Next: Basic Statistical Functions, Previous: Descriptive Statistics, Up: Statistics [Contents][Index]
It is often useful to calculate descriptive statistics over a subsection
(i.e., window) of a full dataset. Octave provides the function movfun
which will call an arbitrary function handle with windows of data and
accumulate the results. Many of the most commonly desired functions, such as
the moving average over a window of data (movmean
), are already
provided.
Apply function fcn to a moving window of length wlen on data x.
If wlen is a scalar, the function fcn is applied to a moving
window of length wlen. When wlen is an odd number the window is
symmetric and includes (wlen - 1) / 2
elements on either
side of the central element. For example, when calculating the output at
index 5 with a window length of 3, movfun
uses data elements
[4, 5, 6]
. If wlen is an even number, the window is
asymmetric and has wlen/2
elements to the left of the
central element and wlen/2 - 1
elements to the right of the
central element. For example, when calculating the output at index 5 with a
window length of 4, movfun
uses data elements
[3, 4, 5, 6]
.
If wlen is an array with two elements [nb, na]
,
the function is applied to a moving window -nb:na
. This
window includes nb number of elements before the current
element and na number of elements after the current element.
The current element is always included. For example, given
wlen = [3, 0]
, the data used to calculate index 5 is
[2, 3, 4, 5]
.
During calculations the data input x is reshaped into a 2-dimensional wlen-by-N matrix and fcn is called on this new matrix. Therefore, fcn must accept an array input argument and apply the computation along dimension 1, i.e., down the columns of the array.
When applied to an array (possibly multi-dimensional) with n columns,
fcn may return a result in either of two formats: Format 1)
an array of size 1-by-n-by-dim3-by-…-by-dimN. This
is the typical output format from Octave core functions. Type
demo ("movfun", 5)
for an example of this use case.
Format 2) a row vector of length
n * numel_higher_dims
where numel_higher_dims is
prod (size (x)(3:end))
. The output of fcn for the
i-th input column must be found in the output at indices
i:n:(n*numel_higher_dims)
.
This format is useful when concatenating functions into arrays, or when
using nthargout
. Type demo ("movfun", 6)
for an example of
this case.
The calculation can be controlled by specifying property/value pairs. Valid properties are
"dim"
Operate along the dimension specified, rather than the default of the first non-singleton dimension.
"Endpoints"
This property controls how results are calculated at the boundaries (endpoints) of the window. Possible values are:
"shrink"
(default)The window is truncated at the beginning and end of the array to exclude
elements for which there is no source data. For example, with a window of
length 3, y(1) = fcn (x(1:2))
, and
y(end) = fcn (x(end-1:end))
.
"discard"
Any y values that use a window extending beyond the original
data array are deleted. For example, with a 10-element data vector and a
window of length 3, the output will contain only 8 elements. The first
element would require calculating the function over indices
[0, 1, 2]
and is therefore discarded. The last element would
require calculating the function over indices [9, 10, 11]
and is
therefore discarded.
"fill"
Any window elements outside the data array are replaced by NaN
. For
example, with a window of length 3,
y(1) = fcn ([NaN, x(1:2)])
, and
y(end) = fcn ([x(end-1:end), NaN])
.
This option usually results in y having NaN
values at the
boundaries, although it is influenced by how fcn handles NaN
,
and also by the property "nancond"
.
Any window elements outside the data array are replaced by the specified
value user_value which must be a numeric scalar. For example, with a
window of length 3,
y(1) = fcn ([user_value, x(1:2)])
, and
y(end) = fcn ([x(end-1:end), user_value])
.
A common choice for user_value is 0.
"same"
Any window elements outside the data array are replaced by the value of
x at the boundary. For example, with a window of length 3,
y(1) = fcn ([x(1), x(1:2)])
, and
y(end) = fcn ([x(end-1:end), x(end)])
.
"periodic"
The window is wrapped so that any missing data elements are taken from
the other side of the data. For example, with a window of length 3,
y(1) = fcn ([x(end), x(1:2)])
, and
y(end) = fcn ([x(end-1:end), x(1)])
.
Note that for some of these choices, the window size at the boundaries is not the same as for the central part, and fcn must work in these cases.
"nancond"
Controls whether NaN
and NA
values should be included (value:
"includenan"
), or excluded (value: "omitnan"
), from the data
passed to fcn. The default is "includenan"
. Caution:
The "omitnan"
option is not yet implemented.
"outdim"
A row vector that selects which dimensions of the calculation will appear in the output y. This is only useful when fcn returns an N-dimensional array in Format 1. The default is to return all output dimensions.
