fillmissing
Fill missing entries
Syntax
Description
fills missing entries of an array or table with the constant value F
= fillmissing(A
,'constant',v
)v
. If
A
is a matrix or multidimensional array, then v
can
be either a scalar or a vector. If v
is a vector, then each element
specifies the fill value in the corresponding column of A
. If
A
is a table or timetable, then v
can also be a cell
array whose elements contain fill values for each table variable.
Missing values are defined according to the data type of A
:
NaN
—double
,single
,duration
, andcalendarDuration
NaT
—datetime
<missing>
—string
<undefined>
—categorical
{''}
—cell
of character vectors
If A
is a table, then the data type of each variable defines the
missing value for that variable.
fills missing entries with the mean of the corresponding values from the
F
= fillmissing(A
,'knn'
,k
)k
nearest neighbor rows, calculated based on the pairwise Euclidean
distance between rows. For example, fillmissing(A,'knn',5)
fills missing
entries of A
with the mean of the corresponding values from the five
nearest neighbor rows.
fills gaps of missing entries using a custom method specified by a function handle
F
= fillmissing(A
,fillfun
,gapwindow
)fillfun
and a fixed window surrounding each gap from which the fill
values are computed. fillfun
must have the input arguments
xs
, ts
, and tq
, which are vectors
containing the sample data xs
of length gapwindow
, the
sample data locations ts
of length gapwindow
, and the
missing data locations tq
. The locations in ts
and
tq
are a subset of the sample points vector.
specifies the dimension of F
= fillmissing(___,dim
)A
to operate along in addition to any of the
input argument combinations in previous syntaxes. By default, fillmissing
operates along the first dimension whose size does not equal 1. For example, if
A
is a matrix, then fillmissing(A,2)
operates across
the columns of A
, filling missing data row by row.
specifies additional parameters for filling missing values using one or more namevalue
arguments. For example, if F
= fillmissing(___,Name,Value
)t
is a vector of time values, then
fillmissing(A,'linear','SamplePoints',t)
interpolates the data in
A
relative to the times in t
.
Examples
Vector with NaN
Values
Create a vector that contains NaN
values, and replace each NaN
with the previous nonmissing value.
A = [1 3 NaN 4 NaN NaN 5];
F = fillmissing(A,'previous')
F = 1×7
1 3 3 4 4 4 5
Matrix with NaN
Values
Create a 2by2 matrix with a NaN
value in each column. Fill NaN
with 100
in the first column and 1000
in the second column.
A = [1 NaN; NaN 2]
A = 2×2
1 NaN
NaN 2
F = fillmissing(A,'constant',[100 1000])
F = 2×2
1 1000
100 2
Interpolate Missing Data
Use interpolation to replace NaN
values in nonuniformly sampled data.
Define a vector of nonuniform sample points and evaluate the sine function over the points.
x = [4*pi:0.1:0, 0.1:0.2:4*pi]; A = sin(x);
Inject NaN
values into A
.
A(A < 0.75 & A > 0.5) = NaN;
Fill the missing data using linear interpolation, and return the filled vector F
and the logical vector TF
. The value 1 (true
) in entries of TF
corresponds to the values of F
that were filled.
[F,TF] = fillmissing(A,'linear','SamplePoints',x);
Plot the original data and filled data.
scatter(x,A) hold on scatter(x(TF),F(TF)) legend('Original Data','Filled Data')
Use Moving Median Method
Use a moving median to fill missing numeric data.
Create a vector of sample points x
and a vector of data A
that contains missing values.
x = linspace(0,10,200); A = sin(x) + 0.5*(rand(size(x))0.5); A([1:10 randi([1 length(x)],1,50)]) = NaN;
Replace NaN
values in A
using a moving median with a window of length 10, and plot the original data and the filled data.
F = fillmissing(A,'movmedian',10); plot(x,F,'.') hold on plot(x,A,'.') legend('Original Data','Filled Data')
Use Custom Fill Method
Define a custom function to fill NaN
values with the previous nonmissing value.
Define a vector of sample points t
and a vector of corresponding data A
containing NaN
values. Plot the data.
t = 10:10:100; A = [0.1 0.2 0.3 NaN NaN 0.6 0.7 NaN 0.9 1]; scatter(t,A)
Use the local function forwardfill
(defined at the end of the example) to fill missing gaps with the previous nonmissing value. The function handle inputs include:
xs
— data values used for fillingts
— locations of the values used for filling relative to the sample pointstq
— locations of the missing values relative to the sample pointsn
— number of values in the gap to fill
n = 2;
gapwindow = [10 0];
[F,TF] = fillmissing(A,@(xs,ts,tq) forwardfill(xs,ts,tq,n),gapwindow,'SamplePoints',t);
The gap window value [10 0]
tells fillmissing
to consider one data point before a missing gap and no data points after a gap, since the previous nonmissing value is located 10 units prior to the gap. The function handle input values determined by fillmissing
for the first gap are:
xs = 0.3
ts = 30
tq = [40 50]
The function handle input values for the second gap are:
xs = 0.7
ts = 70
tq = 80
Plot the original data and the filled data.
scatter(t,A)
hold on
scatter(t(TF),F(TF))
function y = forwardfill(xs,ts,tq,n) % Fill n values in the missing gap using the previous nonmissing value y = NaN(1,numel(tq)); y(1:min(numel(tq),n)) = xs; end
Matrix with Missing Endpoints
Create a matrix with missing entries and fill across the columns (second dimension) one row at a time using linear interpolation. For each row, fill leading and trailing missing values with the nearest nonmissing value in that row.
