2d – Calculate the position at given speed and acceleration at a given time

I am attending a Pixar class at the Khan Academy and encountering a simulation of a double spring at a certain time step. I understand how it works and why it behaves that way, but I want to know if the math is actually correct. What interests me are the following lines:

    // mass 1 speed
mass1VelocityY = mass1VelocityY + mass1AccelerationY * timeStep;
mass1VelocityX = mass1VelocityX + mass1AccelerationX * timeStep;

// ground 1 position
mass1PositionY = mass1PositionY + mass1VelocityY * timeStep;
mass1PositionX = mass1PositionX + mass1VelocityX * timeStep;

So we first calculate the speed and add a fraction of the calculated acceleration to it. Then we calculate the position and add a fraction of the calculated speed to it. So we build the final position in time T by summing T / time step Intermediate positions.

Given the formula for the shift s = ut + 0.5at ^ 2 from where:

s = displacement
u = initial speed
a = acceleration
t = time

If I use the values: s = 0, u = 0, a = 1, t = 2, I get s = 2, This means that if I start from zero and build up the speed with an acceleration of 1 m / s / s, I will end up at position 2 with a speed of 2 m / s.

Now, if I try to follow the same logic, but split that result into 20 steps(2 / 0.1 - t = 2 time step = 0.1)If you summarize the results of all these intermediate steps as in this code, I get another result: s = 0.55 at t = 1 and s = 2.1 at t = 2,

My initial intuition is that, because in the code we multiply timeStep twice with the acceleration in the code, this leads to a potentiation and the progression is no longer linear and smaller steps get smaller values ​​at the beginning. So I have 3 questions:

1) Did I understand what the code is doing right?

2) Is what the code does the most correct / accurate method of calculating the displacement?

3) I really want to understand these concepts. So if you have any other advice or know something that might be helpful to me, please let me know.

Parallelization – acceleration of tensor contractions and multiplication

Consider a tensor $ T in mathbb {R} ^ {N times N times N times M} $ and two vectors $ x, y in mathbb {R} ^ N $, I want to calculate that $ N times M $ Vector defined by $ X_ {ij} = operatorname {tr} (x ^ top T _ {:,:, i, j} y) = operatorname {tr} _ {12} (yx ^ top T) $ efficient.

I tried it in two ways:

TCtable[x_, T_, y_] : = Parallel table[Module[{Tslice},
  Tslice = T[[;; , ;; , i, j]];
Tr[x[Transpose].Tslice.y]], {i, 1, length[x]}, {j, 1, last[Dimensions[T]]}];

TCTRACE[x_, T_, y_] : = TensorContract[y.x[Transpose].T, {1, 2}];

My tensors have the very nice property of that $ T _ {:,:, i, j} $ is very economical for everyone $ i, j $ (So ​​I represent my tensor in Mathematica as a sparse array).

With $ N = 500, M = 3 $ The parallel table method takes about 1 second, while the explicit tensor multiplication and partial tracking takes about 20 seconds. Are there other clever ways to speed things up? I would like to calculate this for many different tensors and vectors of the same size. So, if there's a way to compile the code or amortize the complexity, that would be great too!

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real analysis – convergence acceleration of a series using optimal parameters

One way to speed up the convergence of a series is to turn it into a faster series using optimal parameters. Examples of this approach can be found in this article. I have obtained a generalization of this method to express a series with two other independent variables:

If $ | frac {x} {x + y} | <1 $, Then,

$$ sum_ {n = 1} ^ { infty} a_nx ^ n = big ( frac {y} {x + y} big) ^ {r + 1}
sum_ {n = 0} ^ { infty} Big ( frac {x} {x + y} Big) ^ {n} sum_ {k = 0} ^ {n}
{n + r select k + r} a_k y ^ k $$

This expresses a power series in the LHS as two independent variables $ y $ and $ r $ This feature can be theoretically optimized to accelerate the convergence of the series.

question: How to choose the optimum $ y $ and $ r $ so that the RHS converges fastest?

Note: Asked this in MSE, but got no answers in a week. Post it here and delete it from MSE to avoid duplicates.

Algorithms – Understand the linear acceleration set and how strong it is

The linear acceleration set says this for every constant $ c $You can choose the language $ c $ faster It does not mean that you can make it faster by a non-constant function.

