DIFF2.1D.PCHIP Function

DIFF2.1D.PCHIP

Second derivative using Monotone Cubic Spline (Pchip). A special case of cubic spline that preserves monotonicity of the data.

Syntax

=DIFF2.1D.PCHIP(dataX, dataY, queryPoints, extrapolate)

Parameters

Name	Type	Required	Description
dataX	Double[]	Yes	Known x values.
dataY	Double[]	Yes	Known y values.
queryPoints	Object	Yes	Points to differentiate at.
extrapolate	Boolean	No	Allow extrapolation (true/false).

Returns

Calculated result based on input parameters

Examples

Error Conditions

Error	Cause	Solution

About Second Derivatives

The second derivative measures the rate of change of the rate of change - essentially the curvature or acceleration. This function uses PCHIP interpolation for computation.

Understanding Second Derivatives

The second derivative reveals:

• Curvature: How the slope itself is changing
• Acceleration: Rate of change of velocity
• Concavity: Whether curves bend up or down
• Inflection Points: Where curvature changes sign

Practical Applications

• Physics: Calculate acceleration from position
• Optimization: Find maxima and minima
• Structural Analysis: Analyze beam curvature
• Quality Control: Detect trend changes

Related Functions

DIFF2.1D.LINEAR

Second derivative using Linear Spline Interpolation. Note: second derivative of linear spline is zero except at knot points.

DIFF2.1D.CUBIC.SPLINE

Second derivative using Cubic Spline Interpolation.

DIFF2.1D.AKIMA

Second derivative using Akima Spline Interpolation. A special case of cubic spline that is more robust to outliers.

DIFF2.1D.STEP

Second derivative using Step Interpolation. Note: second derivative of step function is zero.

DIFF2.1D.LOGLINEAR

Second derivative using Piece-wise Log-Linear Interpolation. This is equivalent to a linear interpolation in the log-scale.

DIFF2.1D.NEVILLE

Second derivative using Lagrange Polynomial Interpolation (Neville's Algorithm).

See Also

• Method Comparison - Compare different methods
• Quick Start Guide - Get started with the add-in