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aa_aafapprox.cpp
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aa_aafapprox.cpp
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/*
* aa_aafapprox.c -- Standart non-affine operations
* Copyright (c) 2003 EPFL (Ecole Polytechnique Federale de Lausanne)
* Copyright (c) 2004 LIRIS (University Claude Bernard Lyon 1)
* Copyright (C) 2009 LUH (Leibniz Universitaet Hannover)
*
* This file is part of aaflib.
*
* This program is free software; you can redistribute it and/or modify it
* under the terms of the GNU Lesser General Public License as
* published by the Free Software Foundation; either version 2 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
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with libaa; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
#include "aa.h"
#include <algorithm>
#include <cmath>
#include <cstdio>
//#define AAF_DEBUG
#define EPSILON 1E-20
#define AAF_MINRAD 1E-10
/************************************************************
* INTERPOLATION INFO
*
* a is the lower bound of the argument AAF
* b is the upper bound of the argument AAF
*
* alpha is the slope of the line r(x) that interpolates
* i) CHEBYSHEV: (a, f(a)) and (b, f(b))
* ii) MINRANGE: MIN(f'(a), f'(b))
*
* dzeta is the central y-intercept of the parallelogram
* including (a,f(a) .. b,f(b))
*
* delta is the new deviation value being half a hight of
* the parallelogram
************************************************************/
/************************************************************
* Operator: *
* Author & Date: ??? - ???
* Description:
* computes the affine product (*this * P)
*
* Input : const AAF & : AAF argument
* Output : AAF : AAF result
************************************************************/
AAF AAF::operator*(const AAF& P)
{
unsigned l1 = length;
unsigned l2 = P.length;
if (l1 + l2 == 0) {
AAF Temp(cvalue * P.cvalue);
return Temp;
}
if (l1 == 0) {
// if *this is double
AAF Temp(P);
Temp *= cvalue;
return Temp;
}
if (l2 == 0) {
// if P is double
AAF Temp(*this);
Temp *= P.cvalue;
return Temp;
}
unsigned* id1 = indexes;
unsigned* id2 = P.indexes;
double* va1 = deviations;
double* va2 = P.deviations;
unsigned* pu1 = id1;
unsigned* pu2 = id2;
AAF Temp(cvalue * P.cvalue); // Create our resulting AAF
Temp.indexes = new unsigned[l1 + l2 + 1];
unsigned* idtemp = Temp.indexes;
// Fill the indexes array
unsigned* fin = std::set_union(id1, id1 + l1, id2, id2 + l2, idtemp);
unsigned ltemp = fin - idtemp;
Temp.deviations = new double[ltemp + 1];
double* vatempg = Temp.deviations;
Temp.length = ltemp + 1;
Temp.size = Temp.length;
double commonTermCenter = 0.0;
double commonTermDeviation = 0.0;
// Fill the deviations array
for (unsigned i = 0; i < ltemp; i++) {
unsigned a = pu1 - id1;
unsigned b = pu2 - id2;
if (a == l1 || id1[a] != idtemp[i]) {
vatempg[i] = cvalue * va2[b]; // cvalue*va2[b]+(P.cvalue)*0
pu2++;
continue;
}
if (b == l2 || id2[b] != idtemp[i]) {
vatempg[i] = (P.cvalue) * va1[a]; // cvalue*0+(P.cvalue)*va1[a]
pu1++;
continue;
}
vatempg[i] = cvalue * va2[b] + (P.cvalue) * va1[a];
commonTermCenter += va2[b] * va1[a];
commonTermDeviation += fabs(va2[b] * va1[a]);
pu1++;
pu2++;
}
// Compute the error
// in a new deviation symbol
double delta = rad() * P.rad();
Temp.indexes[ltemp] = inclast();
if (AAF::approximationType == SECANT) {
commonTermCenter *= 0.5;
commonTermDeviation *= 0.5;
delta -= commonTermDeviation;
// new deviation equals zero
Temp.deviations[ltemp] = 0.;
