Среднеквадратическая ошибка матлаб

• F and A must either be the same size or
  have sizes that are compatible.

• If F and A are vectors of the same size,
  then E is a scalar.

• If F-A is a matrix, then E is a row vector
  containing the RMSE for each column.

• If F and A are multidimensional arrays,
  then E contains the RMSE computed along the first array dimension
  of size greater than 1, with elements treated as vectors. The size of
  E in this dimension is 1, while the sizes of all other
  dimensions are the same as in F-A.

RMSE of Two Forecasts

Create two column vectors of forecast (predicted) data and one column vector of actual (observed) data.

F1 = [1; 10; 9];
F2 = [2; 5; 10];
A = [1; 9; 10];

Compute the RMSE between each forecast and the actual data.

Alternatively, create a matrix containing both forecasts and compute the RMSE between each forecast and the actual data in one command.

The first element of E is the RMSE between the first forecast column and the actual data. The second element of E is the RMSE between the second forecast column and the actual data.

RMSE of Matrix Rows

Create a matrix of forecast data and a matrix of actual data.

F = [17 19; 1 6; 16 15];
A = [17 25; 3 4; 16 13];

Compute the RMSE between the forecast and the actual data across each row by specifying the operating dimension as 2. The smallest RMSE corresponds to the RMSE between the third rows of the forecast data and actual data.

E = 3×1

    4.2426
    2.0000
    1.4142

RMSE of Array Pages

Create a 3-D array with pages containing forecast data and a matrix of actual data.

F(:,:,1) = [2 4; -2 1];
F(:,:,2) = [4 4; 8 -3];
A = [6 7; 1 4];

Compute the RMSE between the predicted data in each page of the forecast array and the actual data matrix by specifying a vector of operating dimensions 1 and 2.

E = 
E(:,:,1) =

    3.2787


E(:,:,2) =

    5.2678

The first page of E contains the RMSE between the first page of F and the matrix A. The second page of E contains the RMSE between the second page of F and the matrix A.

RMSE Excluding Missing Values

Create a matrix of forecast data and a matrix of actual data containing NaN values.

F = [17 19 3; 6 16 NaN];
A = [17 25 NaN; 4 16 NaN];

Compute the RMSE between the forecast and the actual data, ignoring NaN values. For columns that contain all NaN values in F or A, the RMSE is NaN.

E = 1×3

    1.4142    4.2426       NaN

Specify RMSE Weight Vector

Create a forecast column vector and an actual column vector.

F = [2; 10; 13];
A = [1; 9; 10];

Compute the RMSE between the forecast and actual data according to a weighting scheme specified by W.

W = [0.5; 0.25; 0.25];
E = rmse(F,A,Weight=W)

For a forecast array F and actual array
A made up of n scalar observations, the
root-mean-square error is defined as

with the summation performed along the specified dimension.

For a forecast array F and actual array
A made up of n scalar observations and weighting
scheme W, the weighted root-mean-square error is defined as

with the summation performed along the specified dimension.

The rmse function shows improved performance when computing over a
real vector when the operating dimension is not specified. The function determines the
default operating dimension more quickly in R2023a than in R2022b.

For example, this code computes the root-mean-square error along the default vector
dimension. The code is about 2x faster than in the previous release.

function timingRmse
F = rand(10,1);
A = rand(10,1);
for i = 1:8e5
    rmse(F,A);
end
end

The approximate execution times are:

R2022b: 4.12 s

R2023a: 2.07 s

The code was timed on a Windows^® 10, Intel^®
Xeon^® CPU E5-1650 v4 @ 3.60 GHz test system using the timeit
function.

Вычислите среднеквадратическую ошибку в шумном изображении

Считайте изображение и отобразите его.

ref = imread('pout.tif');
imshow(ref)

Создайте другое изображение путем добавления шума в копию ссылочного изображения.

A = imnoise(ref,'salt & pepper', 0.02);
imshow(A)

Вычислите среднеквадратическую ошибку между двумя изображениями.

err = immse(A, ref);
fprintf('n The mean-squared error is %0.4fn', err);

 The mean-squared error is 353.7631

err — Среднеквадратическая ошибка
положительное число

Среднеквадратическая ошибка, возвращенная как положительное число. Тип данных err double если входные параметры не имеют типа данных single, в этом случае err имеет тип данных single

Типы данных: single | double

Bart

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Furkan GözükaraFurkan Gözükara

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This finds the mean of the squared errors:

MSE = mean(errors.^2)

Each element is squared separately, and then the mean of the resulting vector is found.

answered Nov 8, 2012 at 21:38

sum(errors.^2) / numel(errors)

answered Nov 8, 2012 at 21:38

tashuhkatashuhka

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