109 lines
4.6 KiB
C#
109 lines
4.6 KiB
C#
//-----------------------------------------------------------------------
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// -----------------------------------------------------------------------
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// file="MatrixCompute.Factorize"
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// Project: StgSharp
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// AuthorGroup: Nitload
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// Copyright (c) Nitload. All rights reserved.
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//
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// Permission is hereby granted, free of charge, to any person obtaining a copy
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// of this software and associated documentation files (the "Software"), to deal
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// in the Software without restriction, including without limitation the rights
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// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the Software is
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// furnished to do so, subject to the following conditions:
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//
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// The above copyright notice and this permission notice shall be included in all
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// copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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// SOFTWARE.
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//
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// -----------------------------------------------------------------------
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// -----------------------------------------------------------------------
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using System;
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using System.Collections.Generic;
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using System.Linq;
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using System.Text;
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using System.Threading.Tasks;
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namespace StgSharp.Mathematics.Numeric
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{
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public static partial class MatrixCompute
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{
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public static void FactorizePLU(
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Matrix<float> matrix,
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Span<float> pivot,
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Matrix<float> lower,
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Matrix<float> upper)
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{
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if (matrix.ColumnLength != matrix.RowLength) {
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throw new InvalidOperationException("Matrix must be square.");
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}
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if (matrix.Layout != MatrixLayout.DenseRectangle) {
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throw new NotSupportedException("Only dense square matrices are supported.");
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}
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int n = matrix.RowLength;
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if (pivot.Length < n) {
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throw new ArgumentException("Pivot span length is insufficient.", nameof(pivot));
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}
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if (lower.RowLength != n ||
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lower.ColumnLength != n ||
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lower.Layout != MatrixLayout.LowerTriangle) {
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throw new ArgumentException("Lower matrix must be lower-triangular with same dimensions as input.", nameof(lower));
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}
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if (upper.RowLength != n ||
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upper.ColumnLength != n ||
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upper.Layout != MatrixLayout.UpperTriangle) {
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throw new ArgumentException("Upper matrix must be upper-triangular with same dimensions as input.", nameof(upper));
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}
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int size = matrix.KernelColumnLength * matrix.KernelRowLength;
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if (size < 256)
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{
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// Naive Doolittle-style PLU without row swaps (for illustration).
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for (int i = 0; i < n; i++)
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{
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pivot[i] = i; // identity pivot
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lower[i, i] = 1.0f; // unit diagonal for L
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}
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for (int k = 0; k < n; k++)
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{
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// Compute U[k, j] for j >= k
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for (int j = k; j < n; j++)
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{
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float sum = 0f;
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for (int s = 0; s < k; s++) {
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sum += lower[k, s] * upper[s, j];
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}
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upper[k, j] = matrix[k, j] - sum;
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}
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// Compute L[i, k] for i > k
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for (int i = k + 1; i < n; i++)
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{
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float sum = 0f;
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for (int s = 0; s < k; s++) {
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sum += lower[i, s] * upper[s, k];
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}
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float u = upper[k, k];
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if (u == 0f) {
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throw new InvalidOperationException("Zero pivot encountered in demonstration PLU.");
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}
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lower[i, k] = (matrix.GetElementUnsafe(i, k) - sum) / u;
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}
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}
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// TODO: For larger kernels, consider calling native pivot helper to extract 4 pivots at once.
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} else if (size < 1024) { } else { }
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}
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}
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}
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