Print the edge distortions

Also, tighten the convergence requirements to account for how the
softness parameter affects the loss function.

app-proto/main.css

@@ -227,6 +227,16 @@ details[open]:has(li) .element-switch::after {
   border-radius: 8px;
 }
 
+#distortion-bar {
+  display: flex;
+  margin-top: 8px;
+  gap: 8px;
+}
+
+#distortion-gauge {
+  flex-grow: 1;
+}
+
 /* display */
 
 #display {

app-proto/src/assembly.rs

@@ -3,6 +3,7 @@ use std::{
     cell::Cell,
     cmp::Ordering,
     collections::{BTreeMap, BTreeSet},
+    f64::consts::SQRT_2,
     fmt,
     fmt::{Debug, Formatter},
     hash::{Hash, Hasher},
@@ -122,6 +123,11 @@ pub trait Element: Serial + ProblemPoser + DisplayItem {
     // be used carefully to preserve invariant (1), described in the comment on
     // the `tangent` field of the `Assembly` structure
     fn set_column_index(&self, index: usize);
+    
+    /* KLUDGE */
+    fn has_distortion(&self) -> bool {
+        false
+    }
 }
 
 impl Debug for dyn Element {
@@ -334,6 +340,10 @@ impl Element for Point {
     fn set_column_index(&self, index: usize) {
         self.column_index.set(Some(index));
     }
+    
+    fn has_distortion(&self) -> bool {
+        true
+    }
 }
 
 impl Serial for Point {
@@ -357,6 +367,12 @@ pub trait Regulator: Serial + ProblemPoser + OutlineItem {
     fn subjects(&self) -> Vec<Rc<dyn Element>>;
     fn measurement(&self) -> ReadSignal<f64>;
     fn set_point(&self) -> Signal<SpecifiedValue>;
+    fn soft(&self) -> Option<Signal<bool>> {
+        None
+    }
+    fn distortion(&self) -> Option<ReadSignal<f64>> { /* KLUDGE */
+        None
+    }
 }
 
 impl Hash for dyn Regulator {
@@ -389,6 +405,8 @@ pub struct InversiveDistanceRegulator {
     pub subjects: [Rc<dyn Element>; 2],
     pub measurement: ReadSignal<f64>,
     pub set_point: Signal<SpecifiedValue>,
+    pub soft: Signal<bool>,
+    distortion: Option<ReadSignal<f64>>, /* KLUDGE */
     serial: u64,
 }
 
@@ -404,9 +422,24 @@ impl InversiveDistanceRegulator {
         });
         
         let set_point = create_signal(SpecifiedValue::from_empty_spec());
+        let distortion = if subjects.iter().all(|subj| subj.has_distortion()) {
+            Some(create_memo(move || {
+                let set_point_opt = set_point.with(|set_pt| set_pt.value);
+                let measurement_val = measurement.get();
+                match set_point_opt {
+                    None => 0.0,
+                    Some(set_point_val) => SQRT_2 * (
+                        (-measurement_val).sqrt() - (-set_point_val).sqrt()
+                    ),
+                }
+            }))
+        } else {
+            None
+        };
+        let soft = create_signal(false);
         let serial = Self::next_serial();
         
-        Self { subjects, measurement, set_point, serial }
+        Self { subjects, measurement, set_point, soft, distortion, serial }
     }
 }
 
@@ -422,6 +455,14 @@ impl Regulator for InversiveDistanceRegulator {
     fn set_point(&self) -> Signal<SpecifiedValue> {
         self.set_point
     }
+    
+    fn soft(&self) -> Option<Signal<bool>> {
+        Some(self.soft)
+    }
+    
+    fn distortion(&self) -> Option<ReadSignal<f64>> {
+        self.distortion
+    }
 }
 
 impl Serial for InversiveDistanceRegulator {
@@ -432,6 +473,7 @@ impl Serial for InversiveDistanceRegulator {
 
 impl ProblemPoser for InversiveDistanceRegulator {
     fn pose(&self, problem: &mut ConstraintProblem) {
+        let soft = self.soft.get_untracked();
         self.set_point.with_untracked(|set_pt| {
             if let Some(val) = set_pt.value {
                 let [row, col] = self.subjects.each_ref().map(
@@ -439,7 +481,11 @@ impl ProblemPoser for InversiveDistanceRegulator {
                         "Subjects should be indexed before inversive distance regulator writes problem data"
                     )
                 );
-                problem.gram.push_sym(row, col, val);
+                if soft {
+                    problem.soft.push_sym(row, col, val);
+                } else {
+                    problem.gram.push_sym(row, col, val);
+                }
             }
         });
     }
@@ -705,7 +751,7 @@ impl Assembly {
         
