[R] spatial analysis
Dear all, I am a PhD student in energy modelling. I am completely stuck with the following problem and would be very grateful for any kind of help. I have cells and each cell is assigned a number. I would like to form clusters of cells where the sum of the cell numbers in each cluster must not exceed 250. One restriction is that only neighbouring cells can be formed into clusters. In the end I would like to have a list with all possible cell combinations. Is it possible to do this with R If yes, I would very much appreciate all possible hints how to solve it. Thanks a lot in advance and kindest regards, Marianne [[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] fitting a sinus curve
Dear all,
Thanks again for your help. I looked at a polynomial regression of 12th order
and the sinus regression and to me the polynomial model seems to fit better.
What do you think?
Thanks a lot,
Mariannne
time <-
c(0.15,0.30,0.45,1.00,1.15,1.30,1.45,2.00,2.15,2.30,2.45,3.00,3.15,3.30,3.45,4.00,4.15,4.30,4.45,5.00,5.15,5.30,5.45,6.00,6.15,6.30,6.45,7.00,7.15,7.30,7.45,8.00,8.15,8.30,8.45,9.00,9.15,9.30,9.45,10.00,10.15,10.30,10.45,11.00,11.15,11.30,11.45,12.00,12.15,12.30,12.45,13.00,13.15,13.30,13.45,14.00,14.15,14.30,14.45,15.00,15.15,15.30,15.45,16.00,16.15,16.30,16.45,17.00,17.15,17.30,17.45,18.00,18.15,18.30,18.45,19.00,19.15,19.30,19.45,20.00,20.15,20.30,20.45,21.00,21.15,21.30,21.45,22.00,22.15,22.30,22.45,23.00,23.15,23.30,23.45,0.00)
watt <-
c(70.8,68.2,65.9,63.3,59.5,55,50.5,46.6,43.9,42.3,41.4,40.8,40.3,39.9,39.5,39.1,38.8,38.5,38.3,38.3,38.5,39.1,40.3,42.4,45.6,49.9,55.3,61.6,68.9,77.1,86.1,95.7,105.8,115.8,124.9,132.3,137.6,141.1,143.3,144.8,146,147.2,148.4,149.8,151.5,153.5,156,159,162.4,165.8,168.4,169.8,169.4,167.6,164.8,161.5,158.1,154.9,151.8,149,146.5,144.4,142.7,141.5,140.9,141.7,144.9,151.5,161.9,174.6,187.4,198.1,205.2,209.1,211.1,212.2,213.2,213,210.4,203.9,192.9,179,164.4,151.5,141.9,135.3,131,128.2,126.1,124.1,121.6,118.2,113.4,107.4,100.8,94.1)
df <- data.frame(conc, vel)
df
polyfit12 <-
lm(watt~time+I(time^2)+I(time^3)+I(time^4)+I(time^5)+I(time^6)+I(time^7)+I(time^8)+I(time^9)+I(time^10)+I(time^11)+(time^12)),
data=df)
coef12<-coef(polyfit12)
coef12
plot(df$conc, df$vel, xlim=c(0,23.45), ylim=c(0,220))
x <- seq(0, 23.34,length=100)
y3 <- cbind(1,x,x^2,x^3,x^4,x^5,x^6,x^7,x^8,x^9,x^10,x^11,x^12) %*% coef12
lines(x,y3)
I am slowly transferring things to a new computer when I found this
Snews post from Bill Venables - it comes in handy from time to time.
http://www.biostat.wustl.edu/archives/html/s-news/1999-09/msg00059.html
sin.cos.fcn <-
function(k, time) {
X <- matrix(0, length(time), 2*k)
for(i in 1:k) {
X[,i] <- sin(i*2*pi*time/96)
X[,k+i] <- cos(i*2*pi*time/96)
}
X
}
mod8 <- lm(watt ~ sin.cos.fcn(8, time/24))
mod8.pred <- predict(mod8)
mod24 <- lm(watt ~ sin.cos.fcn(24, time/24))
mod24.pred <- predict(mod24)
so replotting
plot(pi*time/24, watt, col = "red",
xlim=c(0, pi), ylim=range(watt), main = "Trigonometric Regression")
lines(pi*time/24, mod8.pred, col="cyan")
lines(pi*time/24, mod24.pred, col="blue")
It depends on how well you want to go close to the data and will need
some refinement.
Now for some sustenance!
Regards
Duncan
Duncan Mackay
Department of Agronomy and Soil Science
University of New England
ARMIDALE NSW 2351
Email: home mac...@northnet.com.au
At 20:21 29/07/2011, you wrote:
>David Winsemius comcast.net> writes:
>
> >
> >
> > On Jul 28, 2011, at 1:07 PM, Hans W Borchers wrote:
> >
> > > maaariiianne ec.europa.eu> writes:
> > >
> > >> Dear R community!
