Collection of linear algebra functions. More...

Functions
int	allocateMatrix (std::vector< std::vector< double > > &A, int m, int n)
	Allocates a matrix of size m x n. More...

int	allocateVector (std::vector< double > &x, int n)
	Allocates a vector of size n. More...

int	cholBackSolve (const std::vector< std::vector< double > > &L, std::vector< double > &x, const std::vector< double > &b)
	Solves the equation LL'x = b where L is lower triangular matrix. More...

int	cholFactor (std::vector< std::vector< double > > &A)
	The subroutine which does cholesky factorization of a given Symmetric positive definite matrix (say) A. More...

int	eye (std::vector< std::vector< double > > &M, int n)
	Creates an n x n identity matrix for M. More...

double	gammln (double xx)
	Calculates natural log of a gamma function. More...

double	gammq (double a, double x)
	Calculates Q, the probability that the chi2 should exceed a particilar chi2 (input) by chance. More...

void	gcf (double gammcf, double a, double x, double gln)
	Calculates Q, the probability that the chi2 should exceed a particilar chi2 (input) by chance, by using continued fractions. More...

void	gser (double gamser, double a, double x, double gln)
	Calculates Q, the probability that the chi2 should exceed a particilar chi2 (input) by chance, by using series approximation. More...

double	innerProduct (const std::vector< double > &a, const std::vector< double > &b)
	Computes the dot or the inner product of two vectors(i.e. More...

int	invertMatrix (const std::vector< std::vector< double > > &A, std::vector< std::vector< double > > &Ainv)
	Inverts a SPD matrix a to get inverse Ainv using the cholesky factorization. More...

double	norm (const std::vector< double > &a)
	Computes the two norm of the vector. More...

std::vector< double >	operator* (double a, const std::vector< double > &x)
	Given a scalar a and a vector x this function performs operation y = ax. More...

std::vector< std::vector < double > >	operator* (double a, const std::vector< std::vector< double > > &A)
	Computes the scalar matrix product B = aA. More...

std::vector< double >	operator* (const std::vector< std::vector< double > > &A, const std::vector< double > &x)
	Computes the Matrix vector product y = Ax. More...

std::vector< double >	operator* (const std::vector< double > &x, const std::vector< std::vector< double > > &A)
	Computes the vector matrix product y = x'A. More...

std::vector< vector< double > >	operator* (const std::vector< std::vector< double > > &A, const std::vector< std::vector< double > > &B)
	Computes Matrix Matrix Product C=A*B. More...

std::vector< double >	operator+ (const std::vector< double > &x, const std::vector< double > &y)
	Given two vectors x and y this function performs operation z = x + y. More...

std::vector< vector< double > >	operator+ (const std::vector< std::vector< double > > &A, const std::vector< std::vector< double > > &B)
	Given two matrices A and B this function performs operation C = A + B. More...

std::vector< double >	operator- (const std::vector< double > &x, const std::vector< double > &y)
	Given two vectors x and y this function performs operation z = x - y. More...

std::vector< double >	operator- (const std::vector< double > &y)
	Given a vector y this function performs operation z = - y. More...

std::vector< vector< double > >	operator- (const std::vector< std::vector< double > > &A, const std::vector< std::vector< double > > &B)
	Given two matrices A and B this function performs operation C = A - B. More...

std::vector< double >	operator/ (const std::vector< double > &x, double a)
	Given a scalar and a vector x this function performs operation y = x/a. More...

std::vector< std::vector < double > >	operator/ (const std::vector< std::vector< double > > &A, double a)
	Computes the scalar matrix product B = A/a. More...

vector< vector< double > >	outerProduct (const std::vector< double > &a, const std::vector< double > &b)
	Computes the outer product of two vectors (i.e. More...

double	quadraticProduct (const std::vector< std::vector< double > > &A, const std::vector< double > x)
	Calculates the vector-matrix-vector product x'Ax. More...

int	write (const std::vector< double > &x)
	Given the vector it writes it to std stream. More...

int	write (const std::vector< std::vector< double > > &A)
	Given the matrix it writes it to std stream. More...

