b, c} - {x, y, z}]EuclideanDistance 的平方是 SquaredEuclideanDistance：
EuclideanDistance[{a, b, c}, {x, y, z}] ^ 2SquaredEuclideanDistance[{a, b, c}, {x, y, z}]EuclideanDistance 大于或等于 ChessboardDistance:
u = {a, b, c};
v = {x, y, z};Simplify[EuclideanDistance[u, v] ≥ ChessboardDistance[u, v]]CosineDistance 包含一个点积，由距离原点的欧几里得距离确定大小：
u = {a, b, c};
v = {x, y, z};scale = (EuclideanDistance[u, {0, 0, 0}]EuclideanDistance[v, {0, 0, 0}])1 - u.v / scale == CosineDistance[u, v]CorrelationDistance 包含一个点积，由距离平均值的欧几里得距离确定大小：
u = {a, b, c};
v = {x, y, z};scale = (EuclideanDistance[u, Mean[u]]EuclideanDistance[v, Mean[v]])CorrelationDistance[u, v] == 1 - (u - Mean[u]).(v - Mean[v]) / scaleStandardDeviation 作为一个距离 Mean 的 EuclideanDistance：
data = {a, b, c}mean = Table[Mean[data], {Length[data]}]StandardDeviation[data]% == EuclideanDistance[data, mean] / Sqrt[Length[data] - 1]//FullSimplifyEuclideanDistance 从一个差的 RootMeanSquare 计算得出：
EuclideanDistance[{1, 2, 3}, {2, 4, 6}]RootMeanSquare[{1, 2, 3} - {2, 4, 6}] Sqrt[Length[{1, 2, 3}]]文本
Wolfram Research (2007)，EuclideanDistance，Wolfram 语言函数，https://reference.wolfram.com/language/ref/EuclideanDistance.html.
CMS
Wolfram 语言. 2007. "EuclideanDistance." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/EuclideanDistance.html.
APA
Wolfram 语言. (2007). EuclideanDistance. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/EuclideanDistance.html 年