numerical-methods

Pretty noob question so please bear with me. I am following the example given here--> http://www.codeproject.com/Articles/268589/odeint-v2-Solving-ordinary-differential-equations In particular, I am looking at this function: void lorenz( state_type &x , state_type &dxdt , double t ) { dxdt[0] = sigma * ( x[1] - x[0] ); dxdt[1] = R * x[0] - x[1] - x[0] * x[2]; dxdt[2] = x[0]*x[1] - b * x[2]; } In my case, R takes on a series of values (vector with 100 doubles). odeint is called as: integrate_const( runge_kutta4< state_type >() , lorenz , x , 0.0 , 10.0 , dt ); I would like to do this for each

I am running a numerical experiment that requires many iterations. After each iteration, I would like to store the data in a pickle file or pickle-like file in case the program times-out or a data structure becomes tapped. What is the best way to proceed. Here is the skeleton code: data_dict = {} # maybe a dictionary is not the best choice for j in parameters: # j = (alpha, beta, gamma) and cycle through for k in number_of_experiments: # lots of experiments (10^4) file = open('storage.pkl', 'ab') data = experiment() # experiment returns some numerical value # experiment takes ~ 1 seconds, but

How can I make sure the user inputs numerical values only instead of alphanumeric or any other character? Also what to look for to insert error message for incorrent input? #include<stdio.h> int main() { int a, b, c; printf("Enter first number to add\n"); scanf("%d",&a); printf("Enter second number to add\n"); scanf("%d",&b); c = a + b; printf("Sum of entered numbers = %d\n",c); return 0; } If you really want to deal with user input that could be hostile use a separate function for getting the number. Allows - leading spaces : " 123" - trailing spaces : "123 " - leading zeros :

what's the best way to calculate the average? With this question I want to know which algorithm for calculating the average is the best in a numerical sense. It should have the least rounding errors, should not be sensitive to over- or underflows and so on. Thank you. Additional information: incremental approaches preferred since the number of values may not fit into RAM (several parallel calculations on files larger than 4 GB). You can have a look at http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.43.3535 (Nick Higham, "The accuracy of floating point summation", SIAM Journal of

How do I numerically solve an ODE in Python? Consider \ddot{u}(\phi) = -u + \sqrt{u} with the following conditions u(0) = 1.49907 and \dot{u}(0) = 0 with the constraint 0 <= \phi <= 7\pi. Then finally, I want to produce a parametric plot where the x and y coordinates are generated as a function of u. The problem is, I need to run odeint twice since this is a second order differential equation. I tried having it run again after the first time but it comes back with a Jacobian error. There must be a way to run it twice all at once. Here is the error: odepack.error: The function and its Jacobian

I am starting to learn CUDA and I think calculating long digits of pi would be a nice, introductory project. I have already implemented the simple Monte Carlo method which is easily parallelize-able. I simply have each thread randomly generate points on the unit square, figure out how many lie within the unit circle, and tally up the results using a reduction operation. But that is certainly not the fastest algorithm for calculating the constant. Before, when I did this exercise on a single threaded CPU, I used Machin-like formulae to do the calculation for far faster convergence. For those