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// -*- Mode: C++; tab-width: 2; -*-
// vi: set ts=2:
//
#include <BALL/CONCEPT/classTest.h>
///////////////////////////
#include <BALL/MOLMEC/MINIMIZATION/lineSearch.h>
///////////////////////////
START_TEST(LineSearch)
/////////////////////////////////////////////////////////////
/////////////////////////////////////////////////////////////
using namespace BALL;
CHECK(LineSearch::takeStep(double &st_a, double &f_a, double &g_a, double &st_b,
double &f_b, double &g_b, double &stp, double f, double g, double minstp, double maxstp))
LineSearch ls;
// Check different cases by f(x) = -x^3 + 2x^2 - x - 1
// This function has a minimum at 1/3 and a maximum at 1 and tends to -infinity for x->infinity
// We also check every time if the interval bounds are set correctly.
// Slight correction test: bracketed flag not set, but we set stp to almost the minimizer
ls.setBracketedFlag(false);
double st_a = 0.;
double f_a = -1.;
double g_a = -1.;
double st_b = 1.;
double f_b = 1.;
double g_b = 0.;
double stp = 0.33333;
double f = -1.148148147;
double g = -.6667e-4;
double minstp = 0.;
double maxstp = 2.;
ls.takeStep(st_a, f_a, g_a, st_b, f_b, g_b, stp, f, g, minstp, maxstp);
TEST_REAL_EQUAL(st_a, 0.33333)
TEST_REAL_EQUAL(f_a, -1.148148147)
TEST_REAL_EQUAL(g_a, -6.667e-05)
TEST_REAL_EQUAL(st_b, 1.0)
TEST_REAL_EQUAL(f_b, 1.0)
TEST_REAL_EQUAL(g_b, 0.0)
TEST_REAL_EQUAL(stp, 0.333363348343)
TEST_EQUAL(ls.isBracketed(), false)
// First case: f > f_a
// Result: correct cubic step
ls.setBracketedFlag(false);
st_a = 0.1;
f_a = -1.081;
g_a = -0.63;
st_b = 1.;
f_b = -1.;
g_b = 0.;
stp = 0.9;
f = -1.009;
g = 0.17;
minstp = 0.;
maxstp = 2.;
ls.takeStep(st_a, f_a, g_a, st_b, f_b, g_b, stp, f, g, minstp, maxstp);
TEST_REAL_EQUAL(st_a, 0.1)
TEST_REAL_EQUAL(f_a, -1.081)
TEST_REAL_EQUAL(g_a, -0.63)
TEST_REAL_EQUAL(st_b, 0.9)
TEST_REAL_EQUAL(f_b, -1.009)
TEST_REAL_EQUAL(g_b, 0.17)
TEST_REAL_EQUAL(stp, 0.333333333333)
TEST_EQUAL(ls.isBracketed(), true)
// Second case: f <= f_a but sgn(g) != sgn(g_a)
ls.setBracketedFlag(false);
st_a = 0.;
f_a = -1.;
g_a = -1.;
st_b = 1.;
f_b = -1.;
g_b = 0.;
stp = 0.9;
f = -1.009;
g = 0.17;
minstp = 0.;
maxstp = 2.;
ls.takeStep(st_a, f_a, g_a, st_b, f_b, g_b, stp, f, g, minstp, maxstp);
TEST_REAL_EQUAL(st_a, 0.9)
TEST_REAL_EQUAL(f_a, -1.009)
TEST_REAL_EQUAL(g_a, 0.17)
TEST_REAL_EQUAL(st_b, 0.0)
TEST_REAL_EQUAL(f_b, -1.0)
TEST_REAL_EQUAL(g_b, -1.0)
TEST_REAL_EQUAL(stp, 0.333333333333)
TEST_EQUAL(ls.isBracketed(), true)
// Third case: |g| < |g_a| and f <= f_a and sgn(g) == sgn(g_a)
// AND the cubic (interpolation) tends to -infinity but its minimum is beyond stp
ls.setBracketedFlag(false);
st_a = 0.;
f_a = -1.;
g_a = -1.;
st_b = 1.;
f_b = -1.;
g_b = 0.;
stp = 0.2;
f = -1.128;
g = -0.32;
minstp = 0.;
maxstp = 2.;
