# HG changeset patch
# User Tuomo Valkonen <tuomov@iki.fi>
# Date 1730905206 18000
# Node ID ad68dacabe4f49e7bd17ce07c4cd64af829090d9
# Parent  a6efe0fafd902344e1991c1c9c528e629a6e7388
Implement prox for DistTo

diff -r a6efe0fafd90 -r ad68dacabe4f src/dist.rs
--- a/src/dist.rs	Fri Oct 25 13:16:25 2024 -0500
+++ b/src/dist.rs	Wed Nov 06 10:00:06 2024 -0500
@@ -3,8 +3,9 @@
 */
 
 use alg_tools::mapping::Apply;
+use alg_tools::euclidean::Euclidean;
 use crate::manifold::ManifoldPoint;
-use crate::fb::{Grad, Desc};
+use crate::fb::{Grad, Desc, Prox};
 
 /// Structure for distance-to functions
 pub struct DistTo<M : ManifoldPoint>(pub M);
@@ -58,3 +59,16 @@
        x.log(&self.0)
     }
 }
+
+impl<M : ManifoldPoint> Prox<M> for DistTo<M> {
+    /// This is proximal map is a type of soft-thresholding on manifolds.
+    fn prox(&self, τ : f64, x : M) -> M {
+        let v = x.log(&self.0);
+        let d = v.norm2();
+        if d <= τ {
+            self.0.clone()
+        } else {
+            x.exp( &(v * (τ / d)) )
+        }
+    }
+}