Improve performance of issym and ishermitian for sparse matrices

base/functors.jl

@@ -24,6 +24,9 @@ call(::ExpFun, x) = exp(x)
 immutable LogFun <: Func{1} end
 call(::LogFun, x) = log(x)
 
+immutable ConjFun <: Func{1} end
+call(::ConjFun, x) = conj(x)
+
 immutable AndFun <: Func{2} end
 call(::AndFun, x, y) = x & y
 

base/sparse.jl

@@ -2,7 +2,7 @@
 
 module SparseMatrix
 
-using Base: Func, AddFun, OrFun
+using Base: Func, AddFun, OrFun, ConjFun, IdFun
 using Base.Sort: Forward
 using Base.LinAlg: AbstractTriangular
 

base/sparse/sparsematrix.jl

@@ -2376,17 +2376,41 @@ end
 squeeze(S::SparseMatrixCSC, dims::Dims) = throw(ArgumentError("squeeze is not available for sparse matrices"))
 
 ## Structure query functions
+issym(A::SparseMatrixCSC) = is_hermsym(A, IdFun())
 
-function issym(A::SparseMatrixCSC)
-    m, n = size(A)
-    if m != n; return false; end
-    return countnz(A - A.') == 0
-end
+ishermitian(A::SparseMatrixCSC) = is_hermsym(A, ConjFun())
 
-function ishermitian(A::SparseMatrixCSC)
+function is_hermsym(A::SparseMatrixCSC, check::Func)
     m, n = size(A)
     if m != n; return false; end
-    return countnz(A - A') == 0
+
+    colptr = A.colptr
+    rowval = A.rowval
+    nzval = A.nzval
+    tracker = copy(A.colptr)
+    @inbounds for col = 1:A.n
+        for p = tracker[col]:colptr[col+1]-1
+            val = nzval[p]
+            if val == 0; continue; end # In case of explicit zeros
+            row = rowval[p]
+            if row < col; return false; end
+            if row == col # Diagonal element
+                if val != check(val)
+                    return false
+                end
+            else
+                row2 = rowval[tracker[row]]
+                if row2 > col; return false; end
+                if row2 == col # A[i,j] and A[j,i] exists
+                    if val != check(nzval[tracker[row]])
+                        return false
+                    end
+                    tracker[row] += 1
+                end
+            end
+        end
+    end
+    return true
 end
 
 function istriu{Tv}(A::SparseMatrixCSC{Tv})

test/sparsedir/sparse.jl

@@ -930,3 +930,41 @@ A = sparse([1.0])
 @test norm(A) == 1.0
 @test_throws ArgumentError norm(sprand(5,5,0.2),3)
 @test_throws ArgumentError norm(sprand(5,5,0.2),2)
+
+# test ishermitian and issym real matrices
+A = speye(5,5)
+@test ishermitian(A) == true
+@test issym(A) == true
+A[1,3] = 1.0
+@test ishermitian(A) == false
+@test issym(A) == false
+A[3,1] = 1.0
+@test ishermitian(A) == true
+@test issym(A) == true
+
+# test ishermitian and issym complex matrices
+A = speye(5,5) + im*speye(5,5)
+@test ishermitian(A) == false
+@test issym(A) == true
+A[1,4] = 1.0 + im
+@test ishermitian(A) == false
+@test issym(A) == false
+
+A = speye(Complex128, 5,5)
+A[3,2] = 1.0 + im
+@test ishermitian(A) == false
+@test issym(A) == false
+A[2,3] = 1.0 - im
+@test ishermitian(A) == true
+@test issym(A) == false
+
+A = sparse(zeros(5,5))
+@test ishermitian(A) == true
+@test issym(A) == true
+
+# Test with explicit zeros
+A = speye(Complex128, 5,5)
+A[3,1] = 2
+A.nzval[2] = 0.0
+@test ishermitian(A) == true
+@test issym(A) == true