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Thread Subject:
Numeric Laplace transform

Subject: Numeric Laplace transform

From: Lucien Hardy

Date: 3 Jun, 2003 10:03:44

Message: 1 of 13

Hello,


I would like to know if somebody can provide me a way to calculate
the inverse Laplace transform (numeric) of discrete set of
experimental point.


In fact, I know it can be done for the Fourier transform (with the
"ifft" function) and I would like to get the same but for inverse
Laplace transform.


Can anyone help with this, it would be of a GREAT help for me.


Thans in advance.


Lucien.

Subject: Numeric Laplace transform

From: Andrew M. Ross

Date: 3 Jun, 2003 10:57:19

Message: 2 of 13

Lucien Hardy wrote:
> I would like to know if somebody can provide me a way to calculate
> the inverse Laplace transform (numeric) of discrete set of
> experimental point.
> In fact, I know it can be done for the Fourier transform (with the
> "ifft" function) and I would like to get the same but for inverse
> Laplace transform.
> Can anyone help with this, it would be of a GREAT help for me.
> Thans in advance.
> Lucien.

There is a small body of literature on this, much of it by Ward
Whitt and his co-authors. See
http://www.columbia.edu/~ww2040/B.html
for a list. If your experimental points are not regularly
spaced, you might need to interpolate so the inversion routine
can get regular samples. I don't think there's yet any
general-purpose Matlab code to do the inversion, unfortunately.

Andrew

--
Andrew Ross
Industrial and Systems Engineering (www.lehigh.edu/~inime/)
Lehigh University
Bethlehem, Pennsylvania, USA
remove all digits <=4 from my e-mail address to reply

Subject: Numeric Laplace transform

From: Lucien Hardy

Date: 3 Jun, 2003 12:15:03

Message: 3 of 13

Andrew M. Ross wrote:
>
>
> Lucien Hardy wrote:
>> I would like to know if somebody can provide me a way to
> calculate
>> the inverse Laplace transform (numeric) of a discrete set of
>> experimental point.
>> In fact, I know it can be done for the Fourier transform (with
> the
>> "ifft" function) and I would like to get the same but for
inverse
>> Laplace transform.
>> Can anyone help me with this, it would be of a GREAT help for
me.
>> Thanks in advance.
>> Lucien.
>
> There is a small body of literature on this, much of it by Ward
> Whitt and his co-authors. See
> <http://www.columbia.edu/~ww2040/B.html>
> for a list. If your experimental points are not regularly
> spaced, you might need to interpolate so the inversion routine
> can get regular samples. I don't think there's yet any
> general-purpose Matlab code to do the inversion, unfortunately.
>
> Andrew
>
> --
> Andrew Ross
> Industrial and Systems Engineering (www.lehigh.edu/~inime/)
> Lehigh University
> Bethlehem, Pennsylvania, USA
> remove all digits <=4 from my e-mail address to reply
>
>


Hello Andrew,


Thanks a lot for your help. I have downloaded two papers on Laplace
inversion methods.
I will check them to see if I can write a matlab code (though job for
me as I am not an expert of matlab at all !).


Anyway, I find it quite odd that it is not included in Matlab because
the definition of both Laplace and Fourier transforms are very
similar (if I am not wrong) ...


Thanks again !


If anyone else has got other informations/advices, please let me
know.


Lucien.

Subject: Numeric Laplace transform

From: Jinsong

Date: 4 Jun, 2003 03:22:26

Message: 4 of 13

Lucien Hardy wrote:
> Hello,
>
>
> I would like to know if somebody can provide me a way to calculate
> the inverse Laplace transform (numeric) of discrete set of
> experimental point.
>
>
> In fact, I know it can be done for the Fourier transform (with the
> "ifft" function) and I would like to get the same but for inverse
> Laplace transform.
>
>
> Can anyone help with this, it would be of a GREAT help for me.
>
>
> Thans in advance.
>
>
> Lucien.

Lucien,

I have sent you a paper with Matlab code in it. It is rather stable,
from my experience. Hope it helps.

