Fix cholesky computation.
This commit is contained in:
sebcrozet
parent
7ecbacacda
commit
9bf1d0280d
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@ -52,6 +52,15 @@ where
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pub(crate) vals: Vec<N>,
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}
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impl<N: Scalar, R: Dim, C: Dim> CsVecStorage<N, R, C>
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where
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DefaultAllocator: Allocator<usize, C>,
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{
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pub fn values(&self) -> &[N] {
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&self.vals
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}
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}
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impl<N: Scalar, R: Dim, C: Dim> CsVecStorage<N, R, C> where DefaultAllocator: Allocator<usize, C> {}
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impl<'a, N: Scalar, R: Dim, C: Dim> CsStorageIter<'a, N, R, C> for CsVecStorage<N, R, C>
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@ -187,10 +196,35 @@ where
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}
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impl<N: Scalar, R: Dim, C: Dim, S: CsStorage<N, R, C>> CsMatrix<N, R, C, S> {
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pub fn from_data(data: S) -> Self {
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CsMatrix {
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data,
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_phantoms: PhantomData,
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}
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}
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pub fn len(&self) -> usize {
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self.data.len()
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}
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pub fn nrows(&self) -> usize {
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self.data.shape().0.value()
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}
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pub fn ncols(&self) -> usize {
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self.data.shape().1.value()
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}
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pub fn shape(&self) -> (usize, usize) {
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let (nrows, ncols) = self.data.shape();
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(nrows.value(), ncols.value())
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}
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pub fn is_square(&self) -> bool {
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let (nrows, ncols) = self.data.shape();
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nrows.value() == ncols.value()
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}
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pub fn transpose(&self) -> CsMatrix<N, C, R>
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where
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DefaultAllocator: Allocator<usize, R>,
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@ -1,184 +0,0 @@
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use alga::general::{ClosedAdd, ClosedMul};
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use num::{One, Zero};
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use std::iter;
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use std::marker::PhantomData;
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use std::ops::{Add, Mul, Range};
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use std::slice;
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use allocator::Allocator;
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use constraint::{AreMultipliable, DimEq, SameNumberOfRows, ShapeConstraint};
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use sparse::{CsMatrix, CsStorage, CsVector};
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use storage::{Storage, StorageMut};
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use {DefaultAllocator, Dim, Matrix, MatrixMN, Real, Scalar, Vector, VectorN, U1};
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pub struct SymbolicAnalysis {
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pinv: Vec<usize>,
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q: Vec<usize>,
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elimination_tree: Vec<usize>,
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cp: Vec<usize>,
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leftmost: Vec<usize>,
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m2: usize,
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lnz: usize,
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unz: usize,
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}
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#[derive(Copy, Clone, Debug)]
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pub struct EliminationTreeNode {
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parent: usize,
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}
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impl EliminationTreeNode {
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pub fn root() -> Self {
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EliminationTreeNode {
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parent: usize::max_value(),
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}
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}
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pub fn with_parent(parent: usize) -> Self {
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EliminationTreeNode { parent }
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}
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pub fn is_root(&self) -> bool {
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self.parent == usize::max_value()
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}
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pub fn parent(&self) -> usize {
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self.parent
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}
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}
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impl<N: Real, D: Dim, S: CsStorage<N, D, D>> CsMatrix<N, D, D, S> {
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fn elimination_tree(&self) -> Vec<EliminationTreeNode> {
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let (nrows, ncols) = self.data.shape();
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assert_eq!(
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nrows.value(),
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ncols.value(),
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"The matrix `self` must be square to compute its elimination tree."
