MTKpp::pca Class Reference

Principal Component Analysis. More...

#include <mtkpp/src/Statistics/pca.h>

Inheritance diagram for MTKpp::pca:

Collaboration diagram for MTKpp::pca:

List of all members.

Public Member Functions
	pca ()
	pca Constructor
	pca (table< double > *X, sheet *output)
	pca Constructor
int	run (int nKeep)
	pca Destructor
double	meanColumn (Eigen::Matrix< double, Dynamic, Dynamic > &m, const int &i)
	BaseStats Destructor.
double	meanColumn (ublas::matrix< double > &m, const int &i)
	BaseStats Destructor.
double	meanRow (Eigen::Matrix< double, Dynamic, Dynamic > &m, const int &i)
	Get sample mean of row.
double	meanRow (ublas::matrix< double > &m, const int &i)
	Get sample mean of row.
double	sumColumn (Eigen::Matrix< double, Dynamic, Dynamic > &m, const int &i)
	Get sum of column.
double	sumColumn (ublas::matrix< double > &m, const int &i)
	Get sum of column.
double	sumRow (Eigen::Matrix< double, Dynamic, Dynamic > &m, const int &i)
	Get sum of row.
double	sumRow (ublas::matrix< double > &m, const int &i)
	Get sum of row.
double	maxColumn (Eigen::Matrix< double, Dynamic, Dynamic > &m, const int &i)
	Get max value of column.
double	maxColumn (Eigen::Matrix< double, Dynamic, Dynamic > &m, const int &i, int &r)
	Get max value of column.
double	maxColumn (ublas::matrix< double > &m, const int &i)
	Get max value of column.
double	maxColumn (ublas::matrix< double > &m, const int &i, int &r)
	Get max value of column.
double	maxRow (Eigen::Matrix< double, Dynamic, Dynamic > &m, const int &i)
	Get max value of row.
double	maxRow (ublas::matrix< double > &m, const int &i)
	Get max value of row.
double	minColumn (Eigen::Matrix< double, Dynamic, Dynamic > &m, const int &i)
	Get min value of column.
double	minColumn (Eigen::Matrix< double, Dynamic, Dynamic > &m, const int &i, int &r)
	Get min value of column.
double	minColumn (ublas::matrix< double > &m, const int &i)
	Get min value of column.
double	minColumn (ublas::matrix< double > &m, const int &i, int &r)
	Get min value of column.
double	minRow (Eigen::Matrix< double, Dynamic, Dynamic > &m, const int &i)
	Get min value of row.
double	minRow (ublas::matrix< double > &m, const int &i)
	Get min value of row.
int	getColumnCenters (Eigen::Matrix< double, Dynamic, Dynamic > &mat, Eigen::Matrix< double, Dynamic, Dynamic > &mat_centers)
	Get Mean values for each column in the matrix.
int	getColumnCenters (ublas::matrix< double > &mat, ublas::matrix< double > &mat_centers)
	Get Mean values for each column in the matrix.
void	centerColumns (Eigen::Matrix< double, Dynamic, Dynamic > &m1, Eigen::Matrix< double, Dynamic, Dynamic > &m2)
	Center matrix by column.
void	centerColumns (ublas::matrix< double > &m1, ublas::matrix< double > &m2)
	Center matrix by column.
void	centerRows (Eigen::Matrix< double, Dynamic, Dynamic > &m1, Eigen::Matrix< double, Dynamic, Dynamic > &m2)
	Center matrix by row.
void	centerRows (ublas::matrix< double > &m1, ublas::matrix< double > &m2)
	Center matrix by row.
void	zScoreColumns (Eigen::Matrix< double, Dynamic, Dynamic > &m1, Eigen::Matrix< double, Dynamic, Dynamic > &m2)
	Calculate Z-Scores of matrix by column.
void	zScoreColumns (ublas::matrix< double > &m1, ublas::matrix< double > &m2)
	Calculate Z-Scores of matrix by column.
void	zScoreRows (Eigen::Matrix< double, Dynamic, Dynamic > &m1, Eigen::Matrix< double, Dynamic, Dynamic > &m2)
	Calculate Z-Scores of matrix by row.
void	zScoreRows (ublas::matrix< double > &m1, ublas::matrix< double > &m2)
	Calculate Z-Scores of matrix by row.
int	autoScale (Eigen::Matrix< double, Dynamic, Dynamic > &old_mat, Eigen::Matrix< double, Dynamic, Dynamic > &new_mat, Eigen::Matrix< double, Dynamic, Dynamic > &centers, Eigen::Matrix< double, Dynamic, Dynamic > &stdDevs)
	Autoscale using previously computed means and standard deviations.
int	autoScale (ublas::matrix< double > &old_mat, ublas::matrix< double > &new_mat, ublas::matrix< double > &centers, ublas::matrix< double > &stdDevs)
	Autoscale using previously computed means and standard deviations.
double	varianceColumn (Eigen::Matrix< double, Dynamic, Dynamic > &m, const int &i)
	Get variance of column.
double	varianceColumn (ublas::matrix< double > &m, const int &i)
	Get variance of column.
double	varianceRow (Eigen::Matrix< double, Dynamic, Dynamic > &m, const int &i)
	Get variance of row.
double	varianceRow (ublas::matrix< double > &m, const int &i)
	Get variance of row.
int	getStdDevColumns (Eigen::Matrix< double, Dynamic, Dynamic > &mat, Eigen::Matrix< double, Dynamic, Dynamic > &stdDev_mat)
	Get standard deviation for each column.
int	getStdDevColumns (ublas::matrix< double > &mat, ublas::matrix< double > &stdDev_mat)
	Get standard deviation for each column.
double	standardDeviationColumn (Eigen::Matrix< double, Dynamic, Dynamic > &m, const int &i)
	Get standard deviation of column.
double	standardDeviationColumn (ublas::matrix< double > &m, const int &i)
	Get standard deviation of column.
double	standardDeviationRow (Eigen::Matrix< double, Dynamic, Dynamic > &m, const int &i)
	Get standard deviation of row.
double	standardDeviationRow (ublas::matrix< double > &m, const int &i)
