A set of general purpose matrix functions. All functions are static. More...

#include "us_matrix.h"

Static Public Member Functions
static bool	lsfit (double , double , double *, int, int)
	Function to solve general linear least squares problem: More...

static bool	Cholesky_Decomposition (double **, int)
	Function to factor an n x n symmetric positive definite matrix. More...

static bool	Cholesky_SolveSystem (double *, double , int)
	Function to solve a Cholesky-decomposed L-matrix. More...

static bool	Cholesky_Invert (double , double , int)
	Cholesky Invert to solve Ax=b by Cholesky decomposition. More...

static void	LU_SolveSystem (double *, double &, int)
	Solve a set of linear equations. More...

static void	LU_Decomposition (double *, int , bool, int)
	LU Decomposition of a matrix. More...

static void	LU_BackSubstitute (double *, double &, int *, int)
	Back substitution on a matrix which is the LU decomposition of the original matrix. More...

static double **	construct (QVector< double * > &, QVector< double > &, int, int)
	Create a matrix array from QVectors. More...

static void	tmm (double , double , int, int)
	Calculates A' * A , A-transpose times A. More...

static void	tmm (double , double , int, int, bool)
	Calculates A' * A: A-transpose times A. More...

static void	mvv (double *, double , double *, int, int)
	Calculates A * b: a vector product whose size is A's rows. More...

static void	tvv (double *, double , double *, int, int)
	Calculates A' * b: a vector product whose size is A's columns. More...

static void	mmm (double , double , double **, int, int, int)
	Calculates A * B: a matrix product of A-rows by B-columns. More...

static void	msum (double , double , double **, int, int)
	Calculate A + B: a matrix sum with all matrices rows x columns. More...

static void	vsum (double , double , double *, int)
	Calculate a + b: a vector sum with all vectors the same size. More...

static void	mident (double **, int)
	Fills matrix C: Cij = ( i != j ? 0.0 : 1.0 ) More...

static void	mcopy (double , double , int, int)
	Matrix copy: C = A. More...

static void	vcopy (double , double , int)
	Vector copy: c = a. More...

static void	add_diag (double **, double, int)
	Diagonal add: Cii = Cii + s. More...

static void	add (double **, double, int, int)
	Matrix-scalar-add: Cij += s. More...

static void	scale (double **, double, int, int)
	Matrix-scalar-multiply: Cij *= s. More...

static double	dotproduct (double , double , int)
	Vector dot product: p = sum( a[i] * b[i] ) More...

static double	dotproduct (double *, int)
	Vector dot product: p = sum( a[i] * a[i] ) More...

Static Private Member Functions
static void	print_matrix (double **, int, int)

static void	print_vector (double *, int)

Detailed Description

A set of general purpose matrix functions. All functions are static.

A class of general purpose static matrix functions. The elements of all matrices and vectors are doubles. The matrix arguments are arrays of pointers to arrays of doubles (rows). The vector arguments are arrays of doubles.

Definition at line 14 of file us_matrix.h.

Member Function Documentation

void US_Matrix::add	(	double **	CC,
		double	ss,
		int	rows,
		int	columns
	)

static

Matrix-scalar-add: Cij += s.

Add a scalar to all elements of a matrix

Parameters

CC	The source,destination matrix
ss	The scalar to add to all elements
rows	The number of rows in the matrix
columns	The number of columns in the matrix

Definition at line 373 of file us_matrix.cpp.

void US_Matrix::add_diag	(	double **	CC,
		double	ss,
		int	size
	)

static

Diagonal add: Cii = Cii + s.

Add a scalar to the diagonal of a square matrix

Parameters

CC	The source,destination matrix
ss	The scalar to add to the diagonal
size	The size (rows, columns) of the matrix

Definition at line 366 of file us_matrix.cpp.

bool US_Matrix::Cholesky_Decomposition	(	double **	a,
		int	n
	)

static

Function to factor an n x n symmetric positive definite matrix.

This method factors the n by n symmetric positive definite matrix A as LL(T) where L is a lower triangular matrix. The method assumes that at least the lower triangle of A is filled on entry. On exit, the lower triangle of A has been replaced by L.

Parameters

a	Input symmetric positive definite matrix A; lower triangle replaced by L on exit.
n	Dimensions of A.

Definition at line 95 of file us_matrix.cpp.

bool US_Matrix::Cholesky_Invert	(	double **	AA,
		double **	AI,
		int	nn
	)

static

Cholesky Invert to solve Ax=b by Cholesky decomposition.

Cholesky Invert: solve Ax=b using Cholesky decomposition: A * A(-1) = I ; A = LL' ; L (L' * A(-1) ) = I ; L * y = I (solve for y) , now L' * A(-1) = y (solve for A(-1)) .

