Implement spmm_pattern

nalgebra-sparse/src/ops/serial/csr.rs

@@ -1,10 +1,11 @@
 use crate::csr::CsrMatrix;
 use crate::ops::{Transpose};
+use crate::SparseEntryMut;
+use crate::ops::serial::{OperationError, OperationErrorType};
 use nalgebra::{Scalar, DMatrixSlice, ClosedAdd, ClosedMul, DMatrixSliceMut};
 use num_traits::{Zero, One};
-use crate::ops::serial::{OperationError, OperationErrorType};
 use std::sync::Arc;
-use crate::SparseEntryMut;
+use std::borrow::Cow;
 
 /// Sparse-dense matrix-matrix multiplication `C <- beta * C + alpha * trans(A) * trans(B)`.
 pub fn spmm_csr_dense<'a, T>(c: impl Into<DMatrixSliceMut<'a, T>>,

nalgebra-sparse/src/ops/serial/pattern.rs

@@ -32,7 +32,7 @@ pub fn spadd_build_pattern(pattern: &mut SparsityPattern,
     for lane_idx in 0 .. a.major_dim() {
         let lane_a = a.lane(lane_idx);
         let lane_b = b.lane(lane_idx);
-        indices.extend(iterate_intersection(lane_a, lane_b));
+        indices.extend(iterate_union(lane_a, lane_b));
         offsets.push(indices.len());
     }
 
@@ -43,11 +43,44 @@ pub fn spadd_build_pattern(pattern: &mut SparsityPattern,
     swap(input_pattern, &mut new_pattern);
 }
 
-/// Iterate over the intersection of the two sets represented by sorted slices
+/// Sparse matrix multiplication pattern construction, `C <- A * B`.
+pub fn spmm_pattern(a: &SparsityPattern, b: &SparsityPattern) -> SparsityPattern {
+    // TODO: Proper error message
+    assert_eq!(a.minor_dim(), b.major_dim());
+
+    let mut offsets = Vec::new();
+    let mut indices = Vec::new();
+    offsets.push(0);
+
+    let mut c_lane_workspace = Vec::new();
+    for i in 0 .. a.major_dim() {
+        let a_lane_i = a.lane(i);
+        let c_lane_i_offset = *offsets.last().unwrap();
+        for &k in a_lane_i {
+            // We have that the set of elements in lane i in C is given by the union of all
+            // B_k, where B_k is the set of indices in lane k of B. More precisely, let C_i
+            // denote the set of indices in lane i in C, and similarly for A_i and B_k. Then
+            //  C_i = union B_k for all k in A_i
+            // We incrementally compute C_i by incrementally computing the union of C_i with
+            // B_k until we're through all k in A_i.
+            let b_lane_k = b.lane(k);
+            let c_lane_i = &indices[c_lane_i_offset..];
+            c_lane_workspace.clear();
+            c_lane_workspace.extend(iterate_union(c_lane_i, b_lane_k));
+            indices.truncate(c_lane_i_offset);
+            indices.append(&mut c_lane_workspace);
+        }
+        offsets.push(indices.len());
+    }
+
+    SparsityPattern::try_from_offsets_and_indices(a.major_dim(), b.minor_dim(), offsets, indices)
+        .expect("Internal error: Invalid pattern during matrix multiplication pattern construction")
+}
+
+/// Iterate over the union of the two sets represented by sorted slices
 /// (with unique elements)
-fn iterate_intersection<'a>(mut sorted_a: &'a [usize],
-                            mut sorted_b: &'a [usize]) -> impl Iterator<Item=usize> + 'a {
-    // TODO: Can use a kind of simultaneous exponential search to speed things up here
+fn iterate_union<'a>(mut sorted_a: &'a [usize],
+                     mut sorted_b: &'a [usize]) -> impl Iterator<Item=usize> + 'a {
     iter::from_fn(move || {
         if let (Some(a_item), Some(b_item)) = (sorted_a.first(), sorted_b.first()) {
             let item = if a_item < b_item {

nalgebra-sparse/tests/common/mod.rs

@@ -2,6 +2,7 @@ use proptest::strategy::Strategy;
 use nalgebra_sparse::csr::CsrMatrix;
 use nalgebra_sparse::proptest::{csr, csc};
 use nalgebra_sparse::csc::CscMatrix;
+use std::ops::RangeInclusive;
 
