/// <summary>Constructs a QR decomposition.</summary>
/// <param name="value">The matrix A to be decomposed.</param>
/// <param name="transpose">True if the decomposition should be performed on
/// the transpose of A rather than A itself, false otherwise. Default is false.</param>
public QrDecompositionD(decimal[,] value, bool transpose)
{
if (value == null)
{
throw new ArgumentNullException("value", "Matrix cannot be null.");
}
if ((!transpose && value.GetLength(0) < value.GetLength(1)) ||
(transpose && value.GetLength(1) < value.GetLength(0)))
{
throw new ArgumentException("Matrix has more columns than rows.", "value");
}
this.qr = transpose ? value.Transpose() : (decimal[, ])value.Clone();
int rows = qr.GetLength(0);
int cols = qr.GetLength(1);
this.Rdiag = new decimal[cols];
for (int k = 0; k < cols; k++)
{
// Compute 2-norm of k-th column without under/overflow.
decimal nrm = 0;
for (int i = k; i < rows; i++)
{
nrm = Tools.Hypotenuse(nrm, qr[i, k]);
}
if (nrm != 0)
{
// Form k-th Householder vector.
if (qr[k, k] < 0)
{
nrm = -nrm;
}
for (int i = k; i < rows; i++)
{
qr[i, k] /= nrm;
}
qr[k, k] += 1;
// Apply transformation to remaining columns.
for (int j = k + 1; j < cols; j++)
{
decimal s = 0;
for (int i = k; i < rows; i++)
{
s += qr[i, k] * qr[i, j];
}
s = -s / qr[k, k];
for (int i = k; i < rows; i++)
{
qr[i, j] += s * qr[i, k];
}
}
}
this.Rdiag[k] = -nrm;
}
}
/// <summary>
/// Constructs a new LU decomposition.
/// </summary>
/// <param name="value">The matrix A to be decomposed.</param>
/// <param name="transpose">True if the decomposition should be performed on
/// the transpose of A rather than A itself, false otherwise. Default is false.</param>
/// <param name="inPlace">True if the decomposition should be performed over the
/// <paramref name="value"/> matrix rather than on a copy of it. If true, the
/// matrix will be destroyed during the decomposition. Default is false.</param>
///
public LuDecompositionD(decimal[,] value, bool transpose, bool inPlace)
{
if (value == null)
{
throw new ArgumentNullException("value", "Matrix cannot be null.");
}
if (transpose)
{
this.lu = value.Transpose(inPlace);
}
else
{
this.lu = inPlace ? value : (decimal[, ])value.Clone();
}
this.rows = lu.GetLength(0);
this.cols = lu.GetLength(1);
this.pivotSign = 1;
this.pivotVector = new int[rows];
for (int i = 0; i < rows; i++)
{
pivotVector[i] = i;
}
var LUcolj = new decimal[rows];
unsafe
{
fixed(decimal *LU = lu)
{
// Outer loop.
for (int j = 0; j < cols; 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++)
{
decimal s = 0;
// Most of the time is spent in
// the following dot product:
int kmax = Math.Min(i, j);
decimal *LUrowi = &LU[i * cols];
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 < cols; k++)
{
var 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)
{
for (int i = j + 1; i < rows; i++)
{
lu[i, j] /= lu[j, j];
}
}
}
}
}
}
/// <summary>Least squares solution of <c>X * A = B</c></summary>
/// <param name="value">Right-hand-side matrix with as many columns as <c>A</c> and any number of rows.</param>
/// <returns>A matrix that minimized the two norm of <c>X * Q * R - B</c>.</returns>
/// <exception cref="T:System.ArgumentException">Matrix column dimensions must be the same.</exception>
/// <exception cref="T:System.InvalidOperationException">Matrix is rank deficient.</exception>
public decimal[,] SolveTranspose(decimal[,] value)
{
if (value == null)
{
throw new ArgumentNullException("value", "Matrix cannot be null.");
}
if (value.GetLength(1) != qr.GetLength(0))
{
throw new ArgumentException("Matrix row dimensions must agree.");
}
if (!this.FullRank)
{
throw new InvalidOperationException("Matrix is rank deficient.");
}
// Copy right hand side
int count = value.GetLength(0);
var X = value.Transpose();
int m = qr.GetLength(0);
int n = qr.GetLength(1);
// Compute Y = transpose(Q)*B
for (int k = 0; k < n; k++)
{
for (int j = 0; j < count; j++)
{
decimal s = 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];
}
}
}
var r = new decimal[count, n];
for (int i = 0; i < n; i++)
{
for (int j = 0; j < count; j++)
{
r[j, i] = X[i, j];
}
}
return(r);
}
