SpInterp
Advanced Analysis Library Only
AnalysisLibErrType SpInterp (double arrayX[], double arrayY[], double y2[], ssize_t numberOfElements, double xValue, double *interpolatedYValue);
Purpose
Performs a cubic spline interpolation of the function f at a value x_value, where x_value is in the same range as xi, given a tabulated function of the form yi = f(xi) for i = 0, 1, . . ., numberOfElements – 1, with x < xi + 1, and given the second derivatives that specify the interpolant at the numberOfElements nodes of arrayX. The Spline procedure supplies the second derivatives. You can then call SpInterp as many times as you need, assuming the same tabulated function. If x_value falls in the interval [xi, xi + 1], the interpolated value is as follows:
interpolatedValue = Ayi + Byi + 1 + Cy"i + Dy"i + 1
| where |  |
B = 1 - A |
|
 |
|
 |
y" denotes the second derivative of arrayY.
Example Code
/* Choose ascending X-values. Pick corresponding Y-values randomly. Set
boundary conditions and specify the cubic spline interpolant to run through the
points. Pick an x in the same range as X and interpolate. Pick another x and
interpolate again. */
double X[100], Y[100], Y2[100], b1, b2, x_val;
int n, i;
n = 100;
for(i=0; i<n; i++)
X[i] = i * 0.1;
WhiteNoise (n, 5.0, 17, Y);
b1=0.0;
b2=0.0;
Spline (X, Y, n, b1, b2, Y2);
x_val = 0.331;
SpInterp (X, Y, Y2, n, x_val, &Interp_Val);
x_val = 0.7698;
SpInterp (X, Y, Y2, n, x_val, &Interp_Val);
Parameters
| Input | ||
| Name | Type | Description |
| arrayX | double [] | The known x-values for the planar function; these values must be in ascending order. |
| arrayY | double [] | The known y-values for the planar function. |
| secondDerivatives | double [] | Array of second derivatives that specify the interpolant. |
| numberOfElements | ssize_t | Number of elements in arrayX, arrayY, and secondDerivatives. |
| xValue | double | Value at which tabulated function is interpolated. |
| interpolatedYValue | double * | Interpolated value. |
Return Value
| Name | Type | Description |
| status | AnalysisLibErrType | A value that specifies the type of error that occurred. Refer to analysis.h for definitions of these constants. |
Additional Information
Library: Advanced Analysis Library
Include file: analysis.h
LabWindows/CVI compatibility: LabWindows/CVI 3.1 and later
Example
Refer to analysis\interp.cws for an example of using the SpInterp function.