Programming Note: The property "outdim"
can be used to save memory
when the output of fcn has many dimensions, or when a wrapper to the
base function that selects the desired outputs is too costly. When memory
is not an issue, the easiest way to select output dimensions is to first
calculate the complete result with movfun
and then filter that result
with indexing. If code complexity is not an issue then a wrapper can be
created using anonymous functions. For example, if basefcn
is a function returning a K-dimensional row output, and only
dimension D is desired, then the following wrapper could be used.
fcn = @(x) basefcn (x)(:,columns(x) * (D-1) + (1:columns(x))); y = movfun (@fcn, …);
Generate indices to slice a vector of length N into windows of length wlen.
The input N must be a positive integer.
The moving window length input wlen can either be a scalar not equal
to 1 or a 2-element array of integers. For scalar values, if odd the window
is symmetric and includes (wlen - 1) / 2
elements on either
side of the central element. If wlen is even the window is asymmetric
and has wlen/2
elements to the left of the central element
and wlen/2 - 1
elements to the right of the central
element. When wlen is a 2-element array,
[nb, na]
, the window includes nb elements to
the left of the current element and na elements to the right of the
current element.
The output slcidx is an array of indices of the slices that fit fully
within the vector, where each column is an individual slice as the window
moves from left to right. The slices have wlen elements for scalar
wlen, or nb + na + 1
elements for array valued
wlen.
Optional output C is an row vector of window center positions where the window stays fully within the vector.
Optional outputs Cpre and Cpost contain the vector elements at the start and end of the vector, respectively, that result in the window extending beyond the ends of the vector.
Optional output win is a column vector with the same number of rows as slcidx that contains the moving window defined as a center relative position stencil.
See also: movfun.
Calculate the moving mean absolute deviation over a sliding window of length wlen on data x.
If wlen is a scalar, the function mad
is applied to a
moving window of length wlen. When wlen is an odd number the
window is symmetric and includes (wlen - 1) / 2
elements on
either side of the central element. For example, when calculating the
output at index 5 with a window length of 3, movmad
uses data
elements [4, 5, 6]
. If wlen is an even number, the window
is asymmetric and has wlen/2
elements to the left of the
central element and wlen/2 - 1
elements to the right of the
central element. For example, when calculating the output at index 5 with a
window length of 4, movmad
uses data elements
[3, 4, 5, 6]
.
If wlen is an array with two elements [nb, na]
,
the function is applied to a moving window -nb:na
. This
window includes nb number of elements before the current
element and na number of elements after the current element.
The current element is always included. For example, given
wlen = [3, 0]
, the data used to calculate index 5 is
[2, 3, 4, 5]
.
If the optional argument dim is given, operate along this dimension.
The optional string argument "nancond"
controls whether
NaN
and NA
values should be included ("includenan"
),
or excluded ("omitnan"
), from the data passed to mad
. The
default is "includenan"
. Caution: the "omitnan"
option is
not yet implemented.
The calculation can be controlled by specifying property/value pairs. Valid properties are
"Endpoints"
This property controls how results are calculated at the boundaries (endpoints) of the window. Possible values are:
"shrink"
(default)The window is truncated at the beginning and end of the array to exclude
elements for which there is no source data. For example, with a window of
length 3, y(1) = mad (x(1:2))
, and
y(end) = mad (x(end-1:end))
.
"discard"
Any y values that use a window extending beyond the original
data array are deleted. For example, with a 10-element data vector and a
window of length 3, the output will contain only 8 elements. The first
element would require calculating the function over indices
[0, 1, 2]
and is therefore discarded. The last element would
require calculating the function over indices [9, 10, 11]
and is
therefore discarded.
"fill"
Any window elements outside the data array are replaced by NaN
. For
example, with a window of length 3,
y(1) = mad ([NaN, x(1:2)])
, and
y(end) = mad ([x(end-1:end), NaN])
.
This option usually results in y having NaN
values at the
boundaries, although it is influenced by how mad
handles NaN
,
and also by the property "nancond"
.
Any window elements outside the data array are replaced by the specified
value user_value which must be a numeric scalar. For example, with a
window of length 3,
y(1) = mad ([user_value, x(1:2)])
, and
y(end) = mad ([x(end-1:end), user_value])
.
A common choice for user_value is 0.
"same"
Any window elements outside the data array are replaced by the value of
x at the boundary. For example, with a window of length 3,
y(1) = mad ([x(1), x(1:2)])
, and
y(end) = mad ([x(end-1:end), x(end)])
.
