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 | with Ada.Text_IO; use Ada.Text_IO;
with Ada.Text_IO.C_Streams;
with Ada.Long_Float_Text_IO; use Ada.Long_Float_Text_IO;
with Ada.Integer_Text_IO; use Ada.Integer_Text_IO;
with Interfaces.C; use Interfaces.C;
with Interfaces.C.Strings; use Interfaces.C.Strings;
with Ada.Strings.Unbounded; use Ada.Strings.Unbounded;
with Ada.Command_Line; use Ada.Command_Line;
with Ada.Numerics.Elementary_Functions ; use Ada.Numerics.Elementary_Functions ;
with GNAT.Source_Info; use GNAT.Source_Info;
with gsl;
with gsl.vector_double;
with gsl.matrix_double;
with gsl.bspline;
with gsl.rng;
with gsl.randist;
with gsl.version;
procedure bspline is
use gsl.double_text_Io ;
use gsl.size_t_text_Io ;
Verbose : boolean := true ;
Status : Int ;
procedure Test1 is
-- 42.13.1 Example 1: Basis Splines and Uniform Knots
myname : String := gnat.Source_Info.enclosing_entity ;
logfile : File_Type ;
procedure print_basis ( knotsfn : String ;
splinefn : String ;
order, nbreak : size_t ) is
bspws : access gsl.bspline.gsl_bspline_workspace
:= gsl.bspline.alloc (order,nbreak);
ncontrol : size_t := nbreak + order - 2;
N : constant := 300 ;
a, b, dx : double ;
vec : access gsl.vector_double.gsl_vector ;
u : double ;
splinefile : File_Type ;
begin
a := 0.0 ;
b := 1.0 ;
dx := (b - a)/(double(N) - 1.0) ;
vec := gsl.vector_double.alloc(ncontrol) ;
Status := gsl.bspline.knots_uniform(a,b,bspws);
gsl.vector_double.WriteCSV(bspws.knots,knotsfn);
-- Status := gsl.vector_double.fprintf(bspws.knots,knotsfn & ".txt" , "%f");
Create(splinefile,Out_File,splinefn);
Set_Output(splinefile);
for i in 1..N
loop
u := double(i-1) * dx ;
Status := gsl.bspline.eval(u,vec,bspws);
Put(u) ; Put(" ; ");
for j in 1..ncontrol
loop
Put( gsl.vector_double.get(vec,j-1) ); Put(" ; ");
end loop ;
New_Line ;
end loop ;
gsl.vector_double.free(vec) ;
gsl.bspline.free(bspws);
--Close(knotsfile);
Set_Output(Standard_Output);
Close(splinefile);
end print_basis ;
begin
if Verbose
then
Put_Line(myname);
end if ;
print_basis(myname & ".linear.knots.csv" ,
myname & ".linear.spline.csv" , 2 , 11) ;
print_basis(myname & ".quad.knots.csv" ,
myname & ".quad.spline.csv" , 3 , 11) ;
print_basis(myname & ".cubic.knots.csv" ,
myname & ".cubic.spline.csv" , 4 , 11) ;
print_basis(myname & ".quartic.knots.csv" ,
myname & ".quartic.spline.csv" , 5 , 11) ;
end Test1 ;
procedure Test2 is
myname : String := gnat.Source_Info.enclosing_entity ;
logfile : File_Type ;
nbreak : constant := 6 ;
spline_order : constant := 4 ;
bspws : access gsl.bspline.gsl_bspline_workspace
:= gsl.bspline.alloc(spline_order,nbreak);
ncontrol : size_t := nbreak + spline_order - 2;
n : constant := 300;
a : constant double := 0.0;
b : constant double := 1.0;
dx : constant double := (b - a) / (double(n) - 1.0);
dB : access gsl.matrix_double.gsl_matrix
:= gsl.matrix_double.alloc(ncontrol, spline_order);
lnum : Integer := 0;
order_name : String := "0123" ;
begin
if Verbose
