# InterpN
N-dimensional interpolation/extrapolation methods, no-std and no-alloc compatible,
prioritizing correctness, performance, and compatiblity with memory-constrained environments.

# Performance Scalings
Note that for a self-consistent multidimensional linear interpolation, there are 2^ndims grid values that contribute
to each observation point, and as such, that is the theoretical floor for performance scaling. That said,
depending on the implementation, the constant term can vary by more than an order of magnitude.

Cubic interpolations require two more degrees of freedom per dimension, which results in a minimal runtime scaling of 4^ndims.
Similar to the linear methods, depending on implementation, the constant term can vary by orders of magnitude,
as can the RAM usage.

Rectilinear methods perform a bisection search to find the relevant grid cell, which takes
a worst-case number of iterations of log2(number of grid elements).

| Method                        | RAM       | Interp. / Extrap. Cost       |
|-------------------------------|-----------|------------------------------|
| multilinear::regular          | O(ndims)  | O(2^ndims)                   |
| multilinear::rectilinear      | O(ndims)  | O(2^ndims) + log2(gridsize)  |
| multicubic::regular           | O(ndims)  | O(4^ndims)                   |
| multicubic::rectilinear       | O(ndims)  | O(4^ndims) + log2(gridsize)  |

# Example: Multilinear and Multicubic w/ Regular Grid
```rust
use interpn::{multilinear, multicubic};

// Define a grid
let x = [1.0_f64, 2.0, 3.0, 4.0];
let y = [0.0_f64, 1.0, 2.0, 3.0];

// Grid input for rectilinear method
let grids = &[&x[..], &y[..]];

// Grid input for regular grid method
let dims = [x.len(), y.len()];
let starts = [x[0], y[0]];
let steps = [x[1] - x[0], y[1] - y[0]];

// Values at grid points
let z = [2.0; 16];

// Observation points to interpolate/extrapolate
let xobs = [0.0_f64, 5.0];
let yobs = [-1.0, 3.0];
let obs = [&xobs[..], &yobs[..]];

// Storage for output
let mut out = [0.0; 2];

// Do interpolation
multilinear::regular::interpn(&dims, &starts, &steps, &z, &obs, &mut out);
multicubic::regular::interpn(&dims, &starts, &steps, &z, false, &obs, &mut out);
```

# Example: Multilinear and Multicubic w/ Rectilinear Grid
```rust
use interpn::{multilinear, multicubic};

// Define a grid
let x = [1.0_f64, 2.0, 3.0, 4.0];
let y = [0.0_f64, 1.0, 2.0, 3.0];

// Grid input for rectilinear method
let grids = &[&x[..], &y[..]];

// Values at grid points
let z = [2.0; 16];

// Points to interpolate/extrapolate
let xobs = [0.0_f64, 5.0];
let yobs = [-1.0, 3.0];
let obs = [&xobs[..], &yobs[..]];

// Storage for output
let mut out = [0.0; 2];

// Do interpolation
multilinear::rectilinear::interpn(grids, &z, &obs, &mut out).unwrap();
multicubic::rectilinear::interpn(grids, &z, false, &obs, &mut out).unwrap();
```

# Development Roadmap
* Methods for unstructured triangular and tetrahedral meshes

# License
Licensed under either of

- Apache License, Version 2.0, ([LICENSE-APACHE](LICENSE-APACHE) or http://www.apache.org/licenses/LICENSE-2.0)
- MIT license ([LICENSE-MIT](LICENSE-MIT) or http://opensource.org/licenses/MIT)

at your option.