// distribute delta on current deviations
double r = 0.0;
for (unsigned i = 0; i < ltemp; i++)
r += fabs(Temp.deviations[i]);
double fac;
if (fabs(r) < EPSILON)
fac = 1.;
else
fac = 1.0 + delta / r;
for (unsigned i = 0; i < ltemp; i++)
Temp.deviations[i] *= fac;
#ifdef FAST_RAD
Temp.radius = r + delta;
#endif
Temp.cvalue += commonTermCenter;
return Temp;
} else {
Temp.deviations[ltemp] = delta;
}
// consider deviations occuring in both expressions
commonTermCenter *= 0.5;
commonTermDeviation *= 0.5;
Temp.cvalue += commonTermCenter;
Temp.deviations[ltemp] -= commonTermDeviation;
#ifdef FAST_RAD
Temp.radius = 0.0;
for (unsigned i = 0; i < Temp.length; i++)
Temp.radius += fabs(Temp.deviations[i]);
#endif
return Temp;
}
/************************************************************
* Operator: *=
* Author & Date: Darius Grabowski - 2006
* Description:
* computes the affine product (*this *= P)
*
* Input : const AAF & : AAF argument
* Output : AAF & : AAF result
************************************************************/
AAF& AAF::operator*=(const AAF& P)
{
unsigned l1 = length;
unsigned l2 = P.length;
if (l1 == 0) {
// if *this is double
double temp = cvalue;
*this = P;
*this *= temp;
return *this;
}
if (l2 == 0) {
// if P is double
*this *= P.cvalue;
return *this;
}
unsigned* id1 = indexes;
unsigned* id2 = P.indexes;
double* va1 = deviations;
double* va2 = P.deviations;
unsigned* pu1 = id1;
unsigned* pu2 = id2;
unsigned* tempIndexes = new unsigned[l1 + l2 + 1];
unsigned* idtemp = tempIndexes;
// Fill the indexes array
unsigned* fin = std::set_union(id1, id1 + l1, id2, id2 + l2, idtemp);
unsigned ltemp = fin - idtemp;
double* tempDeviations = new double[ltemp + 1];
double* vatempg = tempDeviations;
double commonTermCenter = 0.0;
double commonTermDeviation = 0.0;
// Fill the deviations array
for (unsigned i = 0; i < ltemp; i++) {
unsigned a = pu1 - id1;
unsigned b = pu2 - id2;
if (a == l1 || id1[a] != idtemp[i]) {
vatempg[i] = cvalue * va2[b]; // cvalue*va2[b]+(P.cvalue)*0
pu2++;
continue;
}
if (b == l2 || id2[b] != idtemp[i]) {
vatempg[i] = (P.cvalue) * va1[a]; // cvalue*0+(P.cvalue)*va1[a]
pu1++;
continue;
}
vatempg[i] = cvalue * va2[b] + (P.cvalue) * va1[a];
commonTermCenter += va2[b] * va1[a];
commonTermDeviation += fabs(va2[b] * va1[a]);
pu1++;
pu2++;
}
// Compute the error in a new deviation symbol
double delta = rad() * P.rad();
// multiply cvalue
cvalue *= P.cvalue;
tempIndexes[ltemp] = inclast();
if (AAF::approximationType == SECANT) {
commonTermCenter *= 0.5;
commonTermDeviation *= 0.5;
delta -= commonTermDeviation;
// new deviation equals zero
tempDeviations[ltemp] = 0.;
// distribute delta on current deviations
double r = 0.0;
for (unsigned i = 0; i < ltemp; i++)
r += fabs(tempDeviations[i]);
double fac;
if (fabs(r) < EPSILON)
fac = 1.;
else
fac = 1.0 + delta / r;
for (unsigned i = 0; i < ltemp; i++)
tempDeviations[i] *= fac;
#ifdef FAST_RAD
radius = r + delta;
#endif
cvalue += commonTermCenter;
} else {
tempDeviations[ltemp] = delta;
// consider deviations occuring in both expressions
commonTermCenter *= 0.5;
commonTermDeviation *= 0.5;
cvalue += commonTermCenter;
tempDeviations[ltemp] -= commonTermDeviation;
}
length = ltemp + 1;
size = length;
delete[] indexes;
delete[] deviations;
indexes = tempIndexes;
deviations = tempDeviations;
#ifdef FAST_RAD
radius = 0.0;
for (unsigned i = 0; i < length; i++)
radius += fabs(deviations[i]);
#endif
return *this;
}
/************************************************************
* Operator: /
* Author & Date: ??? - ???
