public OptVector Solve(
OptVector[] A,
OptVector b,
OptVector startX,
int nIter)
{
OptVector[] normA = A;
OptVector normb = b;
if (!OptVector.Equals(A, OptVector.Transpose(A)))
{
OptVector[] At = OptVector.Transpose(A);
normA = OptVector.Mult(At, A);
normb = OptVector.Mult(At, b);
}
OptVector rNew = normb - OptVector.Mult(normA, startX);
OptVector p = rNew;
OptVector x = new OptVector(startX);
double r2Old = rNew * rNew;
double alpha = 1.0;
double beta = 1.0;
for (int i = 0; i < nIter; i++)
{
alpha = GetAlpha(normA, p, r2Old);
x = x + alpha * p;
rNew = rNew - alpha * OptVector.Mult(normA, p);
double r2New = rNew * rNew;
if (r2New < Precision)
{
return(x);
}
beta = GetBeta(r2New, r2Old);
p = rNew + beta * p;
r2Old = r2New;
}
return(x);
}
static void Main(string[] args)
{
double oneOver2Pi = 1.0 / (1.0 * Math.Sqrt(2 * Math.PI));
Console.WriteLine(NormalCDFInverse(0.99));
Console.WriteLine(inv_cdf(0.99));
Console.WriteLine(InverseCDF.QNorm(0.99, 0, 1, true, false));
Console.WriteLine(NormalCDFInverse(0.5));
Console.WriteLine(inv_cdf(0.5));
Console.WriteLine(InverseCDF.QNorm(0.5, 0, 1, true, false));
Console.WriteLine(NormalCDFInverse(0.31));
Console.WriteLine(inv_cdf(0.31));
Console.WriteLine(InverseCDF.QNorm(0.31, 0, 1, true, false));
//x4−8x2 + 5
Func <double[], double> testFunc1 = (x) =>
{
return(Math.Pow(x[0], 4) - 8 * Math.Pow(x[0], 2) + 5);
};
Func <double[], double>[] dtestFunc1 = new Func <double[], double> [1];
dtestFunc1[0] = (x) =>
{
return(4 * Math.Pow(x[0], 3) - 16 * x[0]);
};
Func <double[], double> testConstr = (x) =>
{
return(5 - Math.Exp(x[0]) + 2.0 * Math.Pow(x[0] - 1, 2));
};
Func <double[], double> testv = (x) =>
{
double a = x[0];
return(0.0);
};
//Func<Variables, double> testFunc = (x) => {
// return Math.Pow(x.Vars[0], 4) - 3 * Math.Pow(x.Vars[0], 3) + 2;
//};
//Func<Variables, double> dTestfunc = (x) =>
//{
// return 4 * Math.Pow(x.Vars[0], 3) - 9 * Math.Pow(x.Vars[0], 2);
//};
//x4−3x3 + 2
//TestFunc();
Func <double[], double> bananaFunc = (x) =>
{
return(Math.Pow(1 - x[0], 2) + 100 * Math.Pow(x[1] - x[0] * x[0], 2));
};
Func <double[], double> powell = (x) =>
{
return(Math.Pow(x[0] + 10 * x[1], 2) +
5 * Math.Pow(x[2] - x[3], 2) +
Math.Pow(x[1] + 2 * x[2], 4) +
10 * Math.Pow(x[0] - x[3], 4));
};
OptVector[] ttt = new OptVector[3];
ttt[0] = new OptVector(new double[3] {
1, 2, 3
});
ttt[1] = new OptVector(new double[3] {
4, 5, 6
});
ttt[2] = new OptVector(new double[3] {
7, 8, 9
});
var tr = OptVector.Transpose(ttt);
//TestsSQP.Test0();
TestsSQP.Test1();
TestsSQP.Test2();
TestsSQP.Test3();
////TestsSQP.Test4();
////TestsSQP.Test5();
TestsSQP.Test6();
TestsSQP.Test7();
TestsSQP.Test8();
TestsSQP.Test9();
TestsSQP.Test10();
TestsSQP.Test11();
TestsSQP.Test12();
TestsSQP.Test13();
TestsSQP.Test14();
TestsSQP.Test15();
TestsSQP.Test16();
TestsSQP.Test17();
TestsSQP.Test18();
TestsSQP.Test19();
TestsSQP.Test20();
TestsSQP.Test21();
TestsSQP.Test22();
TestsSQP.Test23();
TestsSQP.Test24();
TestsSQP.Test25();
TestsSQP.Test26();
TestsSQP.Test27();
TestsSQP.Test28();
//TestCGMethod();
BFGS bfsg = new BFGS();
var result0 = bfsg.Solve(powell, new double[] { 3.0, -1.0, 0.0, 1.0 }, 10000);
Console.WriteLine("Min " + powell(result0));
NLCG gradient = new NLCG();
var result = gradient.Solve(powell, new double[] { 3.0, -1.0, 0.0, 1.0 }, 4000);
Console.WriteLine("Min " + powell(result));
SteepestDescent gradientSteep = new SteepestDescent();
var result1 = gradientSteep.Solve(powell, new double[] { 3.0, -1.0, 0.0, 1.0 }, 10000);
Console.WriteLine("Min " + powell(result1));
//Variables result = SteepestDescent(testFunc, dTestFunc, 2, 20);
for (int i = 0; i < result.Length; i++)
{
Console.WriteLine("result " + result[i]);
}
//Console.WriteLine("ver " + testFunc(result));
Console.ReadLine();
}
public OptVector Solve(
OptVector[] A,
OptVector b,
OptVector startX,
int nIter)
{
OptVector[] symmA = A;
OptVector normb = b;
//Symmetrize matrix
if (CheckSymmetry)
{
OptVector[] At = OptVector.Transpose(A);
if (!OptVector.Equals(A, At))
{
symmA = OptVector.Mult(At, A);
normb = OptVector.Mult(At, b);
}
}
OptVector v0 = new OptVector(b.Count);
OptVector v1 = normb - OptVector.Mult(symmA, startX);
double beta1 = v1.Length();
double betaN = 0.0;
double n = beta1;
double c0 = 1.0;
double c1 = 1.0;
double s0 = 0.0;
double s1 = 0.0;
OptVector w0 = new OptVector(v1.Count);
OptVector w_1 = new OptVector(v1.Count);
OptVector x = new OptVector(startX);
for (int i = 0; i < nIter; i++)
{
//Calculate Lanczos Vectors
OptVector v = (1.0 / beta1) * v1;
OptVector Av = OptVector.Mult(symmA, v);
double alpha = v * Av;
v1 = Av - alpha * v - beta1 * v0;
betaN = v1.Length();
//Calculate QR factors
double lambda = c1 * alpha - c0 * s1 * beta1;
double p1 = Math.Sqrt(lambda * lambda + betaN * betaN);
double p2 = s1 * alpha + c0 * c1 * beta1;
double p3 = s0 * beta1;
//Calculate New Givens Rotations
c0 = c1;
c1 = lambda / p1;
s0 = s1;
s1 = betaN / p1;
//Update Solution
OptVector w = (1.0 / p1) * (v - p3 * w_1 - p2 * w0);
x = x + c1 * n * w;
n = -s1 * n;
residual = Math.Abs(n);
if (residual < precisionConst)
{
break;
}
beta1 = betaN;
v0 = v;
w_1 = w0;
w0 = w;
}
return(x);
}