Re: [R] Derivative of expm function
Wagner Bonat wbo...@gmail.com on Wed, 23 Apr 2014 12:12:17 +0200 writes: Hi all ! I am look for some efficient method to compute the derivative of exponential matrix function in R. For example, I have a simple matrix like log.Sigma - matrix(c(par1, rho, rho, par2),2,2) require(Matrix) Sigma - expm(log.Sigma) I want some method to compute the derivatives of Sigma in relation the parameters par1, par2 and rho. Some idea ? The 'expm' package has slightly newer / more reliable algorithms for the matrix exponential. It also contains an expmFrechet() function which computes the Frechet derivative of the matrix exponential. I'm pretty confident -- but did not start thinking more deeply -- that this should provide the necessary parts to get partial derivatives like yours as well. Martin Maechler, ETH Zurich Wagner Hugo Bonat LEG - Laboratório de Estatística e Geoinformação UFPR - Universidade Federal do Paraná __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
[R] Derivative of expm function
Hi all ! I am look for some efficient method to compute the derivative of exponential matrix function in R. For example, I have a simple matrix like log.Sigma - matrix(c(par1, rho, rho, par2),2,2) require(Matrix) Sigma - expm(log.Sigma) I want some method to compute the derivatives of Sigma in relation the parameters par1, par2 and rho. Some idea ? -- Wagner Hugo Bonat LEG - Laboratório de EstatÃstica e Geoinformação UFPR - Universidade Federal do Paraná [[alternative HTML version deleted]] __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Derivative of a function
This is not a homework. I just want to see if there are some R functions or some ideas I can borrow to solve my problem. -- View this message in context: http://r.789695.n4.nabble.com/Derivative-of-a-function-tp3631814p3633071.html Sent from the R help mailing list archive at Nabble.com. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Derivative of a function
On Jun 29, 2011, at 10:48 AM, Lisa wrote: This is not a homework. I just want to see if there are some R functions or some ideas I can borrow to solve my problem. There is a deriv function that provides limited support for symbolic differentiation. The Rhelp list is advertised ( http://www.R-project.org/posting-guide.html ) as expecting you to have made some efforts at searching. This answer might not have floated to the surface among the thousand or so hits, but at least you should have tried. RSiteSearch(derivative) And there is, of course, CrossValidated: http://stats.stackexchange.com/ -- View this message in context: http://r.789695.n4.nabble.com/Derivative-of-a-function-tp3631814p3633071.html Sent from the R help mailing list archive at Nabble.com. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. David Winsemius, MD West Hartford, CT __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Derivative of a function
On Tue, Jun 28, 2011 at 10:03 PM, Lisa lisa...@gmail.com wrote: Dear all, I just want to get the derivative of a function that looks like: y = exp(x1*b) / (exp(x1*b) + exp(x2*b)) where y is a scalar, x1, x2, and b are vectors. I am going to take the derivative of b with respect to y, but I cannot derive an expression in which b is function of y. I know there is another way to get the similar result, i.e., first take the derivative of y with respect to each element of b, and then take its reciprocal. But it is not what I want. Could someone please tell me how to solve this problem? Thank you in advance. Assuming you meant the derivative of y with respect to b: D(expression(exp(x1*b) / (exp(x1*b) + exp(x2*b))), b) exp(x1 * b) * x1/(exp(x1 * b) + exp(x2 * b)) - exp(x1 * b) * (exp(x1 * b) * x1 + exp(x2 * b) * x2)/(exp(x1 * b) + exp(x2 * b))^2 See ?D and also note deriv on the same help page for another alternative. -- Statistics Software Consulting GKX Group, GKX Associates Inc. tel: 1-877-GKX-GROUP email: ggrothendieck at gmail.com __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Derivative of a function
On 30/06/11 06:16, Gabor Grothendieck wrote: On Tue, Jun 28, 2011 at 10:03 PM, Lisalisa...@gmail.com wrote: Dear all, I just want to get the derivative of a function that looks like: y = exp(x1*b) / (exp(x1*b) + exp(x2*b)) where y is a scalar, x1, x2, and b are vectors. I am going to take the derivative of b with respect to y, but I cannot derive an expression in which b is function of y. I know there is another way to get the similar result, i.e., first take the derivative of y with respect to each element of b, and then take its reciprocal. But it is not what I want. Could someone please tell me how to solve this problem? Thank you in advance. Assuming you meant the derivative of y with respect to b: I think the original post made it quite clear that the derivative of b with respect to y was indeed what was wanted; i.e. the OP needs to do implicit differentiation which R does not do automatically. cheers, Rolf Turner D(expression(exp(x1*b) / (exp(x1*b) + exp(x2*b))), b) exp(x1 * b) * x1/(exp(x1 * b) + exp(x2 * b)) - exp(x1 * b) * (exp(x1 * b) * x1 + exp(x2 * b) * x2)/(exp(x1 * b) + exp(x2 * b))^2 See ?D and also note deriv on the same help page for another alternative. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Derivative of a function
