Implement arithmetic operations for CSC matrices

nalgebra-sparse/src/cs.rs

@@ -144,9 +144,19 @@ impl<T> CsMatrix<T> {
             values: &mut values[range]
         })
     }
+
+    #[inline]
+    pub fn lane_iter(&self) -> CsLaneIter<T> {
+        CsLaneIter::new(self.pattern().as_ref(), self.values())
+    }
+
+    #[inline]
+    pub fn lane_iter_mut(&mut self) -> CsLaneIterMut<T> {
+        CsLaneIterMut::new(self.sparsity_pattern.as_ref(), &mut self.values)
+    }
 }
 
-pub fn get_entry_from_slices<'a, T>(
+fn get_entry_from_slices<'a, T>(
     minor_dim: usize,
     minor_indices: &'a [usize],
     values: &'a [T],
@@ -161,7 +171,7 @@ pub fn get_entry_from_slices<'a, T>(
     }
 }
 
-pub fn get_mut_entry_from_slices<'a, T>(
+fn get_mut_entry_from_slices<'a, T>(
     minor_dim: usize,
     minor_indices: &'a [usize],
     values: &'a mut [T],
@@ -178,16 +188,16 @@ pub fn get_mut_entry_from_slices<'a, T>(
 
 #[derive(Debug, Clone, PartialEq, Eq)]
 pub struct CsLane<'a, T> {
-    pub minor_dim: usize,
+    minor_dim: usize,
-    pub minor_indices: &'a [usize],
+    minor_indices: &'a [usize],
-    pub values: &'a [T]
+    values: &'a [T]
 }
 
 #[derive(Debug, PartialEq, Eq)]
 pub struct CsLaneMut<'a, T> {
-    pub minor_dim: usize,
+    minor_dim: usize,
-    pub minor_indices: &'a [usize],
+    minor_indices: &'a [usize],
-    pub values: &'a mut [T]
+    values: &'a mut [T]
 }
 
 pub struct CsLaneIter<'a, T> {
@@ -280,4 +290,59 @@ impl<'a, T> Iterator for CsLaneIterMut<'a, T>
     }
 }
 
+/// Implement the methods common to both CsLane and CsLaneMut. See the documentation for the
+/// methods delegated here by CsrMatrix and CscMatrix members for more information.
+macro_rules! impl_cs_lane_common_methods {
+    ($name:ty) => {
+        impl<'a, T> $name {
+            #[inline]
+            pub fn minor_dim(&self) -> usize {
+                self.minor_dim
+            }
 
+            #[inline]
+            pub fn nnz(&self) -> usize {
+                self.minor_indices.len()
+            }
+
+            #[inline]
+            pub fn minor_indices(&self) -> &[usize] {
+                self.minor_indices
+            }
+
+            #[inline]
+            pub fn values(&self) -> &[T] {
+                self.values
+            }
+
+            #[inline]
+            pub fn get_entry(&self, global_col_index: usize) -> Option<SparseEntry<T>> {
+                get_entry_from_slices(
+                    self.minor_dim,
+                    self.minor_indices,
+                    self.values,
+                    global_col_index)
+            }
+        }
+    }
+}
+
+impl_cs_lane_common_methods!(CsLane<'a, T>);
+impl_cs_lane_common_methods!(CsLaneMut<'a, T>);
+
+impl<'a, T> CsLaneMut<'a, T> {
+    pub fn values_mut(&mut self) -> &mut [T] {
+        self.values
+    }
+
+    pub fn indices_and_values_mut(&mut self) -> (&[usize], &mut [T]) {
+        (self.minor_indices, self.values)
+    }
+
+    pub fn get_entry_mut(&mut self, global_minor_index: usize) -> Option<SparseEntryMut<T>> {
+        get_mut_entry_from_slices(self.minor_dim,
+                                  self.minor_indices,
+                                  self.values,
+                                  global_minor_index)
+    }
+}

nalgebra-sparse/src/csc.rs

@@ -3,8 +3,7 @@
 use crate::{SparseFormatError, SparseFormatErrorKind, SparseEntry, SparseEntryMut};
 use crate::pattern::{SparsityPattern, SparsityPatternFormatError, SparsityPatternIter};
 use crate::csr::CsrMatrix;
-use crate::cs::{CsMatrix, CsLane, CsLaneMut, CsLaneIter, CsLaneIterMut,
+use crate::cs::{CsMatrix, CsLane, CsLaneMut, CsLaneIter, CsLaneIterMut};
-                get_entry_from_slices, get_mut_entry_from_slices};
 
 use std::sync::Arc;
 use std::slice::{IterMut, Iter};
@@ -21,7 +20,7 @@ use nalgebra::Scalar;
 #[derive(Debug, Clone, PartialEq, Eq)]
 pub struct CscMatrix<T> {
     // Cols are major, rows are minor in the sparsity pattern
-    cs: CsMatrix<T>,
+    pub(crate) cs: CsMatrix<T>,
 }
 
 impl<T> CscMatrix<T> {
@@ -435,25 +434,25 @@ macro_rules! impl_csc_col_common_methods {
             /// The number of global rows in the column.
             #[inline]
             pub fn nrows(&self) -> usize {
-                self.lane.minor_dim
+                self.lane.minor_dim()
             }
 
             /// The number of non-zeros in this column.
             #[inline]
             pub fn nnz(&self) -> usize {
-                self.lane.minor_indices.len()
+                self.lane.nnz()
             }
 
             /// The row indices corresponding to explicitly stored entries in this column.
             #[inline]
             pub fn row_indices(&self) -> &[usize] {
-                self.lane.minor_indices
+                self.lane.minor_indices()
             }
 
             /// The values corresponding to explicitly stored entries in this column.
             #[inline]
             pub fn values(&self) -> &[T] {
-                self.lane.values
+                self.lane.values()
             }
 
             /// Returns an entry for the given global row index.
@@ -461,11 +460,7 @@ macro_rules! impl_csc_col_common_methods {
             /// Each call to this function incurs the cost of a binary search among the explicitly
             /// stored row entries.
             pub fn get_entry(&self, global_row_index: usize) -> Option<SparseEntry<T>> {
-                get_entry_from_slices(
+                self.lane.get_entry(global_row_index)
-                    self.lane.minor_dim,
-                    self.lane.minor_indices,
-                    self.lane.values,
-                    global_row_index)
             }
         }
     }
@@ -477,7 +472,7 @@ impl_csc_col_common_methods!(CscColMut<'a, T>);
 impl<'a, T> CscColMut<'a, T> {
     /// Mutable access to the values corresponding to explicitly stored entries in this column.
     pub fn values_mut(&mut self) -> &mut [T] {
-        self.lane.values
+        self.lane.values_mut()
     }
 
     /// Provides simultaneous access to row indices and mutable values corresponding to the
@@ -486,15 +481,12 @@ impl<'a, T> CscColMut<'a, T> {
     /// This method primarily facilitates low-level access for methods that process data stored
     /// in CSC format directly.
     pub fn rows_and_values_mut(&mut self) -> (&[usize], &mut [T]) {
-        (self.lane.minor_indices, self.lane.values)
+        self.lane.indices_and_values_mut()
     }
 
