Add DFT

.gitignore

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+/target
+Cargo.lock

Cargo.toml

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+[package]
+name = "fft-rs"
+version = "0.1.0"
+authors = ["arnaucube <root@arnaucube.com>"]
+edition = "2018"
+
+# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
+
+[dependencies]
+rand = "0.7.3"
+num = "0.3.0"
+num-complex= "0.3"
+
+[dev-dependencies]
+criterion = "0.3"
+
+[[bench]]
+name = "bench_fft"
+harness = false

src/lib.rs

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+use num::complex::{Complex, Complex64};
+use std::f64::consts::PI;
+
+// dft computes the Discrete Fourier Transform
+pub fn dft(x: &Vec<f64>) -> Vec<Complex64> {
+    let mut x_compl: Vec<Complex64> = vec![Complex::new(0_f64, 0_f64); x.len()];
+    for i in 0..x.len() {
+        x_compl[i] = Complex::new(x[i], 0_f64);
+    }
+
+    let mut w = Complex::new(0_f64, -2_f64 * PI / x.len() as f64);
+
+    // f_k = SUM{n=0, N-1} f_n * e^(-j2pi*k*n)/N
+    // https://en.wikipedia.org/wiki/Discrete_Fourier_transform
+    let mut f: Vec<Vec<Complex64>> = Vec::new();
+    for i in 0..x.len() {
+        let mut f_k: Vec<Complex64> = Vec::new();
+        for j in 0..x.len() {
+            let i_compl = Complex::new(0_f64, i as f64);
+            let j_compl = Complex::new(0_f64, j as f64);
+            let fe = (w * i_compl * j_compl).exp();
+            f_k.push(fe);
+        }
+        f.push(f_k.clone());
+    }
+    let r = mul_vv(f, x_compl);
+    r
+}
+
+// mul_vv multiplies a Matrix by a Vector
+fn mul_vv(a: Vec<Vec<Complex64>>, b: Vec<Complex64>) -> Vec<Complex64> {
+    if a[0].len() != a.len() {
+        panic!("err b[0].len():{:?} != b.len():{:?}", a[0].len(), a.len());
+    }
+    if a.len() != b.len() {
+        panic!("err a.len():{:?} != b.len():{:?}", a.len(), b.len());
+    }
+
+    let rows = a.len();
+    let cols = a.len();
+
+    let mut c: Vec<Complex64> = vec![Complex::new(0_f64, 0_f64); cols];
+    for i in 0..rows {
+        for j in 0..cols {
+            c[i] += a[i][j] * b[j];
+        }
+    }
+    c
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_dft_simple_values() {
+        let values: Vec<f64> = vec![0.2, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8];
+        let r = dft(&values);
+        assert_eq!(r.len(), 8);
+
+        assert_eq!(format!("{:.2}", r[0]), "3.70+0.00i");
+        assert_eq!(format!("{:.2}", r[1]), "-0.30-0.97i");
+        assert_eq!(format!("{:.2}", r[2]), "-0.30-0.40i");
+        assert_eq!(format!("{:.2}", r[3]), "-0.30-0.17i");
+        assert_eq!(format!("{:.2}", r[4]), "-0.30+0.00i");
+    }
+}