dimforge / dimforge/nalgebra

Issue with lu solver

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Rust
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Description

I think there's a gotcha situation in which the LU solver fails.

```rs
let decomp = mat.lu();
let res = decomp.solve(&b).expect(format!("{} {}", mat, b).as_str());
```

Consider the following linear system:

```
┌ ┐
│ -0 -120.864365 0 1 │
│ 0 -120.864365 0 1 │
│ 173502.55 -120.86603 45485.008 1 │
│ 1 0 0 0 │
└ ┘


┌ ┐
│ 0 │
│ 0 │
│ 0 │
│ 0 │
└ ┘
```

Since the matrix has a repeated row, there are classes of inputs for which a solution does not exist. However, since it is asking for $b=0$, there is at least one trivial solution of x=0;

I don't know if this is something that wants to be taken into account but I will mention it just in case.

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