     /// Returns a mutable entry for the given global row index.
     pub fn get_entry_mut(&mut self, global_row_index: usize) -> Option<SparseEntryMut<T>> {
-        get_mut_entry_from_slices(self.lane.minor_dim,
+        self.lane.get_entry_mut(global_row_index)
-                                  self.lane.minor_indices,
-                                  self.lane.values,
-                                  global_row_index)
     }
 }
 

nalgebra-sparse/src/csr.rs

@@ -2,7 +2,7 @@
 use crate::{SparseFormatError, SparseFormatErrorKind, SparseEntry, SparseEntryMut};
 use crate::pattern::{SparsityPattern, SparsityPatternFormatError, SparsityPatternIter};
 use crate::csc::CscMatrix;
-use crate::cs::{CsMatrix, get_entry_from_slices, get_mut_entry_from_slices, CsLaneIterMut, CsLaneIter, CsLane, CsLaneMut};
+use crate::cs::{CsMatrix, CsLaneIterMut, CsLaneIter, CsLane, CsLaneMut};
 
 use nalgebra::Scalar;
 use num_traits::Zero;
@@ -20,7 +20,7 @@ use std::slice::{IterMut, Iter};
 #[derive(Debug, Clone, PartialEq, Eq)]
 pub struct CsrMatrix<T> {
     // Rows are major, cols are minor in the sparsity pattern
-    cs: CsMatrix<T>,
+    pub(crate) cs: CsMatrix<T>,
 }
 
 impl<T> CsrMatrix<T> {
@@ -435,37 +435,34 @@ macro_rules! impl_csr_row_common_methods {
             /// The number of global columns in the row.
             #[inline]
             pub fn ncols(&self) -> usize {
-                self.lane.minor_dim
+                self.lane.minor_dim()
             }
 
             /// The number of non-zeros in this row.
             #[inline]
             pub fn nnz(&self) -> usize {
-                self.lane.minor_indices.len()
+                self.lane.nnz()
             }
 
             /// The column indices corresponding to explicitly stored entries in this row.
             #[inline]
             pub fn col_indices(&self) -> &[usize] {
-                self.lane.minor_indices
+                self.lane.minor_indices()
             }
 
             /// The values corresponding to explicitly stored entries in this row.
             #[inline]
             pub fn values(&self) -> &[T] {
-                self.lane.values
+                self.lane.values()
             }
 
             /// Returns an entry for the given global column index.
             ///
             /// Each call to this function incurs the cost of a binary search among the explicitly
             /// stored column entries.
+            #[inline]
             pub fn get_entry(&self, global_col_index: usize) -> Option<SparseEntry<T>> {
-                get_entry_from_slices(
+                self.lane.get_entry(global_col_index)
-                    self.lane.minor_dim,
-                    self.lane.minor_indices,
-                    self.lane.values,
-                    global_col_index)
             }
         }
     }
@@ -476,8 +473,9 @@ impl_csr_row_common_methods!(CsrRowMut<'a, T>);
 
 impl<'a, T> CsrRowMut<'a, T> {
     /// Mutable access to the values corresponding to explicitly stored entries in this row.
+    #[inline]
     pub fn values_mut(&mut self) -> &mut [T] {
-        self.lane.values
+        self.lane.values_mut()
     }
 
     /// Provides simultaneous access to column indices and mutable values corresponding to the
@@ -485,16 +483,15 @@ impl<'a, T> CsrRowMut<'a, T> {
     ///
     /// This method primarily facilitates low-level access for methods that process data stored
     /// in CSR format directly.
+    #[inline]
     pub fn cols_and_values_mut(&mut self) -> (&[usize], &mut [T]) {
-        (self.lane.minor_indices, self.lane.values)
+        self.lane.indices_and_values_mut()
     }
 
     /// Returns a mutable entry for the given global column index.
+    #[inline]
     pub fn get_entry_mut(&mut self, global_col_index: usize) -> Option<SparseEntryMut<T>> {
-        get_mut_entry_from_slices(self.lane.minor_dim,
+        self.lane.get_entry_mut(global_col_index)
-                                  self.lane.minor_indices,
-                                  self.lane.values,
-                                  global_col_index)
     }
 }
 

nalgebra-sparse/src/lib.rs

@@ -90,7 +90,7 @@ pub mod pattern;
 pub mod ops;
 pub mod convert;
 
-mod cs;
+pub(crate) mod cs;
 
 #[cfg(feature = "proptest-support")]
 pub mod proptest;

nalgebra-sparse/src/ops/impl_std_ops.rs

@@ -1,103 +1,112 @@
 use crate::csr::CsrMatrix;
+use crate::csc::CscMatrix;
 
 use std::ops::{Add, Mul};
-use crate::ops::serial::{spadd_csr_prealloc, spadd_pattern, spmm_pattern, spmm_csr_prealloc};
+use crate::ops::serial::{spadd_csr_prealloc, spadd_csc_prealloc, spadd_pattern,
+                         spmm_pattern, spmm_csr_prealloc, spmm_csc_prealloc};
 use nalgebra::{ClosedAdd, ClosedMul, Scalar};
 use num_traits::{Zero, One};
 use std::sync::Arc;
 use crate::ops::{Op};
 
-impl<'a, T> Add<&'a CsrMatrix<T>> for &'a CsrMatrix<T>
+/// Helper macro for implementing binary operators for different matrix types
-where
-    // TODO: Consider introducing wrapper trait for these things? It's technically a "Ring",
-    // I guess...
-    T: Scalar + ClosedAdd + ClosedMul + Zero + One
-{
-    type Output = CsrMatrix<T>;
-
-    fn add(self, rhs: &'a CsrMatrix<T>) -> Self::Output {
-        let pattern = spadd_pattern(self.pattern(), rhs.pattern());
-        let values = vec![T::zero(); pattern.nnz()];
-        // We are giving data that is valid by definition, so it is safe to unwrap below
-        let mut result = CsrMatrix::try_from_pattern_and_values(Arc::new(pattern), values)
-            .unwrap();
-        spadd_csr_prealloc(T::zero(), &mut result, T::one(), Op::NoOp(&self)).unwrap();
-        spadd_csr_prealloc(T::one(), &mut result, T::one(), Op::NoOp(&rhs)).unwrap();
-        result
-    }
-}
-
-impl<'a, T> Add<&'a CsrMatrix<T>> for CsrMatrix<T>
-where
-    T: Scalar + ClosedAdd + ClosedMul + Zero + One
-{
-    type Output = CsrMatrix<T>;
-
-    fn add(mut self, rhs: &'a CsrMatrix<T>) -> Self::Output {
-        if Arc::ptr_eq(self.pattern(), rhs.pattern()) {
-            spadd_csr_prealloc(T::one(), &mut self, T::one(), Op::NoOp(rhs)).unwrap();
-            self
-        } else {
-            &self + rhs
-        }
-    }
-}
-
-impl<'a, T> Add<CsrMatrix<T>> for &'a CsrMatrix<T>
-    where
-        T: Scalar + ClosedAdd + ClosedMul + Zero + One
-{
-    type Output = CsrMatrix<T>;
-
-    fn add(self, rhs: CsrMatrix<T>) -> Self::Output {
-        rhs + self
-    }
-}
-
-impl<T> Add<CsrMatrix<T>> for CsrMatrix<T>
-where
-    T: Scalar + ClosedAdd + ClosedMul + Zero + One
-{
-    type Output = Self;
-
-    fn add(self, rhs: CsrMatrix<T>) -> Self::Output {
-        self + &rhs
-    }
-}
-
-/// Helper macro for implementing matrix multiplication for different matrix types
 /// See below for usage.
-macro_rules! impl_matrix_mul {
+macro_rules! impl_bin_op {
-    (<$($life:lifetime),*>($a_name:ident : $a:ty, $b_name:ident : $b:ty) -> $ret:ty $body:block)
+    ($trait:ident, $method:ident,
+        <$($life:lifetime),*>($a:ident : $a_type:ty, $b:ident : $b_type:ty) -> $ret:ty $body:block)
         =>
     {
-        impl<$($life,)* T> Mul<$b> for $a
+        impl<$($life,)* T> $trait<$b_type> for $a_type
         where
             T: Scalar + ClosedAdd + ClosedMul + Zero + One
         {
             type Output = $ret;
-            fn mul(self, rhs: $b) -> Self::Output {
+            fn $method(self, rhs: $b_type) -> Self::Output {
-                let $a_name = self;
+                let $a = self;
-                let $b_name = rhs;
+                let $b = rhs;
                 $body
             }
         }
     }
 }
 
