Change default derivative impl to reverse mode

CHANGELOG.md

@@ -2,6 +2,15 @@
 
 ## [unreleased]
 
+- #170:
+
+  - changes `D` and `partial` to use reverse mode automatic differentiation by
+    default, and fixes all associated tests
+
+  - adds `emmy.generic/{zero?,one?,identity?}` implementations (all false) to
+    `emmy.tape/Completed`, in case some collection type tries to simplify these
+    during reverse-mode AD
+
 - #185:
 
   - adds a dynamic variable `emmy.calculus.derivative/*mode*` that allows the

src/emmy/calculus/derivative.cljc

@@ -237,7 +237,7 @@
 ;; implementation for the components. I vote to back out this `::s/structure`
 ;; installation.
 
-(def ^:dynamic *mode* d/FORWARD-MODE)
+(def ^:dynamic *mode* d/REVERSE-MODE)
 
 (doseq [t [::v/function ::s/structure]]
   (defmethod g/partial-derivative [t v/seqtype] [f selectors]
@@ -266,9 +266,9 @@
   the [Jacobian](https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant)
   of `f`."
   (o/make-operator
-   (fn [x]
+   (fn [f]
      (binding [*mode* d/FORWARD-MODE]
-       (g/partial-derivative x [])))
+       (g/partial-derivative f [])))
    g/derivative-symbol))
 
 (def ^{:arglists '([f])}
@@ -282,9 +282,9 @@
   the [Jacobian](https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant)
   of `f`."
   (o/make-operator
-   (fn [x]
+   (fn [f]
      (binding [*mode* d/REVERSE-MODE]
-       (g/partial-derivative x [])))
+       (g/partial-derivative f [])))
    g/derivative-symbol))
 
 (def ^{:arglists '([f])}
@@ -299,9 +299,9 @@
   of `f`.
 
   The related [[emmy.env/Grad]] returns a function that produces a structure of
-  the opposite orientation as [[D]]. Both of these functions use forward-mode
+  the opposite orientation as [[D]]. Both of these functions use reverse-mode
   automatic differentiation."
-  D-forward)
+  D-reverse)
 
 (defn D-as-matrix [F]
   (fn [s]
@@ -337,7 +337,7 @@
   "Returns an operator that, when applied to a function `f`, produces a function
   that uses forward-mode automatic differentiation to compute the partial
   derivative of `f` at the (zero-based) slot index provided via `selectors`."
-  partial-forward)
+  partial-reverse)
 
 ;; ## Derivative Utilities
 ;;

src/emmy/calculus/manifold.cljc

@@ -656,7 +656,6 @@
                            (g/+ (g/square x)
                                 (g/square y)
                                 (g/square z)))]
-                    (println "r is" r)
                     (when (g/zero? r)
                       (u/illegal-state "SphericalCylindrical singular"))
                     (-> rep

src/emmy/calculus/vector_calculus.cljc

@@ -30,10 +30,9 @@
 
   The related [[emmy.env/D]] operator returns a function that produces a
   structure of the opposite orientation as [[Grad]]. Both of these functions use
-  forward-mode automatic differentiation."
+  reverse-mode automatic differentiation."
   (-> (fn [f]
-        (f/compose s/opposite
-                   (g/partial-derivative f [])))
+        (f/compose s/opposite (d/D f)))
       (o/make-operator 'Grad)))
 
 (defn gradient

src/emmy/dual.cljc

@@ -371,6 +371,13 @@
 (def ^:const REVERSE-MODE ::reverse)
 (def ^:const REVERSE-EMPTY (->Completed {}))
 