Regards,

Jinsong

Subject: Numeric Laplace transform

From: spellucci@mathematik.tu-darmstadt.de (Peter Spellucci)

Date: 4 Jun, 2003 14:38:32

Message: 5 of 13


In article <eebed25.-1@WebX.raydaftYaTP>,
 "Lucien Hardy" <lhardy@chm.ulaval.ca> writes:
 >Hello,
 >
 >
 >I would like to know if somebody can provide me a way to calculate
 >the inverse Laplace transform (numeric) of discrete set of
 >experimental point.
 >
 >
 >In fact, I know it can be done for the Fourier transform (with the
 >"ifft" function) and I would like to get the same but for inverse
 >Laplace transform.
 >
 >
 >Can anyone help with this, it would be of a GREAT help for me.
 >
if you find nothing in matlab directly, then netlib may help:
http://www.netlib.org/toms
has the codes 619 , 662 and 682 for this. you may "mex" them.
hth
peter

Subject: Numeric Laplace transform : THANKS !

From: Lucien Hardy

Date: 4 Jun, 2003 10:23:59

Message: 6 of 13

Hello everyone,


I have got several answers which look very helpful, so this message
is just intended to thank everyone who helped (in order of answering)
: Andrew, Jinsong, Peter and also Paul and Robyn.


Hoping it will solve my problem, thanks to them ! :-)


Lucien.


P.S. If other people want to add anything else, just keep answering
to this topic !

Subject: Numeric Laplace transform

From: DJL

Date: 4 Jun, 2003 21:29:10

Message: 7 of 13

You could try invlap.m from Karl Hollenbeck. (See below for the shortish
comments and reference).
Note however, that in this case you are required to specify a function F(s)
as an m-file.
I'm not sure exactly what you mean by "experimental points" for F(s).

David Wilson.

% INVLAP numerical inverse Laplace transform
%
% f = invlap(F, t, alpha, tol, P1,P2,P3,P4,P5,P6,P7,P8,P9);
%
% F laplace-space function (string refering to an m-file),
% must have form F(s, P1,..,P9), where s is the Laplace parameter,
% and return column vector as result
% t column vector of times for which real-space function values are
% sought
% alpha largest pole of F (default zero)
% tol numerical tolerance of approaching pole (default 1e-9)
% P1-P9 optional parameters to be passed on to F
% f vector of real-space values f(t)
%
% example: identity function in Laplace space:
% function F = identity(s); % save these two lines
% F = 1./(s.^2); % ... as "identity.m"
% invlap('identity', [1;2;3]) % gives [1;2;3]
%
% algorithm: de Hoog et al's quotient difference method with accelerated
% convergence for the continued fraction expansion
% [de Hoog, F. R., Knight, J. H., and Stokes, A. N. (1982). An improved
% method for numerical inversion of Laplace transforms. S.I.A.M. J. Sci.
% and Stat. Comput., 3, 357-366.]
% Modification: The time vector is split in segments of equal magnitude
% which are inverted individually. This gives a better overall accuracy.

% details: de Hoog et al's algorithm f4 with modifications (T->2*T and
% introduction of tol). Corrected error in formulation of z.
%
% Copyright: Karl Hollenbeck
% Department of Hydrodynamics and Water Resources
% Technical University of Denmark, DK-2800 Lyngby
% email: karl@isv16.isva.dtu.dk
% 22 Nov 1996, MATLAB 5 version 27 Jun 1997 updated 1 Oct 1998
% IF YOU PUBLISH WORK BENEFITING FROM THIS M-FILE, PLEASE CITE IT AS:
% Hollenbeck, K. J. (1998) INVLAP.M: A matlab function for numerical
% inversion of Laplace transforms by the de Hoog algorithm,
% http://www.isva.dtu.dk/staff/karl/invlap.htm


"Lucien Hardy" <lhardy@chm.ulaval.ca> wrote in message
news:eebed25.-1@WebX.raydaftYaTP...
> Hello,
>
>
> I would like to know if somebody can provide me a way to calculate
> the inverse Laplace transform (numeric) of discrete set of
> experimental point.
>
>
> In fact, I know it can be done for the Fourier transform (with the
> "ifft" function) and I would like to get the same but for inverse
> Laplace transform.
>
>
> Can anyone help with this, it would be of a GREAT help for me.
>
>
> Thans in advance.
>
>
> Lucien.

Subject: Numeric Laplace transform

From: Lucien Hardy

Date: 4 Jun, 2003 13:59:41

Message: 8 of 13

DJL wrote:
>
>
> You could try invlap.m from Karl Hollenbeck. (See below for the
> shortish
> comments and reference).
> Note however, that in this case you are required to specify a
> function F(s)
> as an m-file.
> I'm not sure exactly what you mean by "experimental points" for
> F(s).
>
> David Wilson.