ls.takeStep(st_a, f_a, g_a, st_b, f_b, g_b, stp, f, g, minstp, maxstp);
TEST_REAL_EQUAL(st_a, 0.2)
TEST_REAL_EQUAL(f_a, -1.128)
TEST_REAL_EQUAL(g_a, -0.32)
TEST_REAL_EQUAL(st_b, 1.0)
TEST_REAL_EQUAL(f_b, -1.0)
TEST_REAL_EQUAL(g_b, 0.0)
TEST_REAL_EQUAL(stp, 0.333333333333)
TEST_EQUAL(ls.isBracketed(), false)
// Third case: |g| < |g_a| and f <= f_a and sgn(g) == sgn(g_a)
// AND the cubic (interpolation) tends to -infinity and its minimum is on this side of stp
// (so stp has to be maxstp)
ls.setBracketedFlag(false);
st_a = 0.;
f_a = -1.;
g_a = -1.;
st_b = 1.9;
f_b = -2.539;
g_b = -4.23;
stp = 1.1;
f = -1.011;
g = -0.23;
minstp = 0.;
maxstp = 2.;
ls.takeStep(st_a, f_a, g_a, st_b, f_b, g_b, stp, f, g, minstp, maxstp);
TEST_REAL_EQUAL(st_a, 1.1)
TEST_REAL_EQUAL(f_a, -1.011)
TEST_REAL_EQUAL(g_a, -0.23)
TEST_REAL_EQUAL(st_b, 1.9)
TEST_REAL_EQUAL(f_b, -2.539)
TEST_REAL_EQUAL(g_b, -4.23)
TEST_REAL_EQUAL(stp, 2.0)
TEST_EQUAL(ls.isBracketed(), false)
// Same case as above but now we force the step computation to
// assume that a minimizer has already been bracketed
ls.setBracketedFlag(true);
st_a = 0.;
f_a = -1.;
g_a = -1.;
st_b = 1.9;
f_b = -2.539;
g_b = -4.23;
stp = 1.1;
f = -1.011;
g = -0.23;
minstp = 0.;
maxstp = 2.;
ls.takeStep(st_a, f_a, g_a, st_b, f_b, g_b, stp, f, g, minstp, maxstp);
TEST_REAL_EQUAL(st_a, 1.1)
TEST_REAL_EQUAL(f_a, -1.011)
TEST_REAL_EQUAL(g_a, -0.23)
TEST_REAL_EQUAL(st_b, 1.9)
TEST_REAL_EQUAL(f_b, -2.539)
TEST_REAL_EQUAL(g_b, -4.23)
TEST_REAL_EQUAL(stp, 1.42857142857)
TEST_EQUAL(ls.isBracketed(), true)
// Fourth case: f <= f_a, sgn(g) == sgn(g_a), |g| >= |g_a|
// AND we force the step computation to assume that a minimizer could not have been bracketed so far
// (so stp has to be maxstp in this case)
ls.setBracketedFlag(false);
st_a = 0.;
f_a = -1.;
g_a = -1.;
st_b = 1.9;
f_b = -2.539;
g_b = -4.23;
stp = 1.5;
f = -1.375;
g = -1.75;
minstp = 0.;
maxstp = 2.;
ls.takeStep(st_a, f_a, g_a, st_b, f_b, g_b, stp, f, g, minstp, maxstp);
TEST_REAL_EQUAL(st_a, 1.5)
TEST_REAL_EQUAL(f_a, -1.375)
TEST_REAL_EQUAL(g_a, -1.75)
TEST_REAL_EQUAL(st_b, 1.9)
TEST_REAL_EQUAL(f_b, -2.539)
TEST_REAL_EQUAL(g_b, -4.23)
TEST_REAL_EQUAL(stp, 2.0)
TEST_EQUAL(ls.isBracketed(), false)
// Same case as above but now we force the step computation to
// assume that a minimizer has already been bracketed (so a cubic should be taken).
ls.setBracketedFlag(true);
st_a = 0.;
f_a = -1.;
g_a = -1.;
st_b = 1.9;
f_b = -2.539;
g_b = -4.23;
stp = 1.5;
f = -1.375;
g = -1.75;
minstp = 0.;
maxstp = 2.;
ls.takeStep(st_a, f_a, g_a, st_b, f_b, g_b, stp, f, g, minstp, maxstp);
TEST_REAL_EQUAL(st_a, 1.5)
TEST_REAL_EQUAL(f_a, -1.375)
TEST_REAL_EQUAL(g_a, -1.75)
TEST_REAL_EQUAL(st_b, 1.9)
TEST_REAL_EQUAL(f_b, -2.539)
TEST_REAL_EQUAL(g_b, -4.23)
TEST_REAL_EQUAL(stp, 0.333333333333)
TEST_EQUAL(ls.isBracketed(), true)
// Now chek a few things we couldn't check so far.
