#include <CovarianceMatrix.h>

Inheritance diagram for cbl::data::CovarianceMatrix:

Public Member Functions
Constructors/destructors
	CovarianceMatrix ()
	default constructor

	CovarianceMatrix (std::vector< std::vector< double >> covariance_matrix, const double nmeasures=-1, const double prec=1.e-10)
	constructor which sets the covariance matrix More...

	CovarianceMatrix (std::vector< double > standard_deviation, const double nmeasures=-1)
	constructor which gets the data from an input vector More...

	CovarianceMatrix (const std::string filename, const int cov_col=2, const int skipped_lines=0, const double nmeasures=-1, const double prec=1.e-10)
	constructs with sets the covariance matrix reading from an input file More...

virtual	~CovarianceMatrix ()=default
	default destructor

Member functions to get the private/protected members
double	operator() (const int i, const int j) const
	get the value of the covariance matrix at index i,j More...

std::vector< std::vector< double > >	operator() () const
	get the covariance matrix More...

double	correlation (const int i, const int j) const
	get the value of the correlation matrix at index i,j More...

std::vector< std::vector< double > >	correlation () const
	get the value of the correlation matrix at index i,j More...

double	precision (const int i, const int j) const
	get the value of the precision matrix at index i,j More...

std::vector< std::vector< double > >	precision () const
	get the precision matrix More...

double	determinant () const
	get the determinant More...

double	precision_hartlap (const int i, const int j) const
	get the value of the precision matrix at index i,j times the Hartlap factor More...

std::vector< std::vector< double > >	precision_hartlap () const
	get the value of the precision matrix at index i,j times the Hartlap factor More...

double	standard_deviation (const int i) const
	get value of the standard deviation at index i More...

std::vector< double >	standard_deviation () const
	get the standard deviation More...

double	variance (const int i) const
	get value of the variance at index i More...

std::vector< double >	variance () const
	get the variance More...

size_t	order () const
	return the covariance matrix order More...

Member functions to set the private/protected members
void	set_from_matrix (const std::vector< std::vector< double >> covariance, const double nmeasures=-1, const double prec=1.e-10)
	set the covariance matrix by passing a std::vector<std::vector<double>> object; More...

void	set_from_standard_deviation (const std::vector< double > standard_deviation, const double nmeasures=-1)
	set the covariance by passing the diagonal square root More...

void	measure (const std::vector< std::shared_ptr< Data >> dataset, const double normalization=1, const double prec=1.e-10)
	measure the covariance from a collection of dataset More...

void	measure (const std::vector< std::vector< std::shared_ptr< Data >>> dataset, const double normalization=1, const double prec=1.e-10)
	measure the covariance from a collection of dataset More...

Member functions used for Input/Output
void	read (const std::string filename, const int cov_col=2, const int skipped_lines=0, const double nmeasures=-1, const double prec=1.e-10)
	set the covariance matrix, reading from an input file More...

void	write (const std::string dir, const std::string file, const int precision=4, const int rank=0) const
	write the covariance matrix More...

Member functions for covariance matrix cut
CovarianceMatrix	cut (const std::vector< bool > mask) const
	cut the data, for Data1D More...

Member functions to add two (or more) covariance matrices
CovarianceMatrix	operator+= (const CovarianceMatrix covariance) const
	overloading of the += operator, to sum two catalogues More...

CovarianceMatrix	operator+= (const std::shared_ptr< CovarianceMatrix > covariance) const
	overloading of the += operator, to sum two covariance matrices More...

CovarianceMatrix	operator+= (const std::vector< CovarianceMatrix > covariance) const
	overloading of the += operator, to sum several covariance matrices, passed in a vector More...

CovarianceMatrix	operator+= (const std::vector< std::shared_ptr< CovarianceMatrix >> covariance) const
	overloading of the += operator, to sum several covariance matrices, passed in a vector More...