	Get standard deviation of row.
double	covarianceColumn (Eigen::Matrix< double, Dynamic, Dynamic > &m1, const int &i1, Eigen::Matrix< double, Dynamic, Dynamic > &m2, const int &i2)
	Calculate covariance between two column in different matrices.
double	covarianceColumn (Eigen::Matrix< double, Dynamic, Dynamic > &m, const int &i, const int &j)
	Calculate covariance between two columns in the same matrix.
double	covarianceColumn (ublas::matrix< double > &m1, const int &i1, ublas::matrix< double > &m2, const int &i2)
	Calculate covariance between two column in different matrices.
double	covarianceColumn (ublas::matrix< double > &m, const int &i, const int &j)
	Calculate covariance between two columns in the same matrix.
void	covarianceMatrix (Eigen::Matrix< double, Dynamic, Dynamic > &A, Eigen::Matrix< double, Dynamic, Dynamic > &CovMat)
	Calculates the Covariance Matrix (or variance, variance-covariance, dispersion)
void	covarianceMatrix (ublas::matrix< double > &A, ublas::matrix< double > &CovMat)
	Calculates the Covariance Matrix (or variance, variance-covariance, dispersion)
void	covarianceMatrix (ublas::matrix< double > &A, ublas::matrix< double, ublas::column_major > &CovMat)
double	correlationCoefficientColumn (Eigen::Matrix< double, Dynamic, Dynamic > &m1, const int &i1, Eigen::Matrix< double, Dynamic, Dynamic > &m2, const int &i2)
	Calculate correlation coefficient by column.
double	correlationCoefficientColumn (ublas::matrix< double > &m1, const int &i1, ublas::matrix< double > &m2, const int &i2)
	Calculate correlation coefficient by column.
double	rSquaredColumn (Eigen::Matrix< double, Dynamic, Dynamic > &m1, const int &i1, Eigen::Matrix< double, Dynamic, Dynamic > &m2, const int &i2)
	Calculate R^2 by column.
double	rSquaredColumn (ublas::matrix< double > &m1, const int &i1, ublas::matrix< double > &m2, const int &i2)
	Calculate R^2 by column.
double	AdjustedRSquaredColumn (Eigen::Matrix< double, Dynamic, Dynamic > &Ys, const int &i1, Eigen::Matrix< double, Dynamic, Dynamic > &Y_Pred, const int &i2, const int &i3)
	Calculate Adjusted R^2 by column.
double	AdjustedRSquaredColumn (ublas::matrix< double > &Ys, const int &i1, ublas::matrix< double > &Y_Pred, const int &i2, const int &i3)
	Calculate Adjusted R^2 by column.
double	RMSE (Eigen::Matrix< double, Dynamic, Dynamic > &Ys, const int &i, Eigen::Matrix< double, Dynamic, Dynamic > &Y_Pred, const int &j)
	Calculate root mean squared error.
double	RMSE (ublas::matrix< double > &Ys, const int &i, ublas::matrix< double > &Y_Pred, const int &j)
	Calculate root mean squared error.
double	MSE (Eigen::Matrix< double, Dynamic, Dynamic > &Ys, const int &i, Eigen::Matrix< double, Dynamic, Dynamic > &Y_Pred, const int &j)
	Calculate mean squared error.
double	MSE (ublas::matrix< double > &Ys, const int &i, ublas::matrix< double > &Y_Pred, const int &j)
	Calculate mean squared error.
double	UnsignedError (Eigen::Matrix< double, Dynamic, Dynamic > &Ys, const int &i, Eigen::Matrix< double, Dynamic, Dynamic > &Y_Pred, const int &j)
	Calculate unsigned/absolute error.
double	UnsignedError (ublas::matrix< double > &Ys, const int &i, ublas::matrix< double > &Y_Pred, const int &j)
	Calculate unsigned/absolute error.
double	SignedError (Eigen::Matrix< double, Dynamic, Dynamic > &Ys, const int &i, Eigen::Matrix< double, Dynamic, Dynamic > &Y_Pred, const int &j)
	Calculate signed error.
double	SignedError (ublas::matrix< double > &Ys, const int &i, ublas::matrix< double > &Y_Pred, const int &j)
	Calculate signed error.
double	SumSquaredDeviationsColumn (Eigen::Matrix< double, Dynamic, Dynamic > &Ys, const int &i)
	Calculates the Sum of squared deviations.
double	SumSquaredDeviationsColumn (ublas::matrix< double > &Ys, const int &i)
	Calculates the Sum of squared deviations.
double	SumSquaredRegressionColumn (Eigen::Matrix< double, Dynamic, Dynamic > &Ys, Eigen::Matrix< double, Dynamic, Dynamic > &Y_Pred)
	Calculates the Sum of squared due to regression.
double	SumSquaredRegressionColumn (ublas::matrix< double > &Ys, ublas::matrix< double > &Y_Pred)
	Calculates the Sum of squared due to regression.
double	SumSquaredResidualErrorsColumn (Eigen::Matrix< double, Dynamic, Dynamic > &Ys, Eigen::Matrix< double, Dynamic, Dynamic > &Y_Pred, Eigen::Matrix< double, Dynamic, Dynamic > &Residuals)
	Calculates the Sum of squared residuals (Errors)
double	SumSquaredResidualErrorsColumn (Eigen::Matrix< double, Dynamic, Dynamic > &Ys, const int &c, Eigen::Matrix< double, Dynamic, Dynamic > &Y_Pred, const int &d)
	Calculates the Sum of squared residuals (Errors)
double	SumSquaredResidualErrorsColumn (ublas::matrix< double > &Ys, ublas::matrix< double > &Y_Pred, ublas::matrix< double > &Residuals)
	Calculates the Sum of squared residuals (Errors)
double	SumSquaredResidualErrorsColumn (ublas::matrix< double > &Ys, const int &c, ublas::matrix< double > &Y_Pred, const int &d)
	Calculates the Sum of squared residuals (Errors)
Protected Attributes
table< double > *	itsX
	X matrix.
unsigned int	nRows
	Number of rows in X.
unsigned int	nColumns
	Number of Columns in X.
sheet *	outModel
	The sheet where the model is stored.

