[Quantlib-dev] [ quantlib-Bugs-1121342 ] Implementation of Monotone Spline

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Bugs item #1121342, was opened at 2005-02-12 15:37
Message generated for change (Comment added) made by nando
You can respond by visiting: 
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Category: None
Group: None
Status: Open
Resolution: None
Priority: 5
Submitted By: Nobody/Anonymous (nobody)
Assigned to: Nobody/Anonymous (nobody)
Summary: Implementation of Monotone Spline 

Initial Comment:
My email address is ala...@gm...

The implementation of the Hyman filter for the 
monotonising of the cubic spline is wrong.  The Hyman 
constraints are corrrectly specified but are applied to the
second derivative of the function (y'') rather than to y'.  
In order to implement correctly you need to

i) solve for the y'' values at the node in the usual way
ii) compute the first derivative values y' at each node
iii) generate the appropriate lagrange cubic polynomials 
through the node points with the correct y' value at the 
ends.

The incorrect approach does not guarantee to produce 
monotone splines.  

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>Comment By: Ferdinando Ametrano (nando)
Date: 2005-02-14 11:20

Message:
Logged In: YES 
user_id=34616

why do you say that the contraints are "applied to the
second derivative of the function (y'') rather than to y'." ?

I wrote the code some time ago and I might be rusty, but it
looks to me that the Hyman filter is correctly applied to
the first derivative.

Beside the test suite is able to correctly reproduce Hyman
numerical examples.

Do you have a numerical examples to show a possible
monotonicity failure of the current implementation?

thank you


ciao -- Nando

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