linearalgebra.cpp File Reference

#include <vector>
#include <iostream>
#include <cmath>

Include dependency graph for linearalgebra.cpp:

Go to the source code of this file.

Functions
std::vector< double >	VectorDifference (std::vector< double > A, std::vector< double > B)
	Vector difference between two vectors. More...
std::vector< double >	VectorScalarProduct (std::vector< double > A, double b)
	Vector scalar prodcut of vector and scalar. More...
std::vector< double >	VectorSum (std::vector< double > A, std::vector< double > B)
	Vector sum between two vectors. More...
std::vector< double >	MatrixVectorProduct (std::vector< std::vector< double > > M, std::vector< double > A)
double	VectorVectorProduct (std::vector< double > A, std::vector< double > B)
	Dot product of vectors. More...
std::vector< double >	GetMatrixColumn (std::vector< std::vector< double >> M, int column)
	Function to get a column from a matrix. More...
std::vector< double >	GetMatrixRow (std::vector< std::vector< double >> M, int row)
	Function to get a row from a matrix. More...
std::vector< std::vector< double > >	TransposeMatrix (std::vector< std::vector< double > > M)
std::vector< double >	MatrixTrace (std::vector< std::vector< double >> M)
	Function to the trace of a square \(n \times n\) matrix \(M\). More...
std::vector< std::vector< double > >	InvertMatrixElements (std::vector< std::vector< double >> M)
	Function to take the inverse of the individual matrix elements. More...
std::vector< std::vector< double > >	VectorToDiagonal (std::vector< double > A)
	Function which takes a std::vector of double to make a diagonal matrix of it, such that \( A_{i} = M_{ii} \). More...
std::vector< std::vector< double > >	MatrixMatrixProduct (std::vector< std::vector< double >> M, std::vector< std::vector< double >> N)
	Function incorporating the standard matrix-matrix product, producing a new matrix. Matrix M should have as many columns as N has rows, otherwise an exception is thrown. More...
std::vector< std::vector< double > >	MatrixMatrixSum (std::vector< std::vector< double >> M, std::vector< std::vector< double >> N)
	A function to calculate the sum of the entries of two matrices. More...
std::vector< std::vector< double > >	operator+ (std::vector< std::vector< double >> M, std::vector< std::vector< double >> N)
	Operator form of MatrixMatrixSum(), using std library forwarding. More...
std::vector< std::vector< double > >	operator* (std::vector< std::vector< double >> M, std::vector< std::vector< double >> N)
	Operator form of MatrixMatrixProduct(), using std library forwarding. More...
double	operator* (std::vector< double > A, std::vector< double > B)
	Operator form of VectorVectorProduct(), using std library forwarding. More...
std::vector< double >	operator* (std::vector< std::vector< double >> M, std::vector< double > A)
	Operator form of MatrixVectorProduct(), using std library forwarding. More...
std::vector< double >	operator+ (std::vector< double > A, std::vector< double > B)
	Operator form of VectorSum(), using std library forwarding. More...
std::vector< double >	operator- (std::vector< double > A, std::vector< double > B)
	Operator form of VectorDifference(), using std library forwarding. More...
std::vector< double >	operator* (double b, std::vector< double > A)
	Operator form of VectorScalarProduct(), using std library forwarding. More...
std::vector< double >	operator* (std::vector< double > A, double b)
	Operator form of VectorScalarProduct(), using std library forwarding. More...
std::vector< std::vector< double > >	CholeskyDecompose (std::vector< std::vector< double >> A)
	Cholesky-decomposition of a positive definite Hermitian \( n \times n\) matrix \( M \). More...
std::vector< double >	SolveLowerTriangular (std::vector< std::vector< double >> L, std::vector< double > x)
	Solve linear equation \( L y = x\) where \( L \) is a lower triangular \( n \times n\) matrix and \( x \) and \( y \) are \( n\) dimensional vectors. Uses forward and backward substitution to iteratively solve the system. More...
std::vector< std::vector< double > >	InvertLowerTriangular (std::vector< std::vector< double >> L)
	Invert a lower triangular \( n \times n\) matrix by use of solving the system \( L L^{-1} = I\) per column of \( I \) using SolveLowerTriangular(), the identity matrix. More...
std::vector< double >	operator/ (std::vector< double > A, double b)
	Operator form of vector by scalar division. Uses VectorScalarProduct() with std library forwarding. More...
std::vector< double >	NormalizeVector (std::vector< double > A)
	Normalizes a vector to unit length. More...