---

Detailed Description

Principal Component Analysis.

Author:

Martin Peters

Date:

2006

---

Constructor & Destructor Documentation

MTKpp::pca::pca

(

)

pca Constructor

MTKpp::pca::pca	(	table< double > *	X,
		sheet *	output
	)

pca Constructor

Parameters:

X	X matrix
output	sheet pointer

References MTKpp::table< T >::getNumColumns(), MTKpp::table< T >::getNumRows(), itsX, nColumns, nRows, outModel, and X.

---

Member Function Documentation

int MTKpp::pca::run

(

int

nKeep

)

pca Destructor

Run PCA

Parameters:

nKeep

Number of components to keep

References MTKpp::sheet::addTable(), MTKpp::BaseStats::centerColumns(), MTKpp::BaseStats::covarianceMatrix(), MTKpp::eigenValueSort(), MTKpp::errorLogger, MTKpp::BaseStats::getColumnCenters(), MTKpp::table< T >::getColumnLabel(), MTKpp::table< T >::getMatrix(), MTKpp::table< T >::getRowLabel(), MTKpp::INFO, itsX, MTKpp::MTK_ERROR, nColumns, nRows, outModel, MTKpp::table< T >::setColumnLabel(), MTKpp::table< T >::setName(), MTKpp::table< T >::setRowLabel(), MTKpp::table< T >::setSizes(), MTKpp::errorHandler::throwError(), and X.

Referenced by main().

double MTKpp::BaseStats::meanColumn	(	Eigen::Matrix< double, Dynamic, Dynamic > &	m,
		const int &	i
	)		[inherited]

BaseStats Destructor.

Get sample mean of column

Parameters:

m	Matrix pointer
i	column index

Returns:

sample average

Referenced by MTKpp::BaseStats::centerColumns(), MTKpp::BaseStats::correlationCoefficientColumn(), MTKpp::BaseStats::covarianceColumn(), MTKpp::BaseStats::covarianceMatrix(), MTKpp::BaseStats::getColumnCenters(), MTKpp::ols::LeastSquaresRegressionLine(), main(), MTKpp::BaseStats::SumSquaredDeviationsColumn(), MTKpp::BaseStats::SumSquaredRegressionColumn(), and MTKpp::BaseStats::varianceColumn().

double MTKpp::BaseStats::meanColumn	(	ublas::matrix< double > &	m,
		const int &	i
	)		[inherited]

BaseStats Destructor.

Get sample mean of column

Parameters:

m	Matrix pointer
i	column index

Returns:

sample average

double MTKpp::BaseStats::meanRow	(	Eigen::Matrix< double, Dynamic, Dynamic > &	m,
		const int &	i
	)		[inherited]

Get sample mean of row.

Parameters:

m	Matrix pointer
i	row index

Returns:

sample average

Referenced by main(), and MTKpp::BaseStats::varianceRow().

double MTKpp::BaseStats::meanRow	(	ublas::matrix< double > &	m,
		const int &	i
	)		[inherited]

Get sample mean of row.

Parameters:

m	Matrix pointer
i	row index

Returns:

sample average

double MTKpp::BaseStats::sumColumn	(	Eigen::Matrix< double, Dynamic, Dynamic > &	m,
		const int &	i
	)		[inherited]

Get sum of column.

Parameters:

m	Matrix pointer
i	column index

Returns:

sum of values

Referenced by main().

double MTKpp::BaseStats::sumColumn	(	ublas::matrix< double > &	m,
		const int &	i
	)		[inherited]

Get sum of column.

Parameters:

m	Matrix pointer
i	column index

Returns:

sum of values

double MTKpp::BaseStats::sumRow	(	Eigen::Matrix< double, Dynamic, Dynamic > &	m,
		const int &	i
	)		[inherited]

Get sum of row.

