This is the base class for generating objects with methods and storage components for computing and storing the covariance matrix of an input data.
More...

Inheritance diagram for Cov:

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Collaboration diagram for Cov:

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Public Member Functions
function	Cov (in df, in method)
	Return an object of class pm.stats.Cov. More...

function	get (in self, in df, in method)
	Return the covariance matrix of the input data. More...

Data Fields
Property	method

Property	val

Detailed Description

This is the base class for generating objects with methods and storage components for computing and storing the covariance matrix of an input data.

This is convenience class for easy computation of covariance and its storage all in one place.
The primary advantage of this class over the MATLAB intrinsic functions is in the ability of this class to compute the result for input dataframe table and return the results always in MATLAB table format.

Note: See the documentation of the class constructor pm.stats.Cov below.

Final Remarks ⛓

If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.

If you use any parts or concepts from this library to any extent, please acknowledge the usage by citing the relevant publications of the ParaMonte library.
If you regenerate any parts/ideas from this library in a programming environment other than those currently supported by this ParaMonte library (i.e., other than C, C++, Fortran, MATLAB, Python, R), please also ask the end users to cite this original ParaMonte library.

This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

Copyright: Computational Data Science Lab

Author:: Joshua Alexander Osborne, May 21 2024, 4:25 AM, University of Texas at Arlington
Fatemeh Bagheri, May 20 2024, 1:25 PM, NASA Goddard Space Flight Center (GSFC), Washington, D.C.
Amir Shahmoradi, July 5 2024, 1:07 PM, NASA Goddard Space Flight Center (GSFC), Washington, D.C.

Definition at line 23 of file Cov.m.

Constructor & Destructor Documentation

◆ Cov()

function Cov::Cov	(	in	df,
		in	method
	)

Return an object of class pm.stats.Cov.

This is the constructor of the pm.stats.Cov class.

Parameters

[in]	df	: The input MATLAB matrix or table of rank `2` containing the data as `ncol` columns of `nrow` observations whose covariance matrix must be computed. (optional. If missing, the covariance matrix will not be computed.)
[in]	method	: The input scalar MATLAB string that can be either: "pearson" : for computing the Pearson covariance matrix of the input data. "spearman" : for computing the Spearman rank covariance matrix of the input data. (optional, default = `"pearson"`)

Returns: self : The output object of class pm.stats.Cov.

Possible calling interfaces ⛓

: mat = pm.stats.Cov()

mat = pm.stats.Cov(df)

mat = pm.stats.Cov(df, method)

Cov::method
Property method
Definition: Cov.m:41

Example usage ⛓

: 1cd(fileparts(mfilename('fullpath'))); % Change working directory to source code directory.

2addpath('../../../'); % Add the ParaMonte library root directory to the search path.

3

4% Make a positive-definite random matrix.

5pm.matlab.show()

6pm.matlab.show("cholow = chol(pm.stats.dist.cov.getRand(5), 'lower');")

7 cholow = chol(pm.stats.dist.cov.getRand(5), 'lower');

8pm.matlab.show("df = pm.stats.dist.mvn.getRand(zeros(length(cholow), 1), cholow, 5000)';")

9 df = pm.stats.dist.mvn.getRand(zeros(length(cholow), 1), cholow, 5000)';

10

11pm.matlab.show()

12pm.matlab.show('c = pm.stats.Cov(df); c.val')

13 c = pm.stats.Cov(df); c.val

14

15pm.matlab.show()

16pm.matlab.show('c = pm.stats.Cov(df, "pearson"); c.val')

17 c = pm.stats.Cov(df, "pearson"); c.val

18

19pm.matlab.show()

20pm.matlab.show('c = pm.stats.Cov(df, "spearman"); c.val')

21 c = pm.stats.Cov(df, "spearman"); c.val

22

23pm.matlab.show()

24pm.matlab.show('c = pm.stats.Cov(df, "kendall"); c.val')

