Hi,
I use the outdated MKL 10.2 to generated multi-variate normal distributed random numbers. My results are not what I expect, perhaps I have misinterpreted the arguments or there is a bug in the MKL release I use. I hope someone has an idea:
I applied vRngGaussianMV to dimension 2, 50.000 2-dimensional vectorsof random numbers are generated. Moverover VSL_RNG_METHOD_GAUSSIANMV_ICDF is used as well as the VSL_MATRIX_STORAGE_FULL storage type, mean vector is {0, 1.5}. The Fortran interface of vRngGaussianMV is used, the argument t with the Pseuo-Squareroot of the covariance matrix is set to {5, 0, 2, 4}. If understand it correctly, the matrix argument is interpreted as
T^t = (5 2 \\ 0 4)
I calculate the estimated mean and variance of the first and second component of the outcome, i.e. the projection of each second random number starting at the first, second random number of argument r respectively.I use MT19937 as well as for example MCG59 Random Number Generator with seed = 1234.
Results w.r.t MT19937
projection_0: estimation mean = -0.0001 \approx 0, estimated variance = 24,9984 \approx 25
projection_1: estimated mean=1,49958 \approx 1.5, estimated variance = 31.701
Results w.r.t. MCG59
projection_0: estimated mean = -0.012 \approx 0, estimated variance = 24.87 \approx 25
projection_1: estimated mean = 1.492 \approx 1.5, estimated variance = 19.983
The result of the MCG59 Random Number is reasonable, because the variance of the second projection should be 2² + 4² = 20. Even if I increase the number of realisiations nothing changed. I played around with the seed but I did not get reasonable results for the Mersenner Twister (MT19937) Random Number Generator. Any ideas why the values are that far away? As I said I use MKL 10.2.
Kind regards
Markus Wendt