/// <summary>
/// Compute $A^T A$, where A is a matrix. </summary>
/// <param name="a"> The matrix </param>
/// <returns> The result of $A^T A$ </returns>
public virtual DoubleMatrix matrixTransposeMultiplyMatrix(DoubleMatrix a)
{
ArgChecker.notNull(a, "a");
int n = a.rowCount();
int m = a.columnCount();
//JAVA TO C# CONVERTER NOTE: The following call to the 'RectangularArrays' helper class reproduces the rectangular array initialization that is automatic in Java:
//ORIGINAL LINE: double[][] data = new double[m][m];
double[][] data = RectangularArrays.ReturnRectangularDoubleArray(m, m);
for (int i = 0; i < m; i++)
{
double sum = 0d;
for (int k = 0; k < n; k++)
{
sum += a.get(k, i) * a.get(k, i);
}
data[i][i] = sum;
for (int j = i + 1; j < m; j++)
{
sum = 0d;
for (int k = 0; k < n; k++)
{
sum += a.get(k, i) * a.get(k, j);
}
data[i][j] = sum;
data[j][i] = sum;
}
}
return(DoubleMatrix.ofUnsafe(data));
}
//-------------------------------------------------------------------------
private double[] weights(double forward, double strike, double[] strikes, double timeToExpiry, double atmVol)
{
//JAVA TO C# CONVERTER NOTE: The following call to the 'RectangularArrays' helper class reproduces the rectangular array initialization that is automatic in Java:
//ORIGINAL LINE: double[][] mat = new double[3][3];
double[][] mat = RectangularArrays.ReturnRectangularDoubleArray(3, 3);
double[] vec = new double[3];
for (int i = 0; i < 3; ++i)
{
mat[0][i] = BlackFormulaRepository.vega(forward, strikes[i], timeToExpiry, atmVol);
mat[1][i] = BlackFormulaRepository.vanna(forward, strikes[i], timeToExpiry, atmVol);
mat[2][i] = BlackFormulaRepository.volga(forward, strikes[i], timeToExpiry, atmVol);
}
vec[0] = BlackFormulaRepository.vega(forward, strike, timeToExpiry, atmVol);
vec[1] = BlackFormulaRepository.vanna(forward, strike, timeToExpiry, atmVol);
vec[2] = BlackFormulaRepository.volga(forward, strike, timeToExpiry, atmVol);
DecompositionResult res = SVD.apply(DoubleMatrix.ofUnsafe(mat));
return(res.solve(vec));
}
/// <summary>
/// Returns the Kronecker product of two matrices. If $\mathbf{A}$ is an $m
/// \times n$ matrix and $\mathbf{B}$ is a $p \times q$ matrix, then the
/// Kronecker product $A \otimes B$ is an $mp \times nq$ matrix with elements
/// $$
/// \begin{align*}
/// A \otimes B &=
/// \begin{pmatrix}
/// a_{11}\mathbf{B} & \cdots & a_{1n}\mathbf{B} \\
/// \vdots & \ddots & \vdots \\
/// a_{m1}\mathbf{B} & \cdots & a_{mn}\mathbf{B}
/// \end{pmatrix}\\
/// &=
/// \begin{pmatrix}
/// a_{11}b_{11} & a_{11}b_{12} & \cdots & a_{11}b_{1q} & \cdots & a_{1n}b_{11} & a_{1n}b_{12} & \cdots & a_{1n}b_{1q}\\
/// a_{11}b_{21} & a_{11}b_{22} & \cdots & a_{11}b_{2q} & \cdots & a_{1n}b_{21} & a_{1n}b_{22} & \cdots & a_{1n}b_{2q} \\
/// \vdots & \vdots & \ddots & \vdots & \cdots & \vdots & \vdots & \ddots & \cdots \\
/// a_{11}b_{p1} & a_{11}b_{p2} & \cdots & a_{11}b_{pq} & \cdots & a_{1n}b_{p1} & a_{1n}b_{p2} & \cdots & a_{1n}b_{pq} \\
/// \vdots & \vdots & & \vdots & \ddots & \vdots & \vdots & & \cdots \\
/// a_{m1}b_{11} & a_{m1}b_{12} & \cdots & a_{m1}b_{1q} & \cdots & a_{mn}b_{11} & a_{mn}b_{12} & \cdots & a_{mn}b_{1q} \\
/// a_{m1}b_{21} & a_{m1}b_{22} & \cdots & a_{m1}b_{2q} & \cdots & a_{mn}b_{21} & a_{mn}b_{22} & \cdots & a_{mn}b_{2q} \\
/// \vdots & \vdots & \ddots & \vdots & \cdots & \vdots & \vdots & \ddots & \cdots \\
