/* robust_wfun.c
*
* Copyright (C) 2013 Patrick Alken
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 3 of the License, or (at
* your option) any later version.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
#include <config.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_vector.h>
#include <gsl/gsl_multifit.h>
/* default tuning constants */
#define TUNING_BISQUARE (4.685)
#define TUNING_CAUCHY (2.385)
#define TUNING_FAIR (1.4)
#define TUNING_HUBER (1.345)
#define TUNING_OLS (1.0)
#define TUNING_WELSCH (2.985)
/*
* Note: for each of the weighting functions below, it
* is safe to call them with in-place parameters, so that
* input/output vectors are the same
*/
static int
bisquare(const gsl_vector *r, gsl_vector *w)
{
size_t i;
size_t n = r->size;
for (i = 0; i < n; ++i)
{
double ri = gsl_vector_get(r, i);
if (fabs(ri) < 1.0)
gsl_vector_set(w, i, (1.0 - ri*ri)*(1.0 - ri*ri));
else
gsl_vector_set(w, i, 0.0);
}
return GSL_SUCCESS;
} /* bisquare() */
static int
bisquare_dpsi(const gsl_vector *r, gsl_vector *dpsi)
{
size_t i;
size_t n = r->size;
for (i = 0; i < n; ++i)
{
double ri = gsl_vector_get(r, i);
if (fabs(ri) < 1.0)
gsl_vector_set(dpsi, i, (1.0 - ri*ri)*(1.0 - 5.0*ri*ri));
else
gsl_vector_set(dpsi, i, 0.0);
}
return GSL_SUCCESS;
} /* bisquare_dpsi() */
static const gsl_multifit_robust_type bisquare_type = {
"bisquare",
&bisquare,
&bisquare_dpsi,
TUNING_BISQUARE
};
static int
cauchy(const gsl_vector *r, gsl_vector *w)
{
size_t i;
size_t n = r->size;
for (i = 0; i < n; ++i)
{
double ri = gsl_vector_get(r, i);
gsl_vector_set(w, i, 1.0 / (1.0 + ri*ri));
}
return GSL_SUCCESS;
} /* cauchy() */
static int
cauchy_dpsi(const gsl_vector *r, gsl_vector *dpsi)
{
size_t i;
size_t n = r->size;
for (i = 0; i < n; ++i)
{
double ri = gsl_vector_get(r, i);
double rsq = ri * ri;
gsl_vector_set(dpsi, i, (1 - rsq) / (1.0 + rsq) / (1.0 + rsq));
}
return GSL_SUCCESS;
} /* cauchy_dpsi() */
static const gsl_multifit_robust_type cauchy_type = {
"cauchy",
&cauchy,
&cauchy_dpsi,
TUNING_CAUCHY
};
static int
fair(const gsl_vector *r, gsl_vector *w)
{
size_t i;
size_t n = r->size;
for (i = 0; i < n; ++i)
{
double ri = gsl_vector_get(r, i);
gsl_vector_set(w, i, 1.0 / (1.0 + fabs(ri)));
}
return GSL_SUCCESS;
} /* fair() */
static int
fair_dpsi(const gsl_vector *r, gsl_vector *dpsi)
{
size_t i;
size_t n = r->size;
for (i = 0; i < n; ++i)
{
double ri = gsl_vector_get(r, i);
gsl_vector_set(dpsi, i, 1.0 / (1.0 + fabs(ri)) / (1.0 + fabs(ri)));
}
return GSL_SUCCESS;
} /* fair_dpsi() */
static const gsl_multifit_robust_type fair_type = {
"fair",
&fair,
&fair_dpsi,
TUNING_FAIR
};
static int
huber(const gsl_vector *r, gsl_vector *w)
{
size_t i;
size_t n = r->size;
for (i = 0; i < n; ++i)
{
double absri = fabs(gsl_vector_get(r, i));
if (absri <= 1.0)
gsl_vector_set(w, i, 1.0);
else
gsl_vector_set(w, i, 1.0 / absri);
}
return GSL_SUCCESS;
} /* huber() */
static int
huber_dpsi(const gsl_vector *r, gsl_vector *dpsi)
{
size_t i;
size_t n = r->size;
for (i = 0; i < n; ++i)
{
double ri = gsl_vector_get(r, i);
if (fabs(ri) <= 1.0)
gsl_vector_set(dpsi, i, 1.0);
else
gsl_vector_set(dpsi, i, 0.0);
}
return GSL_SUCCESS;
} /* huber_dpsi() */
static const gsl_multifit_robust_type huber_type = {
"huber",
&huber,
&huber_dpsi,
TUNING_HUBER
};
static int
ols(const gsl_vector *r, gsl_vector *w)
{
gsl_vector_set_all(w, 1.0);
return GSL_SUCCESS;
}
static int
ols_dpsi(const gsl_vector *r, gsl_vector *dpsi)
{
gsl_vector_set_all(dpsi, 1.0);
return GSL_SUCCESS;
}
static const gsl_multifit_robust_type ols_type = {
"ols",
&ols,
&ols_dpsi,
TUNING_OLS
};
static int
welsch(const gsl_vector *r, gsl_vector *w)
{
size_t i;
size_t n = r->size;
for (i = 0; i < n; ++i)
{
double ri = gsl_vector_get(r, i);
gsl_vector_set(w, i, exp(-ri*ri));
}
return GSL_SUCCESS;
} /* welsch() */
static int
welsch_dpsi(const gsl_vector *r, gsl_vector *dpsi)
{
size_t i;
size_t n = r->size;
for (i = 0; i < n; ++i)
{
double ri = gsl_vector_get(r, i);
gsl_vector_set(dpsi, i, (1.0 - 2.0*ri*ri) * exp(-ri*ri));
}
return GSL_SUCCESS;
} /* welsch_dpsi() */
static const gsl_multifit_robust_type welsch_type = {
"welsch",
&welsch,
&welsch_dpsi,
TUNING_WELSCH
};
const gsl_multifit_robust_type *gsl_multifit_robust_default = &bisquare_type;
const gsl_multifit_robust_type *gsl_multifit_robust_bisquare = &bisquare_type;
const gsl_multifit_robust_type *gsl_multifit_robust_cauchy = &cauchy_type;
const gsl_multifit_robust_type *gsl_multifit_robust_fair = &fair_type;
const gsl_multifit_robust_type *gsl_multifit_robust_huber = &huber_type;
const gsl_multifit_robust_type *gsl_multifit_robust_ols = &ols_type;
const gsl_multifit_robust_type *gsl_multifit_robust_welsch = &welsch_type;