| public static transpose ( Matrix m ) : Matrix | ||
| m | Matrix | |
| Результат | Matrix | |
//! compute vector of derivatives of the least square function
public void gradient(ref Vector grad_f, Vector x)
{
// size of target and function to fit vectors
Vector target = new Vector(lsp_.size());
Vector fct2fit = new Vector(lsp_.size());
// size of gradient matrix
Matrix grad_fct2fit = new Matrix(lsp_.size(), x.size());
// compute its values
lsp_.targetValueAndGradient(x, ref grad_fct2fit, ref target, ref fct2fit);
// do the difference
Vector diff = target - fct2fit;
// compute derivative
grad_f = -2.0 * (Matrix.transpose(grad_fct2fit) * diff);
}
protected override void generateArguments()
{
double rho = arguments_[0].value(0.0);
double beta = arguments_[1].value(0.0);
for (int i = 0; i < size_; ++i)
{
for (int j = i; j < size_; ++j)
{
corrMatrix_[i, j] = corrMatrix_[j, i]
= rho + (1 - rho) * Math.Exp(-beta * Math.Abs((double)i - (double)j));
}
}
pseudoSqrt_ = MatrixUtilitites.rankReducedSqrt(corrMatrix_, factors_, 1.0, MatrixUtilitites.SalvagingAlgorithm.None);
corrMatrix_ = pseudoSqrt_ * Matrix.transpose(pseudoSqrt_);
}
//! compute value and gradient of the least square function
public double valueAndGradient(ref Vector grad_f, Vector x)
{
// size of target and function to fit vectors
Vector target = new Vector(lsp_.size());
Vector fct2fit = new Vector(lsp_.size());
// size of gradient matrix
Matrix grad_fct2fit = new Matrix(lsp_.size(), x.size());
// compute its values
lsp_.targetValueAndGradient(x, ref grad_fct2fit, ref target, ref fct2fit);
// do the difference
Vector diff = target - fct2fit;
// compute derivative
grad_f = -2.0 * (Matrix.transpose(grad_fct2fit) * diff);
// and compute the scalar product (square of the norm)
return(Vector.DotProduct(diff, diff));
}
// Take a matrix and make all the eigenvalues non-negative
private static Matrix projectToPositiveSemidefiniteMatrix(Matrix M)
{
int size = M.rows();
Utils.QL_REQUIRE(size == M.columns(), () => "matrix not square");
Matrix diagonal = new Matrix(size, size);
SymmetricSchurDecomposition jd = new SymmetricSchurDecomposition(M);
for (int i = 0; i < size; ++i)
{
diagonal[i, i] = Math.Max(jd.eigenvalues()[i], 0.0);
}
Matrix result = jd.eigenvectors() * diagonal * Matrix.transpose(jd.eigenvectors());
return(result);
}
//! QR Solve
/*! This implementation is based on MINPACK
* (<http://www.netlib.org/minpack>,
* <http://www.netlib.org/cephes/linalg.tgz>)
*
* Given an m by n matrix A, an n by n diagonal matrix d,
* and an m-vector b, the problem is to determine an x which
* solves the system
*
* A*x = b , d*x = 0 ,
*
* in the least squares sense.
*
* d is an input array of length n which must contain the
* diagonal elements of the matrix d.
*
* See lmdiff.cpp for further details.
*/
public static Vector qrSolve(Matrix a, Vector b, bool pivot = true, Vector d = null)
{
int m = a.rows();
int n = a.columns();
if (d == null)
{
d = new Vector();
}
Utils.QL_REQUIRE(b.Count == m, () => "dimensions of A and b don't match");
Utils.QL_REQUIRE(d.Count == n || d.empty(), () => "dimensions of A and d don't match");
Matrix q = new Matrix(m, n), r = new Matrix(n, n);
List <int> lipvt = MatrixUtilities.qrDecomposition(a, ref q, ref r, pivot);
List <int> ipvt = new List <int>(n);
ipvt = lipvt;
//std::copy(lipvt.begin(), lipvt.end(), ipvt.get());
Matrix aT = Matrix.transpose(a);
Matrix rT = Matrix.transpose(r);
Vector sdiag = new Vector(n);
Vector wa = new Vector(n);
Vector ld = new Vector(n, 0.0);
if (!d.empty())
{
ld = d;
//std::copy(d.begin(), d.end(), ld.begin());
}
Vector x = new Vector(n);
Vector qtb = Matrix.transpose(q) * b;
MINPACK.qrsolv(n, rT, n, ipvt, ld, qtb, x, sdiag, wa);
return(x);
}
public Matrix jacFcn(int m, int n, Vector x, int iflag)
{
Vector xt = new Vector(x);
Matrix fjac;
// constraint handling needs some improvement in the future:
// starting point should not be close to a constraint violation
if (currentProblem_.constraint().test(xt))
{
Matrix tmp = new Matrix(m, n);
currentProblem_.costFunction().jacobian(tmp, xt);
Matrix tmpT = Matrix.transpose(tmp);
fjac = new Matrix(tmpT);
}
else
{
Matrix tmpT = Matrix.transpose(initJacobian_);
fjac = new Matrix(tmpT);
}
return(fjac);
}
public void updateInterpolators()
{
for (int k = 0; k < nLayers_; ++k)
{
transposedPoints_[k] = Matrix.transpose(points_[k]);
Interpolation2D interpolation;
if (k <= 4 && backwardFlat_)
{
interpolation = new BackwardflatLinearInterpolation(
optionTimes_, optionTimes_.Count,
swapLengths_, swapLengths_.Count,
transposedPoints_[k]);
}
else
{
interpolation = new BilinearInterpolation(
optionTimes_, optionTimes_.Count,
swapLengths_, swapLengths_.Count,
transposedPoints_[k]);
}
interpolators_[k] = new FlatExtrapolator2D(interpolation);
interpolators_[k].enableExtrapolation();
}
}
public override double value(Vector x)
{
int i, j, k;
currentRoot_.fill(1);
if (lowerDiagonal_)
{
for (i = 0; i < size_; i++)
{
for (k = 0; k < size_; k++)
{
if (k > i)
{
currentRoot_[i, k] = 0;
}
else
{
for (j = 0; j <= k; j++)
{
if (j == k && k != i)
{
currentRoot_[i, k] *= Math.Cos(x[i * (i - 1) / 2 + j]);
}
else if (j != i)
{
currentRoot_[i, k] *= Math.Sin(x[i * (i - 1) / 2 + j]);
}
}
}
}
}
}
else
{
for (i = 0; i < size_; i++)
{
for (k = 0; k < size_; k++)
{