* Description:
* computes the division, we use the identity x/y = x * (1/y)
*
* Input : const AAF & : AAF argument
* Output : AAF : AAF result
************************************************************/
AAF AAF::operator/(const AAF& P)
{
if (this == &P)
return AAF(1.0);
else
return (*this) * inv(P);
}
/************************************************************
* Operator: /
* Author & Date: Darius Grabowski - 10.06.2005
* Description:
* computes the division <double> / <AAF>
*
* Input : double : divisor
* AAF : dividend
* Output : AAF : AAF result
************************************************************/
AAF operator/(double cst, const AAF P)
{
return inv(P) * cst;
}
/************************************************************
* Operator: ^
* Author & Date: Darius Grabowski - 10.06.2005
* Description:
* computes the power function
*
* Input : const int : exponent
* Output : AAF : AAF result
************************************************************/
AAF AAF::operator^(const int exponent) const
{
double a, b;
double fa, fb;
double r;
double alpha = 0.0;
double dzeta = 0.0;
double delta = 0.0;
if (length == 0) {
AAF Temp(pow((double)cvalue, double(exponent)));
return Temp;
}
if (exponent == 0) {
return AAF(1.0);
}
if (exponent == 1) {
return *this;
}
if (exponent == -1) {
return inv(*this);
}
r = rad();
a = cvalue - r;
b = cvalue + r;
fa = pow(a, (double)exponent);
fb = pow(b, (double)exponent);
if ((b * a < EPSILON) && (exponent < 0)) {
throw(AAF_Exception(AAF_DIVZERO_EXCEPTION,
std::string("Error <AAF::^>: computing zero inversion").c_str(),
a, b));
}
if (AAF::approximationType == CHEBYSHEV) {
// use Chebyshev approximation
if (r > AAF_MINRAD) {
alpha = (fb - fa) / (b - a);
} else {
// avoid division by zero
alpha = exponent * fa / (a + EPSILON);
}
// we have two points having the slope alpha
double x_1 = -pow(fabs((double)alpha / exponent), (double)1.0 / (exponent - 1.0));
double x_2 = -x_1;
double fx_1, fx_2;
// check valid points
if (x_1 > a) {
// x_1 is valid
fx_1 = pow(x_1, (double)exponent);
} else {
x_1 = a;
fx_1 = fa;
}
if (x_2 < b) {
// x_2 is valid
fx_2 = pow(x_2, (double)exponent);
} else {
x_2 = b;
fx_2 = fb;
}
double y_2 = fx_2 - alpha * x_2;
double y_1 = fx_1 - alpha * x_1;
delta = 0.5 * (y_1 - y_2);
dzeta = 0.5 * (y_1 + y_2);
#ifdef AAF_DEBUG
fprintf(stdout, "Function: x^%d\n", exponent);
fprintf(stdout, "Interval: [%f, %f]\n", a, b);
fprintf(stdout, "f(Interval): [%f, %f]\n", fa, fb);
fprintf(stdout, "x_1: %f, f(x_1): %f\n", x_1, fx_1);
fprintf(stdout, "x_2: %f, f(x_2): %f\n", x_2, fx_2);
fprintf(stdout, "alpha: %f, delta: %f, dzeta: %f\n", alpha, delta, dzeta);
#endif
} else if (AAF::approximationType == MINRANGE) {
// use MinRange approximation
// special case: 0.0 in [a,b] : alpha = f'(0.0)
// exp > 0 and exp even and [a,b] > 0 : MINRANGE: alpha = f'(a), y0_b > y0_a : e1 = 1 e2 = 1 e3 = 1