"periodic"
The window is wrapped so that any missing data elements are taken from
the other side of the data. For example, with a window of length 3,
y(1) = mad ([x(end), x(1:2)])
, and
y(end) = mad ([x(end-1:end), x(1)])
.
"SamplePoints"
Caution: This option is not yet implemented.
Programming Note: This function is a wrapper which calls movfun
.
For additional options and documentation, see movfun
.
See also: movfun, movslice, movmax, movmean, movmedian, movmin, movprod, movstd, movsum, movvar.
Calculate the moving maximum over a sliding window of length wlen on data x.
If wlen is a scalar, the function max
is applied to a
moving window of length wlen. When wlen is an odd number the
window is symmetric and includes (wlen - 1) / 2
elements on
either side of the central element. For example, when calculating the
output at index 5 with a window length of 3, movmax
uses data
elements [4, 5, 6]
. If wlen is an even number, the window
is asymmetric and has wlen/2
elements to the left of the
central element and wlen/2 - 1
elements to the right of the
central element. For example, when calculating the output at index 5 with a
window length of 4, movmax
uses data elements
[3, 4, 5, 6]
.
If wlen is an array with two elements [nb, na]
,
the function is applied to a moving window -nb:na
. This
window includes nb number of elements before the current
element and na number of elements after the current element.
The current element is always included. For example, given
wlen = [3, 0]
, the data used to calculate index 5 is
[2, 3, 4, 5]
.
If the optional argument dim is given, operate along this dimension.
The optional string argument "nancond"
controls whether
NaN
and NA
values should be included ("includenan"
),
or excluded ("omitnan"
), from the data passed to max
. The
default is "includenan"
. Caution: the "omitnan"
option is
not yet implemented.
The calculation can be controlled by specifying property/value pairs. Valid properties are
"Endpoints"
This property controls how results are calculated at the boundaries (endpoints) of the window. Possible values are:
"shrink"
(default)The window is truncated at the beginning and end of the array to exclude
elements for which there is no source data. For example, with a window of
length 3, y(1) = max (x(1:2))
, and
y(end) = max (x(end-1:end))
.
"discard"
Any y values that use a window extending beyond the original
data array are deleted. For example, with a 10-element data vector and a
window of length 3, the output will contain only 8 elements. The first
element would require calculating the function over indices
[0, 1, 2]
and is therefore discarded. The last element would
require calculating the function over indices [9, 10, 11]
and is
therefore discarded.
"fill"
Any window elements outside the data array are replaced by NaN
. For
example, with a window of length 3,
y(1) = max ([NaN, x(1:2)])
, and
y(end) = max ([x(end-1:end), NaN])
.
This option usually results in y having NaN
values at the
boundaries, although it is influenced by how max
handles NaN
,
and also by the property "nancond"
.
Any window elements outside the data array are replaced by the specified
value user_value which must be a numeric scalar. For example, with a
window of length 3,
y(1) = max ([user_value, x(1:2)])
, and
y(end) = max ([x(end-1:end), user_value])
.
A common choice for user_value is 0.
"same"
Any window elements outside the data array are replaced by the value of
x at the boundary. For example, with a window of length 3,
y(1) = max ([x(1), x(1:2)])
, and
y(end) = max ([x(end-1:end), x(end)])
.
"periodic"
The window is wrapped so that any missing data elements are taken from
the other side of the data. For example, with a window of length 3,
y(1) = max ([x(end), x(1:2)])
, and
y(end) = max ([x(end-1:end), x(1)])
.
"SamplePoints"
Caution: This option is not yet implemented.
Programming Note: This function is a wrapper which calls movfun
.
For additional options and documentation, see movfun
.
See also: movfun, movslice, movmad, movmean, movmedian, movmin, movprod, movstd, movsum, movvar.
Calculate the moving average over a sliding window of length wlen on data x.
If wlen is a scalar, the function mean
is applied to a
moving window of length wlen. When wlen is an odd number the
window is symmetric and includes (wlen - 1) / 2
elements on
either side of the central element. For example, when calculating the
output at index 5 with a window length of 3, movmean
uses data
elements [4, 5, 6]
. If wlen is an even number, the window
is asymmetric and has wlen/2
elements to the left of the
central element and wlen/2 - 1
elements to the right of the
central element. For example, when calculating the output at index 5 with a
window length of 4, movmean
uses data elements
[3, 4, 5, 6]
.
If wlen is an array with two elements [nb, na]
,
the function is applied to a moving window -nb:na
. This
window includes nb number of elements before the current
element and na number of elements after the current element.
