//! 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 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.IsNotEqual(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);
}
//! 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);
}