+;; These are here to handle cases where some collection type might see instances
+;; of [[Completed]] and try and handle them during simplification.
+
+(defmethod g/zero? [Completed] [_] false)
+(defmethod g/one? [Completed] [_] false)
+(defmethod g/identity? [Completed] [_] false)
+
 ;; `replace-tag` exists to handle subtle bugs that can arise in the case of
 ;; functional return values. See the "Amazing Bug" sections
 ;; in [[emmy.calculus.derivative-test]] for detailed examples on how this might

src/emmy/mechanics/hamilton.cljc

@@ -224,10 +224,9 @@
                          (g/zero?
                           (g/simplify
                            (g/determinant M))))
-                  (do (println "determinant" (g/determinant M))
-                      (throw
-                       (ex-info "Legendre Transform Failure: determinant = 0"
-                                {:F F :w w})))
+                  (throw
+                   (ex-info "Legendre Transform Failure: determinant = 0"
+                            {:F F :w w}))
                   (let [v (g/solve-linear-left M (- w b))]
                     (- (* w v) (F v))))))]
       (let [Dpg (D putative-G)]
@@ -442,11 +441,12 @@
   "p.326"
   [C]
   (fn [s]
-    ((- J-func
-        (f/compose (Phi ((D C) s))
-                   J-func
-                   (Phi* ((D C) s))))
-     (s/compatible-shape s))))
+    (let [s-syms (s/compatible-shape s)]
+      ((- J-func
+          (f/compose (Phi ((D C) s))
+                     J-func
+                     (Phi* ((D C) s))))
+       s-syms))))
 
 ;; Time-Varying code
 ;;

src/emmy/numbers.cljc

@@ -95,8 +95,8 @@
         (g/infinite? a) 0
         :else (g// (g/sin a) a)))
 
-(defmethod g/sin [::v/real] [a] (Math/sin a))
-(defmethod g/cos [::v/real] [a] (Math/cos a))
+(defmethod g/sin [::v/real] [a] (if (g/zero? a) 0 (Math/sin a)))
+(defmethod g/cos [::v/real] [a] (if (g/zero? a) 1 (Math/cos a)))
 (defmethod g/tan [::v/real] [a] (Math/tan a))
 
 (defmethod g/cosh [::v/real] [a] (Math/cosh a))

test/emmy/abstract/number_test.cljc

@@ -153,10 +153,13 @@
         values like (cos 0) can be exactly evaluated.")))
 
   (checking "inexact numbers" 100 [x sg/native-integral]
-            (is (=  (+ 1 (Math/cos x))
-                    (g/+ 1 (g/cos x)))
-                "You get a floating-point inexact result by calling generic fns
-    on a number directly, by comparison."))
+            (if (g/zero? x)
+              (is (= 2 (g/+ 1 (g/cos x)))
+                  "special-cased exact output at 0")
+              (is (= (+ 1 (Math/cos x))
+                     (g/+ 1 (g/cos x)))
+                  "You get a floating-point inexact result by calling generic fns
+    on a number directly, by comparison.")))
 
   (testing "literal-number properly prints wrapped sequences, even if they're lazy."
     (is (= "(* 2 x)"

test/emmy/calculus/covariant_test.cljc

@@ -48,24 +48,24 @@
                       (-> (simplify expr)
                           (x/substitute '(up x0 y0 z0) 'p)))]
 
