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
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
|
require 'test_helper'
class OdeivTest < GSL::TestCase
def setup
@rhs_func_lin = GSL::Odeiv::System.alloc(lambda { |t, y, f|
f[0] = 0.0
f[1] = y[0]
GSL::SUCCESS
}, lambda { |t, y, dfdy, dfdt|
dfdy.set(0, 0, 0.0)
dfdy.set(0, 1, 0.0)
dfdy.set(1, 0, 1.0)
dfdy.set(1, 1, 0.0)
dfdt[0] = 0.0
dfdt[1] = 0.0
GSL::SUCCESS
}, 2)
@rhs_func_sin = GSL::Odeiv::System.alloc(lambda { |t, y, f|
f[0] = -y[1]
f[1] = y[0]
GSL::SUCCESS
}, lambda { |t, y, dfdy, dfdt|
dfdy.set(0, 0, 0.0)
dfdy.set(0, 1, -1.0)
dfdy.set(1, 0, 1.0)
dfdy.set(1, 1, 0.0)
dfdt[0] = 0.0
dfdt[1] = 0.0
GSL::SUCCESS
}, 2)
@rhs_func_exp = GSL::Odeiv::System.alloc(lambda { |t, y, f|
f[0] = y[1]
f[1] = y[0]
GSL::SUCCESS
}, lambda { |t, y, dfdy, dfdt|
dfdy.set(0, 0, 0.0)
dfdy.set(0, 1, 1.0)
dfdy.set(1, 0, 1.0)
dfdy.set(1, 1, 0.0)
dfdt[0] = 0.0
dfdt[1] = 0.0
GSL::SUCCESS
}, 2)
@rhs_func_stiff = GSL::Odeiv::System.alloc(lambda { |t, y, f|
f[0] = 998.0 * y[0] + 1998.0 * y[1]
f[1] = -999.0 * y[0] - 1999.0 * y[1]
GSL::SUCCESS
}, lambda { |t, y, dfdy, dfdt|
dfdy.set(0, 0, 998.0)
dfdy.set(0, 1, 1998.0)
dfdy.set(1, 0, -999.0)
dfdy.set(1, 1, -1999.0)
dfdt[0] = 0.0
dfdt[1] = 0.0
GSL::SUCCESS
}, 2)
end
def self.define_test(test, type, h, b)
define_method("test_#{test}_#{type}") { send("_test_#{test}", type, h, b) }
end
h, b = 1e-3, GSL::SQRT_DBL_EPSILON
h2, b2 = h / 10, 1e-8
%w[rk2 rk2imp rk4 rk4imp rkf45 rk8pd rkck bsimp gear1 gear2].each { |type|
define_test(:stepper_err, type, h, b) unless type == 'bsimp'
unless type == 'gear2'
define_test(:stepper_linear, type, h, b)
define_test(:stepper_sin, type, h2, b2)
define_test(:stepper_exp, type, h2, b2)
define_test(:stepper_stiff, type, h, b)
end
define_test(:evolve_sin, type, h, b)
define_test(:evolve_exp, type, h, b)
define_test(:evolve_stiff1, type, h, b)
define_test(:evolve_stiff5, type, h, b)
}
def _test_stepper_err(type, h, b)
t = 0.0
y = GSL::Vector.alloc(1.0, 0.0)
yerr = GSL::Vector.alloc(2)
stepper = GSL::Odeiv::Step.alloc(type, 2)
while t < GSL::M_PI
y1_t = y[1]
dy_exp = Math.cos(t) * Math.sin(h) - 2 * Math.sin(t) * GSL.pow(Math.sin(h / 2), 2.0)
stepper.apply(t, h, y, yerr, @rhs_func_sin)
dy_t = y[1] - y1_t
del = (dy_t - dy_exp).abs
refute t > 0.1 && t < 0.2 && del > 10.0 * yerr[1].abs + GSL::DBL_EPSILON * y[1].abs,
"#{stepper.name}, sine [0,pi], accurary of estimate error = #{del} vs #{yerr[1].abs}"
t += h
end
end
def _test_stepper_linear(type, h, b)
delmax, n, t = 0.0, 0, 0.0
stepper = GSL::Odeiv::Step.alloc(type, 2)
y = GSL::Vector.alloc(1.0, 0.0)
yerr = GSL::Vector.alloc(2)
while t < 4.0
stepper.apply(t, h, y, yerr, @rhs_func_lin)
del = ((y[1] - (t + h)) / y[1]).abs
delmax = GSL.MAX_DBL(del, delmax)
refute del > (n + 1.0) * b,
"#{stepper.name}, linear [0,4], max relative error = #{delmax}"
n += 1
t += h
end
end
def _test_stepper_sin(type, h, b)
delmax, n, t, pi = 0.0, 0, 0.0, GSL::M_PI
stepper = GSL::Odeiv::Step.alloc(type, 2)
y = GSL::Vector.alloc(1.0, 0.0)
yerr = GSL::Vector.alloc(2)
while t < pi
sin_th = Math.sin(t + h)
