fix infinite loop in cond (#682)

Closes #680

For `n==2` this code was trying to find three non-parallel +-1 vectors,
which is mathematically impossible.

Author: araujoms

src/linalg.jl

@@ -1745,7 +1745,7 @@ function opnormestinv(A::AbstractSparseMatrixCSC{T}, t::Integer = min(2,maximum(
                             repeated = true
                         end
                     end
-                    if !repeated
+                    if !repeated && 2^(n-1) ≥ 2t #we need enough non-parallel ±1 vectors
                         saux2 = S[1:n,j]' * S_old[1:n,1:t]
                         if _any_abs_eq(saux2,n)
                             repeated = true

test/linalg_solvers.jl

@@ -129,20 +129,24 @@ end
 
 @testset "sparse matrix cond" begin
     local A = sparse(reshape([1.0], 1, 1))
-    Ac = sprandn(20, 20,.5) + im*sprandn(20, 20,.5)
-    Ar = sprandn(20, 20,.5) + eps()*I
     @test cond(A, 1) == 1.0
-    # For a discussion of the tolerance, see #14778
-    @test 0.99 <= cond(Ar, 1) \ opnorm(Ar, 1) * opnorm(inv(Array(Ar)), 1) < 3
-    @test 0.99 <= cond(Ac, 1) \ opnorm(Ac, 1) * opnorm(inv(Array(Ac)), 1) < 3
-    @test 0.99 <= cond(Ar, Inf) \ opnorm(Ar, Inf) * opnorm(inv(Array(Ar)), Inf) < 3
-    @test 0.99 <= cond(Ac, Inf) \ opnorm(Ac, Inf) * opnorm(inv(Array(Ac)), Inf) < 3
     @test_throws ArgumentError cond(A,2)
     @test_throws ArgumentError cond(A,3)
     Arect = spzeros(10, 6)
     @test_throws DimensionMismatch cond(Arect, 1)
     @test_throws ArgumentError cond(Arect,2)
     @test_throws DimensionMismatch cond(Arect, Inf)
+    Ac = sprandn(20, 20,.5) + im*sprandn(20, 20,.5)
+    Ar = sprandn(20, 20,.5) + eps()*I
+    # For a discussion of the tolerance, see #14778
+    @test 0.99 <= cond(Ar, 1) \ opnorm(Ar, 1) * opnorm(inv(Array(Ar)), 1) < 3
+    @test 0.99 <= cond(Ac, 1) \ opnorm(Ac, 1) * opnorm(inv(Array(Ac)), 1) < 3
+    @test 0.99 <= cond(Ar, Inf) \ opnorm(Ar, Inf) * opnorm(inv(Array(Ar)), Inf) < 3
+    @test 0.99 <= cond(Ac, Inf) \ opnorm(Ac, Inf) * opnorm(inv(Array(Ac)), Inf) < 3
+    #issue 680
+    A22 = sparse(randn(2,2))
+    @test 0.99 ≤ cond(Array(A22), 1) / cond(A22, 1) < 3
+    @test 0.99 ≤ cond(Array(A22), Inf) / cond(A22, Inf) < 3
 end
 
 @testset "sparse matrix opnormestinv" begin
@@ -158,6 +162,9 @@ end
     @test_throws ArgumentError SparseArrays.opnormestinv(Ac,0)
     @test_throws ArgumentError SparseArrays.opnormestinv(Ac,21)
     @test_throws DimensionMismatch SparseArrays.opnormestinv(sprand(3,5,.9))
+    #issue 680
+    A33 = sparse(randn(3,3))
+    @test SparseArrays.opnormestinv(A33,3) ≈ opnorm(inv(Array(A33)),1) atol=1e-4
 end
 
 @testset "factorization" begin