-        (is (= '(+ (* (Y↑0 p) (((partial 0) w_0) p) (X↑0 p))
-                   (* (Y↑0 p) (w_0 p) (((partial 0) X↑0) p))
-                   (* (Y↑0 p) (w_1 p) (((partial 0) X↑1) p))
-                   (* (Y↑0 p) (w_2 p) (((partial 0) X↑2) p))
-                   (* (Y↑0 p) (((partial 1) w_0) p) (X↑1 p))
-                   (* (Y↑0 p) (((partial 2) w_0) p) (X↑2 p))
-                   (* (X↑0 p) (Y↑1 p) (((partial 0) w_1) p))
-                   (* (X↑0 p) (Y↑2 p) (((partial 0) w_2) p))
-                   (* (w_0 p) (Y↑1 p) (((partial 1) X↑0) p))
-                   (* (w_0 p) (Y↑2 p) (((partial 2) X↑0) p))
-                   (* (w_1 p) (Y↑1 p) (((partial 1) X↑1) p))
-                   (* (w_1 p) (Y↑2 p) (((partial 2) X↑1) p))
+        (is (= '(+ (* (w_2 p) (Y↑2 p) (((partial 2) X↑2) p))
                    (* (w_2 p) (Y↑1 p) (((partial 1) X↑2) p))
-                   (* (w_2 p) (Y↑2 p) (((partial 2) X↑2) p))
-                   (* (X↑1 p) (Y↑1 p) (((partial 1) w_1) p))
-                   (* (X↑1 p) (Y↑2 p) (((partial 1) w_2) p))
-                   (* (X↑2 p) (Y↑1 p) (((partial 2) w_1) p))
-                   (* (X↑2 p) (Y↑2 p) (((partial 2) w_2) p)))
+                   (* (w_2 p) (Y↑0 p) (((partial 0) X↑2) p))
+                   (* (Y↑2 p) (((partial 0) w_2) p) (X↑0 p))
+                   (* (Y↑2 p) (w_1 p) (((partial 2) X↑1) p))
+                   (* (Y↑2 p) (w_0 p) (((partial 2) X↑0) p))
+                   (* (Y↑2 p) (((partial 1) w_2) p) (X↑1 p))
+                   (* (Y↑2 p) (((partial 2) w_2) p) (X↑2 p))
+                   (* (Y↑1 p) (X↑0 p) (((partial 0) w_1) p))
+                   (* (Y↑1 p) (w_1 p) (((partial 1) X↑1) p))
+                   (* (Y↑1 p) (w_0 p) (((partial 1) X↑0) p))
+                   (* (Y↑1 p) (X↑1 p) (((partial 1) w_1) p))
+                   (* (Y↑1 p) (X↑2 p) (((partial 2) w_1) p))
+                   (* (Y↑0 p) (X↑0 p) (((partial 0) w_0) p))
+                   (* (Y↑0 p) (w_1 p) (((partial 0) X↑1) p))
+                   (* (Y↑0 p) (w_0 p) (((partial 0) X↑0) p))
+                   (* (Y↑0 p) (X↑1 p) (((partial 1) w_0) p))
+                   (* (Y↑0 p) (X↑2 p) (((partial 2) w_0) p)))
                (present
                 ((((g/Lie-derivative X) w) Y) R3-rect-point))))
 
@@ -92,14 +92,14 @@
                       (-> (simplify expr)
                           (x/substitute '(up x0 y0) 'p)))]
 
-        (is (= '(+ (* -1 (Y↑0 p) (((partial 0) f) p) (((partial 0) X↑0) p))
-                   (* -1 (Y↑0 p) (((partial 1) f) p) (((partial 0) X↑1) p))
-                   (* (((partial 0) f) p) (X↑1 p) (((partial 1) Y↑0) p))
-                   (* (((partial 0) f) p) (((partial 0) Y↑0) p) (X↑0 p))
-                   (* -1 (((partial 0) f) p) (Y↑1 p) (((partial 1) X↑0) p))
-                   (* (X↑1 p) (((partial 1) f) p) (((partial 1) Y↑1) p))
-                   (* (((partial 1) f) p) (X↑0 p) (((partial 0) Y↑1) p))
-                   (* -1 (((partial 1) f) p) (Y↑1 p) (((partial 1) X↑1) p)))
+        (is (= '(+ (* (((partial 1) f) p) (((partial 0) Y↑1) p) (X↑0 p))
+                   (* -1 (((partial 1) f) p) (Y↑1 p) (((partial 1) X↑1) p))
+                   (* -1 (((partial 1) f) p) (Y↑0 p) (((partial 0) X↑1) p))
+                   (* (((partial 1) f) p) (((partial 1) Y↑1) p) (X↑1 p))
+                   (* (X↑0 p) (((partial 0) f) p) (((partial 0) Y↑0) p))
+                   (* -1 (Y↑1 p) (((partial 0) f) p) (((partial 1) X↑0) p))
+                   (* -1 (Y↑0 p) (((partial 0) f) p) (((partial 0) X↑0) p))
+                   (* (X↑1 p) (((partial 0) f) p) (((partial 1) Y↑0) p)))
                (present
                 ((((g/Lie-derivative X) Y) f) R2-rect-point))))
 
@@ -114,7 +114,7 @@
 
         ;; we only need linear terms in phi_t(x)
 