// We use the function f(x) = x^3 - 2x^2 - x - 1.
// This function has a minimizer at 2/3 + sqrt(7)/3 (about 1.54858)
// and tends to infinity for x->infinity
// Third case, but the cubic (interpolation) tends to infinity
// We force the step computation to assume that a minimizer could not have been bracketed
// so far. In this case the quadratic step should be taken.
ls.setBracketedFlag(false);
st_a = 0.;
f_a = -1.;
g_a = -1.;
st_b = 2.;
f_b = -3.;
g_b = 3.;
stp = 1.4;
f = -3.576;
g = -0.72;
minstp = 0.;
maxstp = 10.;
ls.takeStep(st_a, f_a, g_a, st_b, f_b, g_b, stp, f, g, minstp, maxstp);
TEST_REAL_EQUAL(st_a, 1.4)
TEST_REAL_EQUAL(f_a, -3.576)
TEST_REAL_EQUAL(g_a, -0.72)
TEST_REAL_EQUAL(st_b, 2.0)
TEST_REAL_EQUAL(f_b, -3.0)
TEST_REAL_EQUAL(g_b, 3.0)
TEST_REAL_EQUAL(stp, 5.0)
TEST_EQUAL(ls.isBracketed(), false)
// Same case as above but we force the step computation to assume that a
// minimizer has already been bracketed.
ls.setBracketedFlag(true);
st_a = 0.;
f_a = -1.;
g_a = -1.;
st_b = 2.;
f_b = -3.;
g_b = 3.;
stp = 1.4;
f = -3.576;
g = -0.72;
minstp = 0.;
maxstp = 10.;
ls.takeStep(st_a, f_a, g_a, st_b, f_b, g_b, stp, f, g, minstp, maxstp);
TEST_REAL_EQUAL(st_a, 1.4)
TEST_REAL_EQUAL(f_a, -3.576)
TEST_REAL_EQUAL(g_a, -0.72)
TEST_REAL_EQUAL(st_b, 2.0)
TEST_REAL_EQUAL(f_b, -3.0)
TEST_REAL_EQUAL(g_b, 3.0)
TEST_REAL_EQUAL(stp, 1.54858377035)
TEST_EQUAL(ls.isBracketed(), true)
// Two more examples where stp is not between st_a and st_b
// (to check cases when the quadratic (or the cubic) seems to be better.
ls.setBracketedFlag(false);
st_a = 0.;
f_a = -1.;
g_a = -1.;
st_b = 2.;
f_b = -3.;
g_b = 3.;
stp = -1.4;
f = -6.264;
g = 10.48;
minstp = 0.;
maxstp = 10.;
ls.takeStep(st_a, f_a, g_a, st_b, f_b, g_b, stp, f, g, minstp, maxstp);
TEST_REAL_EQUAL(st_a, -1.4)
TEST_REAL_EQUAL(f_a, -6.264)
TEST_REAL_EQUAL(g_a, 10.48)
TEST_REAL_EQUAL(st_b, 0.0)
TEST_REAL_EQUAL(f_b, -1.0)
TEST_REAL_EQUAL(g_b, -1.0)
TEST_REAL_EQUAL(stp, 1.54858377035)
TEST_EQUAL(ls.isBracketed(), true)
// Now the quadratic seems to be better (since the cubic step is not farther from
// stp than the quadratic step)
ls.setBracketedFlag(false);
st_a = 0.;
f_a = -1.;
g_a = -1.;
st_b = 2.;
f_b = -3.;
g_b = 3.;
stp = 15.;
f = 2909.;
g = 614.;
minstp = 0.;
maxstp = 10.;
ls.takeStep(st_a, f_a, g_a, st_b, f_b, g_b, stp, f, g, minstp, maxstp);
TEST_REAL_EQUAL(st_a, 0.0)
TEST_REAL_EQUAL(f_a, -1.0)
TEST_REAL_EQUAL(g_a, -1.0)
TEST_REAL_EQUAL(st_b, 15.0)
TEST_REAL_EQUAL(f_b, 2909.0)
TEST_REAL_EQUAL(g_b, 614.0)
TEST_REAL_EQUAL(stp, 0.793522654408)
TEST_EQUAL(ls.isBracketed(), true)
RESULT
/////////////////////////////////////////////////////////////
/////////////////////////////////////////////////////////////
END_TEST
|
