I want to plot a function in scilab in order to find the maximum over a range of numbers:
function y=pr(a,b)
m=1/(1/270000+1/a);
n=1/(1/150000+1/a);
y=5*(b/(n+b)-b/(m+b))
endfunction
x=linspace(10,80000,50)
y=linspace(10,200000,50)
z=feval(x,y,pr)
surf(x,y,z);
disp( max(z))
For these values this is the plot:
It's obvious that increasing the X axis will not increase the maximum but Y axis will.
However from my tests it seems the two axis are mixed up. Increasing the X axis will actually double the max Z value.
For example, this is what happens when I increase the Y axis by a factor of ten (which intuitively should increase the function value):
It seems to increase the other axis (in the sense that z vector is calculated for y,x pair of numbers instead of x,y)!
What am I doing wrong here?
With Scilab's surf you have to use transposed z if comming from feval. It is easy so realize if you use a different number of points in X and Y directions, as surf will complain about the size of the third argument. So in your case, use:
surf(x,y,z')
For more information see the help page of surf.
Stephane's answer is correct, but I thought I'd try to explain better why / what is happening.
From the help surf page (emphasis mine):
X,Y:
two vectors of real numbers, of lengths nx and ny ; or two real matrices of sizes ny x nx: They define the data grid (horizontal coordinates of the grid nodes). All grid cells are quadrangular but not necessarily rectangular. By default, X = 1:size(Z,2) and Y = 1:size(Z,1) are used.
Z:
a real matrix explicitly defining the heights of nodes, of sizes ny x nx.
In other words, think of surf as surf( Col, Row, Z )
From the help feval page (changed notation for convenience):
z=feval(u,v,f):
returns the matrix z such as z(i,j)=f(u(i),v(j))
In other words, in your z output, the i become rows (and therefore u should represent your rows), and j becomes your columns (and therefore v should represent your columns).
Therefore, you can see that you've called feval with the x, y arguments the other way round. In a sense, you should have designed pr so that it should have expected to be called as pr(y,x) instead, so that when passed to feval as feval(y,x,pr), you would end up with an output whose rows increase with y, and columns increase with x.
Then you could have called surf(x, y, z) normally, knowing that x corresponds to columns, and y corresponds to rows.
However, if you don't want to change your whole function just for this, which presumably you don't want to, then you simply have to transpose z in the call to surf, to ensure that you match x to the columns or z' (i.e, the rows of z), and y to the rows of z' (i.e. the columns of z).
Having said all that, it would probably be much better to make your function vectorized, and just use the surf(x, y, pr) syntax directly.
Related
I'm rather new to programming and the site so let me know if I screw up on this explanation.
I have a rather long series of x, y coordinates representing a character in 2d space. Let's say that space is 200 x 400. I want to represent the amount of time the character is in each x, y coordinate by means of a pretty chloropleth.
I want to use heatmaply for this because I think the output is pretty and I want my audience to be able to zoom in on the data. It isn't really meant to do density estimation (I think?) so I'm trying to work around it.
I suppose the way to do this is to fill a 200x400 dataframe with counts of the number of occurrences of each x, y coordinate in the data at each x, y coordinate in the frame. Essentially, to build a 2d map out of the data frame and impose the counts upon it
So, I suppose my questions are:
1). How do I get the count of each unique x, y coordinate in my set
2). How might I pass those counts easily to the matching x, y cell in my 200x400 dataframe full of zeroes?
This seems like it should be easy but I can't seem to figure it out! I'm a novice to r and can't see the shape of what I need to do.
You can use the table function to get your matrix of counts.
table(X,Y)
X and Y should be columns of coordinates.
Output based on some sample data
E.g., when processing the set of plane contours:
each one consists of N nodes and may be described by the matrix N*2
(x, y coordinates of every node).
The number of nodes in the contour is changed during processing.
What is the simplest recommended object (data type) in Julia for such set of contours?
Simplest possible in what way? See GeometryTypes.jl. The "simplest" object, by some definitions of simple, is a vector of 3D points, with (x, y) the node coordinates and z the contour height value. You could use Point3f0 with Float32 or Point3d{T} for Int or Float64. Here you could index with ranges, as Matt suggested above.
