Ejemplo n.º 1
0
def check_RungeKutta4_exact_multi(platform, func_src, func_pyf):
    from runge_kutta import RungeKutta


    #----------------------------------------------------
    # Allocate
    #----------------------------------------------------
    ps = PreSetup()
    nx, dt, tmax, yinit = ps.nx, ps.dt, ps.tmax, ps.yinit

    y = ArrayAs(platform, yinit, 'y')

    rk = RungeKutta(platform, nx, dt)


    #----------------------------------------------------
    # Core function
    #----------------------------------------------------
    lib = platform.source_compile(func_src, func_pyf)
    func_core = platform.get_function(lib, 'func')
    func_core.prepare('iDOO', nx)   # (t, y, ret)

    func = lambda t, y, ret: func_core.prepared_call(t,y,ret)
    comm = lambda k: None


    #----------------------------------------------------
    # RK4
    #----------------------------------------------------
    t = 0
    for tstep in xrange(tmax):
        rk.update_rk4(t, y, func, comm)
        t += dt

    aa_equal(ps.exact_func(t), y.get(), 13)
Ejemplo n.º 2
0
def main():
    print MENU
    INPUT = int(raw_input("Option: "))

    if INPUT == 1:
        handle_simpsons_task()
    elif INPUT == 2:
        handle_gaussian_task()
    elif INPUT == 3:
        u0 = float(raw_input("Enter u0: "))
        handle_runge_kutta(u0)
    elif INPUT == 4:
        u0 = float(raw_input("Enter u0: "))
        ranges = float(raw_input("Enter ranges: "))
        runge = RungeKutta(FUNCTION2, u0=u0, start=0.0, end=1.0, ranges=ranges)
        result, h = runge.solve(output=True)
        print "RESULT: {0} with h={1}".format(result, h)
    def __init__(self, config: Config):
        '''The function arguments represent the following polynomial terms:\n
        Ly(x) = g(x)y"(x) + p(x)y'(x) + q(x)y(x) = f(x)\n
        with the following boundary conditions:\n
        a0*y(a) + a1*y'(a) = A,\n
        b0*y(b) + b1*y'(b) = B'''

        a = config['a']
        b = config['b']
        a0 = config['a0']
        a1 = config['a1']
        b0 = config['b0']
        b1 = config['b1']
        A = config['A']
        B = config['B']
        p = config['p(x)']
        q = config['q(x)']
        g = config['g(x)']
        f = config['f(x)']
        if abs(a0) + abs(a1) == 0 or abs(b0) + abs(b1) == 0:
            raise RuntimeError('The boundary condition does not exist.')

        else:
            self.a = a
            self.b = b
            self.C = lambda v, dv, u, du: (B - b0 * v - b1 * dv) / (b0 * u + b1
                                                                    * du)

            self.Lu = f"0 - ({p})*y' / ({g}) - ({q})*y / ({g})"
            self.Lv = f"({f}) / ({g}) - ({p})*y' / ({g}) - ({q})*y / ({g})"

            self.u_func_val = -(a1 / a0) if a0 != 0 else 1
            self.u_diff_val = 1 if a0 != 0 else -(a0 / a1)
            self.v_func_val = A / a0 if a0 != 0 else 0
            self.v_diff_val = 0 if a0 != 0 else A / a1

            self.u_rk = RungeKutta(self.Lu, a, self.u_func_val,
                                   self.u_diff_val)  # First Cauchy problem
            self.v_rk = RungeKutta(self.Lv, a, self.v_func_val,
                                   self.v_diff_val)  # Second Cauchy problem
Ejemplo n.º 4
0
def handle_runge_kutta(u0):
    print "{0: >16}\t{1: <16} {2: <14}".format(
                "H", "Result", "Runge")
    ranges = 10
    prev_result = 0.0
    prev_runge = 0.0
    runge = 0.0
    while ranges <= TASK3.N_LIMIT:
        runge_kutta = RungeKutta(FUNCTION2, u0=u0, start=0.0, end=1.0, ranges=ranges)
        result, h = runge_kutta.solve()
        if prev_result != 0:
            runge = runge_error(prev_result, result, TASK3.PRECISION)
            output = "{0: >16}\t{1: <16} {2: <14} {3: <14}".format(
                h, result, runge, prev_runge*1.0/runge)
        else:
            output = "{0: >16}\t{1: <16}".format(
                h, result)
        print output

        prev_result = result
        prev_runge = runge
        ranges *= 2
Ejemplo n.º 5
0
import os
import matplotlib.pyplot as plt
from problem import Problem1, Problem2
from runge_kutta import RungeKutta


if __name__ == '__main__':
    out_dir = '../report_tex'

    # Problem 1
    for i, epsilon in enumerate([0.05, 0.1, 0.3, 1.0]):
        h = 0.05
        n_iter = 4000
        p1 = Problem1(h, n_iter, epsilon, 0.1, 0.1)
        rk = RungeKutta(p1.h, p1.n_iter, p1.dxdt, p1.dydt, p1.x0, p1.y0)
        rk.solve()
        x, y = rk.get_output()

        plt.figure(figsize=(18, 6))
        plt.subplot(131)
        plt.plot(x, y)
        plt.title(u'$x$-$\dot{x}$')
        plt.xlabel(u'$x$')
        plt.ylabel(u'$\dot{x}$')

        plt.subplot(132)
        plt.plot(x)
        plt.title(u'$t$-$x$')
        plt.xlabel(u'$t$')
        plt.ylabel(u'$\dot{x}$')
Ejemplo n.º 6
0
                velocity[0,gi,gj,0,ie] = 2*pi*(cos(lat)*cos(alpha) + sin(lat)*cos(lon)*sin(alpha))
                velocity[1,gi,gj,0,ie] = - 2*pi*sin(lon)*sin(alpha)
                '''
    """


