public SQP(
double precision,
bool earlyExit)
{
numericalDerivative = new OptimizationNumericalDerivative(5, 3);
linearSolver = new MINRES(1E-50, false);
strongWolfeLineSearch = new StrongWolfeLineSearch();
Precision = precision;
EarlyExit = earlyExit;
}
static void TestCGMethod()
{
MINRES minres = new MINRES();
CGMethod cg = new CGMethod();
OptVector[] A2 = new OptVector[3];
A2[0] = new OptVector(new double[] { 2, 1, 3 });
A2[1] = new OptVector(new double[] { 2, 6, 8 });
A2[2] = new OptVector(new double[] { 6, 8, 18 });
OptVector b2 = new OptVector(new double[] { 1, 3, 5 });
var minresSol = minres.Solve(A2, b2, new OptVector(new double[3]), 50);
var sol2 = cg.Solve(A2, b2, new OptVector(new double[3]), 50);
OptVector[] A = new OptVector[3];
A[0] = new OptVector(new double[] { 2, 0, 1 });
A[1] = new OptVector(new double[] { 1, 6, 0 });
A[2] = new OptVector(new double[] { 3, 2, 3 });
OptVector x = new OptVector(new double[] { 2, 5, 7 });
var sol = cg.Solve(A, x, new OptVector(new double[3]), 50);
var solm = minres.Solve(A, x, new OptVector(new double[3]), 50);
OptVector[] A1 = new OptVector[3];
A1[0] = new OptVector(new double[] { 3, 1, -6 });
A1[1] = new OptVector(new double[] { 2, 1, -5 });
A1[2] = new OptVector(new double[] { 6, -3, 3 });
OptVector b1 = new OptVector(new double[] { -10, -8, 0 });
var sol1 = cg.Solve(A1, b1, new OptVector(new double[3]), 200);
var solm1 = minres.Solve(A1, b1, new OptVector(new double[3]), 200);
OptVector diff = b1 - OptVector.Mult(A1, solm1);
OptVector diff1 = b1 - OptVector.Mult(A1, sol1);
}
private static void TestGmres()
{
var luSolver = new LUSolver();
var solver = new MINRES();
var cg = new ConjugateGradient();
SparseMatrix A = new SparseMatrix(6, 6);
A.Rows[0] = SparseVector.GetSparseElement(new double[] { 10.0, 0.0, 0.0, 0.0, 0.0, 0.0 });
A.Rows[1] = SparseVector.GetSparseElement(new double[] { 0.0, 10.0, -3.0, -1.0, 0.0, 0.0 });
A.Rows[2] = SparseVector.GetSparseElement(new double[] { 0.0, 0.0, 15.0, 0.0, 0.0, 0.0 });
A.Rows[3] = SparseVector.GetSparseElement(new double[] { -2.0, 0.0, 0.0, 10.0, -1.0, 0.0 });
A.Rows[4] = SparseVector.GetSparseElement(new double[] { -1.0, 0.0, 0.0, -5.0, 1.0, -3.0 });
A.Rows[5] = SparseVector.GetSparseElement(new double[] { -1.0, -2.0, 0.0, 0.0, 0.0, 6.0 });
double[] b = new double[] { 10.0, 7.0, 45.0, 33.0, -34.0, 31.0 };
double[] x = new double[b.Length];
for (int i = 0; i < x.Length; i++)
{
x[i] = 0.0;
}
//symmetrize system
SparseMatrix At = SparseMatrix.Transpose(A);
//SparseMatrix AA = SparseMatrix.Square(At);
SparseMatrix AA = SparseMatrix.Multiply(At, A);
double[] Ab = SparseMatrix.Multiply(At, b);
var cgout = solver.Solve(AA, Ab, x, 10);
var out1 = solver.Solve(AA, Ab, x, 30000);
var solver1 = new GMRES();
var out2 = solver1.Solve(A, b, x, 30, 6);
//var lout = luSolver.Solve(A, b, out bool valid);
HouseholderQR hs = new HouseholderQR();
SparseMatrix B = new SparseMatrix(5, 3);
B.Rows[0] = SparseVector.GetSparseElement(new double[] { 12.0, -51.0, 4.0 });
B.Rows[1] = SparseVector.GetSparseElement(new double[] { 6.0, 167.0, -68.0 });
B.Rows[2] = SparseVector.GetSparseElement(new double[] { -4.0, 24.0, -41.0 });