A = [NaN NaN 5 3 NaN 5 7 NaN 9 NaN; 8 9 NaN 1 4 5 NaN 5 NaN 5; NaN 4 9 8 7 2 4 1 1 NaN]
A = 3×10
NaN NaN 5 3 NaN 5 7 NaN 9 NaN
8 9 NaN 1 4 5 NaN 5 NaN 5
NaN 4 9 8 7 2 4 1 1 NaN
F = fillmissing(A,'linear',2,'EndValues','nearest')
F = 3×10
5 5 5 3 4 5 7 8 9 9
8 9 5 1 4 5 5 5 5 5
4 4 9 8 7 2 4 1 1 1
Table with Multiple Data Types
Fill missing values for table variables with different data types.
Create a table whose variables include categorical
, double
, and char
data types.
A = table(categorical({'Sunny'; 'Cloudy'; ''}),[66; NaN; 54],{''; 'N'; 'Y'},[37; 39; NaN],... 'VariableNames',{'Description' 'Temperature' 'Rain' 'Humidity'})
A=3×4 table
Description Temperature Rain Humidity
___________ ___________ __________ ________
Sunny 66 {0x0 char} 37
Cloudy NaN {'N' } 39
<undefined> 54 {'Y' } NaN
Replace all missing entries with the value from the previous entry. Since there is no previous element in the Rain
variable, the missing character vector is not replaced.
F = fillmissing(A,'previous')
F=3×4 table
Description Temperature Rain Humidity
___________ ___________ __________ ________
Sunny 66 {0x0 char} 37
Cloudy 66 {'N' } 39
Cloudy 54 {'Y' } 39
Replace the NaN
values from the Temperature
and Humidity
variables in A
with 0.
F = fillmissing(A,'constant',0,'DataVariables',{'Temperature','Humidity'})
F=3×4 table
Description Temperature Rain Humidity
___________ ___________ __________ ________
Sunny 66 {0x0 char} 37
Cloudy 0 {'N' } 39
<undefined> 54 {'Y' } 0
Alternatively, use the isnumeric
function to identify the numeric variables to operate on.
F = fillmissing(A,'constant',0,'DataVariables',@isnumeric)
F=3×4 table
Description Temperature Rain Humidity
___________ ___________ __________ ________
Sunny 66 {0x0 char} 37
Cloudy 0 {'N' } 39
<undefined> 54 {'Y' } 0
Now fill the missing values in A
with a specified constant for each table variable, which are contained in a cell array.
F = fillmissing(A,'constant',{categorical({'None'}),1000,'Unknown',1000})
F=3×4 table
Description Temperature Rain Humidity
___________ ___________ ___________ ________
Sunny 66 {'Unknown'} 37
Cloudy 1000 {'N' } 39
None 54 {'Y' } 1000
Specify Maximum Gap
Create a time vector t
in seconds and a corresponding vector of data A
that contains NaN
values.
t = seconds([2 4 8 17 98 134 256 311 1001]); A = [1 3 23 NaN NaN NaN 100 NaN 233];
Fill only missing values in A
that correspond to a maximum gap size of 250 seconds. Because the second gap is larger than 250 seconds, the NaN
value is not filled.
F = fillmissing(A,'linear','SamplePoints',t,'MaxGap',seconds(250))
F = 1×9
1.0000 3.0000 23.0000 25.7944 50.9435 62.1210 100.0000 NaN 233.0000
Use Custom Distance Functions
Use custom distance functions to fill missing entries using values from nearest neighbor rows.
Create a matrix that contains a NaN
value, and then create a logical vector that indicates the locations of missing entries in the third row.
A = [1 3 9 3; 5 1 7 2; 1 1 7 NaN; 12 1 9 1]; m = isnan(A(3,:));
Define two custom functions to measure distances between rows.
The function d1
measures distances between rows by summing up the distances between each coordinate pair; the function dinf
measures distances between rows by finding the maximum distance among the coordinate pairs.
d1 = @(x,~) sum(abs(diff(x)),'omitnan'); dinf = @(x,isNaN) norm(diff(x(:,~isNaN(1,:))),'inf');
Compute the d1
measured distance between the third row and each of the other three rows. The second row is the closest.
d1s = arrayfun(@(r) d1(A([r 3],:),m), setdiff(1:4,3))
d1s = 1×3
6 4 15
The fillmissing
function replaces the NaN
in the third row with the corresponding 2
from the second row.
F1 = fillmissing(A,'knn','Distance',d1)
F1 = 4×4
1 3 9 3
5 1 7 2
1 1 7 2
12 1 9 1
A similar analysis with dinf
measured distances finds the first row to be closest to the third. Now the fillmissing
function replaces the NaN
in the third row with the corresponding 3 from the first row.
dinfs = arrayfun(@(r) dinf(A([r 3],:),m), setdiff(1:4,3))
dinfs = 1×3
2 4 13
Finf = fillmissing(A,'knn','Distance',dinf)
Finf = 4×4
1 3 9 3
5 1 7 2
1 1 7 3
12 1 9 1
Input Arguments
A
— Input data
vector  matrix  multidimensional array  cell array of character vectors  table  timetable
Input data, specified as a vector, matrix, multidimensional array, cell array of character vectors, table, or timetable.
If
A
is a timetable, then only table values are filled. If the associated vector of row times contains aNaT
orNaN
value, thenfillmissing
produces an error. Row times must be unique and listed in ascending order.If
A
is a cell array or a table with cell array variables, thenfillmissing
only fills missing elements when the cell array contains character vectors.
v
— Fill constant
scalar  vector  cell array
Fill constant, specified as a scalar, vector, or cell array.
If
A
is a matrix or multidimensional array, thenv
can be a vector indicating a different fill value for each operating dimension. The length ofv
must match the length of the operating dimension.If
A
is a table or timetable, thenv
can be a cell array of fill values indicating a different fill value for each variable. The number of elements in the cell array must match the number of variables in the table.
method
— Fill method
'previous'
 'next'
 'nearest'
 'linear'
 'spline'
 'pchip'
 'makima'
Fill method, specified as one of these values:
Method  Description 