Parameters

AA	An nn x nn input matrix
AI	An nn x nn solved inverted matrix
nn	Number of rows and columns in the matrices

Returns: A flag for whether a solution was found

Definition at line 178 of file us_matrix.cpp.

bool US_Matrix::Cholesky_SolveSystem	(	double **	L,
		double *	b,
		int	n
	)

static

Function to solve a Cholesky-decomposed L-matrix.

Cholesky_SolveSystem expects a Cholesky-decomposed L-matrix (n x n) with the lower diagonal filled, and the right hand side "b". Using forward and backward substitution, the right hand side "b" is replaced by the solution vector "x".

Parameters

L	Cholesky-decomposed L-matrix.
b	Right hand side.
n	Dimensions of L.

Definition at line 145 of file us_matrix.cpp.

double ** US_Matrix::construct	(	QVector< double * > &	QVm,
		QVector< double > &	QVd,
		int	rows,
		int	columns
	)

static

Create a matrix array from QVectors.

Construct and initialize a matrix array of double pointers from a QVector of double pointers and a QVector of doubles holding the (rows times columns) contiguous matrix elements, initialized to zero.

Parameters

QVm	The QVector from which the matrix array is constructed
QVd	The QVector for holding contiguous data elements
rows	The number of rows for the matrix
columns	The number of columns for the matrix

Returns: The double** matrix array

Definition at line 210 of file us_matrix.cpp.

double US_Matrix::dotproduct	(	double *	aa,
		double *	bb,
		int	size
	)

static

Vector dot product: p = sum( a[i] * b[i] )

Compute the dot product of two vectors

Parameters

aa	The operand "a" vector
bb	The operator "b" vector
size	The size of the vectors

Returns: Dot product of vectors

Definition at line 389 of file us_matrix.cpp.

double US_Matrix::dotproduct	(	double *	aa,
		int	size
	)

static

Vector dot product: p = sum( a[i] * a[i] )

Compute the dot product of a vector with itself

Parameters

aa	The operand "a" vector
size	The size of the vector

Returns: Dot product of vector with itself

Definition at line 400 of file us_matrix.cpp.

bool US_Matrix::lsfit	(	double *	c,
		double *	x,
		double *	y,
		int	N,
		int	order
	)

static

Function to solve general linear least squares problem:

Parameters

c	returns the coefficients for best least-squares fit
x	contains the x values of the raw data
y	contains the y values of the raw data
N	contains the dimension of x and y
order	is the order of the function to be fitted

Definition at line 8 of file us_matrix.cpp.

void US_Matrix::LU_BackSubstitute	(	double **	A,
		double *&	b,
		int *	index,
		int	n
	)

static

Back substitution on a matrix which is the LU decomposition of the original matrix.

Do the backsubstitution on matrix A which is the LU decomposition of the original matrix. b is the n x 1 right hand side vector. b is replaced by the solution. index is the array that marks the row permutations.

Parameters

A	Input decomposed and output back-substituted matrix.
b	Right hand side vector on input and solution on output.
index	Array to be used to mark row permutations.
n	Dimension of sides.

Definition at line 545 of file us_matrix.cpp.

void US_Matrix::LU_Decomposition	(	double **	matrix,
		int *	index,
		bool	parity,
		int	n
	)

static

LU Decomposition of a matrix.

Performs LU Decomposition on a matrix. This routine must be given an array to mark the row permutations and a flag to mark whether the number of permutations was even or odd. Reference: Numerical Recipes in C.

Parameters

matrix	The matrix to decompose.
index	An index array to mark row permutations.
parity	Flag of even number of permutations.
n	Dimension of matrix sides.

Definition at line 433 of file us_matrix.cpp.

void US_Matrix::LU_SolveSystem	(	double **	A,
		double *&	b,
		int	n
	)

static

Solve a set of linear equations.

Solve a set of linear equations. A is a square matrix of coefficients. b is the right hand side. b is replaced by solution. Target is replaced by its LU decomposition.

Parameters

A	Square matrix of coefficients.
b	Right hand side on input and solution on output.
n	Dimension of matrix sides and vectors.

Definition at line 583 of file us_matrix.cpp.

void US_Matrix::mcopy	(	double **	AA,
		double **	CC,
		int	rows,
		int	columns
	)

static

Matrix copy: C = A.

Copy the contents of one matrix to another of the same size

Parameters

AA	The source A matrix
CC	The destination C matrix copy
rows	The number of rows in A and C
columns	The number of columns in A and C

Definition at line 351 of file us_matrix.cpp.

void US_Matrix::mident	(	double **	CC,
		int	size
	)

static

Fills matrix C: Cij = ( i != j ? 0.0 : 1.0 )

Fill a square matrix so that it is the identity matrix.

Parameters

CC	The matrix product
size	The number of rows and columns in the matrix

Definition at line 343 of file us_matrix.cpp.

void US_Matrix::mmm	(	double **	AA,
		double **	BB,
		double **	CC,
		int	rows,
		int	size,
		int	columns
	)

static

Calculates A * B: a matrix product of A-rows by B-columns.