-impl_matrix_mul!(<'a>(a: &'a CsrMatrix<T>, b: &'a CsrMatrix<T>) -> CsrMatrix<T> {
+macro_rules! impl_add {
-    let pattern = spmm_pattern(a.pattern(), b.pattern());
+    ($($args:tt)*) => {
-    let values = vec![T::zero(); pattern.nnz()];
+        impl_bin_op!(Add, add, $($args)*);
-    let mut result = CsrMatrix::try_from_pattern_and_values(Arc::new(pattern), values)
+    }
-        .unwrap();
+}
-    spmm_csr_prealloc(T::zero(),
+
-             &mut result,
+/// Implements a + b for all combinations of reference and owned matrices, for
-             T::one(),
+/// CsrMatrix or CscMatrix.
-             Op::NoOp(a),
+macro_rules! impl_spadd {
-             Op::NoOp(b))
+    ($matrix_type:ident, $spadd_fn:ident) => {
-        .expect("Internal error: spmm failed (please debug).");
+        impl_add!(<'a>(a: &'a $matrix_type<T>, b: &'a $matrix_type<T>) -> $matrix_type<T> {
-    result
+            // If both matrices have the same pattern, then we can immediately re-use it
-});
+            let pattern = if Arc::ptr_eq(a.pattern(), b.pattern()) {
-impl_matrix_mul!(<'a>(a: &'a CsrMatrix<T>, b: CsrMatrix<T>) -> CsrMatrix<T> { a * &b});
+                Arc::clone(a.pattern())
-impl_matrix_mul!(<'a>(a: CsrMatrix<T>, b: &'a CsrMatrix<T>) -> CsrMatrix<T> { &a * b});
+            } else {
-impl_matrix_mul!(<>(a: CsrMatrix<T>, b: CsrMatrix<T>) -> CsrMatrix<T> { &a * &b});
+                Arc::new(spadd_pattern(a.pattern(), b.pattern()))
+            };
+            let values = vec![T::zero(); pattern.nnz()];
+            // We are giving data that is valid by definition, so it is safe to unwrap below
+            let mut result = $matrix_type::try_from_pattern_and_values(pattern, values)
+                .unwrap();
+            $spadd_fn(T::zero(), &mut result, T::one(), Op::NoOp(&a)).unwrap();
+            $spadd_fn(T::one(), &mut result, T::one(), Op::NoOp(&b)).unwrap();
+            result
+        });
+
+        impl_add!(<'a>(a: $matrix_type<T>, b: &'a $matrix_type<T>) -> $matrix_type<T> {
+            let mut a = a;
+            if Arc::ptr_eq(a.pattern(), b.pattern()) {
+                $spadd_fn(T::one(), &mut a, T::one(), Op::NoOp(b)).unwrap();
+                a
+            } else {
+                &a + b
+            }
+        });
+
+        impl_add!(<'a>(a: &'a $matrix_type<T>, b: $matrix_type<T>) -> $matrix_type<T> {
+            b + a
+        });
+        impl_add!(<>(a: $matrix_type<T>, b: $matrix_type<T>) -> $matrix_type<T> {
+            a + &b
+        });
+    }
+}
+
+impl_spadd!(CsrMatrix, spadd_csr_prealloc);
+impl_spadd!(CscMatrix, spadd_csc_prealloc);
+
+macro_rules! impl_mul {
+    ($($args:tt)*) => {
+        impl_bin_op!(Mul, mul, $($args)*);
+    }
+}
+
+/// Implements a + b for all combinations of reference and owned matrices, for
+/// CsrMatrix or CscMatrix.
+macro_rules! impl_spmm {
+    ($matrix_type:ident, $pattern_fn:expr, $spmm_fn:expr) => {
+        impl_mul!(<'a>(a: &'a $matrix_type<T>, b: &'a $matrix_type<T>) -> $matrix_type<T> {
+            let pattern = $pattern_fn(a.pattern(), b.pattern());
+            let values = vec![T::zero(); pattern.nnz()];
+            let mut result = $matrix_type::try_from_pattern_and_values(Arc::new(pattern), values)
+                .unwrap();
+            $spmm_fn(T::zero(),
+                     &mut result,
+                     T::one(),
+                     Op::NoOp(a),
+                     Op::NoOp(b))
+                .expect("Internal error: spmm failed (please debug).");
+            result
+        });
+        impl_mul!(<'a>(a: &'a $matrix_type<T>, b: $matrix_type<T>) -> $matrix_type<T> { a * &b});
+        impl_mul!(<'a>(a: $matrix_type<T>, b: &'a $matrix_type<T>) -> $matrix_type<T> { &a * b});
+        impl_mul!(<>(a: $matrix_type<T>, b: $matrix_type<T>) -> $matrix_type<T> { &a * &b});
+    }
+}
+
+impl_spmm!(CsrMatrix, spmm_pattern, spmm_csr_prealloc);
+// Need to switch order of operations for CSC pattern
+impl_spmm!(CscMatrix, |a, b| spmm_pattern(b, a), spmm_csc_prealloc);

nalgebra-sparse/src/ops/mod.rs

@@ -48,6 +48,17 @@ impl<T> Op<T> {
             Op::NoOp(obj) | Op::Transpose(obj) => obj,
         }
     }
+
+    /// Applies the transpose operation.
+    ///
+    /// This operation follows the usual semantics of transposition. In particular, double
+    /// transposition is equivalent to no transposition.
+    pub fn transposed(self) -> Self {
+        match self {
+            Op::NoOp(obj) => Op::Transpose(obj),
+            Op::Transpose(obj) => Op::NoOp(obj)
+        }
+    }
 }
 
