* Re: Some (probably) ridiculous questions
2001-12-19 13:20 Some (probably) ridiculous questions Jean-Max Redonnet
@ 2001-12-19 13:20 ` Brian Gough
2001-12-19 13:20 ` Jean-Max Redonnet
0 siblings, 1 reply; 4+ messages in thread
From: Brian Gough @ 2001-12-19 13:20 UTC (permalink / raw)
To: redonnetNO; +Cc: gsl-discuss
Jean-Max Redonnet writes:
> Sorry, if this point is obvious, but I'm not very familiar with GSL and I
> would like to use it in the right way.
>
> My question is : How to declare a function of multiple variables ?
>
> I manage with parametric curves and surfaces, so I need functions of one or
> two parameters. Futhermore This functions should be vectorial.
> For example : I need to deal with a ruled surface.
Hello,
The gsl_function type is mainly designed for interfacing to the
univariate gsl routines. It is not really a general facility so it
does not handle other cases that are not used in the library, such as
surfaces.
The way to handle this sort of situation is,
-- define your own surface function type in the way that you normally
would in your C-programs
-- if you need to use a gsl routine, for example to integrate along a
line, define a function to create the appropriate gsl_function by
mapping from your surface type.
Philosophically, calls to GSL routines, and the GSL types, can be at a
"lower-level" than your program.
regards
Brian Gough
^ permalink raw reply [flat|nested] 4+ messages in thread
* Re: Some (probably) ridiculous questions
2001-12-19 13:20 ` Brian Gough
@ 2001-12-19 13:20 ` Jean-Max Redonnet
2001-12-19 13:20 ` Brian Gough
0 siblings, 1 reply; 4+ messages in thread
From: Jean-Max Redonnet @ 2001-12-19 13:20 UTC (permalink / raw)
To: Brian Gough; +Cc: gsl-discuss
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Le Vendredi 6 Juillet 2001 17:35, Brian Gough a écrit :
<snip>
>
> Hello,
>
> The gsl_function type is mainly designed for interfacing to the
> univariate gsl routines. It is not really a general facility so it
> does not handle other cases that are not used in the library, such as
> surfaces.
>
> The way to handle this sort of situation is,
>
> -- define your own surface function type in the way that you normally
> would in your C-programs
>
> -- if you need to use a gsl routine, for example to integrate along a
> line, define a function to create the appropriate gsl_function by
> mapping from your surface type.
>
> Philosophically, calls to GSL routines, and the GSL types, can be at a
> "lower-level" than your program.
>
> regards
> Brian Gough
Thanks for your help to a definitively poor programmer (and mathematician)
But I'm not sure I really understand what you mean...
I think I have defined a surface function type as you proposed.
This part seems to work as expected.
but I don't see how to define a function to create the appropriate
gsl_function...
Here the code :
#include <stdlib.h>
#include <stdio.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_diff.h>
#define RAD2DEG(X) (X*180/M_PI)
#define DEG2RAD(X) (X*M_PI/180)
struct surf_function_struct {
double (* fx)(double u, double v);
double (* fy)(double u, double v);
double (* fz)(double u, double v);;
};
typedef struct surf_function_struct surf_function ;
double C0_fx(double u)
{
return 80*u;
}
double C0_fy(double u)
{
return 80*tan(DEG2RAD(22.5))*(u-0.5);
}
double C0_fz(double u)
{
return 40;
}
double C1_fx(double u)
{
return 80*u;
}
double C1_fy(double u)
{
return -80*tan(DEG2RAD(22.5))*(u-0.5);
}
double C1_fz(double u)
{
return -40;
}
double S_fx(double u, double v)
{
return (1-v)*C0_fx(u)+v*C1_fx(u);
}
double S_fy(double u, double v)
{
return (1-v)*C0_fy(u)+v*C1_fy(u);
}
double S_fz(double u, double v)
{
return (1-v)*C0_fz(u)+v*C1_fz(u);
}
int main (void)
{
double u,v;
surf_function surf;
u = 0.5;
v = 0.5;
surf.fx = &S_fx;
surf.fy = &S_fy;
surf.fz = &S_fz;
printf(" | %f \n", S_fx(u,v));
printf(" S(%.1f,%.1f) = | %f \n", u, v, S_fy(u,v));
printf(" | %f \n", S_fz(u,v));
printf(" | %f \n", surf.fx(u,v));
printf(" S(%.1f,%.1f) = | %f \n", u, v, surf.fy(u,v));
printf(" | %f \n", surf.fz(u,v));
return 0;
}
You would be my definitive heroe if you can help me on this point.
