private static void test04()
//******************************************************************************
//
// Purpose:
//
// TEST04 tests PMGMRES_ILU_CR on a simple 5 by 5 matrix.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 25 July 2007
//
// Author:
//
// John Burkardt
//
{
const int N = 5;
const int NZ_NUM = 9;
double[] a =
{
1.0, 2.0, 1.0,
2.0,
3.0, 3.0,
4.0,
1.0, 5.0
};
int i;
int[] ia = { 0, 3, 4, 6, 7, 9 };
int itr_max = 0;
int[] ja =
{
0, 3, 4,
1,
0, 2,
3,
1, 4
};
int mr = 0;
double[] rhs = { 14.0, 4.0, 12.0, 16.0, 27.0 };
int test;
double[] x_estimate = new double[N];
double[] x_exact = { 1.0, 2.0, 3.0, 4.0, 5.0 };
Console.WriteLine("");
Console.WriteLine("TEST04");
Console.WriteLine(" Test PMGMRES_ILU_CR on a simple 5 x 5 matrix.");
Console.WriteLine("");
for (i = 0; i < N + 1; i++)
{
Console.WriteLine(" ia[" + i + "] = " + ia[i] + "");
}
for (test = 1; test <= 3; test++)
{
//
// Set the initial solution estimate.
//
for (i = 0; i < N; i++)
{
x_estimate[i] = 0.0;
}
double x_error = 0.0;
for (i = 0; i < N; i++)
{
x_error += Math.Pow(x_exact[i] - x_estimate[i], 2);
}
x_error = Math.Sqrt(x_error);
switch (test)
{
case 1:
itr_max = 1;
mr = 20;
break;
case 2:
itr_max = 2;
mr = 10;
break;
case 3:
itr_max = 5;
mr = 4;
break;
}
const double tol_abs = 1.0E-08;
const double tol_rel = 1.0E-08;
Console.WriteLine("");
Console.WriteLine(" Test " + test + "");
Console.WriteLine(" Matrix order N = " + N + "");
Console.WriteLine(" Inner iteration limit = " + mr + "");
Console.WriteLine(" Outer iteration limit = " + itr_max + "");
Console.WriteLine(" Initial X_ERROR = " + x_error + "");
RestartedGeneralizedMinimumResidual.pmgmres_ilu_cr(N, NZ_NUM, ia, ja, a, ref x_estimate, rhs, itr_max,
mr,
tol_abs, tol_rel);
x_error = 0.0;
for (i = 0; i < N; i++)
{
x_error += Math.Pow(x_exact[i] - x_estimate[i], 2);
}
x_error = Math.Sqrt(x_error);
Console.WriteLine(" Final X_ERROR = " + x_error + "");
}
}
private static void test03()
//******************************************************************************
//
// Purpose:
//
// TEST03 tests PMGMRES_ILU_CR on the simple -1,2-1 matrix.
//
// Discussion:
//
// This is a very weak test, since the matrix has such a simple
// structure, is diagonally dominant (though not strictly),
// and is symmetric.
//
// To make the matrix bigger, simply increase the value of N.
//
// Note that PGMRES_ILU_CR expects the matrix to be stored using the
// sparse compressed row format.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 25 July 2007
//
// Author:
//
// John Burkardt
//
{
const int N = 20;
const int NZ_NUM = 3 * N - 2;
double[] a = new double[NZ_NUM];
int i;
int[] ia = new int[N + 1];
int itr_max = 0;
int[] ja = new int[NZ_NUM];
int mr = 0;
double[] rhs = new double[N];
int test;
double[] x_estimate = new double[N];
double[] x_exact = new double[N];
Console.WriteLine("");
Console.WriteLine("TEST03");
Console.WriteLine(" Test PMGMRES_ILU_CR on the simple -1,2-1 matrix.");
//
// Set the matrix.
// Note that we use zero based index valuesin IA and JA.
//
int k = 0;
ia[0] = 0;
Console.WriteLine("");
Console.WriteLine(" ia[" + 0 + "] = " + ia[0] + "");
for (i = 0; i < N; i++)
{
ia[i + 1] = ia[i];
switch (i)
{
case > 0:
ia[i + 1] += 1;
ja[k] = i - 1;
a[k] = -1.0;
k += 1;
break;
}
ia[i + 1] += 1;
ja[k] = i;
a[k] = 2.0;
k += 1;
if (i < N - 1)
{
ia[i + 1] += 1;
ja[k] = i + 1;
a[k] = -1.0;
k += 1;
}
Console.WriteLine(" ia[" + i + 1 + "] = " + ia[i + 1] + "");
}
//
// Set the right hand side:
//
for (i = 0; i < N - 1; i++)
{
rhs[i] = 0.0;
}
rhs[N - 1] = N + 1;
//
// Set the exact solution.
//
for (i = 0; i < N; i++)
{
x_exact[i] = i + 1;
}
for (test = 1; test <= 3; test++)
{
//
// Set the initial solution estimate.
//
for (i = 0; i < N; i++)
{
x_estimate[i] = 0.0;
}
double x_error = 0.0;
for (i = 0; i < N; i++)
{
x_error += Math.Pow(x_exact[i] - x_estimate[i], 2);
}
x_error = Math.Sqrt(x_error);
switch (test)
{
case 1:
itr_max = 1;
mr = 20;
break;
case 2:
itr_max = 2;
mr = 10;
break;
case 3:
itr_max = 5;
mr = 4;
break;
}
const double tol_abs = 1.0E-08;
const double tol_rel = 1.0E-08;
Console.WriteLine("");
Console.WriteLine(" Test " + test + "");
Console.WriteLine(" Matrix order N = " + N + "");
Console.WriteLine(" Inner iteration limit = " + mr + "");
Console.WriteLine(" Outer iteration limit = " + itr_max + "");
Console.WriteLine(" Initial X_ERROR = " + x_error + "");
RestartedGeneralizedMinimumResidual.pmgmres_ilu_cr(N, NZ_NUM, ia, ja, a, ref x_estimate, rhs, itr_max,
mr,
tol_abs, tol_rel);
x_error = 0.0;
for (i = 0; i < N; i++)
{
x_error += Math.Pow(x_exact[i] - x_estimate[i], 2);
}
x_error = Math.Sqrt(x_error);
Console.WriteLine(" Final X_ERROR = " + x_error + "");
}
}