NAG Library Function Document

nag_1d_quad_vals (d01gac)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{n}$ – IntegerInput

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

Constraint: $\mathbf{n}\ge 4$.

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

On entry: the values of the independent variable, i.e., the $x_1,x_2,\dots ,x_n$.

Constraint: either$\mathbf{x}\left[0\right]<\mathbf{x}\left[1\right]<\cdots <\mathbf{x}\left[\mathbf{n}-1\right]$ or $\mathbf{x}\left[0\right]>\mathbf{x}\left[1\right]>\cdots >\mathbf{x}\left[\mathbf{n}-1\right]$.

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

On entry: the values of the dependent variable $y_{\mathit{i}}$ at the points $x_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n$.

4:    $\mathbf{ans}$ – double *Output

On exit: the estimated value of the integral.

5:    $\mathbf{er}$ – double *Output

On exit: an estimate of the uncertainty in ans.

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.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_INT

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 4$.

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.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

NE_NOT_STRICTLY_DECREASING

The sequence x is not strictly decreasing: $\mathbf{x}\left[〈\mathit{\text{value}}〉\right]=〈\mathit{\text{value}}〉$ and $\mathbf{x}\left[〈\mathit{\text{value}}〉\right]=〈\mathit{\text{value}}〉$.

NE_NOT_STRICTLY_INCREASING

The sequence x is not strictly increasing: $\mathbf{x}\left[〈\mathit{\text{value}}〉\right]=〈\mathit{\text{value}}〉$, $\mathbf{x}\left[〈\mathit{\text{value}}〉\right]=〈\mathit{\text{value}}〉$.

NE_QUAD_FIRST_TWO_PTS_EQL

The sequence x has first two points equal: $\mathbf{x}\left[0\right]=〈\mathit{\text{value}}〉$ and $\mathbf{x}\left[1\right]=〈\mathit{\text{value}}〉$.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (d01gace.c)

10.2

Program Data

Program Data (d01gace.d)

10.3

Program Results

Program Results (d01gace.r)