Protected Member Functions
void	m_set_default ()
	set internal attributes to default values

virtual void	m_set (const std::vector< double > matrix, const double nmeasures=-1, const double prec=1.e-10)
	set internal attributes More...

double	hartlap_factor (const double order, const double nmeasures=-1)
	compute the hartlap factor. This is used to de-bias precision matrix measured from covariance measured from limited number of datasets More...

Protected Attributes
size_t	m_order
	number of data

Eigen::MatrixXd	m_matrix
	covariance matrix

Eigen::MatrixXd	m_precision
	precision matrix

Eigen::MatrixXd	m_correlation
	correlation matrix

Eigen::VectorXd	m_variance
	diagonal of the covariance matrix

Eigen::VectorXd	m_std
	standard deviation

double	m_determinant
	determinant

double	m_hartlap_factor
	The hartlap factor, only set when.

Detailed Description

The class CovarianceMatrix.

"Headers/CovarianceMatrix.h"

This is the base class used to manage covariance matrices

Definition at line 59 of file CovarianceMatrix.h.

Constructor & Destructor Documentation

◆ CovarianceMatrix() [1/3]

cbl::data::CovarianceMatrix::CovarianceMatrix	(	std::vector< std::vector< double >>	covariance_matrix,
		const double	nmeasures = `-1`,
		const double	prec = `1.e-10`
	)

inline

constructor which sets the covariance matrix

Parameters

covariance_matrix	array containing the covariance matrix
nmeasures	number of measures used to compute the covariance
prec	the precision required in the inversion of the covariance matrix

Definition at line 151 of file CovarianceMatrix.h.

◆ CovarianceMatrix() [2/3]

cbl::data::CovarianceMatrix::CovarianceMatrix	(	std::vector< double >	standard_deviation,
		const double	nmeasures = `-1`
	)

inline

constructor which gets the data from an input vector

Parameters

standard_deviation	the standard deviation
nmeasures	number of measures used to compute the covariance

Definition at line 163 of file CovarianceMatrix.h.

◆ CovarianceMatrix() [3/3]

cbl::data::CovarianceMatrix::CovarianceMatrix	(	const std::string	filename,
		const int	cov_col = `2`,
		const int	skipped_lines = `0`,
		const double	nmeasures = `-1`,
		const double	prec = `1.e-10`
	)

inline

constructs with sets the covariance matrix reading from an input file

Parameters

filename	file containing the covariance matrix in the format: column 0 \( \rightarrow \) x_i, column 1 \( \rightarrow \) x_j, column cov_col → cov(x_i,x_j)
cov_col	covariance matrix column, starting from 0
skipped_lines	comment lines to be skipped
nmeasures	number of measures used to compute the covariance
prec	the precision required in the inversion of the covariance matrix

Definition at line 186 of file CovarianceMatrix.h.

Member Function Documentation

◆ correlation() [1/2]

vector< vector< double > > cbl::data::CovarianceMatrix::correlation ( ) const

get the value of the correlation matrix at index i,j

Returns: the value of the correlation \( Corr_{i,j} = \frac{Cov_{i,j}}{\sqrt{Cov_{i,i} \cdot Cov{j,j}}} \)

Definition at line 95 of file CovarianceMatrix.cpp.

◆ correlation() [2/2]

double cbl::data::CovarianceMatrix::correlation	(	const int	i,
		const int	j
	)		const

inline

get the value of the correlation matrix at index i,j

Parameters

i	index
j	index

Returns: the value of the correlation \( Corr_{i,j} = \frac{Cov_{i,j}}{\sqrt{Cov_{i,i} \cdot Cov{j,j}}} \)

Definition at line 229 of file CovarianceMatrix.h.

◆ cut()

CovarianceMatrix cbl::data::CovarianceMatrix::cut ( const std::vector< bool > mask ) const

cut the data, for Data1D

Parameters

[in] mask std::vector containing values to be masked

Returns: pointer to an object of type Data1D

Definition at line 275 of file CovarianceMatrix.cpp.

◆ determinant()

double cbl::data::CovarianceMatrix::determinant ( ) const

inline

get the determinant

Returns: the determinant

Definition at line 262 of file CovarianceMatrix.h.