Parameters:

m	Matrix pointer
i	row index

Returns:

sum of values

Referenced by main().

double MTKpp::BaseStats::sumRow	(	ublas::matrix< double > &	m,
		const int &	i
	)		[inherited]

Get sum of row.

Parameters:

m	Matrix pointer
i	row index

Returns:

sum of values

double MTKpp::BaseStats::maxColumn	(	Eigen::Matrix< double, Dynamic, Dynamic > &	m,
		const int &	i
	)		[inherited]

Get max value of column.

Parameters:

m	Matrix pointer
i	column index

Returns:

max value

Referenced by main().

double MTKpp::BaseStats::maxColumn	(	Eigen::Matrix< double, Dynamic, Dynamic > &	m,
		const int &	i,
		int &	r
	)		[inherited]

Get max value of column.

Parameters:

m	Matrix pointer
i	column index
r	row index [index of max value]

Returns:

max value

double MTKpp::BaseStats::maxColumn	(	ublas::matrix< double > &	m,
		const int &	i
	)		[inherited]

Get max value of column.

Parameters:

m	Matrix pointer
i	column index

Returns:

max value

double MTKpp::BaseStats::maxColumn	(	ublas::matrix< double > &	m,
		const int &	i,
		int &	r
	)		[inherited]

Get max value of column.

Parameters:

m	Matrix pointer
i	column index
r	row index [index of max value]

Returns:

max value

double MTKpp::BaseStats::maxRow	(	Eigen::Matrix< double, Dynamic, Dynamic > &	m,
		const int &	i
	)		[inherited]

Get max value of row.

Parameters:

m	Matrix pointer
i	row index

Returns:

max value

Referenced by main().

double MTKpp::BaseStats::maxRow	(	ublas::matrix< double > &	m,
		const int &	i
	)		[inherited]

Get max value of row.

Parameters:

m	Matrix pointer
i	row index

Returns:

max value

double MTKpp::BaseStats::minColumn	(	Eigen::Matrix< double, Dynamic, Dynamic > &	m,
		const int &	i
	)		[inherited]

Get min value of column.

Parameters:

m	Matrix pointer
i	column index

Returns:

min value

Referenced by main().

double MTKpp::BaseStats::minColumn	(	Eigen::Matrix< double, Dynamic, Dynamic > &	m,
		const int &	i,
		int &	r
	)		[inherited]

Get min value of column.

Parameters:

m	Matrix pointer
i	column index
r	row index [index of min value]

Returns:

min value

double MTKpp::BaseStats::minColumn	(	ublas::matrix< double > &	m,
		const int &	i
	)		[inherited]

Get min value of column.

Parameters:

m	Matrix pointer
i	column index

Returns:

min value

double MTKpp::BaseStats::minColumn	(	ublas::matrix< double > &	m,
		const int &	i,
		int &	r
	)		[inherited]

Get min value of column.

Parameters:

m	Matrix pointer
i	column index
r	row index [index of min value]

Returns:

min value

double MTKpp::BaseStats::minRow	(	Eigen::Matrix< double, Dynamic, Dynamic > &	m,
		const int &	i
	)		[inherited]

Get min value of row.

Parameters:

m	Matrix pointer
i	row index

Returns:

min value

Referenced by main().

double MTKpp::BaseStats::minRow	(	ublas::matrix< double > &	m,
		const int &	i
	)		[inherited]

Get min value of row.

Parameters:

m	Matrix pointer
i	row index

Returns:

min value

int MTKpp::BaseStats::getColumnCenters	(	Eigen::Matrix< double, Dynamic, Dynamic > &	mat,
		Eigen::Matrix< double, Dynamic, Dynamic > &	mat_centers
	)		[inherited]

Get Mean values for each column in the matrix.

Parameters:

mat	Matrix pointer
mat_centers	Matrix pointer

Returns:

sucess

References MTKpp::BaseStats::meanColumn().

Referenced by main(), and run().

int MTKpp::BaseStats::getColumnCenters	(	ublas::matrix< double > &	mat,
		ublas::matrix< double > &	mat_centers
	)		[inherited]

Get Mean values for each column in the matrix.

Parameters:

mat	Matrix pointer
mat_centers	Matrix pointer

Returns:

sucess

References MTKpp::BaseStats::meanColumn().

void MTKpp::BaseStats::centerColumns	(	Eigen::Matrix< double, Dynamic, Dynamic > &	m1,
		Eigen::Matrix< double, Dynamic, Dynamic > &	m2
	)		[inherited]

Center matrix by column.

Parameters:

m1	Matrix pointer
m2	Matrix pointer

References MTKpp::BaseStats::meanColumn().

Referenced by main(), run(), and MTKpp::BaseStats::zScoreColumns().

void MTKpp::BaseStats::centerColumns	(	ublas::matrix< double > &	m1,
		ublas::matrix< double > &	m2
	)		[inherited]

Center matrix by column.

Parameters:

m1	Matrix pointer
m2	Matrix pointer

References MTKpp::BaseStats::meanColumn().

void MTKpp::BaseStats::centerRows	(	Eigen::Matrix< double, Dynamic, Dynamic > &	m1,
		Eigen::Matrix< double, Dynamic, Dynamic > &	m2
	)		[inherited]

Center matrix by row.