         // look for a configuration with the given Gram matrix
         let Realization { result, history } = realize_gram(
-            &problem, 1.0e-12, 0.5, 0.9, 1.1, 200, 110
+            &problem, 1.0e-20, 0.5, 0.9, 1.1, 400, 110
         );
         
         /* DEBUG */

app-proto/src/components/diagnostics.rs

@@ -111,6 +111,80 @@ fn StepInput() -> View {
     }
 }
 
+#[component]
+fn DistortionGauge() -> View {
+    let state = use_context::<AppState>();
+    let total_distortion = create_memo(move || {
+        state.assembly.regulators.with(|regs| {
+            let mut total = 0.0;
+            for reg in regs {
+                if let Some(distortion) = reg.distortion() {
+                    total += distortion.get().abs();
+                }
+            }
+            total
+        })
+    });
+    
+    view! {
+        div(id = "distortion-gauge") {
+            "Distortion: " (total_distortion.with(|distort| distort.to_string()))
+        }
+    }
+}
+
+#[component]
+fn DistortionPrintButton() -> View {
+    view! {
+        button(
+            on:click = |_| {
+                let state = use_context::<AppState>();
+                let mut hard_distortion_table = String::new();
+                let mut soft_distortion_table = String::new();
+                let mut highest_distortion = f64::NEG_INFINITY;
+                let mut lowest_distortion = f64::INFINITY;
+                let mut largest_hard_distortion = f64::NEG_INFINITY;
+                state.assembly.regulators.with_untracked(|regs| {
+                    for reg in regs {
+                        if let Some(distortion) = reg.distortion() {
+                            let distortion_val = distortion.get();
+                            let subjects = reg.subjects();
+                            let distortion_line = format!(
+                                "{}, {}: {distortion_val}\n",
+                                subjects[0].id(),
+                                subjects[1].id(),
+                            );
+                            match reg.soft() {
+                                Some(soft) if soft.get() => {
+                                    soft_distortion_table += &distortion_line;
+                                    highest_distortion = highest_distortion.max(distortion_val);
+                                    lowest_distortion = lowest_distortion.min(distortion_val);
+                                },
+                                _ => {
+                                    hard_distortion_table += &distortion_line;
+                                    largest_hard_distortion = largest_hard_distortion.max(distortion_val.abs());
+                                }
+                            };
+                        }
+                    }
+                });
+                console_log!("\
+                    === Distortions of flexible edges (for labels) ===\n\n\
+                    --- Range ---\n\n\
+                    Highest: {highest_distortion}\n\
+                    Lowest: {lowest_distortion}\n\n\
+                    --- Table ---\n\n{soft_distortion_table}\n\
+                    === Distortions of rigid edges (for validation) ===\n\n\
+                    These values should be small relative to the ones for the flexible edges\n\n\
+                    --- Range ---\n\n\
+                    Largest absolute: {largest_hard_distortion}\n\n\
+                    --- Table ---\n\n{hard_distortion_table}\
+                ");
+            },
+        ) { "Print" }
+    }
+}
+
 fn into_log10_time_point((step, value): (usize, f64)) -> Vec<Option<f64>> {
     vec![
         Some(step as f64),
@@ -315,6 +389,10 @@ pub fn Diagnostics() -> View {
             }
             DiagnosticsPanel(name = "loss") { LossHistory {} }
             DiagnosticsPanel(name = "spectrum") { SpectrumHistory {} }
+            div(id = "distortion-bar") {
+                DistortionGauge {}
+                DistortionPrintButton {}
+            }
         }
     }
 }