stepper.apply(t, h, y, yerr, @rhs_func_sin)
del = ((y[1] - sin_th) / sin_th).abs
delmax = GSL.MAX_DBL(del, delmax)
refute del > (
t < 0.5 * pi ? 1.0 + n :
t < 0.7 * pi ? 1.0e+04 :
t < 0.9 * pi ? 1.0e+06 : 1.0e+09) * b,
"#{stepper.name}, sine [0,pi], max relative error = #{delmax}"
n += 1
t += h
end
refute delmax > 1.0e+09 * b,
"#{stepper.name}, sine [0,pi], max relative error = #{delmax}"
delmax = 0.0
while t < 3 * pi
stepper.apply(t, h, y, yerr, @rhs_func_sin)
del = (y[1] - Math.sin(t)).abs
delmax = GSL.MAX_DBL(del, delmax)
n += 1
t += h
end
refute del > n * 2.0 * b,
"#{stepper.name}, sin [pi,3*pi], max absolute error = #{delmax}"
end
def _test_stepper_exp(type, h, b)
delmax, n, t = 0.0, 0, 0.0
stepper = GSL::Odeiv::Step.alloc(type, 2)
y = GSL::Vector.alloc(1.0, 1.0)
yerr = GSL::Vector.alloc(2)
while t < 5.0
stepper.apply(t, h, y, yerr, @rhs_func_exp)
del = ((y[1] - Math.exp(t + h)) / y[1]).abs
delmax = GSL.MAX_DBL(del, delmax)
refute del > (n + 1.0) * 2.0 * b,
"#{stepper.name}, exponential [0,5], max relative error = #{delmax}"
n += 1
t += h
end
end
def _test_stepper_stiff(type, h, b)
delmax, n, t = 0.0, 0, 0.0
stepper = GSL::Odeiv::Step.alloc(type, 2)
y = GSL::Vector.alloc(1.0, 0.0)
yerr = GSL::Vector.alloc(2)
while t < 5.0
stepper.apply(t, h, y, yerr, @rhs_func_stiff)
if t > 0.04
arg = t + h
e1 = Math.exp(-arg)
e2 = Math.exp(-1000.0 * arg)
del = ((y[0] - 2.0 * e1 + e2) / y[0]).abs
delmax = GSL.MAX_DBL(del, delmax)
refute del > (n + 1.0) * 100.0 * b,
"#{stepper.name}, stiff [0,5], max relative error = #{delmax}"
end
n += 1
t += h
end
end
def _test_evolve_system_flat(type, sys, t0, t1, h, y, yfin, err_target, desc, control = nil)
stepper = GSL::Odeiv::Step.alloc(type, sys.dimension)
evolve = GSL::Odeiv::Evolve.alloc(sys.dimension)
while t0 < t1
t0, h, _ = evolve.apply(control, stepper, sys, t0, t1, h, y)
end
frac = ((y[1] - yfin[1]) / yfin[1]).abs + ((y[0] - yfin[0]) / yfin[0]).abs
refute frac > 2.0 * evolve.count * err_target, "#{stepper.name}, #{desc}, evolve" <<
", #{control ? 'standard' : 'no'} control, relative error = #{frac}"
end
def _test_evolve_system(type, sys, t0, t1, h, y, yfin, err_target, desc)
_test_evolve_system_flat(type, sys, t0, t1, h, y, yfin, err_target, desc,
GSL::Odeiv::Control.standard_alloc(0.0, err_target, 1.0, 1.0))
end
def _test_evolve_sin(type, h, err)
y = GSL::Vector.alloc(1.0, 0.0)
yfin = GSL::Vector.alloc(Math.cos(2.0), Math.sin(2.0))
_test_evolve_system(type, @rhs_func_sin, 0.0, 2.0, h, y, yfin, err, 'sin [0,2]')
end
def _test_evolve_exp(type, h, err)
eee = Math.exp(5.0)
y = GSL::Vector.alloc(1.0, 1.0)
yfin = GSL::Vector.alloc(eee, eee)
_test_evolve_system(type, @rhs_func_exp, 0.0, 5.0, h, y, yfin, err, 'exp [0,5]')
end
def _test_evolve_stiff1(type, h, err, arg = 1.0)
e1 = Math.exp(-arg)
e2 = Math.exp(-1000.0 * arg)
y = GSL::Vector.alloc(1.0, 0.0)
yfin = GSL::Vector.alloc(2.0 * e1 - e2, -e1 + e2)
_test_evolve_system(type, @rhs_func_stiff, 0.0, arg, h, y, yfin, err, 'stiff [0,%d]' % arg)
end
def _test_evolve_stiff5(type, h, err)
_test_evolve_stiff1(type, h, err, 5.0)
end
end
|