for (j = 0; j <= k; j++)
{
if (j == k && k != size_ - 1)
{
currentRoot_[i, k] *= Math.Cos(x[j * size_ + i]);
}
else if (j != size_ - 1)
{
currentRoot_[i, k] *= Math.Sin(x[j * size_ + i]);
}
}
}
}
}
double temp, error = 0;
tempMatrix_ = Matrix.transpose(currentRoot_);
currentMatrix_ = currentRoot_ * tempMatrix_;
for (i = 0; i < size_; i++)
{
for (j = 0; j < size_; j++)
{
temp = currentMatrix_[i, j] * targetVariance_[i] * targetVariance_[j] - targetMatrix_[i, j];
error += temp * temp;
}
}
return(error);
}
// Optimization function for hypersphere and lower-diagonal algorithm
private static Matrix hypersphereOptimize(Matrix targetMatrix, Matrix currentRoot, bool lowerDiagonal)
{
int i, j, k, size = targetMatrix.rows();
Matrix result = new Matrix(currentRoot);
Vector variance = new Vector(size);
for (i = 0; i < size; i++)
{
variance[i] = Math.Sqrt(targetMatrix[i, i]);
}
if (lowerDiagonal)
{
Matrix approxMatrix = result * Matrix.transpose(result);
result = MatrixUtilities.CholeskyDecomposition(approxMatrix, true);
for (i = 0; i < size; i++)
{
for (j = 0; j < size; j++)
{
result[i, j] /= Math.Sqrt(approxMatrix[i, i]);
}
}
}
else
{
for (i = 0; i < size; i++)
{
for (j = 0; j < size; j++)
{
result[i, j] /= variance[i];
}
}
}
ConjugateGradient optimize = new ConjugateGradient();
EndCriteria endCriteria = new EndCriteria(100, 10, 1e-8, 1e-8, 1e-8);
HypersphereCostFunction costFunction = new HypersphereCostFunction(targetMatrix, variance, lowerDiagonal);
NoConstraint constraint = new NoConstraint();
// hypersphere vector optimization
if (lowerDiagonal)
{
Vector theta = new Vector(size * (size - 1) / 2);
const double eps = 1e-16;
for (i = 1; i < size; i++)
{
for (j = 0; j < i; j++)
{
theta[i * (i - 1) / 2 + j] = result[i, j];
if (theta[i * (i - 1) / 2 + j] > 1 - eps)
{
theta[i * (i - 1) / 2 + j] = 1 - eps;
}
if (theta[i * (i - 1) / 2 + j] < -1 + eps)
{
theta[i * (i - 1) / 2 + j] = -1 + eps;
}
for (k = 0; k < j; k++)
{
theta[i * (i - 1) / 2 + j] /= Math.Sin(theta[i * (i - 1) / 2 + k]);
if (theta[i * (i - 1) / 2 + j] > 1 - eps)
{
theta[i * (i - 1) / 2 + j] = 1 - eps;
}
if (theta[i * (i - 1) / 2 + j] < -1 + eps)
{
theta[i * (i - 1) / 2 + j] = -1 + eps;
}
}
theta[i * (i - 1) / 2 + j] = Math.Acos(theta[i * (i - 1) / 2 + j]);
if (j == i - 1)
{
if (result[i, i] < 0)
{
theta[i * (i - 1) / 2 + j] = -theta[i * (i - 1) / 2 + j];
}
}
}
}
Problem p = new Problem(costFunction, constraint, theta);
optimize.minimize(p, endCriteria);
theta = p.currentValue();
result.fill(1);
for (i = 0; i < size; i++)
{
for (k = 0; k < size; k++)
{
if (k > i)
{
result[i, k] = 0;
}
else
{
for (j = 0; j <= k; j++)
{
if (j == k && k != i)
{
result[i, k] *= Math.Cos(theta[i * (i - 1) / 2 + j]);
}
else if (j != i)
{
result[i, k] *= Math.Sin(theta[i * (i - 1) / 2 + j]);
}
}
}
}
}
}
else
{
Vector theta = new Vector(size * (size - 1));
const double eps = 1e-16;
for (i = 0; i < size; i++)
{
for (j = 0; j < size - 1; j++)
{
theta[j * size + i] = result[i, j];
if (theta[j * size + i] > 1 - eps)
{
theta[j * size + i] = 1 - eps;
}
if (theta[j * size + i] < -1 + eps)
{
theta[j * size + i] = -1 + eps;
}
for (k = 0; k < j; k++)
{
theta[j * size + i] /= Math.Sin(theta[k * size + i]);
if (theta[j * size + i] > 1 - eps)
{
theta[j * size + i] = 1 - eps;
}
if (theta[j * size + i] < -1 + eps)
{
theta[j * size + i] = -1 + eps;
}
}
theta[j * size + i] = Math.Acos(theta[j * size + i]);
if (j == size - 2)
{
if (result[i, j + 1] < 0)
{
theta[j * size + i] = -theta[j * size + i];
}
}
}
}
Problem p = new Problem(costFunction, constraint, theta);
optimize.minimize(p, endCriteria);
theta = p.currentValue();
result.fill(1);
for (i = 0; i < size; i++)
{
for (k = 0; k < size; k++)
{
for (j = 0; j <= k; j++)
{
if (j == k && k != size - 1)
{
result[i, k] *= Math.Cos(theta[j * size + i]);
}
else if (j != size - 1)
{
result[i, k] *= Math.Sin(theta[j * size + i]);
}
}
}
}
}
for (i = 0; i < size; i++)
{
for (j = 0; j < size; j++)
{
result[i, j] *= variance[i];
}
}
return(result);
}
public Matrix correlation()
{
return(sqrtCorrelation_ * Matrix.transpose(sqrtCorrelation_));
}
public override Matrix covariance(double t0, Vector x0, double dt)
{
Matrix tmp = stdDeviation(t0, x0, dt);
return(tmp * Matrix.transpose(tmp));
}
public SVD(Matrix M)
{
Matrix A;
/* The implementation requires that rows > columns.
* If this is not the case, we decompose M^T instead.
* Swapping the resulting U and V gives the desired
* result for M as
*
* M^T = U S V^T (decomposition of M^T)
*
* M = (U S V^T)^T (transpose)
*
* M = (V^T^T S^T U^T) ((AB)^T = B^T A^T)
*
* M = V S U^T (idempotence of transposition,
* symmetry of diagonal matrix S)
*/
if (M.rows() >= M.columns())
{
A = new Matrix(M);
transpose_ = false;
}
else
{
A = Matrix.transpose(M);
transpose_ = true;
}
m_ = A.rows();
n_ = A.columns();
// we're sure that m_ >= n_
s_ = new Vector(n_);
U_ = new Matrix(m_, n_);
V_ = new Matrix(n_, n_);
Vector e = new Vector(n_);
Vector work = new Vector(m_);
int i, j, k;
// Reduce A to bidiagonal form, storing the diagonal elements
// in s and the super-diagonal elements in e.
int nct = Math.Min(m_ - 1, n_);
int nrt = Math.Max(0, n_ - 2);
for (k = 0; k < Math.Max(nct, nrt); k++)
{
if (k < nct)
{
// Compute the transformation for the k-th column and
// place the k-th diagonal in s[k].