'previous'  Previous nonmissing value 
'next'  Next nonmissing value 
'nearest'  Nearest nonmissing value 
'linear'  Linear interpolation of neighboring, nonmissing values (numeric, duration ,
and datetime data types only) 
'spline'  Piecewise cubic spline interpolation (numeric, duration , and
datetime data types only) 
'pchip'  Shapepreserving piecewise cubic spline interpolation (numeric, duration ,
and datetime data types only) 
'makima'  Modified Akima cubic Hermite interpolation (numeric,
duration , and datetime data types
only) 
movmethod
— Moving method
'movmean'
 'movmedian'
Moving method to fill missing data, specified as one of these values:
Method  Description 

'movmean'  Moving average over a window of length window (numeric
data types only) 
'movmedian'  Moving median over a window of length window (numeric
data types only) 
window
— Window length
positive integer scalar  twoelement vector of positive integers  positive duration scalar  twoelement vector of positive durations
Window length for moving methods, specified as a positive integer scalar, a twoelement vector of positive integers, a positive duration scalar, or a twoelement vector of positive durations. The window is defined relative to the sample points.
If window
is a positive integer scalar, then the window is
centered about the current element and contains window1
neighboring
elements. If window
is even, then the window is centered about the
current and previous elements.
If window
is a twoelement vector of positive integers
[b f]
, then the window contains the current element,
b
elements backward, and f
elements
forward.
If A
is a timetable or SamplePoints
is
specified as a datetime
or duration
vector, then
the window must be of type duration
.
k
— Number of nearest neighbors
1
(default)  positive integer scalar
Number of nearest neighbors to average with the 'knn'
method,
specified as a positive integer scalar.
fillfun
— Custom fill method
function handle
Example: @(xs,ts,tq) myfun(xs,ts,tq)
Custom fill method, specified as a function handle. Valid function handles must include the following three input arguments:
Input Argument  Description 