-;; Perhaps
+        ;; Perhaps
 
         ;; phi_t(x) = (I + t v(I))(x)
 
@@ -186,14 +186,14 @@
             present (fn [expr]
                       (-> (simplify expr)
                           (x/substitute '(up q_x q_y) 'p)))]
-        (is (= '(+ (* -1 (Y↑0 p) (((partial 0) f) p) (((partial 0) X↑0) p))
-                   (* -1 (Y↑0 p) (((partial 1) f) p) (((partial 0) X↑1) p))
-                   (* (((partial 0) f) p) (((partial 0) Y↑0) p) (X↑0 p))
-                   (* -1 (((partial 0) f) p) (Y↑1 p) (((partial 1) X↑0) p))
-                   (* (((partial 0) f) p) (((partial 1) Y↑0) p) (X↑1 p))
-                   (* (((partial 1) f) p) (X↑0 p) (((partial 0) Y↑1) p))
+        (is (= '(+ (* (((partial 1) f) p) (((partial 0) Y↑1) p) (X↑0 p))
                    (* -1 (((partial 1) f) p) (Y↑1 p) (((partial 1) X↑1) p))
-                   (* (((partial 1) f) p) (X↑1 p) (((partial 1) Y↑1) p)))
+                   (* -1 (((partial 1) f) p) (Y↑0 p) (((partial 0) X↑1) p))
+                   (* (((partial 1) f) p) (((partial 1) Y↑1) p) (X↑1 p))
+                   (* (X↑0 p) (((partial 0) f) p) (((partial 0) Y↑0) p))
+                   (* -1 (Y↑1 p) (((partial 0) f) p) (((partial 1) X↑0) p))
+                   (* -1 (Y↑0 p) (((partial 0) f) p) (((partial 0) X↑0) p))
+                   (* (X↑1 p) (((partial 0) f) p) (((partial 1) Y↑0) p)))
                (present
                 ((D (fn [t]
                       (- ((Y f) ((phiX t) m_0))
@@ -207,7 +207,7 @@
                               ((Y (compose f (phiX t))) m_0))))
                       0)))))
 
-(is (= 0 (simplify
+        (is (= 0 (simplify
                   (- result-via-Lie
                      ((D (fn [t]
                            (- ((Y f) ((phiX t) m_0))
@@ -750,7 +750,7 @@
       (is (= '(down
                (+ (* -1 (cos (theta t)) (sin (theta t)) (expt ((D phi) t) 2))
                   (((expt D 2) theta) t))
-               (+ (* 2 (cos (theta t)) ((D theta) t) (sin (theta t)) ((D phi) t))
+               (+ (* 2 (cos (theta t)) (sin (theta t)) ((D phi) t) ((D theta) t))
                   (* (expt (sin (theta t)) 2) (((expt D 2) phi) t))))
              (g/freeze
               (simplify
@@ -813,7 +813,7 @@
           ;; So \Gammar_{\theta \theta} = -r, \Gamma\theta_{\theta \theta} = 0
           ;;
           ;; These are correct Christoffel symbols...
-)))))
+          )))))
 
 (defn CD
   "Computation of Covariant derivatives by difference quotient. [[CD]] is parallel

test/emmy/calculus/form_field_test.cljc

@@ -331,18 +331,18 @@
                   ((((g/square ff/d) (m/literal-scalar-field 'f R3-rect)) X Y)
                    R3-cyl-point))))
 
