Merge branch '35-support-complex-number' into dev (#35)

Cargo.toml

@@ -10,7 +10,14 @@ categories = ["science"]
 readme = "README.md"
 documentation = "https://axect.github.io/Peroxide_Doc"
 keywords = ["Numeric", "Science", "Dataframe", "Plot", "LinearAlgebra"]
-exclude = ["example_data/", "src/bin/", "benches/", "example/", "test_data/", "peroxide-ad2"]
+exclude = [
+    "example_data/",
+    "src/bin/",
+    "benches/",
+    "example/",
+    "test_data/",
+    "peroxide-ad2",
+]
 
 [badges]
 travis-ci = { repository = "axect/peroxide" }
@@ -32,17 +39,26 @@ anyhow = "1.0"
 paste = "1.0"
 #num-complex = "0.3"
 netcdf = { version = "0.7", optional = true, default-features = false }
-pyo3 = { version = "0.22", optional = true, features = ["auto-initialize", "gil-refs"] }
+pyo3 = { version = "0.22", optional = true, features = [
+    "auto-initialize",
+    "gil-refs",
+] }
 blas = { version = "0.22", optional = true }
 lapack = { version = "0.19", optional = true }
 serde = { version = "1.0", features = ["derive"], optional = true }
 json = { version = "0.12", optional = true }
-arrow2 = { version = "0.18", features = ["io_parquet", "io_parquet_compression"], optional = true }
+arrow2 = { version = "0.18", features = [
+    "io_parquet",
+    "io_parquet_compression",
+], optional = true }
 num-complex = { version = "0.4", optional = true }
-lambert_w = { version = "0.4.0", default-features = false, features = ["24bits", "50bits"] }
+lambert_w = { version = "0.4.0", default-features = false, features = [
+    "24bits",
+    "50bits",
+] }
 
 [package.metadata.docs.rs]
-rustdoc-args = [ "--html-in-header", "katex-header.html", "--cfg", "docsrs"]
+rustdoc-args = ["--html-in-header", "katex-header.html", "--cfg", "docsrs"]
 
 [features]
 default = []

src/complex/integral.rs

@@ -0,0 +1,53 @@
+use crate::complex::C64;
+use crate::numerical::integral::{GKIntegrable, GLKIntegrable, NCIntegrable};
+use crate::structure::polynomial::{lagrange_polynomial, Calculus, Polynomial};
+
+// Newton Cotes Quadrature for Complex Functions of one Real Variable
+impl NCIntegrable for C64 {
+    type NodeY = (Vec<f64>, Vec<f64>);
+    type NCPolynomial = (Polynomial, Polynomial);
+
+    fn compute_node_y<F>(f: F, node_x: &[f64]) -> Self::NodeY
+    where
+        F: Fn(f64) -> Self,
+    {
+        node_x
+            .iter()
+            .map(|x| {
+                let z = f(*x);
+                (z.re, z.im)
+            })
+            .unzip()
+    }
+
+    fn compute_polynomial(node_x: &[f64], node_y: &Self::NodeY) -> Self::NCPolynomial {
+        (
+            lagrange_polynomial(node_x.to_vec(), node_y.0.to_vec()),
+            lagrange_polynomial(node_x.to_vec(), node_y.1.to_vec()),
+        )
+    }
+
+    fn integrate_polynomial(p: &Self::NCPolynomial) -> Self::NCPolynomial {
+        (p.0.integral(), p.1.integral())
+    }
+
+    fn evaluate_polynomial(p: &Self::NCPolynomial, x: f64) -> Self {
+        p.0.eval(x) + C64::I * p.1.eval(x)
+    }
+}
+
+// Gauss Lagrange and Kronrod Quadrature for Complex Functions of one Real Variable
+impl GLKIntegrable for C64 {
+    const ZERO: Self = C64::ZERO;
+}
+
+// Gauss Kronrod Quadrature for Complex Functions of one Real Variable
+impl GKIntegrable for C64 {
+    fn is_finite(&self) -> bool {
+        C64::is_finite(*self)
+    }
+
+    fn gk_norm(&self) -> f64 {
+        self.norm()
+    }
+}