// Compute 2-norm of k-th column without under/overflow.
s_[k] = 0;
for (i = k; i < m_; i++)
{
s_[k] = hypot(s_[k], A[i, k]);
}
if (s_[k] != 0.0)
{
if (A[k, k] < 0.0)
{
s_[k] = -s_[k];
}
for (i = k; i < m_; i++)
{
A[i, k] /= s_[k];
}
A[k, k] += 1.0;
}
s_[k] = -s_[k];
}
for (j = k + 1; j < n_; j++)
{
if ((k < nct) && (s_[k] != 0.0))
{
// Apply the transformation.
double t = 0;
for (i = k; i < m_; i++)
{
t += A[i, k] * A[i, j];
}
t = -t / A[k, k];
for (i = k; i < m_; i++)
{
A[i, j] += t * A[i, k];
}
}
// Place the k-th row of A into e for the
// subsequent calculation of the row transformation.
e[j] = A[k, j];
}
if (k < nct)
{
// Place the transformation in U for subsequent back multiplication.
for (i = k; i < m_; i++)
{
U_[i, k] = A[i, k];
}
}
if (k < nrt)
{
// Compute the k-th row transformation and place the k-th super-diagonal in e[k].
// Compute 2-norm without under/overflow.
e[k] = 0;
for (i = k + 1; i < n_; i++)
{
e[k] = hypot(e[k], e[i]);
}
if (e[k] != 0.0)
{
if (e[k + 1] < 0.0)
{
e[k] = -e[k];
}
for (i = k + 1; i < n_; i++)
{
e[i] /= e[k];
}
e[k + 1] += 1.0;
}
e[k] = -e[k];
if ((k + 1 < m_) & (e[k] != 0.0))
{
// Apply the transformation.
for (i = k + 1; i < m_; i++)
{
work[i] = 0.0;
}
for (j = k + 1; j < n_; j++)
{
for (i = k + 1; i < m_; i++)
{
work[i] += e[j] * A[i, j];
}
}
for (j = k + 1; j < n_; j++)
{
double t = -e[j] / e[k + 1];
for (i = k + 1; i < m_; i++)
{
A[i, j] += t * work[i];
}
}
}
// Place the transformation in V for subsequent back multiplication.
for (i = k + 1; i < n_; i++)
{
V_[i, k] = e[i];
}
}
}
// Set up the final bidiagonal matrix or order n.
if (nct < n_)
{
s_[nct] = A[nct, nct];
}
if (nrt + 1 < n_)
{
e[nrt] = A[nrt, n_ - 1];
}
e[n_ - 1] = 0.0;
// generate U
for (j = nct; j < n_; j++)
{
for (i = 0; i < m_; i++)
{
U_[i, j] = 0.0;
}
U_[j, j] = 1.0;
}
for (k = nct - 1; k >= 0; --k)
{
if (s_[k] != 0.0)
{
for (j = k + 1; j < n_; ++j)
{
double t = 0;
for (i = k; i < m_; i++)
{
t += U_[i, k] * U_[i, j];
}
t = -t / U_[k, k];
for (i = k; i < m_; i++)
{
U_[i, j] += t * U_[i, k];
}
}
for (i = k; i < m_; i++)
{
U_[i, k] = -U_[i, k];
}
U_[k, k] = 1.0 + U_[k, k];
for (i = 0; i < k - 1; i++)
{
U_[i, k] = 0.0;
}
}
else
{
for (i = 0; i < m_; i++)
{
U_[i, k] = 0.0;
}
U_[k, k] = 1.0;
}
}
// generate V
for (k = n_ - 1; k >= 0; --k)
{
if ((k < nrt) & (e[k] != 0.0))
{
for (j = k + 1; j < n_; ++j)
{
double t = 0;
for (i = k + 1; i < n_; i++)
{
t += V_[i, k] * V_[i, j];
}
t = -t / V_[k + 1, k];
for (i = k + 1; i < n_; i++)
{
V_[i, j] += t * V_[i, k];
}
}
}
for (i = 0; i < n_; i++)
{
V_[i, k] = 0.0;
}
V_[k, k] = 1.0;
}
// Main iteration loop for the singular values.
int p = n_, pp = p - 1;
int iter = 0;
double eps = Math.Pow(2.0, -52.0);
while (p > 0)
{
int kase;
// Here is where a test for too many iterations would go.
// This section of the program inspects for
// negligible elements in the s and e arrays. On
// completion the variables kase and k are set as follows.
// kase = 1 if s(p) and e[k-1] are negligible and k<p
// kase = 2 if s(k) is negligible and k<p
// kase = 3 if e[k-1] is negligible, k<p, and
// s(k), ..., s(p) are not negligible (qr step).
// kase = 4 if e(p-1) is negligible (convergence).
for (k = p - 2; k >= -1; --k)
{
if (k == -1)
{
break;
}
if (Math.Abs(e[k]) <= eps * (Math.Abs(s_[k]) + Math.Abs(s_[k + 1])))
{
e[k] = 0.0;
break;
}
}
if (k == p - 2)
{
kase = 4;
}
else
{
int ks;
for (ks = p - 1; ks >= k; --ks)
{
if (ks == k)
{
break;
}
double t = (ks != p ? Math.Abs(e[ks]) : 0) +
(ks != k + 1 ? Math.Abs(e[ks - 1]) : 0);
if (Math.Abs(s_[ks]) <= eps * t)
{
s_[ks] = 0.0;
break;
}
}
if (ks == k)
{
kase = 3;
}
else if (ks == p - 1)
{
kase = 1;
}
else
{
kase = 2;
k = ks;
}
}
k++;
// Perform the task indicated by kase.
switch (kase)
{
// Deflate negligible s(p).
case 1: {
double f = e[p - 2];
e[p - 2] = 0.0;
for (j = p - 2; j >= k; --j)
{
double t = hypot(s_[j], f);
double cs = s_[j] / t;
double sn = f / t;
s_[j] = t;
if (j != k)
{
f = -sn * e[j - 1];
e[j - 1] = cs * e[j - 1];
}
for (i = 0; i < n_; i++)
{
t = cs * V_[i, j] + sn * V_[i, p - 1];
V_[i, p - 1] = -sn * V_[i, j] + cs * V_[i, p - 1];
V_[i, j] = t;
}
}
}
break;
// Split at negligible s(k).
