revDeriv for HMul.hMul

lecopivo · Nov 27, 2023 · f99275d · f99275d
1 parent 231672c
commit f99275d
Showing 1 changed file with 65 additions and 0 deletions.
diff --git a/SciLean/Core/FunctionTransformations/RevDeriv.lean b/SciLean/Core/FunctionTransformations/RevDeriv.lean
@@ -1247,3 +1247,68 @@ theorem Neg.neg.arg_a0.revDerivProjUpdate_rule
       (-ydf.1, fun i dy dx => ydf.2 i (-dy) dx) :=
 by 
   unfold revDerivProjUpdate; ftrans
+
+
+-- HMul.hmul -------------------------------------------------------------------
+--------------------------------------------------------------------------------
+open ComplexConjugate
+
+@[ftrans]
+theorem HMul.hMul.arg_a0a1.revDeriv_rule
+  (f g : X → K)
+  (hf : HasAdjDiff K f) (hg : HasAdjDiff K g)
+  : (revDeriv K fun x => f x * g x)
+    =
+    fun x => 
+      let ydf := revDerivUpdate K f x
+      let zdg := revDeriv K g x
+      (ydf.1 * zdg.1, fun dx' => (ydf.2 (conj zdg.1 * dx') (zdg.2 (conj ydf.1 * dx')))) :=
+by 
+  have ⟨_,_⟩ := hf
+  have ⟨_,_⟩ := hg
+  unfold revDerivUpdate; unfold revDeriv; simp; ftrans; ftrans;
+  simp [smul_push]
+
+@[ftrans]
+theorem HMul.hMul.arg_a0a1.revDerivUpdate_rule
+  (f g : X → K)
+  (hf : HasAdjDiff K f) (hg : HasAdjDiff K g)
+  : (revDerivUpdate K fun x => f x * g x)
+    =
+    fun x => 
+      let ydf := revDerivUpdate K f x
+      let zdg := revDerivUpdate K g x
+      (ydf.1 * zdg.1, fun dx' dx => (ydf.2 (conj zdg.1 * dx') (zdg.2 (conj ydf.1 * dx') dx))) :=
+by 
+  have ⟨_,_⟩ := hf
+  have ⟨_,_⟩ := hg
+  unfold revDerivUpdate; unfold revDeriv; simp; ftrans; ftrans;
+  simp [smul_push,add_assoc]
+
+@[ftrans]
+theorem HMul.hMul.arg_a0a1.revDerivProj_rule
+  (f g : X → K)
+  (hf : HasAdjDiff K f) (hg : HasAdjDiff K g)
+  : (revDerivProj K fun x => f x * g x)
+    =
+    fun x => 
+      let ydf := revDerivUpdate K f x
+      let zdg := revDeriv K g x
+      (ydf.1 * zdg.1, fun _ dy => ydf.2 ((conj zdg.1)*dy) (zdg.2 (conj ydf.1* dy))) :=
+by 
+  unfold revDerivProj
+  ftrans; simp[StructLike.oneHot, StructLike.make]
+
+@[ftrans]
+theorem HMul.hMul.arg_a0a1.revDerivProjUpdate_rule
+  (f g : X → K)
+  (hf : HasAdjDiff K f) (hg : HasAdjDiff K g)
+  : (revDerivProjUpdate K fun x => f x * g x)
+    =
+    fun x => 
+      let ydf := revDerivUpdate K f x
+      let zdg := revDerivUpdate K g x
+      (ydf.1 * zdg.1, fun _ dy dx => ydf.2 ((conj zdg.1)*dy) (zdg.2 (conj ydf.1* dy) dx)) :=
+by 
+  unfold revDerivProjUpdate
+  ftrans; simp[revDerivUpdate,add_assoc]