//-----------------------------------------------------------------------
// -----------------------------------------------------------------------
// file="MatrixCompute.Factorize"
// Project: StgSharp
// AuthorGroup: Nitload
// Copyright (c) Nitload. All rights reserved.
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using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace StgSharp.Mathematics.Numeric
{
    public static partial class MatrixCompute
    {

        public static void FactorizePLU(
                           Matrix<float> matrix,
                           Span<float> pivot,
                           Matrix<float> lower,
                           Matrix<float> upper)
        {
            if (matrix.ColumnLength != matrix.RowLength) {
                throw new InvalidOperationException("Matrix must be square.");
            }
            if (matrix.Layout != MatrixLayout.DenseRectangle) {
                throw new NotSupportedException("Only dense square matrices are supported.");
            }
            int n = matrix.RowLength;
            if (pivot.Length < n) {
                throw new ArgumentException("Pivot span length is insufficient.", nameof(pivot));
            }
            if (lower.RowLength != n ||
                lower.ColumnLength != n ||
                lower.Layout != MatrixLayout.LowerTriangle) {
                throw new ArgumentException("Lower matrix must be lower-triangular with same dimensions as input.", nameof(lower));
            }
            if (upper.RowLength != n ||
                upper.ColumnLength != n ||
                upper.Layout != MatrixLayout.UpperTriangle) {
                throw new ArgumentException("Upper matrix must be upper-triangular with same dimensions as input.", nameof(upper));
            }

            int size = matrix.KernelColumnLength * matrix.KernelRowLength;
            if (size < 256)
            {
                // Naive Doolittle-style PLU without row swaps (for illustration).
                for (int i = 0; i < n; i++)
                {
                    pivot[i] = i;          // identity pivot
                    lower[i, i] = 1.0f;    // unit diagonal for L
                }

                for (int k = 0; k < n; k++)
                {
                    // Compute U[k, j] for j >= k
                    for (int j = k; j < n; j++)
                    {
                        float sum = 0f;
                        for (int s = 0; s < k; s++) {
                            sum += lower[k, s] * upper[s, j];
                        }
                        upper[k, j] = matrix[k, j] - sum;
                    }

                    // Compute L[i, k] for i > k
                    for (int i = k + 1; i < n; i++)
                    {
                        float sum = 0f;
                        for (int s = 0; s < k; s++) {
                            sum += lower[i, s] * upper[s, k];
                        }
                        float u = upper[k, k];
                        if (u == 0f) {
                            throw new InvalidOperationException("Zero pivot encountered in demonstration PLU.");
                        }
                        lower[i, k] = (matrix.GetElementUnsafe(i, k) - sum) / u;
                    }
                }

                // TODO: For larger kernels, consider calling native pivot helper to extract 4 pivots at once.
            } else if (size < 1024) { } else { }
        }

    }
}