case 2: {
double f = e[k - 1];
e[k - 1] = 0.0;
for (j = k; j < p; j++)
{
double t = hypot(s_[j], f);
double cs = s_[j] / t;
double sn = f / t;
s_[j] = t;
f = -sn * e[j];
e[j] = cs * e[j];
for (i = 0; i < m_; i++)
{
t = cs * U_[i, j] + sn * U_[i, k - 1];
U_[i, k - 1] = -sn * U_[i, j] + cs * U_[i, k - 1];
U_[i, j] = t;
}
}
}
break;
// Perform one qr step.
case 3: {
// Calculate the shift.
double scale = Math.Max(
Math.Max(
Math.Max(
Math.Max(Math.Abs(s_[p - 1]),
Math.Abs(s_[p - 2])),
Math.Abs(e[p - 2])),
Math.Abs(s_[k])),
Math.Abs(e[k]));
double sp = s_[p - 1] / scale;
double spm1 = s_[p - 2] / scale;
double epm1 = e[p - 2] / scale;
double sk = s_[k] / scale;
double ek = e[k] / scale;
double b = ((spm1 + sp) * (spm1 - sp) + epm1 * epm1) / 2.0;
double c = (sp * epm1) * (sp * epm1);
double shift = 0.0;
if ((b != 0.0) | (c != 0.0))
{
shift = Math.Sqrt(b * b + c);
if (b < 0.0)
{
shift = -shift;
}
shift = c / (b + shift);
}
double f = (sk + sp) * (sk - sp) + shift;
double g = sk * ek;
// Chase zeros.
for (j = k; j < p - 1; j++)
{
double t = hypot(f, g);
double cs = f / t;
double sn = g / t;
if (j != k)
{
e[j - 1] = t;
}
f = cs * s_[j] + sn * e[j];
e[j] = cs * e[j] - sn * s_[j];
g = sn * s_[j + 1];
s_[j + 1] = cs * s_[j + 1];
for (i = 0; i < n_; i++)
{
t = cs * V_[i, j] + sn * V_[i, j + 1];
V_[i, j + 1] = -sn * V_[i, j] + cs * V_[i, j + 1];
V_[i, j] = t;
}
t = hypot(f, g);
cs = f / t;
sn = g / t;
s_[j] = t;
f = cs * e[j] + sn * s_[j + 1];
s_[j + 1] = -sn * e[j] + cs * s_[j + 1];
g = sn * e[j + 1];
e[j + 1] = cs * e[j + 1];
if (j < m_ - 1)
{
for (i = 0; i < m_; i++)
{
t = cs * U_[i, j] + sn * U_[i, j + 1];
U_[i, j + 1] = -sn * U_[i, j] + cs * U_[i, j + 1];
U_[i, j] = t;
}
}
}
e[p - 2] = f;
iter = iter + 1;
}
break;
// Convergence.
case 4: {
// Make the singular values positive.
if (s_[k] <= 0.0)
{
s_[k] = (s_[k] < 0.0 ? -s_[k] : 0.0);
for (i = 0; i <= pp; i++)
{
V_[i, k] = -V_[i, k];
}
}
// Order the singular values.
while (k < pp)
{
if (s_[k] >= s_[k + 1])
{
break;
}
s_.swap(k, k + 1);
if (k < n_ - 1)
{
for (i = 0; i < n_; i++)
{
V_.swap(i, k, i, k + 1);
}
}
if (k < m_ - 1)
{
for (i = 0; i < m_; i++)
{
U_.swap(i, k, i, k + 1);
}
}
k++;
}
iter = 0;
--p;
}
break;
}
}
}
public LfmHullWhiteParameterization(
LiborForwardModelProcess process,
OptionletVolatilityStructure capletVol,
Matrix correlation, int factors)
: base(process.size(), factors)
{
diffusion_ = new Matrix(size_ - 1, factors_);
fixingTimes_ = process.fixingTimes();
Matrix sqrtCorr = new Matrix(size_ - 1, factors_, 1.0);
if (correlation.empty())
{
if (!(factors_ == 1))
{
throw new ApplicationException("correlation matrix must be given for " +
"multi factor models");
}
}
else
{
if (!(correlation.rows() == size_ - 1 &&
correlation.rows() == correlation.columns()))
{
throw new ApplicationException("wrong dimesion of the correlation matrix");
}
if (!(factors_ <= size_ - 1))
{
throw new ApplicationException("too many factors for given LFM process");
}
Matrix tmpSqrtCorr = MatrixUtilitites.pseudoSqrt(correlation,
MatrixUtilitites.SalvagingAlgorithm.Spectral);
// reduce to n factor model
// "Reconstructing a valid correlation matrix from invalid data"
// (<http://www.quarchome.org/correlationmatrix.pdf>)
for (int i = 0; i < size_ - 1; ++i)
{
double d = 0;
tmpSqrtCorr.row(i).GetRange(0, factors_).ForEach((ii, vv) => d += vv * tmpSqrtCorr.row(i)[ii]);
//sqrtCorr.row(i).GetRange(0, factors_).ForEach((ii, vv) => sqrtCorr.row(i)[ii] = tmpSqrtCorr.row(i).GetRange(0, factors_)[ii] / Math.Sqrt(d));
for (int k = 0; k < factors_; ++k)
{
sqrtCorr[i, k] = tmpSqrtCorr.row(i).GetRange(0, factors_)[k] / Math.Sqrt(d);
}
}
}
List <double> lambda = new List <double>();
DayCounter dayCounter = process.index().dayCounter();
List <double> fixingTimes = process.fixingTimes();
List <Date> fixingDates = process.fixingDates();
for (int i = 1; i < size_; ++i)
{
double cumVar = 0.0;
for (int j = 1; j < i; ++j)
{
cumVar += lambda[i - j - 1] * lambda[i - j - 1]
* (fixingTimes[j + 1] - fixingTimes[j]);
}
double vol = capletVol.volatility(fixingDates[i], 0.0, false);
double var = vol * vol
* capletVol.dayCounter().yearFraction(fixingDates[0],
fixingDates[i]);
lambda.Add(Math.Sqrt((var - cumVar)
/ (fixingTimes[1] - fixingTimes[0])));
for (int q = 0; q < factors_; ++q)
{
diffusion_[i - 1, q] = sqrtCorr[i - 1, q] * lambda.Last();
}
}
covariance_ = diffusion_ * Matrix.transpose(diffusion_);
}
public override void update()
{
Vector tmp = new Vector(size_);
