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.