Merge pull request #34 from JuliaDiff/wb/order-derivative

Check that the derivative is nonnegative, and handle the case `q == 0`

Author: willtebbutt

src/methods.jl

@@ -145,6 +145,7 @@ end
 
 # Check the method and derivative orders for consistency
 function _check_p_q(p::Integer, q::Integer)
+    q >= 0 || throw(ArgumentError("order of derivative must be nonnegative"))
     q < p || throw(ArgumentError("order of the method must be strictly greater than that " *
                                  "of the derivative"))
     # Check whether the method can be computed. We require the factorial of the
@@ -225,6 +226,10 @@ function fdm(
     bound > 0 || throw(ArgumentError("bound must be positive, got $bound"))
     0 <= adapt < 20 - m.p || throw(ArgumentError("can't perform $adapt adaptation steps"))
 
+    # The below calculation can fail for `m.q == 0`, because then `C₂` may be zero. We
+    # therefore handle this edge case here.
+    m.q == 0 && return m, f(x)
+
     p = m.p
     q = m.q
     grid = m.grid

test/methods.jl

@@ -2,15 +2,27 @@ using FiniteDifferences: Forward, Backward, Central, Nonstandard
 
 @testset "Methods" begin
     for f in [:forward_fdm, :backward_fdm, :central_fdm]
+        @eval @test $f(1, 0; bound=1)(sin, 1) == sin(1)
+        @eval @test $f(2, 0; bound=1)(sin, 1) == sin(1)
+        @eval @test $f(3, 0; bound=1)(sin, 1) == sin(1)
         @eval @test $f(10, 1; bound=1)(sin, 1) ≈ cos(1)
         @eval @test $f(10, 2; bound=1)(sin, 1) ≈ -sin(1)
 
+        @eval @test $f(1, 0; bound=1)(exp, 1) == exp(1)
+        @eval @test $f(2, 0; bound=1)(exp, 1) == exp(1)
+        @eval @test $f(3, 0; bound=1)(exp, 1) == exp(1)
         @eval @test $f(10, 1; bound=1)(exp, 1) ≈ exp(1)
         @eval @test $f(10, 2; bound=1)(exp, 1) ≈ exp(1)
 
+        @eval @test $f(1, 0; bound=1)(abs2, 1) == 1
+        @eval @test $f(2, 0; bound=1)(abs2, 1) == 1
+        @eval @test $f(3, 0; bound=1)(abs2, 1) == 1
         @eval @test $f(10, 1; bound=1)(abs2, 1) ≈ 2
         @eval @test $f(10, 2; bound=1)(abs2, 1) ≈ 2
 
+        @eval @test $f(1, 0; bound=1)(sqrt, 1) == 1
+        @eval @test $f(2, 0; bound=1)(sqrt, 1) == 1
+        @eval @test $f(3, 0; bound=1)(sqrt, 1) == 1
         @eval @test $f(10, 1; bound=1)(sqrt, 1) ≈ .5
         @eval @test $f(10, 2; bound=1)(sqrt, 1) ≈ -.25
     end
@@ -64,6 +76,7 @@ using FiniteDifferences: Forward, Backward, Central, Nonstandard
     @testset "Types" begin
         @testset "$T" for T in (Forward, Backward, Central)
             @test T(5, 1)(sin, 1; adapt=4) ≈ cos(1)
+            @test_throws ArgumentError T(3, 3)
             @test_throws ArgumentError T(3, 4)
             @test_throws ArgumentError T(40, 5)
             @test_throws ArgumentError T(5, 1)(sin, 1; adapt=200)