The current element is always included. For example, given
wlen = [3, 0]
, the data used to calculate index 5 is
[2, 3, 4, 5]
.
If the optional argument dim is given, operate along this dimension.
The optional string argument "nancond"
controls whether
NaN
and NA
values should be included ("includenan"
),
or excluded ("omitnan"
), from the data passed to mean
. The
default is "includenan"
. Caution: the "omitnan"
option is
not yet implemented.
The calculation can be controlled by specifying property/value pairs. Valid properties are
"Endpoints"
This property controls how results are calculated at the boundaries (endpoints) of the window. Possible values are:
"shrink"
(default)The window is truncated at the beginning and end of the array to exclude
elements for which there is no source data. For example, with a window of
length 3, y(1) = mean (x(1:2))
, and
y(end) = mean (x(end-1:end))
.
"discard"
Any y values that use a window extending beyond the original
data array are deleted. For example, with a 10-element data vector and a
window of length 3, the output will contain only 8 elements. The first
element would require calculating the function over indices
[0, 1, 2]
and is therefore discarded. The last element would
require calculating the function over indices [9, 10, 11]
and is
therefore discarded.
"fill"
Any window elements outside the data array are replaced by NaN
. For
example, with a window of length 3,
y(1) = mean ([NaN, x(1:2)])
, and
y(end) = mean ([x(end-1:end), NaN])
.
This option usually results in y having NaN
values at the
boundaries, although it is influenced by how mean
handles NaN
,
and also by the property "nancond"
.
Any window elements outside the data array are replaced by the specified
value user_value which must be a numeric scalar. For example, with a
window of length 3,
y(1) = mean ([user_value, x(1:2)])
, and
y(end) = mean ([x(end-1:end), user_value])
.
A common choice for user_value is 0.
"same"
Any window elements outside the data array are replaced by the value of
x at the boundary. For example, with a window of length 3,
y(1) = mean ([x(1), x(1:2)])
, and
y(end) = mean ([x(end-1:end), x(end)])
.
"periodic"
The window is wrapped so that any missing data elements are taken from
the other side of the data. For example, with a window of length 3,
y(1) = mean ([x(end), x(1:2)])
, and
y(end) = mean ([x(end-1:end), x(1)])
.
"SamplePoints"
Caution: This option is not yet implemented.
Programming Note: This function is a wrapper which calls movfun
.
For additional options and documentation, see movfun
.
See also: movfun, movslice, movmad, movmax, movmedian, movmin, movprod, movstd, movsum, movvar.
Calculate the moving median over a sliding window of length wlen on data x.
If wlen is a scalar, the function movmedian
is applied to a
moving window of length wlen. When wlen is an odd number the
window is symmetric and includes (wlen - 1) / 2
elements on
either side of the central element. For example, when calculating the
output at index 5 with a window length of 3, movmedian
uses data
elements [4, 5, 6]
. If wlen is an even number, the window
is asymmetric and has wlen/2
elements to the left of the
central element and wlen/2 - 1
elements to the right of the
central element. For example, when calculating the output at index 5 with a
window length of 4, movmedian
uses data elements
[3, 4, 5, 6]
.
If wlen is an array with two elements [nb, na]
,
the function is applied to a moving window -nb:na
. This
window includes nb number of elements before the current
element and na number of elements after the current element.
The current element is always included. For example, given
wlen = [3, 0]
, the data used to calculate index 5 is
[2, 3, 4, 5]
.
If the optional argument dim is given, operate along this dimension.
The optional string argument "nancond"
controls whether
NaN
and NA
values should be included ("includenan"
),
or excluded ("omitnan"
), from the data passed to
movmedian
. The default is "includenan"
. Caution: the
"omitnan"
option is not yet implemented.
The calculation can be controlled by specifying property/value pairs. Valid properties are
"Endpoints"
This property controls how results are calculated at the boundaries (endpoints) of the window. Possible values are:
"shrink"
(default)The window is truncated at the beginning and end of the array to exclude
elements for which there is no source data. For example, with a window of
length 3, y(1) = movmedian (x(1:2))
, and
y(end) = movmedian (x(end-1:end))
.
"discard"
Any y values that use a window extending beyond the original
data array are deleted. For example, with a 10-element data vector and a
window of length 3, the output will contain only 8 elements. The first
element would require calculating the function over indices
[0, 1, 2]
and is therefore discarded. The last element would
require calculating the function over indices [9, 10, 11]
and is
therefore discarded.
"fill"
Any window elements outside the data array are replaced by NaN
. For
example, with a window of length 3,
y(1) = movmedian ([NaN, x(1:2)])
, and
y(end) = movmedian ([x(end-1:end), NaN])
.
