Overview
Cranley-Patterson rotation preserves low-discrepancy structure while reducing deterministic artifacts and enabling randomized error estimates.
ExtendedSource checked
Cranley-Patterson Rotation
Randomizes low-discrepancy samples by adding a random offset modulo one.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Randomness & Sampling
- Difficulty
- Advanced
- Family
- Quasi-Monte Carlo Randomization
- Tier
- Extended
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 1
- Relationships
- 2
- Code example
- Ready
- Visualization
- Ready
Core Concepts
random shiftmodulo onelow discrepancysample randomization
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(dimensions)
Average
O(samples * dimensions)
Worst
O(samples * dimensions)
Space
O(dimensions)
When to Use
- Use when monte Carlo simulation needs random shift.
- Use when the input matches the assumptions behind quasi-Monte Carlo Randomization.
When Not to Use
- Avoid when independence, reproducibility, or distribution quality cannot be checked.
- Avoid when a simpler algorithm gives the required result with less setup.
What It Does
- Randomizes low-discrepancy samples by adding a random offset modulo one
- Uses random shift and modulo one to guide the work.
- Produces samples.
Use Cases
- Monte Carlo simulation
- Randomized algorithms
- Sampling distributions
Inputs
- Random source
- Distribution or weights
- Sample count
Outputs
- Samples
- Estimated statistic
- Randomized selection
Key Formulas (1)
Rotated sample
xrotated = (x + shift) mod 1
x_rotated = (x + shift) mod 1Applies the same random offset to every sample coordinate.
Pseudocode
- 1.Prepare the inputs and state needed for Cranley-Patterson Rotation.
- 2.Apply the random shift step while the stopping condition has not been met.
- 3.Update intermediate state and discard invalid candidates.
- 4.Return samples.
Canonical Example
- Input
- Cranley-Patterson Rotation input with a small representative case
- Output
- Samples
- Explanation
- Cranley-Patterson Rotation applies random shift to produce samples.
Implementation Notes
- Expose seed handling when reproducibility is important.
- Keep the random shift step separate enough to test independently.
Common Pitfalls
- Using a biased random source can quietly invalidate downstream estimates.
- Forgetting to check edge cases can make Cranley-Patterson Rotation look correct on only ideal inputs.
Interactive Mechanism Walkthrough
Iterative Convergence & State TrajectoryPlot generated samples against the target distribution or domain.
Step 1 of 4: Prepare the inputs and state needed for Cranley-Patterson Rotation.
randomness-sampling-mechanismNotes
Cranley-Patterson Rotation should be used with the assumptions and tradeoffs of quasi-Monte Carlo Randomization in mind.
Sources (1)
What each reference supports for this entry.
Monte Carlo Statistical Methods
BookMonte Carlo reference for randomized lattice rules and Cranley-Patterson rotation of low-discrepancy samples.
Explore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageOften paired withHalton Sequence
It can reduce structured artifacts in deterministic sample sets.
Often paired withSobol Sequence
Cranley-Patterson rotation can randomize low-discrepancy samples.
Related Algorithms
Tags
Randomness & SamplingQuasi Monte CarloLow-DiscrepancySampling