naginterfaces.library.interp.dim1_​monotonic_​intg

naginterfaces.library.interp.dim1_monotonic_intg(x, f, d, a, b)

dim1_monotonic_intg evaluates the definite integral of a piecewise cubic Hermite interpolant over the interval $[a,b]$.

For full information please refer to the NAG Library document for e01bh

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/e01/e01bhf.html

Parameters

xfloat, array-like, shape $\left(n\right)$

$\text{n}$, $x$, $f$ and $d$ must be unchanged from the previous call of dim1_monotonic().

ffloat, array-like, shape $\left(n\right)$

$\text{n}$, $x$, $f$ and $d$ must be unchanged from the previous call of dim1_monotonic().

dfloat, array-like, shape $\left(n\right)$

$\text{n}$, $x$, $f$ and $d$ must be unchanged from the previous call of dim1_monotonic().

afloat

The interval $[a,b]$ over which integration is to be performed.

bfloat

The interval $[a,b]$ over which integration is to be performed.

Returns

pintfloat

The value of the definite integral of the interpolant over the interval $[a,b]$.

Raises

NagValueError

(errno $1$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 2$.

(errno $2$)

On entry, $r=⟨value⟩$, $x[r-2]=⟨value⟩$ and $x[r-1]=⟨value⟩$.

Constraint: $x[r-2]<x[r-1]$ for all $r$.

Warns

NagAlgorithmicWarning

(errno $3$)

Warning – either $a$ or $b$ is outside the range $x\left[0\right]\cdots x[n-1]$. The result has been computed by extrapolation and is unreliable. $a=⟨value⟩$ $b=⟨value⟩$.

Notes

In the NAG Library the traditional C interface for this routine uses a different algorithmic base. Please contact NAG if you have any questions about compatibility.

dim1_monotonic_intg evaluates the definite integral of a piecewise cubic Hermite interpolant, as computed by dim1_monotonic(), over the interval $[a,b]$.

If either $a$ or $b$ lies outside the interval from $x\left[0\right]$ to $x[n-1]$ computation of the integral involves extrapolation and a warning is returned.

The function is derived from function PCHIA in Fritsch (1982).

References

Fritsch, F N, 1982, PCHIP final specifications, Report UCID-30194, Lawrence Livermore National Laboratory