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Application: Unblocked LU Factorization                                 [TOC]
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LU factorization with pivoting
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Implement the LU factorization with pivoting:

- Solve your example problem with pencil and paper
- Change your factorization such that it also handles pivoting.  Implement for
  this the following BLAS functions as auxiliary tools:

  - Write a function `dswap` for interchanging values of two vectors:

    ---- CODE(type=c) ----------------------------------------------------------
    void
    dswap(size_t n, double *x, ptrdiff_t incX, double *y, ptrdiff_t incY)
    {
        // Your code
    }
    ----------------------------------------------------------------------------

  - Write a function `idamx` that returns for a vector the index with maximal
    absolute value:

    ---- CODE(type=c) ----------------------------------------------------------
    size_t
    idamax(size_t n, const double *x, ptrdiff_t incX)
    {
        // Your code
    }
    ----------------------------------------------------------------------------

- Change `main` such that it also prints the pivot vector after the
  factorization.