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using System;

namespace IStation.Numerics.LinearAlgebra.Factorization
{
    /// <summary>
    /// <para>A class which encapsulates the functionality of a Cholesky factorization.</para>
    /// <para>For a symmetric, positive definite matrix A, the Cholesky factorization
    /// is an lower triangular matrix L so that A = L*L'.</para>
    /// </summary>
    /// <remarks>
    /// The computation of the Cholesky factorization is done at construction time. If the matrix is not symmetric
    /// or positive definite, the constructor will throw an exception.
    /// </remarks>
    /// <typeparam name="T">Supported data types are double, single, <see cref="Complex"/>, and <see cref="Complex32"/>.</typeparam>
    public abstract class Cholesky<T> : ISolver<T>
        where T : struct, IEquatable<T>, IFormattable
    {
        protected Cholesky(Matrix<T> factor)
        {
            Factor = factor;
        }

        /// <summary>
        /// Gets the lower triangular form of the Cholesky matrix.
        /// </summary>
        public Matrix<T> Factor { get; private set; }

        /// <summary>
        /// Gets the determinant of the matrix for which the Cholesky matrix was computed.
        /// </summary>
        public abstract T Determinant { get; }

        /// <summary>
        /// Gets the log determinant of the matrix for which the Cholesky matrix was computed.
        /// </summary>
        public abstract T DeterminantLn { get; }

        /// <summary>
        /// Calculates the Cholesky factorization of the input matrix.
        /// </summary>
        /// <param name="matrix">The matrix to be factorized<see cref="Matrix{T}"/>.</param>
        public abstract void Factorize(Matrix<T> matrix);

        /// <summary>
        /// Solves a system of linear equations, <b>AX = B</b>, with A Cholesky factorized.
        /// </summary>
        /// <param name="input">The right hand side <see cref="Matrix{T}"/>, <b>B</b>.</param>
        /// <returns>The left hand side <see cref="Matrix{T}"/>, <b>X</b>.</returns>
        public virtual Matrix<T> Solve(Matrix<T> input)
        {
            var x = Matrix<T>.Build.SameAs(input, input.RowCount, input.ColumnCount, fullyMutable: true);
            Solve(input, x);
            return x;
        }

        /// <summary>
        /// Solves a system of linear equations, <b>AX = B</b>, with A Cholesky factorized.
        /// </summary>
        /// <param name="input">The right hand side <see cref="Matrix{T}"/>, <b>B</b>.</param>
        /// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>X</b>.</param>
        public abstract void Solve(Matrix<T> input, Matrix<T> result);

        /// <summary>
        /// Solves a system of linear equations, <b>Ax = b</b>, with A Cholesky factorized.
        /// </summary>
        /// <param name="input">The right hand side vector, <b>b</b>.</param>
        /// <returns>The left hand side <see cref="Vector{T}"/>, <b>x</b>.</returns>
        public virtual Vector<T> Solve(Vector<T> input)
        {
            var x = Vector<T>.Build.SameAs(input, input.Count);
            Solve(input, x);
            return x;
        }

        /// <summary>
        /// Solves a system of linear equations, <b>Ax = b</b>, with A Cholesky factorized.
        /// </summary>
        /// <param name="input">The right hand side vector, <b>b</b>.</param>
        /// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>x</b>.</param>
        public abstract void Solve(Vector<T> input, Vector<T> result);
    }
}