-        (is (= '(+ (* (X↑0 p) (Y↑1 p) (((partial 0) w_1) p))
-                   (* -1 (X↑0 p) (Y↑1 p) (((partial 1) w_0) p))
-                   (* (X↑0 p) (Y↑2 p) (((partial 0) w_2) p))
+        (is (= '(+ (* (X↑0 p) (Y↑2 p) (((partial 0) w_2) p))
                    (* -1 (X↑0 p) (Y↑2 p) (((partial 2) w_0) p))
-                   (* -1 (X↑1 p) (((partial 0) w_1) p) (Y↑0 p))
-                   (* (X↑1 p) (((partial 1) w_0) p) (Y↑0 p))
+                   (* (X↑0 p) (Y↑1 p) (((partial 0) w_1) p))
+                   (* -1 (X↑0 p) (Y↑1 p) (((partial 1) w_0) p))
                    (* (X↑1 p) (Y↑2 p) (((partial 1) w_2) p))
                    (* -1 (X↑1 p) (Y↑2 p) (((partial 2) w_1) p))
-                   (* -1 (X↑2 p) (Y↑1 p) (((partial 1) w_2) p))
-                   (* (X↑2 p) (Y↑1 p) (((partial 2) w_1) p))
+                   (* -1 (X↑1 p) (((partial 0) w_1) p) (Y↑0 p))
+                   (* (X↑1 p) (((partial 1) w_0) p) (Y↑0 p))
                    (* -1 (X↑2 p) (((partial 0) w_2) p) (Y↑0 p))
-                   (* (X↑2 p) (((partial 2) w_0) p) (Y↑0 p)))
+                   (* (X↑2 p) (((partial 2) w_0) p) (Y↑0 p))
+                   (* -1 (X↑2 p) (Y↑1 p) (((partial 1) w_2) p))
+                   (* (X↑2 p) (Y↑1 p) (((partial 2) w_1) p)))
                (-> (((ff/d w) X Y) R3-rect-point)
                    (simplify)
                    (x/substitute '(up x0 y0 z0) 'p))))
@@ -353,24 +353,24 @@
 	                        (ff/wedge dy dz))
                        (* (m/literal-scalar-field 'omega_2 R3-rect)
 	                        (ff/wedge dz dx)))]
-          (is (= '(+ (* (X↑0 p) (Y↑1 p) (Z↑2 p) (((partial 0) omega_1) p))
-                     (* (X↑0 p) (Y↑1 p) (Z↑2 p) (((partial 1) omega_2) p))
-                     (* (X↑0 p) (Y↑1 p) (Z↑2 p) (((partial 2) omega_0) p))
-                     (* -1 (X↑0 p) (Y↑2 p) (((partial 0) omega_1) p) (Z↑1 p))
-                     (* -1 (X↑0 p) (Y↑2 p) (((partial 1) omega_2) p) (Z↑1 p))
-                     (* -1 (X↑0 p) (Y↑2 p) (((partial 2) omega_0) p) (Z↑1 p))
+          (is (= '(+ (* -1 (X↑0 p) (Y↑2 p) (Z↑1 p) (((partial 0) omega_1) p))
+                     (* -1 (X↑0 p) (Y↑2 p) (Z↑1 p) (((partial 1) omega_2) p))
+                     (* -1 (X↑0 p) (Y↑2 p) (Z↑1 p) (((partial 2) omega_0) p))
+                     (* (X↑0 p) (Y↑1 p) (((partial 0) omega_1) p) (Z↑2 p))
+                     (* (X↑0 p) (Y↑1 p) (((partial 1) omega_2) p) (Z↑2 p))
+                     (* (X↑0 p) (Y↑1 p) (((partial 2) omega_0) p) (Z↑2 p))
                      (* (X↑1 p) (Y↑2 p) (((partial 0) omega_1) p) (Z↑0 p))
                      (* (X↑1 p) (Y↑2 p) (((partial 1) omega_2) p) (Z↑0 p))
                      (* (X↑1 p) (Y↑2 p) (((partial 2) omega_0) p) (Z↑0 p))
-                     (* -1 (X↑1 p) (Y↑0 p) (Z↑2 p) (((partial 0) omega_1) p))
-                     (* -1 (X↑1 p) (Y↑0 p) (Z↑2 p) (((partial 1) omega_2) p))
-                     (* -1 (X↑1 p) (Y↑0 p) (Z↑2 p) (((partial 2) omega_0) p))
+                     (* -1 (X↑1 p) (Y↑0 p) (((partial 0) omega_1) p) (Z↑2 p))
+                     (* -1 (X↑1 p) (Y↑0 p) (((partial 1) omega_2) p) (Z↑2 p))
+                     (* -1 (X↑1 p) (Y↑0 p) (((partial 2) omega_0) p) (Z↑2 p))
                      (* -1 (X↑2 p) (Y↑1 p) (((partial 0) omega_1) p) (Z↑0 p))
                      (* -1 (X↑2 p) (Y↑1 p) (((partial 1) omega_2) p) (Z↑0 p))
                      (* -1 (X↑2 p) (Y↑1 p) (((partial 2) omega_0) p) (Z↑0 p))
-                     (* (X↑2 p) (Y↑0 p) (((partial 0) omega_1) p) (Z↑1 p))
-                     (* (X↑2 p) (Y↑0 p) (((partial 1) omega_2) p) (Z↑1 p))
-                     (* (X↑2 p) (Y↑0 p) (((partial 2) omega_0) p) (Z↑1 p)))
+                     (* (X↑2 p) (Y↑0 p) (Z↑1 p) (((partial 0) omega_1) p))
+                     (* (X↑2 p) (Y↑0 p) (Z↑1 p) (((partial 1) omega_2) p))
+                     (* (X↑2 p) (Y↑0 p) (Z↑1 p) (((partial 2) omega_0) p)))
                  (-> (((ff/d omega) X Y Z) R3-rect-point)
                      (simplify)
                      (x/substitute '(up x0 y0 z0) 'p))))