List <double> dx = new InitializedList <double>(size_ - 1),
S = new InitializedList <double>(size_ - 1);
for (int i = 0; i < size_ - 1; ++i)
{
dx[i] = xBegin_[i + 1] - xBegin_[i];
S[i] = (yBegin_[i + 1] - yBegin_[i]) / dx[i];
}
// first derivative approximation
if (da_ == CubicInterpolation.DerivativeApprox.Spline)
{
TridiagonalOperator L = new TridiagonalOperator(size_);
for (int i = 1; i < size_ - 1; ++i)
{
L.setMidRow(i, dx[i], 2.0 * (dx[i] + dx[i - 1]), dx[i - 1]);
tmp[i] = 3.0 * (dx[i] * S[i - 1] + dx[i - 1] * S[i]);
}
// left boundary condition
switch (leftType_)
{
case CubicInterpolation.BoundaryCondition.NotAKnot:
// ignoring end condition value
L.setFirstRow(dx[1] * (dx[1] + dx[0]), (dx[0] + dx[1]) * (dx[0] + dx[1]));
tmp[0] = S[0] * dx[1] * (2.0 * dx[1] + 3.0 * dx[0]) + S[1] * dx[0] * dx[0];
break;
case CubicInterpolation.BoundaryCondition.FirstDerivative:
L.setFirstRow(1.0, 0.0);
tmp[0] = leftValue_;
break;
case CubicInterpolation.BoundaryCondition.SecondDerivative:
L.setFirstRow(2.0, 1.0);
tmp[0] = 3.0 * S[0] - leftValue_ * dx[0] / 2.0;
break;
case CubicInterpolation.BoundaryCondition.Periodic:
// ignoring end condition value
throw new NotImplementedException("this end condition is not implemented yet");
case CubicInterpolation.BoundaryCondition.Lagrange:
L.setFirstRow(1.0, 0.0);
tmp[0] = cubicInterpolatingPolynomialDerivative(
this.xBegin_[0], this.xBegin_[1],
this.xBegin_[2], this.xBegin_[3],
this.yBegin_[0], this.yBegin_[1],
this.yBegin_[2], this.yBegin_[3],
this.xBegin_[0]);
break;
default:
throw new ArgumentException("unknown end condition");
}
// right boundary condition
switch (rightType_)
{
case CubicInterpolation.BoundaryCondition.NotAKnot:
// ignoring end condition value
L.setLastRow(-(dx[size_ - 2] + dx[size_ - 3]) * (dx[size_ - 2] + dx[size_ - 3]),
-dx[size_ - 3] * (dx[size_ - 3] + dx[size_ - 2]));
tmp[size_ - 1] = -S[size_ - 3] * dx[size_ - 2] * dx[size_ - 2] -
S[size_ - 2] * dx[size_ - 3] * (3.0 * dx[size_ - 2] + 2.0 * dx[size_ - 3]);
break;
case CubicInterpolation.BoundaryCondition.FirstDerivative:
L.setLastRow(0.0, 1.0);
tmp[size_ - 1] = rightValue_;
break;
case CubicInterpolation.BoundaryCondition.SecondDerivative:
L.setLastRow(1.0, 2.0);
tmp[size_ - 1] = 3.0 * S[size_ - 2] + rightValue_ * dx[size_ - 2] / 2.0;
break;
case CubicInterpolation.BoundaryCondition.Periodic:
// ignoring end condition value
throw new NotImplementedException("this end condition is not implemented yet");
case CubicInterpolation.BoundaryCondition.Lagrange:
L.setLastRow(0.0, 1.0);
tmp[size_ - 1] = cubicInterpolatingPolynomialDerivative(
this.xBegin_[size_ - 4], this.xBegin_[size_ - 3],
this.xBegin_[size_ - 2], this.xBegin_[size_ - 1],
this.yBegin_[size_ - 4], this.yBegin_[size_ - 3],
this.yBegin_[size_ - 2], this.yBegin_[size_ - 1],
this.xBegin_[size_ - 1]);
break;
default:
throw new ArgumentException("unknown end condition");
}
// solve the system
tmp = L.solveFor(tmp);
}
else if (da_ == CubicInterpolation.DerivativeApprox.SplineOM1)
{
Matrix T_ = new Matrix(size_ - 2, size_, 0.0);
for (int i = 0; i < size_ - 2; ++i)
{
T_[i, i] = dx[i] / 6.0;
T_[i, i + 1] = (dx[i + 1] + dx[i]) / 3.0;
T_[i, i + 2] = dx[i + 1] / 6.0;
}
Matrix S_ = new Matrix(size_ - 2, size_, 0.0);
for (int i = 0; i < size_ - 2; ++i)
{
S_[i, i] = 1.0 / dx[i];
S_[i, i + 1] = -(1.0 / dx[i + 1] + 1.0 / dx[i]);
S_[i, i + 2] = 1.0 / dx[i + 1];
}
Matrix Up_ = new Matrix(size_, 2, 0.0);
Up_[0, 0] = 1;
Up_[size_ - 1, 1] = 1;
Matrix Us_ = new Matrix(size_, size_ - 2, 0.0);
for (int i = 0; i < size_ - 2; ++i)
{
Us_[i + 1, i] = 1;
}
Matrix Z_ = Us_ * Matrix.inverse(T_ * Us_);
Matrix I_ = new Matrix(size_, size_, 0.0);
for (int i = 0; i < size_; ++i)
{
I_[i, i] = 1;
}
Matrix V_ = (I_ - Z_ * T_) * Up_;
Matrix W_ = Z_ * S_;
Matrix Q_ = new Matrix(size_, size_, 0.0);
Q_[0, 0] = 1.0 / (size_ - 1) * dx[0] * dx[0] * dx[0];
Q_[0, 1] = 7.0 / 8 * 1.0 / (size_ - 1) * dx[0] * dx[0] * dx[0];
for (int i = 1; i < size_ - 1; ++i)
{
Q_[i, i - 1] = 7.0 / 8 * 1.0 / (size_ - 1) * dx[i - 1] * dx[i - 1] * dx[i - 1];
Q_[i, i] = 1.0 / (size_ - 1) * dx[i] * dx[i] * dx[i] + 1.0 / (size_ - 1) * dx[i - 1] * dx[i - 1] * dx[i - 1];
Q_[i, i + 1] = 7.0 / 8 * 1.0 / (size_ - 1) * dx[i] * dx[i] * dx[i];
}
Q_[size_ - 1, size_ - 2] = 7.0 / 8 * 1.0 / (size_ - 1) * dx[size_ - 2] * dx[size_ - 2] * dx[size_ - 2];
Q_[size_ - 1, size_ - 1] = 1.0 / (size_ - 1) * dx[size_ - 2] * dx[size_ - 2] * dx[size_ - 2];
Matrix J_ = (I_ - V_ * Matrix.inverse(Matrix.transpose(V_) * Q_ * V_) * Matrix.transpose(V_) * Q_) * W_;
