# Documentation

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## Missing Data

### Representing Missing Data Values

Often, you represent missing or unavailable data values in MATLAB® code with the special value, NaN, which stands for Not-a-Number.

The IEEE® floating-point arithmetic convention defines NaN as the result of an undefined operation, such as 0/0.

### Calculating with NaNs

When you perform calculations on an IEEE variable that contains NaNs, the NaN values are often propagated to the final result. This behavior might render the result useless.

For example, consider a matrix containing the 3-by-3 magic square with its center element replaced with NaN:

a = magic(3); a(2,2) = NaN

a =
8     1     6
3   NaN     7
4     9     2

Compute the sum for each column in the matrix:

sum(a)

ans =
15   NaN    15

Notice that the sum of the elements in the middle column is a NaN value because that column contains a NaN. Sometimes removing NaNs from the data yields a more meaningful result.

### Identifying and Removing NaNs

There are multiple strategies for removing NaNs from array computations. Some functions, such as sum, allow an optional input argument that causes MATLAB to ignore NaNs in the calculation. Instead of using sum(a) in the previous example, you can use the following command:

sum(a,'omitnan')

ans =

15    10    15
The NaN in the second column is ignored and only the non-NaN elements are summed.

It is often useful to identify where the NaNs are located within an array before deciding on a strategy that removes them. The functions isnan and ismissing can identify which elements of an array are NaNs. For an input array a, both of these functions return a logical array of the same size as a. Elements of the logical array are 1 (true) when the corresponding elements of a are NaNs, and 0 (false) otherwise.

The rmmissing function directly removes NaNs from data. rmmissing removes NaNs from vectors and can remove entire rows or columns from a matrix if there is at least one NaN in that row or column. The following table summarizes techniques for removing NaNs from data.

 Note:   By IEEE arithmetic convention, the logical comparison NaN == NaN always produces 0 (that is, it never evaluates to true). Therefore, you cannot use x(x==NaN) = [] to remove NaNs from your data.

Code

Description

rmmissing(x);

Remove NaNs from a vector x.

x = x(~isnan(x));

Remove NaNs from a vector x.

x(isnan(x)) = [];

Remove NaNs from a vector x.

i = find(~isnan(x));

x = x(i)

Find the indices of elements in a vector x that are not NaNs. Keep only the non-NaN elements.

rmmissing(A);

Remove any rows containing NaNs from a matrix A.

A(any(isnan(A),2),:) = [];

Remove any rows containing NaNs from a matrix A.

rmmissing(M,dim)

Remove NaNs along any dimension dim of a multidimensional array M. For example, if M is a matrix, use rmmissing(M,2) to remove columns containing NaN.

### Fill Missing Data

When NaNs are present in data, you can replace them with non-NaN values. The fillmissing function offers several methods for replacing missing values. You can fill NaNs with the following:

• a constant

• 'previous' — previous non-missing value

• 'next' — next non-missing value

• 'nearest' — nearest non-missing value

• 'linear' — linear interpolation of neighboring, non-missing values

• 'spline' — piecewise cubic spline interpolation

• 'pchip' — shape-preserving piecewise cubic interpolation

While fillmissing works on numeric arrays containing NaNs, it also operates on arrays, tables, and timetables that can contain non-numeric data types such as categorical, datetime, duration, and string. For example, a missing datetime value can be represented with NaT, and a missing categorical value is represented as <undefined>. fillmissing, ismissing, standardizeMissing, and rmmissing all can operate on arrays, tables, and timetables containing non-numeric data types.

For numeric 1-D data, you also can interpolate over missing values with the interp1 function. For more information, see interp1.