Calculate the matrix product of two matrices, the rows by columns product of a (rows x size) matrix and a (size x columns) matrix.

Parameters

AA	The A matrix operand (rows x size)
BB	The B matrix operator (size x columns)
CC	The C matrix product (rows x columns)
rows	The number of rows in A and C
size	The number of columns in A and rows in B
columns	The number of columns in B and C

Definition at line 309 of file us_matrix.cpp.

void US_Matrix::msum	(	double **	AA,
		double **	BB,
		double **	CC,
		int	rows,
		int	columns
	)

static

Calculate A + B: a matrix sum with all matrices rows x columns.

Calculate the matrix sum of two matrices of the same dimensions.

Parameters

AA	The A matrix operand (rows x columns)
BB	The B matrix operator (rows x columns)
CC	The C matrix sum (rows x columns)
rows	The number of rows in all matrices
columns	The number of columns in all matrices

Definition at line 327 of file us_matrix.cpp.

void US_Matrix::mvv	(	double **	AA,
		double *	bb,
		double *	cc,
		int	rows,
		int	columns
	)

static

Calculates A * b: a vector product whose size is A's rows.

Calculate the (rows size) product of a (rows x columns) matrix and a (columns size) vector.

Parameters

AA	The A matrix operand (rows x columns)
bb	The b vector operator (columns x 1)
cc	The c vector product (rows x 1)
rows	The number of rows in the matrix (output vector elements)
columns	The number of columns in the matrix (operator vector size)

Definition at line 279 of file us_matrix.cpp.

void US_Matrix::print_matrix	(	double **	A,
		int	rows,
		int	columns
	)

staticprivate

Definition at line 421 of file us_matrix.cpp.

void US_Matrix::print_vector	(	double *	v,
		int	n
	)

staticprivate

Definition at line 411 of file us_matrix.cpp.

void US_Matrix::scale	(	double **	CC,
		double	ss,
		int	rows,
		int	columns
	)

static

Matrix-scalar-multiply: Cij *= s.

Scale all matrix elements by a value

Parameters

CC	The source,destination matrix
ss	The scalar with which to multiply elements
rows	The number of rows in the matrix
columns	The number of columns in the matrix

Definition at line 381 of file us_matrix.cpp.

void US_Matrix::tmm	(	double **	AA,
		double **	CC,
		int	rows,
		int	columns
	)

static

Calculates A' * A , A-transpose times A.

Calculate the (columns x columns) square matrix product of a matrix transpose and the matrix. Only the lower triangle is computed.

Parameters

AA	The A matrix operand.
CC	The C square matrix product of A-tranpose and A.
rows	The number of A rows
columns	The number of A columns (and output C size)

Definition at line 230 of file us_matrix.cpp.

void US_Matrix::tmm	(	double **	AA,
		double **	CC,
		int	rows,
		int	columns,
		bool	fill
	)

static

Calculates A' * A: A-transpose times A.

Calculate the (columns x columns) square matrix product of a matrix transpose and the matrix. The entire matrix may optionally be filled.

Parameters

AA	The A matrix operand.
CC	The C square matrix product of A-tranpose and A.
rows	The number of A rows
columns	The number of A columns (and output C size)
fill	A flag for whether to fill in the upper triangle

Definition at line 264 of file us_matrix.cpp.

void US_Matrix::tvv	(	double **	AA,
		double *	bb,
		double *	cc,
		int	rows,
		int	columns
	)

static

Calculates A' * b: a vector product whose size is A's columns.

Calculate the (columns size) product of a (columns x rows) matrix-tranpose and a (rows size) vector.

Parameters

AA	The A matrix whose transpose is the operand
bb	The b vector operator (rows x 1)
cc	The c vector product (columns x 1)
rows	The number of matrix rows (operator vector size)
columns	The number of matrix columns (product vector size)

Definition at line 294 of file us_matrix.cpp.

void US_Matrix::vcopy	(	double *	aa,
		double *	cc,
		int	size
	)

static

Vector copy: c = a.

Copy the contents of one vector to another of the same size

Parameters

aa	The source "a" vector
cc	The destination "c" vector copy
size	The size of the vectors

Definition at line 359 of file us_matrix.cpp.

void US_Matrix::vsum	(	double *	aa,
		double *	bb,
		double *	cc,
		int	size
	)

static

Calculate a + b: a vector sum with all vectors the same size.

Calculate the vector sum of two vectors of the same dimensions. The destination sum vector may be the same as the operand.

Parameters

aa	The "a" vector operand
bb	The "b" vector operator
cc	The "c" vector sum (may be the same as "a")
size	The size of all vectors

Definition at line 336 of file us_matrix.cpp.

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

Static Public Member Functions

Static Private Member Functions

Detailed Description

Member Function Documentation