NAG CL Interface
e02adc (dim1_​cheb_​arb)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{m}$ – Integer Input

On entry: the number $m$ of data points.

Constraint: $\mathbf{m}\ge \mathit{mdist}\ge 2$, where $\mathit{mdist}$ is the number of distinct $x$ values in the data.

2: $\mathbf{kplus1}$ – Integer Input

On entry: $k+1$, where $k$ is the maximum degree required.

Constraint: $0<\mathbf{kplus1}\le \mathit{mdist}$, where $\mathit{mdist}$ is the number of distinct $x$ values in the data.

3: $\mathbf{tda}$ – Integer Input

On entry: the stride separating matrix column elements in the array a.

Constraint: $\mathbf{tda}\ge \mathbf{kplus1}$.

4: $\mathbf{x}\left[\mathbf{m}\right]$ – const double Input

On entry: the values $x_{\mathit{r}}$ of the independent variable, for $\mathit{r}=1,2,\dots ,m$.

Constraint: the values must be supplied in nondecreasing order with $\mathbf{x}\left[m-1\right]>\mathbf{x}\left[0\right]$.

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

On entry: the values $y_{\mathit{r}}$ of the dependent variable, for $\mathit{r}=1,2,\dots ,m$.

6: $\mathbf{w}\left[\mathbf{m}\right]$ – const double Input

On entry: the set of weights, $w_{\mathit{r}}$, for $\mathit{r}=1,2,\dots ,m$. For advice on the choice of weights, see the E02 Chapter Introduction.

Constraint: $\mathbf{w}\left[\mathit{r}\right]>0.0$, for $\mathit{r}=0,1,\dots ,\mathbf{m}-1$.

7: $\mathbf{a}\left[\mathbf{kplus1}\times \mathbf{tda}\right]$ – double Output

On exit: the coefficients of ${\mathrm{T}}_{\mathit{j}}\left(\overline{x}\right)$ in the approximating polynomial of degree $\mathit{i}$. $\mathbf{a}\left[\left(\mathit{i}\right)\times \mathbf{tda}+\mathit{j}\right]$ contains the coefficient $a_{\mathit{i}+1,\mathit{j}+1}$, for $\mathit{i}=0,1,\dots ,k$ and $\mathit{j}=0,1,\dots ,\mathit{i}$.

8: $\mathbf{s}\left[\mathbf{kplus1}\right]$ – double Output

On exit: $\mathbf{s}\left[\mathit{i}\right]$ contains the root mean square residual $s_{\mathit{i}}$, for $\mathit{i}=0,1,\dots ,k$, as described in Section 3. For the interpretation of the values of the $s_{\mathit{i}}$ and their use in selecting an appropriate degree, see the E02 Chapter Introduction.

9: $\mathbf{fail}$ – 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_2_INT_ARG_GT

On entry, $\mathbf{kplus1}=〈\mathit{\text{value}}〉$ while the number of distinct $x$ values, $\mathit{mdist}=〈\mathit{\text{value}}〉$. These arguments must satisfy $\mathbf{kplus1}\le \mathit{mdist}$.

NE_2_INT_ARG_LT

On entry, $\mathbf{tda}=〈\mathit{\text{value}}〉$ while $\mathbf{kplus1}=〈\mathit{\text{value}}〉$.
The arguments must satisfy $\mathbf{tda}\ge \mathbf{kplus1}$.

NE_ALLOC_FAIL

Dynamic memory allocation failed.

NE_INT_ARG_LT

On entry, kplus1 must not be less than 1: $\mathbf{kplus1}=〈\mathit{\text{value}}〉$.

NE_NO_NORMALISATION

On entry, all the $\mathbf{x}\left[r\right]$ in the sequence $\mathbf{x}\left[r\right]$, $r=0,1,\dots ,\mathbf{m}-1$ are the same.

NE_NOT_NON_DECREASING

On entry, the sequence $\mathbf{x}\left[r\right]$, $r=0,1,\dots ,\mathbf{m}-1$ is not in nondecreasing order.

NE_WEIGHTS_NOT_POSITIVE

On entry, the weights are not strictly positive: $\mathbf{w}\left[〈\mathit{\text{value}}〉\right]=〈\mathit{\text{value}}〉$.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results