I am trying to take a derivative of an array but am having trouble. The array is two dimensional, x and y directions. I would like to take a derivative along x and along y using central difference discretization. The array has random values of numbers, no values are NaN. I will provide a basic portion of the code below to illustrate my point (assume the array u is defined and has some initial values already inputted into it)
integer :: i,j
integer, parameter :: nx=10, ny=10
real, dimension(-nx:nx, -ny:ny) :: u,v,w
real, parameter :: h
do i=-nx,nx
do j=-ny,ny
v = (u(i+1,j)-u(i-1,j))/(2*h)
w = (u(i,j+1)-u(i,j-1))/(2*h)
end do
end do
Note, assume the array u is defined and filled up before I find v,w. v,w are supposed to be derivatives of the array u along x and along y,respectively. Is this the correct way to take a derivative of an array?
I can see several problems in your code.
1.You must be careful what you have on the left hand side.
v = (u(i+1,j)-u(i-1,j))/(2*h)
means that the whole array v will be set to the same number everywhere. You don't want this in a loop. In a loop you want to set just one point at a time
v(i,j) = (u(i+1,j)-u(i-1,j)) / (2*h)
and 2) You are accessing the array out of bounds. You can keep the simple loop, but you must use the boundary points as "ghost points" which store the boundary values. If I assume that points -nx,nx,-nyandny` are lying on the boundary, then you can only compute the derivative using the central difference inside the domain:
do i=-nx+1,nx-1
do j=-ny+1,ny-1
v(i,j) = (u(i+1,j)-u(i-1,j)) / (2*h)
w(i,j) = (u(i,j+1)-u(i,j-1)) / (2*h)
end do
end do
If you need the derivative on the boundary, you must use a on-sided difference like
do j=-ny+1,ny-1
v(nx,j) = (u(nx,j)-u(nx-1,j)) / h
w(nx,j) = (u(nx,j+1)-u(nx,j-1)) / h
end do
Related
I was looking for a way to generate a logarithmic spaced array in IDL.
From the L3 Harris Geospatial website I came across "arrgen" and was trying to use it for this purpose. However,
arrgen(1,215,/log)
returns the error: Variable is undefined: ARRGEN.
What would be the correct way to do it?
Thanks in advance for your help
Start by defining your lower and upper bounds in which ever log-base you prefer. I will use base $e$ for brevity sake.
lowe = ALOG(low[0])
uppe = ALOG(upp[0])
where low and upp are scalar, numerical values you, the user, define (e.g., 1 and 215 in your example). Then construct an evenly spaced array of n elements, such as:
dinde = DINDGEN(n[0])*(uppe[0] - lowe[0])/(n[0] - 1L) + lowe[0]
where n is a scalar integer. Now convert back to linear space to get:
dind = EXP(dinde)
This will be a logarithmically spaced array. If you want to use base-10 log, then substitute ALOG for ALOG10. If you need another base, then you can use the logarithmic change of base rule given by:
logb x = logc x / logc b
I have 3 graphs of an IV curve (monotonic increasing function. consider a positive quadratic function in the 1st quadrant. Photo attached.) at 3 different temperatures that are not obtained linearly. That is, one is obtained at 25C, one at 125C and one at 150C.
What I want to make is an interpolated 2D array to fill in the other temperatures. My current method to build a meshgrid-type array is as follows:
H = 5;
W = 6;
[Wmat,Hmat] = meshgrid(1:W,1:H);
X = [1:W; 1:W];
Y = [ones(1,W); H*ones(1,W)];
Z = [vecsatIE25; vecsatIE125];
img = griddata(X,Y,Z,Wmat,Hmat,'linear')
This works to build a 6x6 array, which I can then index one row from, then interpolate from that 1D array.
This is really not what I want to do.
For example, the rows are # temps = 25C, 50C, 75C, 100C, 125C and 150C. So I must select a temperature of, say, 50C when my temperature is actually 57.5C. Then I can interpolate my I to get my V output. So again for example, my I is 113.2A, and I can actually interpolate a value and get a V for 113.2A.