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);
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let mut forest: Vec<_> = iter::repeat(EliminationTreeNode::root())
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.take(nrows.value())
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.collect();
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let mut ancestor: Vec<_> = iter::repeat(usize::max_value())
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.take(nrows.value())
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.collect();
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for k in 0..nrows.value() {
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for irow in self.data.column_row_indices(k) {
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let mut i = irow;
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while i < k {
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let i_ancestor = ancestor[i];
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ancestor[i] = k;
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if i_ancestor == usize::max_value() {
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forest[i] = EliminationTreeNode::with_parent(k);
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break;
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}
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i = i_ancestor;
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}
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}
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}
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forest
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}
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fn reach(
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&self,
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j: usize,
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max_j: usize,
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tree: &[EliminationTreeNode],
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marks: &mut Vec<bool>,
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out: &mut Vec<usize>,
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) {
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marks.clear();
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marks.resize(tree.len(), false);
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for irow in self.data.column_row_indices(j) {
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let mut curr = irow;
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while curr != usize::max_value() && curr <= max_j && !marks[curr] {
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marks[curr] = true;
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out.push(curr);
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curr = tree[curr].parent;
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}
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}
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}
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fn column_counts(&self, tree: &[EliminationTreeNode]) -> Vec<usize> {
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let len = self.data.shape().0.value();
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let mut counts: Vec<_> = iter::repeat(0).take(len).collect();
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let mut reach = Vec::new();
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let mut marks = Vec::new();
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for i in 0..len {
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self.reach(i, i, tree, &mut marks, &mut reach);
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for j in reach.drain(..) {
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counts[j] += 1;
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}
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}
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counts
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}
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fn tree_postorder(tree: &[EliminationTreeNode]) -> Vec<usize> {
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// FIXME: avoid all those allocations?
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let mut first_child: Vec<_> = iter::repeat(usize::max_value()).take(tree.len()).collect();
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let mut other_children: Vec<_> =
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iter::repeat(usize::max_value()).take(tree.len()).collect();
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// Build the children list from the parent list.
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// The set of children of the node `i` is given by the linked list
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// starting at `first_child[i]`. The nodes of this list are then:
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// { first_child[i], other_children[first_child[i]], other_children[other_children[first_child[i]], ... }
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for (i, node) in tree.iter().enumerate() {
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if !node.is_root() {
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let brother = first_child[node.parent];
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first_child[node.parent] = i;
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other_children[i] = brother;
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}
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}
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let mut stack = Vec::with_capacity(tree.len());
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let mut postorder = Vec::with_capacity(tree.len());
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for (i, node) in tree.iter().enumerate() {
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if node.is_root() {
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Self::dfs(
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i,
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&mut first_child,
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&other_children,
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&mut stack,
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&mut postorder,
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)
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}
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}
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postorder
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}
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fn dfs(
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i: usize,
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first_child: &mut [usize],
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other_children: &[usize],
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stack: &mut Vec<usize>,
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result: &mut Vec<usize>,
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) {
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stack.clear();
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stack.push(i);
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while let Some(n) = stack.pop() {
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let child = first_child[n];
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if child == usize::max_value() {
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// No children left.
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result.push(n);
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} else {
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stack.push(n);
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stack.push(child);
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first_child[n] = other_children[child];
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}
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}
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}
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}
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@ -1 +1,331 @@
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use alga::general::{ClosedAdd, ClosedMul};
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use num::{One, Zero};
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use std::iter;
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use std::marker::PhantomData;
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use std::mem;
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use std::ops::{Add, Mul, Range};
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use std::slice;
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use allocator::Allocator;
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use constraint::{AreMultipliable, DimEq, SameNumberOfRows, ShapeConstraint};
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use sparse::{CsMatrix, CsStorage, CsStorageIter, CsVecStorage, CsVector};
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use storage::{Storage, StorageMut};
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use {DefaultAllocator, Dim, Matrix, MatrixMN, Real, Scalar, Vector, VectorN, U1};
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pub struct CsCholesky<N: Real, D: Dim>
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where
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DefaultAllocator: Allocator<usize, D> + Allocator<N, D>,
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{
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// Non-zero pattern of the original matrix upper-triangular part.
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// Unlike the original matrix, the `original_p` array does contain the last sentinel value
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// equal to `original_i.len()` at the end.
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original_p: Vec<usize>,
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original_i: Vec<usize>,
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original_len: usize, // Number of elements on the numerical value vector of the original matrix.
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// Decomposition result.
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l: CsMatrix<N, D, D>,
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// Used only for the pattern.
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// FIXME: store only the nonzero pattern instead.
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u: CsMatrix<N, D, D>,
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ok: bool,
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// Workspaces.
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work_x: VectorN<N, D>,
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work_c: VectorN<usize, D>,
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}
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impl<N: Real, D: Dim> CsCholesky<N, D>
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where
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DefaultAllocator: Allocator<usize, D> + Allocator<N, D>,
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{
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/// Computes the cholesky decomposition of the sparse matrix `m`.