 impl<T> From<T> for Op<T> {

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

@@ -0,0 +1,194 @@
+use crate::cs::CsMatrix;
+use crate::ops::Op;
+use crate::ops::serial::{OperationErrorType, OperationError};
+use nalgebra::{Scalar, ClosedAdd, ClosedMul, DMatrixSliceMut, DMatrixSlice};
+use num_traits::{Zero, One};
+use crate::SparseEntryMut;
+use std::sync::Arc;
+
+fn spmm_cs_unexpected_entry() -> OperationError {
+    OperationError::from_type_and_message(
+        OperationErrorType::InvalidPattern,
+        String::from("Found unexpected entry that is not present in `c`."))
+}
+
+/// Helper functionality for implementing CSR/CSC SPMM.
+///
+/// Since CSR/CSC matrices are basically transpositions of each other, which lets us use the same
+/// algorithm for the SPMM implementation. The implementation here is written in a CSR-centric
+/// manner. This means that when using it for CSC, the order of the matrices needs to be
+/// reversed (since transpose(AB) = transpose(B) * transpose(A) and CSC(A) = transpose(CSR(A)).
+///
+/// We assume here that the matrices have already been verified to be dimensionally compatible.
+pub fn spmm_cs_prealloc<T>(
+    beta: T,
+    c: &mut CsMatrix<T>,
+    alpha: T,
+    a: &CsMatrix<T>,
+    b: &CsMatrix<T>)
+    -> Result<(), OperationError>
+    where
+        T: Scalar + ClosedAdd + ClosedMul + Zero + One
+{
+    for i in 0 .. c.pattern().major_dim() {
+        let a_lane_i = a.get_lane(i).unwrap();
+        let mut c_lane_i = c.get_lane_mut(i).unwrap();
+        for c_ij in c_lane_i.values_mut() {
+            *c_ij = beta.inlined_clone() * c_ij.inlined_clone();
+        }
+
+        for (&k, a_ik) in a_lane_i.minor_indices().iter().zip(a_lane_i.values()) {
+            let b_lane_k = b.get_lane(k).unwrap();
+            let (mut c_lane_i_cols, mut c_lane_i_values) = c_lane_i.indices_and_values_mut();
+            let alpha_aik = alpha.inlined_clone() * a_ik.inlined_clone();
+            for (j, b_kj) in b_lane_k.minor_indices().iter().zip(b_lane_k.values()) {
+                // Determine the location in C to append the value
+                let (c_local_idx, _) = c_lane_i_cols.iter()
+                    .enumerate()
+                    .find(|(_, c_col)| *c_col == j)
+                    .ok_or_else(spmm_cs_unexpected_entry)?;
+
+                c_lane_i_values[c_local_idx] += alpha_aik.inlined_clone() * b_kj.inlined_clone();
+                c_lane_i_cols = &c_lane_i_cols[c_local_idx ..];
+                c_lane_i_values = &mut c_lane_i_values[c_local_idx ..];
+            }
+        }
+    }
+
+    Ok(())
+}
+
+fn spadd_cs_unexpected_entry() -> OperationError {
+    OperationError::from_type_and_message(
+        OperationErrorType::InvalidPattern,
+        String::from("Found entry in `op(a)` that is not present in `c`."))
+}
+
+/// Helper functionality for implementing CSR/CSC SPADD.
+pub fn spadd_cs_prealloc<T>(beta: T,
+                             c: &mut CsMatrix<T>,
+                             alpha: T,
+                             a: Op<&CsMatrix<T>>)
+                             -> Result<(), OperationError>
+    where
+        T: Scalar + ClosedAdd + ClosedMul + Zero + One
+{
+
+    if Arc::ptr_eq(&c.pattern(), &a.inner_ref().pattern()) {
+        // Special fast path: The two matrices have *exactly* the same sparsity pattern,
+        // so we only need to sum the value arrays
+        // TODO: Test this fast path
+        for (c_ij, a_ij) in c.values_mut().iter_mut().zip(a.inner_ref().values()) {
+            let (alpha, beta) = (alpha.inlined_clone(), beta.inlined_clone());
+            *c_ij = beta * c_ij.inlined_clone() + alpha * a_ij.inlined_clone();
+        }
+        Ok(())
+    } else {
+        match a {
+            Op::NoOp(a) => {
+                for (mut c_lane_i, a_lane_i) in c.lane_iter_mut().zip(a.lane_iter()) {
+                    if beta != T::one() {
+                        for c_ij in c_lane_i.values_mut() {
+                            *c_ij *= beta.inlined_clone();
+                        }
+                    }
+
+                    let (mut c_minors, mut c_vals) = c_lane_i.indices_and_values_mut();
+                    let (a_minors, a_vals) = (a_lane_i.minor_indices(), a_lane_i.values());
+
+                    for (a_col, a_val) in a_minors.iter().zip(a_vals) {
+                        // TODO: Use exponential search instead of linear search.
+                        // If C has substantially more entries in the row than A, then a line search
+                        // will needlessly visit many entries in C.
+                        let (c_idx, _) = c_minors.iter()
+                            .enumerate()
+                            .find(|(_, c_col)| *c_col == a_col)
+                            .ok_or_else(spadd_cs_unexpected_entry)?;
+                        c_vals[c_idx] += alpha.inlined_clone() * a_val.inlined_clone();
+                        c_minors = &c_minors[c_idx ..];
+                        c_vals = &mut c_vals[c_idx ..];
+                    }
+                }
+            }
+            Op::Transpose(a) => {
+                if beta != T::one() {
+                    for c_ij in c.values_mut() {
+                        *c_ij *= beta.inlined_clone();
+                    }
+                }
+
+                for (i, a_lane_i) in a.lane_iter().enumerate() {
+                    for (&j, a_val) in a_lane_i.minor_indices().iter().zip(a_lane_i.values()) {
+                        let a_val = a_val.inlined_clone();
+                        let alpha = alpha.inlined_clone();
+                        match c.get_entry_mut(j, i).unwrap() {
+                            SparseEntryMut::NonZero(c_ji) => { *c_ji += alpha * a_val }
+                            SparseEntryMut::Zero => return Err(spadd_cs_unexpected_entry()),
+                        }
+                    }
+                }
+            }
+        }
+        Ok(())
+    }
+}
+
+/// Helper functionality for implementing CSR/CSC SPMM.
+///
+/// The implementation essentially assumes that `a` is a CSR matrix. To use it with CSC matrices,
+/// the transposed operation must be specified for the CSC matrix.
+pub fn spmm_cs_dense<T>(beta: T,
+                        mut c: DMatrixSliceMut<T>,
+                        alpha: T,
+                        a: Op<&CsMatrix<T>>,
+                        b: Op<DMatrixSlice<T>>)
+    where
+        T: Scalar + ClosedAdd + ClosedMul + Zero + One
+{
+    match a {
+        Op::NoOp(a) => {
+            for j in 0..c.ncols() {
+                let mut c_col_j = c.column_mut(j);
+                for (c_ij, a_row_i) in c_col_j.iter_mut().zip(a.lane_iter()) {
+                    let mut dot_ij = T::zero();
+                    for (&k, a_ik) in a_row_i.minor_indices().iter().zip(a_row_i.values()) {
+                        let b_contrib =
+                            match b {
+                                Op::NoOp(ref b) => b.index((k, j)),
+                                Op::Transpose(ref b) => b.index((j, k))
+                            };
+                        dot_ij += a_ik.inlined_clone() * b_contrib.inlined_clone();
+                    }
+                    *c_ij = beta.inlined_clone() * c_ij.inlined_clone() + alpha.inlined_clone() * dot_ij;
+                }
+            }
+        },
+        Op::Transpose(a) => {
+            // In this case, we have to pre-multiply C by beta
+            c *= beta;
+
+            for k in 0..a.pattern().major_dim() {
+                let a_row_k = a.get_lane(k).unwrap();
+                for (&i, a_ki) in a_row_k.minor_indices().iter().zip(a_row_k.values()) {
+                    let gamma_ki = alpha.inlined_clone() * a_ki.inlined_clone();
+                    let mut c_row_i = c.row_mut(i);
+                    match b {
+                        Op::NoOp(ref b) => {
+                            let b_row_k = b.row(k);
+                            for (c_ij, b_kj) in c_row_i.iter_mut().zip(b_row_k.iter()) {
+                                *c_ij += gamma_ki.inlined_clone() * b_kj.inlined_clone();
+                            }
+                        },
+                        Op::Transpose(ref b) => {
+                            let b_col_k = b.column(k);
+                            for (c_ij, b_jk) in c_row_i.iter_mut().zip(b_col_k.iter()) {
+                                *c_ij += gamma_ki.inlined_clone() * b_jk.inlined_clone();
+                            }
+                        },
+                    }
+                }
+            }
+        },
+    }
+}
+

