FIX: Remove 0.0 from candidates in solve_discrete_riccati (#185)

* FIX: Remove 0.0 from `candidates` in `solve_discrete_riccati`

QuantEcon/QuantEcon.py#364

* FIX: Replace `isfinite(cn)` with `cn * eps() < 1` in solve_discrete_riccati

QuantEcon/QuantEcon.py#361

src/matrix_eqn.jl

@@ -115,14 +115,14 @@ function solve_discrete_riccati(A::ScalarOrArray, B::ScalarOrArray,
     I = eye(k)
 
     current_min = Inf
-    candidates = [0.0, 0.01, 0.1, 0.25, 0.5, 1.0, 2.0, 10.0, 100.0, 10e5]
+    candidates = [0.01, 0.1, 0.25, 0.5, 1.0, 2.0, 10.0, 100.0, 10e5]
     BB = B' * B
     BTA = B' * A
 
     for gamma in candidates
         Z = getZ(R, gamma, BB)
         cn = cond(Z)
-        if isfinite(cn)
+        if cn * eps() < 1
             Q_tilde = -Q + N' * (Z \ (N + gamma .* BTA)) + gamma .* I
             G0 = B * (Z \ B')
             A0 = (I - gamma .* G0) * A - B * (Z \ N)

test/test_matrix_eqn.jl

@@ -1,6 +1,6 @@
 @testset "Testing matrix_eqn.jl" begin
     rough_kwargs = Dict(:atol => 1e-7, :rtol => 1e-7)
-    
+
     @testset "simple test where X is all zero" begin
         A = eye(4) .* .95
         B = zeros(4, 4)
@@ -38,14 +38,14 @@
     @testset "testing ricatti golden_num_float" begin
         val = solve_discrete_riccati(1.0, 1.0, 1.0, 1.0)
         gold_ratio = (1 + sqrt(5)) / 2.
-        @test val[1] == (gold_ratio)
+        @test isapprox(val[1], gold_ratio; rough_kwargs...)
     end
 
     @testset "testing ricatti golden_num_2d" begin
         A, B, R, Q = eye(2), eye(2), eye(2), eye(2)
         gold_diag = eye(2) .* (1 + sqrt(5)) ./ 2.
         val = solve_discrete_riccati(A, B, Q, R)
-        @test val == (gold_diag)
+        @test isapprox(val, gold_diag; rough_kwargs...)
     end
 
     @testset "test tjm 1" begin