When I take the attached photo and digitize the plot information, I get an array of points. So my goal is to input any Temperature and any current to get a voltage by interpolation. The type of interpolation is not as important, so long as it produces reasonable values - I do not want nearest neighbor interpolation, linear or something similar is preferred. If it is an option, I will try different kinds of interpolation later (cubic, linear).
I am not sure how I can accomplish this, ideally. The meshgrid array does not need to exist. I simply need the 1 value.
Thank you.
If I understand the question properly, I think what you're looking for is interp2:
Vq = interp2(X,Y,V,Xq,Yq) where Vq is the V you want, Xq and Yq are the temperature and current, and X, Y, and V are the input arrays for temperature, current, and voltage.
As an option, you can change method between 'linear', 'nearest', 'cubic', 'makima', and 'spline'
I have a large data set with two arrays, say x and y. The arrays have over 1 million data points in size. Is there a simple way to do a scatter plot of only 2000 of these points but have it be representative of the entire set?
I'm thinking along the lines of creating another array r ; r = max(x)*rand(2000,1) to get a random sample of the x array. Is there a way to then find where a value in r is equal to, or close to a value in x ? They wouldn't have to be in the same indexed location but just throughout the whole matrix. We could then plot the y values associated with those found x values against r
I'm just not sure how to code this. Is there a better way than doing this?
I'm not sure how representative this procedure will be of your data, because it depends on what your data looks like, but you can certainly code up something like that. The easiest way to find the closest value is to take the min of the abs of the difference between your test vector and your desired value.
r = max(x)*rand(2000,1);
for i = 1:length(r)
[~,z(i)] = min(abs(x-r(i)));
end
plot(x(z),y(z),'.')
Note that the [~,z(i)] in the min line means we want to store the index of the minimum value in vector z.
You might also try something like a moving average, see this video: http://blogs.mathworks.com/videos/2012/04/17/using-convolution-to-smooth-data-with-a-moving-average-in-matlab/
Or you can plot every n points, something like (I haven't tested this, so no guarantees):
n = 1000;
plot(x(1:n:end),y(1:n:end))
Or, if you know the number of points you want (again, untested):
npoints = 2000;
interval = round(length(x)/npoints);
plot(x(1:interval:end),y(1:interval:end))
Perhaps the easiest way is to use round function and convert things to integers, then they can be compared. For example, if you want to find points that are within 0.1 of the values of r, multiply the values by 10 first, then round:
r = max(x) * round(2000,1);
rr = round(r / 0.1);
xx = round(x / 0.1);
inRR = ismember(xx, rr)
plot(x(inRR), y(inRR));
By dividing by 0.1, any values that have the same integer value are within 0.1 of each other.
ismember returns a 1 for each value of xx if that value is in rr, otherwise a 0. These can be used to select entries to plot.
I'm trying to check if my arrays are returning nonsense by accessing out of bounds elements, in fortran. And I want to check these values are less than one, and if they are, change them to one.
This is the piece of my code causing issues:
lastNeighLabel=(/clusterLabel(jj-1,kk,ll), clusterLabel(jj,kk-1,ll), clusterLabel(jj,kk,ll-1)/)
LastNeighLabel contains the cluster label (between 1 and n, where n isthe total number of unique seperate clusters found) for the last neighbour in the x,y,z direction respectively.
When jj or kk or ll are 1, they try and access the 0th element in the array, and as FORTRAN counts from 1 in arrays, it tries to destroy the universe. I'm currently in a tangled mess of about 8 if/elseif statements trying to code for every eventuality. But I was hoping there was a way of operating on each element. So basically I'd like to say where((/jj-1,kk-1,ll-1/).lt.1) do clusterLabel(jj-1,kk,ll)=0 etc depending on which element is causing the problem.
But I can't think of a way to do that because where will only manipulate the variables passed to it, not a different array at the same index. Or am I wrong?
Will gladly edit if this doesn't make sense.
It is not obligatory that Fortran accesses arrays starting from one. Any starting value is allowed. If it more convenient to you to have a zero indexed array, declare the array as:
real, dimension (0:N-1, 0:M-1) :: array
Or
real, dimension (0:N, 0:M) :: array
and have the 0 indices be extra to catch special cases.