xs  Vector containing data values used for filling. The length of
xs must match the length of the specified window. 
ts  Vector containing locations of the values used for filling. The length of
ts must match the length of the specified window.
ts is a subset of the sample points vector. 
tq  Vector containing locations of the missing values. tq
is a subset of the sample points vector. 
The function must return either a scalar or a vector with the same
length as tq
.
gapwindow
— Gap window length
positive integer scalar  twoelement vector of positive integers  positive duration scalar  twoelement vector of positive durations
Gap window length for custom fill functions, specified as a positive integer scalar, a twoelement vector of positive integers, a positive duration scalar, or a twoelement vector of positive durations. The gap window is defined relative to the sample points.
When specifying a function handle fillfun
for the fill method,
the value of gapwindow
represents a fixed window length that
surrounds each gap of missing values in the input data. The fill value is then computed
by fillfun
using the values in that window. For example, for default
sample points t = 1:10
and data A = [10 20 NaN NaN 50 60 70
NaN 90 100]
, a window length gapwindow = 3
specifies the
first gap window as [20 NaN NaN 50]
that fillfun
operates on to compute the fill value. The second gap window that
fillfun
operates on is [70 NaN 90]
.
When A
is a timetable or SamplePoints
is
specified as a datetime
or duration
vector,
gapwindow
must be of type duration
.
dim
— Operating dimension
positive integer scalar
Operating dimension, specified as a positive integer scalar. If no value is specified, then the default is the first array dimension whose size does not equal 1.
Consider an m
byn
input matrix,
A
:
fillmissing(A,method,1)
fills missing values according to the data in each column ofA
and returns anm
byn
matrix.fillmissing(A,method,2)
fills missing values according to the data in each row ofA
and returns anm
byn
matrix.
For table or timetable input data, dim
is not supported and
operation is along each table or timetable variable separately.
NameValue Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Namevalue arguments must appear after other arguments, but the order of the
pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.
Example: fillmissing(T,method,'SamplePoints',"Var1")
SamplePoints
— Sample points
vector  table variable name  scalar  function handle  table vartype
subscript
Sample points, specified as a vector of sample point values or one of the options
in the following table when the input data is a table. The sample points represent the
xaxis locations of the data, and must be sorted and contain
unique elements. Sample points do not need to be uniformly sampled. The vector
[1 2 3 ...]
is the default.
When the input data is a table, you can specify the sample points as a table variable using one of these options:
Indexing Scheme  Examples 

Variable name:


Variable index:


Function handle:


Variable type:


Note
This namevalue argument is not supported when the input data is a
timetable
. Timetables use the vector of row times as the sample
points. To use different sample points, you must edit the timetable so that the row times
contain the desired sample points.
Moving windows are defined relative to the sample points. For example, if
t
is a vector of times corresponding to the input data, then
fillmissing(rand(1,10),'movmean',3,'SamplePoints',t)
has a window
that represents the time interval between t(i)1.5
and
t(i)+1.5
.
When the sample points vector has data type datetime
or
duration
, the moving window length must have type
duration
.
Example: fillmissing([1 NaN 3 4],'linear','SamplePoints',[1 2.5 3
4])
Example: fillmissing(T,'linear','SamplePoints',"Var1")
Data Types: single
 double
 datetime
 duration
DataVariables
— Table variables to operate on
table variable name  scalar  vector  cell array  pattern  function handle  table vartype
subscript
Table variables to operate on, specified as one of the options in this table. The
DataVariables
value indicates which variables of the input table
to fill.
Other variables in the table not specified by DataVariables
pass through to the output without being filled.
Indexing Scheme  Examples 

