public void FindMinimum_EasyFun_YieldsExpectedValue(int dim, double minVal, double expect)
{
var constraintMatrix = new double[dim, dim];
var constraintVals = new double[dim];
for (int i = 0; i < dim; i++)
{
constraintMatrix[i, i] = -1;
constraintVals[i] = -minVal;
}
var lincoa = new Lincoa(EasyFun, constraintMatrix, constraintVals)
{
TrustRegionRadiusStart = 1,
TrustRegionRadiusEnd = 0.01,
MaximumFunctionCalls = 10000,
PrintLevel = 3,
Logger = Console.Out
};
var result = lincoa.FindMinimum(new double[dim]);
var actual = result.F;
Assert.AreEqual(expect, actual, 0.1);
}
public void FindMinimum_EasyFun_YieldsExpectedValue(int dim, double minVal, double expect)
{
var constraintMatrix = new double[dim,dim];
var constraintVals = new double[dim];
for (int i = 0; i < dim; i++)
{
constraintMatrix[i, i] = -1;
constraintVals[i] = -minVal;
}
var lincoa = new Lincoa(EasyFun, constraintMatrix, constraintVals)
{
TrustRegionRadiusStart = 1,
TrustRegionRadiusEnd = 0.01,
MaximumFunctionCalls = 10000,
PrintLevel = 3,
Logger = Console.Out
};
var result = lincoa.FindMinimum(new double[dim]);
var actual = result.F;
Assert.AreEqual(expect, actual, 0.1);
}
public void FindMinimum_PtsinTet_YieldsExpectedValue(int npt, double tol)
{
// Set some constants.
const int n = 12;
// Set the data points.
const int np = 50;
var sumx = 0.0;
var sumy = 0.0;
var sumz = 0.0;
var xp = new double[50];
var yp = new double[50];
var zp = new double[50];
for (var j = 0; j < np; ++j)
{
var theta = j * Math.PI / (np - 1.0);
xp[j] = Math.Cos(theta) * Math.Cos(2.0 * theta);
sumx += xp[j];
yp[j] = Math.Sin(theta) * Math.Cos(2.0 * theta);
sumy += yp[j];
zp[j] = Math.Sin(2.0 * theta);
sumz += zp[j];
}
sumx /= np;
sumy /= np;
sumz /= np;
for (var j = 0; j < np; ++j)
{
xp[j] -= sumx;
yp[j] -= sumy;
zp[j] -= sumz;
}
// Set the linear constraints.
const int m = 4 * np;
var a = new double[m, n];
var b = new double[m];
for (var k = 0; k < m; ++k)
{
b[k] = 1.0;
for (var i = 0; i < n; ++i)
{
a[k, i] = 0.0;
}
}
for (var j = 0; j < np; ++j)
{
for (var i = 0; i < 4; ++i)
{
var k = 4 * j + i;
var iw = 3 * i;
a[k, iw] = xp[j];
a[k, iw + 1] = yp[j];
a[k, iw + 2] = zp[j];
}
}
// Set the initial vector of variables.
var xs = 0.0;
var ys = 0.0;
var zs = 0.0;
var ss = 0.0;
for (var j = 0; j < np; ++j)
{
xs = Math.Min(xs, xp[j]);
ys = Math.Min(ys, yp[j]);
zs = Math.Min(zs, zp[j]);
ss = Math.Max(ss, xp[j] + yp[j] + zp[j]);
}
var x = new double[12];
x[0] = 1.0 / xs;
x[4] = 1.0 / ys;
x[8] = 1.0 / zs;
x[9] = 1.0 / ss;
x[10] = 1.0 / ss;
x[11] = 1.0 / ss;
this._fmax = Math.Pow(ss - xs - ys - zs, 3.0) / 6.0;
// Call of LINCOA, which provides the printing given at the end of this note.
const double rhobeg = 1.0;
const double rhoend = 1.0E-6;
const int iprint = 1;
const int maxfun = 10000;
var lincoa = new Lincoa(this.PtsinTet, a, b)
{
InterpolationConditions = npt,
TrustRegionRadiusStart = rhobeg,
TrustRegionRadiusEnd = rhoend,
MaximumFunctionCalls = maxfun,
PrintLevel = iprint,
Logger = Console.Out
};
var result = lincoa.FindMinimum(x);
const double expected = 2.761;
var actual = result.F;
Assert.AreEqual(expected, actual, tol);
}
public void FindMinimum_PtsinTet_YieldsExpectedValue(int npt, double tol)
{
// Set some constants.
const int n = 12;
// Set the data points.
const int np = 50;
var sumx = 0.0;
var sumy = 0.0;
var sumz = 0.0;
var xp = new double[50];
var yp = new double[50];
var zp = new double[50];
for (var j = 0; j < np; ++j)
{
var theta = j * Math.PI / (np - 1.0);
xp[j] = Math.Cos(theta) * Math.Cos(2.0 * theta);
sumx += xp[j];
yp[j] = Math.Sin(theta) * Math.Cos(2.0 * theta);
sumy += yp[j];
zp[j] = Math.Sin(2.0 * theta);
sumz += zp[j];
}
sumx /= np;
sumy /= np;
sumz /= np;
for (var j = 0; j < np; ++j)
{
xp[j] -= sumx;
yp[j] -= sumy;
zp[j] -= sumz;
}
// Set the linear constraints.
const int m = 4 * np;
var a = new double[m, n];
var b = new double[m];
for (var k = 0; k < m; ++k)
{
b[k] = 1.0;
for (var i = 0; i < n; ++i)
a[k, i] = 0.0;
}
for (var j = 0; j < np; ++j)
{
for (var i = 0; i < 4; ++i)
{
var k = 4 * j + i;
var iw = 3 * i;
a[k, iw] = xp[j];
a[k, iw + 1] = yp[j];
a[k, iw + 2] = zp[j];
}
}
// Set the initial vector of variables.
var xs = 0.0;
var ys = 0.0;
var zs = 0.0;
var ss = 0.0;
for (var j = 0; j < np; ++j)
{
xs = Math.Min(xs, xp[j]);
ys = Math.Min(ys, yp[j]);
zs = Math.Min(zs, zp[j]);
ss = Math.Max(ss, xp[j] + yp[j] + zp[j]);
}
var x = new double[12];
x[0] = 1.0 / xs;
x[4] = 1.0 / ys;
x[8] = 1.0 / zs;
x[9] = 1.0 / ss;
x[10] = 1.0 / ss;
x[11] = 1.0 / ss;
this._fmax = Math.Pow(ss - xs - ys - zs, 3.0) / 6.0;
// Call of LINCOA, which provides the printing given at the end of this note.
const double rhobeg = 1.0;
const double rhoend = 1.0E-6;
const int iprint = 1;
const int maxfun = 10000;
var lincoa = new Lincoa(this.PtsinTet, a, b)
{
InterpolationConditions = npt,
TrustRegionRadiusStart = rhobeg,
TrustRegionRadiusEnd = rhoend,
MaximumFunctionCalls = maxfun,
PrintLevel = iprint,
Logger = Console.Out
};
var result = lincoa.FindMinimum(x);
const double expected = 2.761;
var actual = result.F;
Assert.AreEqual(expected, actual, tol);
}