Parameters:

m1	Matrix pointer
m2	Matrix pointer

void MTKpp::BaseStats::centerRows	(	ublas::matrix< double > &	m1,
		ublas::matrix< double > &	m2
	)		[inherited]

Center matrix by row.

Parameters:

m1	Matrix pointer
m2	Matrix pointer

void MTKpp::BaseStats::zScoreColumns	(	Eigen::Matrix< double, Dynamic, Dynamic > &	m1,
		Eigen::Matrix< double, Dynamic, Dynamic > &	m2
	)		[inherited]

Calculate Z-Scores of matrix by column.

Parameters:

m1	Matrix pointer
m2	Matrix pointer

References MTKpp::BaseStats::centerColumns(), and MTKpp::BaseStats::standardDeviationColumn().

Referenced by main().

void MTKpp::BaseStats::zScoreColumns	(	ublas::matrix< double > &	m1,
		ublas::matrix< double > &	m2
	)		[inherited]

Calculate Z-Scores of matrix by column.

Parameters:

m1	Matrix pointer
m2	Matrix pointer

References MTKpp::BaseStats::centerColumns(), and MTKpp::BaseStats::standardDeviationColumn().

void MTKpp::BaseStats::zScoreRows	(	Eigen::Matrix< double, Dynamic, Dynamic > &	m1,
		Eigen::Matrix< double, Dynamic, Dynamic > &	m2
	)		[inherited]

Calculate Z-Scores of matrix by row.

Parameters:

m1	Matrix pointer
m2	Matrix pointer

void MTKpp::BaseStats::zScoreRows	(	ublas::matrix< double > &	m1,
		ublas::matrix< double > &	m2
	)		[inherited]

Calculate Z-Scores of matrix by row.

Parameters:

m1	Matrix pointer
m2	Matrix pointer

int MTKpp::BaseStats::autoScale	(	Eigen::Matrix< double, Dynamic, Dynamic > &	old_mat,
		Eigen::Matrix< double, Dynamic, Dynamic > &	new_mat,
		Eigen::Matrix< double, Dynamic, Dynamic > &	centers,
		Eigen::Matrix< double, Dynamic, Dynamic > &	stdDevs
	)		[inherited]

Autoscale using previously computed means and standard deviations.

Parameters:

old_mat	matrix pointer
new_mat	matrix pointer
centers	matrix of means
stdDevs	matrix of standard deviations

Returns:

success

Referenced by main().

int MTKpp::BaseStats::autoScale	(	ublas::matrix< double > &	old_mat,
		ublas::matrix< double > &	new_mat,
		ublas::matrix< double > &	centers,
		ublas::matrix< double > &	stdDevs
	)		[inherited]

Autoscale using previously computed means and standard deviations.

Parameters:

old_mat	matrix pointer
new_mat	matrix pointer
centers	matrix of means
stdDevs	matrix of standard deviations

Returns:

success

double MTKpp::BaseStats::varianceColumn	(	Eigen::Matrix< double, Dynamic, Dynamic > &	m,
		const int &	i
	)		[inherited]

Get variance of column.

Parameters:

m	Matrix pointer
i	column index

Returns:

variance

References MTKpp::BaseStats::meanColumn().

Referenced by MTKpp::BaseStats::getStdDevColumns(), main(), and MTKpp::BaseStats::standardDeviationColumn().

double MTKpp::BaseStats::varianceColumn	(	ublas::matrix< double > &	m,
		const int &	i
	)		[inherited]

Get variance of column.

Parameters:

m	Matrix pointer
i	column index

Returns:

variance

References MTKpp::BaseStats::meanColumn().

double MTKpp::BaseStats::varianceRow	(	Eigen::Matrix< double, Dynamic, Dynamic > &	m,
		const int &	i
	)		[inherited]

Get variance of row.

Parameters:

m	Matrix pointer
i	row index

Returns:

variance

References MTKpp::BaseStats::meanRow().

Referenced by main(), and MTKpp::BaseStats::standardDeviationRow().

double MTKpp::BaseStats::varianceRow	(	ublas::matrix< double > &	m,
		const int &	i
	)		[inherited]

Get variance of row.

Parameters:

m	Matrix pointer
i	row index

Returns:

variance

References MTKpp::BaseStats::meanRow().

int MTKpp::BaseStats::getStdDevColumns	(	Eigen::Matrix< double, Dynamic, Dynamic > &	mat,
		Eigen::Matrix< double, Dynamic, Dynamic > &	stdDev_mat
	)		[inherited]

Get standard deviation for each column.

Parameters:

mat	matrix pointer
stdDev_mat	matrix of standard deviations

Returns:

success

References MTKpp::BaseStats::varianceColumn().

Referenced by main().

int MTKpp::BaseStats::getStdDevColumns	(	ublas::matrix< double > &	mat,
		ublas::matrix< double > &	stdDev_mat
	)		[inherited]

Get standard deviation for each column.

Parameters:

mat	matrix pointer
stdDev_mat	matrix of standard deviations

Returns:

success

References MTKpp::BaseStats::varianceColumn().

double MTKpp::BaseStats::standardDeviationColumn	(	Eigen::Matrix< double, Dynamic, Dynamic > &	m,
		const int &	i
	)		[inherited]

Get standard deviation of column.

Parameters:

m	Matrix pointer
i	column index

Returns:

standard deviation

References MTKpp::BaseStats::varianceColumn().

