Wichmann-Hill brng

Each generator from the set of 273 Wichmann-Hill’s combined multiplicative congruential generators can be initialized with either an integral seed, a list of integral seeds, or automatically.

An individual member of the set can be addressed by using a tuple to specify the generator as brng=("WH", set_id) where \(0 \leq \text{set_id} < 273\).

Construction for WH basic psuedo-random number generator with scalar seed

    import mkl_random
    seed = 777
    # initialize representative generator from the set
    rs0 = mkl_random.RandomState(seed, brng="WH")

    # initialize 0-th member of the set
    rs0 = mkl_random.RandomState(seed, brng=("WH", 0))

    # initialize 5-th member of the set
    rs5 = mkl_random.RandomState(seed, brng=("WH", 5))

    sample = rs5.uniform(0, 1, size=1_000_000)

Construction for WH basic pseudo-random number generator with vector seed

    import mkl_random
    rs = mkl_random.RandomState([1234, 567, 89, 0], brng=("WH", 200))

    # Use random state instance to generate 1000 random numbers from
    # Gamma(3, 1) distibution
    gsample = rs_vec.gamma(3, 1, size=1000)

When seed is not specified, the generator is initialized using system clock, e.g.:

Construction for WH basic pseudo-random number generator with automatic seed

    import mkl_random
    rs_def = mkl_random.RandomState(brng="WH")

    # Use random state instance to generate 1000 random numbers
    # from discrete uniform distribution [1, 6]
    isample = rs_def.randint(1, 6 + 1, size=1000)

Different members of the set of generators initialized with the same seed are designed to generate statistically independent streams of randomness. This property makes MT2203 generator suitable for parallelizing stochastic algorithms. Please refer to “examples/” folder in the GitHub repo.