[](https://docs.rs/static-math)
[](https://crates.io/crates/static-math)
# Static Math in Rust programming language
"*Simple things should be simple, complex things should be possible*" Alan Kay.
- This crate take advantage of the static arrays in Rust for fast operations in
stack memory.
- We use a tuple to indexing elements: `m[(i, j)]` allowing nice interface with the `match` feature of Rust
- No `unsafe` code :ballot_box_with_check:
- Could be optimize more with the use of SIMD
- This crate could be used in an `no-std` environment.
by enabling the feature `no-std`, for example in your `Cargo.toml`:
```toml
[dependencies.static-math]
default-features = false
version = "0.2.0"
features = ["no-std"]
```
- You can visualize the matrices
```text
inverse:
|0.21 -0.42 -0.39 0.15 0.20 0.62|
|0.70 -0.24 -0.53 0.20 -0.21 0.73|
|0.85 -0.47 -0.83 0.11 0.11 1.20|
|-3.91 2.47 4.17 -0.87 -0.31 -6.08|
```
- The determinant of the matrices are evaluated "in-place" without loops and code
bifurcations
- The use cases can be: Robotics, Game programming, Simulations ...etc.
The matrix types `Mnn` (where `n=2..6`) implements the Methods from the
`LinearAlgebra` trait:
- `det()`: Determinant of the matrix
- `inverse()`: Inverse of the matrix
- `qr()`: QR decomposition of the matrix
- `norm2()`: norm of the matrix
- `transpose()`: transpose of the matrix
- `trace()`: trace of the matrix
- `shape()`: shape of the matrix
- We have implemented `Quaternion`s (and all the most used methods)
- We have implemented `DualQuaternion`s (and all the most used methods in Robotics and graphics like *Screw Linear Interpolation*)
- We have implemented in the `transformations.rs` module a wide variety of functions used in Robotics (which conforms to the screw theory)
## Benchmarks
Using the criterion crate:
https://github.com/bheisler/criterion.rs
run with: `cargo bench`
Others benches comparing the performance with others crates are in this repo: https://github.com/bitshifter/mathbench-rs
*NOTE*: this is the only crate that not have unsafe code
with the following results:
| euler 2d x10000 | __7.555 us__ | __7.521 us__ | 16.38 us | 11.86 us | __7.513 us__ | 9.806 us | 11.83 us | __7.499 us__ |
| euler 3d x10000 | __16.2 us__ | 25.04 us | 106.3 us | 25.05 us | 25.16 us | 16.76 us | 25.03 us | 25.05 us |
| matrix2 determinant | __2.0332 ns__ | __2.0311 ns__ | __2.0250 ns__ | N/A | __2.0209 ns__ | __2.0323 ns__ | __2.0254 ns__ | N/A |
| matrix2 inverse | __2.6114 ns__ | 3.0331 ns | 2.9792 ns | N/A | N/A | 2.7550 ns | 3.0132 ns | N/A |
| matrix2 mul matrix2 | 2.6047 ns | __2.5346 ns__ | __2.5426 ns__ | N/A | 8.7573 ns | __2.5381 ns__ | 2.6028 ns | 2.9668 ns |
| matrix2 mul vector2 x1 | 2.6592 ns | 2.6104 ns | 2.6214 ns | N/A | 4.2512 ns | __2.0663 ns__ | 2.8674 ns | 2.6172 ns |
| matrix2 mul vector2 x100 | 245.2897 ns | 233.7149 ns | 238.7395 ns | N/A | 399.3148 ns | __218.4107 ns__ | 260.6645 ns | 234.7099 ns |
| matrix2 return self | __2.4740 ns__ | 2.5994 ns | 2.5968 ns | N/A | 2.5969 ns | __2.4607 ns__ | 2.5928 ns | 2.5974 ns |
| matrix2 transpose | __2.0852 ns__ | __2.0814 ns__ | 2.3426 ns | N/A | __2.1053 ns__ | N/A | __2.0829 ns__ | N/A |
| matrix3 determinant | __3.3675 ns__ | __3.4261 ns__ | __3.3780 ns__ | N/A | __3.4479 ns__ | N/A | __3.4375 ns__ | N/A |
| matrix3 inverse | 11.4209 ns | __8.3701 ns__ | 9.4315 ns | N/A | N/A | N/A | 9.1710 ns | 20.1731 ns |
| matrix3 mul matrix3 | __5.8501 ns__ | 6.5350 ns | 9.8196 ns | N/A | 47.9203 ns | N/A | 9.5170 ns | 6.5211 ns |
| matrix3 mul vector3 x1 | __3.9266 ns__ | 4.3876 ns | 4.3333 ns | N/A | 16.0858 ns | N/A | 4.4220 ns | 4.3304 ns |
| matrix3 mul vector3 x100 | __0.4372 us__ | __0.4416 us__ | 0.4594 us | N/A | 1.59 us | N/A | 0.454 us | __0.4425 us__ |