Function Documentation

CholeskyDecompose()

std::vector<std::vector<double> > CholeskyDecompose

(

std::vector< std::vector< double >>

A

)

Cholesky-decomposition of a positive definite Hermitian \( n \times n\) matrix \( M \).

Parameters

A	A positive definite Hermitian \( n \times n\) matrix.

Returns

A lower triangular \( n \times n\) matrix for which holds \( L L^\dagger = M \), where \( L^\dagger \) is the adjoint of \( L \) (which of course simplifies to transposition for real matrices).

Definition at line 275 of file linearalgebra.cpp.

GetMatrixColumn()

std::vector<double> GetMatrixColumn	(	std::vector< std::vector< double >>	M,
		int	column
	)

Function to get a column from a matrix.

Parameters

M	Any \( n \times m \) matrix \(M\).
row	Integer indicating the column. Numbering starts at 0.

Returns

An \( n \) dimensional vector containing the extracted matrix column.

Definition at line 93 of file linearalgebra.cpp.

GetMatrixRow()

std::vector<double> GetMatrixRow	(	std::vector< std::vector< double >>	M,
		int	row
	)

Function to get a row from a matrix.

Parameters

M	Any \( n \times m \) matrix \(M\).
row	Integer indicating the row. Numbering starts at 0.

Returns

An \( m \) dimensional vector containing the extracted matrix row.

Definition at line 110 of file linearalgebra.cpp.

InvertLowerTriangular()

std::vector<std::vector<double> > InvertLowerTriangular

(

std::vector< std::vector< double >>

L

)

Invert a lower triangular \( n \times n\) matrix by use of solving the system \( L L^{-1} = I\) per column of \( I \) using SolveLowerTriangular(), the identity matrix.

Parameters

L	Any lower triangular \( n \times n\) matrix.

Returns

The inverse of \( L \), another lower triangular \( n \times n\) matrix.

Definition at line 325 of file linearalgebra.cpp.

InvertMatrixElements()

std::vector<std::vector<double> > InvertMatrixElements

(

std::vector< std::vector< double >>

M

)

Function to take the inverse of the individual matrix elements.

Parameters

M	Any \( n \times m \) matrix \(M\).

Returns

The inverted elements \( 1/M_{ij}\) in a std::vector of std::vector of double.

Definition at line 158 of file linearalgebra.cpp.

MatrixMatrixProduct()

std::vector<std::vector<double> > MatrixMatrixProduct	(	std::vector< std::vector< double >>	M,
		std::vector< std::vector< double >>	N
	)

Function incorporating the standard matrix-matrix product, producing a new matrix. Matrix M should have as many columns as N has rows, otherwise an exception is thrown.

Parameters

M	Any \( n \times m \) matrix \(M\).
N	Any \( m \times p \) matrix \(N\).

Returns

A \( n \times p \) matrix P defined by \( P_{ij} = \sum_{k=1}^m M_{ik} N_{kj} \).

Definition at line 184 of file linearalgebra.cpp.

MatrixMatrixSum()

std::vector<std::vector<double> > MatrixMatrixSum	(	std::vector< std::vector< double >>	M,
		std::vector< std::vector< double >>	N
	)

A function to calculate the sum of the entries of two matrices.

Parameters

M	Any \( n \times m \) matrix \(M\).
N	Any \( n \times m \) matrix \(N\).

Returns

A \( n \times m \) matrix \( S \) containing the sum of the entries of \(M\) and \(N\).

Definition at line 213 of file linearalgebra.cpp.

MatrixTrace()

std::vector<double> MatrixTrace

(

std::vector< std::vector< double >>

M

)

Function to the trace of a square \(n \times n\) matrix \(M\).

Parameters

M	Any square matrix.

Returns

The trace of \( M \).

Definition at line 144 of file linearalgebra.cpp.

MatrixVectorProduct()

std::vector<double> MatrixVectorProduct	(	std::vector< std::vector< double > >	M,
		std::vector< double >	A
	)

Definition at line 54 of file linearalgebra.cpp.

NormalizeVector()

std::vector<double> NormalizeVector

(

std::vector< double >

A

)

Normalizes a vector to unit length.

Parameters

A	Any vector \( A \).

Returns

Vector \( B' \) where \( \sqrt{\sum_i {B_{i}}^{2} }= 1\) and \( A \cdot B = |A| |B| = |A|\) .

Definition at line 345 of file linearalgebra.cpp.

operator*() [1/5]

std::vector<std::vector<double> > operator*	(	std::vector< std::vector< double >>	M,
		std::vector< std::vector< double >>	N
	)

Operator form of MatrixMatrixProduct(), using std library forwarding.