This option usually results in y having NaN
values at the
boundaries, although it is influenced by how movmedian
handles
NaN
, and also by the property "nancond"
.
Any window elements outside the data array are replaced by the specified
value user_value which must be a numeric scalar. For example, with a
window of length 3,
y(1) = movmedian ([user_value, x(1:2)])
, and
y(end) = movmedian ([x(end-1:end), user_value])
.
A common choice for user_value is 0.
"same"
Any window elements outside the data array are replaced by the value of
x at the boundary. For example, with a window of length 3,
y(1) = movmedian ([x(1), x(1:2)])
, and
y(end) = movmedian ([x(end-1:end), x(end)])
.
"periodic"
The window is wrapped so that any missing data elements are taken from
the other side of the data. For example, with a window of length 3,
y(1) = movmedian ([x(end), x(1:2)])
, and
y(end) = movmedian ([x(end-1:end), x(1)])
.
"SamplePoints"
Caution: This option is not yet implemented.
Programming Note: This function is a wrapper which calls movfun
.
For additional options and documentation, see movfun
.
See also: movfun, movslice, movmad, movmax, movmean, movmin, movprod, movstd, movsum, movvar.
Calculate the moving minimum over a sliding window of length wlen on data x.
If wlen is a scalar, the function min
is applied to a
moving window of length wlen. When wlen is an odd number the
window is symmetric and includes (wlen - 1) / 2
elements on
either side of the central element. For example, when calculating the
output at index 5 with a window length of 3, movmin
uses data
elements [4, 5, 6]
. If wlen is an even number, the window
is asymmetric and has wlen/2
elements to the left of the
central element and wlen/2 - 1
elements to the right of the
central element. For example, when calculating the output at index 5 with a
window length of 4, movmin
uses data elements
[3, 4, 5, 6]
.
If wlen is an array with two elements [nb, na]
,
the function is applied to a moving window -nb:na
. This
window includes nb number of elements before the current
element and na number of elements after the current element.
The current element is always included. For example, given
wlen = [3, 0]
, the data used to calculate index 5 is
[2, 3, 4, 5]
.
If the optional argument dim is given, operate along this dimension.
The optional string argument "nancond"
controls whether
NaN
and NA
values should be included ("includenan"
),
or excluded ("omitnan"
), from the data passed to min
. The
default is "includenan"
. Caution: the "omitnan"
option is
not yet implemented.
The calculation can be controlled by specifying property/value pairs. Valid properties are
"Endpoints"
This property controls how results are calculated at the boundaries (endpoints) of the window. Possible values are:
"shrink"
(default)The window is truncated at the beginning and end of the array to exclude
elements for which there is no source data. For example, with a window of
length 3, y(1) = min (x(1:2))
, and
y(end) = min (x(end-1:end))
.
"discard"
Any y values that use a window extending beyond the original
data array are deleted. For example, with a 10-element data vector and a
window of length 3, the output will contain only 8 elements. The first
element would require calculating the function over indices
[0, 1, 2]
and is therefore discarded. The last element would
require calculating the function over indices [9, 10, 11]
and is
therefore discarded.
"fill"
Any window elements outside the data array are replaced by NaN
. For
example, with a window of length 3,
y(1) = min ([NaN, x(1:2)])
, and
y(end) = min ([x(end-1:end), NaN])
.
This option usually results in y having NaN
values at the
boundaries, although it is influenced by how min
handles NaN
,
and also by the property "nancond"
.
Any window elements outside the data array are replaced by the specified
value user_value which must be a numeric scalar. For example, with a
window of length 3,
y(1) = min ([user_value, x(1:2)])
, and
y(end) = min ([x(end-1:end), user_value])
.
A common choice for user_value is 0.
"same"
Any window elements outside the data array are replaced by the value of
x at the boundary. For example, with a window of length 3,
y(1) = min ([x(1), x(1:2)])
, and
y(end) = min ([x(end-1:end), x(end)])
.
"periodic"
The window is wrapped so that any missing data elements are taken from
the other side of the data. For example, with a window of length 3,
y(1) = min ([x(end), x(1:2)])
, and
y(end) = min ([x(end-1:end), x(1)])
.
"SamplePoints"
Caution: This option is not yet implemented.
Programming Note: This function is a wrapper which calls movfun
.
For additional options and documentation, see movfun
.
See also: movfun, movslice, movmad, movmax, movmean, movmedian, movprod, movstd, movsum, movvar.
Calculate the moving product over a sliding window of length wlen on data x.