// exp > 0 and exp odd and [a,b] > 0 : MINRANGE: alpha = f'(a), y0_b > y0_a : e1 = 1 e2 = 0 e3 = 1
// exp > 0 and exp even and [a,b] < 0 : MINRANGE: alpha = f'(b), y0_a > y0_b : e1 = 1 e2 = 1 e3 = 0
// exp > 0 and exp odd and [a,b] < 0 : MINRANGE: alpha = f'(b), y0_b > y0_a : e1 = 1 e2 = 0 e3 = 0
// exp < 0 and exp even and [a,b] > 0 : MINRANGE: alpha = f'(b), y0_a > y0_b : e1 = 0 e2 = 1 e3 = 1
// exp < 0 and exp odd and [a,b] > 0 : MINRANGE: alpha = f'(b), y0_a > y0_b : e1 = 0 e2 = 0 e3 = 1
// exp < 0 and exp even and [a,b] < 0 : MINRANGE: alpha = f'(a), y0_b > y0_a : e1 = 0 e2 = 1 e3 = 0
// exp < 0 and exp odd and [a,b] < 0 : MINRANGE: alpha = f'(a), y0_a > y0_b : e1 = 0 e2 = 0 e3 = 0
if (b * a < 0.0) {
alpha = 0.0;
if (exponent % 2 == 0) {
delta = 0.5 * ((fa > fb) ? fa : fb);
dzeta = delta;
} else {
delta = 0.5 * (fb - fa);
dzeta = 0.5 * (fb + fa);
}
} else {
if (((exponent > 0) && (a > 0.0)) || ((exponent < 0) && (a < 0.0))) {
alpha = exponent * fa / (a + EPSILON);
} else {
alpha = exponent * fb / (b + EPSILON);
}
double y_a = fa - alpha * a;
double y_b = fb - alpha * b;
delta = 0.5 * fabs(y_a - y_b);
dzeta = 0.5 * (y_a + y_b);
#ifdef AAF_DEBUG
fprintf(stdout, "Function: x^%d\n", exponent);
fprintf(stdout, "Interval: [%f, %f]\n", a, b);
fprintf(stdout, "f(Interval): [%f, %f]\n", fa, fb);
fprintf(stdout, "alpha: %f, delta: %f, dzeta: %f\n", alpha, delta, dzeta);
#endif
}
} else // (AAF::approximationType == SECANT)
{
if (r > AAF_MINRAD) {
alpha = (fb - fa) / (b - a);
} else {
// avoid division by zero
alpha = exponent * fa / (a + EPSILON);
}
dzeta = fa - alpha * a;
delta = 0.;
}
// z0 = alpha*x0 + dzeta
AAF Temp(alpha * (cvalue) + dzeta);
Temp.length = length + 1;
Temp.size = Temp.length;
Temp.deviations = new double[Temp.size];
Temp.indexes = new unsigned[Temp.size];
// zi = alpha*xi
for (unsigned i = 0; i < length; i++) {
Temp.indexes[i] = indexes[i];
Temp.deviations[i] = alpha * (deviations[i]);
}
// Compute the error in a new deviation symbol
// zk = delta
Temp.indexes[length] = Temp.inclast();
Temp.deviations[length] = delta;
#ifdef FAST_RAD
Temp.radius = fabs(alpha) * radius + fabs(delta);
#endif
#ifdef AAF_DEBUG
fprintf(stdout, "Ergebnis:\n");
fprintf(stdout, "Mittelwert: %f!\n", Temp.cvalue);
for (unsigned i = 0; i < Temp.length; i++) {
fprintf(stdout, "Abweichung %d: Index: %u Wert: %f!\n", i, Temp.indexes[i], Temp.deviations[i]);
}
#endif
return Temp;
}
/************************************************************
* Operator: ^
* Author & Date: Anna Krause - 01.03.2010
* Description: Operator for the affine exponentiation
* computes the power function
*
* Input : AAF : exp
* Output : AAF : AAF result
************************************************************/
AAF AAF::operator^(const AAF exp) const
{
AAF base = *this;
AAF temp = aaf_pow(*this, exp);
return temp;
}
/************************************************************