Vector Y_ = new Vector(size_);
for (int i = 0; i < size_; ++i)
{
Y_[i] = this.yBegin_[i];
}
Vector D_ = J_ * Y_;
for (int i = 0; i < size_ - 1; ++i)
{
tmp[i] = (Y_[i + 1] - Y_[i]) / dx[i] - (2.0 * D_[i] + D_[i + 1]) * dx[i] / 6.0;
}
tmp[size_ - 1] = tmp[size_ - 2] + D_[size_ - 2] * dx[size_ - 2] + (D_[size_ - 1] - D_[size_ - 2]) * dx[size_ - 2] / 2.0;
}
else if (da_ == CubicInterpolation.DerivativeApprox.SplineOM2)
{
Matrix T_ = new Matrix(size_ - 2, size_, 0.0);
for (int i = 0; i < size_ - 2; ++i)
{
T_[i, i] = dx[i] / 6.0;
T_[i, i + 1] = (dx[i] + dx[i + 1]) / 3.0;
T_[i, i + 2] = dx[i + 1] / 6.0;
}
Matrix S_ = new Matrix(size_ - 2, size_, 0.0);
for (int i = 0; i < size_ - 2; ++i)
{
S_[i, i] = 1.0 / dx[i];
S_[i, i + 1] = -(1.0 / dx[i + 1] + 1.0 / dx[i]);
S_[i, i + 2] = 1.0 / dx[i + 1];
}
Matrix Up_ = new Matrix(size_, 2, 0.0);
Up_[0, 0] = 1;
Up_[size_ - 1, 1] = 1;
Matrix Us_ = new Matrix(size_, size_ - 2, 0.0);
for (int i = 0; i < size_ - 2; ++i)
{
Us_[i + 1, i] = 1;
}
Matrix Z_ = Us_ * Matrix.inverse(T_ * Us_);
Matrix I_ = new Matrix(size_, size_, 0.0);
for (int i = 0; i < size_; ++i)
{
I_[i, i] = 1;
}
Matrix V_ = (I_ - Z_ * T_) * Up_;
Matrix W_ = Z_ * S_;
Matrix Q_ = new Matrix(size_, size_, 0.0);
Q_[0, 0] = 1.0 / (size_ - 1) * dx[0];
Q_[0, 1] = 1.0 / 2 * 1.0 / (size_ - 1) * dx[0];
for (int i = 1; i < size_ - 1; ++i)
{
Q_[i, i - 1] = 1.0 / 2 * 1.0 / (size_ - 1) * dx[i - 1];
Q_[i, i] = 1.0 / (size_ - 1) * dx[i] + 1.0 / (size_ - 1) * dx[i - 1];
Q_[i, i + 1] = 1.0 / 2 * 1.0 / (size_ - 1) * dx[i];
}
Q_[size_ - 1, size_ - 2] = 1.0 / 2 * 1.0 / (size_ - 1) * dx[size_ - 2];
Q_[size_ - 1, size_ - 1] = 1.0 / (size_ - 1) * dx[size_ - 2];
Matrix J_ = (I_ - V_ * Matrix.inverse(Matrix.transpose(V_) * Q_ * V_) * Matrix.transpose(V_) * Q_) * W_;
Vector Y_ = new Vector(size_);
for (int i = 0; i < size_; ++i)
{
Y_[i] = this.yBegin_[i];
}
Vector D_ = J_ * Y_;
for (int i = 0; i < size_ - 1; ++i)
{
tmp[i] = (Y_[i + 1] - Y_[i]) / dx[i] - (2.0 * D_[i] + D_[i + 1]) * dx[i] / 6.0;
}
tmp[size_ - 1] = tmp[size_ - 2] + D_[size_ - 2] * dx[size_ - 2] + (D_[size_ - 1] - D_[size_ - 2]) * dx[size_ - 2] / 2.0;
}
else
{
// local schemes
if (size_ == 2)
{
tmp[0] = tmp[1] = S[0];
}
else
{
switch (da_)
{
case CubicInterpolation.DerivativeApprox.FourthOrder:
throw new NotImplementedException("FourthOrder not implemented yet");
case CubicInterpolation.DerivativeApprox.Parabolic:
// intermediate points
for (int i = 1; i < size_ - 1; ++i)
{
tmp[i] = (dx[i - 1] * S[i] + dx[i] * S[i - 1]) / (dx[i] + dx[i - 1]);
}
// end points
tmp[0] = ((2.0 * dx[0] + dx[1]) * S[0] - dx[0] * S[1]) / (dx[0] + dx[1]);
tmp[size_ - 1] = ((2.0 * dx[size_ - 2] + dx[size_ - 3]) * S[size_ - 2] -
dx[size_ - 2] * S[size_ - 3]) / (dx[size_ - 2] + dx[size_ - 3]);
break;
case CubicInterpolation.DerivativeApprox.FritschButland:
// intermediate points
for (int i = 1; i < size_ - 1; ++i)
{
double Smin = Math.Min(S[i - 1], S[i]);
double Smax = Math.Max(S[i - 1], S[i]);
tmp[i] = 3.0 * Smin * Smax / (Smax + 2.0 * Smin);
}
// end points
tmp[0] = ((2.0 * dx[0] + dx[1]) * S[0] - dx[0] * S[1]) / (dx[0] + dx[1]);
tmp[size_ - 1] = ((2.0 * dx[size_ - 2] + dx[size_ - 3]) * S[size_ - 2] -
dx[size_ - 2] * S[size_ - 3]) / (dx[size_ - 2] + dx[size_ - 3]);
break;
case CubicInterpolation.DerivativeApprox.Akima:
tmp[0] = (Math.Abs(S[1] - S[0]) * 2 * S[0] * S[1] +
Math.Abs(2 * S[0] * S[1] - 4 * S[0] * S[0] * S[1]) * S[0]) /
(Math.Abs(S[1] - S[0]) + Math.Abs(2 * S[0] * S[1] - 4 * S[0] * S[0] * S[1]));
tmp[1] = (Math.Abs(S[2] - S[1]) * S[0] + Math.Abs(S[0] - 2 * S[0] * S[1]) * S[1]) /
(Math.Abs(S[2] - S[1]) + Math.Abs(S[0] - 2 * S[0] * S[1]));
for (int i = 2; i < size_ - 2; ++i)
{
if ((S[i - 2].IsEqual(S[i - 1])) && (S[i].IsNotEqual(S[i + 1])))
{
tmp[i] = S[i - 1];
}
else if ((S[i - 2].IsNotEqual(S[i - 1])) && (S[i].IsEqual(S[i + 1])))
{
tmp[i] = S[i];
}
else if (S[i].IsEqual(S[i - 1]))
{
tmp[i] = S[i];
}
else if ((S[i - 2].IsEqual(S[i - 1])) && (S[i - 1].IsNotEqual(S[i])) && (S[i].IsEqual(S[i + 1])))
{
tmp[i] = (S[i - 1] + S[i]) / 2.0;
}
else
{
tmp[i] = (Math.Abs(S[i + 1] - S[i]) * S[i - 1] + Math.Abs(S[i - 1] - S[i - 2]) * S[i]) /
(Math.Abs(S[i + 1] - S[i]) + Math.Abs(S[i - 1] - S[i - 2]));
}
}
tmp[size_ - 2] = (Math.Abs(2 * S[size_ - 2] * S[size_ - 3] - S[size_ - 2]) * S[size_ - 3] +
Math.Abs(S[size_ - 3] - S[size_ - 4]) * S[size_ - 2]) /
(Math.Abs(2 * S[size_ - 2] * S[size_ - 3] - S[size_ - 2]) +
Math.Abs(S[size_ - 3] - S[size_ - 4]));
tmp[size_ - 1] =