If wlen is a scalar, the function movprod
is applied to a
moving window of length wlen. When wlen is an odd number the
window is symmetric and includes (wlen - 1) / 2
elements on
either side of the central element. For example, when calculating the
output at index 5 with a window length of 3, movprod
uses data
elements [4, 5, 6]
. If wlen is an even number, the window
is asymmetric and has wlen/2
elements to the left of the
central element and wlen/2 - 1
elements to the right of the
central element. For example, when calculating the output at index 5 with a
window length of 4, movprod
uses data elements
[3, 4, 5, 6]
.
If wlen is an array with two elements [nb, na]
,
the function is applied to a moving window -nb:na
. This
window includes nb number of elements before the current
element and na number of elements after the current element.
The current element is always included. For example, given
wlen = [3, 0]
, the data used to calculate index 5 is
[2, 3, 4, 5]
.
If the optional argument dim is given, operate along this dimension.
The optional string argument "nancond"
controls whether
NaN
and NA
values should be included ("includenan"
),
or excluded ("omitnan"
), from the data passed to movprod
.
The default is "includenan"
. Caution: the "omitnan"
option is not yet implemented.
The calculation can be controlled by specifying property/value pairs. Valid properties are
"Endpoints"
This property controls how results are calculated at the boundaries (endpoints) of the window. Possible values are:
"shrink"
(default)The window is truncated at the beginning and end of the array to exclude
elements for which there is no source data. For example, with a window of
length 3, y(1) = movprod (x(1:2))
, and
y(end) = movprod (x(end-1:end))
.
"discard"
Any y values that use a window extending beyond the original
data array are deleted. For example, with a 10-element data vector and a
window of length 3, the output will contain only 8 elements. The first
element would require calculating the function over indices
[0, 1, 2]
and is therefore discarded. The last element would
require calculating the function over indices [9, 10, 11]
and is
therefore discarded.
"fill"
Any window elements outside the data array are replaced by NaN
. For
example, with a window of length 3,
y(1) = movprod ([NaN, x(1:2)])
, and
y(end) = movprod ([x(end-1:end), NaN])
.
This option usually results in y having NaN
values at the
boundaries, although it is influenced by how movprod
handles
NaN
, and also by the property "nancond"
.
Any window elements outside the data array are replaced by the specified
value user_value which must be a numeric scalar. For example, with a
window of length 3,
y(1) = movprod ([user_value, x(1:2)])
, and
y(end) = movprod ([x(end-1:end), user_value])
.
A common choice for user_value is 0.
"same"
Any window elements outside the data array are replaced by the value of
x at the boundary. For example, with a window of length 3,
y(1) = movprod ([x(1), x(1:2)])
, and
y(end) = movprod ([x(end-1:end), x(end)])
.
"periodic"
The window is wrapped so that any missing data elements are taken from
the other side of the data. For example, with a window of length 3,
y(1) = movprod ([x(end), x(1:2)])
, and
y(end) = movprod ([x(end-1:end), x(1)])
.
"SamplePoints"
Caution: This option is not yet implemented.
Programming Note: This function is a wrapper which calls movfun
.
For additional options and documentation, see movfun
.
See also: movfun, movslice, movmad, movmax, movmean, movmedian, movmin, movstd, movsum, movvar.
Calculate the moving standard deviation over a sliding window of length wlen on data x.
If wlen is a scalar, the function movstd
is applied to a
moving window of length wlen. When wlen is an odd number the
window is symmetric and includes (wlen - 1) / 2
elements on
either side of the central element. For example, when calculating the
output at index 5 with a window length of 3, movstd
uses data
elements [4, 5, 6]
. If wlen is an even number, the window
is asymmetric and has wlen/2
elements to the left of the
central element and wlen/2 - 1
elements to the right of the
central element. For example, when calculating the output at index 5 with a
window length of 4, movstd
uses data elements
[3, 4, 5, 6]
.
If wlen is an array with two elements [nb, na]
,
the function is applied to a moving window -nb:na
. This
window includes nb number of elements before the current
element and na number of elements after the current element.
The current element is always included. For example, given
wlen = [3, 0]
, the data used to calculate index 5 is
[2, 3, 4, 5]
.
The optional argument opt determines the type of normalization to use. Valid values are
normalize with N-1, provides the square root of the best unbiased estimator of the variance [default]
normalize with N, this provides the square root of the second moment around the mean
If the optional argument dim is given, operate along this dimension. The normalization argument opt must be given before the dimension.
