public void TridiagonalMatrixDuplicationTest()
{
TridiagonalMatrix T = CreateRandomTridiagonalMatrix(4);
// check that clone is clone
TridiagonalMatrix TC = T.Copy();
Assert.IsTrue(TC == T);
// check that clone is independend
TC[0, 0] += 1.0;
Assert.IsTrue(TC != T);
// check that transpose of transpose is original
TridiagonalMatrix TT = T.Transpose();
Assert.IsTrue(TT != T);
TridiagonalMatrix TTT = TT.Transpose();
Assert.IsTrue(TTT == T);
// check that transpose is independent
TTT[0, 0] += 1.0;
Assert.IsTrue(TTT != T);
}
public void TridiagonalMatrixFibinacciDeterminant()
{
// The n X n tri-diagonal matrix with 1s on the diagonal,
// 1s on the super-diagonal, and -1s on the sub-diagonal
// has determinant equal to the (n+1)th Fibonacci number.
foreach (int n in TestUtilities.GenerateIntegerValues(2, 128, 4))
{
TridiagonalMatrix T = new TridiagonalMatrix(n);
for (int i = 0; i < n; i++)
{
T[i, i] = 1.0;
}
for (int i = 1; i < n; i++)
{
T[i - 1, i] = 1.0;
T[i, i - 1] = -1.0;
}
Assert.IsTrue(TestUtilities.IsNearlyEqual(
T.Determinant(),
AdvancedIntegerMath.FibonacciNumber(n + 1)
));
}
}
//JAVA TO C# CONVERTER TODO TASK: Most Java annotations will not have direct .NET equivalent attributes:
//ORIGINAL LINE: @Test public void testTridiagonalMultiply()
public virtual void testTridiagonalMultiply()
{
const int n = 37;
double[] l = new double[n - 1];
double[] c = new double[n];
double[] u = new double[n - 1];
double[] x = new double[n];
for (int ii = 0; ii < n; ii++)
{
c[ii] = RANDOM.nextRandom();
x[ii] = RANDOM.nextRandom();
if (ii < n - 1)
{
l[ii] = RANDOM.nextRandom();
u[ii] = RANDOM.nextRandom();
}
}
//JAVA TO C# CONVERTER WARNING: The original Java variable was marked 'final':
//ORIGINAL LINE: final com.opengamma.strata.math.impl.linearalgebra.TridiagonalMatrix m = new com.opengamma.strata.math.impl.linearalgebra.TridiagonalMatrix(c, u, l);
TridiagonalMatrix m = new TridiagonalMatrix(c, u, l);
//JAVA TO C# CONVERTER WARNING: The original Java variable was marked 'final':
//ORIGINAL LINE: final com.opengamma.strata.collect.array.DoubleArray xVec = com.opengamma.strata.collect.array.DoubleArray.copyOf(x);
DoubleArray xVec = DoubleArray.copyOf(x);
DoubleArray y1 = (DoubleArray)ALGEBRA.multiply(m, xVec);
DoubleMatrix full = m.toDoubleMatrix();
DoubleArray y2 = (DoubleArray)ALGEBRA.multiply(full, xVec);
for (int i = 0; i < n; i++)
{
assertEquals(y1.get(i), y2.get(i), 1e-12);
}
}
public void TestInvert4()
{
TridiagonalMatrix m = new TridiagonalMatrix(4);
m.Data[0, 0] = 2; m.Data[0, 1] = 1; m.Data[0, 2] = 0; m.Data[0, 3] = 0;
m.Data[1, 0] = 1; m.Data[1, 1] = 4; m.Data[1, 2] = 1; m.Data[1, 3] = 0;
m.Data[2, 0] = 0; m.Data[2, 1] = 1; m.Data[2, 2] = 4; m.Data[2, 3] = 1;
m.Data[3, 0] = 0; m.Data[3, 1] = 0; m.Data[3, 2] = 1; m.Data[3, 3] = 2;
m.Invert();
// Check data.
Assert.AreEqual(1, m.Data[0, 0]);
Assert.AreEqual(0, m.Data[0, 1]);
Assert.AreEqual(0, m.Data[0, 2]);
Assert.AreEqual(0, m.Data[0, 3]);
Assert.AreEqual(0, m.Data[1, 0]);
Assert.AreEqual(1, m.Data[1, 1]);
Assert.AreEqual(0, m.Data[1, 2]);
Assert.AreEqual(0, m.Data[1, 3]);
Assert.AreEqual(0, m.Data[2, 0]);
Assert.AreEqual(0, m.Data[2, 1]);
Assert.AreEqual(1, m.Data[2, 2]);
Assert.AreEqual(0, m.Data[2, 3]);
Assert.AreEqual(0, m.Data[3, 0]);
Assert.AreEqual(0, m.Data[3, 1]);
Assert.AreEqual(0, m.Data[3, 2]);
Assert.AreEqual(1, m.Data[3, 3]);
// Check inverse.