(Math.Abs(4 * S[size_ - 2] * S[size_ - 2] * S[size_ - 3] - 2 * S[size_ - 2] * S[size_ - 3]) *
S[size_ - 2] + Math.Abs(S[size_ - 2] - S[size_ - 3]) * 2 * S[size_ - 2] * S[size_ - 3]) /
(Math.Abs(4 * S[size_ - 2] * S[size_ - 2] * S[size_ - 3] - 2 * S[size_ - 2] * S[size_ - 3]) +
Math.Abs(S[size_ - 2] - S[size_ - 3]));
break;
case CubicInterpolation.DerivativeApprox.Kruger:
// intermediate points
for (int i = 1; i < size_ - 1; ++i)
{
if (S[i - 1] * S[i] < 0.0)
{
// slope changes sign at point
tmp[i] = 0.0;
}
else
{
// slope will be between the slopes of the adjacent
// straight lines and should approach zero if the
// slope of either line approaches zero
tmp[i] = 2.0 / (1.0 / S[i - 1] + 1.0 / S[i]);
}
}
// end points
tmp[0] = (3.0 * S[0] - tmp[1]) / 2.0;
tmp[size_ - 1] = (3.0 * S[size_ - 2] - tmp[size_ - 2]) / 2.0;
break;
case CubicInterpolation.DerivativeApprox.Harmonic:
// intermediate points
for (int i = 1; i < size_ - 1; ++i)
{
double w1 = 2 * dx[i] + dx[i - 1];
double w2 = dx[i] + 2 * dx[i - 1];
if (S[i - 1] * S[i] <= 0.0)
{
// slope changes sign at point
tmp[i] = 0.0;
}
else
{
// weighted harmonic mean of S[i] and S[i-1] if they
// have the same sign; otherwise 0
tmp[i] = (w1 + w2) / (w1 / S[i - 1] + w2 / S[i]);
}
}
// end points [0]
tmp[0] = ((2 * dx[0] + dx[1]) * S[0] - dx[0] * S[1]) / (dx[1] + dx[0]);
if (tmp[0] * S[0] < 0.0)
{
tmp[0] = 0;
}
else if (S[0] * S[1] < 0)
{
if (Math.Abs(tmp[0]) > Math.Abs(3 * S[0]))
{
tmp[0] = 3 * S[0];
}
}
// end points [n-1]
tmp[size_ - 1] = ((2 * dx[size_ - 2] + dx[size_ - 3]) * S[size_ - 2] - dx[size_ - 2] * S[size_ - 3]) / (dx[size_ - 3] + dx[size_ - 2]);
if (tmp[size_ - 1] * S[size_ - 2] < 0.0)
{
tmp[size_ - 1] = 0;
}
else if (S[size_ - 2] * S[size_ - 3] < 0)
{
if (Math.Abs(tmp[size_ - 1]) > Math.Abs(3 * S[size_ - 2]))
{
tmp[size_ - 1] = 3 * S[size_ - 2];
}
}
break;
default:
throw new ArgumentException("unknown scheme");
}
}
}
monotonicityAdjustments_.Erase();
// Hyman monotonicity constrained filter
if (monotonic_)
{
double correction;
double pm, pu, pd, M;
for (int i = 0; i < size_; ++i)
{
if (i == 0)
{
if (tmp[i] * S[0] > 0.0)
{
correction = tmp[i] / Math.Abs(tmp[i]) *
Math.Min(Math.Abs(tmp[i]),
Math.Abs(3.0 * S[0]));
}
else
{
correction = 0.0;
}
if (correction.IsNotEqual(tmp[i]))
{
tmp[i] = correction;
monotonicityAdjustments_[i] = true;
}
}
else if (i == size_ - 1)
{
if (tmp[i] * S[size_ - 2] > 0.0)
{
correction = tmp[i] / Math.Abs(tmp[i]) *
Math.Min(Math.Abs(tmp[i]), Math.Abs(3.0 * S[size_ - 2]));
}
else
{
correction = 0.0;
}
if (correction.IsNotEqual(tmp[i]))
{
tmp[i] = correction;
monotonicityAdjustments_[i] = true;
}
}
else
{
pm = (S[i - 1] * dx[i] + S[i] * dx[i - 1]) /
(dx[i - 1] + dx[i]);
M = 3.0 * Math.Min(Math.Min(Math.Abs(S[i - 1]), Math.Abs(S[i])),
Math.Abs(pm));
if (i > 1)
{
if ((S[i - 1] - S[i - 2]) * (S[i] - S[i - 1]) > 0.0)
{
pd = (S[i - 1] * (2.0 * dx[i - 1] + dx[i - 2])
- S[i - 2] * dx[i - 1]) /
(dx[i - 2] + dx[i - 1]);
if (pm * pd > 0.0 && pm * (S[i - 1] - S[i - 2]) > 0.0)
{
M = Math.Max(M, 1.5 * Math.Min(
Math.Abs(pm), Math.Abs(pd)));
}
}
}
if (i < size_ - 2)
{
if ((S[i] - S[i - 1]) * (S[i + 1] - S[i]) > 0.0)
{
pu = (S[i] * (2.0 * dx[i] + dx[i + 1]) - S[i + 1] * dx[i]) /
(dx[i] + dx[i + 1]);
if (pm * pu > 0.0 && -pm * (S[i] - S[i - 1]) > 0.0)
{
M = Math.Max(M, 1.5 * Math.Min(
Math.Abs(pm), Math.Abs(pu)));
}
}
}
if (tmp[i] * pm > 0.0)
{
correction = tmp[i] / Math.Abs(tmp[i]) *
Math.Min(Math.Abs(tmp[i]), M);
}
else
{
correction = 0.0;
}
if (correction.IsNotEqual(tmp[i]))
{
tmp[i] = correction;
monotonicityAdjustments_[i] = true;
}
}
}
}
// cubic coefficients
for (int i = 0; i < size_ - 1; ++i)
{
a_[i] = tmp[i];
b_[i] = (3.0 * S[i] - tmp[i + 1] - 2.0 * tmp[i]) / dx[i];
c_[i] = (tmp[i + 1] + tmp[i] - 2.0 * S[i]) / (dx[i] * dx[i]);
}
primitiveConst_[0] = 0.0;
for (int i = 1; i < size_ - 1; ++i)
{
primitiveConst_[i] = primitiveConst_[i - 1]
+ dx[i - 1] *
(yBegin_[i - 1] + dx[i - 1] *
(a_[i - 1] / 2.0 + dx[i - 1] *
(b_[i - 1] / 3.0 + dx[i - 1] * c_[i - 1] / 4.0)));
}
}
//! QR decompoisition
/*! This implementation is based on MINPACK
* (<http://www.netlib.org/minpack>,
* <http://www.netlib.org/cephes/linalg.tgz>)
*
* This subroutine uses householder transformations with column
* pivoting (optional) to compute a qr factorization of the
* m by n matrix A. That is, qrfac determines an orthogonal
* matrix q, a permutation matrix p, and an upper trapezoidal
* matrix r with diagonal elements of nonincreasing magnitude,
* such that A*p = q*r.