Thanks.
--
===============================================================================
Veuillez noter ma nouvelle adresse électronique :
mailto:redonnetNO@SPAMlgmt.ups-tlse.fr
^ permalink raw reply [flat|nested] 4+ messages in thread
* Some (probably) ridiculous questions
@ 2001-12-19 13:20 Jean-Max Redonnet
2001-12-19 13:20 ` Brian Gough
0 siblings, 1 reply; 4+ messages in thread
From: Jean-Max Redonnet @ 2001-12-19 13:20 UTC (permalink / raw)
To: gsl-discuss
Sorry, if this point is obvious, but I'm not very familiar with GSL and I
would like to use it in the right way.
My question is : How to declare a function of multiple variables ?
I manage with parametric curves and surfaces, so I need functions of one or
two parameters. Futhermore This functions should be vectorial.
For example : I need to deal with a ruled surface.
Its definition is
C0(u) : vectorial function with 3 components : C0x(u), C0y(u) and C0z(u)
C1(u) : idem with C1x(u), C1y(u) and C1z(u)
then surface S(u,v) is built from C0 and C1 with
S(u,v) = (1-v)C0(u) + vC1(u)
How can I define this with GSL ?
For moment I've defined a
struct v3func
{
gsl_function fx;
gsl_function fy;
gsl_function fz;
};
then, once declared
struct v3func *C0;
I can do
C0 = (struct v3func *)malloc(sizeof(struct v3func *));
C0->fx.function = &C0_fx;
C0->fy.function = &C0_fy;
C0->fz.function = &C0_fz;
with C0_fx, C0_fy and C0_fz declared by
double C0_fx(double u, void * params);
double C0_fy(double u, void * params);
double C0_fz(double u, void * params);
This seems to work. Idem for C1 (of course).
But I have a problem to declare S(u,v)...
I've tried to do the same with S_fx(double u, double v, void * params)
but compilation says : "assignment from incompatible pointer type"
Any help would be very appreciated...
--
===============================================================================
Jean-Max Redonnet
PhD University Paul Sabatier - Toulouse (France)
mailto:redonnetNO@SPAMlgmt.ups-tlse.fr
^ permalink raw reply [flat|nested] 4+ messages in thread
* Re: Some (probably) ridiculous questions
2001-12-19 13:20 ` Jean-Max Redonnet
@ 2001-12-19 13:20 ` Brian Gough
0 siblings, 0 replies; 4+ messages in thread
From: Brian Gough @ 2001-12-19 13:20 UTC (permalink / raw)
To: redonnet; +Cc: gsl-discuss
Jean-Max Redonnet writes:
> I think I have defined a surface function type as you proposed.
> This part seems to work as expected.
> but I don't see how to define a function to create the appropriate
> gsl_function...
>
The gsl_function has to be a parametric function. The example below
defines a gsl_function 'line.f' for |F|^2 on a path P(t),
(u(t),v(t)) = (0.5,0.5) + 0.1*(cos(t),sin(t))
and then finds the minimum (which is at t=pi) using the standard gsl
minimization routines. The relevant functions are line_eval() and
make_line_function().