Variable names:


Variable index:


Function handle:


Variable type:


Example: fillmissing(T,'linear','DataVariables',["Var1" "Var2"
"Var4"])
ReplaceValues
— Replace values indicator
true
or 1
(default)  false
or 0
Replace values indicator, specified as one of these values when
A
is a table or timetable:
true
or1
— Replace input table variables containing missing entries with filled table variables.false
or0
— Append the input table with all table variables that were checked for missing entries. The missing entries in the appended variables are filled.
For vector, matrix, or multidimensional array input data,
ReplaceValues
is not supported.
Example: fillmissing(T,'previous','ReplaceValues',false)
EndValues
— Method for handling endpoints
'extrap'
(default)  'previous'
 'next'
 'nearest'
 'none'
 scalar
Method for handling endpoints, specified as 'extrap'
,
'previous'
, 'next'
,
'nearest'
, 'none'
, or a constant scalar value.
The endpoint fill method handles leading and trailing missing values based on these
definitions:
Method  Description 

'extrap'  Same as method 
'previous'  Previous nonmissing value 
'next'  Next nonmissing value 
'nearest'  Nearest nonmissing value 
'none'  No fill value 
scalar  Constant value (numeric, duration , and datetime data
types only) 
MissingLocations
— Known missing indicator
vector  matrix  multidimensional array
Known missing indicator, specified as a logical vector, matrix, or
multidimensional array of the same size as A
. The indicator
elements can be 1
(true
) to indicate a missing
value in the corresponding location of A
or 0
(false
) otherwise.
Data Types: logical
MaxGap
— Maximum gap size to fill
numeric scalar  duration
scalar  calendarDuration
scalar
Maximum gap size to fill, specified as a numeric scalar,
duration
scalar, or calendarDuration
scalar.
Gaps are clusters of consecutive missing values whose size is the distance between the
nonmissing values surrounding the gap. The gap size is computed relative to the sample
points. Gaps smaller than or equal to the max gap size are filled, and gaps larger
than the gap size are not.
For example, consider the vector y = [25 NaN NaN 100]
using the
default sample points [1 2 3 4]
. The gap size in the vector is
computed from the sample points as 4  1 = 3
, so a
MaxGap
value of 2
leaves the missing values
unaltered, while a MaxGap
value of 3
fills in
the missing values.
For missing values at the beginning or end of the data:
A single missing value at the beginning or at the end of the input data has a gap size of 0 and is always filled.
Clusters of missing values occurring at the beginning or end of the input data are not completely surrounded by nonmissing values, so the gap size is computed using the nearest existing sample points. For the default sample points
1:N
, this produces a gap size that is 1 smaller than if the same cluster occurred in the middle of the data.
Distance
— Distance function
'euclidean'
(default)  'seuclidean'
 function handle
Distance function to use when finding nearest neighbor rows, specified as
'euclidean'
(Euclidean distance), 'seuclidean'
(scaled Euclidean distance), or a function handle for a distance function.
If you specify a function handle for a distance function, the function must satisfy these conditions:
The function must accept two inputs.
The first input of the function must be a tworow matrix, table, or timetable that contains the two vectors to be compared.
The second input of the function must be a logical matrix that indicates the locations of missing values in the vectors. You can ignore the second input by specifying it as
~
.The function must return the distance as a real, scalar value of type
double
.
Example: fillmissing(A,'knn','Distance',@(x,~)
sum(abs(diff(x)),'omitmissing'))
Output Arguments
F
— Filled data
vector  matrix  multidimensional array  table  timetable
Filled data, returned as a vector, matrix, multidimensional array, table, or timetable.
F
is the same size as A
unless the value of
ReplaceValues
is false
. If the value of
ReplaceValues
is false
, then the width of
F
is the sum of the input data width and the number of data
variables specified.
TF
— Filled data indicator
vector  matrix  multidimensional array
Filled data indicator, returned as a vector, matrix, or multidimensional array.
TF
is a logical array where 1
(true
) corresponds to filled entries in F
that
were previously missing and 0
(false
) corresponds
to unchanged entries.