* Method: aaf_pow
* Author & Date: Anna Krause - 01.03.2010
* Description:
* computes the power function
*
* Input : AAF : base
* AAF : exponent
* Output : AAF : AAF result
************************************************************/
AAF aaf_pow(const AAF& base, const AAF& exp)
{
// Properties of the input aafs
double centre_b = base.getcenter();
double centre_e = exp.getcenter();
unsigned length_b = base.getlength();
unsigned length_e = exp.getlength();
double min_b = base.getMin();
const double pi = 3.14159265;
// Variables
double fx, fy, fc;
double dmin, dmax, x1, x2, x3, y1, y2, y3, phi, phi0, phi_max, d1, d2, d3, dyc;
unsigned* merge;
unsigned* help;
double* dev_array_b;
double* dev_array_e;
double* eps_vec;
unsigned dev_b, dev_e;
unsigned i = 0, j = 0, last_eps;
double alpha, gamma;
// Properties of the resulting aaf
unsigned length_r;
double* devs_r;
unsigned* ind_r;
// Area of validity
if (min_b <= 0) {
throw(AAF_Exception(AAF_NEGBASE_EXCEPTION,
std::string("Error <AAF::aaf_pow>: Exponentiation of negative numbers is only possible for integer exponents and currently not defined in this scope.").c_str(),
min_b));
}
// Special cases
if (length_b == 0) {
if (length_e == 0) {
// b and e are real numbers
AAF result(pow(centre_b, centre_e));
std::cout << result << std::endl;
return result;
} else { // b is a real number, e is an affine form
AAF result = aaf_pow(centre_b, exp);
return result;
}
} else {
if (length_e == 0) { //b is an affine form, e is a real number
AAF result = aaf_pow(base, centre_e);
return result;
}
}
unsigned* ind_e = exp.indexes;
double* devs_e = exp.deviations;
unsigned* ind_b = base.indexes;
double* devs_b = base.deviations;
// Two dimensional Taylor series at the centre value
fc = pow(centre_b, centre_e);
fx = centre_e * pow(centre_b, (centre_e - 1.0));
fy = pow(centre_b, centre_e) * log(centre_b);
// Evaluate the edge of the polygon defined by the base and the exponent
dmin = 0.0;
dmax = 0.0;
x1 = centre_b;
y1 = centre_e;
x2 = 0.0;
y2 = 0.0;
x3 = 0.0;
y3 = 0.0;
last_eps = 0;
// Merge vector of indexes and construct array for the deviations and the epsilon
//TODO: Pr�fen: mehrere unabh�ngige Abweichungssymbole, die nur in einer AAF vorkommen? - sollte egal sein
help = new unsigned[length_b + length_e + 1];
merge = std::set_union(ind_b, ind_b + length_b, ind_e, ind_e + length_e, help);
length_r = merge - help + 1;
dev_b = 0;
dev_e = 0;
dev_array_b = new double[length_r - 1];
dev_array_e = new double[length_r - 1];
eps_vec = new double[length_r - 1];
for (i = 0; i < length_r - 1; i++) {
fprintf(stdout, "i: %d, help: %d, desb: %f, devse. %f\n", i, help[i], devs_b[dev_b], devs_e[dev_e]);
if (dev_b < length_b && ind_b[dev_b] == help[i]) {
dev_array_b[i] = devs_b[dev_b];
dev_b++;
} else {
dev_array_b[i] = 0.0;
}
if (dev_e < length_e && ind_e[dev_e] == help[i]) {
dev_array_e[i] = devs_e[dev_e];