Referenced by main(), and MTKpp::BaseStats::zScoreColumns().

double MTKpp::BaseStats::standardDeviationColumn	(	ublas::matrix< double > &	m,
		const int &	i
	)		[inherited]

Get standard deviation of column.

Parameters:

m	Matrix pointer
i	column index

Returns:

standard deviation

References MTKpp::BaseStats::varianceColumn().

double MTKpp::BaseStats::standardDeviationRow	(	Eigen::Matrix< double, Dynamic, Dynamic > &	m,
		const int &	i
	)		[inherited]

Get standard deviation of row.

Parameters:

m	Matrix pointer
i	row index

Returns:

standard deviation

References MTKpp::BaseStats::varianceRow().

Referenced by main().

double MTKpp::BaseStats::standardDeviationRow	(	ublas::matrix< double > &	m,
		const int &	i
	)		[inherited]

Get standard deviation of row.

Parameters:

m	Matrix pointer
i	row index

Returns:

standard deviation

References MTKpp::BaseStats::varianceRow().

double MTKpp::BaseStats::covarianceColumn	(	Eigen::Matrix< double, Dynamic, Dynamic > &	m1,
		const int &	i1,
		Eigen::Matrix< double, Dynamic, Dynamic > &	m2,
		const int &	i2
	)		[inherited]

Calculate covariance between two column in different matrices.

Parameters:

m1	Matrix pointer
i1	column index
m2	Matrix pointer
i2	column index

Returns:

covariance

References MTKpp::BaseStats::meanColumn().

double MTKpp::BaseStats::covarianceColumn	(	Eigen::Matrix< double, Dynamic, Dynamic > &	m,
		const int &	i,
		const int &	j
	)		[inherited]

Calculate covariance between two columns in the same matrix.

Parameters:

m	Matrix pointer
i	column index
j	column index

Returns:

covariance

References MTKpp::BaseStats::meanColumn().

double MTKpp::BaseStats::covarianceColumn	(	ublas::matrix< double > &	m1,
		const int &	i1,
		ublas::matrix< double > &	m2,
		const int &	i2
	)		[inherited]

Calculate covariance between two column in different matrices.

Parameters:

m1	Matrix pointer
i1	column index
m2	Matrix pointer
i2	column index

Returns:

covariance

References MTKpp::BaseStats::meanColumn().

double MTKpp::BaseStats::covarianceColumn	(	ublas::matrix< double > &	m,
		const int &	i,
		const int &	j
	)		[inherited]

Calculate covariance between two columns in the same matrix.

Parameters:

m	Matrix pointer
i	column index
j	column index

Returns:

covariance

References MTKpp::BaseStats::meanColumn().

void MTKpp::BaseStats::covarianceMatrix	(	Eigen::Matrix< double, Dynamic, Dynamic > &	A,
		Eigen::Matrix< double, Dynamic, Dynamic > &	CovMat
	)		[inherited]

Calculates the Covariance Matrix (or variance, variance-covariance, dispersion)

The covariance matrix is the matrix of sample variances [i][i] and covariances [i][j] of p variables.

Parameters:

A	Matrix object
CovMat	covariance matrix

References MTKpp::BaseStats::meanColumn().

Referenced by main(), and run().

void MTKpp::BaseStats::covarianceMatrix	(	ublas::matrix< double > &	A,
		ublas::matrix< double > &	CovMat
	)		[inherited]

Calculates the Covariance Matrix (or variance, variance-covariance, dispersion)

The covariance matrix is the matrix of sample variances [i][i] and covariances [i][j] of p variables.

Parameters:

A	Matrix object
CovMat	covariance matrix

References MTKpp::BaseStats::meanColumn().

void MTKpp::BaseStats::covarianceMatrix	(	ublas::matrix< double > &	A,
		ublas::matrix< double, ublas::column_major > &	CovMat
	)		[inherited]

References MTKpp::BaseStats::meanColumn().

double MTKpp::BaseStats::correlationCoefficientColumn	(	Eigen::Matrix< double, Dynamic, Dynamic > &	m1,
		const int &	i1,
		Eigen::Matrix< double, Dynamic, Dynamic > &	m2,
		const int &	i2
	)		[inherited]

Calculate correlation coefficient by column.

Parameters:

m1	Matrix object
i1	column index
m2	Matrix object
i2	column index

Returns:

correlation coefficient

References MTKpp::BaseStats::meanColumn(), and MTKpp::BaseStats::SumSquaredDeviationsColumn().

Referenced by main(), and MTKpp::BaseStats::rSquaredColumn().

double MTKpp::BaseStats::correlationCoefficientColumn	(	ublas::matrix< double > &	m1,
		const int &	i1,
		ublas::matrix< double > &	m2,
		const int &	i2
	)		[inherited]

Calculate correlation coefficient by column.

Parameters:

m1	Matrix object
i1	column index
m2	Matrix object
i2	column index

Returns:

correlation coefficient

References MTKpp::BaseStats::meanColumn(), and MTKpp::BaseStats::SumSquaredDeviationsColumn().

double MTKpp::BaseStats::rSquaredColumn	(	Eigen::Matrix< double, Dynamic, Dynamic > &	m1,
		const int &	i1,
		Eigen::Matrix< double, Dynamic, Dynamic > &	m2,
		const int &	i2
	)		[inherited]

Calculate R^2 by column.