◆ hartlap_factor()

double cbl::data::CovarianceMatrix::hartlap_factor	(	const double	order,
		const double	nmeasures = `-1`
	)

inlineprotected

compute the hartlap factor. This is used to de-bias precision matrix measured from covariance measured from limited number of datasets

\[ \hat{\Psi}=\left(1-\frac{N_{\mathrm{b}}+1}{N_{\mathrm{s}}-1}\right) \hat{\mathrm{c}}^{-1} \]

Parameters

order	the matrix order (or the number of data points)
nmeasures	number of measures used to compute the covariance

Returns: the hartlap factor

Definition at line 122 of file CovarianceMatrix.h.

◆ m_set()

void cbl::data::CovarianceMatrix::m_set	(	const std::vector< double >	matrix,
		const double	nmeasures = `-1`,
		const double	prec = `1.e-10`
	)

protectedvirtual

set internal attributes

Parameters

matrix	the covariance matrix
nmeasures	number of measures
prec	the precision required in the inversion of the covariance matrix

Reimplemented in cbl::data::TaperedCovarianceMatrix.

Definition at line 64 of file CovarianceMatrix.cpp.

◆ measure() [1/2]

void cbl::data::CovarianceMatrix::measure	(	const std::vector< std::shared_ptr< Data >>	dataset,
		const double	normalization = `1`,
		const double	prec = `1.e-10`
	)

measure the covariance from a collection of dataset

This use the standard estimator of the covariance

\[ \hat{C}_{i j}=\frac{f}{N_{\mathrm{s}}-1} \sum_{k=1}^{N_{\mathrm{s}}} \left(D_{i}^{k}-\bar{D}_{i}\right)\left(D_{j}^{k}-\bar{D}_{j}\right) \]

where \(D_{i}\) is the i-th measure \( \bar{D}_{i}\) the mean. \(f\) is a normalization factor the user can provide in input.

Parameters

dataset	vector of pointers of object of type Data
normalization	the normalization factor
prec	the precision required in the inversion of the covariance matrix

Definition at line 205 of file CovarianceMatrix.cpp.

◆ measure() [2/2]

void cbl::data::CovarianceMatrix::measure	(	const std::vector< std::vector< std::shared_ptr< Data >>>	dataset,
		const double	normalization = `1`,
		const double	prec = `1.e-10`
	)

measure the covariance from a collection of dataset

This use the standard estimator of the covariance

\[ \hat{C}_{i j}=\frac{f}{N_{\mathrm{s}}-1} \sum_{k=1}^{N_{\mathrm{s}}} \left(D_{i}^{k}-\bar{D}_{i}\right)\left(D_{j}^{k}-\bar{D}_{j}\right) \]

where \(D_{i}\) is the i-th measure \( \bar{D}_{i}\) the mean. \(f\) is a normalization factor the user can provide in input.

This function takes a vector of measurement. Each measurement is a vector of dataset. This should be used when multiple measurements are made

Parameters

dataset	vector of pointers of object of type Data
normalization	the normalization factor
prec	the precision required in the inversion of the covariance matrix

Definition at line 233 of file CovarianceMatrix.cpp.

◆ operator()() [1/2]

vector< vector< double > > cbl::data::CovarianceMatrix::operator() ( ) const

get the covariance matrix

Returns: the covariance matrix

Definition at line 86 of file CovarianceMatrix.cpp.

◆ operator()() [2/2]

double cbl::data::CovarianceMatrix::operator()	(	const int	i,
		const int	j
	)		const

inline

get the value of the covariance matrix at index i,j

Parameters

i	index
j	index

Returns: the value of the covariance matrix

Definition at line 211 of file CovarianceMatrix.h.

◆ operator+=() [1/4]

cbl::data::CovarianceMatrix cbl::data::CovarianceMatrix::operator+= ( const CovarianceMatrix covariance ) const

overloading of the += operator, to sum two catalogues

This function add two covariance matrices of order N and M. It creates a block matrix of order N+M

Parameters

covariance object of class CovarianceMatrix

Returns: object of class CovarianceMatrix

Definition at line 296 of file CovarianceMatrix.cpp.