Assert.AreEqual(new Fraction(26, 45), m.Inverse[0, 0]);
Assert.AreEqual(new Fraction(-7, 45), m.Inverse[0, 1]);
Assert.AreEqual(new Fraction(2, 45), m.Inverse[0, 2]);
Assert.AreEqual(new Fraction(-1, 45), m.Inverse[0, 3]);
Assert.AreEqual(new Fraction(-7, 45), m.Inverse[1, 0]);
Assert.AreEqual(new Fraction(14, 45), m.Inverse[1, 1]);
Assert.AreEqual(new Fraction(-4, 45), m.Inverse[1, 2]);
Assert.AreEqual(new Fraction(2, 45), m.Inverse[1, 3]);
Assert.AreEqual(new Fraction(2, 45), m.Inverse[2, 0]);
Assert.AreEqual(new Fraction(-4, 45), m.Inverse[2, 1]);
Assert.AreEqual(new Fraction(14, 45), m.Inverse[2, 2]);
Assert.AreEqual(new Fraction(-7, 45), m.Inverse[2, 3]);
Assert.AreEqual(new Fraction(-1, 45), m.Inverse[3, 0]);
Assert.AreEqual(new Fraction(2, 45), m.Inverse[3, 1]);
Assert.AreEqual(new Fraction(-7, 45), m.Inverse[3, 2]);
Assert.AreEqual(new Fraction(26, 45), m.Inverse[3, 3]);
}
public void TestInvert3()
{
TridiagonalMatrix m = new TridiagonalMatrix(4);
m.Data[0, 0] = 3; m.Data[0, 1] = 2; m.Data[0, 2] = 0; m.Data[0, 3] = 0;
m.Data[1, 0] = 2; m.Data[1, 1] = 5; m.Data[1, 2] = 2; m.Data[1, 3] = 0;
m.Data[2, 0] = 0; m.Data[2, 1] = 2; m.Data[2, 2] = 1; m.Data[2, 3] = 2;
m.Data[3, 0] = 0; m.Data[3, 1] = 0; m.Data[3, 2] = 2; m.Data[3, 3] = 7;
m.Invert();
// Check data.
Assert.AreEqual(1, m.Data[0, 0]);
Assert.AreEqual(0, m.Data[0, 1]);
Assert.AreEqual(0, m.Data[0, 2]);
Assert.AreEqual(0, m.Data[0, 3]);
Assert.AreEqual(0, m.Data[1, 0]);
Assert.AreEqual(1, m.Data[1, 1]);
Assert.AreEqual(0, m.Data[1, 2]);
Assert.AreEqual(0, m.Data[1, 3]);
Assert.AreEqual(0, m.Data[2, 0]);
Assert.AreEqual(0, m.Data[2, 1]);
Assert.AreEqual(1, m.Data[2, 2]);
Assert.AreEqual(0, m.Data[2, 3]);
Assert.AreEqual(0, m.Data[3, 0]);
Assert.AreEqual(0, m.Data[3, 1]);
Assert.AreEqual(0, m.Data[3, 2]);
Assert.AreEqual(1, m.Data[3, 3]);
// Check inverse.
