Linear Algebra Library Requirements

Matrix

The matrix type represents a matrix of double and must have the following interface:

• Matrix::Matrix()

  Default constructor.

• Matrix::Matrix(int m, int n)

  Creates a m*n matrix.

• double Matrix::operator()(subscript i, subscript j)

  returns element (i,j) of the matrix. The indices have offset 1: the first element is (1,1), not (0,0). subscript is a type convertible to int.

• int Matrix::num_rows()

  returns the number of rows of the matrix

• int Matrix::num_cols()

  returns the number of columns of the matrix

• void Matrix::resize(int n, int m)

  Resizes the matrix to size n*m.

Vector

Vector type is a vector of double which has the following interface:

• Vector::Vector()

  Default constructor.

• Vector::Vector(int m)

  Creates a vector of size m.

• double Vector::operator()(subscript i)

  returns element i of the vector. The index has offset 1: the first element is number 1, not 0. subscript is a type convertible to int.

• void Vector::resize(int n)

  Resizes the vector to size n.

LU solve

The prototype of the function must be: template< class random_iterator>
int LU_solve(Matrix& A, Vector& b, iterator solution_begin)

This function solves linear system Ax = b using a LU decomposition of A, and stores the resulting vector x in the container solution_begin points to. This container must be of size equal to the size of vector b. The iterator must be a Random Access Iterator. A Random Access Iterator is a refinement of Forward Iterator. If it is a Random Access Iterator, it[j] is a valid expression which makes iterator it point to the j-th element of the container.

Cholesky solve

The prototype of the function must be: template< class random_iterator>
int Cholesky_solve(Matrix& A, Vector& b, iterator solution_begin)

This function solves linear system Ax = b using a Cholesky decomposition of A (A must be positive-definite), and stores the resulting vector x in the container solution_begin points to. This container must be of size equal to the size of vector b.