    #----------------------------------------------
    # spectral element
    #----------------------------------------------
    interact = InteractBetweenElems()
    inside = InsideElems(N, ngll, nelem, state, interact)

    # minimum dx, dt
    max_v = 2*pi
    dt = cfl*min_dx/max_v
    tloop = RungeKutta(dt, inside)
    tloop.allocate(state.psi.shape, state.psi.dtype)


    #----------------------------------------------
    # print the setup information
    #----------------------------------------------
    print '-'*47
    print 'N\t\t', N
    print 'ngll\t\t', ngll
    print 'nelem\t\t', nelem
    print 'cfl\t\t', cfl
    print 'min_dx\t\t', min_dx
    print 'dt\t\t', dt

    #tmax = int( numpy.ceil(1/dt) )
class ReductionMethod:
    '''Solution of the boundary value problem by dividing it into 2 Cauchy problems.'''

    #def __init__(self, a: float, b: float, a0: float, a1: float, A: float, b0: float, b1: float, B: float, p: str, q: str, f: str, g: str = '1'):
    def __init__(self, config: Config):
        '''The function arguments represent the following polynomial terms:\n
        Ly(x) = g(x)y"(x) + p(x)y'(x) + q(x)y(x) = f(x)\n
        with the following boundary conditions:\n
        a0*y(a) + a1*y'(a) = A,\n
        b0*y(b) + b1*y'(b) = B'''

        a = config['a']
        b = config['b']
        a0 = config['a0']
        a1 = config['a1']
        b0 = config['b0']
        b1 = config['b1']
        A = config['A']
        B = config['B']
        p = config['p(x)']
        q = config['q(x)']
        g = config['g(x)']
        f = config['f(x)']
        if abs(a0) + abs(a1) == 0 or abs(b0) + abs(b1) == 0:
            raise RuntimeError('The boundary condition does not exist.')

        else:
            self.a = a
            self.b = b
            self.C = lambda v, dv, u, du: (B - b0 * v - b1 * dv) / (b0 * u + b1
                                                                    * du)

            self.Lu = f"0 - ({p})*y' / ({g}) - ({q})*y / ({g})"
            self.Lv = f"({f}) / ({g}) - ({p})*y' / ({g}) - ({q})*y / ({g})"

            self.u_func_val = -(a1 / a0) if a0 != 0 else 1
            self.u_diff_val = 1 if a0 != 0 else -(a0 / a1)
            self.v_func_val = A / a0 if a0 != 0 else 0
            self.v_diff_val = 0 if a0 != 0 else A / a1

            self.u_rk = RungeKutta(self.Lu, a, self.u_func_val,
                                   self.u_diff_val)  # First Cauchy problem
            self.v_rk = RungeKutta(self.Lv, a, self.v_func_val,
                                   self.v_diff_val)  # Second Cauchy problem

    def get_values(self, step: float) -> float:
        '''Calculates the approximate values of the needed funciton and yields them.'''

        un, vn, dun, dvn = None, None, None, None
        crutch_u = copy(self.u_rk)
        crutch_v = copy(self.v_rk)

        for u_zip, v_zip in zip(
                crutch_u.get_values(
                    self.a, self.b, step
                ),  # Just a crutch for getting the values of v(b) and u(b).
                crutch_v.get_values(self.a, self.b, step)
        ):  # Year, I've made the separate loop for getting these values.
            un, dun = u_zip[1], u_zip[
                2]  # Year, I've gone through this loop twice.
            vn, dvn = v_zip[1], v_zip[
                2]  # I just don't know how to get it without this loop, so this will be depricated in future.

        C = self.C(vn, dvn, un, dun)
        for u_zip, v_zip in zip(self.u_rk.get_values(self.a, self.b, step),
                                self.v_rk.get_values(self.a, self.b, step)):
            x, u, _ = u_zip  # We don't need the derivate here, so it's ommited.
            x, v, _ = v_zip
            yield x, C * u + v
Ejemplo n.º 8
0
    lat1, lon1 = latlons[0,:]
    lat2, lon2 = latlons[1,:]
    min_dx = arccos( sin(lat1)*sin(lat2) + cos(lat1)*cos(lat2)*cos( abs(lon1-lon2) ) ) 

    # minimum dt
    max_v = 2*pi
    dt = cfl*min_dx/max_v


    #----------------------------------------------
    # spectral element
    #----------------------------------------------
    print 'a'
    se = SpectralElement2D(platform, cubegrid, velocity)
    print 'b'
    rk = RungeKutta(platform, ep_size, dt)
    print 'c'


    #----------------------------------------------
    # print the setup information
    #----------------------------------------------
    print '-'*47
    print 'ne\t\t', ne
    print 'ngq\t\t', ngq
    print 'cfl\t\t', cfl
    print 'min_dx\t\t', min_dx
    print 'dt\t\t', dt

    #tmax = int( numpy.ceil(1/dt) )
    tmax = 1000