The optional string argument "nancond"
controls whether
NaN
and NA
values should be included ("includenan"
),
or excluded ("omitnan"
), from the data passed to movstd
. The
default is "includenan"
. Caution: the "omitnan"
option is
not yet implemented.
The calculation can be controlled by specifying property/value pairs. Valid properties are
"Endpoints"
This property controls how results are calculated at the boundaries (endpoints) of the window. Possible values are:
"shrink"
(default)The window is truncated at the beginning and end of the array to exclude
elements for which there is no source data. For example, with a window of
length 3, y(1) = movstd (x(1:2))
, and
y(end) = movstd (x(end-1:end))
.
"discard"
Any y values that use a window extending beyond the original
data array are deleted. For example, with a 10-element data vector and a
window of length 3, the output will contain only 8 elements. The first
element would require calculating the function over indices
[0, 1, 2]
and is therefore discarded. The last element would
require calculating the function over indices [9, 10, 11]
and is
therefore discarded.
"fill"
Any window elements outside the data array are replaced by NaN
. For
example, with a window of length 3,
y(1) = movstd ([NaN, x(1:2)])
, and
y(end) = movstd ([x(end-1:end), NaN])
.
This option usually results in y having NaN
values at the
boundaries, although it is influenced by how movstd
handles
NaN
, and also by the property "nancond"
.
Any window elements outside the data array are replaced by the specified
value user_value which must be a numeric scalar. For example, with a
window of length 3,
y(1) = movstd ([user_value, x(1:2)])
, and
y(end) = movstd ([x(end-1:end), user_value])
.
A common choice for user_value is 0.
"same"
Any window elements outside the data array are replaced by the value of
x at the boundary. For example, with a window of length 3,
y(1) = movstd ([x(1), x(1:2)])
, and
y(end) = movstd ([x(end-1:end), x(end)])
.
"periodic"
The window is wrapped so that any missing data elements are taken from
the other side of the data. For example, with a window of length 3,
y(1) = movstd ([x(end), x(1:2)])
, and
y(end) = movstd ([x(end-1:end), x(1)])
.
"SamplePoints"
Caution: This option is not yet implemented.
Programming Note: This function is a wrapper which calls movfun
.
For additional options and documentation, see movfun
.
See also: movfun, movslice, movmad, movmax, movmean, movmedian, movmin, movprod, movsum, movvar.
Calculate the moving sum over a sliding window of length wlen on data x.
If wlen is a scalar, the function movsum
is applied to a
moving window of length wlen. When wlen is an odd number the
window is symmetric and includes (wlen - 1) / 2
elements on
either side of the central element. For example, when calculating the
output at index 5 with a window length of 3, movsum
uses data
elements [4, 5, 6]
. If wlen is an even number, the window
is asymmetric and has wlen/2
elements to the left of the
central element and wlen/2 - 1
elements to the right of the
central element. For example, when calculating the output at index 5 with a
window length of 4, movsum
uses data elements
[3, 4, 5, 6]
.
If wlen is an array with two elements [nb, na]
,
the function is applied to a moving window -nb:na
. This
window includes nb number of elements before the current
element and na number of elements after the current element.
The current element is always included. For example, given
wlen = [3, 0]
, the data used to calculate index 5 is
[2, 3, 4, 5]
.
If the optional argument dim is given, operate along this dimension.
The optional string argument "nancond"
controls whether
NaN
and NA
values should be included ("includenan"
),
or excluded ("omitnan"
), from the data passed to movsum
. The
default is "includenan"
. Caution: the "omitnan"
option is
not yet implemented.
The calculation can be controlled by specifying property/value pairs. Valid properties are
"Endpoints"
This property controls how results are calculated at the boundaries (endpoints) of the window. Possible values are:
"shrink"
(default)The window is truncated at the beginning and end of the array to exclude
elements for which there is no source data. For example, with a window of
length 3, y(1) = movsum (x(1:2))
, and
y(end) = movsum (x(end-1:end))
.
"discard"
Any y values that use a window extending beyond the original
data array are deleted. For example, with a 10-element data vector and a
window of length 3, the output will contain only 8 elements. The first
element would require calculating the function over indices
[0, 1, 2]
and is therefore discarded. The last element would
require calculating the function over indices [9, 10, 11]
and is
therefore discarded.
"fill"
Any window elements outside the data array are replaced by NaN
. For
example, with a window of length 3,
y(1) = movsum ([NaN, x(1:2)])
, and
y(end) = movsum ([x(end-1:end), NaN])
.
This option usually results in y having NaN
values at the
boundaries, although it is influenced by how movsum
handles
NaN
, and also by the property "nancond"
.