dev_e++;
} else {
dev_array_e[i] = 0.0;
}
// Write epsilon vector
if (dev_array_b[i] > 0)
eps_vec[i] = -1.0;
else if (dev_array_b[i] < 0)
eps_vec[i] = 1.0;
else {
if (dev_array_e[i] >= 0)
eps_vec[i] = -1.0;
else
eps_vec[i] = 1.0;
}
}
// Find minimum and maximum distance between taylor series and exponentiation
for (i = 0; i < (length_r - 1); i++) {
x1 += eps_vec[i] * dev_array_b[i];
y1 += eps_vec[i] * dev_array_e[i];
}
for (i = 0; i < 2 * (length_r - 1); i++) {
// Find the outmost segment
phi0 = atan2((centre_e - y1), (centre_b - x1));
phi_max = 0.0;
for (j = 0; j < (length_r - 1); j++) {
if (dev_array_b[j] == 0 && dev_array_e[j] != 0) { //x=const
x2 = x1;
x3 = x1;
y2 = y1 + (-1) * eps_vec[j] * dev_array_e[j];
y3 = y1 + (-2) * eps_vec[j] * dev_array_e[j];
phi = atan2((y3 - y1), (x3 - x1)) - phi0;
if (phi > phi_max && phi > 0 && phi < pi) {
phi_max = phi;
last_eps = j;
}
} else if (dev_array_b[j] != 0 && dev_array_e[j] == 0) { //y=const
y2 = y1;
y3 = y1;
x2 = x1 + (-1) * eps_vec[j] * dev_array_b[j];
x3 = x1 + (-2) * eps_vec[j] * dev_array_b[j];
phi = atan2((y3 - y1), (x3 - x1)) - phi0;
if (phi > phi_max && phi > 0 && phi < pi) {
phi_max = phi;
last_eps = j;
}
} else {
x2 = x1 + (-1) * eps_vec[j] * dev_array_b[j];
x3 = x1 + (-2) * eps_vec[j] * dev_array_b[j];
y2 = y1 + (-1) * eps_vec[j] * dev_array_e[j];
y3 = y1 + (-2) * eps_vec[j] * dev_array_e[j];
phi = atan2((y3 - y1), (x3 - x1)) - phi0;
if (phi > phi_max && phi > 0 && phi < pi) {
phi_max = phi;
last_eps = j;
}
}
}
x2 = x1 + (-1) * eps_vec[last_eps] * dev_array_b[last_eps];
x3 = x1 + (-2) * eps_vec[last_eps] * dev_array_b[last_eps];
y2 = y1 + (-1) * eps_vec[last_eps] * dev_array_e[last_eps];
y3 = y1 + (-2) * eps_vec[last_eps] * dev_array_e[last_eps];
d1 = fc + fx * (x1 - centre_b) + fy * (y1 - centre_e) - pow(x1, y1);
d2 = fc + fx * (x2 - centre_b) + fy * (y2 - centre_e) - pow(x2, y2);
d3 = fc + fx * (x3 - centre_b) + fy * (y3 - centre_e) - pow(x3, y3);
if ((d1 < d2) && (d2 < d3)) {
if (i == 0) {
dmin = d1;
dmax = d3;
}
if (d1 < dmin)
dmin = d1;
if (d3 > dmax)
dmax = d3;
} else if ((d1 > d2) && (d2 > d3)) {
if (i == 0) {
dmin = d3;
dmax = d1;
}
if (d3 < dmin)
dmin = d3;
if (d1 > dmax)
dmax = d1;
} else {
fprintf(stdout, "\t Warning: The distance function is not monotone on the straight line from (%f,%f) to (%f,%f) \n", x1, y1, x3, y3);
if (i == 0) { //initial values for dmin and dmay
if (d1 > d3) {
dmin = d3;
dmax = d1;
} else if (d1 < d3) {
dmin = d1;
dmax = d3;
} else {
dmin = d1;
dmax = d1;
}
}
if (dev_array_b[last_eps] == 0) {
if (fy / log(x1) > 0) {
dyc = log(fy / log(x1)) / log(x1);
d2 = fc + fx * (x1 - centre_b) + fy * (dyc - centre_e) - pow(x1, dyc);
}
} else if (dev_array_e[last_eps] == 0) {
if (fx / y1 > 0) {
dyc = pow(fx / y1, 1 / (y1 - 1));
d2 = fc + fx * (dyc - centre_b) + fy * (y1 - centre_e) - pow(dyc, y1);
}
} else {
//Todo: eine beliebige Gerade
