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I was looking at this post since I would like to create an array where each column is one x vector aranged by dx with the corresponding dx, respectively. Hopefully this makes sense.

import numpy as np
L = 80.0
N = 2 ** np.arange(-4, 10, dtype = np.float64)
dx = L / N

With my original code, I was on looking at one dx where now I have an array of dx values. When I was only using one dx, I set up my x vector up as follows:

x = np.arange(-L / 2., L / 2. - dx, dx)

However, I need an x for each dx but I am not sure on how to do this. I looked at the post I mentioned in the beginning which has provided, I think, some insight. I can't seem to tailor it to my needs though--maybe it isn't even the correct approach.

Maybe I need a for loop?

for i in len(dx):
    x[i] = np.arange(-L / 2., L / 2. - dx, dx)

Then I would probably need to nest another for loop to pick one dx for each iteration.

I am not sure what would be the correct approach or most efficient though.

To clarify the confusion, in the one dx situation, I had the following set up:

x = np.arange(-L / 2.0, L / 2.0 - dx, dx)                                         
k = np.hstack((np.arange(0, N / 2.0 - 1.0),                                       
               np.arange(-N / 2.0, 0))).T * 2.0 * np.pi / L                       
k1 = 1j * k                                                                       
k3 = (1j * k) ** 3                                                                
u = 2 * (2 / (np.exp(x + 20.0) + np.exp(-x - 20.0))) ** 2                                   
udata = u                                                                         
tdata = 0.0 

Integration here

I then ran the pseudo spectral method with Runge Kutta 4 integration to numerical determine u of the nonlinear KdV equation. I would like to run the code on different dx values so I can find the error and plot 1/dx vs the error where 1/dx is the on the x-axis.

I hope this helps with what I am trying to accomplish.

Since I want to find the error, would I need the same step size? I know the error will plot in the form of exp(-c * dx) where c is an arbitrary constant. I know this because the pseudo spectral method has error of exp(-c / dx) but I will be plotting against 1 / dx.

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    I don't know how to answer your question, but are the different spellings of arrange/arange intentional? I see both in the text, but I don't know enough about python to edit (if it even needs it) Commented Sep 25, 2013 at 13:18
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    I'm not entirely sure what you're asking, do you want to have an NxM array where each column is a different arange? Commented Sep 25, 2013 at 13:34
  • Yeah I also don't quite understand the question. If it's what @bheklilr suggests then you can use broadcasting to do things like np.arange(-2, 2)[..., None] + np.arange(3)[None, ...] Commented Sep 25, 2013 at 13:39
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    Since you want an array composed of these columns, each column will need the same number of elements. But the number of elements would depend on your dx. You might try to use np.linspace where you can specify the number of elements to use but then this would change your dx. Commented Sep 25, 2013 at 13:46

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I'm not sure how you want to deal with the issue that @Joel brought up, because as it stands, having 

x = np.arange(-L / 2., L / 2. - dx, dx)

For different dx will give different sized arrays, which cannot stack. You could create a list of such arrays by using the for loop you propose:

L = 10
dxs =  np.array([1,2,3])
xs = [ np.arange(-L/2, L/2, dx) for dx in dxs ]

Then, xs is:

[array([-5, -4, -3, -2, -1,  0,  1,  2,  3,  4]),
 array([-5, -3, -1,  1,  3]),
 array([-5, -2,  1,  4])]

N.B.: I removed the -dx from the upper limit (L/2 - dx => L/2) because arange already excludes the last point, which you can see because the result never ends with L/2 which is 5.

If you want the stepsize to increase while keeping the same boundaries, this is unavoidable.

If you can change the boundaries and want the step size to increase, but keeping the same number of elements, then I'd suggest something like the following, which allows the boundaries to increase.

x = np.arange(-L/2, L/2)
x
#array([-5, -4, -3, -2, -1,  0,  1,  2,  3,  4])

x * dxs[...,None]
#array([[ -5,  -4,  -3,  -2,  -1,   0,   1,   2,   3,   4],
#       [-10,  -8,  -6,  -4,  -2,   0,   2,   4,   6,   8],
#       [-15, -12,  -9,  -6,  -3,   0,   3,   6,   9,  12]])
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2 Comments

Since I want to find the error, would I need the same step size? I know the error will plot in the form of exp(-c * dx) where c is an arbitrary constant. I know this because the pseudo spectral method has error of exp(-c / dx) but I will be plotting against 1 / dx.
I'm not sure that I understand your application well enough to help. It sounds like dx is the spacing of your points, but that the limits of your problem should set the boundaries (L should be fixed) so you probably want the first solution. You can't make this into an array because the number of points is going to be different for each x, so your original question is perhaps moot, but that shouldn't really be a problem. Just solve it for x in xs.

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