Merge branch 'features/spline' into dev

Author: Axect

src/numerical/spline.rs

@@ -194,9 +194,15 @@
 //! }
 //! ```
 //!
+//! # B-Spline (incomplete)
+//!
+//! - `UnitCubicBasis`: Single cubic B-Spline basis function
+//! - `CubicBSplineBases`: Uniform Cubic B-Spline basis functions
+//!
 //! # References
 //!
-//! * Gary D. Knott, *Interpolating Splines*, Birkhäuser Boston, MA, (2000).
+//! - Gary D. Knott, *Interpolating Splines*, Birkhäuser Boston, MA, (2000).
+/// - [Wikipedia - Irwin-Hall distribution](https://en.wikipedia.org/wiki/Irwin%E2%80%93Hall_distribution#Special_cases)
 
 use self::SplineError::{NotEnoughNodes, NotEqualNodes, NotEqualSlopes, RedundantNodeX};
 #[allow(unused_imports)]
@@ -843,3 +849,141 @@ fn quadratic_slopes(x: &[f64], y: &[f64]) -> Result<Vec<f64>> {
 
     Ok(m)
 }
+
+// =============================================================================
+// B-Spline
+// =============================================================================
+/// Unit Cubic Basis Function
+///
+/// # Description
+/// Unit cubic basis function from Irwin-Hall distribution (n=4).
+/// For general interval, we substitute t = 4 * (x - a) / (b - a).
+///
+/// # Reference
+/// [Wikipedia](https://en.wikipedia.org/wiki/Irwin%E2%80%93Hall_distribution#Special_cases)
+#[derive(Debug, Copy, Clone)]
+#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
+pub struct UnitCubicBasis {
+    pub x_min: f64,
+    pub x_max: f64,
+    pub scale: f64,
+}
+
+impl UnitCubicBasis {
+    pub fn new(x_min: f64, x_max: f64, scale: f64) -> Self {
+        Self { x_min, x_max, scale }
+    }
+
+    pub fn eval(&self, x: f64) -> f64 {
+        let t = 4f64 * (x - self.x_min) / (self.x_max - self.x_min);
+
+        let result = if (0f64..1f64).contains(&t) {
+            t.powi(3) / 6f64
+        } else if (1f64..2f64).contains(&t) {
+            (-3f64 * t.powi(3) + 12f64 * t.powi(2) - 12f64 * t + 4f64) / 6f64
+        } else if (2f64..3f64).contains(&t) {
+            (3f64 * t.powi(3) - 24f64 * t.powi(2) + 60f64 * t - 44f64) / 6f64
+        } else if (3f64..4f64).contains(&t) {
+            (4f64 - t).powi(3) / 6f64
+        } else {
+            0f64
+        };
+
+        self.scale * result
+    }
+
+    pub fn eval_vec(&self, x: &[f64]) -> Vec<f64> {
+        x.iter().map(|x| self.eval(*x)).collect()
+    }
+}
+
+/// Uniform Cubic B-Spline basis functions
+///
+/// # Example
+///
+/// ```rust
+/// use peroxide::fuga::*;
+/// use core::ops::Range;
+/// 
+/// # #[allow(unused_variables)]
+/// fn main() -> anyhow::Result<()> {
+///     let cubic_b_spline = CubicBSplineBases::from_interval((0f64, 1f64), 5);
+///     let x = linspace(0f64, 1f64, 1000);
+///     let y = cubic_b_spline.eval_vec(&x);
+/// 
+/// #   #[cfg(feature = "plot")] {
+///     let mut plt = Plot2D::new();
+///     plt.set_domain(x.clone());
+/// 
+///     for basis in &cubic_b_spline.bases {
+///         plt.insert_image(basis.eval_vec(&x));
+///     }
+///
+///     plt
+///         .insert_image(y)
+///         .set_xlabel(r"$x$")
+///         .set_ylabel(r"$y$")
+///         .set_style(PlotStyle::Nature)
+///         .tight_layout()
+///         .set_dpi(600)
+///         .set_path("example_data/cubic_b_spline.png")
+///         .savefig()?;
+/// #   }
+///     Ok(())
+/// }
+/// ```
+#[derive(Debug, Clone)]
+#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
+pub struct CubicBSplineBases {
+    pub ranges: Vec<Range<f64>>,
+    pub bases: Vec<UnitCubicBasis>,
+}
+
+impl CubicBSplineBases {
+    /// Create new Cubic B-Spline basis functions
+    pub fn new(ranges: Vec<Range<f64>>, bases: Vec<UnitCubicBasis>) -> Self {
+        Self { ranges, bases }
+    }
+
+    /// Create new Cubic B-Spline basis functions for `[a, b]`
+    pub fn from_interval((a, b): (f64, f64), num_bases: usize) -> Self {
+        let nodes = linspace(a, b, num_bases + 4);
+        let (ranges, bases) = nodes
+            .iter()
+            .zip(nodes.iter().skip(4))
+            .map(|(a, b)| (Range { start: *a, end: *b }, UnitCubicBasis::new(*a, *b, 1f64)))
+            .unzip();
+        
+        Self::new(ranges, bases)
+    }
+
+    /// Rescale all basis functions
+    ///
+    /// # Arguments
+    /// - `scale_vec` - scale vector
+    pub fn rescale(&mut self, scale_vec: &[f64]) -> Result<()> {
+        if scale_vec.len() != self.bases.len() {
+            bail!("The number of scales should be equal to the number of basis functions");
+        }
+
+        for (basis, scale) in self.bases.iter_mut().zip(scale_vec) {
+            basis.scale = *scale;
+        }
+
+        Ok(())
+    }
+
+    pub fn eval(&self, x: f64) -> f64 {
+        self.ranges.iter()
+            .enumerate()
+            .filter(|(_, range)| range.contains(&x))
+            .fold(0f64, |acc, (i, _)| {
+                let basis = &self.bases[i];
+                acc + basis.eval(x)
+            })
+    }
+
+    pub fn eval_vec(&self, x: &[f64]) -> Vec<f64> {
+        x.iter().map(|x| self.eval(*x)).collect()
+    }
+}