Hello David,


By "experimental points", I mean that the set of data points which
for I need to calculate the inverse Laplace transform is obtained
experimentally. More precisely it is a file containing two columns of
data, one for the abscissa and the other for the measured signal
itself.
Note that,in that particular case, the abscissa are "time", I know it
should be frequency as in common case but in that particular case it
is time.
I hope it does not matter as I see it to be regarded as a matter of
"convention".


Regards.


Lucien.

Subject: Numeric Laplace transform

From: Duane Bozarth

Date: 4 Jun, 2003 13:29:37

Message: 9 of 13



Lucien Hardy wrote:
>
> DJL wrote:
> >
> >
> > You could try invlap.m from Karl Hollenbeck. (See below for the
> > shortish
> > comments and reference).
> > Note however, that in this case you are required to specify a
> > function F(s)
> > as an m-file.
> > I'm not sure exactly what you mean by "experimental points" for
> > F(s).
> >
> > David Wilson.
>
> Hello David,
>
> By "experimental points", I mean that the set of data points which
> for I need to calculate the inverse Laplace transform is obtained
> experimentally. More precisely it is a file containing two columns of
> data, one for the abscissa and the other for the measured signal
> itself.
> Note that,in that particular case, the abscissa are "time", I know it
> should be frequency as in common case but in that particular case it
> is time.
> I hope it does not matter as I see it to be regarded as a matter of
> "convention".

What do you intend the "inverse" Laplace transform of a time history to
represent?

Subject: Numeric Laplace transform

From: Lucien Hardy

Date: 4 Jun, 2003 14:47:58

Message: 10 of 13

Duane Bozarth wrote:


> What do you intend the "inverse" Laplace transform of a time
> history to
> represent?
>


According to a reference I have found, my signal should be of the
following form :


H(t)=int[-oo;+oo]{f(k)exp(-kt)dk}=L{f(k)}


(int : integral, L: Laplace transform)


So by inverting H(t) (in terms of Laplace transform), I should get
what I am looking for : f(k).
That's it, I hope my answer is correct ...

Subject: Numeric Laplace transform

From: Lucien Hardy

Date: 4 Jun, 2003 14:49:58

Message: 11 of 13

Duane Bozarth wrote:


> What do you intend the "inverse" Laplace transform of a time
> history to
> represent?
>


According to a reference I have found, my signal H(t) should be of
the following form :


H(t)=int[-oo;+oo]{f(k)exp(-kt)dk}=L{f(k)}


(int : integral, L: Laplace transform)


So by inverting H(t) (in terms of Laplace transform) as stated in
this ref., I should get what I am looking for : f(k).


That's it, I hope my answer is correct ...

Subject: Numeric Laplace transform

From: Eric

Date: 9 Oct, 2014 13:07:11

Message: 12 of 13

Jinsong <jinsongliang@yahoo.com_nospam> wrote in message <b1Vpd89EGHgw@cc.usu.edu>...
> Lucien Hardy wrote:
> > Hello,
> >
> >
> > I would like to know if somebody can provide me a way to calculate
> > the inverse Laplace transform (numeric) of discrete set of
> > experimental point.
> >
> >
> > In fact, I know it can be done for the Fourier transform (with the
> > "ifft" function) and I would like to get the same but for inverse
> > Laplace transform.
> >
> >
> > Can anyone help with this, it would be of a GREAT help for me.
> >
> >
> > Thans in advance.
> >
> >
> > Lucien.
>
> Lucien,
>
> I have sent you a paper with Matlab code in it. It is rather stable,
> from my experience. Hope it helps.
>
> Regards,
>
> Jinsong
>

Hello Jinsong,

I'm really interested in this post. Could you send me too the matlab code to perform the inverse laplace transform of a discrete set of experimental points, please?

Thank you very much in advance,

Eric

Subject: Numeric Laplace transform

From: Eric

Date: 9 Oct, 2014 13:09:11

Message: 13 of 13

"Lucien Hardy" <lhardy@chm.ulaval.ca> wrote in message <eebed25.-1@WebX.raydaftYaTP>...
> Hello,
>
>
> I would like to know if somebody can provide me a way to calculate
> the inverse Laplace transform (numeric) of discrete set of
> experimental point.
>
>
> In fact, I know it can be done for the Fourier transform (with the
> "ifft" function) and I would like to get the same but for inverse
> Laplace transform.
>
>
> Can anyone help with this, it would be of a GREAT help for me.
>
>
> Thans in advance.
>
>
> Lucien.


Hello Luciend,

I'm really interested in this post. Could you send me the matlab code to perform the inverse laplace transform of a discrete set of experimental points, please?

Thank you very much in advance,

Eric

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