app-proto/src/components/display.rs

@@ -597,16 +597,16 @@ pub fn Display() -> View {
                 |status| status.is_ok()
             );
             let step_val = state.assembly.step.with_untracked(|step| step.value);
-            let on_init_step = step_val.is_some_and(|n| n == 0.0);
             let on_last_step = step_val.is_some_and(
                 |n| state.assembly.descent_history.with_untracked(
                     |history| n as usize + 1 == history.config.len().max(1)
                 )
             );
-            let on_manipulable_step =
-                !realization_successful && on_init_step
-                || realization_successful && on_last_step;
-            if on_manipulable_step && state.selection.with(|sel| sel.len() == 1) {
+            if
+                state.selection.with(|sel| sel.len() == 1)
+                && realization_successful
+                && on_last_step
+            {
                 let sel = state.selection.with(
                     |sel| sel.into_iter().next().unwrap().clone()
                 );

app-proto/src/engine.rs

@@ -1,6 +1,7 @@
 use lazy_static::lazy_static;
 use nalgebra::{Const, DMatrix, DVector, DVectorView, Dyn, SymmetricEigen};
 use std::fmt::{Display, Error, Formatter};
+use sycamore::prelude::console_log; /* DEBUG */
 
 // --- elements ---
 
@@ -240,6 +241,7 @@ impl DescentHistory {
 
 pub struct ConstraintProblem {
     pub gram: PartialMatrix,
+    pub soft: PartialMatrix,
     pub frozen: PartialMatrix,
     pub guess: DMatrix<f64>,
 }
@@ -249,6 +251,7 @@ impl ConstraintProblem {
         const ELEMENT_DIM: usize = 5;
         Self {
             gram: PartialMatrix::new(),
+            soft: PartialMatrix::new(),
             frozen: PartialMatrix::new(),
             guess: DMatrix::<f64>::zeros(ELEMENT_DIM, element_count),
         }
@@ -258,6 +261,7 @@ impl ConstraintProblem {
     pub fn from_guess(guess_columns: &[DVector<f64>]) -> Self {
         Self {
             gram: PartialMatrix::new(),
+            soft: PartialMatrix::new(),
             frozen: PartialMatrix::new(),
             guess: DMatrix::from_columns(guess_columns),
         }
@@ -280,14 +284,18 @@ lazy_static! {
 struct SearchState {
     config: DMatrix<f64>,
     err_proj: DMatrix<f64>,
+    loss_hard: f64,
     loss: f64,
 }
 
 impl SearchState {
-    fn from_config(gram: &PartialMatrix, config: DMatrix<f64>) -> Self {
-        let err_proj = gram.sub_proj(&(config.tr_mul(&*Q) * &config));
+    fn from_config(gram: &PartialMatrix, soft: &PartialMatrix, softness: f64, config: DMatrix<f64>) -> Self {
+        let config_gram = &(config.tr_mul(&*Q) * &config);
+        let err_proj_hard = gram.sub_proj(config_gram);
+        let err_proj = &err_proj_hard + softness * soft.sub_proj(config_gram);
+        let loss_hard = err_proj_hard.norm_squared();
         let loss = err_proj.norm_squared();
-        Self { config, err_proj, loss }
+        Self { config, err_proj, loss_hard, loss }
     }
 }
 
@@ -331,6 +339,8 @@ pub fn local_unif_to_std(v: DVectorView<f64>) -> DMatrix<f64> {
 // use backtracking line search to find a better configuration
 fn seek_better_config(
     gram: &PartialMatrix,
+    soft: &PartialMatrix,
+    softness: f64,
     state: &SearchState,
     base_step: &DMatrix<f64>,
     base_target_improvement: f64,
@@ -341,7 +351,7 @@ fn seek_better_config(
     let mut rate = 1.0;
     for backoff_steps in 0..max_backoff_steps {
         let trial_config = &state.config + rate * base_step;
-        let trial_state = SearchState::from_config(gram, trial_config);
+        let trial_state = SearchState::from_config(gram, soft, softness, trial_config);
         let improvement = state.loss - trial_state.loss;
         if improvement >= min_efficiency * rate * base_target_improvement {
             return Some((trial_state, backoff_steps));
@@ -376,7 +386,7 @@ pub fn realize_gram(
     max_backoff_steps: i32,
 ) -> Realization {
     // destructure the problem data
-    let ConstraintProblem { gram, guess, frozen } = problem;
+    let ConstraintProblem { gram, soft, guess, frozen } = problem;
     