> > >> I am new to R and would be very grateful for any kind of help. I am
> > >> a PhD
> > >> student and need to fit a model to an electricity load profile of a
> > >> household (curve with two peaks). I was thinking of looking if a
> > >> polynomial
> > >> of 4th order, a sinus/cosinus combination or a combination of 3
> > >> parabels
> > >> fits the data best. I have problems with the sinus/cosinus
> > >> regression:
>
>time <- c(
>0.00, 0.15, 0.30, 0.45, 1.00, 1.15, 1.30, 1.45, 2.00, 2.15, 2.30, 2.45,
>3.00, 3.15, 3.30, 3.45, 4.00, 4.15, 4.30, 4.45, 5.00, 5.15, 5.30, 5.45, 6.00,
>6.15, 6.30, 6.45, 7.00, 7.15, 7.30, 7.45, 8.00, 8.15, 8.30, 8.45, 9.00, 9.15,
>9.30, 9.45, 10.00, 10.15, 10.30, 10.45, 11.00, 11.15, 11.30, 11.45, 12.00,
>12.15, 12.30, 12.45, 13.00, 13.15, 13.30, 13.45, 14.00, 14.15, 14.30, 14.45,
>15.00, 15.15, 15.30, 15.45, 16.00, 16.15, 16.30, 16.45, 17.00, 17.15, 17.30,
>17.45, 18.00, 18.15, 18.30, 18.45, 19.00, 19.15, 19.30, 19.45, 20.00, 20.15,
>20.30, 20.45, 21.00, 21.15, 21.30, 21.45, 22.00, 22.15, 22.30, 22.45, 23.00,
>23.15, 23.30, 23.45)
>
>watt <- c(
>94.1, 70.8, 68.2, 65.9, 63.3, 59.5, 55, 50.5, 46.6, 43.9, 42.3, 41.4, 40.8,
>40.3, 39.9, 39.5, 39.1, 38.8, 38.5, 38.3, 38.3, 38.5, 39.1, 40.3, 42.4, 45.6,
>49.9, 55.3, 61.6, 68.9, 77.1, 86.1, 95.7, 105.8, 115.8, 124.9, 132.3, 137.6,
>141.1, 143.3, 144.8, 146, 147.2, 148.4, 149.8, 151.5, 153.5, 156, 159, 162.4,
>165.8, 168.4, 169.8, 169.4, 167.6, 164.8, 161.5, 158.1, 154.9, 151.8, 149,
>146.5, 144.4, 142.7, 141.5, 140.9, 141.7, 144.9, 151.5, 161.9, 174.6, 187.4,
>198.1, 205.2, 209.1, 211.1, 212.2, 213.2, 213, 210.4, 203.9, 192.9, 179,
>164.4, 151.5, 141.9, 135.3, 131, 128.2, 126.1, 124.1, 121.6, 118.2, 113.4,
>107.4, 100.8)
>
> > >> df<-data.frame(time, watt)
> > >> lmfit <- lm(time ~ watt + cos(time) + sin(time), data = df)
> > >
> > > Your regression formula does not make sense to me.
> > > You seem to expect a periodic function within 24 hours, and if not
> > > it would
> > > still be possible to subtract the tren
Re: [R] fitting a sinus curve
Dear David and Hans- Werner, Thank you very much for your help. I would like to compare now if a polynomial or the sinus model fits better. How can I see R-squared or the F- Statistic for the sinus regression, so as to be able to compare it with the polynomial model? Thanks a lot and have a nice evening. Best, Mairanne -Original Message- From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On Behalf Of Hans W Borchers Sent: Friday, July 29, 2011 12:21 PM To: r-h...@stat.math.ethz.ch Subject: Re: [R] fitting a sinus curve David Winsemius comcast.net> writes: > > > On Jul 28, 2011, at 1:07 PM, Hans W Borchers wrote: > > > maaariiianne ec.europa.eu> writes: > > > >> Dear R community! > >> I am new to R and would be very grateful for any kind of help. I am > >> a PhD student and need to fit a model to an electricity load > >> profile of a household (curve with two peaks). I was thinking of > >> looking if a polynomial of 4th order, a sinus/cosinus combination > >> or a combination of 3 parabels fits the data best. I have problems > >> with the sinus/cosinus > >> regression: time <- c( 0.00, 0.15, 0.30, 0.45, 1.00, 1.15, 1.30, 1.45, 2.00, 2.15, 2.30, 2.45, 3.00, 3.15, 3.30, 3.45, 4.00, 4.15, 4.30, 4.45, 5.00, 5.15, 5.30, 5.45, 6.00, 6.15, 6.30, 6.45, 7.00, 7.15, 7.30, 7.45, 8.00, 8.15, 8.30, 8.45, 9.00, 9.15, 9.30, 9.45, 10.00, 10.15, 10.30, 10.45, 11.00, 11.15, 