-
Notifications
You must be signed in to change notification settings - Fork 0
/
methods.py
247 lines (192 loc) · 8.22 KB
/
methods.py
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
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
from formulas import *
from sympy.parsing.sympy_parser import parse_expr
def definedOrderMethods(params, formula):
y0 = float(params[0])
t0 = float(params[1])
h = float(params[2])
steps = float(params[3])
f = parse_expr(params[4])
i = 0
yn = y0
ypoints = [y0]
while i < steps:
yn1 = formula(f, yn, t0+(i*h), h)
ypoints.append(yn1)
yn = yn1
i += 1
return ypoints
def adamsBashforthMethod(params):
order = int(params[len(params)-1])
f = parse_expr(params[len(params)-2])
steps = float(params[len(params)-3])-order+1
h = float(params[len(params)-4])
t0 = float(params[len(params)-5])
prev_ypoints = params[0:order]
j = 0
coeffs = []
while j < order:
coeffs.append(calculateAdamsBashforthCoeffs(order, j))
j += 1
recurrence_relation = buildAdamsBashforthRecurrenceRelation(order, h, coeffs)
i = 0
while i < order:
prev_ypoints[i] = float(prev_ypoints[i])
i += 1
i = 0
ypoints = []
ypoints.extend(prev_ypoints)
while i < steps:
ynk = adamsBashforthFormula(f, prev_ypoints, t0+(h*i), h, order, recurrence_relation)
ypoints.append(ynk)
prev_ypoints.append(ynk)
prev_ypoints.pop(0)
i += 1
return ypoints
def adamsMoultonMethod(params):
order = int(params[len(params)-1])-1
f = parse_expr(params[len(params)-2])
steps = float(params[len(params)-3])-order+1
h = float(params[len(params)-4])
t0 = float(params[len(params)-5])
prev_ypoints = params[0:order]
j = 0
coeffs = []
while j <= order:
coeffs.append(calculateAdamsMoultonCoeffs(order, j))
j += 1
recurrence_relation = buildAdamsMoultonRecurrenceRelation(order, h, coeffs)
i = 0
while i < order:
prev_ypoints[i] = float(prev_ypoints[i])
i += 1
i = 0
ypoints = []
ypoints.extend(prev_ypoints)
while i < steps:
ynk = adamsMoultonFormula(f, prev_ypoints, t0+(h*i), h, order, recurrence_relation)
ypoints.append(ynk)
prev_ypoints.append(ynk)
prev_ypoints.pop(0)
i += 1
return ypoints
def backwardDifferentiationMethod(params):
order = int(params[len(params)-1])-1
f = parse_expr(params[len(params)-2])
steps = float(params[len(params)-3])-order+1
h = float(params[len(params)-4])
t0 = float(params[len(params)-5])
prev_ypoints = params[0:order]
i = 0
while i < order:
prev_ypoints[i] = float(prev_ypoints[i])
i += 1
i = 0
ypoints = []
ypoints.extend(prev_ypoints)
while i < steps:
ynk = backwardDifferentiationFormula(f, prev_ypoints, t0+(h*i), h, order)
ypoints.append(ynk)
prev_ypoints.append(ynk)
prev_ypoints.pop(0)
i += 1
return ypoints
def writePoints(params, ypoints, title):
y0 = float(params[0])
t0 = float(params[1])
h = float(params[2])
o = open('output.txt', 'a')
o.write(title)
o.write('y( {} ) = {}\n'.format(t0, y0))
o.write('h = {}\n'.format(h))
i = 0
for yp in ypoints:
o.write('{} {}\n'.format(i, yp))
i += 1
o.write('\n')
o.close()
def euler(params):
writePoints(params, definedOrderMethods(params, eulerFormula), 'Metodo de Euler\n')
def euler_inverso(params):
writePoints(params, definedOrderMethods(params, backwardEulerFormula), 'Metodo de Euler Inverso\n')
def euler_aprimorado(params):
writePoints(params, definedOrderMethods(params, improvedEulerFormula), 'Metodo de Euler Aprimorado\n')
def runge_kutta(params):
writePoints(params, definedOrderMethods(params, rungeKuttaFormula), 'Metodo de Runge-Kutta\n')
def adam_bashforth(params):
writePoints([params[0], params[len(params)-5], params[len(params)-4]], adamsBashforthMethod(params), 'Metodo de Adams-Bashforth\n')
def adam_bashforth_by_euler(params):
euler_params = params[0:5]
euler_params[3] = params[5]
ypoints = definedOrderMethods(euler_params, eulerFormula)
adam_params = ypoints + params[1:6]
writePoints(params, adamsBashforthMethod(adam_params), 'Metodo de Adams-Bashforth por Euler\n')
def adam_bashforth_by_euler_inverso(params):
