Rectangular matrices

General matrix class

Name

Matrix

Inheritance

array of vectors: Array<Vector>

Constituents

• Number of rows and columns, rows, cols.
• Total number of elements, n.
• Dynamically allocated array, indexed from base 0 using square brackets e.g. m[i][j].

Methods

Creation

• Matrix(rows,columns)

  e.g. matrix x(3,2); or y = matrix(n,m);.

• Matrix(existing_matrix_to_copy)

  e.g. Matrix y; cin >> y; Matrix x(y);

  This should be faster than initialising a new matrix

• Matrix(existing_array<Vector>_to_copy)

  e.g. Array<Vector>y; cin >> y; Matrix x(y);

Input and output

The << and >> operators can be used.

Data format:

rows columns
For each row:
   For each column:
      value

The class also provides Read_elements and Write_elements methods to read and write the elements only, without the number of rows and columns.) e.g.

Matrix x; cin >> x; cout << x << endl; x.Write_elements(cout);

Assignment

=

e.g. Matrix x,y; cin >> x; y = x;

Tests

• int square() const returns 1 if the matrix is square, 0 otherwise
• int symmetric(const double eps = 0.0) const returns 1 if the matrix is symmetric (elements reflected across the main diagonal differ by not more than eps), 0 otherwise

Decompose into symmetric and antisymmetric parts

void symm_antisymm(Matrix& symm, Matrix& antisymm) const returns the symmetric part in symm and the antisymmetric part in antisymm

Extract a sub-matrix

   Matrix submatrix(
      const int row0, // first row of submatrix
      const int row1  // last row of submatrix
      const int col0, // first column of submatrix
      const int col1  // last column of submatrix
   ) const

e.g. Matrix y = x.submatrix(0,4,1,3);

Matrices of zeroes

• void nullmatrix(): existing matrix (rows and columns already set)
• friend matrix nullmatrix(unsigned int reqrows, unsigned int reqcols) : creates a new, null matrix

Identity matrix

• void identitymatrix(): existing matrix (rows and columns already set)
• friend matrix identitymatrix(unsigned int reqrows, unsigned int reqcols): creates a new identity matrix

Trace

friend double trace(const Matrix& a)

Norm (sum of squares of elements)

friend double norm(const Matrix& a)

Diagonal matrix from vector

friend Matrix diag(const Vector& v)

Inner product

The following methods all return a.b, where a and b are matrixs with the same number of elements.

• friend Vector inner_product(const Matrix& a, const Matrix& b)
• friend Vector dot(const Matrix& a, const Matrix& b)
• friend Vector operator*(const Matrix& a, const Matrix& b)

e.g.

   Matrix x,y; cin >> x >> y;
   Matrix a = inner_product(x,y), b = dot(x,y), c = x * y; // a = b = c

Norm

(Sum of squares of elements.) friend double norm(const Matrix& a)

e.g. Matrix a; cin >> a; double anorm = norm(a);

Arithmetic operations

These methods allow conventional-looking equations to be written with matrix quantities.

• Add (a + b): friend Matrix operator+(const Matrix& a, const Matrix& b)
• Subtract (a - b): friend Matrix operator-(const Matrix& a, const Matrix& b)
• Negate (-a): friend Matrix operator-(const Matrix& a)
• Multiply by a scalar, integer or real (s * a or a * s):
  • friend Matrix operator*(const Matrix& a, const int s)
  • friend Matrix operator*(const int s, const Matrix& a)
  • friend Matrix operator*(const Matrix& a, const vector s)
  • friend Matrix operator*(const vector s, const Matrix& a)
• Divide by a scalar, integer or real (a / s):
  • friend Matrix operator/(const Matrix& a, const int s)
  • friend Matrix operator/(const Matrix& a, const vector s)

General matrix class (fixed dimension)

Name

Matrix_fixed_dimension

Inheritance

matrix

This class is the base for matrixs of a specific dimension.

6D matrix class

Name

Matrix6d

Inheritance

Matrix_fixed_dimension

5D matrix class

Name

Matrix5d

Inheritance

Matrix_fixed_dimension

4D matrix class

Name

Matrix4d

Inheritance

Matrix_fixed_dimension

3D matrix class

Name

Matrix3d

Inheritance

Matrix_fixed_dimension

2D matrix class

Name

Matrix2d

Inheritance

Matrix_fixed_dimension

Methods

Cross product

Calculates the real value a^b.

   friend vector operator^(const Matrix2d& a, const Matrix2d& b)

Rotation

•    friend Matrix2d rotate(
        const Matrix2d& a,    // initial matrix
        const vector phi      // rotation angle in radians (anticlockwise)
     )
  

• About an arbitrary axis through an arbitrary point (e.g. for rotating position matrixs)

     friend Matrix2d rotate_about(
        const Matrix2d& a,    // initial matrix
        const Matrix2d& p,    // point through which axis passes
        const vector phi      // rotation angle in radians (anticlockwise)
     )
  

General real matrix class

Name

real_matrix

Inheritance

Arithmetic_matrix<Vector>