/// a_{m1}b_{p1} & a_{m1}b_{p2} & \cdots & a_{m1}b_{pq} & \cdots & a_{mn}b_{p1} & a_{mn}b_{p2} & \cdots & a_{mn}b_{pq}
/// \end{pmatrix}
/// \end{align*}
/// $$ </summary>
/// <param name="m1"> The first matrix, not null. This matrix must be a <seealso cref="DoubleMatrix"/>. </param>
/// <param name="m2"> The second matrix, not null. This matrix must be a <seealso cref="DoubleMatrix"/>. </param>
/// <returns> The Kronecker product </returns>
public virtual Matrix kroneckerProduct(Matrix m1, Matrix m2)
{
ArgChecker.notNull(m1, "m1");
ArgChecker.notNull(m2, "m2");
if (m1 is DoubleMatrix && m2 is DoubleMatrix)
{
DoubleMatrix matrix1 = (DoubleMatrix)m1;
DoubleMatrix matrix2 = (DoubleMatrix)m2;
int aRows = matrix1.rowCount();
int aCols = matrix1.columnCount();
int bRows = matrix2.rowCount();
int bCols = matrix2.columnCount();
int rRows = aRows * bRows;
int rCols = aCols * bCols;
//JAVA TO C# CONVERTER NOTE: The following call to the 'RectangularArrays' helper class reproduces the rectangular array initialization that is automatic in Java:
//ORIGINAL LINE: double[][] res = new double[rRows][rCols];
double[][] res = RectangularArrays.ReturnRectangularDoubleArray(rRows, rCols);
for (int i = 0; i < aRows; i++)
{
for (int j = 0; j < aCols; j++)
{
double t = matrix1.get(i, j);
if (t != 0.0)
{
for (int k = 0; k < bRows; k++)
{
for (int l = 0; l < bCols; l++)
{
res[i * bRows + k][j * bCols + l] = t * matrix2.get(k, l);
}
}
}
}
}
return(DoubleMatrix.ofUnsafe(res));
}
throw new System.ArgumentException("Can only calculate the Kronecker product of two DoubleMatrix.");
}
public virtual void test_volatilities()
{
BlackFxOptionSmileVolatilitiesSpecification @base = BlackFxOptionSmileVolatilitiesSpecification.builder().name(VOL_NAME).currencyPair(EUR_GBP).dayCount(ACT_360).nodes(NODES).timeInterpolator(PCHIP).strikeInterpolator(PCHIP).build();
LocalDate date = LocalDate.of(2017, 9, 25);
ZonedDateTime dateTime = date.atStartOfDay().atZone(ZoneId.of("Europe/London"));
DoubleArray parameters = DoubleArray.of(0.05, -0.05, 0.15, 0.25, 0.1, -0.1);
BlackFxOptionSmileVolatilities computed = @base.volatilities(dateTime, parameters, REF_DATA);
LocalDate spotDate = SPOT_OFFSET.adjust(dateTime.toLocalDate(), REF_DATA);
DaysAdjustment expOffset = DaysAdjustment.ofBusinessDays(-2, TA_LO);
DoubleArray expiries = DoubleArray.of(ACT_360.relativeYearFraction(date, expOffset.adjust(BUS_ADJ.adjust(spotDate.plus(Tenor.TENOR_3M), REF_DATA), REF_DATA)), ACT_360.relativeYearFraction(date, expOffset.adjust(BUS_ADJ.adjust(spotDate.plus(Tenor.TENOR_1Y), REF_DATA), REF_DATA)));
SmileDeltaTermStructure smiles = InterpolatedStrikeSmileDeltaTermStructure.of(expiries, DoubleArray.of(0.1), DoubleArray.of(0.25, 0.15), DoubleMatrix.ofUnsafe(new double[][]
{
new double[] { -0.1 },
new double[] { -0.05 }
}), DoubleMatrix.ofUnsafe(new double[][]
{
new double[] { 0.1 },
new double[] { 0.05 }
}), ACT_360, PCHIP, FLAT, FLAT, PCHIP, FLAT, FLAT);
BlackFxOptionSmileVolatilities expected = BlackFxOptionSmileVolatilities.of(VOL_NAME, EUR_GBP, dateTime, smiles);
assertEquals(computed, expected);
}
/// <summary>
/// Unwraps a matrix.
/// </summary>
/// <param name="x"> a Commons matrix </param>
/// <returns> an OG 2-D matrix of doubles </returns>
public static DoubleMatrix unwrap(RealMatrix x)
{
ArgChecker.notNull(x, "x");
return(DoubleMatrix.ofUnsafe(x.Data));
}