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pub fn new(m: &CsMatrix<N, D, D>) -> Self {
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let mut me = Self::new_symbolic(m);
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let _ = me.decompose(&m.data.vals);
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me
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}
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/// Perform symbolic analysis for the given matrix.
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///
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/// This does not access the numerical values of `m`.
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pub fn new_symbolic(m: &CsMatrix<N, D, D>) -> Self {
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assert!(
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m.is_square(),
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"The matrix `m` must be square to compute its elimination tree."
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);
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let (l, u) = Self::nonzero_pattern(m);
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// Workspaces.
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let work_x = unsafe { VectorN::new_uninitialized_generic(m.data.shape().0, U1) };
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let work_c = unsafe { VectorN::new_uninitialized_generic(m.data.shape().1, U1) };
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let mut original_p = m.data.p.as_slice().to_vec();
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original_p.push(m.data.i.len());
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CsCholesky {
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original_p,
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original_i: m.data.i.clone(),
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original_len: m.data.i.len(),
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l,
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u,
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ok: false,
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work_x,
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work_c,
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}
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}
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pub fn l(&self) -> Option<&CsMatrix<N, D, D>> {
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if self.ok {
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Some(&self.l)
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} else {
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None
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}
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}
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pub fn unwrap_l(self) -> Option<CsMatrix<N, D, D>> {
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if self.ok {
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Some(self.l)
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} else {
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None
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}
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}
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// Performs the numerical Cholesky decomposition given the set of numerical values.
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pub fn decompose(&mut self, values: &[N]) -> bool {
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assert!(
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values.len() >= self.original_len,
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"The set of values is too small."
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);
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// Reset `work_c` to the column pointers of `l`.
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self.work_c.copy_from(&self.l.data.p);
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// Perform the decomposition.
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for k in 0..self.l.nrows() {
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// Scatter the k-th column of the original matrix with the values provided.
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let column_range = self.original_p[k]..self.original_p[k + 1];
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self.work_x[k] = N::zero();
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for p in column_range.clone() {
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let irow = self.original_i[p];
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if irow <= k {
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self.work_x[irow] = values[p];
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}
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}
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let mut diag = self.work_x[k];
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self.work_x[k] = N::zero();
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// Triangular solve.
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for irow in self.u.data.column_row_indices(k) {
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if irow >= k {
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continue;
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}
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let lki = self.work_x[irow] / self.l.data.vals[self.l.data.p[irow]];
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self.work_x[irow] = N::zero();
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for p in self.l.data.p[irow] + 1..self.work_c[irow] {
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self.work_x[self.l.data.i[p]] -= self.l.data.vals[p] * lki;
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}
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diag -= lki * lki;
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let p = self.work_c[irow];
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self.work_c[irow] += 1;
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self.l.data.i[p] = k;
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self.l.data.vals[p] = lki;
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}
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if diag <= N::zero() {
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self.ok = false;
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return false;
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}
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// Deal with the diagonal element.
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let p = self.work_c[k];
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self.work_c[k] += 1;
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self.l.data.i[p] = k;
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self.l.data.vals[p] = diag.sqrt();
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}
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self.ok = true;
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true
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}
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fn elimination_tree<S: CsStorage<N, D, D>>(m: &CsMatrix<N, D, D, S>) -> Vec<usize> {
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let nrows = m.nrows();
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let mut forest: Vec<_> = iter::repeat(usize::max_value()).take(nrows).collect();
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let mut ancestor: Vec<_> = iter::repeat(usize::max_value()).take(nrows).collect();
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for k in 0..nrows {
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for irow in m.data.column_row_indices(k) {
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let mut i = irow;
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while i < k {
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let i_ancestor = ancestor[i];
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ancestor[i] = k;
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if i_ancestor == usize::max_value() {
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forest[i] = k;
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break;
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}
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i = i_ancestor;
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}
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}
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}
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forest
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}
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fn reach<S: CsStorage<N, D, D>>(
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m: &CsMatrix<N, D, D, S>,
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j: usize,
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max_j: usize,
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tree: &[usize],
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marks: &mut Vec<bool>,
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out: &mut Vec<usize>,
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) {
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marks.clear();
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marks.resize(tree.len(), false);
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// FIXME: avoid all those allocations.