Detailed Description

Collection of linear algebra functions.

Function Documentation

int allocateMatrix	(	std::vector< std::vector< double > > &	A,
		int	m,
		int	n
	)

Allocates a matrix of size m x n.

Definition at line 452 of file NumLinAlg.cxx.

References i.

int allocateVector	(	std::vector< double > &	x,
		int	n
	)

Allocates a vector of size n.

Definition at line 467 of file NumLinAlg.cxx.

int cholBackSolve	(	const std::vector< std::vector< double > > &	L,
		std::vector< double > &	x,
		const std::vector< double > &	b
	)

Solves the equation LL'x = b where L is lower triangular matrix.

Definition at line 325 of file NumLinAlg.cxx.

References i.

Referenced by invertMatrix().

int cholFactor ( std::vector< std::vector< double > > & A )

The subroutine which does cholesky factorization of a given Symmetric positive definite matrix (say) A.

It over-writes A by resulting lower triangular matrix

Definition at line 292 of file NumLinAlg.cxx.

References i.

Referenced by BFGSFitter::calcCovariance(), and invertMatrix().

int eye	(	std::vector< std::vector< double > > &	I,
		int	n
	)

Creates an n x n identity matrix for M.

Definition at line 405 of file NumLinAlg.cxx.

References i.

Referenced by BFGSFitter::calcBestFit().

double gammln ( double xx )

Calculates natural log of a gamma function.

Definition at line 24 of file Gammaq.cxx.

Referenced by gcf(), and gser().

double gammq	(	double	a,
		double	x
	)

Calculates Q, the probability that the chi2 should exceed a particilar chi2 (input) by chance.

It internally calls gser and gcf depending on the input range.

Definition at line 116 of file Gammaq.cxx.

References gcf(), and gser().

Referenced by FunctionController::ellipsoidNTuple().

void gcf	(	double *	gammcf,
		double	a,
		double	x,
		double *	gln
	)

Calculates Q, the probability that the chi2 should exceed a particilar chi2 (input) by chance, by using continued fractions.

Definition at line 78 of file Gammaq.cxx.

References EPS, FPMIN, gammln(), i, and ITMAX.

Referenced by gammq().

void gser	(	double *	gamser,
		double	a,
		double	x,
		double *	gln
	)

Calculates Q, the probability that the chi2 should exceed a particilar chi2 (input) by chance, by using series approximation.

Definition at line 43 of file Gammaq.cxx.

References EPS, gammln(), and ITMAX.

Referenced by gammq().

double innerProduct	(	const std::vector< double > &	a,
		const std::vector< double > &	b
	)

Computes the dot or the inner product of two vectors(i.e.

a'b)

Definition at line 239 of file NumLinAlg.cxx.

References i.

Referenced by BFGSFitter::calcBestFit(), and norm().

int invertMatrix	(	const std::vector< std::vector< double > > &	A,
		std::vector< std::vector< double > > &	Ainv
	)

Inverts a SPD matrix a to get inverse Ainv using the cholesky factorization.

It inverts the matrix by repeatedly solving Ax = ei

Definition at line 356 of file NumLinAlg.cxx.

References cholBackSolve(), cholFactor(), and i.

Referenced by LMFitter::calcCovariance(), and FunctionController::ellipsoidNTuple().

double norm ( const std::vector< double > & a )

Computes the two norm of the vector.

Definition at line 285 of file NumLinAlg.cxx.

References innerProduct().

Referenced by LinearTransform::adjustValues(), BFGSFitter::calcBestFit(), Chi2Dist::Chi2Dist(), Gaussian::derivByMean(), Landau::derivByNorm(), Gaussian::derivByParm(), Gaussian::derivBySigma(), Gaussian::Gaussian(), Gaussian::initialParameters(), Landau::initialParameters(), Landau::Landau(), BinningProjector::normalize(), Gaussian::operator()(), and Landau::operator()().

std::vector< double > operator*	(	double	a,
		const std::vector< double > &	x
	)

Given a scalar a and a vector x this function performs operation y = ax.

