Vectorised Computation and Libraries

Vectorised Computation

Scientific computing rests on two pillars: vectorised computation and numerical libraries. Modern code avoids explicit element loops.

Vectorisation expresses operations on whole arrays at once. Instead of c[i] = a[i] + b[i], you write $c = a + b$.

This is dramatically faster. Python loops are slow; vectorised operations dispatch to compiled C or Fortran code using CPU SIMD parallel instructions.

Numerical Libraries

Numerical libraries provide tested routines so you never reimplement fundamentals. They handle stability and pivoting correctly.

Common Pitfall: Writing explicit element-by-element loops or reimplementing standard solvers. Always prefer robust library routines over reinventing the wheel.