PollardRho: prime factorisation with Pollard's rho (exact for
n below 2^52). LegendrePolynomials: Bonnet recurrence.
ResolutionRefutation: propositional resolution saturation.
PolarTransform: recursive polar transform (PolarQuant) and its
inverse. PanterDiteBound: high-rate Gaussian quantisation
distortion. LogitProportion: logit proportions and variances.
McStandardError: Geyer initial-sequence Monte Carlo standard error.
Identical to the Python arm morie.fn.mathalg.
Usage
PollardRho(n)
LegendrePolynomials(x, degree, normalized = FALSE)
ResolutionRefutation(clauses, max_clauses = 1e+05)
PolarTransform(x, inverse = FALSE)
PanterDiteBound(bits, sigma2 = 1)
LogitProportion(events, n)
McStandardError(draws)Arguments
- n
Integer to factor, or sample sizes.
- x
Values (or, for the inverse transform, a list of radius and angles).
- degree
Largest degree.
- normalized
Orthonormal scaling.
- clauses
List of integer vectors (DIMACS literals).
- max_clauses
Clause limit.
- inverse
Apply the inverse transform.
- bits
Bits per value.
- sigma2
Source variance.
- events
Event counts.
- draws
Chain draws.
References
Pollard, J. M. (1975). A Monte Carlo method for factorization. BIT 15, 331-334.
Robinson, J. A. (1965). A machine-oriented logic based on the resolution principle. Journal of the ACM 12, 23-41.
Panter, P. F. and Dite, W. (1951). Quantization distortion in pulse-count modulation with nonuniform spacing of levels. Proceedings of the IRE 39, 44-48.
Geyer, C. J. (1992). Practical Markov chain Monte Carlo. Statistical Science 7, 473-483.