naginterfaces.library.rand.quasi_​normal_​bydim

naginterfaces.library.rand.quasi_normal_bydim(n, xmean, std, fdim, ldim, comm, sorder=1)

quasi_normal_bydim generates a quasi-random sequence from a Normal (Gaussian) distribution. 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 g05yq

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/g05/g05yqf.html

Parameters

nint

The number of quasi-random numbers required.

xmeanfloat, array-like, shape $\left(\text{idim}\right)$

Specifies, for each dimension, the mean of the Normal distribution.

stdfloat, array-like, shape $\left(\text{idim}\right)$

Specifies, for each dimension, the standard deviation of the Normal distribution.

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 $i=1,2,\dots ,n$, $j=fdim,fdim+1,\dots ,ldim$ and $k=\text{j}-fdim+1$, the $\text{i}$th value for the $\text{j}$th dimension is held in

$quas[\text{i}-1,k-1]$, if $sorder=1$,

$quas[k-1,\text{i}-1]$, if $sorder=2$.

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 $41$)

On entry, $i=⟨value⟩$ and $std[i-1]=⟨value⟩$.

Constraint: $std[i-1]\ge 0.0$.

(errno $61$)

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

Constraint: $1\le fdim\le ldim$

(errno $71$)

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

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

(errno $92$)

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

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

(errno $111$)

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

(errno $113$)

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

(errno $114$)

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 $115$)

quasi_normal_bydim can not be used with the Faure generator.

Notes

quasi_normal_bydim generates a quasi-random sequence, for a specified subset of dimensions, from a Normal distribution by first generating a uniform quasi-random sequence, for the specified subset of dimensions, which is then transformed into a Normal sequence using the inverse of the Normal CDF. The type of uniform sequence used depends on the initialization function called and can include the low-discrepancy sequences proposed by Sobol, Faure or Niederreiter. If the initialization function quasi_init_scrambled() was used then the underlying uniform sequence is first scrambled prior to being transformed (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

Wichura, 1988, Algorithm AS 241: the percentage points of the Normal distribution, Appl. Statist. (37), 477–484