Update interpolation method and handle insufficient points error

The interpolation method used in qlab-math has been updated to handle cases where there are insufficient points for interpolation, returning an error. Also, the interpolation method used in yield curve calculation within the calculate_bond test has been changed from Linear to Natural Cubic. These changes enhance the accuracy and reliability of the calculations.

crates/qlab-math/src/interpolation.rs

@@ -76,11 +76,17 @@ fn find_index_at_left_boundary<V: PartialOrd>(
     points: &[impl X<V>],
     x: V,
 ) -> Result<usize, InterpolationError<V>> {
+    if points.is_empty() {
+        return Err(InterpolationError::InsufficientPointsError(points.len()));
+    }
     let pos = points.partition_point(|point| *point.x() < x);
+    if pos.is_zero() && *points.iter().next().unwrap().x() <= x {
+        return Ok(0);
+    }
     if pos.is_zero() {
         return Err(InterpolationError::OutOfLowerBound(x));
     }
-    if pos > points.len() {
+    if pos == points.len() {
         return Err(InterpolationError::OutOfUpperBound(x));
     }
     Ok(pos - 1)

crates/qlab/tests/calculate_bond.rs

@@ -1,5 +1,5 @@
 use qlab_instrument::bond::Bond;
-use qlab_math::interpolation::linear::Linear;
+use qlab_math::interpolation::spline::natural_cubic::NaturalCubic;
 use qlab_termstructure::yield_curve::YieldCurve;
 use qlab_time::date::Date;
 use qlab_time::day_count::act_365::Act365;
@@ -44,11 +44,11 @@ fn main() {
     let spot_yields: Vec<f64> = vec![
         0.02, 0.0219, 0.0237, 0.0267, 0.0312, 0.0343, 0.0378, 0.0393, 0.04, 0.0401, 0.0401, 0.04,
     ];
-    let yield_curve: YieldCurve<Act365, _, Linear<f64>> =
+    let yield_curve: YieldCurve<Act365, _, NaturalCubic<f64>> =
         YieldCurve::new(spot_settle_date, &maturities, &spot_yields).unwrap();
     let val = bond_20_yr
         .discounted_value(spot_settle_date, &yield_curve)
         .unwrap();
     println!("{}", bond_20_yr.bond_id());
-    println!("{val}"); // 1314.934419206669
+    println!("{val}"); // 1314.5664389486494
 }