The acceleration set works by defining a new Turing machine that writes $ c $ Character of the old Turing machine in a single tape cell, and customize the transient function to simulate in a single step everything that the original machine did between entering and leaving the individual $ c $-Zeichenblock. If $ c $ Since this is a constant, it does not depend on the input. You only have to calculate the new machine once and use it for the input you want. But if you want $ c $ To have a non-constant function, you have to find out what the new machine is each time you run it. This takes an exponentially long time because exponentially many are possible $ c $Token blocks for which you need to find out the transfer function.

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Windows 7 – Disable the annoying acceleration for the volume keys

I have volume keys on my keyboard to increase or decrease the volume. This ad will appear when I change the volume: https://i.imgur.com/9EGglRq.png

Each key changes the volume by 2% per single press. If I press the raise key ten times quickly, the volume will increase by 20%. But as far as the removal of the button is concerned – I have reduced the volume by 50%! It starts slowly, at 2% per 1 press, but eventually the percentage rises above 10% per single press. I wanted to reduce the volume by about 20%, but got too low a sound or was even muted. Now it gets very annoying for me!

Does anyone know how to lower the volume when the acceleration decreases?

android studio – Emulator: Emulator: ERROR: The x86 emulation currently requires hardware acceleration! and Emulator: Operation terminated with exit code 1

I can not virtualize my mobile devices in Android Studio

Try to follow this question:
https://stackoverflow.com/questions/29136173/emulator-error-x86-emulation-currently-erquires-hardware-acceleration

The first was to see if the hardware acceleration was installed and so it was ro

2) I went to the SDK directory C: Users % USERNAME% AppData Local Android sdk extras intel Hardware_Accelerated_Execution_Manager and run the file intelhaxm-android.exe

but it tells me that virtualization is disabled
Enter the description of the picture here

Download this program and ….
Enter the description of the picture here

Virtualization appears activated

If someone can help me, I would appreciate it very much. I just bought a new computer with an Intel processor and was very excited because I thought it would be easy to virtualize

Startup acceleration Ubuntu 18.04

I also have the same issue that I have been looking for a lot, but I can find anything to fix it (I have processor = Intel Core i3, RAM = 4G, Swap = 9G) and my boot info is:

~$ systemd analysis
Startup completed in 10.299s (kernel) + 49.706s (user space) = 1min 6ms
graphics.target reached 49,694s in user space

and graphical analysis

~$ systemd-analysis critical-chain graphical.target
The time after activating or starting the device is printed after the "@" mark.
The time taken for the device to start up is printed after the "+" sign.

graphical.target @ 49.694s
Ultmulti-user.target @ 49.693s
└─mysql.service @ 39.610s + 10.082s
    Worknetwork.target @ 39.607s
└─wpa_supplicant.service @ 34.142s + 5.464s
        └─dbus.service @ 28.807s
└─Basic.target @ 28.749s
└─sockets.target @ 28.749s
└─snapd.socket @ 28,747s + 1 ms
                └─sysinit.target @ 28.719s
└─systemd-timesyncd.service @ 28.477s + 240ms
                    └─systemd-tmpfiles-setup.service @ 27.622s + 716ms
                      └─systemd-journal-flush.service @ 5,195s + 22,426s
                        └─systemd-remount-fs.service @ 4.389s + 803ms
                          └─systemd-journald.socket @ 4.354s
└─system.slice @ 4.354s
└─-.slice @ 4.334s

Time complexity – Definition of acceleration for Amdahl's law

Suppose I have an algorithm C that runs in time T, which decomposes into two "subalgorithms" A and B that run in time p * T and (1-p).T, so the algorithm C needs the time pT + (1-p) * T.

Suppose I have another algorithm C & # 39; that calculates the same thing as the algorithm C that is in time T & # 39; running, where two sub-algorithms A & # 39; and B & # 39; Similar to A and B s.t. p & # 39; * T & # 39; + (1-p & # 39;) * T & # 39; = T & # 39;

I would like to measure the "partial acceleration" of the p-part A of C as in Amdahl's law. Must I

  1. have the subalgorithm A & # 39; to compute exactly the same as A or
  2. can I have another subalgorithm A & # 39; that computes more than A.

In Case 2, can I still use the ratio of execution times from A to A? As acceleration with ratio p?

Suppose I can not do 1. because I do not have such a subalgorithm A # 2. How can I then measure the execution times of A & # 39; and A if p and p are different?