naginterfaces.library.rand.quasi_​uniform_​bydim

naginterfaces.library.rand.quasi_uniform_bydim(n, fdim, ldim, comm, sorder=1)

quasi_uniform_bydim generates a uniformly distributed low-discrepancy sequence as proposed by Sobol or Niederreiter. Values are generated for a subset of dimensions. It must be preceded by a call to one of the initialization functions quasi_init() or quasi_init_scrambled().

For full information please refer to the NAG Library document for g05yp

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/g05/g05ypf.html

Parameters

nint

The number of quasi-random numbers required.

fdimint

The first dimension to return.

ldimint

The last dimension to return.

commdict, communication object, modified in place

Communication structure.

This argument must have been initialized by a prior call to quasi_init() or quasi_init_scrambled().

sorderint, optional

The order in which the generated values are returned.

Returns

quasfloat, ndarray, shape $(:,:)$

Contains the $n$ quasi-random numbers for the required dimensions of a sequence with idim dimensions.

For $i=1,2,\dots ,n$, $j=fdim,fdim+1,\dots ,ldim$ the $\text{i}$th value for the $\text{j}$th dimension is held in $quas[\text{i}-1,k-1]$, where $k=\text{j}-fdim+1$.

Raises

NagValueError

(errno $11$)

On entry, $sorder=⟨value⟩$.

Constraint: $sorder=1$ or $2$.

(errno $21$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 0$.

(errno $22$)

On entry, value of $n$ would result in too many calls to the generator: $n=⟨value⟩$, generator has previously been called $⟨value⟩$ times.

(errno $31$)

On entry, $fdim=⟨value⟩$ and $ldim=⟨value⟩$.

Constraint: $1\le fdim\le ldim$

(errno $41$)

On entry, $ldim=⟨value⟩$ and $\text{idim}=⟨value⟩$.

Constraint: $ldim\le \text{idim}$

(errno $62$)

On entry, $\text{ldquas}=⟨value⟩$ and $ldim-fdim+1=⟨value⟩$.

Constraint: $\text{ldquas}\ge ldim-fdim+1$.

(errno $81$)

On entry, $comm$[‘iref’] has either not been initialized or has been corrupted.

(errno $83$)

On entry, $comm$[‘iref’] is too short to use with quasi_uniform_bydim.

(errno $84$)

On entry, the specified dimensions are out of sync.

A different number of values have been generated from at least one of the specified dimensions.

(errno $85$)

quasi_uniform_bydim can not be used with the Faure generator.

Notes

quasi_uniform_bydim generates a sequence of low discrepancy (quasi-random) values for a specified subset of dimensions. See the G05 Introduction for more details.

Prior to calling this function one of the initialization functions quasi_init() or quasi_init_scrambled() must be called and the type of sequence returned by quasi_uniform_bydim can include the low-discrepancy sequences proposed by Sobol or Niederreiter, depending on the arguments supplied to the initialization routine used. If the initialization function quasi_init_scrambled() was used then the returned sequence is scrambled (see Notes for quasi_init_scrambled for details).

References

Bratley, P and Fox, B L, 1988, Algorithm 659: implementing Sobol’s quasirandom sequence generator, ACM Trans. Math. Software (14(1)), 88–100

Fox, B L, 1986, Algorithm 647: implementation and relative efficiency of quasirandom sequence generators, ACM Trans. Math. Software (12(4)), 362–376