Parameters:

m1	Matrix object
i1	column index
m2	Matrix object
i2	column index

Returns:

R-Squared

References MTKpp::BaseStats::correlationCoefficientColumn().

Referenced by main().

double MTKpp::BaseStats::rSquaredColumn	(	ublas::matrix< double > &	m1,
		const int &	i1,
		ublas::matrix< double > &	m2,
		const int &	i2
	)		[inherited]

Calculate R^2 by column.

Parameters:

m1	Matrix object
i1	column index
m2	Matrix object
i2	column index

Returns:

R-Squared

References MTKpp::BaseStats::correlationCoefficientColumn().

double MTKpp::BaseStats::AdjustedRSquaredColumn	(	Eigen::Matrix< double, Dynamic, Dynamic > &	Ys,
		const int &	i1,
		Eigen::Matrix< double, Dynamic, Dynamic > &	Y_Pred,
		const int &	i2,
		const int &	i3
	)		[inherited]

Calculate Adjusted R^2 by column.

Parameters:

Ys	Matrix object
i1	column index
Y_Pred	Matrix object
i2	column index
i3	column index

Returns:

Adjusted R-Squared

References MTKpp::BaseStats::SumSquaredDeviationsColumn(), and MTKpp::BaseStats::SumSquaredResidualErrorsColumn().

Referenced by main().

double MTKpp::BaseStats::AdjustedRSquaredColumn	(	ublas::matrix< double > &	Ys,
		const int &	i1,
		ublas::matrix< double > &	Y_Pred,
		const int &	i2,
		const int &	i3
	)		[inherited]

Calculate Adjusted R^2 by column.

Parameters:

Ys	Matrix object
i1	column index
Y_Pred	Matrix object
i2	column index
i3	column index

Returns:

Adjusted R-Squared

References MTKpp::BaseStats::SumSquaredDeviationsColumn(), and MTKpp::BaseStats::SumSquaredResidualErrorsColumn().

double MTKpp::BaseStats::RMSE	(	Eigen::Matrix< double, Dynamic, Dynamic > &	Ys,
		const int &	i,
		Eigen::Matrix< double, Dynamic, Dynamic > &	Y_Pred,
		const int &	j
	)		[inherited]

Calculate root mean squared error.

Parameters:

Ys	Matrix object
i	column index
Y_Pred	Matrix object
j	column index

Returns:

rmse

Referenced by main(), and MTKpp::BaseStats::RMSE().

double MTKpp::BaseStats::RMSE	(	ublas::matrix< double > &	Ys,
		const int &	i,
		ublas::matrix< double > &	Y_Pred,
		const int &	j
	)		[inherited]

Calculate root mean squared error.

Parameters:

Ys	Matrix object
i	column index
Y_Pred	Matrix object
j	column index

Returns:

rmse

References MTKpp::BaseStats::RMSE().

double MTKpp::BaseStats::MSE	(	Eigen::Matrix< double, Dynamic, Dynamic > &	Ys,
		const int &	i,
		Eigen::Matrix< double, Dynamic, Dynamic > &	Y_Pred,
		const int &	j
	)		[inherited]

Calculate mean squared error.

Parameters:

Ys	Matrix object
i	column index
Y_Pred	Matrix object
j	column index

Returns:

mse

Referenced by main(), and MTKpp::BaseStats::MSE().

double MTKpp::BaseStats::MSE	(	ublas::matrix< double > &	Ys,
		const int &	i,
		ublas::matrix< double > &	Y_Pred,
		const int &	j
	)		[inherited]

Calculate mean squared error.

Parameters:

Ys	Matrix object
i	column index
Y_Pred	Matrix object
j	column index

Returns:

mse

References MTKpp::BaseStats::MSE().

double MTKpp::BaseStats::UnsignedError	(	Eigen::Matrix< double, Dynamic, Dynamic > &	Ys,
		const int &	i,
		Eigen::Matrix< double, Dynamic, Dynamic > &	Y_Pred,
		const int &	j
	)		[inherited]

Calculate unsigned/absolute error.

Parameters:

Ys	Matrix object
i	column index
Y_Pred	Matrix object
j	column index

Returns:

unsigned error

Referenced by main().

double MTKpp::BaseStats::UnsignedError	(	ublas::matrix< double > &	Ys,
		const int &	i,
		ublas::matrix< double > &	Y_Pred,
		const int &	j
	)		[inherited]

Calculate unsigned/absolute error.

Parameters:

Ys	Matrix object
i	column index
Y_Pred	Matrix object
j	column index

Returns:

unsigned error

double MTKpp::BaseStats::SignedError	(	Eigen::Matrix< double, Dynamic, Dynamic > &	Ys,
		const int &	i,
		Eigen::Matrix< double, Dynamic, Dynamic > &	Y_Pred,
		const int &	j
	)		[inherited]

Calculate signed error.

Parameters:

Ys	Matrix object
i	column index
Y_Pred	Matrix object
j	column index

Returns:

signed error

Referenced by main().

double MTKpp::BaseStats::SignedError	(	ublas::matrix< double > &	Ys,
		const int &	i,
		ublas::matrix< double > &	Y_Pred,
		const int &	j
	)		[inherited]

Calculate signed error.

