Matlab中，可以使用movsum函数求解移动总和，可以理解为由局部 k 个数据点总和组成的数组。本文，将从以下几个方面介绍movsum函数：movsum函数常见用法、movsum函数语法说明、movsum函数实例。其中，movsum函数实例包括：向量的中心移动和、向量的尾部移动和、矩阵的移动和、包含 NaN 元素的向量的移动和、基于样本点计算移动和、仅返回满窗口和。
movsum函数帮助文档如下：
>> help movsum
movsum Moving sum value.
Y = movsum(X,K) for a vector X and positive integer scalar K computes a
centered moving sum by sliding a window of length K along X. Each
element of Y is the local sum of the corresponding values of X inside
the window, with Y the same size as X. When K is even, the window is
centered about the current and previous elements of X. The sliding
window is truncated at the endpoints where there are fewer than K
elements from X to fill the window.
For N-D arrays, movsum operates along the first array dimension whose
size does not equal 1.
Y = movsum(X,[NB NF]) for a vector X and nonnegative integers NB and NF
computes a moving sum along the length of X, returning the local sum of
the previous NB elements, the current element, and the next NF elements
of X.
Y = movsum(...,DIM) operates along dimension DIM of X.
movsum(...,MISSING) specifies how NaN (Not-a-Number) values are treated
and can be one of the following:
'includenan' - (default) the sum of any window containing NaN
values is also NaN.
'omitnan' - the sum of any window containing NaN values is the
sum of all its non-NaN elements. If all elements
are NaN, the result is 0.
movsum(...,'Endpoints',ENDPT) controls how the sum is calculated at the
endpoints of X, where there are not enough elements to fill the window.
ENDPT can be either a scalar numeric or logical value or one of the
following:
'shrink' - (default) compute the sum over the number of elements
of X that are inside the window, effectively reducing
the window size to fit X at the endpoints.
'fill' - compute the sum over the full window size, filling
missing values from X with NaN. This is equivalent to
padding X with NaN at the endpoints.
'discard' - compute the sum only when the window is filled with
elements of X, discarding partial endpoint
calculations and their corresponding elements in Y.
This truncates the output; for a vector X and window
length K, Y has length LENGTH(X)-K+1.
When ENDPT is a scalar numeric or logical value, the missing elements
of X inside the window are replaced with that value and Y remains the
same size as X.
Example: Compute a 5-point centered moving sum.
t = 1:10;
x = [4 8 6 -1 -2 -3 -1 3 4 5];
yc = movsum(x,5);
plot(t,x,t,yc);
Example: Compute a 5-point trailing moving sum.
t = 1:10;
x = [4 8 6 -1 -2 -3 -1 3 4 5];
yt = movsum(x,[4 0]);
plot(t,x,t,yt);
Example: Compute a 5-point centered moving sum, padding the ends of the
input with NaN.
t = 1:10;
x = [4 8 6 -1 -2 -3 -1 3 4 5];
yp = movsum(x,5,'Endpoints','fill');
plot(t,x,t,yp);
Example: Compute a 5-point trailing moving sum, ignoring the first 4
window shifts that do not contain 5 input elements.
