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Johannes Bauer

2008-Oct-20 17:41 UTC

[R] R Newbie Question

Hello list,

I just started R today and tried something quite simple. I wanted to
create a colored plot and eventually after hours of fiddling around got
it working. However, my solution seems very suboptimal and I'd really
appreciate your hints on how to improve. I believe that R already offers
many functions I coded (e.g. distance between two vectors, vector
length, vector normalization and so on). I generally didn't even figure
out how to create a simple vector or how to extract a row from a matrix
so the result is a vector (to get scalars, I use the "sum" functions,
which is an incredibly ugly workaround).

To sum the problem up: one has a binary star system with a large star
(e.g. red giant) and a small star (e.g. white dwarf). Gravitation
between them is directly proportional to the mass and indirectly
proportional to the square of the distance. If correctly plotted, one
should be able to see the inner lagrange point L1 which is the point
where the gravitational potentials of the stars "cancel out", e.g. an
object would not be attracted to any star. Well, enough background
information, here's my rookie code - please feel free to comment on
anything :-)

Kind regards,
Johannes



star1center = vector("numeric", 2)
star1center[1] = -0.5
star1center[2] = 0
star1mass = 30

star2center = vector("numeric", 2)
star2center[1] = 0.5
star2center[2] = 0
star2mass = 1

sqr = function(x) {
	return(x * x)
}

distance = function(a, b) {
	return(sqrt(sqr(a[1] - b[1]) + sqr(a[2] - b[2])))
}

len = function(x) {
	return(sqrt(sqr(x[1]) + sqr(x[2])))
}

norm = function(x) {
	return(x / len(x))
}

gravitation = function(invecx, invecy) {
	invec = vector("numeric", 2)
	invec[1] = invecx
	invec[2] = invecy
	vec1 = star1mass * norm(star1center - invec) / sqr(distance(invec,
star1center))
	vec2 = star2mass * norm(star2center - invec) / sqr(distance(invec,
star2center))
	return(len(vec1 + vec2))
}

vmin = -1
vmax = 1
step = 0.1
vals = ((vmax - vmin) / step) + 1

xvals = seq(vmin, vmax, step)
yvals = seq(vmin, vmax, step)

a = expand.grid(seq(vmin, vmax, step), seq(vmin, vmax, step))
b = matrix(seq(1, vals*vals), vals)

for (x in 1:vals) {
	for (y in 1:vals) {
		b[x, y] = gravitation(sum(a[x,][1]), sum(a[y,][1]))
	}
}
filled.contour(xvals, yvals, z = b, color = heat.colors, ylim = c(-1,
1), xlim = c(-1, 1), zlim = c(0, 100), nlevels = 100)

Nordlund, Dan (DSHS/RDA)

2008-Oct-20 18:55 UTC

head link

[R] R Newbie Question

> -----Original Message-----
> From: r-help-bounces at r-project.org 
> [mailto:r-help-bounces at r-project.org] On Behalf Of Johannes Bauer
> Sent: Monday, October 20, 2008 10:42 AM
> To: r-help at r-project.org
> Subject: [R] R Newbie Question
> 
> Hello list,
> 
> I just started R today and tried something quite simple. I wanted to
> create a colored plot and eventually after hours of fiddling 
> around got
> it working. However, my solution seems very suboptimal and I'd really
> appreciate your hints on how to improve. I believe that R 
> already offers
> many functions I coded (e.g. distance between two vectors, vector
> length, vector normalization and so on). I generally didn't 
> even figure
> out how to create a simple vector 
See ?c (i.e. type "?c" without quotes at R prompt)

star1center = c(-0.5, 0)

or how to extract a row > from a matrix
> so the result is a vector (to get scalars, I use the "sum"
functions,
> which is an incredibly ugly workaround).
In your code a[] is not a matrix, it is a data frame.  However, you should be
able to index it just like you would a matrix.  For your code,

b[x, y] = gravitation(a[x,1], a[y,1])

Without the need for the sum() function.
> 
> To sum the problem up: one has a binary star system with a large star
> (e.g. red giant) and a small star (e.g. white dwarf). Gravitation
> between them is directly proportional to the mass and indirectly
> proportional to the square of the distance. If correctly plotted, one
> should be able to see the inner lagrange point L1 which is the point
> where the gravitational potentials of the stars "cancel out",
e.g. an
> object would not be attracted to any star. Well, enough background
> information, here's my rookie code - please feel free to comment on
> anything :-)
> 
> Kind regards,
> Johannes
> 
> 
> <<<snip>>>

I have edited your code to simplify some of your functions and use vectorized
computations.  I'm sure others could provide even more optimized code.  I
will leave it to others to respond concerning already written functions for
norm, len, etc.  You could try using the various search functions with key terms
(like distance) to see what may be available.