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

@@ -0,0 +1,92 @@
+use crate::csc::CscMatrix;
+use crate::ops::Op;
+use crate::ops::serial::cs::{spmm_cs_prealloc, spmm_cs_dense, spadd_cs_prealloc};
+use crate::ops::serial::OperationError;
+use nalgebra::{Scalar, ClosedAdd, ClosedMul, DMatrixSliceMut, DMatrixSlice};
+use num_traits::{Zero, One};
+
+use std::borrow::Cow;
+
+/// Sparse-dense matrix-matrix multiplication `C <- beta * C + alpha * op(A) * op(B)`.
+pub fn spmm_csc_dense<'a, T>(beta: T,
+                             c: impl Into<DMatrixSliceMut<'a, T>>,
+                             alpha: T,
+                             a: Op<&CscMatrix<T>>,
+                             b: Op<impl Into<DMatrixSlice<'a, T>>>)
+    where
+        T: Scalar + ClosedAdd + ClosedMul + Zero + One
+{
+    let b = b.convert();
+    spmm_csc_dense_(beta, c.into(), alpha, a, b)
+}
+
+fn spmm_csc_dense_<T>(beta: T,
+                      c: DMatrixSliceMut<T>,
+                      alpha: T,
+                      a: Op<&CscMatrix<T>>,
+                      b: Op<DMatrixSlice<T>>)
+    where
+        T: Scalar + ClosedAdd + ClosedMul + Zero + One
+{
+    assert_compatible_spmm_dims!(c, a, b);
+    // Need to interpret matrix as transposed since the spmm_cs_dense function assumes CSR layout
+    let a = a.transposed().map_same_op(|a| &a.cs);
+    spmm_cs_dense(beta, c, alpha, a, b)
+}
+
+/// Sparse matrix addition `C <- beta * C + alpha * op(A)`.
+///
+/// If the pattern of `c` does not accommodate all the non-zero entries in `a`, an error is
+/// returned.
+pub fn spadd_csc_prealloc<T>(beta: T,
+                             c: &mut CscMatrix<T>,
+                             alpha: T,
+                             a: Op<&CscMatrix<T>>)
+                             -> Result<(), OperationError>
+    where
+        T: Scalar + ClosedAdd + ClosedMul + Zero + One
+{
+    assert_compatible_spadd_dims!(c, a);
+    spadd_cs_prealloc(beta, &mut c.cs, alpha, a.map_same_op(|a| &a.cs))
+}
+
+
+/// Sparse-sparse matrix multiplication, `C <- beta * C + alpha * op(A) * op(B)`.
+pub fn spmm_csc_prealloc<T>(
+    beta: T,
+    c: &mut CscMatrix<T>,
+    alpha: T,
+    a: Op<&CscMatrix<T>>,
+    b: Op<&CscMatrix<T>>)
+    -> Result<(), OperationError>
+    where
+        T: Scalar + ClosedAdd + ClosedMul + Zero + One
+{
+    assert_compatible_spmm_dims!(c, a, b);
+
+    use Op::{NoOp, Transpose};
+
+    match (&a, &b) {
+        (NoOp(ref a), NoOp(ref b)) => {
+            // Note: We have to reverse the order for CSC matrices
+            spmm_cs_prealloc(beta, &mut c.cs, alpha, &b.cs, &a.cs)
+        },
+        _ => {
+            // Currently we handle transposition by explicitly precomputing transposed matrices
+            // and calling the operation again without transposition
+            let a_ref: &CscMatrix<T> = a.inner_ref();
+            let b_ref: &CscMatrix<T> = b.inner_ref();
+            let (a, b) = {
+                use Cow::*;
+                match (&a, &b) {
+                    (NoOp(_), NoOp(_)) => unreachable!(),
+                    (Transpose(ref a), NoOp(_)) => (Owned(a.transpose()), Borrowed(b_ref)),
+                    (NoOp(_), Transpose(ref b)) => (Borrowed(a_ref), Owned(b.transpose())),
+                    (Transpose(ref a), Transpose(ref b)) => (Owned(a.transpose()), Owned(b.transpose()))
+                }
+            };
+
+            spmm_csc_prealloc(beta, c, alpha, NoOp(a.as_ref()), NoOp(b.as_ref()))
+        }
+    }
+}

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

@@ -1,11 +1,10 @@
 use crate::csr::CsrMatrix;
 use crate::ops::{Op};
-use crate::SparseEntryMut;
+use crate::ops::serial::{OperationError};
-use crate::ops::serial::{OperationError, OperationErrorType};
 use nalgebra::{Scalar, DMatrixSlice, ClosedAdd, ClosedMul, DMatrixSliceMut};
 use num_traits::{Zero, One};
-use std::sync::Arc;
 use std::borrow::Cow;
+use crate::ops::serial::cs::{spmm_cs_prealloc, spmm_cs_dense, spadd_cs_prealloc};
 
 /// Sparse-dense matrix-matrix multiplication `C <- beta * C + alpha * op(A) * op(B)`.
 pub fn spmm_csr_dense<'a, T>(beta: T,
@@ -21,7 +20,7 @@ pub fn spmm_csr_dense<'a, T>(beta: T,
 }
 
 fn spmm_csr_dense_<T>(beta: T,
-                      mut c: DMatrixSliceMut<T>,
+                      c: DMatrixSliceMut<T>,
                       alpha: T,
                       a: Op<&CsrMatrix<T>>,
                       b: Op<DMatrixSlice<T>>)
@@ -29,58 +28,7 @@ where
     T: Scalar + ClosedAdd + ClosedMul + Zero + One
 {
     assert_compatible_spmm_dims!(c, a, b);
-
+    spmm_cs_dense(beta, c, alpha, a.map_same_op(|a| &a.cs), b)
-    match a {
-        Op::NoOp(ref a) => {
-            for j in 0..c.ncols() {
-                let mut c_col_j = c.column_mut(j);
-                for (c_ij, a_row_i) in c_col_j.iter_mut().zip(a.row_iter()) {
-                    let mut dot_ij = T::zero();
-                    for (&k, a_ik) in a_row_i.col_indices().iter().zip(a_row_i.values()) {
-                        let b_contrib =
-                            match b {
-                                Op::NoOp(ref b) => b.index((k, j)),
-                                Op::Transpose(ref b) => b.index((j, k))
-                            };
-                        dot_ij += a_ik.inlined_clone() * b_contrib.inlined_clone();
-                    }
-                    *c_ij = beta.inlined_clone() * c_ij.inlined_clone() + alpha.inlined_clone() * dot_ij;
-                }
-            }
-        },
-        Op::Transpose(ref a) => {
-            // In this case, we have to pre-multiply C by beta
-            c *= beta;
-
-            for k in 0..a.nrows() {
-                let a_row_k = a.row(k);
-                for (&i, a_ki) in a_row_k.col_indices().iter().zip(a_row_k.values()) {
-                    let gamma_ki = alpha.inlined_clone() * a_ki.inlined_clone();
-                    let mut c_row_i = c.row_mut(i);
-                    match b {
-                        Op::NoOp(ref b) => {
-                            let b_row_k = b.row(k);
-                            for (c_ij, b_kj) in c_row_i.iter_mut().zip(b_row_k.iter()) {
-                                *c_ij += gamma_ki.inlined_clone() * b_kj.inlined_clone();
-                            }
-                        },
-                        Op::Transpose(ref b) => {
-                            let b_col_k = b.column(k);
-                            for (c_ij, b_jk) in c_row_i.iter_mut().zip(b_col_k.iter()) {
-                                *c_ij += gamma_ki.inlined_clone() * b_jk.inlined_clone();
-                            }
-                        },
-                    }
-                }
-            }
-        },
-    }
-}
-
-fn spadd_csr_unexpected_entry() -> OperationError {
-    OperationError::from_type_and_message(
-        OperationErrorType::InvalidPattern,
-        String::from("Found entry in `a` that is not present in `c`."))
 }
 
 /// Sparse matrix addition `C <- beta * C + alpha * op(A)`.
@@ -96,70 +44,7 @@ where
     T: Scalar + ClosedAdd + ClosedMul + Zero + One
 {
     assert_compatible_spadd_dims!(c, a);
-
+    spadd_cs_prealloc(beta, &mut c.cs, alpha, a.map_same_op(|a| &a.cs))
-    // TODO: Change CsrMatrix::pattern() to return `&Arc` instead of `Arc`
-    if Arc::ptr_eq(&c.pattern(), &a.inner_ref().pattern()) {
-        // Special fast path: The two matrices have *exactly* the same sparsity pattern,
-        // so we only need to sum the value arrays
-        for (c_ij, a_ij) in c.values_mut().iter_mut().zip(a.inner_ref().values()) {
-            let (alpha, beta) = (alpha.inlined_clone(), beta.inlined_clone());
-            *c_ij = beta * c_ij.inlined_clone() + alpha * a_ij.inlined_clone();
-        }
-        Ok(())
-    } else {
-        match a {
-            Op::NoOp(a) => {
-                for (mut c_row_i, a_row_i) in c.row_iter_mut().zip(a.row_iter()) {
-                    if beta != T::one() {
-                        for c_ij in c_row_i.values_mut() {
-                            *c_ij *= beta.inlined_clone();
-                        }
-                    }
-
-                    let (mut c_cols, mut c_vals) = c_row_i.cols_and_values_mut();
-                    let (a_cols, a_vals) = (a_row_i.col_indices(), a_row_i.values());
-
-                    for (a_col, a_val) in a_cols.iter().zip(a_vals) {
-                        // TODO: Use exponential search instead of linear search.
-                        // If C has substantially more entries in the row than A, then a line search
-                        // will needlessly visit many entries in C.
-                        let (c_idx, _) = c_cols.iter()
-                            .enumerate()
-                            .find(|(_, c_col)| *c_col == a_col)
-                            .ok_or_else(spadd_csr_unexpected_entry)?;
-                        c_vals[c_idx] += alpha.inlined_clone() * a_val.inlined_clone();
-                        c_cols = &c_cols[c_idx ..];
-                        c_vals = &mut c_vals[c_idx ..];
-                    }
-                }
-            }
-            Op::Transpose(a) => {
-                if beta != T::one() {
-                    for c_ij in c.values_mut() {
-                        *c_ij *= beta.inlined_clone();
-                    }
-                }
-
-                for (i, a_row_i) in a.row_iter().enumerate() {
-                    for (&j, a_val) in a_row_i.col_indices().iter().zip(a_row_i.values()) {
-                        let a_val = a_val.inlined_clone();
-                        let alpha = alpha.inlined_clone();
-                        match c.index_entry_mut(j, i) {
-                            SparseEntryMut::NonZero(c_ji) => { *c_ji += alpha * a_val }
-                            SparseEntryMut::Zero => return Err(spadd_csr_unexpected_entry()),
-                        }
-                    }
-                }
-            }
-        }
-        Ok(())
-    }
-}
-
-fn spmm_csr_unexpected_entry() -> OperationError {
-    OperationError::from_type_and_message(
-        OperationErrorType::InvalidPattern,
-        String::from("Found unexpected entry that is not present in `c`."))
 }
 