if ((d2 < d1 && d2 < dmin) || (d2 > d1 && d2 > dmax))
fprintf(stdout, "Warning: Information may have been lost!\n");
}
// write minimum and maximum distance if applicable
if (d2 <= d1) {
if (d2 < dmin)
dmin = d2;
if (d1 < d3 && d3 > dmax)
dmax = d3;
else if (d1 > d3 && d1 > dmax)
dmax = d1;
} else {
if (d2 > dmax)
dmax = d2;
if (d1 < d3 && d1 < dmin)
dmin = d1;
else if (d1 > d3 && d3 < dmin)
dmin = d3;
}
}
x1 = x3;
y1 = y3;
eps_vec[last_eps] = (-1) * eps_vec[last_eps];
for (j = 0; j < length_r - 1; j++) {
}
}
// Calculate the shift of the centre and the new deviation
alpha = (dmax + dmin) / 2;
gamma = (dmax - dmin) / 2;
fprintf(stdout, "alpha: %f, gamma: %f\n", alpha, gamma);
AAF result(pow(centre_b, centre_e) + alpha);
result.length = length_r;
result.size = length_r;
result.indexes = new unsigned[length_r];
result.deviations = new double[length_r];
devs_r = result.deviations;
ind_r = result.indexes;
for (i = 0; i < (length_r - 1); i++) {
ind_r[i] = help[i];
devs_r[i] = fx * dev_array_b[i] + fy * dev_array_e[i];
fprintf(stdout, "index: %d, devb: %f, deve: %f\n", help[i], dev_array_b[i], dev_array_e[i]);
}
result.indexes[length_r - 1] = result.inclast();
result.deviations[length_r - 1] = gamma;
#ifdef FAST_RAD
result.radius = 0.0;
for (unsigned i = 0; i < length_r; i++)
result.radius += fabs(result.deviations[i]);
#endif
//std::cout << result << std::endl;
return result;
}
/************************************************************
* Operator: ^
* Author & Date: Bogdan Burlacu - 15.09.2020
* Description:
* computes the power function
*
* Input : double : exponent
* Output : AAF : AAF result
************************************************************/
AAF AAF::operator^(const double exp) const
{
AAF base = *this;
AAF temp = aaf_pow(*this, exp);
return temp;
}
/************************************************************
* Method: aaf_pow
* Author & Date: Anna Krause - 01.03.2010
* Description:
* computes the power function
*
* Input : AAF : base
* double : exponent
* Output : AAF : AAF result
************************************************************/
AAF aaf_pow(const AAF& base, const double& exp)
{
// AAF properties
double centre_b = base.getcenter();
unsigned length_b = base.getlength();
double min_b = base.getMin();
double max_b = base.getMax();
unsigned* ind_b = base.indexes;
double* devs_b = base.deviations;
// Variables
double fmin, fmax, alpha, beta, gamma, x2;
fmin = pow(min_b, exp);
fmax = pow(max_b, exp);
beta = 0.0;
alpha = 0.0;
gamma = 0.0;
if (exp > 1.0) {
//fprintf(stdout, "Exponent > 1!\n");
if (AAF::approximationType == MINRANGE) {
beta = exp * pow(min_b, exp - 1);
alpha = 0.5 * (-beta * (min_b + max_b) + fmin + fmax);
gamma = 0.5 * (beta * (min_b - max_b) - fmin + fmax);
} else { //CHEBYSHEV
beta = (fmax - fmin) / (max_b - min_b);
x2 = pow((beta / exp), 1 / (exp - 1));
alpha = 0.5 * (-beta * (min_b + x2) + fmin + pow(x2, exp));