Parameters:

Ys	Matrix object
i	column index
Y_Pred	Matrix object
j	column index

Returns:

signed error

double MTKpp::BaseStats::SumSquaredDeviationsColumn	(	Eigen::Matrix< double, Dynamic, Dynamic > &	Ys,
		const int &	i
	)		[inherited]

Calculates the Sum of squared deviations.

total sum of squared deviations in Y from its mean (SST) -- \ SST = / (y[i] - y_mean)^2 --

Parameters:

Ys	Matrix object
i	column index

Returns:

Sum Squared Deviation

References MTKpp::BaseStats::meanColumn().

Referenced by MTKpp::BaseStats::AdjustedRSquaredColumn(), MTKpp::BaseStats::correlationCoefficientColumn(), MTKpp::ols::LeastSquaresRegressionLine(), and main().

double MTKpp::BaseStats::SumSquaredDeviationsColumn	(	ublas::matrix< double > &	Ys,
		const int &	i
	)		[inherited]

Calculates the Sum of squared deviations.

total sum of squared deviations in Y from its mean (SST) -- \ SST = / (y[i] - y_mean)^2 --

Parameters:

Ys	Matrix object
i	column index

Returns:

Sum Squared Deviation

References MTKpp::BaseStats::meanColumn().

double MTKpp::BaseStats::SumSquaredRegressionColumn	(	Eigen::Matrix< double, Dynamic, Dynamic > &	Ys,
		Eigen::Matrix< double, Dynamic, Dynamic > &	Y_Pred
	)		[inherited]

Calculates the Sum of squared due to regression.

total sum of squares due to regression (SSR)

__ SSR = \ (y_pred[i] - y_obs_mean)^2 /__

Parameters:

Ys	Matrix object
Y_Pred	Matrix object

Returns:

Sum Squared Deviation

References MTKpp::BaseStats::meanColumn().

Referenced by main().

double MTKpp::BaseStats::SumSquaredRegressionColumn	(	ublas::matrix< double > &	Ys,
		ublas::matrix< double > &	Y_Pred
	)		[inherited]

Calculates the Sum of squared due to regression.

total sum of squares due to regression (SSR)

__ SSR = \ (y_pred[i] - y_obs_mean)^2 /__

Parameters:

Ys	Matrix object
Y_Pred	Matrix object

Returns:

Sum Squared Deviation

References MTKpp::BaseStats::meanColumn().

double MTKpp::BaseStats::SumSquaredResidualErrorsColumn	(	Eigen::Matrix< double, Dynamic, Dynamic > &	Ys,
		Eigen::Matrix< double, Dynamic, Dynamic > &	Y_Pred,
		Eigen::Matrix< double, Dynamic, Dynamic > &	Residuals
	)		[inherited]

Calculates the Sum of squared residuals (Errors)

residuals --> e[i] = y_obs[i] - y_pred[i] sum of squared residuals (SSE) -- \ SSE = / e[i]^2 --

Parameters:

Ys
Y_Pred
Residuals

Referenced by MTKpp::BaseStats::AdjustedRSquaredColumn(), and main().

double MTKpp::BaseStats::SumSquaredResidualErrorsColumn	(	Eigen::Matrix< double, Dynamic, Dynamic > &	Ys,
		const int &	c,
		Eigen::Matrix< double, Dynamic, Dynamic > &	Y_Pred,
		const int &	d
	)		[inherited]

Calculates the Sum of squared residuals (Errors)

residuals --> e[i] = y_obs[i] - y_pred[i] sum of squared residuals (SSE) -- \ SSE = / e[i]^2 --

Parameters:

Ys	Orginial Y matrix
c	column in Ys
Y_Pred	Predicted Y matrix
d	column in Y_Pred

double MTKpp::BaseStats::SumSquaredResidualErrorsColumn	(	ublas::matrix< double > &	Ys,
		ublas::matrix< double > &	Y_Pred,
		ublas::matrix< double > &	Residuals
	)		[inherited]

Calculates the Sum of squared residuals (Errors)

residuals --> e[i] = y_obs[i] - y_pred[i] sum of squared residuals (SSE) -- \ SSE = / e[i]^2 --

Parameters:

Ys
Y_Pred
Residuals

double MTKpp::BaseStats::SumSquaredResidualErrorsColumn	(	ublas::matrix< double > &	Ys,
		const int &	c,
		ublas::matrix< double > &	Y_Pred,
		const int &	d
	)		[inherited]

Calculates the Sum of squared residuals (Errors)

residuals --> e[i] = y_obs[i] - y_pred[i] sum of squared residuals (SSE) -- \ SSE = / e[i]^2 --

Parameters:

Ys	Orginial Y matrix
c	column in Ys
Y_Pred	Predicted Y matrix
d	column in Y_Pred

---

Member Data Documentation

table<double>* MTKpp::pca::itsX [protected]

X matrix.

              X[N][R]
         +-                    -+
         | X11 X12  .   .   X1R |
         | X21 X22  .   .   X2R |
         |  .   .   .   .    .  |
         |  .   .   .   .    .  |
         | XN1  .   .   .   XNR |
         +-                    -+

Referenced by pca(), and run().

unsigned int MTKpp::pca::nRows [protected]

Number of rows in X.

Referenced by pca(), and run().

unsigned int MTKpp::pca::nColumns [protected]

Number of Columns in X.

Referenced by pca(), and run().

sheet* MTKpp::pca::outModel [protected]

The sheet where the model is stored.

Referenced by pca(), and run().

---

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

• pca.h
• pca.cpp