naginterfaces.library.interp.dim1_​monotonic_​deriv

naginterfaces.library.interp.dim1_monotonic_deriv(x, f, d, px)

dim1_monotonic_deriv evaluates a piecewise cubic Hermite interpolant and its first derivative at a set of points.

For full information please refer to the NAG Library document for e01bg

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/e01/e01bgf.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().

pxfloat, array-like, shape $\left(m\right)$

The $m$ values of $x$ at which the interpolant is to be evaluated.

Returns

pffloat, ndarray, shape $\left(m\right)$

$pf[\text{i}-1]$ contains the value of the interpolant evaluated at the point $px[\text{i}-1]$, for $\text{i}=1,2,\dots ,m$.

pdfloat, ndarray, shape $\left(m\right)$

$pd[\text{i}-1]$ contains the first derivative of the interpolant evaluated at the point $px[\text{i}-1]$, for $\text{i}=1,2,\dots ,m$.

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 $r$.

(errno $3$)

On entry, $m=⟨value⟩$.

Constraint: $m\ge 1$.

Warns

NagAlgorithmicWarning

(errno $4$)

Warning – some points in array $px$ lie outside the range $x\left[0\right]\cdots x[n-1]$. Values at these points are unreliable because computed by extrapolation.

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_deriv evaluates a piecewise cubic Hermite interpolant, as computed by dim1_monotonic(), at the points $px[\text{i}-1]$, for $\text{i}=1,2,\dots ,m$. The first derivatives at the points are also computed. If any point lies outside the interval from $x\left[0\right]$ to $x[n-1]$, values of the interpolant and its derivative are extrapolated from the nearest extreme cubic, and a warning is returned.

If values of the interpolant only, and not of its derivative, are required, dim1_monotonic_eval() should be used.

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

References

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