gamma = 0.5 * (beta * (x2 - min_b) + fmin - pow(x2, exp));
}
} else if (exp == 1.0) {
//fprintf(stdout, "Exponent = 1!\n");
beta = 1.0;
alpha = 0.0;
gamma = 0.0;
} else if (exp < 1.0 && exp > 0.0) {
//fprintf(stdout, "Exponent < 1 und > 0!\n");
if (AAF::approximationType == MINRANGE) {
beta = exp * pow(max_b, exp - 1);
alpha = 0.5 * (-beta * (min_b + max_b) + fmin + fmax);
gamma = 0.5 * (beta * (min_b - max_b) - fmin + fmax);
} else {
beta = (fmax - fmin) / (max_b - min_b);
x2 = pow((beta / exp), 1 / (exp - 1));
alpha = 0.5 * (-beta * (min_b + x2) + fmin + pow(x2, exp));
gamma = 0.5 * (beta * (-x2 + min_b) - fmin + pow(x2, exp));
}
} else if (exp == 0.0) {
//fprintf(stdout, "Exponent = 0!\n");
beta = 0.0;
alpha = 1.0;
gamma = 0.0;
} else if (exp < 0.0) {
//fprintf(stdout, "Exponent < 0!\n");
if (AAF::approximationType == MINRANGE) {
beta = exp * pow(min_b, exp - 1);
alpha = 0.5 * (-beta * (min_b + max_b) + fmin + fmax);
gamma = 0.5 * (beta * (min_b - max_b) - fmin + fmax);
} else { //CHEBYSHEV
beta = (fmax - fmin) / (max_b - min_b);
x2 = pow((beta / exp), 1 / (exp - 1));
alpha = 0.5 * (-beta * (min_b + x2) + fmin + pow(x2, exp));
gamma = 0.5 * (beta * (x2 - min_b) + fmin - pow(x2, exp));
}
}
//build result
AAF result(beta * centre_b + alpha);
if (gamma == 0.0) {
result.length = length_b;
result.size = result.length;
result.deviations = new double[result.size];
result.indexes = new unsigned[result.size];
for (unsigned i = 0; i < length_b; i++) {
result.indexes[i] = ind_b[i];
result.deviations[i] = beta * (devs_b[i]);
}
} else {
result.length = length_b + 1;
result.size = result.length;
result.deviations = new double[result.size];
result.indexes = new unsigned[result.size];
for (unsigned i = 0; i < length_b; i++) {
result.indexes[i] = ind_b[i];
result.deviations[i] = beta * (devs_b[i]);
}
result.indexes[length_b] = result.inclast();
result.deviations[length_b] = gamma;
}
#ifdef FAST_RAD
result.radius = fabs(beta) * 0.5 * (max_b - min_b) + fabs(gamma);
#endif
std::cout << result << std::endl;
return result;
}
/************************************************************
* Method: aaf_pow
* Author & Date: Anna Krause - 01.03.2010
* Description:
* computes the power function
*
* Input : double : base
* AAF : exponent
* Output : AAF : AAF result
************************************************************/
AAF aaf_pow(const double& base, const AAF& exp)
{
// AAF properties
double centre_e = exp.getcenter();
unsigned length_e = exp.getlength();
double min_e = exp.getMin();
double max_e = exp.getMax();
unsigned* ind_e = exp.indexes;
double* devs_e = exp.deviations;
// Variables
double fmin, fmax, alpha, beta, gamma, x2;
//fprintf(stdout, "Basis ist reell!\n");
fmin = pow(base, min_e);
fmax = pow(base, max_e);
beta = 0.0;
gamma = 0.0;
alpha = 0.0;
if (base == 1.0) {
fprintf(stdout, "\t und gleich 1!\n");