From: Elassaiss - Schaap, J. <*jeroen.elassaiss-schaap*>

Date: Fri, 23 Sep 2011 09:05:47 +0200

Nick,

The help entry makes sense to me. When one assumes that both tolerances are=

converted as

tolerance = 10^(-TOL)

they are appropriately scaled.

And with regard to the html fragment you referred to, it seems to me like a=

pragmatic advice rather than stating that those numbers should be kept equ=

al. It also makes sense that if you want more accurate positive numbers you=

also may want the zero defined more accurately.

Thanks for the solver link!

Best regards,

Jeroen

-----Original Message-----

From: owner-nmusers

Behalf Of Nick Holford

Sent: Thursday, September 22, 2011 23:02

To: nmusers

Subject: Re: [NMusers] "ERROR IN LSODA: CODE -1"

Hi,

I think it may be useful to understand that numerical differential

equation solvers require an absolute tolerance as well as a relative

tolerance. See

http://www.gnu.org/software/octave/doc/interpreter/Differential_002dAlgebra=

ic-Equations.html

for an explanation and example of how these tolerances are typically used.

The need for an absolute tolerance is when the correct solution of the

DE is zero. In this case a relative tolerance cannot guide the numerical

DE solver to achieve a sufficiently precise solution.

An absolute tolerance is analogous to an additive residual error while

relative tolerance is analogous to a proportional residual error. Thus

the absolute and relative tolerance criteria have no direct numerical

relationship to each other.

The online NM7 help describes ATOL like this:

ATOL=n

Absolute tolerance. Used only with ADVAN13, for which TOL is a rela-

tive tolerance. The default is 12; a smaller value (equal to TOL) may

improve run time. May also be set with $COVARIANCE record.

The NM7 definition is rather mysterious. If ATOL is really an absolute

tolerance criterion then a value of 12 would be ridiculous if the scale

of the solution was in say the 1 to 100 range. Perhaps we are expected

to guess that ATOL means 10D-12?

I cannot see any reason to suggest why ATOL should be set equal to TOL

because these numbers are like apples and oranges and cannot be

compared. Some ODE solvers allow ATOL as a vector to match the DADT

vector so that the absolute tolerance for each solution could be

individually specified.

Nick

Notice: This e-mail message, together with any attachments, contains

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for affiliates is available at

http://www.merck.com/contact/contacts.html) that may be confidential,

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Received on Fri Sep 23 2011 - 03:05:47 EDT

Date: Fri, 23 Sep 2011 09:05:47 +0200

Nick,

The help entry makes sense to me. When one assumes that both tolerances are=

converted as

tolerance = 10^(-TOL)

they are appropriately scaled.

And with regard to the html fragment you referred to, it seems to me like a=

pragmatic advice rather than stating that those numbers should be kept equ=

al. It also makes sense that if you want more accurate positive numbers you=

also may want the zero defined more accurately.

Thanks for the solver link!

Best regards,

Jeroen

-----Original Message-----

From: owner-nmusers

Behalf Of Nick Holford

Sent: Thursday, September 22, 2011 23:02

To: nmusers

Subject: Re: [NMusers] "ERROR IN LSODA: CODE -1"

Hi,

I think it may be useful to understand that numerical differential

equation solvers require an absolute tolerance as well as a relative

tolerance. See

http://www.gnu.org/software/octave/doc/interpreter/Differential_002dAlgebra=

ic-Equations.html

for an explanation and example of how these tolerances are typically used.

The need for an absolute tolerance is when the correct solution of the

DE is zero. In this case a relative tolerance cannot guide the numerical

DE solver to achieve a sufficiently precise solution.

An absolute tolerance is analogous to an additive residual error while

relative tolerance is analogous to a proportional residual error. Thus

the absolute and relative tolerance criteria have no direct numerical

relationship to each other.

The online NM7 help describes ATOL like this:

ATOL=n

Absolute tolerance. Used only with ADVAN13, for which TOL is a rela-

tive tolerance. The default is 12; a smaller value (equal to TOL) may

improve run time. May also be set with $COVARIANCE record.

The NM7 definition is rather mysterious. If ATOL is really an absolute

tolerance criterion then a value of 12 would be ridiculous if the scale

of the solution was in say the 1 to 100 range. Perhaps we are expected

to guess that ATOL means 10D-12?

I cannot see any reason to suggest why ATOL should be set equal to TOL

because these numbers are like apples and oranges and cannot be

compared. Some ODE solvers allow ATOL as a vector to match the DADT

vector so that the absolute tolerance for each solution could be

individually specified.

Nick

Notice: This e-mail message, together with any attachments, contains

information of Merck & Co., Inc. (One Merck Drive, Whitehouse Station,

New Jersey, USA 08889), and/or its affiliates Direct contact information

for affiliates is available at

http://www.merck.com/contact/contacts.html) that may be confidential,

proprietary copyrighted and/or legally privileged. It is intended solely

for the use of the individual or entity named on this message. If you are

not the intended recipient, and have received this message in error,

please notify us immediately by reply e-mail and then delete it from

your system.

Received on Fri Sep 23 2011 - 03:05:47 EDT