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RootMeanSquare

RootMeanSquare[list]

给出 list 中值的均方根.

RootMeanSquare[dist]

给出分布 dist 的均方根.

范例

打开所有单元关闭所有单元

基本范例 (3)

一个列表的 RootMeanSquare ：

Wolfram Language code: RootMeanSquare[ {a, b, c, d}]

矩阵列的 RootMeanSquare：

Wolfram Language code: RootMeanSquare[{{1, 2}, {5, 10}, {5, 2}, {4, 8}}]

参数分布的 RootMeanSquare：

Wolfram Language code: RootMeanSquare[LogNormalDistribution[0, 1]]

范围 (14)

数据 (10)

精确输入产生精确输出：

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

Wolfram Language code: RootMeanSquare[{π, E, 2}]

近似输入产生近似输出：

Wolfram Language code: RootMeanSquare[{1., 2., 3., 4.}]

Wolfram Language code: RootMeanSquare[N[{1, 2, 3, 4}, 30]]

矩阵的 RootMeanSquare 逐列给出均值：

Wolfram Language code:

RootMeanSquare[(⁠|     |     |
| --- | --- |
| a11 | a12 |
| a21 | a22 |⁠)]

作用于大型数组：

Wolfram Language code: RootMeanSquare[RandomReal[1, 10 ^ 7]]

Wolfram Language code: RootMeanSquare[RandomReal[1, {10 ^ 6, 3}]]

可以像使用稠密数组一样使用 SparseArray 数据：

Wolfram Language code: RootMeanSquare[SparseArray[{{1} -> 1, {2} -> 7}]]

Wolfram Language code: RootMeanSquare[SparseArray[{{1, 1} -> 1, {2, 1} -> 2, {2, 2} -> 3}]]

对于 SparseArray 的计算结果：

Wolfram Language code: sp = SparseArray[{{i_, i_} :> i, {i_, j_} /; j == i + 1 :> i - 1}, {100, 10}]

Wolfram Language code: RootMeanSquare[sp]

WeightedData 的 RootMeanSquare：

Wolfram Language code: RootMeanSquare[WeightedData[{1, 2, 3}, {Subscript[w, 1], Subscript[w, 2], Subscript[w, 3]}]]

Wolfram Language code:

data = {8, 3, 5, 4, 9, 1, 4, 2, 2, 3};
weights = {0.15, 0.09, 0.12, 0.10, 0.16, 0.3, 0.11, 0.08, 0.08, 0.09};

Wolfram Language code: RootMeanSquare[WeightedData[data, weights]]

EventData 的 RootMeanSquare：

Wolfram Language code:

e = {1.0, 2.1, 3.2, 4.5, 5.7};
ci = {0, 0, 0, 1, 0};

Wolfram Language code: RootMeanSquare[EventData[e, ci]]

TimeSeries 的 RootMeanSquare：

Wolfram Language code:

RootMeanSquare[TemporalData[TimeSeries, {{{2.3, 1.2, 6.7, 5.8, 7.1, 4.6}}, {{0, 5, 1}}, 1, {"Discrete", 1}, 
  {"Discrete", 1}, 1, {}}, False, 10.]]

均方根仅仅取决于数值：

Wolfram Language code:

RootMeanSquare[TemporalData[TimeSeries, {{{2.3, 1.2, 6.7, 5.8, 7.1, 4.6}}, {{0, 5, 1}}, 1, {"Discrete", 1}, 
  {"Discrete", 1}, 1, {}}, False, 10.]["Values"]]

涉及量的数据的 RootMeanSquare：

Wolfram Language code: data = Quantity[RandomReal[1, 6], "Meters"]

Wolfram Language code: RootMeanSquare[data]

分布和过程 (4)

求单变量分布的 RootMeanSquare：

Wolfram Language code: RootMeanSquare[BinomialDistribution[n, p]]

Wolfram Language code: RootMeanSquare[NormalDistribution[μ, σ]]

多变量分布：

Wolfram Language code: RootMeanSquare[MultinomialDistribution[n, {Subscript[m, 1], Subscript[m, 2]}]]

Wolfram Language code: RootMeanSquare[BinormalDistribution[{Subscript[μ, 1], Subscript[μ, 2]}, {σ1, σ2}, ρ]]

导出分布的 RootMeanSquare：

Wolfram Language code: RootMeanSquare[TransformedDistribution[x^2, xNormalDistribution[μ, σ]]]

Wolfram Language code: RootMeanSquare[ProbabilityDistribution[(Sqrt[2] / π)(1 / (1 + (x - 2)^4)), {x, -∞, ∞}]]

数据分布：

Wolfram Language code: data = RandomVariate[NormalDistribution[], 10 ^ 3];

Wolfram Language code: RootMeanSquare[HistogramDistribution[data]]

含有量的分布的 RootMeanSquare：

Wolfram Language code: RootMeanSquare[QuantityDistribution[MaxwellDistribution[σ], "Meters" / "Seconds"]]

Wolfram Language code: RootMeanSquare[EmpiricalDistribution[QuantityArray[RandomChoice[{0, 5}, 1000], "Volts"]]]

随机过程的 RootMeanSquare：

Wolfram Language code: RootMeanSquare[BrownianBridgeProcess[a, b][t]]

Wolfram Language code: Plot[Evaluate[% /. {a -> 3, b -> 5}], {t, 3, 5}, PlotRange -> All]

应用 (3)

线性拟合的均方根错误：

Wolfram Language code: data = {{1, 2.9}, {2, 5.0}, {3, 7.1}, {4, 8.9}, {5, 10.9}, {6, 13.1}, {7, 14.9}, {8, 16.8}, {9, 18.5}, {10, 22.2}};

Wolfram Language code: f[x_] = Fit[data, {1, x}, x]

Wolfram Language code: RootMeanSquare[data[[All, 2]] - Map[f, data[[All, 1]]]]

对周期信号进行采样：

Wolfram Language code: f[t_] := Sin[5 t] + Cos[7t] / 12

Wolfram Language code: ts = TimeSeries[Table[f[t], {t, 0, 2Pi, 0.01}]]

Wolfram Language code: ListPlot[ts]

计算样本的均方根值：

Wolfram Language code: RootMeanSquare[ts]

与准确值进行比较：

Wolfram Language code: Sqrt[Integrate[f[t] ^ 2, {t, 0, 2Pi}] / (2Pi)]

Wolfram Language code: N[%]

求班级中孩子们身高值的均方根：

Wolfram Language code:

heights = Quantity[{134, 143, 131, 140, 145, 136, 131, 136, 143, 136, 133, 145, 147, 
	        150, 150, 146, 137, 143, 132, 142, 145, 136, 144, 135, 141}, "Centimeters"];

Wolfram Language code: ListPlot[heights, Filling -> Axis, AxesLabel -> Automatic]

Wolfram Language code: (rms = RootMeanSquare[heights])//N

Wolfram Language code:

ListPlot[{heights, {{0, rms}, {Length[heights], rms}}}, Joined -> {False, True}, Filling -> Axis, AxesLabel -> Automatic]