 /// Sparse-sparse matrix multiplication, `C <- beta * C + alpha * op(A) * op(B)`.
@@ -179,29 +64,7 @@ where
 
     match (&a, &b) {
         (NoOp(ref a), NoOp(ref b)) => {
-            for (mut c_row_i, a_row_i) in c.row_iter_mut().zip(a.row_iter()) {
+            spmm_cs_prealloc(beta, &mut c.cs, alpha, &a.cs, &b.cs)
-                for c_ij in c_row_i.values_mut() {
-                    *c_ij = beta.inlined_clone() * c_ij.inlined_clone();
-                }
-
-                for (&k, a_ik) in a_row_i.col_indices().iter().zip(a_row_i.values()) {
-                    let b_row_k = b.row(k);
-                    let (mut c_row_i_cols, mut c_row_i_values) = c_row_i.cols_and_values_mut();
-                    let alpha_aik = alpha.inlined_clone() * a_ik.inlined_clone();
-                    for (j, b_kj) in b_row_k.col_indices().iter().zip(b_row_k.values()) {
-                        // Determine the location in C to append the value
-                        let (c_local_idx, _) = c_row_i_cols.iter()
-                            .enumerate()
-                            .find(|(_, c_col)| *c_col == j)
-                            .ok_or_else(spmm_csr_unexpected_entry)?;
-
-                        c_row_i_values[c_local_idx] += alpha_aik.inlined_clone() * b_kj.inlined_clone();
-                        c_row_i_cols = &c_row_i_cols[c_local_idx ..];
-                        c_row_i_values = &mut c_row_i_values[c_local_idx ..];
-                    }
-                }
-            }
-            Ok(())
         },
         _ => {
             // Currently we handle transposition by explicitly precomputing transposed matrices

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

@@ -49,9 +49,12 @@ macro_rules! assert_compatible_spadd_dims {
     }
 }
 
+mod csc;
 mod csr;
 mod pattern;
+mod cs;
 
+pub use csc::*;
 pub use csr::*;
 pub use pattern::*;
 

nalgebra-sparse/tests/common/mod.rs

@@ -30,9 +30,9 @@ pub const PROPTEST_MAX_NNZ: usize = 40;
 pub const PROPTEST_I32_VALUE_STRATEGY: RangeInclusive<i32> = -5 ..= 5;
 
 pub fn csr_strategy() -> impl Strategy<Value=CsrMatrix<i32>> {
-    csr(-5 ..= 5, PROPTEST_MATRIX_DIM, PROPTEST_MATRIX_DIM, PROPTEST_MAX_NNZ)
+    csr(PROPTEST_I32_VALUE_STRATEGY, PROPTEST_MATRIX_DIM, PROPTEST_MATRIX_DIM, PROPTEST_MAX_NNZ)
 }
 
 pub fn csc_strategy() -> impl Strategy<Value=CscMatrix<i32>> {
-    csc(-5 ..= 5, PROPTEST_MATRIX_DIM, PROPTEST_MATRIX_DIM, PROPTEST_MAX_NNZ)
+    csc(PROPTEST_I32_VALUE_STRATEGY, PROPTEST_MATRIX_DIM, PROPTEST_MATRIX_DIM, PROPTEST_MAX_NNZ)
 }

nalgebra-sparse/tests/unit_tests/ops.rs

@@ -1,9 +1,12 @@
-use crate::common::{csr_strategy, PROPTEST_MATRIX_DIM, PROPTEST_MAX_NNZ,
+use crate::common::{csc_strategy, csr_strategy, PROPTEST_MATRIX_DIM, PROPTEST_MAX_NNZ,
                     PROPTEST_I32_VALUE_STRATEGY};
-use nalgebra_sparse::ops::serial::{spmm_csr_dense, spadd_pattern, spmm_pattern, spadd_csr_prealloc, spmm_csr_prealloc};
+use nalgebra_sparse::ops::serial::{spmm_csr_dense, spmm_csc_dense, spadd_pattern, spmm_pattern,
+                                   spadd_csr_prealloc, spadd_csc_prealloc,
+                                   spmm_csr_prealloc, spmm_csc_prealloc};
 use nalgebra_sparse::ops::{Op};
 use nalgebra_sparse::csr::CsrMatrix;
-use nalgebra_sparse::proptest::{csr, sparsity_pattern};
+use nalgebra_sparse::csc::CscMatrix;
+use nalgebra_sparse::proptest::{csc, csr, sparsity_pattern};
 use nalgebra_sparse::pattern::SparsityPattern;
 
 use nalgebra::{DMatrix, Scalar, DMatrixSliceMut, DMatrixSlice};
@@ -23,6 +26,15 @@ fn dense_csr_pattern(pattern: &SparsityPattern) -> DMatrix<i32> {
     DMatrix::from(&boolean_csr)
 }
 
+/// Represents the sparsity pattern of a CSC matrix as a dense matrix with 0/1
+fn dense_csc_pattern(pattern: &SparsityPattern) -> DMatrix<i32> {
+    let boolean_csc = CscMatrix::try_from_pattern_and_values(
+        Arc::new(pattern.clone()),
+        vec![1; pattern.nnz()])
+        .unwrap();
+    DMatrix::from(&boolean_csc)
+}
+
 #[derive(Debug)]
 struct SpmmCsrDenseArgs<T: Scalar> {
     c: DMatrix<T>,
@@ -32,6 +44,15 @@ struct SpmmCsrDenseArgs<T: Scalar> {
     b: Op<DMatrix<T>>,
 }
 
+#[derive(Debug)]
+struct SpmmCscDenseArgs<T: Scalar> {
+    c: DMatrix<T>,
+    beta: T,
+    alpha: T,
+    a: Op<CscMatrix<T>>,
+    b: Op<DMatrix<T>>,
+}
+
 /// Returns matrices C, A and B with compatible dimensions such that it can be used
 /// in an `spmm` operation `C = beta * C + alpha * trans(A) * trans(B)`.
 fn spmm_csr_dense_args_strategy() -> impl Strategy<Value=SpmmCsrDenseArgs<i32>> {
@@ -70,6 +91,21 @@ fn spmm_csr_dense_args_strategy() -> impl Strategy<Value=SpmmCsrDenseArgs<i32>>
         })
 }
 