| matrix3 return self | __4.8566 ns__ | __4.8401 ns__ | __4.8226 ns__ | N/A | __4.8340 ns__ | N/A | __4.8303 ns__ | __4.8383 ns__ |
| matrix3 transpose | __5.7688 ns__ | __5.6980 ns__ | 8.1508 ns | N/A | __5.6910 ns__ | N/A | __5.6936 ns__ | __5.6766 ns__ |
| matrix4 determinant | __8.3724 ns__ | 11.1604 ns | 52.8697 ns | 16.0723 ns | 17.5301 ns | N/A | 16.1402 ns | N/A |
| matrix4 inverse | __21.3281 ns__ | 38.5833 ns | 64.5172 ns | 61.2347 ns | 275.5253 ns | N/A | 48.0641 ns | 37.1436 ns |
| matrix4 mul matrix4 | __7.5043 ns__ | 8.3723 ns | 9.4094 ns | 10.1761 ns | 90.7185 ns | N/A | 20.6424 ns | 8.4072 ns |
| matrix4 mul vector4 x1 | __3.3645 ns__ | 3.7273 ns | 3.7251 ns | N/A | 24.2185 ns | N/A | 6.1311 ns | 3.7524 ns |
| matrix4 mul vector4 x100 | __0.6105 us__ | __0.6237 us__ | __0.6202 us__ | N/A | 2.402 us | N/A | 0.7044 us | __0.6202 us__ |
| matrix4 return self | 6.8863 ns | 7.1298 ns | __6.6961 ns__ | N/A | __6.7079 ns__ | N/A | __6.6772 ns__ | __6.7079 ns__ |
| matrix4 transpose | __5.7312 ns__ | 10.1612 ns | 14.9424 ns | N/A | 10.2015 ns | N/A | 10.1996 ns | 10.2391 ns |
| rotation3 inverse | __2.1867 ns__ | 2.9086 ns | 2.8853 ns | 2.9092 ns | 2.8987 ns | N/A | N/A | 2.9064 ns |
| rotation3 mul rotation3 | __3.3422 ns__ | 4.3602 ns | 7.0680 ns | 7.7111 ns | 8.9616 ns | N/A | N/A | 18.4088 ns |
| rotation3 mul vector3 | __6.6977 ns__ | __6.7831 ns__ | 6.9924 ns | 6.9801 ns | 32.8778 ns | N/A | N/A | 13.5267 ns |
| rotation3 return self | __2.4622 ns__ | 2.5983 ns | 2.6021 ns | N/A | 2.5989 ns | N/A | N/A | 2.5980 ns |
| transform point2 x1 | 3.8946 ns | 2.8843 ns | 4.6543 ns | 3.2271 ns | 17.0089 ns | __2.3608 ns__ | N/A | N/A |
| transform point2 x100 | 0.4265 us | 0.3677 us | 0.4632 us | __0.322 us__ | 1.712 us | __0.3206 us__ | N/A | N/A |
| transform point3 x1 | 4.9958 ns | 6.3712 ns | 6.6426 ns | 6.1114 ns | 24.8255 ns | __3.1011 ns__ | N/A | N/A |
| transform point3 x100 | __0.6261 us__ | 0.7418 us | 0.7447 us | 0.7296 us | 2.507 us | __0.6295 us__ | N/A | N/A |
| transform vector2 x1 | __2.7159 ns__ | N/A | 3.9917 ns | 2.8070 ns | 16.8257 ns | N/A | N/A | N/A |
| transform vector2 x100 | 0.3463 us | N/A | 0.4018 us | __0.2893 us__ | 1.709 us | N/A | N/A | N/A |
| transform vector3 x1 | __3.9868 ns__ | 5.5573 ns | 8.4892 ns | 4.4068 ns | 25.0274 ns | N/A | N/A | N/A |
| transform vector3 x100 | __0.5905 us__ | 0.6584 us | 0.8936 us | 0.6365 us | 2.513 us | N/A | N/A | N/A |
| transform2 inverse | N/A | N/A | 9.4094 ns | 4.6388 ns | N/A | __3.9983 ns__ | N/A | N/A |
| transform2 mul transform2 | N/A | N/A | 9.8173 ns | 6.2162 ns | N/A | __3.8699 ns__ | N/A | N/A |
| transform2 return self | N/A | N/A | 4.8447 ns | __3.5091 ns__ | N/A | 4.1391 ns | N/A | N/A |
| transform3 inverse | N/A | N/A | 65.3982 ns | 52.6160 ns | N/A | __32.0466 ns__ | N/A | N/A |
| transform3 mul transform3d | N/A | N/A | 10.9731 ns | 9.9741 ns | N/A | __7.6754 ns__ | N/A | N/A |
| transform3 return self | N/A | N/A | 7.1596 ns | __6.6096 ns__ | N/A | 7.0148 ns | N/A | N/A |
| vector3 cross | __2.4542 ns__ | 3.5894 ns | 3.2434 ns | 3.4923 ns | 3.5150 ns | N/A | 3.2947 ns | 7.1968 ns |
| vector3 dot | __2.1001 ns__ | 2.3025 ns | 2.2986 ns | 2.3030 ns | 2.3084 ns | N/A | 2.3072 ns | 3.7322 ns |
| vector3 length | __2.1722 ns__ | __2.1747 ns__ | 2.3414 ns | __2.1716 ns__ | __2.2151 ns__ | N/A | __2.2063 ns__ | 3.4787 ns |
| vector3 normalize | __4.4248 ns__ | __4.3266 ns__ | 8.1124 ns | 8.0704 ns | 8.0747 ns | N/A | N/A | 8.0778 ns |
| vector3 return self | __2.4642 ns__ | 2.9591 ns | 2.9586 ns | N/A | 2.9579 ns | N/A | 2.9633 ns | 2.9572 ns |
## TODOS:
- [X] `Quaternion` type and methods
- [ ] `expm()`: Exponential matrix implementation
- [X] Eigenvalues
- [X] QR decomposition