*
* Return value ipvt is an integer array of length n, which
* defines the permutation matrix p such that A*p = q*r.
* Column j of p is column ipvt(j) of the identity matrix.
*
* See lmdiff.cpp for further details.
*/
//public static List<int> qrDecomposition(Matrix A, Matrix q, Matrix r, bool pivot = true) {
public static List <int> qrDecomposition(Matrix M, Matrix q, Matrix r, bool pivot)
{
Matrix mT = Matrix.transpose(M);
int m = M.rows();
int n = M.columns();
List <int> lipvt = new InitializedList <int>(n);
Vector rdiag = new Vector(n);
Vector wa = new Vector(n);
MINPACK.qrfac(m, n, mT, 0, (pivot)?1:0, ref lipvt, n, ref rdiag, ref rdiag, wa);
if (r.columns() != n || r.rows() != n)
{
r = new Matrix(n, n);
}
for (int i = 0; i < n; ++i)
{
// std::fill(r.row_begin(i), r.row_begin(i)+i, 0.0);
r[i, i] = rdiag[i];
if (i < m)
{
// std::copy(mT.column_begin(i)+i+1, mT.column_end(i),
// r.row_begin(i)+i+1);
}
else
{
// std::fill(r.row_begin(i)+i+1, r.row_end(i), 0.0);
}
}
if (q.rows() != m || q.columns() != n)
{
q = new Matrix(m, n);
}
Vector w = new Vector(m);
//for (int k=0; k < m; ++k) {
// std::fill(w.begin(), w.end(), 0.0);
// w[k] = 1.0;
// for (int j=0; j < Math.Min(n, m); ++j) {
// double t3 = mT[j,j];
// if (t3 != 0.0) {
// double t
// = std::inner_product(mT.row_begin(j)+j, mT.row_end(j),
// w.begin()+j, 0.0)/t3;
// for (int i=j; i<m; ++i) {
// w[i]-=mT[j,i]*t;
// }
// }
// q[k,j] = w[j];
// }
// std::fill(q.row_begin(k) + Math.Min(n, m), q.row_end(k), 0.0);
//}
List <int> ipvt = new InitializedList <int>(n);
//if (pivot) {
// std::copy(lipvt.get(), lipvt.get()+n, ipvt.begin());
//}
//else {
// for (int i=0; i < n; ++i)
// ipvt[i] = i;
//}
return(ipvt);
}
//! QR decompoisition
/*! This implementation is based on MINPACK
* (<http://www.netlib.org/minpack>,
* <http://www.netlib.org/cephes/linalg.tgz>)
*
* This subroutine uses householder transformations with column
* pivoting (optional) to compute a qr factorization of the
* m by n matrix A. That is, qrfac determines an orthogonal
* matrix q, a permutation matrix p, and an upper trapezoidal
* matrix r with diagonal elements of nonincreasing magnitude,
* such that A*p = q*r.
*
* Return value ipvt is an integer array of length n, which
* defines the permutation matrix p such that A*p = q*r.
* Column j of p is column ipvt(j) of the identity matrix.
*
* See lmdiff.cpp for further details.
*/
//public static List<int> qrDecomposition(Matrix A, Matrix q, Matrix r, bool pivot = true) {
public static List <int> qrDecomposition(Matrix M, ref Matrix q, ref Matrix r, bool pivot)
{
Matrix mT = Matrix.transpose(M);
int m = M.rows();
int n = M.columns();
List <int> lipvt = new InitializedList <int>(n);
Vector rdiag = new Vector(n);
Vector wa = new Vector(n);
MINPACK.qrfac(m, n, mT, 0, (pivot)?1:0, ref lipvt, n, ref rdiag, ref rdiag, wa);
if (r.columns() != n || r.rows() != n)
{
r = new Matrix(n, n);
}
for (int i = 0; i < n; ++i)
{
r[i, i] = rdiag[i];
if (i < m)
{
for (int j = i; j < mT.rows() - 1; j++)
{
r[i, j + 1] = mT[j + 1, i];
}
}
}
if (q.rows() != m || q.columns() != n)
{
q = new Matrix(m, n);
}
Vector w = new Vector(m);
for (int k = 0; k < m; ++k)
{
w.Erase();
w[k] = 1.0;
for (int j = 0; j < Math.Min(n, m); ++j)
{
double t3 = mT[j, j];
if (t3 != 0.0)
{
double t = 0;
for (int kk = j; kk < mT.columns(); kk++)
{
t += (mT[j, kk] * w[kk]) / t3;
}
for (int i = j; i < m; ++i)
{
w[i] -= mT[j, i] * t;
}
}
q[k, j] = w[j];
}
}
List <int> ipvt = new InitializedList <int>(n);
if (pivot)
{
for (int i = 0; i < n; ++i)
{
ipvt[i] = lipvt[i];
}
}
else
{
for (int i = 0; i < n; ++i)
{
ipvt[i] = i;
}
}
return(ipvt);
}