25 c = pm.stats.Cov(df, "kendall"); c.val

26

27pm.matlab.show()

28pm.matlab.show('p = pm.vis.PlotHeatmap(c.val); p.make("precision", 2); p.subplot.setColorLim();')

29 p = pm.vis.PlotHeatmap(c.val); p.make("precision", 2); p.subplot.setColorLim();

30pm.matlab.show('p.savefig("Cov.unifrnd.png", "-m3");')

31 p.savefig("Cov.unifrnd.png", "-m3");

root
function root()
Return a scalar MATLAB string containing the root directory of the ParaMonte library package.

Example output ⛓
1

2cholow = chol(pm.stats.dist.cov.getRand(5), 'lower');

3df = pm.stats.dist.mvn.getRand(zeros(length(cholow), 1), cholow, 5000)';

4

5c = pm.stats.Cov(df); c.val

6ans =

7 5x5 table

8 Var1 Var2 Var3 Var4 Var5

9 ___________________ __________________ ___________________ __________________ ___________________

10 Var1 0.992674029862441 -0.600871621525417 -0.0957429099298042 0.0105180670415036 -0.549750430720243

11 Var2 -0.600871621525417 1.0162655365192 0.709336259771752 -0.438145638329126 0.641700070376274

12 Var3 -0.0957429099298042 0.709336259771752 1.00670392296548 -0.720832825802482 0.00854336266219076

13 Var4 0.0105180670415036 -0.438145638329126 -0.720832825802482 0.990561807449415 0.34890637083755

14 Var5 -0.549750430720243 0.641700070376274 0.00854336266219076 0.34890637083755 0.999051033438348

15

16c = pm.stats.Cov(df, "pearson"); c.val

17ans =

18 5x5 table

19 Var1 Var2 Var3 Var4 Var5

20 ___________________ __________________ ___________________ __________________ ___________________

21 Var1 0.992674029862441 -0.600871621525417 -0.0957429099298042 0.0105180670415036 -0.549750430720243

22 Var2 -0.600871621525417 1.0162655365192 0.709336259771752 -0.438145638329126 0.641700070376274

23 Var3 -0.0957429099298042 0.709336259771752 1.00670392296548 -0.720832825802482 0.00854336266219076

24 Var4 0.0105180670415036 -0.438145638329126 -0.720832825802482 0.990561807449415 0.34890637083755

25 Var5 -0.549750430720243 0.641700070376274 0.00854336266219076 0.34890637083755 0.999051033438348

26

27c = pm.stats.Cov(df, "spearman"); c.val

28ans =

29 5x5 table

30 Var1 Var2 Var3 Var4 Var5

31 _________________ _________________ _________________ _________________ _________________

32 Var1 2083750 -1211241.07481496 -193492.678135627 26115.4688937788 -1105669.13822765

33 Var2 -1211241.07481496 2083750 1429189.31726345 -877565.067213443 1291280.78255651

34 Var3 -193492.678135627 1429189.31726345 2083750 -1461681.00720144 27399.1730346069

35 Var4 26115.4688937788 -877565.067213443 -1461681.00720144 2083750 697213.572914583

36 Var5 -1105669.13822765 1291280.78255651 27399.1730346069 697213.572914583 2083750

37

38c = pm.stats.Cov(df, "kendall"); c.val

39ans =

40 5x5 table

41 Var1 Var2 Var3 Var4 Var5

42 ___________________ __________________ ___________________ __________________ ___________________

43 Var1 0.992674029862441 -0.600871621525417 -0.0957429099298042 0.0105180670415036 -0.549750430720243

44 Var2 -0.600871621525417 1.0162655365192 0.709336259771752 -0.438145638329126 0.641700070376274

45 Var3 -0.0957429099298042 0.709336259771752 1.00670392296548 -0.720832825802482 0.00854336266219076

46 Var4 0.0105180670415036 -0.438145638329126 -0.720832825802482 0.990561807449415 0.34890637083755

47 Var5 -0.549750430720243 0.641700070376274 0.00854336266219076 0.34890637083755 0.999051033438348

48

49p = pm.vis.PlotHeatmap(c.val); p.make("precision", 2); p.subplot.setColorLim();

50p.savefig("Cov.unifrnd.png", "-m3");

Visualization of the example output ⛓

Final Remarks ⛓

If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.

