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keep working on PLN facotrize

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This commit is contained in:
Youmu Liu
2025-12-25 11:59:40 +08:00
parent 3b3a90a2af
commit e5539bcc6d
12 changed files with 123 additions and 76 deletions
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StgSharp.Mathematics/Numeric/MatrixCompute.Factorize.cs
+78 -28
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@@ -25,6 +25,7 @@
//
// -----------------------------------------------------------------------
// -----------------------------------------------------------------------
using StgSharp.Internal;
using System;
using System.Collections.Generic;
using System.Linq;
@@ -36,11 +37,11 @@ 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)
public static unsafe void FactorizePLU(
Matrix<float> matrix,
Span<int> pivot,
Matrix<float> lower,
Matrix<float> upper)
{
if (matrix.ColumnLength != matrix.RowLength) {
throw new InvalidOperationException("Matrix must be square.");
@@ -54,7 +55,7 @@ namespace StgSharp.Mathematics.Numeric
}
if (lower.RowLength != n ||
lower.ColumnLength != n ||
lower.Layout != MatrixLayout.LowerTriangle) {
lower.Layout != MatrixLayout.UpperTriangle) {
throw new ArgumentException("Lower matrix must be lower-triangular with same dimensions as input.", nameof(lower));
}
if (upper.RowLength != n ||
@@ -66,37 +67,86 @@ namespace StgSharp.Mathematics.Numeric
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
pivot[i] = i; // identity permutation
}
for (int k = 0; k < n; k++)
// Aggressive: always call native pivot to fetch four-column candidates
ulong* pivots = stackalloc ulong[4];
for (int kBlock = 0; kBlock < n; kBlock += 4)
{
// Compute U[k, j] for j >= k
for (int j = k; j < n; j++)
NativeIntrinsic.Context
.f32_pivot(matrix.Buffer, (ulong)(kBlock >> 2),
(ulong)(matrix.KernelRowLength - (kBlock >> 2)),
(ulong)pivots);
int colsInBlock = Math.Min(4, n - kBlock);
for (int offset = 0; offset < colsInBlock; offset++)
{
float sum = 0f;
for (int s = 0; s < k; s++) {
sum += lower[k, s] * upper[s, j];
}
upper[k, j] = matrix[k, j] - sum;
}
int k = kBlock + offset;
int pivotRow = k;
float maxAbs;
// 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];
int candidateRow = (int)pivots[offset];
int idx = -1;
for (int r = k; r < n; r++)
{
if (pivot[r] == candidateRow)
{
idx = r;
break;
}
}
float u = upper[k, k];
if (u == 0f) {
throw new InvalidOperationException("Zero pivot encountered in demonstration PLU.");
if (idx != -1)
{
pivotRow = idx;
maxAbs = MathF.Abs(matrix.GetElementUnsafe(pivot[idx], k));
} else
{
maxAbs = MathF.Abs(matrix.GetElementUnsafe(pivot[k], k));
for (int r = k + 1; r < n; r++)
{
float val = MathF.Abs(matrix.GetElementUnsafe(pivot[r], k));
if (val > maxAbs)
{
maxAbs = val;
pivotRow = r;
}
}
}
if (maxAbs == 0f) {
throw new InvalidOperationException("Zero pivot encountered in PLU.");
}
if (pivotRow != k) {
(pivot[k], pivot[pivotRow]) = (pivot[pivotRow], pivot[k]);
}
lower[k, k] = 1.0f; // unit diagonal for L
// 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.GetElementUnsafe(pivot[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 PLU.");
}
lower[i, k] = (matrix.GetElementUnsafe(pivot[i], k) - sum) / u;
}
lower[i, k] = (matrix.GetElementUnsafe(i, k) - sum) / u;
}
}