Hi everyone,
I have a vector with atmospheric measurements (x-axis) that is
obtained/calculated at different altitudes (y-axis). The altitude is
uniformly distributed every 7 meters.
For example my dataframe is:
df <- dataframe(
*altitude* = c(1005, 1012, 1019, 1026, 1033, 1040, 1047, 1054, 1061, 1068),
*atm_values* = c(1.41, 1.40, 1.39, 1.38, 1.37, 1.37, 1.38, 1.36, 1.33, 1.31)
)
How can I find the derivatives of the atmospheric measurements at each
altitude?
I look forward to hearing from you!
Thanks,
Kostas
How to calculate the derivatives at each data point?
7 messages · konstantinos christodoulou, PIKAL Petr, Ivan Krylov +1 more
Hi Konstantinos Not exactly derivative but
diff(df[,2])
[1] -0.01 -0.01 -0.01 -0.01 0.00 0.01 -0.02 -0.03 -0.02 May be enaough for you. Cheers Petr
-----Original Message----- From: R-help <r-help-bounces at r-project.org> On Behalf Of konstantinos christodoulou Sent: Tuesday, January 31, 2023 10:16 AM To: r-help mailing list <r-help at r-project.org> Subject: [R] How to calculate the derivatives at each data point? Hi everyone, I have a vector with atmospheric measurements (x-axis) that is obtained/calculated at different altitudes (y-axis). The altitude is
uniformly
distributed every 7 meters. For example my dataframe is: df <- dataframe( *altitude* = c(1005, 1012, 1019, 1026, 1033, 1040, 1047, 1054, 1061,
1068),
*atm_values* = c(1.41, 1.40, 1.39, 1.38, 1.37, 1.37, 1.38, 1.36, 1.33,
1.31)
) How can I find the derivatives of the atmospheric measurements at each altitude? I look forward to hearing from you! Thanks, Kostas [[alternative HTML version deleted]]
______________________________________________ R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see 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.
? Tue, 31 Jan 2023 11:16:21 +0200 konstantinos christodoulou <konstantinos.christodoulou1 at gmail.com> ?????:
How can I find the derivatives of the atmospheric measurements at each altitude?
Welcome to the world of finite difference methods! If you can find a good textbook on them, it may be a good idea to skim it. pracma::fornberg() will give you a numerically stable approximation (otherwise the Vandermonde matrix required to obtain the Taylor series coefficients may get hard to solve) to the derivative values you're interested in, but do note that they are only approximations. In particular, there's less information for the values at the ends of the altitude range than for the points in the middle.
[[alternative HTML version deleted]]
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Best regards, Ivan
Try something like with(df, predict(smooth.spline(x = altitude, y = atm_values), deriv = 1)) Cheers, Andrew -- Andrew Robinson Chief Executive Officer, CEBRA and Professor of Biosecurity, School/s of BioSciences and Mathematics & Statistics University of Melbourne, VIC 3010 Australia Tel: (+61) 0403 138 955 Email: apro at unimelb.edu.au Website: https://researchers.ms.unimelb.edu.au/~apro at unimelb/ I acknowledge the Traditional Owners of the land I inhabit, and pay my respects to their Elders.
On 31 Jan 2023 at 8:17 PM +1100, konstantinos christodoulou <konstantinos.christodoulou1 at gmail.com>, wrote:
External email: Please exercise caution Hi everyone, I have a vector with atmospheric measurements (x-axis) that is obtained/calculated at different altitudes (y-axis). The altitude is uniformly distributed every 7 meters. For example my dataframe is: df <- dataframe( *altitude* = c(1005, 1012, 1019, 1026, 1033, 1040, 1047, 1054, 1061, 1068), *atm_values* = c(1.41, 1.40, 1.39, 1.38, 1.37, 1.37, 1.38, 1.36, 1.33, 1.31) ) How can I find the derivatives of the atmospheric measurements at each altitude? I look forward to hearing from you! Thanks, Kostas ______________________________________________ R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see 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.