 #[macro_export]
 macro_rules! assert_panics {
@@ -24,10 +25,13 @@ macro_rules! assert_panics {
     }};
 }
 
+pub const PROPTEST_MATRIX_DIM: RangeInclusive<usize> = 0..=6;
+pub const PROPTEST_MAX_NNZ: usize = 40;
+
 pub fn csr_strategy() -> impl Strategy<Value=CsrMatrix<i32>> {
-    csr(-5 ..= 5, 0 ..= 6usize, 0 ..= 6usize, 40)
+    csr(-5 ..= 5, PROPTEST_MATRIX_DIM, PROPTEST_MATRIX_DIM, PROPTEST_MAX_NNZ)
 }
 
 pub fn csc_strategy() -> impl Strategy<Value=CscMatrix<i32>> {
-    csc(-5 ..= 5, 0..=6usize, 0..=6usize, 40)
+    csc(-5 ..= 5, PROPTEST_MATRIX_DIM, PROPTEST_MATRIX_DIM, PROPTEST_MAX_NNZ)
 }

nalgebra-sparse/tests/unit_tests/ops.rs

@@ -1,4 +1,4 @@
-use nalgebra_sparse::ops::serial::{spmm_csr_dense, spadd_build_pattern, spadd_csr};
+use nalgebra_sparse::ops::serial::{spmm_csr_dense, spadd_build_pattern, spmm_pattern, spadd_csr};
 use nalgebra_sparse::ops::{Transpose};
 use nalgebra_sparse::csr::CsrMatrix;
 use nalgebra_sparse::proptest::{csr, sparsity_pattern};
@@ -12,7 +12,7 @@ use proptest::prelude::*;
 use std::panic::catch_unwind;
 use std::sync::Arc;
 
-use crate::common::csr_strategy;
+use crate::common::{csr_strategy, PROPTEST_MATRIX_DIM, PROPTEST_MAX_NNZ};
 
 /// Represents the sparsity pattern of a CSR matrix as a dense matrix with 0/1
 fn dense_csr_pattern(pattern: &SparsityPattern) -> DMatrix<i32> {
@@ -127,6 +127,15 @@ fn spadd_build_pattern_strategy() -> impl Strategy<Value=(SparsityPattern, Spars
         })
 }
 
+/// Constructs pairs (a, b) where a and b have compatible dimensions for a matrix product
+fn spmm_pattern_strategy() -> impl Strategy<Value=(SparsityPattern, SparsityPattern)> {
+    pattern_strategy()
+        .prop_flat_map(|a| {
+            let b = sparsity_pattern(Just(a.minor_dim()), PROPTEST_MATRIX_DIM, PROPTEST_MAX_NNZ);
+            (Just(a), b)
+        })
+}
+
 /// Helper function to help us call dense GEMM with our transposition parameters
 fn dense_gemm<'a>(c: impl Into<DMatrixSliceMut<'a, i32>>,
                   beta: i32,
@@ -269,4 +278,26 @@ proptest! {
         prop_assert_eq!(&DMatrix::from(&c_ref_ref), &c_dense);
         prop_assert_eq!(c_ref_ref.pattern(), &c_pattern);
     }
+
+    #[test]
+    fn spmm_pattern_test((a, b) in spmm_pattern_strategy())
+    {
+        // (a, b) are multiplication-wise dimensionally compatible patterns
+        let c_pattern = spmm_pattern(&a, &b);
+
+        // To verify the pattern, we construct CSR matrices with positive integer entries
+        // corresponding to a and b, and convert them to dense matrices.
+        // The product of these dense matrices will then have non-zeros in exactly the same locations
+        // as the result of "multiplying" the sparsity patterns
+        let a_csr = CsrMatrix::try_from_pattern_and_values(Arc::new(a.clone()), vec![1; a.nnz()])
+            .unwrap();
+        let a_dense = DMatrix::from(&a_csr);
+        let b_csr = CsrMatrix::try_from_pattern_and_values(Arc::new(b.clone()), vec![1; b.nnz()])
+            .unwrap();
+        let b_dense = DMatrix::from(&b_csr);
+        let c_dense = a_dense * b_dense;
+        let c_csr = CsrMatrix::from(&c_dense);
+
+        prop_assert_eq!(&c_pattern, c_csr.pattern().as_ref());
+    }
 }