B.Rows[3] = SparseVector.GetSparseElement(new double[] { -1.0, 1.0, 0.0 });
B.Rows[4] = SparseVector.GetSparseElement(new double[] { 2.0, 0.0, 3.0 });
hs.Householder(B);
hs.Solve(A, b);
Lemke lm = new Lemke(SharpEngineMathUtility.Solver.SolverType.HouseHolderQR);
SparseMatrix M = new SparseMatrix(3, 3);
M.Rows[0] = SparseVector.GetSparseElement(new double[] { 21.0, 0.0, 0.0 });
M.Rows[1] = SparseVector.GetSparseElement(new double[] { 28.0, 14.0, 0.0 });
M.Rows[2] = SparseVector.GetSparseElement(new double[] { 24.0, 24.0, 12.0 });
double[] q = new double[] { -1.0, -1.0, -1.0 };
lm.Solve(M, q, 10);
SparseMatrix M1 = new SparseMatrix(2, 2);
M1.Rows[0] = SparseVector.GetSparseElement(new double[] { 2.0, 1.0 });
M1.Rows[1] = SparseVector.GetSparseElement(new double[] { 1.0, 2.0 });
double[] q1 = new double[] { -5.0, -6.0 };
lm.Solve(M1, q1, 10);
double[] q2 = new double[] { 1.0, 2.0 };
lm.Solve(M1, q2, 10);
SparseMatrix M3 = new SparseMatrix(3, 3);
M3.Rows[0] = SparseVector.GetSparseElement(new double[] { 1.0, 0.0, 2.0 });
M3.Rows[1] = SparseVector.GetSparseElement(new double[] { 3.0, 2.0, -1.0 });
M3.Rows[2] = SparseVector.GetSparseElement(new double[] { -2.0, 1.0, 0.0 });
double[] q3 = new double[] { -1.0, 2.0, -3.0 };
lm.Solve(M3, q3, 10);
SparseMatrix M4 = new SparseMatrix(3, 3);
M4.Rows[0] = SparseVector.GetSparseElement(new double[] { 0.0, 0.0, 1.0 });
M4.Rows[1] = SparseVector.GetSparseElement(new double[] { 0.0, 2.0, 1.0 });
M4.Rows[2] = SparseVector.GetSparseElement(new double[] { -1.0, -1.0, 0.0 });
double[] q4 = new double[] { -6.0, 0.0, 4.0 };
lm.Solve(M4, q4, 10);
SparseMatrix M5 = new SparseMatrix(3, 3);
M5.Rows[0] = SparseVector.GetSparseElement(new double[] { 1.0, 2.0, 0.0 });
M5.Rows[1] = SparseVector.GetSparseElement(new double[] { 0.0, 1.0, 2.0 });
M5.Rows[2] = SparseVector.GetSparseElement(new double[] { 2.0, 0.0, 1.0 });
double[] q5 = new double[] { -1.0, -1.0, -1.0 };
lm.Solve(M5, q5, 10);
SparseMatrix M6 = new SparseMatrix(4, 4);
M6.Rows[0] = SparseVector.GetSparseElement(new double[] { 1.0, 1.0, 3.0, 4.0 });
M6.Rows[1] = SparseVector.GetSparseElement(new double[] { 5.0, 3.0, 1.0, 1.0 });
M6.Rows[2] = SparseVector.GetSparseElement(new double[] { 2.0, 1.0, 2.0, 2.0 });
M6.Rows[3] = SparseVector.GetSparseElement(new double[] { 1.0, 4.0, 1.0, 1.0 });
double[] q6 = new double[] { -1.0, 2.0, 1.0, 3.0 };
lm.Solve(M6, q6, 10);
SparseMatrix M8 = new SparseMatrix(6, 6);
M8.Rows[0] = SparseVector.GetSparseElement(new double[] { 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 });
M8.Rows[1] = SparseVector.GetSparseElement(new double[] { 2.0, 4.0, 8.0, 16.0, 32.0, 64.0 });
M8.Rows[2] = SparseVector.GetSparseElement(new double[] { 3.0, 9.0, 27.0, 81.0, 243.0, 729.0 });
M8.Rows[3] = SparseVector.GetSparseElement(new double[] { 4.0, 16.0, 64.0, 256.0, 1024.0, 4096.0 });
M8.Rows[4] = SparseVector.GetSparseElement(new double[] { 5.0, 25.0, 125.0, 625.0, 3125.0, 15625.0 });
M8.Rows[5] = SparseVector.GetSparseElement(new double[] { 6.0, 36.0, 216.0, 1296.0, 7776.0, 46656.0 });
var ll1 = luSolver.Solve(M8, new double[6], out bool valid1);
}