test/emmy/calculus/map_test.cljc

@@ -90,10 +90,10 @@ and the differentials of coordinate functions."
             μ (m/literal-manifold-map 'μ R1-rect R2-rect)
             f (man/literal-manifold-function 'f R2-rect)]
 
-        (is (= '(+ (* (((partial 0) f) (up (μ↑0 τ) (μ↑1 τ)))
-                      ((D μ↑0) τ))
-                   (* (((partial 1) f) (up (μ↑0 τ) (μ↑1 τ)))
-                      ((D μ↑1) τ)))
+        (is (= '(+ (* (((partial 1) f) (up (μ↑0 τ) (μ↑1 τ)))
+                      ((D μ↑1) τ))
+                   (* (((partial 0) f) (up (μ↑0 τ) (μ↑1 τ)))
+                      ((D μ↑0) τ)))
                (simplify
                 ((((m/differential μ) d:dt) f)
                  ((man/point R1-rect) 'τ)))))
@@ -120,10 +120,10 @@ and the differentials of coordinate functions."
 
           ;; "However, if we kludge the correct argument it gives the expected
           ;; answer."
-          (is (= '(/ (+ (* ((D μ↑0) τ) (e1↑1 (up x0 y0)))
-                        (* -1 ((D μ↑1) τ) (e1↑0 (up x0 y0))))
-                     (+ (* (e1↑1 (up x0 y0)) (e0↑0 (up x0 y0)))
-                        (* -1 (e1↑0 (up x0 y0)) (e0↑1 (up x0 y0)))))
+          (is (= '(/ (+ (* -1 ((D μ↑1) τ) (e1↑0 (up x0 y0)))
+                        (* ((D μ↑0) τ) (e1↑1 (up x0 y0))))
+                     (+ (* -1 (e1↑0 (up x0 y0)) (e0↑1 (up x0 y0)))
+                        (* (e1↑1 (up x0 y0)) (e0↑0 (up x0 y0)))))
                  (simplify
                   (((nth edual 0)
                     (vf/procedure->vector-field
@@ -142,8 +142,8 @@ and the differentials of coordinate functions."
                          (man/chart R1-rect))
             f (f/compose (af/literal-function 'f '(-> (UP Real Real) Real))
                          (man/chart S2-spherical))]
-        (is (= '(+ (* (((partial 0) f) (up (θ τ) (φ τ))) ((D θ) τ))
-                   (* (((partial 1) f) (up (θ τ) (φ τ))) ((D φ) τ)))
+        (is (= '(+ (* (((partial 1) f) (up (θ τ) (φ τ))) ((D φ) τ))
+                   (* (((partial 0) f) (up (θ τ) (φ τ))) ((D θ) τ)))
                (simplify ((((m/differential μ) d:dt) f)
                           ((man/point R1-rect) 'τ)))))