backward_euler_params = params[0:5]
backward_euler_params[3] = params[5]
ypoints = definedOrderMethods(backward_euler_params, backwardEulerFormula)
adam_params = ypoints + params[1:6]
writePoints(params, adamsBashforthMethod(adam_params), 'Metodo de Adams-Bashforth por Euler Inverso\n')
def adam_bashforth_by_euler_aprimorado(params):
improved_euler_params = params[0:5]
improved_euler_params[3] = params[5]
ypoints = definedOrderMethods(improved_euler_params, improvedEulerFormula)
adam_params = ypoints + params[1:6]
writePoints(params, adamsBashforthMethod(adam_params), 'Metodo de Adams-Bashforth por Euler Apromirado\n')
def adam_bashforth_by_runge_kutta(params):
runge_kutta_params = params[0:5]
runge_kutta_params[3] = params[5]
ypoints = definedOrderMethods(runge_kutta_params, rungeKuttaFormula)
adam_params = ypoints + params[1:6]
writePoints(params, adamsBashforthMethod(adam_params), 'Metodo de Adams-Bashforth por Runge Kutta\n')
def adam_multon(params):
writePoints([params[0], params[len(params)-5], params[len(params)-4]], adamsMoultonMethod(params), 'Metodo de Adams-Moulton\n')
def adam_multon_by_euler(params):
euler_params = params[0:5]
euler_params[3] = params[5]
ypoints = definedOrderMethods(euler_params, eulerFormula)
adam_params = ypoints + params[1:6]
writePoints(params, adamsMoultonMethod(adam_params), 'Metodo de Adams-Moulton por Euler\n')
def adam_multon_by_euler_inverso(params):
backward_euler_params = params[0:5]
backward_euler_params[3] = params[5]
ypoints = definedOrderMethods(backward_euler_params, backwardEulerFormula)
adam_params = ypoints + params[1:6]
writePoints(params, adamsMoultonMethod(adam_params), 'Metodo de Adams-Moulton por Euler Inverso\n')
def adam_multon_by_euler_aprimorado(params):
improved_euler_params = params[0:5]
improved_euler_params[3] = params[5]
ypoints = definedOrderMethods(improved_euler_params, improvedEulerFormula)
adam_params = ypoints + params[1:6]
writePoints(params, adamsMoultonMethod(adam_params), 'Metodo de Adams-Moulton por Euler Aprimorado\n')
def adam_multon_by_runge_kutta(params):
runge_kutta_params = params[0:5]
runge_kutta_params[3] = params[5]
ypoints = definedOrderMethods(runge_kutta_params, rungeKuttaFormula)
adam_params = ypoints + params[1:6]
writePoints(params, adamsMoultonMethod(adam_params), 'Metodo de Adams-Moulton por Runge Kutta\n')
def formula_inversa(params):
writePoints([params[0], params[len(params)-5], params[len(params)-4]], backwardDifferentiationMethod(params), 'Metodo Formula Inversa de Diferenciacao\n')
def formula_inversa_by_euler(params):
euler_params = params[0:5]
euler_params[3] = params[5]
ypoints = definedOrderMethods(euler_params, eulerFormula)
bdf_params = ypoints + params[1:6]
writePoints(params, backwardDifferentiationMethod(bdf_params), 'Metodo Formula Inversa de Diferenciacao por Euler\n')
def formula_inversa_by_euler_inverso(params):
backward_euler_params = params[0:5]
backward_euler_params[3] = params[5]
ypoints = definedOrderMethods(backward_euler_params, backwardEulerFormula)
bdf_params = ypoints + params[1:6]
writePoints(params, backwardDifferentiationMethod(bdf_params), 'Metodo Formula Inversa de Diferenciacao por Euler Inverso\n')
def formula_inversa_by_euler_aprimorado(params):
improved_euler_params = params[0:5]
improved_euler_params[3] = params[5]
ypoints = definedOrderMethods(improved_euler_params, improvedEulerFormula)
bdf_params = ypoints + params[1:6]
writePoints(params, backwardDifferentiationMethod(bdf_params), 'Metodo Formula Inversa de Diferenciacao por Euler Aprimorado\n')
def formula_inversa_by_runge_kutta(params):
runge_kutta_params = params[0:5]
runge_kutta_params[3] = params[5]
ypoints = definedOrderMethods(runge_kutta_params, rungeKuttaFormula)
bdf_params = ypoints + params[1:6]
writePoints(params, backwardDifferentiationMethod(bdf_params), 'Metodo Formula Inversa de Diferenciacao por Runge Kutta\n')