Assert.AreEqual(new Fraction(13, 51), m.Inverse[0, 0]);
Assert.AreEqual(new Fraction(2, 17), m.Inverse[0, 1]);
Assert.AreEqual(new Fraction(-28, 51), m.Inverse[0, 2]);
Assert.AreEqual(new Fraction(8, 51), m.Inverse[0, 3]);
Assert.AreEqual(new Fraction(2, 17), m.Inverse[1, 0]);
Assert.AreEqual(new Fraction(-3, 17), m.Inverse[1, 1]);
Assert.AreEqual(new Fraction(14, 17), m.Inverse[1, 2]);
Assert.AreEqual(new Fraction(-4, 17), m.Inverse[1, 3]);
Assert.AreEqual(new Fraction(-28, 51), m.Inverse[2, 0]);
Assert.AreEqual(new Fraction(14, 17), m.Inverse[2, 1]);
Assert.AreEqual(new Fraction(-77, 51), m.Inverse[2, 2]);
Assert.AreEqual(new Fraction(22, 51), m.Inverse[2, 3]);
Assert.AreEqual(new Fraction(8, 51), m.Inverse[3, 0]);
Assert.AreEqual(new Fraction(-4, 17), m.Inverse[3, 1]);
Assert.AreEqual(new Fraction(22, 51), m.Inverse[3, 2]);
Assert.AreEqual(new Fraction(1, 51), m.Inverse[3, 3]);
}
public void TridiagonalMatrixAccessTest()
{
TridiagonalMatrix T = CreateRandomTridiagonalMatrix(4);
// check nullity
Assert.IsTrue(T != null);
// check dimension
Assert.IsTrue(T.Dimension == 4);
// check off-diagonal element
Assert.IsTrue(T[0, 3] == 0.0);
}
public TridiagonalMatrix CreateRandomTridiagonalMatrix(int n, Random rng)
{
TridiagonalMatrix T = new TridiagonalMatrix(n);
for (int i = 0; i < (n - 1); i++)
{
T[i, i] = 2.0 * rng.NextDouble() - 1.0;
T[i + 1, i] = 2.0 * rng.NextDouble() - 1.0;
T[i, i + 1] = 2.0 * rng.NextDouble() - 1.0;
}
T[n - 1, n - 1] = 2.0 * rng.NextDouble() - 1.0;
return(T);
}
public void TestRowSubtract2()
{
TridiagonalMatrix m = new TridiagonalMatrix(2);
m.Data[0, 0] = 1;
m.Data[0, 1] = 2;
m.Data[1, 0] = 3;
m.Data[1, 1] = 4;
m.RowSubtract(1, 0);
Assert.AreEqual(1, m.Data[0, 0]);
Assert.AreEqual(2, m.Data[0, 1]);
Assert.AreEqual(2, m.Data[1, 0]);
Assert.AreEqual(2, m.Data[1, 1]);
}
public void TestRowMulitply2()
{
TridiagonalMatrix m = new TridiagonalMatrix(2);
m.Data[0, 0] = 1;
m.Data[0, 1] = 2;
m.Data[1, 0] = 3;
m.Data[1, 1] = 4;
m.RowMultiply(1, -2);
Assert.AreEqual(1, m.Data[0, 0]);
Assert.AreEqual(2, m.Data[0, 1]);
Assert.AreEqual(-6, m.Data[1, 0]);
Assert.AreEqual(-8, m.Data[1, 1]);
}
public void TestRowMulitply1()
{
TridiagonalMatrix m = new TridiagonalMatrix(2);
m.Data[0, 0] = 1;
m.Data[0, 1] = 2;
m.Data[1, 0] = 3;
m.Data[1, 1] = 4;
m.RowMultiply(0, 2);
Assert.AreEqual(2, m.Data[0, 0]);
Assert.AreEqual(4, m.Data[0, 1]);
Assert.AreEqual(3, m.Data[1, 0]);
Assert.AreEqual(4, m.Data[1, 1]);
}
public void TridiagonalMatrixLUDecompositionTest()
{
for (int d = 3; d < 100; d = 2 * d)
{
Console.WriteLine("d={0}", d);
TridiagonalMatrix T = CreateRandomTridiagonalMatrix(d);
Assert.IsTrue(T.Dimension == d);
TridiagonalLUDecomposition LU = T.LUDecomposition();
Assert.IsTrue(LU.Dimension == d);
// check determinant
Assert.IsTrue(TestUtilities.IsNearlyEqual(LU.Determinant(), T.Determinant()));
//SquareMatrix P = LU.PMatrix();
//SquareMatrix L = LU.LMatrix();
//SquareMatrix U = LU.UMatrix();
//SquareMatrixTest.PrintMatrix(T);
//SquareMatrixTest.PrintMatrix(L);
//SquareMatrixTest.PrintMatrix(U);
//SquareMatrixTest.PrintMatrix(L * U);
// check solution to decomposition
ColumnVector b = new ColumnVector(d);
for (int i = 0; i < d; i++)
{
b[i] = i;
}
ColumnVector x = LU.Solve(b);