TF
is the same size as F
.
Data Types: logical
Tips
For input data that is a structure array or a cell array of noncharacter vectors,
fillmissing
does not fill any entries. To fill missing entries in a structure array, applyfillmissing
to each field in the structure by using thestructfun
function. To fill missing entries in a cell array of noncharacter vectors, applyfillmissing
to each cell in the cell array by using thecellfun
function.
Extended Capabilities
Tall Arrays
Calculate with arrays that have more rows than fit in memory.
Usage notes and limitations:
The
'spline'
and'makima'
methods are not supported.Function handle fill methods are not supported.
The
'knn'
fill method andDistance
namevalue argument are not supported.The
MaxGap
,SamplePoints
, andMissingLocations
namevalue arguments are not supported.The
DataVariables
namevalue argument cannot specify a function handle.The
EndValues
namevalue argument can only specify'extrap'
.The syntax
fillmissing(A,movmethod,window)
is not supported whenA
is a tall timetable.The syntax
fillmissing(A,'constant',v)
must specify a scalar value forv
.The syntax
fillmissing(A,___)
does not support character vector variables whenA
is a tall table or tall timetable.
For more information, see Tall Arrays.
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Usage notes and limitations:
The
MaxGap
andReplaceValues
namevalue arguments are not supported.The
'makima'
option is not supported.When the
SamplePoints
value has typedatetime
or the input data is a timetable withdatetime
row times, only the methods'constant'
,'movmean'
, and'movmedian'
are supported.Function handle inputs for the
fillmethod
argument are not supported.The
'knn'
fill method andDistance
namevalue argument are not supported.
ThreadBased Environment
Run code in the background using MATLAB® backgroundPool
or accelerate code with Parallel Computing Toolbox™ ThreadPool
.
This function fully supports threadbased environments. For more information, see Run MATLAB Functions in ThreadBased Environment.
GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.
Usage notes and limitations:
The
'pchip'
fill method is not supported.The
SamplePoints
namevalue argument is not supported for moving window fill methods'movmean'
and'movmedian'
.The
'knn'
fill method andDistance
namevalue argument are not supported.
For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).
Distributed Arrays
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.
Usage notes and limitations:
The
'knn'
fill method andDistance
namevalue argument are not supported.
For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).
Version History
Introduced in R2016bR2023a: Fill with corresponding values from nearest rows
Use the 'knn'
method to fill missing entries with the corresponding
values from the nearest rows. You can optionally specify a k
value to
fill missing entries with the mean of the corresponding values from the
k
nearest rows.
You can also use the Distance
namevalue argument to specify a
custom function with which to measure distances between rows.
R2022b: Character arrays have no standard missing value
Character arrays have no default definition of a standard missing value. Therefore,
fillmissing
treats blank character array elements ('
'
) as nonmissing. For example, fillmissing(['a'; '
'],'previous')
returns ['a'; ' ']
. Previously, it returned
['a'; 'a']
.
To treat blank character array elements as missing, use the
MissingLocations
namevalue argument. For example, find blank character
array elements using TF = ismissing(['a'; ' '],' ')
, and then specify a
known missing indicator, as in F = fillmissing(['a'; '
'],'previous',MissingLocations=TF)
.
R2022a: Append filled values
For table or timetable input data, append the input table with all table variables that
were checked for missing entries. The missing entries in the appended variables are filled.
Append, rather than replace, table variables by setting the ReplaceValues
namevalue argument to false
.
R2021b: Specify sample points as table variable
For table input data, specify the sample points as a table variable using the
SamplePoints
namevalue argument.
R2021a: Specify custom fill method
Fill missing values using a custom method by specifying fillfun
as a
function handle.
See Also
Functions
fillmissing2
ismissing
standardizeMissing
anymissing
rmmissing
filloutliers
isnan
missing
isnat
smoothdata
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