+/// Returns matrices C, A and B with compatible dimensions such that it can be used
+/// in an `spmm` operation `C = beta * C + alpha * trans(A) * trans(B)`.
+fn spmm_csc_dense_args_strategy() -> impl Strategy<Value=SpmmCscDenseArgs<i32>> {
+    spmm_csr_dense_args_strategy()
+        .prop_map(|args| {
+            SpmmCscDenseArgs {
+                c: args.c,
+                beta: args.beta,
+                alpha: args.alpha,
+                a: args.a.map_same_op(|a| CscMatrix::from(&a)),
+                b: args.b
+            }
+        })
+}
+
 #[derive(Debug)]
 struct SpaddCsrArgs<T> {
     c: CsrMatrix<T>,
@@ -78,6 +114,14 @@ struct SpaddCsrArgs<T> {
     a: Op<CsrMatrix<T>>,
 }
 
+#[derive(Debug)]
+struct SpaddCscArgs<T> {
+    c: CscMatrix<T>,
+    beta: T,
+    alpha: T,
+    a: Op<CscMatrix<T>>,
+}
+
 fn spadd_csr_prealloc_args_strategy() -> impl Strategy<Value=SpaddCsrArgs<i32>> {
     let value_strategy = PROPTEST_I32_VALUE_STRATEGY;
 
@@ -99,6 +143,16 @@ fn spadd_csr_prealloc_args_strategy() -> impl Strategy<Value=SpaddCsrArgs<i32>>
         })
 }
 
+fn spadd_csc_prealloc_args_strategy() -> impl Strategy<Value=SpaddCscArgs<i32>> {
+    spadd_csr_prealloc_args_strategy()
+        .prop_map(|args| SpaddCscArgs {
+            c: CscMatrix::from(&args.c),
+            beta: args.beta,
+            alpha: args.alpha,
+            a: args.a.map_same_op(|a| CscMatrix::from(&a))
+        })
+}
+
 fn dense_strategy() -> impl Strategy<Value=DMatrix<i32>> {
     matrix(PROPTEST_I32_VALUE_STRATEGY, PROPTEST_MATRIX_DIM, PROPTEST_MATRIX_DIM)
 }
@@ -150,6 +204,15 @@ struct SpmmCsrArgs<T> {
     b: Op<CsrMatrix<T>>,
 }
 
+#[derive(Debug)]
+struct SpmmCscArgs<T> {
+    c: CscMatrix<T>,
+    beta: T,
+    alpha: T,
+    a: Op<CscMatrix<T>>,
+    b: Op<CscMatrix<T>>,
+}
+
 fn spmm_csr_prealloc_args_strategy() -> impl Strategy<Value=SpmmCsrArgs<i32>> {
     spmm_pattern_strategy()
         .prop_flat_map(|(a_pattern, b_pattern)| {
@@ -181,6 +244,21 @@ fn spmm_csr_prealloc_args_strategy() -> impl Strategy<Value=SpmmCsrArgs<i32>> {
         })
 }
 