Assert.IsTrue(TestUtilities.IsNearlyEqual(T * x, b));
// test inverse
SquareMatrix TI = LU.Inverse();
SquareMatrix I = new SquareMatrix(d);
for (int i = 0; i < d; i++)
{
I[i, i] = 1.0;
}
Assert.IsTrue(TestUtilities.IsNearlyEqual(TI * T, I));
}
}
private DoubleArray multiply(DoubleArray vector, TridiagonalMatrix matrix)
{
double[] a = matrix.LowerSubDiagonalData;
double[] b = matrix.DiagonalData;
double[] c = matrix.UpperSubDiagonalData;
double[] x = vector.toArrayUnsafe();
int n = x.Length;
ArgChecker.isTrue(b.Length == n, "Matrix/vector size mismatch");
double[] res = new double[n];
int i;
res[0] = b[0] * x[0] + a[0] * x[1];
res[n - 1] = b[n - 1] * x[n - 1] + c[n - 2] * x[n - 2];
for (i = 1; i < n - 1; i++)
{
res[i] = a[i] * x[i + 1] + b[i] * x[i] + c[i - 1] * x[i - 1];
}
return(DoubleArray.ofUnsafe(res));
}
internal static DoubleMatrix getInverseTridiagonalMatrix(double[] deltaX, bool leftNatural, bool rightNatural)
{
InverseTridiagonalMatrixCalculator invertor = new InverseTridiagonalMatrixCalculator();
int n = deltaX.Length + 1;
double[] a = new double[n];
double[] b = new double[n - 1];
double[] c = new double[n - 1];
for (int i = 1; i < n - 1; i++)
{
a[i] = (deltaX[i - 1] + deltaX[i]) / 3.0;
b[i] = deltaX[i] / 6.0;
c[i - 1] = deltaX[i - 1] / 6.0;
}
// Boundary condition
if (leftNatural)
{
a[0] = 1.0;
b[0] = 0.0;
}
else
{
a[0] = -deltaX[0] / 3.0;
b[0] = deltaX[0] / 6.0;
}
if (rightNatural)
{
a[n - 1] = 1.0;
c[n - 2] = 0.0;
}
else
{
a[n - 1] = deltaX[n - 2] / 3.0;
c[n - 2] = deltaX[n - 2] / 6.0;
}
TridiagonalMatrix tridiagonal = new TridiagonalMatrix(a, b, c);
return(invertor.apply(tridiagonal));
}
public void TestInvert1()
{
TridiagonalMatrix m = new TridiagonalMatrix(2);
m.Data[0, 0] = 2;
m.Data[0, 1] = 1;
m.Data[1, 0] = 1;
m.Data[1, 1] = 4;
m.Invert();
// Check data.
Assert.AreEqual(1, m.Data[0, 0]);
Assert.AreEqual(0, m.Data[0, 1]);
Assert.AreEqual(0, m.Data[1, 0]);
Assert.AreEqual(1, m.Data[1, 1]);
// Check inverse.
Assert.AreEqual(new Fraction(256, 448), m.Inverse[0, 0]);
Assert.AreEqual(new Fraction(-64, 448), m.Inverse[0, 1]);
Assert.AreEqual(new Fraction(-2, 14), m.Inverse[1, 0]);
Assert.AreEqual(new Fraction(4, 14), m.Inverse[1, 1]);
}
public void TestInvert2()
{
TridiagonalMatrix m = new TridiagonalMatrix(3);
m.Data[0, 0] = 2; m.Data[0, 1] = 1; m.Data[0, 2] = 0;
m.Data[1, 0] = 1; m.Data[1, 1] = 4; m.Data[1, 2] = 1;
m.Data[2, 0] = 0; m.Data[2, 1] = 1; m.Data[2, 2] = 2;
m.Invert();
// Check data.
Assert.AreEqual(1, m.Data[0, 0]);
Assert.AreEqual(0, m.Data[0, 1]);
Assert.AreEqual(0, m.Data[0, 2]);
Assert.AreEqual(0, m.Data[1, 0]);
Assert.AreEqual(1, m.Data[1, 1]);
Assert.AreEqual(0, m.Data[1, 2]);
Assert.AreEqual(0, m.Data[2, 0]);
Assert.AreEqual(0, m.Data[2, 1]);
Assert.AreEqual(1, m.Data[2, 2]);
// Check inverse.
Assert.AreEqual(new Fraction(7, 12), m.Inverse[0, 0]);
Assert.AreEqual(new Fraction(-1, 6), m.Inverse[0, 1]);
Assert.AreEqual(new Fraction(1, 12), m.Inverse[0, 2]);
Assert.AreEqual(new Fraction(-1, 6), m.Inverse[1, 0]);
Assert.AreEqual(new Fraction(1, 3), m.Inverse[1, 1]);
Assert.AreEqual(new Fraction(-1, 6), m.Inverse[1, 2]);
Assert.AreEqual(new Fraction(1, 12), m.Inverse[2, 0]);
Assert.AreEqual(new Fraction(-1, 6), m.Inverse[2, 1]);
Assert.AreEqual(new Fraction(7, 12), m.Inverse[2, 2]);
}
