added sparse matrix inner product

NEWS.md

@@ -692,6 +692,9 @@ Library improvements
   * `Sys.which()` provides a cross-platform method to find executable files, similar to
     the Unix `which` command. ([#26559])
 
+  * Added an optimized method of `vecdot` for taking the Frobenius inner product
+    of sparse matrices. ([#27470])
+
 Compiler/Runtime improvements
 -----------------------------
 

stdlib/SparseArrays/src/SparseArrays.jl

@@ -13,7 +13,7 @@ using LinearAlgebra
 
 import Base: +, -, *, \, /, &, |, xor, ==
 import LinearAlgebra: mul!, ldiv!, rdiv!, chol, adjoint!, diag, dot, eigen,
-    issymmetric, istril, istriu, lu, tr, transpose!, tril!, triu!,
+    issymmetric, istril, istriu, lu, tr, transpose!, tril!, triu!, vecdot,
     vecnorm, cond, diagm, factorize, ishermitian, norm, lmul!, rmul!, tril, triu
 
 import Base: @get!, acos, acosd, acot, acotd, acsch, asech, asin, asind, asinh,

stdlib/SparseArrays/src/linalg.jl

@@ -203,6 +203,37 @@ function spmatmul(A::SparseMatrixCSC{Tv,Ti}, B::SparseMatrixCSC{Tv,Ti};
     return C
 end
 
+# Frobenius inner product: trace(A'B)
+function vecdot(A::SparseMatrixCSC{T1,S1},B::SparseMatrixCSC{T2,S2}) where {T1,T2,S1,S2}
+    m, n = size(A)
+    size(B) == (m,n) || throw(DimensionMismatch("matrices must have the same dimensions"))
+    r = vecdot(zero(T1), zero(T2))
+    @inbounds for j = 1:n
+        ia = A.colptr[j]; ia_nxt = A.colptr[j+1]
+        ib = B.colptr[j]; ib_nxt = B.colptr[j+1]
+        if ia < ia_nxt && ib < ib_nxt
+            ra = A.rowval[ia]; rb = B.rowval[ib]
+            while true
+                if ra < rb
+                    ia += oneunit(S1)
+                    ia < ia_nxt || break
+                    ra = A.rowval[ia]
+                elseif ra > rb
+                    ib += oneunit(S2)
+                    ib < ib_nxt || break
+                    rb = B.rowval[ib]
+                else # ra == rb
+                    r += vecdot(A.nzval[ia], B.nzval[ib])
+                    ia += oneunit(S1); ib += oneunit(S2)
+                    ia < ia_nxt && ib < ib_nxt || break
+                    ra = A.rowval[ia]; rb = B.rowval[ib]
+                end
+            end
+        end
+    end
+    return r
+end
+
 ## solvers
 function fwdTriSolve!(A::SparseMatrixCSCUnion, B::AbstractVecOrMat)
 # forward substitution for CSC matrices

stdlib/SparseArrays/test/sparse.jl

@@ -327,6 +327,15 @@ end
     end
 end
 
+@testset "sparse Frobenius inner product" begin
+    for i = 1:5
+        A = sprand(ComplexF64,10,15,0.4)
+        B = sprand(ComplexF64,10,15,0.5)
+        @test vecdot(A,B) ≈ vecdot(Matrix(A),Matrix(B))
+    end
+    @test_throws DimensionMismatch vecdot(sprand(5,5,0.2),sprand(5,6,0.2))
+end
+
 sA = sprandn(3, 7, 0.5)
 sC = similar(sA)
 dA = Array(sA)