tenflowers-core 0.1.1

// Linear Algebra: LU Decomposition with Partial Pivoting
//
// Performs LU decomposition of a square matrix using partial pivoting.
// This is a simplified version adapted for GPU execution.
// For production use, a more sophisticated block algorithm would be needed.
//
// Input:  Matrix A [n, n]
// Output: Matrix L [n, n] (lower triangular), Matrix U [n, n] (upper triangular)
//         Permutation vector P [n] (pivot indices)

struct LinalgMetadata {
    rows_a: u32,
    cols_a: u32,
    rows_b: u32,
    cols_b: u32,
    batch_size: u32,
    tolerance: f32,
    max_iterations: u32,
    padding: u32,
}

@group(0) @binding(0) var<storage, read> input_matrix: array<f32>;
@group(0) @binding(1) var<storage, read_write> l_matrix: array<f32>;
@group(0) @binding(2) var<storage, read_write> u_matrix: array<f32>;
@group(0) @binding(3) var<storage, read_write> pivot_indices: array<u32>;
@group(0) @binding(4) var<uniform> metadata: LinalgMetadata;

// Helper function to swap rows (requires synchronization)
fn swap_rows(row1: u32, row2: u32, n: u32) {
    // This is a simplified implementation
    // In practice, row swapping on GPU requires careful synchronization
    if (row1 != row2) {
        for (var col = 0u; col < n; col = col + 1u) {
            let idx1 = row1 * n + col;
            let idx2 = row2 * n + col;
            
            let temp = u_matrix[idx1];
            u_matrix[idx1] = u_matrix[idx2];
            u_matrix[idx2] = temp;
        }
    }
}

@compute @workgroup_size(16, 16, 1)
fn main(@builtin(global_invocation_id) global_id: vec3<u32>) {
    let n = metadata.rows_a;
    let row = global_id.y;
    let col = global_id.x;
    
    if (row >= n || col >= n) {
        return;
    }
    
    let idx = row * n + col;
    
    // Initialize U matrix with input data
    u_matrix[idx] = input_matrix[idx];
    
    // Initialize L matrix as identity
    if (row == col) {
        l_matrix[idx] = 1.0;
    } else {
        l_matrix[idx] = 0.0;
    }
    
    // Initialize pivot indices
    if (col == 0u) {
        pivot_indices[row] = row;
    }
    
    // Note: This is a placeholder for the actual LU decomposition algorithm
    // A complete GPU implementation would require:
    // 1. Sequential processing for each column (k = 0 to n-1)
    // 2. Finding pivot element and row swapping
    // 3. Gaussian elimination steps
    // 4. Proper synchronization between steps
    //
    // The algorithm would be structured as multiple kernel dispatches
    // rather than a single compute shader due to synchronization requirements.
}

// Kernel for finding pivot element in column k
@compute @workgroup_size(256, 1, 1)
fn find_pivot(@builtin(global_invocation_id) global_id: vec3<u32>) {
    // Implementation for finding the pivot element
    // This would be a separate kernel dispatch
}

// Kernel for performing elimination step for column k
@compute @workgroup_size(16, 16, 1)
fn elimination_step(@builtin(global_invocation_id) global_id: vec3<u32>) {
    // Implementation for the elimination step
    // This would be another separate kernel dispatch
}