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-----Original Message-----
From: "salah, tarek" <tarek_salah@mentorg.com>
To: oleary@cadence.com, Verilog-ams@server.eda.org,
Verilog-ams@server.eda.org,
        Srikanth.Chandrasekaran@freescale.com
Cc: "Bakalar, Kenneth" <kenneth_bakalar@mentor.com>,
        "Fikry, Maged"
         <maged_fikry@mentor.com>
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Date: Thu, 05 Aug 2004 18:57:58 +0300
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Subject: Re: [Fwd: table model updates [corrected]]
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Please I need to ask about extrapolation of data for more than 1D
case.<br> I think that for 1D case it's simple that if (Xin&gt;Xmax ) or
(Xin&lt;Xmin) then Xin should be treated as a point needing
extrapolation.<br> <br> But, for higher dimensions &amp; given that the
data is <b>scattered,</b> how mathematically is a point defined as
needing extrapolation?<br> <br>

Thanks,<br> Best Regards,<br> Tarek

 -------- Original Message --------
   <pre>[had "paramset" where I meant "table model"]

Sri asked that I send out an e-mail detailing the substantive changes
between the last table model proposal that was sent to the list and the
actual material added to the LRM draft f.

* the table model proposal from Martin had multi-dimensional arrays,
which are not part of AMS; he said I could remove this feature from
table model and wait for m-d arrays to be added to AMS.

* splines have extra degrees of freedom; the following paragraph was
added to address this:

  For both quadratic and cubic interpolation, extra constraints
  are necessary to generate a unique spline over the supplied
  data points. For quadratic interpolation, Lagrange
  interpolation is used to fit a quadratic polynomial over the
  first three data points (those with lowest coordinate values);
  the second derivative of this polynomial is used to specify
  the second derivative of the quadratic spline at the first
  data point. For cubic interpolation, Lagrange interpolation
  is used to fit a cubic polynomial over the first four data
  points and the last four data points, and this polynomial
  is used to determine the second derivative of the cubic
  spline at the first and last data points. If there are not
  enough data points, the second derivatives are assumed to be
  zero.

Note that this differs from the "natural" cubic spline, but gives the
user the flexibility to control the derivative at the endpoints by
adding extra points.

-- 
Geoffrey J. Coram, Ph.D.    Senior CAD Engineer     
Analog Devices, Inc.        <a class="moz-txt-link-abbreviated"
 href="mailto:Geoffrey.Coram@analog.com">Geoffrey.Coram@analog.com</a> 
804 Woburn St., MS-422,     Tel (781) 937-1924
Wilmington, MA 01887        Fax (781) 937-1014