x = [4 8 6 -1 -2 -3 -1 3 4 5];
yd = movsum(x,[4 0],'Endpoints','discard');movsum函数常见用法
M = movsum(A,k)
M = movsum(A,[kb kf])
M = movsum(___,dim)
M = movsum(___,nanflag)
M = movsum(___,Name,Value)movsum函数语法说明
M = movsum(A,k) 返回由局部 k 个数据点总和组成的数组，其中每个总和基于 A 的相邻元素的长度为 k 的滑动窗计算得出。当 k 为奇数时，窗口以当前位置的元素为中心。当 k 为偶数时，窗口以当前元素及其前一个元素为中心。当没有足够的元素填满窗口时，窗口将自动在端点处截断。当窗口被截断时，只根据窗口内的元素计算总和。M 与 A 的大小相同。
- 如果 A 是向量，movsum 将沿向量 A 的长度运算。
- 如果 A 是多维数组，则 movsum 沿 A 的大小不等于 1 的第一个维度进行运算。
M = movsum(A,[kb kf]) 通过长度为 kb+kf+1 的窗口计算和，其中包括当前位置的元素、后面的 kb 个元素和前面的 kf 个元素。
M = movsum(_,dim) 为上述任一语法指定 A 的运算维度。例如，如果 A 是矩阵，则 movsum(A,k,2) 沿 A 的列运算，计算每行的 k 个元素的移动总和。
M = movsum(_,nanflag) 指定在上述任意语法的计算中包括还是忽略 NaN 值。movsum(A,k,’includenan’) 会在计算中包括所有 NaN 值，而 movsum(A,k,’omitnan’) 则忽略这些值并基于较少的点计算和。
M = movsum(_,Name,Value) 使用一个或多个名称-值对组参数指定和的其他参数。例如，如果 x 是时间向量，则 movsum(A,k,’SamplePoints’,x) 相对于 x 中的时间计算 A 的移动和。
movsum函数实例
向量的中心移动和
计算行向量的三点中心移动和。当端点处的窗口中少于三个元素时，将根据可用元素计算和。
>> A = [4 8 6 -1 -2 -3 -1 3 4 5];
>> M = movsum(A,3)
M =
12 18 13 3 -6 -6 -1 6 12 9向量的尾部移动和
计算行向量的三点尾部移动和。当端点处的窗口中少于三个元素时，movsum 将根据可用数量的元素计算和。
>> A = [4 8 6 -1 -2 -3 -1 3 4 5];
>> M = movsum(A,[2 0])
M =
4 12 18 13 3 -6 -6 -1 6 12矩阵的移动和
计算矩阵中每行的三点中心移动和。窗口从第一行开始，沿水平方向移动到该行的末尾，然后移到第二行，依此类推。维度参数为 2，即跨 A 的列移动窗口。
>> A = [4 8 6; -1 -2 -3; -1 3 4]
A =
4 8 6
-1 -2 -3
-1 3 4
>> M = movsum(A,3,2)
M =
12 18 14
-3 -6 -5
2 6 7
包含 NaN 元素的向量的移动和
计算包含两个 NaN 元素的行向量的三点中心移动和。
>> A = [4 8 NaN -1 -2 -3 NaN 3 4 5];
>> M = movsum(A,3)
M =
12 NaN NaN NaN -6 NaN NaN NaN 12 9重新计算和，但忽略 NaN 值。当 movsum 舍弃 NaN 元素时，它将根据窗口中的剩余元素计算和。
>> M = movsum(A,3,'omitnan')
M =
12 12 7 -3 -6 -5 0 7 12 9
基于样本点计算移动和
根据时间向量 t，计算 A 中数据的 3 小时中心移动和。
>> M = movsum(A,3,'omitnan')
M =
12 12 7 -3 -6 -5 0 7 12 9
>> A = [4 8 6 -1 -2 -3];
k = hours(3);
t = datetime(16,1,1,0,0,0) + hours(0:5)
t =
1 至 5 列
0016-01-01 00:00:00 0016-01-01 01:00:00 0016-01-01 02:00:00 0016-01-01 03:00:00 0016-01-01 04:00:00
6 列
0016-01-01 05:00:00
>> M = movsum(A,k,'SamplePoints',t)
M = 1×6
12 18 13 3 -6 -5
仅返回满窗口和
计算行向量的三点中心移动和，但在输出中舍弃使用的点数少于三个的计算。也就是说，只返回从满的三元素窗口计算的和，而舍弃端点计算。
>> A = [4 8 6 -1 -2 -3 -1 3 4 5];
>> M = movsum(A,3,'Endpoints','discard')
M =
18 13 3 -6 -6 -1 6 12原创文章，作者：古哥，转载需经过作者授权同意，并附上原文链接：https://iymark.com/articles/3972.html
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