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let mut tmp = Vec::new();
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let mut res = Vec::new();
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for irow in m.data.column_row_indices(j) {
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let mut curr = irow;
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while curr != usize::max_value() && curr <= max_j && !marks[curr] {
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marks[curr] = true;
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tmp.push(curr);
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curr = tree[curr];
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}
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tmp.append(&mut res);
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mem::swap(&mut tmp, &mut res);
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}
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out.append(&mut res);
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}
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fn nonzero_pattern<S: CsStorage<N, D, D>>(
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m: &CsMatrix<N, D, D, S>,
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) -> (CsMatrix<N, D, D>, CsMatrix<N, D, D>) {
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let etree = Self::elimination_tree(m);
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let (nrows, ncols) = m.data.shape();
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let mut rows = Vec::with_capacity(m.len());
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let mut cols = unsafe { VectorN::new_uninitialized_generic(m.data.shape().0, U1) };
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let mut marks = Vec::new();
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// NOTE: the following will actually compute the non-zero pattern of
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// the transpose of l.
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for i in 0..nrows.value() {
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cols[i] = rows.len();
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Self::reach(m, i, i, &etree, &mut marks, &mut rows);
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}
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let mut vals = Vec::with_capacity(rows.len());
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unsafe {
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vals.set_len(rows.len());
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}
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vals.shrink_to_fit();
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let data = CsVecStorage {
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shape: (nrows, ncols),
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p: cols,
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i: rows,
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vals,
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};
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let u = CsMatrix::from_data(data);
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// XXX: avoid this transpose.
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let l = u.transpose();
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(l, u)
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}
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/*
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*
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* NOTE: All the following methods are untested and currently unused.
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*
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*
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fn column_counts<S: CsStorage<N, D, D>>(
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m: &CsMatrix<N, D, D, S>,
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tree: &[usize],
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) -> Vec<usize> {
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let len = m.data.shape().0.value();
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let mut counts: Vec<_> = iter::repeat(0).take(len).collect();
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let mut reach = Vec::new();
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let mut marks = Vec::new();
|
||||
|
||||
for i in 0..len {
|
||||
Self::reach(m, i, i, tree, &mut marks, &mut reach);
|
||||
|
||||
for j in reach.drain(..) {
|
||||
counts[j] += 1;
|
||||
}
|
||||
}
|
||||
|
||||
counts
|
||||
}
|
||||
|
||||
fn tree_postorder(tree: &[usize]) -> Vec<usize> {
|
||||
// FIXME: avoid all those allocations?
|
||||
let mut first_child: Vec<_> = iter::repeat(usize::max_value()).take(tree.len()).collect();
|
||||
let mut other_children: Vec<_> =
|
||||
iter::repeat(usize::max_value()).take(tree.len()).collect();
|
||||
|
||||
// Build the children list from the parent list.
|
||||
// The set of children of the node `i` is given by the linked list
|
||||
// starting at `first_child[i]`. The nodes of this list are then:
|
||||
// { first_child[i], other_children[first_child[i]], other_children[other_children[first_child[i]], ... }
|
||||
for (i, parent) in tree.iter().enumerate() {
|
||||
if *parent != usize::max_value() {
|
||||
let brother = first_child[*parent];
|
||||
first_child[*parent] = i;
|
||||
other_children[i] = brother;
|
||||
}
|
||||
}
|
||||
|
||||
let mut stack = Vec::with_capacity(tree.len());
|
||||
let mut postorder = Vec::with_capacity(tree.len());
|
||||
|
||||
for (i, node) in tree.iter().enumerate() {
|
||||
if *node == usize::max_value() {
|
||||
Self::dfs(
|
||||
i,
|
||||
&mut first_child,
|
||||
&other_children,
|
||||
&mut stack,
|
||||
&mut postorder,
|
||||
)
|
||||
}
|
||||
}
|
||||
|
||||
postorder
|
||||
}
|
||||
|
||||
fn dfs(
|
||||
i: usize,
|
||||
first_child: &mut [usize],
|
||||
other_children: &[usize],
|
||||
stack: &mut Vec<usize>,
|
||||
result: &mut Vec<usize>,
|
||||
) {
|
||||
stack.clear();
|
||||
stack.push(i);
|
||||
|
||||
while let Some(n) = stack.pop() {
|
||||
let child = first_child[n];
|
||||
|
||||
if child == usize::max_value() {
|
||||
// No children left.
