russell_tensor 3.3.1

Tensor analysis, calculus, and functions for continuum mechanics
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# Russell Tensor — Benchmark Results

Generated by `run_all.py` on 2026-09-23 00:02:25 UTC.

## System information

| component | value |
| --------- | ----- |
| OS        | Omarchy (kernel 7.2.5-3-omarchy) |
| CPU       | 13th Gen Intel(R) Core(TM) i9-13900KF |
| BLAS      | Intel MKL |

## Polar decomposition

### General (3×3): all algorithms

| case | κ | `iterative` | `quaternion` | `eigen` | `svd` |
| --- | --- | --- | --- | --- | --- |
| `mild` | ≈ 1.1 | 63.27 ns | 112.96 ns | 76.13 ns | 183.45 ns |
| `well_conditioned` | ≈ 4 | 97.84 ns | 110.96 ns | 82.38 ns | 590.38 ns |
| `moderate_conditioned` | ≈ 10³ | 352.30 ns | 149.16 ns | 75.15 ns | 490.92 ns |
| `ill_conditioned` | ≈ 10⁸ | 843.32 ns | 184.93 ns | — | 438.77 ns |

### In-plane: all algorithms

| algorithm | time |
| --- | --- |
| `iterative` | 115.27 ns |
| `quaternion` | 115.98 ns |
| `eigen` | 82.00 ns |
| `svd` | 190.16 ns |

## Eigen

Median times (Intel MKL).

### Eigenvalues — `EigenValuesT2::calculate_mx`

| case | `analytical_hz` | `analytical_ha22` | `analytical_ha23` | `iterative` |
| --- | --- | --- | --- | --- |
| `distinct` | 46.18 ns | 35.95 ns | 37.35 ns | 193.39 ns |
| `coalescent` | 47.00 ns | 31.20 ns | 35.16 ns | 192.77 ns |

### Eigenprojectors — `EigenProjsT2::calculate_mx`

| case | `analytical_hz` | `analytical_ha22` | `analytical_ha23` | `iterative` |
| --- | --- | --- | --- | --- |
| `distinct` | 60.81 ns | 52.36 ns | 54.12 ns | 193.92 ns |
| `coalescent` | 63.18 ns | 51.47 ns | 53.61 ns | 193.41 ns |

### Eigenprojector derivatives (distinct) — `EigenProjDerivsT2`

| algorithm | time |
| --- | --- |
| `char_poly` | 133.15 ns |
| `with_inv` | 146.90 ns |