Improve partial ACA compression

src/compressor.jl

@@ -115,6 +115,12 @@ function _aca_partial(K, irange, jrange, atol, rmax, rtol, istart, buffer_ = not
     r = 0 # current rank
     while er > max(atol, rtol * est_norm) && r < rmax
         # remove index i from allowed row
+        if i < 1
+            all(j -> iszero(K[first(irange), j]), jrange) &&
+                all(i -> iszero(K[i, first(jrange)]), irange) ||
+                @warn "aca possibly failed on $irange × $jrange"
+            break
+        end
         I[i] = false
         # pre-allocate row and column
         a = newcol!(A)

test/compressor_test.jl

@@ -22,6 +22,20 @@ Random.seed!(1)
         aca = PartialACA(; atol = atol)
         R = aca(M, irange, jrange)
         @test norm(Matrix(R) - M) < atol
+        # test zero matrix
+        R = aca(zero(M), irange, jrange)
+        @test norm(Matrix(R)) ≈ 0.0
+        # low-rank because singular values decay to zero immediately. Error
+        # estimator fails, and warning is thrown
+        tmp = 0 * M
+        tmp[end-20:end, :] .= rand(T, 21, n)
+        R = aca(tmp, irange, jrange)
+        @test Matrix(R) ≈ tmp
+        tmp = 0 * M
+        tmp[1:20, :] .= rand(T, 20, n)
+        R = aca(tmp, irange, jrange)
+        @test Matrix(R) ≈ tmp
+
         rtol = 1e-5
         aca = PartialACA(; rtol = rtol)
         R = aca(M, irange, jrange)
@@ -31,10 +45,6 @@ Random.seed!(1)
         R = aca(M, irange, jrange)
         @test rank(R) == r
 
-        # test zero matrix
-        R = aca(zero(M), irange, jrange)
-        @test norm(Matrix(R)) ≈ 0.0
-
         # test fast update of frobenius norm
         m, n = 10000, 1000
         r = 10