write a routine in rust to calculate the crosscorrelation of to vectors
Sure! To calculate the cross-correlation of two vectors in Rust, you can follow these steps:
1. Define the function that takes two slices of floats (the vectors) as input.
2. Compute the cross-correlation by shifting one vector over the other and calculating the dot product for each shift.
Below is a simple implementation of this idea in Rust:
```rust
/// Calculates the cross-correlation of two vectors.
fn cross_correlation(x: &[f64], y: &[f64]) -> Vec<f64> {
let len_x = x.len();
let len_y = y.len();
let len_cc = len_x + len_y - 1; // length of the cross-correlation result
let mut cc = vec![0.0; len_cc];
// Shift x and compute dot products
for lag in 0..len_cc {
// For each lag value, compute the dot product
let mut sum = 0.0;
for i in 0..len_x {
let j = lag as isize - i as isize; // calculate the corresponding index in y
if j >= 0 && j < len_y as isize {
sum += x[i] * y[j as usize];
}
}
cc[lag] = sum;
}
cc
}
fn main() {
let x = vec![1.0, 2.0, 3.0];
let y = vec![0.5, 1.5];
let result = cross_correlation(&x, &y);
println!("Cross-correlation: {:?}", result);
}
```
### Explanation:
- The `cross_correlation` function takes two slices of `f64` representing the input vectors `x` and `y`.
- The length of the resulting cross-correlation vector is computed as the sum of the lengths of the two input vectors minus one.
- The outer loop iterates over the possible lag indices, while the inner loop computes the dot product for the current lag. The corresponding index in `y` is calculated based on the current index of `x` and the lag.
- Finally, the resulting cross-correlation vector is printed in the `main` function.
### Example Usage:
You can run the program and see the output, which shows the cross-correlation of the two sample vectors.
This is a straightforward implementation, and you may consider optimizing it further if performance becomes a concern, especially for larger vectors.