NAG Library Function Document

nag_2d_spline_eval (e02dec)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{m}$ – IntegerInput

On entry: $m$, the number of points at which values of the spline are required.

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

2:    $\mathbf{x}\left[\mathbf{m}\right]$ – const doubleInput

3:    $\mathbf{y}\left[\mathbf{m}\right]$ – const doubleInput

On entry: x and y must contain $x_{\mathit{r}}$ and $y_{\mathit{r}}$, for $\mathit{r}=1,2,\dots ,m$, respectively. These are the coordinates of the points at which values of the spline are required. The order of the points is immaterial.

Constraint: x and y must satisfy
$\mathbf{spline}\mathbf{\to }\mathbf{lamda}\left[3\right]\le \mathbf{x}\left[\mathit{r}-1\right]\le \mathbf{spline}\mathbf{\to }\mathbf{lamda}\left[\mathbf{spline}\mathbf{\to }\mathbf{nx}-4\right]$
and
$\mathbf{spline}\mathbf{\to }\mathbf{mu}\left[3\right]\le \mathbf{y}\left[\mathit{r}-1\right]\le \mathbf{spline}\mathbf{\to }\mathbf{mu}\left[\mathbf{spline}\mathbf{\to }\mathbf{ny}-4\right]$.
The spline representation is not valid outside these intervals, for $\mathit{r}=1,2,\dots ,m$.

4:    $\mathbf{ff}\left[\mathbf{m}\right]$ – doubleOutput

On exit: $\mathbf{ff}\left[\mathit{r}-1\right]$ contains the value of the spline at the point $\left(x_{\mathit{r}},y_{\mathit{r}}\right)$, for $\mathit{r}=1,2,\dots ,m$.

5:    $\mathbf{spline}$ – Nag_2dSpline *

Pointer to structure of type Nag_2dSpline with the following members:

nx – IntegerInput

On entry: $\mathbf{nx}$ must specify the total number of knots associated with the variables $x$. It is such that $\mathbf{nx}-8$ is the number of interior knots.

Constraint: $\mathbf{nx}\ge 8$.

lamda – double *Input

On entry: a pointer to which memory of size $\mathbf{nx}$ must be allocated. $\mathbf{lamda}$ must contain the complete sets of knots $\left\{\lambda \right\}$ associated with the $x$ variable.

Constraint: the knots must be in nondecreasing order, with $\mathbf{lamda}\left[\mathbf{nx}-4\right]>\mathbf{lamda}\left[3\right]$.

ny – IntegerInput

On entry: $\mathbf{ny}$ must specify the total number of knots associated with the variable $y$.

It is such that $\mathbf{ny}-8$ is the number of interior knots.

Constraint: $\mathbf{ny}\ge 8$.

mu – double *Input

On entry: a pointer to which memory of size $\mathbf{ny}$ must be allocated. $\mathbf{mu}$ must contain the complete sets of knots $\left\{\mu \right\}$ associated with the $y$ variable.

Constraint: the knots must be in nondecreasing order, with $\mathbf{mu}\left[\mathbf{ny}-4\right]>\mathbf{mu}\left[3\right]$.

c – double *Input

On entry: a pointer to which memory of size $\left(\mathbf{nx}-4\right)\times \left(\mathbf{ny}-4\right)$ must be allocated. $\mathbf{c}\left[\left(\mathbf{ny}-4\right)\times \left(\mathit{i}-1\right)+\mathit{j}-1\right]$ must contain the coefficient $c_{\mathit{i}\mathit{j}}$ described in Section 3, for $\mathit{i}=1,2,\dots ,\mathbf{nx}-4$ and $\mathit{j}=1,2,\dots ,\mathbf{ny}-4$.

In normal usage, the call to nag_2d_spline_eval (e02dec) follows a call to nag_2d_spline_interpolant (e01dac), nag_2d_spline_fit_grid (e02dcc) or nag_2d_spline_fit_scat (e02ddc), in which case, members of the structure spline will have been set up correctly for input to nag_2d_spline_eval (e02dec).

6:    $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.

NE_END_KNOTS_CONS

On entry, the end knots must satisfy $〈\mathit{\text{value}}〉$, $〈\mathit{\text{value}}〉=〈\mathit{\text{value}}〉$, $〈\mathit{\text{value}}〉=〈\mathit{\text{value}}〉$.

NE_INT_ARG_LT

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

On entry, $\mathbf{spline}\mathbf{\to }\mathbf{nx}$ must not be less than 8: $\mathbf{spline}\mathbf{\to }\mathbf{nx}=〈\mathit{\text{value}}〉$.

On entry, $\mathbf{spline}\mathbf{\to }\mathbf{ny}$ must not be less than 8: $\mathbf{spline}\mathbf{\to }\mathbf{ny}=〈\mathit{\text{value}}〉$.

NE_NOT_INCREASING

The sequence $\mathbf{spline}\mathbf{\to }\mathbf{lamda}$ is not increasing: $\mathbf{spline}\mathbf{\to }\mathbf{lamda}\left[〈\mathit{\text{value}}〉\right]=〈\mathit{\text{value}}〉$, $\mathbf{spline}\mathbf{\to }\mathbf{lamda}\left[〈\mathit{\text{value}}〉\right]=〈\mathit{\text{value}}〉$.
The sequence $\mathbf{spline}\mathbf{\to }\mathbf{mu}$ is not increasing: $\mathbf{spline}\mathbf{\to }\mathbf{mu}\left[〈\mathit{\text{value}}〉\right]=〈\mathit{\text{value}}〉$, $\mathbf{spline}\mathbf{\to }\mathbf{mu}\left[〈\mathit{\text{value}}〉\right]=〈\mathit{\text{value}}〉$.

NE_POINT_OUTSIDE_RECT

On entry, point $\left(\mathbf{x}\left[〈\mathit{\text{value}}〉\right]=〈\mathit{\text{value}}〉,\mathbf{y}\left[〈\mathit{\text{value}}〉\right]=〈\mathit{\text{value}}〉\right)$ lies outside the rectangle bounded by $\mathbf{spline}\mathbf{\to }\mathbf{lamda}\left[3\right]=〈\mathit{\text{value}}〉$, $\mathbf{spline}\mathbf{\to }\mathbf{lamda}\left[〈\mathit{\text{value}}〉\right]=〈\mathit{\text{value}}〉$, $\mathbf{spline}\mathbf{\to }\mathbf{mu}\left[3\right]=〈\mathit{\text{value}}〉$, $\mathbf{spline}\mathbf{\to }\mathbf{mu}\left[〈\mathit{\text{value}}〉\right]=〈\mathit{\text{value}}〉$.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (e02dece.c)

10.2

Program Data

Program Data (e02dece.d)

10.3

Program Results

Program Results (e02dece.r)