leapfrog | read your friends better with your internet neighborhood

I'm reading cpdt book (great thanks to the author!). Author gives (unofficial) exercises. There is an exercise 6 below:

1. Using a reflexive inductive definition, define a type nat_tree of infinitary trees, with natural numbers at their leaves and a countable infinity of new trees branching out of each internal node. Define a function increment that increments the number in every leaf of a nat_tree. Define a function leapfrog over a natural i and a tree nt. leapfrog should recurse into the i'th child of nt, the i+1st child of that node, the i+2nd child of the next node, and so on, until reaching a leaf, in which case leapfrog should return the number at that leaf. Prove that the result of any call to leapfrog is incremented by one by calling increment on the tree.

The question is: what datatype does author mean? What I was able to create is kind of

I am writing this OpenCL code that solves an advection equation using leapfrog scheme. I think I've setup the host code and the kernel code correctly but I am getting CL_BUILD_PROGRAM_FAILURE during the kernel compilation.

I did look into the kernel compilation log and here is what I get

I'm trying to test simple leapfrog 2D advection scheme. What I am doing is writing values of each timestep as netCDF4 file. Initial state is set as value of 5.0 in the shape of square. When I print the initial state of the array it looks fine, but when it is written in netCDF4 and look through ncview it looks slanted. I can't figure out why this is happening. I am suspecting that it could be related to the part where I am writing each timestep value as a netCDF4 data (passing p_tf[0][0] in the function nc_put_vara_double). I used the function nc_put_vara_double just how it was used in their coding samples that is on Unidata website.

Does this problem have something to do with p_tf[0][0] and it's indices? Why do you use [0][0] for this function?

Below is the code

Background I am writing a simple N-body simulation code in Python, with core physics solvers such as acceleration and position integration implemented in Cython. The code uses the leapfrog method to integrate the positions.

Conditions

1. Masses: 10, 100 for 2 bodies; 1 for all bodies for number of bodies > 2.
2. Position: Randomly generated
3. Velocity: Randomly generated
4. Timestep: 1e-3

The bug

1. For number of bodies > 2: The bodies repel each other instead of attracting each other.
2. For number of bodies = 2: They do not orbit each other but instead travel in straight lines.
3. General bug (regardless of number of bodies): Repulsive forces

Expected behavior

1. Two bodies must orbit each other
2. The forces must be attractive

Efforts to resolve the bug

1. Negative sign for acceleration
2. Multiply acceleration by -1
3. Add a new temporary expression

Code Acceleration function (Cython):

I am having a problem when save a plot as a PDF. The lines in the plot, as you can see below are much much thicker than the ones in PNG. How do i solve that?

I don't know if i cant place a PDF here, so i took a print screen, sorry for the quality.

And the code i am using is this:

I need to draw a line between point in my analysis.

I have plotted a 2D histogram, and need to plot some points overlaying this histogram and draw a line between them. I already tried plt.plot() but neither the points nor lines appear in the plot. If I use plt.scatter() now the points appear, but I still need to connect the points with a line.

My plot is below:

Any tips in how can I connect those red dots? (I forgot to say it, but i just want to plot some points, in this case 200, not all of them).And the code i used is:

I pretty much deleted the last code and started new. I added a new class called Object which is the replacement for the lists called body_1 and body_2. Also all the calculations are now done from within the Object class. Most previous existing issues were resolved through this process but there is still one that presists. I believe its inside the StartVelocity() function which creates the v1/2 needed to start the Leapfrog algorithm. This should give me a geostationary Orbit but as clearly visible the Satelite escapes very quickly after zooming through earth.

Codes are:

I have been trying to replicate https://diffeqflux.sciml.ai/dev/examples/BayesianNODE_NUTS/, using different ODE equation, but I have received this result without uncertainty quantification, is it because I did the initial value u0 is higher :

Could you please tell me what was wrong?

Considering the following Leapfrog scheme used to discretize a vectorial wave equation with given initial conditions and periodic boundary conditions. I have implemented the scheme and now I want to make numerical convergence tests to show that the scheme is of second order in space and time.

I'm mainly struggling with two points here:

1. I'm not 100% sure if I implemented the scheme correctly. I really wanted to use slicing because it is so much faster than using loops.
2. I don't really know how to get the right error plot, because I'm not sure which norm to use. In the examples I have found (they were in 1D) we've always used the L2-Norm.