/// <summary>Construct a QR decomposition.</summary>
public QrDecomposition(MatrixV value)
{
if (value == null)
{
throw new ArgumentNullException("value");
}
this.QR = (MatrixV)value.Clone();
double[][] qr = this.QR.Array;
int m = value.Rows;
int n = value.Columns;
this.Rdiag = new double[n];
for (int k = 0; k < n; k++)
{
// Compute 2-norm of k-th column without under/overflow.
double nrm = 0;
for (int i = k; i < m; i++)
{
nrm = Hypotenuse(nrm, qr[i][k]);
}
if (nrm != 0.0)
{
// Form k-th Householder vector.
if (qr[k][k] < 0)
{
nrm = -nrm;
}
for (int i = k; i < m; i++)
{
qr[i][k] /= nrm;
}
qr[k][k] += 1.0;
// Apply transformation to remaining columns.
for (int j = k + 1; j < n; j++)
{
double s = 0.0;
for (int i = k; i < m; i++)
{
s += qr[i][k] * qr[i][j];
}
s = -s / qr[k][k];
for (int i = k; i < m; i++)
{
qr[i][j] += s * qr[i][k];
}
}
}
this.Rdiag[k] = -nrm;
}
}
/// <summary>Least squares solution of <c>A * X = B</c></summary>
/// <param name="value">Right-hand-side MatrixV with as many rows as <c>A</c> and any number of columns.</param>
/// <returns>A MatrixV that minimized the two norm of <c>Q * R * X - B</c>.</returns>
/// <exception cref="T:System.ArgumentException">MatrixV row dimensions must be the same.</exception>
/// <exception cref="T:System.InvalidOperationException">MatrixV is rank deficient.</exception>
public MatrixV Solve(MatrixV value)
{
if (value == null)
{
throw new ArgumentNullException("value");
}
if (value.Rows != QR.Rows)
{
throw new ArgumentException("MatrixV row dimensions must agree.");
}
if (!this.FullRank)
{
throw new InvalidOperationException("MatrixV is rank deficient.");
}
// Copy right hand side
int count = value.Columns;
MatrixV X = value.Clone();
int m = QR.Rows;
int n = QR.Columns;
double[][] qr = QR.Array;
// Compute Y = transpose(Q)*B
for (int k = 0; k < n; k++)
{
for (int j = 0; j < count; j++)
{
double s = 0.0;
for (int i = k; i < m; i++)
{
s += qr[i][k] * X[i, j];
}
s = -s / qr[k][k];
for (int i = k; i < m; i++)
{
X[i, j] += s * qr[i][k];
}
}
}
// Solve R*X = Y;
for (int k = n - 1; k >= 0; k--)
{
for (int j = 0; j < count; j++)
{
X[k, j] /= Rdiag[k];
}
for (int i = 0; i < k; i++)
{
for (int j = 0; j < count; j++)
{
X[i, j] -= X[k, j] * qr[i][k];
}
}
}
return(X.Submatrix(0, n - 1, 0, count - 1));
}
/// <summary>Construct a LU decomposition.</summary>
public LuDecomposition(MatrixV value)
{
if (value == null)
{
throw new ArgumentNullException("value");
}
this.LU = (MatrixV)value.Clone();
double[][] lu = LU.Array;
int rows = value.Rows;
int columns = value.Columns;
pivotVector = new int[rows];
for (int i = 0; i < rows; i++)
{
pivotVector[i] = i;
}
pivotSign = 1;
double[] LUrowi;
double[] LUcolj = new double[rows];
// Outer loop.
for (int j = 0; j < columns; j++)
{
// Make a copy of the j-th column to localize references.
for (int i = 0; i < rows; i++)
{
LUcolj[i] = lu[i][j];
}
// Apply previous transformations.
for (int i = 0; i < rows; i++)
{
LUrowi = lu[i];
// Most of the time is spent in the following dot product.
int kmax = Math.Min(i, j);
double s = 0.0;
for (int k = 0; k < kmax; k++)
{
s += LUrowi[k] * LUcolj[k];
}
LUrowi[j] = LUcolj[i] -= s;
}
// Find pivot and exchange if necessary.
int p = j;
for (int i = j + 1; i < rows; i++)
{
if (Math.Abs(LUcolj[i]) > Math.Abs(LUcolj[p]))
{
p = i;
}
}
if (p != j)
{
for (int k = 0; k < columns; k++)
{
double t = lu[p][k];
lu[p][k] = lu[j][k];
lu[j][k] = t;
}
int v = pivotVector[p];
pivotVector[p] = pivotVector[j];
pivotVector[j] = v;
pivotSign = -pivotSign;
}
// Compute multipliers.
if (j < rows & lu[j][j] != 0.0)
{
for (int i = j + 1; i < rows; i++)
{
lu[i][j] /= lu[j][j];
}
}
}
}