star1center = c(-0.5, 0)
star1mass = 30

star2center = c(0.5, 0)
star2mass = 1

sqr = function(x) {
	return(x * x)
}

distance = function(a, b) {
	return(sum((a-b)^2)^0.5)
}

len = function(x) {
	return(sum(x^2)^0.5)
}

norm = function(x) {
	return(x / len(x))
}

gravitation = function(invecx, invecy) {
	invec = c(invecx, invecy)
	vec1 = star1mass * norm(star1center - invec) / sqr(distance(invec,star1center))
	vec2 = star2mass * norm(star2center - invec) / sqr(distance(invec,star2center))
	return(len(vec1 + vec2))
}

vmin = -1
vmax = 1
step = 0.1
vals = ((vmax - vmin) / step) + 1

xvals = seq(vmin, vmax, step)
yvals = seq(vmin, vmax, step)

a = expand.grid(seq(vmin, vmax, step), seq(vmin, vmax, step))
b = matrix(seq(1, vals*vals), vals)

for (x in 1:vals) {
	for (y in 1:vals) {
		b[x, y] = gravitation(a[x,1], a[y,1])
	}
}
filled.contour(xvals, yvals, z = b, color = heat.colors, ylim = c(-1,
1), xlim = c(-1, 1), zlim = c(0, 100), nlevels = 100)

Hope this is helpful,

Dan  

Daniel J. Nordlund
Washington State Department of Social and Health Services
Planning, Performance, and Accountability
Research and Data Analysis Division
Olympia, WA  98504-5204

Gabor Grothendieck

2008-Oct-20 22:43 UTC

head link

[R] R Newbie Question

tIs a bit neater to create list objects for each of
star1 and star2 and then, since the various functions
are not used outside of gravitation stick them right
in gravitation.  Also we can use distance for len
as well by giving it a default second arg of 0 and
sqr does not seem to do much so we can eliminate
that too.

Making the vec computation a function eliminates
some redundant code and using outer eliminates
the two loops.

star1 <- list(mass = 30, center = c(-0.5, 0))
star2 <- list(mass = 1, center = c(0.5, 0))

gravitation2 <- function(v1, v2) {
	distance <- function(a, b = 0) sqrt(sum((a-b)^2))
	norm <- function(x) x/distance(x)
	vec <- function(x) with(x, mass * norm(center - v) / distance(v, center)^2)

	v <- c(v1, v2)
	distance(vec(star1) + vec(star2))
}

xvals2 <- yvals2 <- seq(vmin, vmax, step)
b2 <- outer(xvals, yvals, Vectorize(gravitation2))


On Mon, Oct 20, 2008 at 1:41 PM, Johannes Bauer <dfnsonfsduifb at gmx.de>
wrote:> Hello list,
>
> I just started R today and tried something quite simple. I wanted to
> create a colored plot and eventually after hours of fiddling around got
> it working. However, my solution seems very suboptimal and I'd really
> appreciate your hints on how to improve. I believe that R already offers
> many functions I coded (e.g. distance between two vectors, vector
> length, vector normalization and so on). I generally didn't even figure
> out how to create a simple vector or how to extract a row from a matrix
> so the result is a vector (to get scalars, I use the "sum"
functions,
> which is an incredibly ugly workaround).
>
> To sum the problem up: one has a binary star system with a large star
> (e.g. red giant) and a small star (e.g. white dwarf). Gravitation
> between them is directly proportional to the mass and indirectly
> proportional to the square of the distance. If correctly plotted, one
> should be able to see the inner lagrange point L1 which is the point
> where the gravitational potentials of the stars "cancel out",
e.g. an
> object would not be attracted to any star. Well, enough background
> information, here's my rookie code - please feel free to comment on
> anything :-)
>
> Kind regards,
> Johannes
>
>
>
> star1center = vector("numeric", 2)
> star1center[1] = -0.5
> star1center[2] = 0
> star1mass = 30
>
> star2center = vector("numeric", 2)
> star2center[1] = 0.5
> star2center[2] = 0
> star2mass = 1
>
> sqr = function(x) {
>        return(x * x)
> }
>
> distance = function(a, b) {
>        return(sqrt(sqr(a[1] - b[1]) + sqr(a[2] - b[2])))
> }
>
> len = function(x) {
>        return(sqrt(sqr(x[1]) + sqr(x[2])))
> }
>
> norm = function(x) {
>        return(x / len(x))
> }
>
> gravitation = function(invecx, invecy) {
>        invec = vector("numeric", 2)
>        invec[1] = invecx
>        invec[2] = invecy
>        vec1 = star1mass * norm(star1center - invec) / sqr(distance(invec,
> star1center))
>        vec2 = star2mass * norm(star2center - invec) / sqr(distance(invec,
> star2center))
>        return(len(vec1 + vec2))
> }
>
> vmin = -1
> vmax = 1
> step = 0.1
> vals = ((vmax - vmin) / step) + 1
>
> xvals = seq(vmin, vmax, step)
> yvals = seq(vmin, vmax, step)
>
> a = expand.grid(seq(vmin, vmax, step), seq(vmin, vmax, step))
> b = matrix(seq(1, vals*vals), vals)
>
> for (x in 1:vals) {
>        for (y in 1:vals) {
>                b[x, y] = gravitation(sum(a[x,][1]), sum(a[y,][1]))
>        }
> }
> filled.contour(xvals, yvals, z = b, color = heat.colors, ylim = c(-1,
> 1), xlim = c(-1, 1), zlim = c(0, 100), nlevels = 100)
>
> ______________________________________________
> R-help at 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.
>

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