start cubic init

Author: kylecarow

src/one/strategies.rs

@@ -36,6 +36,29 @@ where
     }
 }
 
+impl<D> Strategy1D<D> for Cubic<D::Elem>
+where
+    D: Data + RawDataClone + Clone,
+    D::Elem: Num + PartialOrd + Copy + Default + Debug,
+{
+    fn init(&self, data: &InterpData1D<D>) -> Result<(), ValidateError> {
+        Ok(())
+    }
+
+    fn interpolate(
+        &self,
+        data: &InterpData1D<D>,
+        point: &[<D>::Elem; 1],
+    ) -> Result<<D>::Elem, InterpolateError> {
+        todo!()
+    }
+
+    /// Returns `true`
+    fn allow_extrapolate(&self) -> bool {
+        true
+    }
+}
+
 impl<D> Strategy1D<D> for Nearest
 where
     D: Data + RawDataClone + Clone,

src/strategy.rs

@@ -207,14 +207,47 @@ pub fn find_nearest_index<T: PartialOrd>(arr: ArrayView1<T>, target: &T) -> usiz
 #[cfg_attr(feature = "serde", derive(Deserialize, Serialize))]
 pub struct Linear;
 
-// TODO: `pub struct Quadratic;`
-// Maybe `pub struct Polynomial(usize);` as well?
-// with `pub type Quadratic = Polynomial(2)` and `pub type Cubic = Polynomial(3)`
-
 /// Cubic spline interpolation: TODO
-#[derive(Debug, Clone, PartialEq)]
+#[derive(Clone, Debug, Default, PartialEq)]
 #[cfg_attr(feature = "serde", derive(Deserialize, Serialize))]
-pub struct Cubic;
+pub struct Cubic<T: Default> {
+    pub boundary_cond: CubicBC<T>,
+    pub coeffs: ArrayD<T>,
+}
+
+impl<T> Cubic<T>
+where
+    T: Default,
+{
+    pub fn new(bc: CubicBC<T>) -> Self {
+        Self {
+            boundary_cond: bc,
+            coeffs: <ArrayD<T> as Default>::default(),
+        }
+    }
+    pub fn solve_coeffs(&mut self) {
+        match &self.boundary_cond {
+            CubicBC::Natural => {
+                todo!()
+            }
+            _ => todo!(),
+        }
+    }
+}
+
+/// Cubic boundary conditions.
+#[derive(Copy, Clone, Debug, Default, PartialEq)]
+pub enum CubicBC<T> {
+    /// Second derivatives at endpoints are 0, thus extrapolation is linear.
+    // https://www.math.ntnu.no/emner/TMA4215/2008h/cubicsplines.pdf
+    #[default]
+    Natural,
+    /// Specific first derivatives at endpoints.
+    Clamped(T, T),
+    NotAKnot,
+    // https://math.ou.edu/~npetrov/project-5093-s11.pdf
+    Periodic,
+}
 
 /// Nearest value interpolation: <https://en.wikipedia.org/wiki/Nearest-neighbor_interpolation>
 ///