If there is a desire for "simple" here to mean keep the contour value in a different category altogether than the (x, y) points, perhaps to save memory, then a Dict{Float32, Vector{Point2f0}}() would do that. The Dict keys would represent the contour numbers. This allows quick indexing by contour but terrible indexing by X and Y ranges as a price for the better memory usage.
If the contour indexes are so regular and predefined that storing them with the points does not matter, you could use Vector{Vector{Point2f0}}, a vector of vectors of Point2f0, with one vector of Point2f0 per contour in your vector of vectors.
I'm having trouble generating a three-dimensional surface plot in Scilab. I keep getting the error:
!--error 999
Objplot3d: x vector is not monotonous.
I'm using the command:
plot3d(x,y,z)
where x and y are 200X1 matrices (aka column vectors) and z is a 200X200 matrix. I thought maybe I had to transpose y, but that led to the same error as well.
help plot3d requires, indeed, that the first two arguments be monotonous (ie sorted). I wish someone could tell me why!
Since your x (and possibly y) is not ordered, which causes the error, you just need to sort them, and then pay some attention to keep the z values where they belong. Something like:
[newx,ix]=gsort(x);
[newy,iy]=gsort(y);
newz = z(ix,iy);
plot3d(newx,newy,newz)
(ix is the permutation such that x(ix)==newx)
Let's say I have a unit vector a = Vector(0,1,0) and I want to add a random spread of something between x = Vector(-0.2,0,-0.2) and y = Vector(0.2,0,0.2), how would I go about doing that?
If I were to simply generate a random vector between x and y, I'd get a value somewhere in the bounds of a square:
What I'd like instead is a value within the circle made up by x and y:
This seems like a simple problem but I can't figure out the solution right now. Any help would be appreciated.
(I didn't ask this on mathoverflow since this isn't really a 'research level mathematics question')
If I read your question correctly, you want a vector in a random direction that's within a particular length (the radius of your circle).
The formula for a circle is: x2 + y2 = r2
So, if you have a maximum radius, r, that constrains the vector length, perhaps proceed something like this:
Choose a random value for x, that lies between -r and +r
Calculate a limit for randomising y, based on your chosen x, so ylim = sqrt(r2 - x2)
Finally, choose a random value of y between -ylim and +ylim
That way, you get a random direction in x and a random direction in y, but the vector length will remain within 0 to r and so will be constrained within a circle of that radius.
In your example, it seems that r should be sqrt(0.22) which is approximately 0.28284.
UPDATE
As 3D vector has length (or magnitude) sqrt(x2+y2+z2) you could extend the technique to 3D although I would probably favour a different approach (which would also work for 2D).
Choose a random direction by choosing any x, y and z
Calculate the magnitude m = sqrt(x2+y2+z2)
Normalise the direction vector (by dividing each element by its magnitude), so x = x/m, y = y/m, z=z/m
Now choose a random length, L between 0 and r
Scale the direction vector by the random length. So x = x * L, y = y * L, z = z * L
If I draw a line from let's say: (2,3) to (42,28), how can I get all points on the line in a Point list? I tried using the slope, but I can't seem to get the hang of it.
To be clear: I would like all the pixels that the line covers. So I can make the line 'clickable'.
This is a math question. The equation of a line is:
y = mx + c
So you need to figure out the gradient (m) and the intercept (c) and then plug in values for x to get values for y.
But what do you mean by "all the points on a line"? There is an infinite number of points if x and y are real numbers.
You can use the formula (x-x1)/(x1-x2) = (y-y1)/(y1-y2). And you know the points with x values ranging from 2 to 42 are on the line and their associated y values have to be found. If any of the resulting y value is not an integer then it should be approximated rightly. And if two consecutive y values differ by more than 1 then the missing y values should be mapped to the last x value.
Here is the pseudo code (tried to capture the crux of the algorithm)
prevY = y1
for(i=x1+1;i<=x2;++i)
{
y = computeY(i);
if(diff(y,prevY)>1) dump_points(prevY,y,i);
prevY = y;
dump_point(i,y);
}
dump_points(prevY,y2,x2);
I am probably not covering all the cases here (esp. not the corner ones). But the idea is that for one value of x there would could be many values of y and vice versa depending on the slope of the line. The algorithm should consider this and generate all the points.