11.30, 11.45, 12.00, 12.15, 12.30, 12.45, 13.00, 13.15, 13.30, 13.45, 14.00, 14.15, 14.30, 14.45, 15.00, 15.15, 15.30, 15.45, 16.00, 16.15, 16.30, 16.45, 17.00, 17.15, 17.30, 17.45, 18.00, 18.15, 18.30, 18.45, 19.00, 19.15, 19.30, 19.45, 20.00, 20.15, 20.30, 20.45, 21.00, 21.15, 21.30, 21.45, 22.00, 22.15, 22.30, 22.45, 23.00, 23.15, 23.30, 23.45) watt <- c( 94.1, 70.8, 68.2, 65.9, 63.3, 59.5, 55, 50.5, 46.6, 43.9, 42.3, 41.4, 40.8, 40.3, 39.9, 39.5, 39.1, 38.8, 38.5, 38.3, 38.3, 38.5, 39.1, 40.3, 42.4, 45.6, 49.9, 55.3, 61.6, 68.9, 77.1, 86.1, 95.7, 105.8, 115.8, 124.9, 132.3, 137.6, 141.1, 143.3, 144.8, 146, 147.2, 148.4, 149.8, 151.5, 153.5, 156, 159, 162.4, 165.8, 168.4, 169.8, 169.4, 167.6, 164.8, 161.5, 158.1, 154.9, 151.8, 149, 146.5, 144.4, 142.7, 141.5, 140.9, 141.7, 144.9, 151.5, 161.9, 174.6, 187.4, 198.1, 205.2, 209.1, 211.1, 212.2, 213.2, 213, 210.4, 203.9, 192.9, 179, 164.4, 151.5, 141.9, 135.3, 131, 128.2, 126.1, 124.1, 121.6, 118.2, 113.4, 107.4, 100.8) > >> df<-data.frame(time, watt) > >> lmfit <- lm(time ~ watt + cos(time) + sin(time), data = df) > > > > Your regression formula does not make sense to me. > > You seem to expect a periodic function within 24 hours, and if not > > it would still be possible to subtract the trend and then look at a > > periodic solution. > > Applying a trigonometric regression results in the following > > approximations: library(pracma) plot(2*pi*time/24, watt, col="red") ts <- seq(0, 2*pi, len = 100) xs6 <- trigApprox(ts, watt, 6) xs8 <- trigApprox(ts, watt, 8) lines(ts, xs6, col="blue", lwd=2) lines(ts, xs8, col="green", lwd=2) grid() > > where as examples the trigonometric fits of degree 6 and 8 are used. > > I would not advise to use higher orders, even if the fit is not > > perfect. > > Thank you ! That is a real gem of a worked example. Not only did it > introduce me to a useful package I was not familiar with, but there > was even a worked example in one of the help pages that might have > specifically answered the question about getting a 2nd(?) order trig > regression. If I understood the commentary on that page, this method > might also be appropriate for an irregular time series, whereas > trigApprox and trigPoly would not? That's true. For the moment, the trigPoly() function works correctly only with equidistant data between 0 and 2*pi. > This is adapted from the trigPoly help page in Hans Werner's pracma > package: The error I made myself was to take the 'time' variable literally, though obviously the numbers after the decimal point were meant as minutes. Thus time <- seq(0, 23.75, len = 96) would be a better choice. The rest in your adaptation is absolutely correct. A <- cbind(1, cos(pi*time/24), sin(pi*time/24), cos(2*pi*time/24), sin(2*pi*time/24)) (ab <- qr.solve(A, watt)) # [1] 127.29131 -26.88824 -10.06134 -36.22793 -38.56219 ts <- seq(0, pi, length.out = 100) xs <- ab[1] + ab[2]*cos(ts) + ab[3]*sin(ts) + ab[4]*cos(2*ts) + ab[5]*sin(2*ts) plot(pi*time/24, watt, col = "red", xlim=c(0, pi), ylim=range(watt), main = "Trigonometric Regression") lines(ts, xs, col="blue") > Hans: I corrected the spelling of "Trigonometric", but other than > that I may well have introduced other errors for which I would be > happy to be corrected. For instance, I'm unsure of the terminology > regarding the ordinality of this model. I'm also not sure if my pi/24 > and 2*pi/24 factors were correct in normalizing the time scale, > although the
