NAG Library Function Document

nag_4d_shep_eval (e01tlc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     m – IntegerInput

On entry: must be the same value supplied for argument m in the preceding call to nag_4d_shep_interp (e01tkc).

Constraint: $\mathbf{m}\ge 16$.

2:     x[$4\times \mathbf{m}$] – const doubleInput

Note: the coordinates of $x_r$ are stored in $\mathbf{x}\left[\left(r-1\right)\times 4\right]\dots \mathbf{x}\left[\left(r-1\right)\times 4+3\right]$.

On entry: must be the same array supplied as argument x in the preceding call to nag_4d_shep_interp (e01tkc). It must remain unchanged between calls.

3:     f[m] – const doubleInput

On entry: must be the same array supplied as argument f in the preceding call to nag_4d_shep_interp (e01tkc). It must remain unchanged between calls.

4:     iq[$2\times \mathbf{m}+1$] – const IntegerInput

On entry: must be the same array returned as argument iq in the preceding call to nag_4d_shep_interp (e01tkc). It must remain unchanged between calls.

5:     rq[$15\times \mathbf{m}+9$] – const doubleInput

On entry: must be the same array returned as argument rq in the preceding call to nag_4d_shep_interp (e01tkc). It must remain unchanged between calls.

6:     n – IntegerInput

On entry: $n$, the number of evaluation points.

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

7:     xe[$4\times \mathbf{n}$] – const doubleInput

Note: the $\left(i,j\right)$th element of the matrix is stored in $\mathbf{xe}\left[\left(j-1\right)\times 4+i-1\right]$.

On entry: $\mathbf{xe}\left[\left(\mathit{r}-1\right)\times 4\right],\dots ,\mathbf{xe}\left[\left(\mathit{r}-1\right)\times 4+3\right]$ must be set to the evaluation point ${\mathbf{x}}_{\mathit{i}}$ , for $\mathit{i}=1,2,\dots ,n$.

8:     q[n] – doubleOutput

On exit: $\mathbf{q}\left[\mathit{i}-1\right]$ contains the value of the interpolant, at ${\mathbf{x}}_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n$. If any of these evaluation points lie outside the region of definition of the interpolant the corresponding entries in q are set to the largest machine representable number (see nag_real_largest_number (X02ALC)), and nag_4d_shep_eval (e01tlc) returns with $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_BAD_POINT.

9:     qx[$4\times \mathbf{n}$] – doubleOutput

Note: the $\left(i,j\right)$th element of the matrix is stored in $\mathbf{qx}\left[\left(j-1\right)\times 4+i-1\right]$.

On exit: $\mathbf{qx}\left[\left(i-1\right)\times 4+j-1\right]$ contains the value of the partial derivatives with respect to ${\mathbf{x}}_j$ of the interpolant $Q\left(\mathbf{x}\right)$ at ${\mathbf{x}}_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n$, and for each of the four partial derivatives $j=1,2,3,4$. If any of these evaluation points lie outside the region of definition of the interpolant, the corresponding entries in qx are set to the largest machine representable number (see nag_real_largest_number (X02ALC)), and nag_4d_shep_eval (e01tlc) returns with $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_BAD_POINT.

10:   fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_BAD_PARAM

On entry, argument $⟨\mathit{\text{value}}⟩$ had an illegal value.

NE_BAD_POINT

On entry, at least one evaluation point lies outside the region of definition of the interpolant. At all such points the corresponding values in q and qx have been set to $\mathbf{nag\_real\_largest\_number}$: $\mathbf{nag\_real\_largest\_number}=⟨\mathit{\text{value}}⟩$.

NE_INT

On entry, $\mathbf{m}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{m}\ge 16$.

On entry, $\mathbf{n}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{n}\ge 1$.

NE_INT_ARRAY

On entry, values in iq appear to be invalid. Check that iq has not been corrupted between calls to nag_4d_shep_interp (e01tkc) and nag_4d_shep_eval (e01tlc).

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.

NE_REAL_ARRAY

On entry, values in rq appear to be invalid. Check that rq has not been corrupted between calls to nag_4d_shep_interp (e01tkc) and nag_4d_shep_eval (e01tlc).

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (e01tlce.c)

10.2  Program Data

Program Data (e01tlce.d)

10.3  Program Results

Program Results (e01tlce.r)