Numerical Differentiation dialog box

 

Use this dialog box to estimate one-dimensional derivatives of empirical data at the given or at interpolated points of selected series.

 

Input

Specifies the worksheet location of the input data for this operation.

 

Valid Input Range

Provides a reference to the extent of the data available in the currently active worksheet. Use this range as a guide for typing valid extents in the Input Range box.

 

Input Range

Type in this box the range of cells containing the data you want to use as input for this command.

 

Values Context

Specifies the context of the values indicated by the Input Range box.

 

Evenly Spaced

Select this option to specify that the data indicated by the Input Range box is spaced at equal intervals of an independent variable.

 

Arbitrarily Spaced

Select this option to specify that the data indicated by the Input Range box is spaced at arbitrary intervals of an independent variable.

 

 

Values in Rows

Check this box to indicate that the data specified by the Input Range box is organized in rows as opposed to columns (the default).

 

Refer to Specifying Input Arguments for additional information on this subject.

 

Output

Specifies the worksheet location for placing the results of this operation.

 

New Workbook

Select this option to place the results of this operation in a new document workbook.

 

New Sheet

Select this option to place the results of this operation in a new worksheet.

 

Range Position

Select this option to place the results of this operation starting at the worksheet location specified in the box to the right of this option.

 

Plot

Check this box to plot the results of this operation.

 

Refer to Specifying Output Locations for additional information on this subject.

 

Options

 

Differentiate

Indicates the points at which differentiation is to take place. Select one of:

 

Given Points

Select this option to differentiate the selected series at the existing series' points.

 

Interpolated Points

Select this option to differentiate the selected series at interpolated points.

 

Method

Specifies the method that will be used to carry out differentiation. Select one of the following:

 

 

Cubic Splines

Select this option to carry differentiation using interpolating cubic splines.

Refer to Cubic Spline Type and Spline End Conditions in this topic or to Interpolating Cubic Splines for additional information on this subject.

 

Difference Formula

Select this option to carry differentiation using difference formulae.

 

Fourier Interpolation

Select this option to carry differentiation in the frequency domain using Fourier transforms.

 

Piecewise Polynomials

Select this option to carry differentiation using piecewise polynomials.

Refer to Piecewise Polynomial Parameters in this topic, or to piecewise polynomials for additional information on this subject.

 

Polynomial Interpolation

Select this option to carry differentiation using polynomial interpolation.

 

Cubic Spline Type

Specifies the type of cubic spline that will be used to carry spline differentiation. Select one of the following:

 

Clamped Spline

Select this option to carry differentiation using splines where the end-point conditions refer to the value of the first derivative of the series at its extreme points.

Refer to Complete Cubic Splines for additional information on this subject.

 

Natural Spline

Select this option to carry differentiation using splines where the end-point conditions refer to the value of the second derivative of the series at its extreme points.

Refer to Natural Cubic Splines for additional information on this subject.

 

Third Derivative

Select this option to carry differentiation using splines where the end-point conditions refer to the value of the third derivative of the series at its extreme points.

Refer to Splines With Specified End-Point Third Derivatives for additional information on this subject.

 

Not-a-Knot Spline

Select this option to carry differentiation using splines where where the third derivative of the spline function is continuous at the second and second-to-last nodes.

Refer to Not-a-knot Splines for additional information on this subject.

 

Refer to Spline End Conditions in this topic, or to Interpolating Cubic Splines for additional information on this subject.

 

Difference

Specifies the type of difference formula that will be used for differentiation. Select one of the following:

 

Backward

Select this option to differentiate using the backward difference formula.

 

Central

Select this option to differentiate using the central difference formula.

 

Forward

Select this option to differentiate using the forward difference formula.

 

Derivatives

Indicates the number of derivatives to calculate at each of the specified points. Type in this box a number equal or greater than one.

 

 

Initial x

This value indicates the initial x-coordinate of the series. Type in this box the x-coordinate of the first point in the series.

 

Delta x

This value indicates the increment between successive x-values. Type in this box the x-increment between successive points in the series.

 

x-Values Range

Specifies a worksheet range containing the x-values related to the functional values of the input range.

Refer to Arbitrarily Spaced on this topic for additional information on this subject.

 

Interpolation and Resampling Values

 

Interval Points

Select this option to interpolate the selected series for the number of points specified in the box to the right of this option, spaced equidistantly between the smallest and largest coordinate values of the independent variables.

 

Values Range

Select this option to interpolate the selected series at particular coordinate values, as specified by the worksheet range in the box to the right of this option.

 

 

Spline End Conditions

Specifies the conditions at the first and last points of the series.  These boxes will have different meanings depending on the type of selected spline. (Cubic Spline Type.)

 

Start Point Condition

Type in this box the value of the condition of the first or start point of the series. For example, type a value of zero (0) for the first derivative of the first point of the series in relation to clamped splines to make the series appear as having extrema at this point..

 

End Point Condition

Type in this box the value of the condition of the last or end point of the series. For example, type a value of one (1) for the first derivative of the last point of the series in relation to clamped splines to make the series appear as increasing at this point.

 

Refer to Cubic Spline Type in this topic, or to Interpolating Cubic Splines for additional information on this subject.

 

Piecewise Polynomial Parameters

Specifies the parameters for calculating derivatives using interpolating piecewise polynomials.

 

Number of Points

Type in this box a number between 3 and 16 to specify the number of consecutive points you want to use for solving the polynomials.

 

 

Center Point

Type in this box a number that specifies the point number of every section where the specified derivatives are calculated.

 

 

Because of length constraints, centering points may differ for derivatives at the extremes of a series. For example, if you choose 3 as the centering point of a 5 points section, derivatives for the series points 1, 2, N-1, and N (N being the length of the series), must be computed at the section point numbers 1, 2, 4 and 5, respectively.

 

OK

Closes the dialog box and carries out this operation.

 

Cancel

Closes the dialog box without carrying out this operation.