|
||||
result.push(n);
|
||||
} else {
|
||||
stack.push(n);
|
||||
stack.push(child);
|
||||
first_child[n] = other_children[child];
|
||||
}
|
||||
}
|
||||
}
|
||||
*/
|
||||
}
|
||||
|
|
|
|||
|
|
@ -1,7 +1,9 @@
|
|||
pub use self::cs_matrix::{CsMatrix, CsStorage, CsStorageMut, CsVector};
|
||||
pub use self::cs_matrix::{
|
||||
CsMatrix, CsStorage, CsStorageIter, CsStorageMut, CsVecStorage, CsVector,
|
||||
};
|
||||
pub use self::cs_matrix_cholesky::CsCholesky;
|
||||
|
||||
mod cs_matrix;
|
||||
mod cs_matrix_analysis;
|
||||
mod cs_matrix_cholesky;
|
||||
mod cs_matrix_conversion;
|
||||
mod cs_matrix_ops;
|
||||
|
|
|
|||
|
|
@ -0,0 +1,55 @@
|
|||
#![cfg_attr(rustfmt, rustfmt_skip)]
|
||||
|
||||
use na::{CsMatrix, CsVector, CsCholesky, Cholesky, Matrix5, Vector5};
|
||||
|
||||
#[test]
|
||||
fn cs_cholesky() {
|
||||
let mut a = Matrix5::new(
|
||||
40.0, 0.0, 0.0, 0.0, 0.0,
|
||||
2.0, 60.0, 0.0, 0.0, 0.0,
|
||||
1.0, 0.0, 11.0, 0.0, 0.0,
|
||||
0.0, 0.0, 0.0, 50.0, 0.0,
|
||||
1.0, 0.0, 0.0, 4.0, 10.0
|
||||
);
|
||||
a.fill_upper_triangle_with_lower_triangle();
|
||||
test_cholesky(a);
|
||||
|
||||
let a = Matrix5::from_diagonal(&Vector5::new(40.0, 60.0, 11.0, 50.0, 10.0));
|
||||
test_cholesky(a);
|
||||
|
||||
let mut a = Matrix5::new(
|
||||
40.0, 0.0, 0.0, 0.0, 0.0,
|
||||
2.0, 60.0, 0.0, 0.0, 0.0,
|
||||
1.0, 0.0, 11.0, 0.0, 0.0,
|
||||
1.0, 0.0, 0.0, 50.0, 0.0,
|
||||
0.0, 0.0, 0.0, 4.0, 10.0
|
||||
);
|
||||
a.fill_upper_triangle_with_lower_triangle();
|
||||
test_cholesky(a);
|
||||
|
||||
let mut a = Matrix5::new(
|
||||
2.0, 0.0, 0.0, 0.0, 0.0,
|
||||
0.0, 2.0, 0.0, 0.0, 0.0,
|
||||
1.0, 1.0, 2.0, 0.0, 0.0,
|
||||
0.0, 0.0, 0.0, 2.0, 0.0,
|
||||
1.0, 1.0, 0.0, 0.0, 2.0
|
||||
);
|
||||
a.fill_upper_triangle_with_lower_triangle();
|
||||
test_cholesky(a);
|
||||
}
|
||||
|
||||
|
||||
fn test_cholesky(a: Matrix5<f32>) {
|
||||
let cs_a: CsMatrix<_, _, _> = a.into();
|
||||
|
||||
let chol_a = Cholesky::new(a).unwrap();
|
||||
let chol_cs_a = CsCholesky::new(&cs_a);
|
||||
let l = chol_a.l();
|
||||
println!("{:?}", chol_cs_a.l());
|
||||
let cs_l: Matrix5<_> = chol_cs_a.unwrap_l().unwrap().into();
|
||||
|
||||
println!("{}", l);
|
||||
println!("{}", cs_l);
|
||||
|
||||
assert_eq!(l, cs_l);
|
||||
}
|
||||
|
|
@ -1,5 +1,6 @@
|
|||
mod cs_cholesky;
|
||||
mod cs_construction;
|
||||
mod cs_conversion;
|
||||
mod cs_matrix;
|
||||
mod cs_ops;
|
||||
mod cs_linalg;
|
||||
mod cs_solve;
|
||||
|
|
|
|||
Loading…
Reference in New Issue