If you use any parts or concepts from this library to any extent, please acknowledge the usage by citing the relevant publications of the ParaMonte library.
If you regenerate any parts/ideas from this library in a programming environment other than those currently supported by this ParaMonte library (i.e., other than C, C++, Fortran, MATLAB, Python, R), please also ask the end users to cite this original ParaMonte library.

This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

Copyright: Computational Data Science Lab

Author:: Joshua Alexander Osborne, May 21 2024, 4:29 AM, University of Texas at Arlington
Fatemeh Bagheri, May 20 2024, 1:25 PM, NASA Goddard Space Flight Center (GSFC), Washington, D.C.
Amir Shahmoradi, May 16 2016, 9:03 AM, Oden Institute for Computational Engineering and Sciences (ICES), UT Austin

Member Function Documentation

◆ get()

function Cov::get	(	in	self,
		in	df,
		in	method
	)

Return the covariance matrix of the input data.

This is a dynamic method of the pm.stats.Cov class.
This method automatically stores any input information in the corresponding components of the parent object.
However, any components of the parent object corresponding to the output of this method must be set explicitly manually.

Parameters

[in]	df	: The input MATLAB matrix or table of rank `2` containing the data as `ncol` columns of `nrow` observations whose covariance matrix must be computed.
[in]	method	: The input scalar MATLAB string that can be either: "pearson" : for computing the Pearson covariance matrix of the input data. "spearman" : for computing the Spearman rank covariance matrix of the input data. (optional, default = `"pearson"`)

Returns: val : The output MATLAB table containing the covariance matrix.

Possible calling interfaces ⛓

: mat = pm.stats.Cov()

mat.val = mat.get(df)

mat.val = mat.get(df, method)

Final Remarks ⛓

If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.

If you use any parts or concepts from this library to any extent, please acknowledge the usage by citing the relevant publications of the ParaMonte library.
If you regenerate any parts/ideas from this library in a programming environment other than those currently supported by this ParaMonte library (i.e., other than C, C++, Fortran, MATLAB, Python, R), please also ask the end users to cite this original ParaMonte library.

This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

Copyright: Computational Data Science Lab

Author:: Joshua Alexander Osborne, May 21 2024, 4:31 AM, University of Texas at Arlington
Fatemeh Bagheri, May 20 2024, 1:25 PM, NASA Goddard Space Flight Center (GSFC), Washington, D.C.
Amir Shahmoradi, May 16 2016, 9:03 AM, Oden Institute for Computational Engineering and Sciences (ICES), UT Austin

Field Documentation

◆ method

Property Cov::method

method

The scalar MATLAB string containing the method of computing the covariance matrix.
It can be either:

"pearson" : for computing the Pearson covariance matrix of the input data.
"kendall" : for computing the Kendall rank covariance matrix of the input data.
"spearman" : for computing the Spearman rank covariance matrix of the input data.

Definition at line 41 of file Cov.m.

◆ val

Property Cov::val

val

The MATLAB table of rank 2 serving as a convenient storage component for the covariance matrix.
This component is automatically populated at the time of constructing an object of class pm.stats.Cov.
It must be populated manually at all other times.

Definition at line 52 of file Cov.m.

The documentation for this class was generated from the following file:

src/matlab/main/+pm/+stats/Cov.m

Public Member Functions

Data Fields

Detailed Description

Constructor & Destructor Documentation

◆ Cov()

Member Function Documentation

◆ get()

Field Documentation

◆ method

◆ val