MATRIX.CPP

Description : Function definitions for matrix operations

Header files called upon : math.h, VECTOR.H , MATRIX.H . The specific statement 'extern "C" int exit(int);' exempts the need for the inclusion of stdlib.h

Class details are as follows:

Further class member definitions : Vector

Constructors (public)

Vector::Vector(const Vector &v)

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

eg Vector vec2(vec1);

NB1 vec2 is previously undeclared, vec1 already initialized

NB2 function is declared in VECTOR.H

Member functions (public)

Vector& Vector::operator= (const Vector& v)

Overloads '=' operator for vector assignment

eg vec1 = vec2;

NB function declared in VECTOR.H

ostream& operator << (ostream &os, Vector &v)

Overloads '<<' operator to write out a vector

eg cout << vec1;

NB function declared in VECTOR.H

Further class member definitions : Matrix

Constructors (public)

Matrix::Matrix(const Matrix &m) : nr(m.nr), nc(m.nc)

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 declared in MATRIX.H

Member functions (public)

Vector Matrix::operator* (Vector &v) const

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

eg vec2 = mat1 * vec1;

NB function declared in MATRIX.H

Matrix Matrix::operator- (Vector &v) const

Subtraction of a vector from each row of a matrix

eg mat2 = mat1 - vec1;

NB function declared in MATRIX.H

void Matrix::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 declared in MATRIX.H

void Matrix::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 declared in MATRIX.H

void Matrix::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 declared in MATRIX.H

Vector Matrix::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 declared in MATRIX.H

void Matrix::cholinv()

Inverts a matrix employing Cholesky decomposition

eg mat1.cholinv();

NB1 mat1 must be square matrix with positive determinant

NB2 function declared in MATRIX.H

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

Overloads '*' operator for matrix multiplication

eg mat1 = mat2 * mat3;

NB function declared in MATRIX.H

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 declared in MATRIX.H

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

Overloads '<<' operator to write out a matrix

eg cout << mat1;

NB function declared in MATRIX.H

Further class member definitions : LtMatrix