# naginterfaces.library.interp.dim1_​monotonic_​intg¶

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

dim1_monotonic_intg evaluates the definite integral of a piecewise cubic Hermite interpolant over the interval .

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

https://www.nag.com/numeric/nl/nagdoc_29/flhtml/e01/e01bhf.html

Parameters
xfloat, array-like, shape

, , and must be unchanged from the previous call of dim1_monotonic().

ffloat, array-like, shape

, , and must be unchanged from the previous call of dim1_monotonic().

dfloat, array-like, shape

, , and must be unchanged from the previous call of dim1_monotonic().

afloat

The interval over which integration is to be performed.

bfloat

The interval over which integration is to be performed.

Returns
pintfloat

The value of the definite integral of the interpolant over the interval .

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, , and .

Constraint: for all .

Warns
NagAlgorithmicWarning
(errno )

Warning – either or is outside the range . The result has been computed by extrapolation and is unreliable. .

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 .

If either or lies outside the interval from to 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