Definition at line 245 of file linearalgebra.cpp.

operator*() [2/5]

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

Operator form of VectorVectorProduct(), using std library forwarding.

Definition at line 250 of file linearalgebra.cpp.

operator*() [3/5]

std::vector<double> operator*	(	std::vector< std::vector< double >>	M,
		std::vector< double >	A
	)

Operator form of MatrixVectorProduct(), using std library forwarding.

Definition at line 254 of file linearalgebra.cpp.

operator*() [4/5]

std::vector<double> operator*	(	double	b,
		std::vector< double >	A
	)

Operator form of VectorScalarProduct(), using std library forwarding.

Definition at line 267 of file linearalgebra.cpp.

operator*() [5/5]

std::vector<double> operator*	(	std::vector< double >	A,
		double	b
	)

Operator form of VectorScalarProduct(), using std library forwarding.

Definition at line 271 of file linearalgebra.cpp.

operator+() [1/2]

std::vector<std::vector<double> > operator+	(	std::vector< std::vector< double >>	M,
		std::vector< std::vector< double >>	N
	)

Operator form of MatrixMatrixSum(), using std library forwarding.

Definition at line 240 of file linearalgebra.cpp.

operator+() [2/2]

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

Operator form of VectorSum(), using std library forwarding.

Definition at line 259 of file linearalgebra.cpp.

operator-()

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

Operator form of VectorDifference(), using std library forwarding.

Definition at line 263 of file linearalgebra.cpp.

operator/()

std::vector<double> operator/	(	std::vector< double >	A,
		double	b
	)

Operator form of vector by scalar division. Uses VectorScalarProduct() with std library forwarding.

Definition at line 341 of file linearalgebra.cpp.

SolveLowerTriangular()

std::vector<double> SolveLowerTriangular	(	std::vector< std::vector< double >>	L,
		std::vector< double >	x
	)

Solve linear equation \( L y = x\) where \( L \) is a lower triangular \( n \times n\) matrix and \( x \) and \( y \) are \( n\) dimensional vectors. Uses forward and backward substitution to iteratively solve the system.

Parameters

L	Any lower triangular \( n \times n\) matrix.
x	Any \( n\) dimensional vector.

Returns

Solution y of the system, an \( n\) dimensional vector.

Definition at line 303 of file linearalgebra.cpp.

TransposeMatrix()

std::vector<std::vector<double> > TransposeMatrix

(

std::vector< std::vector< double > >

M

)

Definition at line 127 of file linearalgebra.cpp.

VectorDifference()

std::vector<double> VectorDifference	(	std::vector< double >	A,
		std::vector< double >	B
	)

Vector difference between two vectors.

Parameters

A	Vector \( A \) of dimension \( n\).
B	Vector \( B \) of dimension \( n\).

Returns

Vector \( C \) where \( C_i = A_i - B_i \).

Definition at line 11 of file linearalgebra.cpp.

VectorScalarProduct()

std::vector<double> VectorScalarProduct	(	std::vector< double >	A,
		double	b
	)

Vector scalar prodcut of vector and scalar.

Parameters

A	Any vector \( A \).
B	Scalar \( b \).

Returns

Vector \( C \) where \( C_{i} = A_{i} \cdot b \).

Definition at line 29 of file linearalgebra.cpp.

VectorSum()

std::vector<double> VectorSum	(	std::vector< double >	A,
		std::vector< double >	B
	)

Vector sum between two vectors.

Parameters

A	Vector \( A \) of dimension \( n\).
B	Vector \( B \) of dimension \( n\).

Returns

Vector \( C \) where \( C_i = A_{i} + B_i \).

Definition at line 36 of file linearalgebra.cpp.

VectorToDiagonal()

std::vector<std::vector<double> > VectorToDiagonal

(

std::vector< double >

A

)

Function which takes a std::vector of double to make a diagonal matrix of it, such that \( A_{i} = M_{ii} \).

Parameters

A	Any Any \( n \) dimensional vector.

Returns

Diagonal \( n \times n \) matrix \(M\).

Definition at line 169 of file linearalgebra.cpp.

VectorVectorProduct()

double VectorVectorProduct	(	std::vector< double >	A,
		std::vector< double >	B
	)

Dot product of vectors.

Parameters

A	Vector \( A \) of dimension \( n\).
B	Vector \( B \) of dimension \( n\).

Returns

Dot product \( c \) of \( A \) and \( B \) where where \( c = A_i \cdot B_i \) (float).

Definition at line 78 of file linearalgebra.cpp.