then
Put_Line(myname);
end if ;
Status := gsl.bspline.knots_uniform(a,b,bspws) ;
gsl.vector_double.WriteCSV(bspws.knots,myname & ".knots.csv");
for i in 1..spline_order
loop
Create(logfile,Out_File,myname & "." & order_name(i) & ".csv");
Set_Output(logfile);
for j in 1..n
loop
Status := gsl.bspline.deriv_eval( double(j-1) * dx , size_t(i-1) , dB , bspws );
lnum := lnum + 1 ;
Put(lnum) ; Put(" ; ");
Put(double(j-1) * dx ); Put (" ; ");
for k in 1..ncontrol
loop
Put( gsl.matrix_double.get(dB,k-1,size_t(i-1))); Put(" ; ");
end loop ;
New_Line ;
end loop ;
Set_Output(Standard_Output);
Close(logfile);
end loop ;
gsl.matrix_double.free(dB) ;
gsl.bspline.free(bspws);
end Test2 ;
procedure Test3 is
-- 2.13.3 Example 3: Least squares and breakpoints
myname : String := gnat.Source_Info.enclosing_entity ;
logfile : File_Type ;
N : constant := 500 ;
spline_order : constant := 4 ;
a : constant double := 0.0 ;
b : constant double := 15.0 ;
sigma : constant double := 0.2 ;
bspws40 : access gsl.bspline.gsl_bspline_workspace
:= gsl.bspline.alloc(spline_order,40);
bspws10 : access gsl.bspline.gsl_bspline_workspace
:= gsl.bspline.alloc(spline_order,10);
ncontrol40 : constant size_t := gsl.bspline.ncontrol(bspws40) ;
ncontrol10 : constant size_t := gsl.bspline.ncontrol(bspws10) ;
dof40 : constant size_t := N - ncontrol40;
dof10 : constant size_t := N - ncontrol10;
c40 : access gsl.vector_double.gsl_vector := gsl.vector_double.alloc(ncontrol40) ;
c10 : access gsl.vector_double.gsl_vector := gsl.vector_double.alloc(ncontrol10) ;
x : access gsl.vector_double.gsl_vector := gsl.vector_double.alloc(N) ;
y : access gsl.vector_double.gsl_vector := gsl.vector_double.alloc(N) ;
w : access gsl.vector_double.gsl_vector := gsl.vector_double.alloc(N) ;
rng : access gsl.rng.gsl_rng := gsl.rng.alloc(gsl.rng.env_setup);
xi,yi,wi,dyi : double ;
chisq40, chisq10 : aliased double ;
begin
if Verbose
then
Put_Line(myname);
end if ;
for i in 1..N
loop
xi := a + (b - a) / (double(N) - 1.0) * double(i-1) ;
yi := double(Cos(Float(xi)) * Exp( - 0.1 * float(xi) ));
dyi := gsl.randist.gaussian(rng,sigma);
yi := yi + dyi ;
gsl.vector_double.set(x,size_t(i-1),xi);
gsl.vector_double.set(y,size_t(i-1),yi);
gsl.vector_double.set(w,size_t(i-1),1.0/(sigma*sigma));
end loop ;
gsl.vector_double.WriteCSV(x, myname & ".xyw.csv" , y , w );
Status := gsl.bspline.knots_uniform(a,b,bspws40);
Status := gsl.bspline.knots_uniform(a,b,bspws10);
Create(logfile,Out_File,myname & ".csv");
Set_Output(logfile);
Set_Output(Standard_Output);
Close(logfile);
gsl.vector_double.free(c40);
gsl.vector_double.free(c10);
gsl.vector_double.free(x) ;
gsl.vector_double.free(y) ;
gsl.vector_double.free(w) ;
gsl.bspline.free(bspws40);
gsl.bspline.free(bspws10);
end Test3 ;
begin
Ada.Long_Float_Text_IO.Default_exp := 0 ;
Ada.Long_Float_Text_IO.Default_aft := 4 ;
gsl.double_text_io.Default_aft := 4 ;
gsl.double_text_Io.Default_exp := 0;
gsl.version.Report ;
Test1;
Test2;
end bspline ;
|