#include <stdlib.h>
#include <stdio.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_diff.h>
#include <gsl/gsl_min.h>
#include <gsl/gsl_errno.h>
#define RAD2DEG(X) (X*180/M_PI)
#define DEG2RAD(X) (X*M_PI/180)
struct surf_function_struct {
double (* fx)(double u, double v);
double (* fy)(double u, double v);
double (* fz)(double u, double v);;
};
typedef struct surf_function_struct surf_function ;
double C0_fx(double u)
{
return 80*u;
}
double C0_fy(double u)
{
return 80*tan(DEG2RAD(22.5))*(u-0.5);
}
double C0_fz(double u)
{
return 40;
}
double C1_fx(double u)
{
return 80*u;
}
double C1_fy(double u)
{
return -80*tan(DEG2RAD(22.5))*(u-0.5);
}
double C1_fz(double u)
{
return -40;
}
double S_fx(double u, double v)
{
return (1-v)*C0_fx(u)+v*C1_fx(u);
}
double S_fy(double u, double v)
{
return (1-v)*C0_fy(u)+v*C1_fy(u);
}
double S_fz(double u, double v)
{
return (1-v)*C0_fz(u)+v*C1_fz(u);
}
struct path_function_struct {
void (* uv)(double t, double *u, double *v);
};
typedef struct path_function_struct path_function ;
void P_uv(double t, double *u, double *v)
{
*u = 0.5 + 0.1 * cos(t);
*v = 0.5 + 0.1 * sin(t);
}
struct line_function_struct
{
path_function p;
surf_function s;
gsl_function f;
};
typedef struct line_function_struct line_function ;
double
line_eval (double t, void * params)
{
line_function * line = (line_function *) params;
double u, v;
line->p.uv(t, &u, &v);
{
double a = line->s.fx(u,v);
double b = line->s.fy(u,v);
double c = line->s.fz(u,v);
/* compute |F|^2 */
return a*a + b*b + c*c;
}
}
void
make_line_function (path_function path, surf_function surf,
line_function * line)
{
line->p = path;
line->s = surf;
line->f.function = &line_eval;
line->f.params = line;
}
int main (void)
{
double u,v,t;
surf_function surf;
path_function path;
surf.fx = &S_fx;
surf.fy = &S_fy;
surf.fz = &S_fz;
path.uv = &P_uv;
for (t = 0 ; t < 2*M_PI; t+= 0.5)
{
path.uv(t, &u, &v);
printf(" | %f \n", S_fx(u,v));
printf(" S(%.3f,%.3f) = | %f \n", u, v, S_fy(u,v));
printf(" | %f \n", S_fz(u,v));
printf(" | %f \n", surf.fx(u,v));
printf(" S(%.3f,%.3f) = | %f \n", u, v, surf.fy(u,v));
printf(" | %f \n", surf.fz(u,v));
}
{
line_function line;
make_line_function(path, surf, &line);
{
int status, iterations = 0;
double m = 1.23;
gsl_interval x = {0.0, 2*M_PI};
gsl_min_fminimizer * s
= gsl_min_fminimizer_alloc (gsl_min_fminimizer_brent);
gsl_min_fminimizer_set (s, &line.f, m, x);
do
{
iterations++;
status = gsl_min_fminimizer_iterate (s);
m = gsl_min_fminimizer_minimum (s);
x = gsl_min_fminimizer_interval (s);
status = gsl_min_test_interval (x, 0.001, 0.0);
if (status == GSL_SUCCESS)
printf ("Converged:\n");
printf ("%5d [%.7f, %.7f] %.7f %.7f %+.7f\n",
iterations, x.lower, x.upper,
m, s->f_minimum, x.upper - x.lower);
}
while (status == GSL_CONTINUE && iterations < 100);
}
}
return 0;
}
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2001-12-19 13:20 ` Brian Gough
2001-12-19 13:20 ` Jean-Max Redonnet
2001-12-19 13:20 ` Brian Gough
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