module CsrMatrix
    module Properties

        def self.included(exceptions)
          exceptions.send :include, Exceptions
        end 
        
        # Determines if the matrix is diagonal; wherein the values outside the main diagonal are all zero.
        def diagonal?
            m = Matrix.rows(self.decompose)
            return m.diagonal?
        end

        # Determines if the matrix is empty; wherein all the values are zero.
        def empty?
            m = Matrix.rows(self.decompose)
            return m.empty?
        end

        # Determine if the matrix is hermitian.
        def hermitian?
            m = Matrix.rows(self.decompose)
            return m.hermitian?
        end

        # Determines if the matrix is lower-diagonal; wherein all the values only exist on and below the diagonal line.
        def lower_triangular?
            m = Matrix.rows(self.decompose)
            return m.lower_triangular?
        end

        # Determines if the matrix is normal; wherein if the number of rows or columns is 0
        def normal? 
            m = Matrix.rows(self.decompose)
            return m.normal?
        end

        # Determines if the matrix is orthogonal; wherein the rows and columns are orthogonal unit vectors.
        def orthogonal?
            m = Matrix.rows(self.decompose)
            return m.orthogonal?
        end

        # Determines if the matrix is a permutation; wherein it is an nxn version of the identity matrix.
        def permutation?
            m = Matrix.rows(self.decompose)
            return m.permutation?
        end

        # Determines if the matrix is real; wherein the matrix consists entirely of real numbers.
        def real?
            m = Matrix.rows(self.decompose)
            return m.real?
        end

        # Determines if the matrix is nonsingular
        def nonsingular?
            return !self.singular?
        end

        # Determines if the matrix is singular
        def singular?
            m = Matrix.rows(self.decompose)
            return m.singular?
        end

        # Determines if the matrix is square
        def square?
            m = Matrix.rows(self.decompose)
            return m.square?
        end

        # Determines if the matrix is symmetric
        def symmetric?
            m = Matrix.rows(self.decompose)
            return m.symmetric?
        end

        # Determines if the matrix is unitary
        def unitary?
            m = Matrix.rows(self.decompose)
            return m.unitary?
        end

        # Determines if the matrix is upper-triangular
        def upper_triangular?
            m = Matrix.rows(self.decompose)
            return m.upper_triangular?
        end

        # Determines if the matrix is zero
        def zero?
            m = Matrix.rows(self.decompose)
            return m.zero?
        end

    end
end