Hi Andrew, I applied your command in another dataset with known derivative values and it gave me very satisfactory results! Therefore, I will use it on my dataset. Thank you so much! Kostas On Tue, Jan 31, 2023 at 12:22 PM Andrew Robinson <apro at unimelb.edu.au> wrote:
Try something like with(df, predict(smooth.spline(x = altitude, y = atm_values), deriv = 1)) Cheers, Andrew -- Andrew Robinson Chief Executive Officer, CEBRA and Professor of Biosecurity, School/s of BioSciences and Mathematics & Statistics University of Melbourne, VIC 3010 Australia Tel: (+61) 0403 138 955 Email: apro at unimelb.edu.au Website: https://researchers.ms.unimelb.edu.au/~apro at unimelb/ I acknowledge the Traditional Owners of the land I inhabit, and pay my respects to their Elders. On 31 Jan 2023 at 8:17 PM +1100, konstantinos christodoulou < konstantinos.christodoulou1 at gmail.com>, wrote: External email: Please exercise caution Hi everyone, I have a vector with atmospheric measurements (x-axis) that is obtained/calculated at different altitudes (y-axis). The altitude is uniformly distributed every 7 meters. For example my dataframe is: df <- dataframe( *altitude* = c(1005, 1012, 1019, 1026, 1033, 1040, 1047, 1054, 1061, 1068), *atm_values* = c(1.41, 1.40, 1.39, 1.38, 1.37, 1.37, 1.38, 1.36, 1.33, 1.31) ) How can I find the derivatives of the atmospheric measurements at each altitude? I look forward to hearing from you! Thanks, Kostas [[alternative HTML version deleted]]
______________________________________________ R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see 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.
Hi Ivan! Thank you for your valuable insights! I look forward to learning more about numerical differentiation and about this subject. The pracma package and the fornberg() function is impressive. I got some really good approximations on my derivatives. Thank you! Kostas
On Tue, Jan 31, 2023 at 12:18 PM Ivan Krylov <krylov.r00t at gmail.com> wrote:
? Tue, 31 Jan 2023 11:16:21 +0200 konstantinos christodoulou <konstantinos.christodoulou1 at gmail.com> ?????:
How can I find the derivatives of the atmospheric measurements at each altitude?
Welcome to the world of finite difference methods! If you can find a good textbook on them, it may be a good idea to skim it. pracma::fornberg() will give you a numerically stable approximation (otherwise the Vandermonde matrix required to obtain the Taylor series coefficients may get hard to solve) to the derivative values you're interested in, but do note that they are only approximations. In particular, there's less information for the values at the ends of the altitude range than for the points in the middle.
[[alternative HTML version deleted]]
P.S. Please compose your messages to R-help in plain text:
Thank you Petr!
On Tue, Jan 31, 2023 at 11:58 AM PIKAL Petr <petr.pikal at precheza.cz> wrote:
Hi Konstantinos Not exactly derivative but
diff(df[,2])
[1] -0.01 -0.01 -0.01 -0.01 0.00 0.01 -0.02 -0.03 -0.02 May be enaough for you. Cheers Petr
-----Original Message----- From: R-help <r-help-bounces at r-project.org> On Behalf Of konstantinos christodoulou Sent: Tuesday, January 31, 2023 10:16 AM To: r-help mailing list <r-help at r-project.org> Subject: [R] How to calculate the derivatives at each data point? Hi everyone, I have a vector with atmospheric measurements (x-axis) that is obtained/calculated at different altitudes (y-axis). The altitude is
uniformly
distributed every 7 meters. For example my dataframe is: df <- dataframe( *altitude* = c(1005, 1012, 1019, 1026, 1033, 1040, 1047, 1054, 1061,
1068),
*atm_values* = c(1.41, 1.40, 1.39, 1.38, 1.37, 1.37, 1.38, 1.36, 1.33,
1.31)
)
How can I find the derivatives of the atmospheric measurements at each
altitude?
I look forward to hearing from you!
Thanks,
Kostas
[[alternative HTML version deleted]]
______________________________________________ R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see 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.