# coding utf8 import math import Numeric import string import copy class

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155``` ```# -*- coding: utf8 -*- import math import Numeric import string import copy class Equation: def __init__(self, f, t0, x0, cnst, values = None): self.f = f self.t0 = t0 self.x0 = x0 self.cnst = {} if values == None: for el in cnst: self.cnst[el] = 1 else: for i in xrange(len(cnst)): self.cnst[cnst[i]] = values[i] def __call__(self, t, x): cnst = copy.deepcopy(self.cnst) cnst['t'] = t for i in xrange(len(self.f)): str = 'x%d' % (i + 1) cnst[str] = x[i] cnst['math'] = math res = [] for i in xrange(len(self.f)): res.append(eval(self.f[i], cnst)) return res def set_cnst(self, cnst): self.cnst = cnst def get_cnst(self): return self.cnst def check_parameters(self): for el in self.x0: if el < 0: return 0 # if there are negative x0[i] return 1 class RungeKutta: def __init__(self, eq, h, t1): self.eq = eq self.h = h self.t1 = t1 def run(self): # returns [... [ti, xi] ...] tn = string.atof(self.eq.t0) xn = [] for i in xrange(len(self.eq.x0)): xn.append(string.atof(self.eq.x0[i])) x = [] x.append([tn, copy.deepcopy(xn)]) self.h = string.atof(self.h) while(tn + self.h <= self.t1): k1 = self.eq(tn, xn) ktmp = [] for i in xrange(len(k1)): ktmp.append(xn[i] + k1[i] * self.h / 2) k2 = self.eq(tn + self.h / 2, ktmp) ktmp = [] for i in xrange(len(k2)): ktmp.append(xn[i] + k2[i] * self.h / 2) k3 = self.eq(tn + self.h / 2, ktmp) ktmp = [] for i in xrange(len(k3)): ktmp.append(xn[i] + k3[i] * self.h) k4 = self.eq(tn + self.h, ktmp) for i in xrange(len(self.eq.x0)): xn[i] += self.h / 6 * (k1[i] + 2 * k2[i] + 2 * k3[i] + k4[i]) tn += self.h x.append([tn, copy.deepcopy(xn)]) return x class MNKO: def __init__(self, X, y): self.X = copy.deepcopy(X) self.y = copy.deepcopy(y) self.tetha = Numeric.zeros((self.X.shape[1], 1), 'f') def run(self): H_s = Numeric.zeros((self.X.shape[1], self.X.shape[1]), 'f') a_s = Numeric.zeros((1, self.X.shape[1]), 'f') h_s = Numeric.zeros((1, self.X.shape[1]), 'f') s = 0 b_s = Numeric.dot(Numeric.transpose(self.X[:,0:1]), self.X[:,0:1])[0][0] gamma_s = Numeric.dot(Numeric.transpose(self.X[:,0:1]), self.y)[0][0] t_s = 1. / b_s * gamma_s self.tetha[0, 0] = t_s print self.tetha for s in xrange(1, self.X.shape[1]): if s != 1: H_s[0:s-1, 0:s-1] += Numeric.multiply(Numeric.dot(a_s[:, 0:s-1], Numeric.transpose(a_s[:, 0:s-1])), 1. / b_s) H_s[0:s-1, s-1:s] -= Numeric.multiply(Numeric.transpose(a_s[:, 0:s-1]), 1. / b_s) H_s[s-1:s, 0:s-1] -= Numeric.product(a_s[:, 0:s-1], 1. / b_s) H_s[s-1, s-1] = 1. / b_s h_s = Numeric.dot(Numeric.transpose(self.X[:,0:s]), self.X[:,s:s+1]) a_s[:, 0:s] = Numeric.dot(H_s[0:s, 0:s], h_s[:, 0:s]) b_s = Numeric.dot(Numeric.transpose(self.X[:,s:s+1]), self.X[:,s:s+1])[0][0] - Numeric.dot(Numeric.transpose(h_s[:,0:s]), a_s[:,0:s])[0][0] gamma_s = Numeric.dot(Numeric.transpose(self.X[:,s:s+1]), self.y)[0][0] t_s = 1. / b_s * (gamma_s - Numeric.dot(Numeric.transpose(h_s[:,0:s]), self.tetha[0:s,:])[0][0]) self.tetha[0:s,:] -= Numeric.multiply(a_s[:,0:s], t_s).astype('f') self.tetha[s,0] = t_s print Numeric.dot(self.X, self.tetha) def main(): newton = Equation(['-tau * (x1 - Tc)'], 0, [0], ['Tc', 'tau'], [10, 1]) rk = RungeKutta(newton, 0.1, 15) result = rk.run() res = [] for i in xrange(11): res.append(result[i*10][1][0]) del result X = [] for el in res[:-1]: X.append([el, 1]) X = Numeric.array(X, 'f') y = [] for el in res[1:]: y.append([el]) y = Numeric.array(y, 'f') del res print X print y mnko = MNKO(X, y) del X, y mnko.run() if __name__ == '__main__': main() ```