     // start the descent history
     let mut history = DescentHistory::new();
@@ -403,13 +413,18 @@ pub fn realize_gram(
     let scale_adjustment = (gram.0.len() as f64).sqrt();
     let tol = scale_adjustment * scaled_tol;
     
+    // set up constants and variables related to minimizing the soft loss
+    const GRAD_TOL: f64 = 1e-12;
+    let mut grad_size = f64::INFINITY;
+    let mut softness = 1.0;
+    
     // convert the frozen indices to stacked format
     let frozen_stacked: Vec<usize> = frozen.into_iter().map(
         |MatrixEntry { index: (row, col), .. }| col*element_dim + row
     ).collect();
     
     // use a regularized Newton's method with backtracking
-    let mut state = SearchState::from_config(gram, frozen.freeze(guess));
+    let mut state = SearchState::from_config(gram, soft, softness, frozen.freeze(guess));
     let mut hess = DMatrix::zeros(element_dim, assembly_dim);
     for _ in 0..max_descent_steps {
         // find the negative gradient of the loss function
@@ -426,7 +441,7 @@ pub fn realize_gram(
                 let neg_d_err =
                     basis_mat.tr_mul(&*Q) * &state.config
                     + state.config.tr_mul(&*Q) * &basis_mat;
-                let neg_d_err_proj = gram.proj(&neg_d_err);
+                let neg_d_err_proj = gram.proj(&neg_d_err) + softness * soft.proj(&neg_d_err);
                 let deriv_grad = 4.0 * &*Q * (
                     -&basis_mat * &state.err_proj
                     + &state.config * &neg_d_err_proj
@@ -455,10 +470,13 @@ pub fn realize_gram(
             hess[(k, k)] = 1.0;
         }
         
-        // stop if the loss is tolerably low
+        // stop if the hard loss is tolerably low and the total loss is close to
+        // stationary. we use `neg_grad_stacked` to measure the size of the
+        // gradient because it's been projected onto the frozen subspace
         history.config.push(state.config.clone());
-        history.scaled_loss.push(state.loss / scale_adjustment);
-        if state.loss < tol { break; }
+        history.scaled_loss.push(state.loss_hard / scale_adjustment);
+        grad_size = neg_grad_stacked.norm_squared();
+        if state.loss_hard < tol && grad_size < softness * GRAD_TOL { break; }
         
         // compute the Newton step
         /* TO DO */
@@ -482,7 +500,7 @@ pub fn realize_gram(
         
         // use backtracking line search to find a better configuration
         if let Some((better_state, backoff_steps)) = seek_better_config(
-            gram, &state, &base_step, neg_grad.dot(&base_step),
+            gram, soft, softness, &state, &base_step, neg_grad.dot(&base_step),
             min_efficiency, backoff, max_backoff_steps,
         ) {
             state = better_state;
@@ -493,8 +511,18 @@ pub fn realize_gram(
                 history,
             };
         }
+        
+        // if we're near a minimum of the total loss, but the hard loss still
+        // isn't tolerably low, make the soft constraints softer
+        const SOFTNESS_BACKOFF_THRESHOLD: f64 = 1e-6;
+        const SOFTNESS_BACKOFF: f64 = 0.95;
+        if state.loss_hard >= tol && grad_size < softness * SOFTNESS_BACKOFF_THRESHOLD {
+            softness *= SOFTNESS_BACKOFF;
+            state = SearchState::from_config(gram, soft, softness, state.config);
+            console_log!("Softness decreased to {softness}");
+        }
     }
-    let result = if state.loss < tol {
+    let result = if state.loss_hard < tol && grad_size < softness * GRAD_TOL {
         // express the uniform basis in the standard basis
         const UNIFORM_DIM: usize = 4;
         let total_dim_unif = UNIFORM_DIM * assembly_dim;