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### Highlights from Hermite cubic interpolating polynomial with specified derivatives

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# Hermite cubic interpolating polynomial with specified derivatives

### Nick Henderson (view profile)

Computes piecewise cubic polynomial which interpolates function values and first derivatives.

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Description

PP = PCHIPD(X,Y,D) provides the piecewise cubic polynomial which interpolates values Y and derivatives D at the sites X. This is meant to augment the built-in Matlab function PCHIP, which does not allow the user to specify derivatives.

X must be a vector.

If Y and D are vectors, then Y(i) and D(i) are the value and derivative to be matched at X(i).

If Y and D are matrices, then size(Y,2) == size(D,2) == length(X). Also, size(Y,1) == size(D,1). Use this for interpolating vector valued functions.

YY = PCHIPD(X,Y,D,XX) is the same as YY = PPVAL(PCHIPD(X,Y,D),XX), thus providing, in YY, the values of the interpolant at XX.

Acknowledgements

This file inspired Vasplab.

MATLAB release MATLAB 7.9 (R2009b)
20 Feb 2015 Nick Henderson

### Nick Henderson (view profile)

That is a good question. The matlab documentation for PCHIP says:

"The slopes at the xj are chosen in such a way that P(x) preserves the shape of the data and respects monotonicity."

This submission asks the user to specify the derivatives. Thus, the user could specify derivative values that preserve monotonicity, however this would have to be done explicitly.

Comment only
20 Feb 2015 Jacco

### Jacco (view profile)

Great submission. The regular pchip "respects" monotonicity, while this solution doesn't. Is there anyway I could go about achieving this? Thanks!

16 Jul 2013 M I