+fn spmm_csc_prealloc_args_strategy() -> impl Strategy<Value=SpmmCscArgs<i32>> {
+    // Note: Converting from CSR is simple, but might be significantly slower than
+    // writing a common implementation that can be shared between CSR and CSC args
+    spmm_csr_prealloc_args_strategy()
+        .prop_map(|args| {
+            SpmmCscArgs {
+                c: CscMatrix::from(&args.c),
+                beta: args.beta,
+                alpha: args.alpha,
+                a: args.a.map_same_op(|a| CscMatrix::from(&a)),
+                b: args.b.map_same_op(|b| CscMatrix::from(&b))
+            }
+        })
+}
+
 /// Helper function to help us call dense GEMM with our `Op` type
 fn dense_gemm<'a>(beta: i32,
                   c: impl Into<DMatrixSliceMut<'a, i32>>,
@@ -310,7 +388,7 @@ proptest! {
         (a, b)
         in csr_strategy()
             .prop_flat_map(|a| {
-                let b = csr(PROPTEST_I32_VALUE_STRATEGY, Just(a.nrows()), Just(a.ncols()), 40);
+                let b = csr(PROPTEST_I32_VALUE_STRATEGY, Just(a.nrows()), Just(a.ncols()), PROPTEST_MAX_NNZ);
                 (Just(a), b)
             }))
     {
@@ -500,4 +578,263 @@ proptest! {
         prop_assert_eq!(&DMatrix::from(&c_ref_ref), &c_dense);
         prop_assert_eq!(c_ref_ref.pattern(), &c_pattern);
     }
+
+    #[test]
+    fn spmm_csc_prealloc_test(SpmmCscArgs { c, beta, alpha, a, b }
+        in spmm_csc_prealloc_args_strategy()
+    ) {
+        // Test that we get the expected result by comparing to an equivalent dense operation
+        // (here we give in the C matrix, so the sparsity pattern is essentially fixed)
+        let mut c_sparse = c.clone();
+        spmm_csc_prealloc(beta, &mut c_sparse, alpha, a.as_ref(), b.as_ref()).unwrap();
+
+        let mut c_dense = DMatrix::from(&c);
+        let op_a_dense = match a {
+            Op::NoOp(ref a) => DMatrix::from(a),
+            Op::Transpose(ref a) => DMatrix::from(a).transpose(),
+        };
+        let op_b_dense = match b {
+            Op::NoOp(ref b) => DMatrix::from(b),
+            Op::Transpose(ref b) => DMatrix::from(b).transpose(),
+        };
+        c_dense = beta * c_dense + alpha * &op_a_dense * op_b_dense;
+
+        prop_assert_eq!(&DMatrix::from(&c_sparse), &c_dense);
+    }
+
+    #[test]
+    fn spmm_csc_prealloc_panics_on_dim_mismatch(
+        (alpha, beta, c, a, b)
+        in (PROPTEST_I32_VALUE_STRATEGY,
+            PROPTEST_I32_VALUE_STRATEGY,
+            csc_strategy(),
+            op_strategy(csc_strategy()),
+            op_strategy(csc_strategy()))
+    ) {
+        // We refer to `A * B` as the "product"
+        let product_rows = match &a {
+            Op::NoOp(ref a) => a.nrows(),
+            Op::Transpose(ref a) => a.ncols(),
+        };
+        let product_cols = match &b {
+            Op::NoOp(ref b) => b.ncols(),
+            Op::Transpose(ref b) => b.nrows(),
+        };
+        // Determine the common dimension in the product
+        // from the perspective of a and b, respectively
+        let product_a_common = match &a {
+            Op::NoOp(ref a) => a.ncols(),
+            Op::Transpose(ref a) => a.nrows(),
+        };
+        let product_b_common = match &b {
+            Op::NoOp(ref b) => b.nrows(),
+            Op::Transpose(ref b) => b.ncols(),
+        };
+
+        let dims_are_compatible = product_rows == c.nrows()
+            && product_cols == c.ncols()
+            && product_a_common == product_b_common;
+
+        // If the dimensions randomly happen to be compatible, then of course we need to
+        // skip the test, so we assume that they are not.
+        prop_assume!(!dims_are_compatible);
+
+        let result = catch_unwind(|| {
+            let mut spmm_result = c.clone();
+            spmm_csc_prealloc(beta, &mut spmm_result, alpha, a.as_ref(), b.as_ref()).unwrap();
+        });
+
+        prop_assert!(result.is_err(),
+            "The SPMM kernel executed successfully despite mismatch dimensions");
+    }
+
+    #[test]
+    fn csc_mul_csc(
+        // a and b have dimensions compatible for multiplication
+        (a, b)
+        in csc_strategy()
+            .prop_flat_map(|a| {
+                let max_nnz = PROPTEST_MAX_NNZ;
+                let cols = PROPTEST_MATRIX_DIM;
+                let b = csc(PROPTEST_I32_VALUE_STRATEGY, Just(a.ncols()), cols, max_nnz);
+                (Just(a), b)
+            })
+            .prop_map(|(a, b)| {
+                println!("a: {} x {}, b: {} x {}", a.nrows(), a.ncols(), b.nrows(), b.ncols());
+                (a, b)
+            }))
+    {
+        assert_eq!(a.ncols(), b.nrows());
+        // We use the dense result as the ground truth for the arithmetic result
+        let c_dense = DMatrix::from(&a) * DMatrix::from(&b);
+        // However, it's not enough only to cover the dense result, we also need to verify the
+        // sparsity pattern. We can determine the exact sparsity pattern by using
+        // dense arithmetic with positive integer values and extracting positive entries.
+        let c_dense_pattern = dense_csc_pattern(a.pattern()) * dense_csc_pattern(b.pattern());
+        let c_pattern = CscMatrix::from(&c_dense_pattern).pattern().clone();
+
+        // Check each combination of owned matrices and references
+        let c_owned_owned = a.clone() * b.clone();
+        prop_assert_eq!(&DMatrix::from(&c_owned_owned), &c_dense);
+        prop_assert_eq!(c_owned_owned.pattern(), &c_pattern);
+
+        let c_owned_ref = a.clone() * &b;
+        prop_assert_eq!(&DMatrix::from(&c_owned_ref), &c_dense);
+        prop_assert_eq!(c_owned_ref.pattern(), &c_pattern);
+
+        let c_ref_owned = &a * b.clone();
+        prop_assert_eq!(&DMatrix::from(&c_ref_owned), &c_dense);
+        prop_assert_eq!(c_ref_owned.pattern(), &c_pattern);
+
+        let c_ref_ref = &a * &b;
+        prop_assert_eq!(&DMatrix::from(&c_ref_ref), &c_dense);
+        prop_assert_eq!(c_ref_ref.pattern(), &c_pattern);
+    }
+
+    #[test]
+    fn spmm_csc_dense_agrees_with_dense_result(
+        SpmmCscDenseArgs { c, beta, alpha, a, b }
+         in spmm_csc_dense_args_strategy()
+    ) {
+        let mut spmm_result = c.clone();
+        spmm_csc_dense(beta, &mut spmm_result, alpha, a.as_ref(), b.as_ref());
+
+        let mut gemm_result = c.clone();
+        let a_dense = a.map_same_op(|a| DMatrix::from(&a));
+        dense_gemm(beta, &mut gemm_result, alpha, a_dense.as_ref(), b.as_ref());
+
+        prop_assert_eq!(spmm_result, gemm_result);
+    }
+
+    #[test]
+    fn spmm_csc_dense_panics_on_dim_mismatch(
+        (alpha, beta, c, a, b)
+        in (PROPTEST_I32_VALUE_STRATEGY,
+            PROPTEST_I32_VALUE_STRATEGY,
+            dense_strategy(),
+            op_strategy(csc_strategy()),
+            op_strategy(dense_strategy()))
+    ) {
+        // We refer to `A * B` as the "product"
+        let product_rows = match &a {
+            Op::NoOp(ref a) => a.nrows(),
+            Op::Transpose(ref a) => a.ncols(),
+        };
+        let product_cols = match &b {
+            Op::NoOp(ref b) => b.ncols(),
+            Op::Transpose(ref b) => b.nrows(),
+        };
+        // Determine the common dimension in the product
+        // from the perspective of a and b, respectively
+        let product_a_common = match &a {
+            Op::NoOp(ref a) => a.ncols(),
+            Op::Transpose(ref a) => a.nrows(),
+        };
+        let product_b_common = match &b {
+            Op::NoOp(ref b) => b.nrows(),
+            Op::Transpose(ref b) => b.ncols()
+        };
+
+        let dims_are_compatible = product_rows == c.nrows()
+            && product_cols == c.ncols()
+            && product_a_common == product_b_common;
+
+        // If the dimensions randomly happen to be compatible, then of course we need to
+        // skip the test, so we assume that they are not.
+        prop_assume!(!dims_are_compatible);
+
+        let result = catch_unwind(|| {
+            let mut spmm_result = c.clone();
+            spmm_csc_dense(beta, &mut spmm_result, alpha, a.as_ref(), b.as_ref());
+        });
+
+        prop_assert!(result.is_err(),
+            "The SPMM kernel executed successfully despite mismatch dimensions");
+    }
+
+    #[test]
+    fn spadd_csc_prealloc_test(SpaddCscArgs { c, beta, alpha, a } in spadd_csc_prealloc_args_strategy()) {
+        // Test that we get the expected result by comparing to an equivalent dense operation
+        // (here we give in the C matrix, so the sparsity pattern is essentially fixed)
+
+        let mut c_sparse = c.clone();
+        spadd_csc_prealloc(beta, &mut c_sparse, alpha, a.as_ref()).unwrap();
+
+        let mut c_dense = DMatrix::from(&c);
+        let op_a_dense = match a {
+            Op::NoOp(a) => DMatrix::from(&a),
+            Op::Transpose(a) => DMatrix::from(&a).transpose(),
+        };
+        c_dense = beta * c_dense + alpha * &op_a_dense;
+
+        prop_assert_eq!(&DMatrix::from(&c_sparse), &c_dense);
+    }
+
+    #[test]
+    fn spadd_csc_prealloc_panics_on_dim_mismatch(
+        (alpha, beta, c, op_a)
+        in (PROPTEST_I32_VALUE_STRATEGY,
+            PROPTEST_I32_VALUE_STRATEGY,
+            csc_strategy(),
+            op_strategy(csc_strategy()))
+    ) {
+        let op_a_rows = match &op_a {
+            &Op::NoOp(ref a) => a.nrows(),
+            &Op::Transpose(ref a) => a.ncols()
+        };
+        let op_a_cols = match &op_a {
+            &Op::NoOp(ref a) => a.ncols(),
+            &Op::Transpose(ref a) => a.nrows()
+        };
+
+        let dims_are_compatible = c.nrows() == op_a_rows && c.ncols() == op_a_cols;
+
+        // If the dimensions randomly happen to be compatible, then of course we need to
+        // skip the test, so we assume that they are not.
+        prop_assume!(!dims_are_compatible);
+
+        let result = catch_unwind(|| {
+            let mut spmm_result = c.clone();
+            spadd_csc_prealloc(beta, &mut spmm_result, alpha, op_a.as_ref()).unwrap();
+        });
+
+        prop_assert!(result.is_err(),
+            "The SPMM kernel executed successfully despite mismatch dimensions");
+    }
+
+    #[test]
+    fn csc_add_csc(
+        // a and b have the same dimensions
+        (a, b)
+        in csc_strategy()
+            .prop_flat_map(|a| {
+                let b = csc(PROPTEST_I32_VALUE_STRATEGY, Just(a.nrows()), Just(a.ncols()), PROPTEST_MAX_NNZ);
+                (Just(a), b)
+            }))
+    {
+        // We use the dense result as the ground truth for the arithmetic result
+        let c_dense = DMatrix::from(&a) + DMatrix::from(&b);
+        // However, it's not enough only to cover the dense result, we also need to verify the
+        // sparsity pattern. We can determine the exact sparsity pattern by using
+        // dense arithmetic with positive integer values and extracting positive entries.
+        let c_dense_pattern = dense_csc_pattern(a.pattern()) + dense_csc_pattern(b.pattern());
+        let c_pattern = CscMatrix::from(&c_dense_pattern).pattern().clone();
+
+        // Check each combination of owned matrices and references
+        let c_owned_owned = a.clone() + b.clone();
+        prop_assert_eq!(&DMatrix::from(&c_owned_owned), &c_dense);
+        prop_assert_eq!(c_owned_owned.pattern(), &c_pattern);
+
+        let c_owned_ref = a.clone() + &b;
+        prop_assert_eq!(&DMatrix::from(&c_owned_ref), &c_dense);
+        prop_assert_eq!(c_owned_ref.pattern(), &c_pattern);
+
+        let c_ref_owned = &a + b.clone();
+        prop_assert_eq!(&DMatrix::from(&c_ref_owned), &c_dense);
+        prop_assert_eq!(c_ref_owned.pattern(), &c_pattern);
+
+        let c_ref_ref = &a + &b;
+        prop_assert_eq!(&DMatrix::from(&c_ref_ref), &c_dense);
+        prop_assert_eq!(c_ref_ref.pattern(), &c_pattern);
+    }
 }