◆ operator+=() [2/4]

cbl::data::CovarianceMatrix cbl::data::CovarianceMatrix::operator+= ( const std::shared_ptr< CovarianceMatrix > covariance ) const

overloading of the += operator, to sum two covariance matrices

This function add two covariance matrices of order N and M. It creates a block matrix of order N+M

Parameters

covariance object of class CovarianceMatrix

Returns: object of class CovarianceMatrix

Definition at line 316 of file CovarianceMatrix.cpp.

◆ operator+=() [3/4]

cbl::data::CovarianceMatrix CovarianceMatrix::operator+= ( const std::vector< CovarianceMatrix > covariance ) const

overloading of the += operator, to sum several covariance matrices, passed in a vector

This function add the current covariance matrix of order N with several covariance matrices of order M_i. It creates a block matrix of order \( N+\sum_i^n M_i\).

Parameters

covariance object of class CovarianceMatrix

Returns: object of class CovarianceMatrix

Definition at line 336 of file CovarianceMatrix.cpp.

◆ operator+=() [4/4]

cbl::data::CovarianceMatrix cbl::data::CovarianceMatrix::operator+= ( const std::vector< std::shared_ptr< CovarianceMatrix >> covariance ) const

overloading of the += operator, to sum several covariance matrices, passed in a vector

This function add the current covariance matrix of order N with several covariance matrices of order M_i. It creates a block matrix of order \( N+\sum_i^n M_i\).

Parameters

covariance object of class CovarianceMatrix

Returns: object of class CovarianceMatrix

Definition at line 368 of file CovarianceMatrix.cpp.

◆ order()

size_t cbl::data::CovarianceMatrix::order ( ) const

inline

return the covariance matrix order

Returns: the covariance matrix order

Definition at line 341 of file CovarianceMatrix.h.

◆ precision() [1/2]

vector< vector< double > > cbl::data::CovarianceMatrix::precision ( ) const

get the precision matrix

Returns: the std::vector containing the precision matrix

Definition at line 104 of file CovarianceMatrix.cpp.

◆ precision() [2/2]

double cbl::data::CovarianceMatrix::precision	(	const int	i,
		const int	j
	)		const

inline

get the value of the precision matrix at index i,j

Parameters

i	index
j	index

Returns: the value of the precision matrix at position i,j

Definition at line 248 of file CovarianceMatrix.h.

◆ precision_hartlap() [1/2]

vector< vector< double > > cbl::data::CovarianceMatrix::precision_hartlap ( ) const

get the value of the precision matrix at index i,j times the Hartlap factor

This function returns the precision matrix times the Hartlap factor at index i,j:

\[ \hat{\Psi}=\left(1-\frac{N_{\mathrm{b}}+1}{N_{\mathrm{s}}-1}\right) \hat{\mathrm{c}}^{-1} \]

where \(N_b\) are the number of bins (the order of the matrix) and \(N_s\) the number of data used to measure the covariance

Returns: the std::vector containing the precision matrix

Definition at line 113 of file CovarianceMatrix.cpp.

◆ precision_hartlap() [2/2]

double cbl::data::CovarianceMatrix::precision_hartlap	(	const int	i,
		const int	j
	)		const

inline

get the value of the precision matrix at index i,j times the Hartlap factor

This function returns the precision matrix times the Hartlap factor at index i,j:

\[ \hat{\Psi}=\left(1-\frac{N_{\mathrm{b}}+1}{N_{\mathrm{s}}-1}\right) \hat{\mathrm{c}}^{-1} \]

where \(N_b\) are the number of bins (the order of the matrix) and \(N_s\) the number of data used to measure the covariance

Parameters

i	index
j	index

Returns: the value of the precision matrix at position i,j

Definition at line 284 of file CovarianceMatrix.h.

