void ParabolicFit2D::find_regression(const algebra::Vector2Ds& data) {
// http://mathforum.org/library/drmath/view/72047.html
double S00(0.0), S10(0.0), S20(0.0), S30(0.0), S40(0.0);
double S01(0.0), S11(0.0), S21(0.0);
S00 = (double)data.size();
for (unsigned int i = 0; i < data.size(); i++) {
S10 += data[i][0];
double x2 = data[i][0] * data[i][0];
S20 += x2;
S30 += x2 * data[i][0];
S40 += x2 * x2;
S01 += data[i][1];
S11 += data[i][0] * data[i][1];
S21 += x2 * data[i][1];
}
double d = S00 * S20 * S40 - S10 * S10 * S40 - S00 * S30 * S30 +
2 * S10 * S20 * S30 - S20 * S20 * S20;
a_ = (S01 * S10 * S30 - S11 * S00 * S30 - S01 * S20 * S20 + S11 * S10 * S20 +
S21 * S00 * S20 - S21 * S10 * S10) /
d;
b_ = (S11 * S00 * S40 - S01 * S10 * S40 + S01 * S20 * S30 - S21 * S00 * S30 -
S11 * S20 * S20 + S21 * S10 * S20) /
d;
c_ = (S01 * S20 * S40 - S11 * S10 * S40 - S01 * S30 * S30 + S11 * S20 * S30 +
S21 * S10 * S30 - S21 * S20 * S20) /
d;
}
IMPALGEBRA_BEGIN_NAMESPACE
ParabolicFit2D::ParabolicFit2D(const algebra::Vector2Ds& data) {
// check that there are at least 3 points
IMP_USAGE_CHECK(data.size() > 2,
"At least 3 points are required for ParabolicFit2D "
<< data.size() << " given");
find_regression(data);
evaluate_error(data);
}
IMPALGEBRA_BEGIN_NAMESPACE
LinearFit2D::LinearFit2D(const algebra::Vector2Ds& data,
const Floats &errors) {
// check that there are at least 3 points
IMP_USAGE_CHECK(data.size() > 1,
"At least 2 points are required for LinearFit2D "
<< data.size() << " given");
IMP_USAGE_CHECK(errors.empty() || errors.size()==data.size(),
"Either there must be no error bars given or one per"
<< " point.");
find_regression(data, errors);
evaluate_error(data, errors);
}
void ParabolicFit2D::evaluate_error(const algebra::Vector2Ds& data) {
error_ = 0.0;
for (unsigned int i = 0; i < data.size(); i++) {
double diff =
a_ * data[i][0] * data[i][0] + b_ * data[i][0] + c_ - data[i][1];
error_ += diff * diff;
}
}
void LinearFit2D::evaluate_error(const algebra::Vector2Ds& data,
const Floats &errors) {
error_ = 0.0;
for(unsigned int i=0; i<data.size(); i++) {
double diff = (a_*data[i][0] + b_ - data[i][1]);
if (!errors.empty()) {
diff/=errors[i];
}
error_ += diff*diff;
}
//std::cerr << error_ << std::endl;
}
void LinearFit2D::find_regression(const algebra::Vector2Ds& data,
const Floats &errors) {
double x(0.0), y(0.0), x2(0.0), xy(0.0), w(0.0);
for(unsigned int i=0; i<data.size(); i++) {
double wi;
if (!errors.empty()) {
wi=1.0/IMP::base::square(errors[i]);
} else {
wi=1.0;
}
w+=wi;
x+= wi*data[i][0];
y+= wi*data[i][1];
xy+= wi*data[i][0]*data[i][1];
x2 += wi*data[i][0]*data[i][0];
}
a_ = (w*xy-x*y)/(w*x2 - x*x);
b_ = y/w - a_*x/w;
}