Difference between revisions of "MonoCubicInterp"

Latest revision as of 22:21, 24 May 2016

MonoCubicInterp(xi, yi, x, i)

MonoCubicInterp is a function that is used internally by Analytica during various computations. It is not publicly supported nor is it exposed on the function finder or Definition menu.

Given arrays of numerical coordinates «xi» and «yi», indexed by «i», it returns the value of the interpolated function at «x». The values in both «xi» and «yi» must be monotonically increasing. The interpolation performed is a type of cubic spline that preserves the monotonicity of the resulting function with a continuous derivative. A standard cubic spline does not guarantee that the interpolated function is monotonic, even if the data points are.

The derivative is continuous at each data point, and the derivative obtained at the first and last data point are used to extrapolate when «x» is outside the range of «xi».

@@ Line 1: / Line 1: @@
-[[category:Interpolation functions]]
+[[Category:Interpolation functions]]
 [[Category:Doc Status D]] <!-- For Lumina use, do not change -->
-= MonoCubicInterp(d,r,x,I) =
+== MonoCubicInterp(xi, yi, x, ''i'') ==
+[[MonoCubicInterp]] is a function that is used internally by Analytica during various computations. It is not publicly supported nor is it exposed on the function finder or [[Definition menu]].
-[[MonoCubicInterp]] is a function that is used internally by Analytica during various computations.  It is not publicly supported nor is it exposed on the function finder or definition menu.  Although the function is present in 4.1.1 and earlier, it is only functional from an expression in Analytica 4.1.2 or later.
+Given arrays of numerical coordinates «xi» and «yi», indexed by «i», it returns the value of the interpolated function at «x».  The values in both  «xi» and «yi» must be monotonically increasing. The interpolation performed is a type of cubic spline that preserves the monotonicity of the resulting function with a continuous derivative.  A standard [[CubicInterp|cubic spline]] does not guarantee that the interpolated function is monotonic, even if the data points are.
-[[MonoCubicInterp]] performs a smooth interpolation on the points ''(d,r)'', returning the value of the interpolated function at ''x''.  The points ''(d,r)'' must have a common index, specified by the fourth parameter, ''I''.  The values in both ''d'' and ''r'' must be monotonically increasing.  The interpolation performed is a type of cubic spline that preserves the monotonicity of the resulting function with a continuous derivative.  A standard [[CubicInterp|cubic spline]] does not guarantee that the interpolated function is monotonic, even if the data points are.
+The derivative is continuous at each data point, and the derivative obtained at the first and last data point are used to extrapolate when «x» is outside the range of «xi».
-The derivative is continuous at each data point, and the derivative obtained at the first and last data point are used to extrapolate when ''x'' is outside the range of ''d''.
+:[[Image:MonoCubicInterp-graph.png]]
-[[Image:MonoCubicInterp-graph.png]]
-= Library =
-None.  This function is not exposed on the definition menu.
-= See Also =
+== See Also ==
 * [[CubicInterp]]
 * [[LinearInterp]]
 * [[StepInterp]]