Reproducible computation
Objective. Validate and communicate computational results.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Reproducible computation means a mathematical result obtained by computer can be independently re-run and verified, requiring recorded inputs, fixed random seeds for stochastic methods, documented algorithm versions, and stated numerical tolerances. Validating a computational result involves checking it against known analytic cases, independent methods, or conservation laws (such as checking energy or momentum stays constant in a simulation). Communicating results clearly means reporting not just the answer but the method, parameters, and estimated error bounds, so another researcher could reach the same conclusion. Silent, undocumented parameter choices undermine trust in a computed result.
Worked example
A reproducible computation of ∫₀¹ x² dx using the trapezium rule with n=4 strips gives an approximate value; find it to check against the exact value 1/3.
- 1Step size: h = (1−0)/4 = 0.25
- 2Evaluate f at x=0,0.25,0.5,0.75,1: 0,0.0625,0.25,0.5625,1
- 3Trapezium rule: T=(h/2)(f₀+2f₁+2f₂+2f₃+f₄)
- 4Compute: T=(0.125)(0+0.125+0.5+1.125+1)=0.34375
Answer: 0.34375
Concept mastery
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Practice
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Start practisingCommon mistake. Reporting a simulated or computed answer without stating the random seed, tolerance or step size used; without these, nobody else can reproduce or verify the exact numerical result obtained.
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