Definition at line 119 of file NumLinAlg.cxx.

References i.

std::vector< std::vector< double > > operator*	(	double	a,
		const std::vector< std::vector< double > > &	A
	)

Computes the scalar matrix product B = aA.

Definition at line 149 of file NumLinAlg.cxx.

References i.

std::vector< double > operator*	(	const std::vector< std::vector< double > > &	A,
		const std::vector< double > &	x
	)

Computes the Matrix vector product y = Ax.

Definition at line 185 of file NumLinAlg.cxx.

References i.

std::vector< double > operator*	(	const std::vector< double > &	x,
		const std::vector< std::vector< double > > &	A
	)

Computes the vector matrix product y = x'A.

Definition at line 202 of file NumLinAlg.cxx.

References i.

std::vector< std::vector< double > > operator*	(	const std::vector< std::vector< double > > &	A,
		const std::vector< std::vector< double > > &	B
	)

Computes Matrix Matrix Product C=A*B.

Definition at line 219 of file NumLinAlg.cxx.

References i.

std::vector< double > operator+	(	const std::vector< double > &	x,
		const std::vector< double > &	y
	)

Given two vectors x and y this function performs operation z = x + y.

Definition at line 38 of file NumLinAlg.cxx.

References i.

std::vector< std::vector< double > > operator+	(	const std::vector< std::vector< double > > &	A,
		const std::vector< std::vector< double > > &	B
	)

Given two matrices A and B this function performs operation C = A + B.

Definition at line 82 of file NumLinAlg.cxx.

References i.

std::vector< double > operator-	(	const std::vector< double > &	x,
		const std::vector< double > &	y
	)

Given two vectors x and y this function performs operation z = x - y.

Definition at line 53 of file NumLinAlg.cxx.

References i.

std::vector< double > operator- ( const std::vector< double > & y )

Given a vector y this function performs operation z = - y.

Definition at line 68 of file NumLinAlg.cxx.

References i.

std::vector< std::vector< double > > operator-	(	const std::vector< std::vector< double > > &	A,
		const std::vector< std::vector< double > > &	B
	)

Given two matrices A and B this function performs operation C = A - B.

Definition at line 100 of file NumLinAlg.cxx.

References i.

std::vector< double > operator/	(	const std::vector< double > &	x,
		double	a
	)

Given a scalar and a vector x this function performs operation y = x/a.

Definition at line 133 of file NumLinAlg.cxx.

References i.

std::vector< std::vector< double > > operator/	(	const std::vector< std::vector< double > > &	A,
		double	a
	)

Computes the scalar matrix product B = A/a.

Definition at line 166 of file NumLinAlg.cxx.

References i.

std::vector< std::vector< double > > outerProduct	(	const std::vector< double > &	a,
		const std::vector< double > &	b
	)

Computes the outer product of two vectors (i.e.

C = ab')

Definition at line 252 of file NumLinAlg.cxx.

References i.

Referenced by BFGSFitter::calcBestFit().

double quadraticProduct	(	const std::vector< std::vector< double > > &	A,
		const std::vector< double >	x
	)

Calculates the vector-matrix-vector product x'*A*x.

Definition at line 268 of file NumLinAlg.cxx.

References i.

Referenced by FunctionController::ellipsoidNTuple().

int write ( const std::vector< double > & a )

Given the vector it writes it to std stream.

Definition at line 421 of file NumLinAlg.cxx.

References i.

int write ( const std::vector< std::vector< double > > & A )

Given the matrix it writes it to std stream.

Definition at line 434 of file NumLinAlg.cxx.

References i.

Functions

Detailed Description

Function Documentation