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
|
// =============================================================================
// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) 2008-2009 - INRIA - Michael Baudin
//
// This file is distributed under the same license as the Scilab package.
// =============================================================================
// <-- JVM NOT MANDATORY -->
//
// assert_close --
// Returns 1 if the two real matrices computed and expected are close,
// i.e. if the relative distance between computed and expected is lesser than epsilon.
// Arguments
// computed, expected : the two matrices to compare
// epsilon : a small number
//
function flag = assert_close ( computed, expected, epsilon )
if expected==0.0 then
shift = norm(computed-expected);
else
shift = norm(computed-expected)/norm(expected);
end
if shift < epsilon then
flag = 1;
else
flag = 0;
end
if flag <> 1 then bugmes();quit;end
endfunction
//
// assert_equal --
// Returns 1 if the two real matrices computed and expected are equal.
// Arguments
// computed, expected : the two matrices to compare
// epsilon : a small number
//
function flag = assert_equal ( computed , expected )
if computed==expected then
flag = 1;
else
flag = 0;
end
if flag <> 1 then bugmes();quit;end
endfunction
// 1. Test with a scalar function
function y = myfunction (x)
y = x*x;
endfunction
x = 1.0;
expected = 2.0;
// 1.1 With default parameters
computed = derivative(myfunction,x);
assert_close ( computed , expected , 1.e-11 );
// 1.2 Test order 1
computed = derivative(myfunction,x,order=1);
assert_close ( computed , expected , 1.e-8 );
// 1.3 Test order 2
computed = derivative(myfunction,x,order=2);
assert_close ( computed , expected , 1.e-11 );
// 1.4 Test order 4
computed = derivative(myfunction,x,order=4);
assert_close ( computed , expected , %eps );
// 1.5 Compute second derivative at the same time
Jexpected = 2.0;
Hexpected = 2.0;
[Jcomputed , Hcomputed] = derivative(myfunction,x);
assert_close ( Jcomputed , Jexpected , 1.e-11 );
assert_close ( Hcomputed , Hexpected , %eps );
// 1.6 Test order 1
[Jcomputed , Hcomputed] = derivative(myfunction,x,order=1);
assert_close ( Jcomputed , Jexpected , 1.e-8 );
assert_close ( Hcomputed , Hexpected , 1.e-6 );
// 1.7 Test order 2
[Jcomputed , Hcomputed] = derivative(myfunction,x,order=2);
assert_close ( Jcomputed , Jexpected , 1.e-11 );
assert_close ( Hcomputed , Hexpected , %eps );
// 1.8 Test order 4
[Jcomputed , Hcomputed] = derivative(myfunction,x,order=4);
assert_close ( Jcomputed , Jexpected , %eps );
assert_close ( Hcomputed , Hexpected , 1.e-11 );
// 2. Test with a vector function
function y = myfunction2 (x)
y = x(1)*x(1) + x(2)+ x(1)*x(2);
endfunction
x = [1.0
2.0];
expected = [4.0 2.0];
// 2.1 With default parameters
computed = derivative(myfunction2,x);
assert_close ( computed , expected , 1.e-10 );
// 2.2 Test order 1
computed = derivative(myfunction2,x,order=1);
assert_close ( computed , expected , 1.e-8 );
// 2.3 Test order 2
computed = derivative(myfunction2,x,order=2);
assert_close ( computed , expected , 1.e-10 );
// 2.4 Test order 4
computed = derivative(myfunction2,x,order=4);
assert_close ( computed , expected , %eps );
// 2.5 Compute second derivative at the same time
Jexpected = [4.0 2.0];
Hexpected = [2.0 1.0 1.0 0];
[Jcomputed , Hcomputed] = derivative(myfunction2,x);
assert_close ( Jcomputed , Jexpected , 1.e-10 );
assert_close ( Hcomputed , Hexpected , %eps );
// 2.6 Test order 1
[Jcomputed , Hcomputed] = derivative(myfunction2,x,order=1);
assert_close ( Jcomputed , Jexpected , 1.e-8 );
assert_close ( Hcomputed , Hexpected , 1.e-5 );
// 2.7 Test order 2
[Jcomputed , Hcomputed] = derivative(myfunction2,x,order=2);
assert_close ( Jcomputed , Jexpected , 1.e-10 );
assert_close ( Hcomputed , Hexpected , %eps );
// 2.8 Test order 4
[Jcomputed , Hcomputed] = derivative(myfunction2,x,order=4);
assert_close ( Jcomputed , Jexpected , %eps );
assert_close ( Hcomputed , Hexpected , 1.e-10 );
// 3. Test H_form
// 3.1 Test H_form="default"
Jexpected = [4.0 2.0];
Hexpected = [2.0 1.0 1.0 0.0];
[Jcomputed , Hcomputed] = derivative(myfunction2 , x , H_form="default");
assert_close ( Jcomputed , Jexpected , 1.e-10 );
assert_close ( Hcomputed , Hexpected , %eps );
// 3.2 Test H_form='hypermat'
Jexpected = [4.0 2.0];
Hexpected = [2.0 1.0
1.0 0.0];
[Jcomputed , Hcomputed] = derivative(myfunction2 , x , H_form='hypermat');
assert_close ( Jcomputed , Jexpected , 1.e-10 );
assert_close ( Hcomputed , Hexpected , %eps );
// 3.3 Test H_form='hypermat'
Jexpected = [4.0 2.0];
Hexpected = [2.0 1.0
1.0 0.0];
[Jcomputed , Hcomputed] = derivative(myfunction2 , x , H_form='hypermat');
assert_close ( Jcomputed , Jexpected , 1.e-10 );
assert_close ( Hcomputed , Hexpected , %eps );
// 4. Test verbose
[Jcomputed , Hcomputed] = derivative(myfunction2 , x , verbose = 1);
h = 6.055454e-06
order = 2
H_form = default
Q =
1. 0.
0. 1.
// 5. Test h parameter
// Test a case where the default step h is very small ~ 1.e-9,
// but, because the function is very flat in the neighbourhood of the
// point, a larger step ~ 1.e-4 reduces the error.
// This means that this test cannot pass if the right step is
// not taken into account, therefore testing the feature "h is used correctly".
myn = 1.e5;
function y = myfunction3 (x)
y = x^(2/myn);
endfunction
x = 1.0;
h = 6.055454e-006
h =
0.0000061
Jexpected = (2/myn) * x^(2/myn-1);
Hexpected = (2/myn) * (2/myn-1) * x^(2/myn-2);
[Jcomputed , Hcomputed] = derivative(myfunction3 , x , h = 1.e-4 , order = 1 );
assert_close ( Jcomputed , Jexpected , 1.e-4 );
assert_close ( Hcomputed , Hexpected , 1.e-3 );
// 6. Test Q parameter
// TODO !
|
