NAG CL Interface
e02dec (dim2_​spline_​evalv)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{m}$ – Integer Input

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 double Input

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

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: $\mathbf{ff}\left[\mathbf{m}\right]$ – double Output

On exit: $\mathbf{ff}\left[\mathit{r}-1\right]$ contains the value of the spline at the point $(x_{\mathit{r}},y_{\mathit{r}})$, 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 $(\mathbf{nx}-4)\times (\mathbf{ny}-4)$ must be allocated. $\mathbf{c}\left[(\mathbf{ny}-4)\times (\mathit{i}-1)+\mathit{j}-1\right]$ 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 e02dec follows a call to e01dac, e02dcc or e02ddc, in which case, members of the structure spline will have been set up correctly for input to e02dec.

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

The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

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 $(\mathbf{x}\left[⟨\mathit{\text{value}}⟩\right]=⟨\mathit{\text{value}}⟩,\mathbf{y}\left[⟨\mathit{\text{value}}⟩\right]=⟨\mathit{\text{value}}⟩)$ 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

10.2 Program Data

10.3 Program Results