Any window elements outside the data array are replaced by the specified
value user_value which must be a numeric scalar. For example, with a
window of length 3,
y(1) = movsum ([user_value, x(1:2)])
, and
y(end) = movsum ([x(end-1:end), user_value])
.
A common choice for user_value is 0.
"same"
Any window elements outside the data array are replaced by the value of
x at the boundary. For example, with a window of length 3,
y(1) = movsum ([x(1), x(1:2)])
, and
y(end) = movsum ([x(end-1:end), x(end)])
.
"periodic"
The window is wrapped so that any missing data elements are taken from
the other side of the data. For example, with a window of length 3,
y(1) = movsum ([x(end), x(1:2)])
, and
y(end) = movsum ([x(end-1:end), x(1)])
.
"SamplePoints"
Caution: This option is not yet implemented.
Programming Note: This function is a wrapper which calls movfun
.
For additional options and documentation, see movfun
.
See also: movfun, movslice, movmad, movmax, movmean, movmedian, movmin, movprod, movstd, movvar.
Calculate the moving variance over a sliding window of length wlen on data x.
If wlen is a scalar, the function var
is applied to a
moving window of length wlen. When wlen is an odd number the
window is symmetric and includes (wlen - 1) / 2
elements on
either side of the central element. For example, when calculating the
output at index 5 with a window length of 3, movvar
uses data
elements [4, 5, 6]
. If wlen is an even number, the window
is asymmetric and has wlen/2
elements to the left of the
central element and wlen/2 - 1
elements to the right of the
central element. For example, when calculating the output at index 5 with a
window length of 4, movvar
uses data elements
[3, 4, 5, 6]
.
If wlen is an array with two elements [nb, na]
,
the function is applied to a moving window -nb:na
. This
window includes nb number of elements before the current
element and na number of elements after the current element.
The current element is always included. For example, given
wlen = [3, 0]
, the data used to calculate index 5 is
[2, 3, 4, 5]
.
The optional argument opt determines the type of normalization to use. Valid values are
normalize with N-1, provides the best unbiased estimator of the variance [default]
normalizes with N, this provides the second moment around the mean
If the optional argument dim is given, operate along this dimension. The normalization argument opt must be given before the dimension.
The optional string argument "nancond"
controls whether
NaN
and NA
values should be included ("includenan"
),
or excluded ("omitnan"
), from the data passed to var
. The
default is "includenan"
. Caution: the "omitnan"
option is
not yet implemented.
The calculation can be controlled by specifying property/value pairs. Valid properties are
"Endpoints"
This property controls how results are calculated at the boundaries (endpoints) of the window. Possible values are:
"shrink"
(default)The window is truncated at the beginning and end of the array to exclude
elements for which there is no source data. For example, with a window of
length 3, y(1) = var (x(1:2))
, and
y(end) = var (x(end-1:end))
.
"discard"
Any y values that use a window extending beyond the original
data array are deleted. For example, with a 10-element data vector and a
window of length 3, the output will contain only 8 elements. The first
element would require calculating the function over indices
[0, 1, 2]
and is therefore discarded. The last element would
require calculating the function over indices [9, 10, 11]
and is
therefore discarded.
"fill"
Any window elements outside the data array are replaced by NaN
. For
example, with a window of length 3,
y(1) = var ([NaN, x(1:2)])
, and
y(end) = var ([x(end-1:end), NaN])
.
This option usually results in y having NaN
values at the
boundaries, although it is influenced by how var
handles NaN
,
and also by the property "nancond"
.
Any window elements outside the data array are replaced by the specified
value user_value which must be a numeric scalar. For example, with a
window of length 3,
y(1) = var ([user_value, x(1:2)])
, and
y(end) = var ([x(end-1:end), user_value])
.
A common choice for user_value is 0.
"same"
Any window elements outside the data array are replaced by the value of
x at the boundary. For example, with a window of length 3,
y(1) = var ([x(1), x(1:2)])
, and
y(end) = var ([x(end-1:end), x(end)])
.
"periodic"
The window is wrapped so that any missing data elements are taken from
the other side of the data. For example, with a window of length 3,
y(1) = var ([x(end), x(1:2)])
, and
y(end) = var ([x(end-1:end), x(1)])
.
"SamplePoints"
Caution: This option is not yet implemented.
Programming Note: This function is a wrapper which calls movfun
.
For additional options and documentation, see movfun
.
See also: movfun, movslice, movmad, movmax, movmean, movmedian, movmin, movprod, movstd, movsum.
Next: Basic Statistical Functions, Previous: Descriptive Statistics, Up: Statistics [Contents][Index]