This might be another solution to your problem, since zero index values would be legal.
Another possible way to approach this, is to create an extended cluster label array (with index bounds starting at 0), which is equal to the cluster label array with a layer of zeroes tacked on the outside. You can then let your loop run safely over all values of jj, kk, and ll. It depends on the size of the array if this is a feasible solution.
integer :: extended_cluster_label(0:size(cluster_label,1), &
0:size(cluster_label,2), &
0:size(cluster_label,3) &
)
extended_cluster_label(0,:,:) = 0
extended_cluster_label(:,0,:) = 0
extended_cluster_label(:,:,0) = 0
extended_cluster_label(1:, 1:, 1:) = cluster_label
Maybe you could use a function?
real function f(A,i,j,k)
real :: A(:,:,:)
integer :: i,j,k
if (i==0.or.j==0.or.k==0) then
f=0
else
f=A(i,j,k)
endif
end function f
and then use f(clusterLabel,jj-1,kk,ll) etc.
I have the following (imperative) algorithm that I want to implement in Haskell:
Given a sequence of pairs [(e0,s0), (e1,s1), (e2,s2),...,(en,sn)], where both "e" and "s" parts are natural numbers not necessarily different, at each time step one element of this sequence is randomly selected, let's say (ei,si), and based in the values of (ei,si), a new element is built and added to the sequence.
How can I implement this efficiently in Haskell? The need for random access would make it bad for lists, while the need for appending one element at a time would make it bad for arrays, as far as I know.
Thanks in advance.
I suggest using either Data.Set or Data.Sequence, depending on what you're needing it for. The latter in particular provides you with logarithmic index lookup (as opposed to linear for lists) and O(1) appending on either end.
"while the need for appending one element at a time would make it bad for arrays" Algorithmically, it seems like you want a dynamic array (aka vector, array list, etc.), which has amortized O(1) time to append an element. I don't know of a Haskell implementation of it off-hand, and it is not a very "functional" data structure, but it is definitely possible to implement it in Haskell in some kind of state monad.
If you know approx how much total elements you will need then you can create an array of such size which is "sparse" at first and then as need you can put elements in it.
Something like below can be used to represent this new array:
data MyArray = MyArray (Array Int Int) Int
(where the last Int represent how many elements are used in the array)
If you really need stop-and-start resizing, you could think about using the simple-rope package along with a StringLike instance for something like Vector. In particular, this might accommodate scenarios where you start out with a large array and are interested in relatively small additions.
That said, adding individual elements into the chunks of the rope may still induce a lot of copying. You will need to try out your specific case, but you should be prepared to use a mutable vector as you may not need pure intermediate results.
If you can build your array in one shot and just need the indexing behavior you describe, something like the following may suffice,
import Data.Array.IArray
test :: Array Int (Int,Int)
test = accumArray (flip const) (0,0) (0,20) [(i, f i) | i <- [0..19]]
where f 0 = (1,0)
f i = let (e,s) = test ! (i `div` 2) in (e*2,s+1)
Taking a note from ivanm, I think Sets are the way to go for this.
import Data.Set as Set
import System.Random (RandomGen, getStdGen)
startSet :: Set (Int, Int)
startSet = Set.fromList [(1,2), (3,4)] -- etc. Whatever the initial set is
-- grow the set by randomly producing "n" elements.
growSet :: (RandomGen g) => g -> Set (Int, Int) -> Int -> (Set (Int, Int), g)
growSet g s n | n <= 0 = (s, g)
| otherwise = growSet g'' s' (n-1)
where s' = Set.insert (x,y) s
((x,_), g') = randElem s g
((_,y), g'') = randElem s g'
randElem :: (RandomGen g) => Set a -> g -> (a, g)
randElem = undefined
main = do
g <- getStdGen
let (grownSet,_) = growSet g startSet 2
print $ grownSet -- or whatever you want to do with it
This assumes that randElem is an efficient, definable method for selecting a random element from a Set. (I asked this SO question regarding efficient implementations of such a method). One thing I realized upon writing up this implementation is that it may not suit your needs, since Sets cannot contain duplicate elements, and my algorithm has no way to give extra weight to pairings that appear multiple times in the list.