◆ read()

void cbl::data::CovarianceMatrix::read	(	const std::string	filename,
		const int	cov_col = `2`,
		const int	skipped_lines = `0`,
		const double	nmeasures = `-1`,
		const double	prec = `1.e-10`
	)

set the covariance matrix, reading from an input file

Parameters

filename	file containing the covariance matrix in the format: column 0 \( \rightarrow \) x_i, column 1 \( \rightarrow \) x_j, column cov_col → cov(x_i,x_j)
cov_col	covariance matrix column, starting from 0
skipped_lines	comment lines to be skipped
nmeasures	number of measures used to compute the covariance
prec	the precision required in the inversion of the covariance matrix

Definition at line 155 of file CovarianceMatrix.cpp.

◆ set_from_matrix()

void cbl::data::CovarianceMatrix::set_from_matrix	(	const std::vector< std::vector< double >>	covariance,
		const double	nmeasures = `-1`,
		const double	prec = `1.e-10`
	)

inline

set the covariance matrix by passing a std::vector<std::vector<double>> object;

Parameters

covariance	std::vector<std::vector<double>> containing the covariance matrix
prec	the precision required in the inversion of the covariance matrix
nmeasures	number of measures used to compute the covariance

Definition at line 362 of file CovarianceMatrix.h.

◆ set_from_standard_deviation()

void cbl::data::CovarianceMatrix::set_from_standard_deviation	(	const std::vector< double >	standard_deviation,
		const double	nmeasures = `-1`
	)

set the covariance by passing the diagonal square root

Parameters

standard_deviation	std::vector containing the standard deviation
nmeasures	number of measures used to compute the covariance

Definition at line 140 of file CovarianceMatrix.cpp.

◆ standard_deviation() [1/2]

vector< double > cbl::data::CovarianceMatrix::standard_deviation ( ) const

get the standard deviation

Returns: the standard deviation

Definition at line 122 of file CovarianceMatrix.cpp.

◆ standard_deviation() [2/2]

double cbl::data::CovarianceMatrix::standard_deviation ( const int i ) const

inline

get value of the standard deviation at index i

Parameters

i index

Returns: the value of the standard deviation vector at position i

Definition at line 311 of file CovarianceMatrix.h.

◆ variance() [1/2]

vector< double > cbl::data::CovarianceMatrix::variance ( ) const

get the variance

Returns: the variance

Definition at line 131 of file CovarianceMatrix.cpp.

◆ variance() [2/2]

double cbl::data::CovarianceMatrix::variance ( const int i ) const

inline

get value of the variance at index i

Parameters

i index

Returns: the value of the variance vector at position i

Definition at line 327 of file CovarianceMatrix.h.

◆ write()

void cbl::data::CovarianceMatrix::write	(	const std::string	dir,
		const std::string	file,
		const int	precision = `4`,
		const int	rank = `0`
	)		const

write the covariance matrix

Parameters

dir	output directory
file	output file

the first line of the output file

Parameters

precision	the float precision
rank	cpu index (for MPI usage)

Definition at line 183 of file CovarianceMatrix.cpp.

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

Headers/CovarianceMatrix.h
Data/CovarianceMatrix.cpp

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ CovarianceMatrix() [1/3]

◆ CovarianceMatrix() [2/3]

◆ CovarianceMatrix() [3/3]

Member Function Documentation

◆ correlation() [1/2]

◆ correlation() [2/2]

◆ cut()

◆ determinant()

◆ hartlap_factor()

◆ m_set()

◆ measure() [1/2]

◆ measure() [2/2]

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator+=() [1/4]

◆ operator+=() [2/4]

◆ operator+=() [3/4]

◆ operator+=() [4/4]

◆ order()

◆ precision() [1/2]

◆ precision() [2/2]

◆ precision_hartlap() [1/2]

◆ precision_hartlap() [2/2]

◆ read()

◆ set_from_matrix()

◆ set_from_standard_deviation()

◆ standard_deviation() [1/2]

◆ standard_deviation() [2/2]

◆ variance() [1/2]

◆ variance() [2/2]

◆ write()