NAG FL Interface
g05xbf (bb)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{npaths}$ – Integer Input

On entry: the number of Wiener sample paths to create.

Constraint: $\mathbf{npaths}\ge 1$.

2: $\mathbf{rcord}$ – Integer Input

On entry: the order in which Normal random numbers are stored in z and in which the generated values are returned in b.

Constraint: $\mathbf{rcord}=1$ or $2$.

3: $\mathbf{d}$ – Integer Input

On entry: the dimension of each Wiener sample path.

Constraint: $\mathbf{d}\ge 1$.

4: $\mathbf{start}\left(\mathbf{d}\right)$ – Real (Kind=nag_wp) array Input

On entry: the starting value of the Wiener process.

5: $\mathbf{a}$ – Integer Input

On entry: if $\mathbf{a}=0$, a free Wiener process is created beginning at start and term is ignored.

If $\mathbf{a}=1$, a non-free Wiener process is created beginning at start and ending at term.

Constraint: $\mathbf{a}=0$ or $1$.

6: $\mathbf{term}\left(\mathbf{d}\right)$ – Real (Kind=nag_wp) array Input

On entry: the terminal value at which the non-free Wiener process should end. If $\mathbf{a}=0$, term is ignored.

7: $\mathbf{z}\left(\mathbf{ldz},*\right)$ – Real (Kind=nag_wp) array Input/Output

Note: the second dimension of the array z must be at least $\mathbf{npaths}$ if $\mathbf{rcord}=1$ and at least $\mathbf{d}\times \left(\mathit{N}+1-\mathbf{a}\right)$ if $\mathbf{rcord}=2$.

On entry: the Normal random numbers used to construct the sample paths.

If $\mathbf{rcord}=1$ and quasi-random numbers are used, the $\mathbf{d}\times \left(\mathit{N}+1-\mathbf{a}\right)$, where $\mathit{N}=\mathrm{nint}$ $\mathbf{rcomm}\left(2\right)$-dimensional quasi-random points should be stored in successive columns of z.

If $\mathbf{rcord}=2$ and quasi-random numbers are used, the $\mathbf{d}\times \left(\mathit{N}+1-\mathbf{a}\right)$, where $\mathit{N}=\mathrm{nint}$ $\mathbf{rcomm}\left(2\right)$-dimensional quasi-random points should be stored in successive rows of z.

On exit: the Normal random numbers premultiplied by $C$.

8: $\mathbf{ldz}$ – Integer Input

On entry: the first dimension of the array z as declared in the (sub)program from which g05xbf is called.

Constraints:

• if $\mathbf{rcord}=1$, $\mathbf{ldz}\ge \mathbf{d}\times \left(\mathit{N}+1-\mathbf{a}\right)$;
• if $\mathbf{rcord}=2$, $\mathbf{ldz}\ge \mathbf{npaths}$.

9: $\mathbf{c}\left(\mathbf{ldc},*\right)$ – Real (Kind=nag_wp) array Input

Note: the second dimension of the array c must be at least $\mathbf{d}$.

On entry: the lower triangular Cholesky factorization $C$ such that $C{C}^{\mathrm{T}}$ gives the covariance matrix of the Wiener process. Elements of $C$ above the diagonal are not referenced.

10: $\mathbf{ldc}$ – Integer Input

On entry: the first dimension of the array c as declared in the (sub)program from which g05xbf is called.

Constraint: $\mathbf{ldc}\ge \mathbf{d}$.

11: $\mathbf{b}\left(\mathbf{ldb},*\right)$ – Real (Kind=nag_wp) array Output

Note: the second dimension of the array b must be at least $\mathbf{npaths}$ if $\mathbf{rcord}=1$ and at least $\mathbf{d}\times \left(\mathit{N}+1\right)$ if $\mathbf{rcord}=2$.

On exit: the values of the Wiener sample paths.

Let $X_{p,i}^k$ denote the $k$th dimension of the $i$th point of the $p$th sample path where $1\le k\le \mathbf{d}$, $1\le i\le \mathit{N}+1$ and $1\le p\le \mathbf{npaths}$.

If $\mathbf{rcord}=1$, the point $X_{p,i}^k$ will be stored at $\mathbf{b}\left(k+\left(i-1\right)\times \mathbf{d},p\right)$.

If $\mathbf{rcord}=2$, the point $X_{p,i}^k$ will be stored at $\mathbf{b}\left(p,k+\left(i-1\right)\times \mathbf{d}\right)$.

The starting value start is never stored, whereas the terminal value is always stored.

12: $\mathbf{ldb}$ – Integer Input

On entry: the first dimension of the array b as declared in the (sub)program from which g05xbf is called.

Constraints:

• if $\mathbf{rcord}=1$, $\mathbf{ldb}\ge \mathbf{d}\times \left(\mathit{N}+1\right)$;
• if $\mathbf{rcord}=2$, $\mathbf{ldb}\ge \mathbf{npaths}$.

13: $\mathbf{rcomm}\left(*\right)$ – Real (Kind=nag_wp) array Communication Array

Note: the dimension of this array is dictated by the requirements of associated functions that must have been previously called. This array must be the same array passed as argument rcomm in the previous call to g05xaf or g05xbf.

On entry: communication array as returned by the last call to g05xaf or g05xbf. This array must not be directly modified.

14: $\mathbf{ifail}$ – Integer Input/Output

On entry: ifail must be set to $0$, $-1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.

A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $-1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ or $\mathbf{1}$ is used it is essential to test the value of ifail on exit.

On exit: $\mathbf{ifail}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

$\mathbf{ifail}=1$

On entry, rcomm was not initialized or has been corrupted.

$\mathbf{ifail}=2$

On entry, $\mathbf{npaths}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{npaths}\ge 1$.

$\mathbf{ifail}=3$

On entry, $\mathbf{rcord}=〈\mathit{\text{value}}〉$ was an illegal value.

$\mathbf{ifail}=4$

On entry, $\mathbf{d}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{d}\ge 1$.

$\mathbf{ifail}=5$

On entry, $\mathbf{a}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{a}=0\text{ or }1$.

$\mathbf{ifail}=6$

On entry, $\mathbf{ldz}=〈\mathit{\text{value}}〉$ and $\mathbf{d}\times \left(\mathbf{ntimes}+1-\mathbf{a}\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ldz}\ge \mathbf{d}\times \left(\mathbf{ntimes}+1-\mathbf{a}\right)$.

On entry, $\mathbf{ldz}=〈\mathit{\text{value}}〉$ and $\mathbf{npaths}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ldz}\ge \mathbf{npaths}$.

$\mathbf{ifail}=7$

On entry, $\mathbf{ldc}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ldc}\ge 〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=8$

On entry, $\mathbf{ldb}=〈\mathit{\text{value}}〉$ and $\mathbf{d}\times \left(\mathbf{ntimes}+1\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ldb}\ge \mathbf{d}\times \left(\mathbf{ntimes}+1\right)$.

On entry, $\mathbf{ldb}=〈\mathit{\text{value}}〉$ and $\mathbf{npaths}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ldb}\ge \mathbf{npaths}$.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results