MATRIX.H

Description : Class library for matrix and vector operations

Header files called upon : VECTOR.H

Files required in project : MATRIX.CPP

Class details are as follows:

Class declaration : Matrix

Member variables (private)

float *mat; float pointer to matrix element

int nr, nc; numbers of rows and columns

Constructors (public)

Matrix(int p, int q) : nr(p), nc(q)

Constructor to allocate space for a matrix of specified size

eg Matrix mat1(3, 2);

NB Object mat1 will be allocated 3 rows and 2 columns

Matrix() : mat(new float[9]), nr(3), nc(3) {}

Default constructor allocating space for 3x3 matrix

eg Matrix mat1;

Matrix(float e1, float e2, float e3, float e4, float e5, float e6, float e7, float e8, float e9) : nr(3), nc(3)

Constructor for an initialized 3x3 matrix

eg Matrix m1(1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0);

Matrix(const Matrix &m)

Constructor to copy an already existing matrix into a previously undeclared matrix

eg Matrix mat2(mat1);

NB1 mat2 is previously undeclared, mat1 already initialized

NB2 function defined in MATRIX.CPP

~Matrix()

Destructor

Member functions (public)

float& operator() (int i, int j) const

Overloads parentheses operator to access a particular element in a matrix

eg float scl1 = mat1(i,j);

NB (i,j)th matrix element corresponds to ([i-1],[j-1])th array element) therefore mat1(1,1) accesses first matrix element but zeroth array element

Vector operator* (Vector& v) const

Overloads '*' operator for pre-multiplication of a vector by a matrix

eg vec2 = mat1 * vec1;

NB function defined in MATRIX.CPP

Matrix operator- (Vector &v) const

Subtraction of a vector from each row of a matrix

eg mat2 = mat1 - vec1;

NB function defined in MATRIX.CPP

Vector colMean()

Returns the column mean of a matrix as a vector, in other words, the nth element of the vector is the mean of the values of the nth row in the matrix

eg vec1 = mat1.colMean(); if mat1 = (1.1 3.3) then vec1 = (2.2)

NB function defined in MATRIX.CPP

void eigens(int n, Vector &eval, Matrix &evec)

Derives 'n' eigenvalues and puts them in decreasing magnitude into specified vector, also derives corresponding eigenvectors and puts them in columns into specified (n x n) matrix

eg mat1.eigens(n,vec_eigenval,mat_eigenvect);

NB1 maximum value of n allowed for is 10

NB2 vec_eigenval is vector of returned eigenvalues

NB3 mat_eigenvect is matrix of returned eigenvectors

NB4 function defined in MATRIX.CPP

void eigen(int mv, int n, float* a, float* r)

Calculates 'n' eigenvalues (mv = 0) or 'n' eigenvalues+eigenvectors (mv = 1)

NB1 'a' is a pointer to a 1D float array of size n*(n+1)/2 used for workspace and also returns eigenvalues, 'r' is a pointer to a 1D float array of size n*n and returns eigenvectors

NB2 'eigen' is called by the above member function 'eigens'

NB3 function defined in MATRIX.CPP

void esort(int mv, int n, float* a, float* r)

Sorts eigenvalues (mv = 0) or eigenvalues+eigenvectors (mv = 1) in order of descending eigenvalue

NB1 arguments must be identical to those for the above member function 'eigen' which must be called first before calling 'esort'

NB2 'esort' is called by member function 'eigens'

NB3 function defined in MATRIX.CPP

void cholinv()

Inverts a matrix employing Cholesky decomposition

eg mat1.cholinv();

NB1 mat1 must be square matrix with positive determinant

NB2 function defined in MATRIX.CPP

friend Matrix operator * (const Matrix& m1, const Matrix& m2)

Overloads '*' operator for matrix multiplication

eg mat1 = mat2 * mat3;

NB defined in MATRIX.CPP

friend Matrix operator & (const Matrix& m1, const Matrix& m2)

Overloads '&' operator to multiply a transpose of a matrix by another matrix

eg mat1 = mat2 & mat3;

NB1 the transpose of mat2 is used but mat2 itself is not affected

NB2 mat2 and mat3 must have same number of rows (errorchecked by function)

NB3 user will need to ensure that the (rows x columns) dimensions of mat1 are (mat2_columns x mat3_columns)

NB4 function defined in MATRIX.CPP

friend ostream& operator << (ostream &os, Matrix &m)

Overloads '<<' operator to write out a matrix

eg cout << mat1;

NB function defined in MATRIX.CPP

Class declaration : LtMatrix