Yes. I need to do implicit differentiation. After rearrangement, I got (x2 – x1) * b = log(1 / y - 1) Take derivative of both sides with respect to y, I have (x2 – x1) * b’[y] = - 1/y(1-y) Since both (x2 – x1) and b’[y] are vectors, I cannot move (x2 – x1) to RHS. This is why I posted my question here to see if there is some R functions or some idea that can help me solve this problem. Thanks. Lisa -- View this message in context: http://r.789695.n4.nabble.com/Derivative-of-a-function-tp3631814p3633947.html Sent from the R help mailing list archive at Nabble.com. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Derivative of a function
On Wed, Jun 29, 2011 at 4:35 PM, Lisa lisa...@gmail.com wrote:
Yes. I need to do implicit differentiation. After rearrangement, I got
(x2 – x1) * b = log(1 / y - 1)
Take derivative of both sides with respect to y, I have
(x2 – x1) * b’[y] = - 1/y(1-y)
Since both (x2 – x1) and b’[y] are vectors, I cannot move (x2 – x1) to
RHS. This is why I posted my question here to see if there is some R
functions or some idea that can help me solve this problem. Thanks.
I am not sure if this counts as an approach that you are trying to exclude but:
db[i]/dy = { dlogit(y)/dy } / { dlogit(y)/db[i] } = { 1/{y(1-y)} / {
x1[i] - x2[i] }
The numerator is taken from your calculation and the denominator is
from linearity.
--
Statistics Software Consulting
GKX Group, GKX Associates Inc.
tel: 1-877-GKX-GROUP
email: ggrothendieck at gmail.com
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Re: [R] Derivative of a function
If you just want the value of the derivative at a particular point, would
numerical derivatives suffice? If so, try (for example) the numDeriv package.
S
From: r-help-boun...@r-project.org [r-help-boun...@r-project.org] On Behalf Of
Lisa [lisa...@gmail.com]
Sent: 29 June 2011 21:35
To: r-help@r-project.org
Subject: Re: [R] Derivative of a function
Yes. I need to do implicit differentiation. After rearrangement, I got
(x2 – x1) * b = log(1 / y - 1)
Take derivative of both sides with respect to y, I have
(x2 – x1) * b’[y] = - 1/y(1-y)
Since both (x2 – x1) and b’[y] are vectors, I cannot move (x2 – x1) to
RHS. This is why I posted my question here to see if there is some R
functions or some idea that can help me solve this problem. Thanks.
Lisa
--
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http://r.789695.n4.nabble.com/Derivative-of-a-function-tp3631814p3633947.html
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[R] Derivative of a function
Dear all, I just want to get the derivative of a function that looks like: y = exp(x1*b) / (exp(x1*b) + exp(x2*b)) where y is a scalar, x1, x2, and b are vectors. I am going to take the derivative of b with respect to y, but I cannot derive an expression in which b is function of y. I know there is another way to get the similar result, i.e., first take the derivative of y with respect to each element of b, and then take its reciprocal. But it is not what I want. Could someone please tell me how to solve this problem? Thank you in advance. Lisa -- View this message in context: http://r.789695.n4.nabble.com/Derivative-of-a-function-tp3631814p3631814.html Sent from the R help mailing list archive at Nabble.com. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] Derivative of a function
(1) You really ought to do your own homework. (2) What has this to do with R? cheers, Rolf Turner On 29/06/11 14:03, Lisa wrote: Dear all, I just want to get the derivative of a function that looks like: y = exp(x1*b) / (exp(x1*b) + exp(x2*b)) where y is a scalar, x1, x2, and b are vectors. I am going to take the derivative of b with respect to y, but I cannot derive an expression in which b is function of y. I know there is another way to get the similar result, i.e., first take the derivative of y with respect to each element of b, and then take its reciprocal. But it is not what I want. Could someone please tell me how to solve this problem? Thank you in advance. Lisa -- View this message in context: http://r.789695.n4.nabble.com/Derivative-of-a-function-tp3631814p3631814.html Sent from the R help mailing list archive at Nabble.com. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
