using System;

namespace Science.Mathematics.LinearAlgebra
{
    public class LeftNullspace : VectorSpace
    {
        public LeftNullspace(Matrix A) 
        {
            if (A.SizeOfRow == A.Rank)
            {
                Vector[] n = new Vector[1];
                n[0] = new Vector(A.SizeOfRow);
                this.Basis = n;
                this.Dimension = 0;
            }
            else
            {
                this.Dimension = A.SizeOfRow - A.Rank;
                Vector[] n = new Vector[this.Dimension];
                Nullspace NAt = new Nullspace(A.Transpose);
                for (int i = 0; i < n.Length; i++)
                {
                    n[i] = new Vector(A.SizeOfRow);
                    for (int j = 0; j < A.SizeOfRow ; j++)
                    {
                        n[i][j] = NAt.NullspaceMatrix[j,i];
                    }
                }
                this.Basis = n;                
            }
        }
        public Vector LinearCombination(double[] x)
        {
            Vector xx = new Vector(this.Basis[0].Size);
            for (int i = 0; i < x.Length; i++)
                xx += x[i] * this.Basis[i];
            return xx;
        }
    }
}