public void AppendRight(IROMatrix a)
{
if (m_NumVectors == 0 && m_VectorLen == 0)
{
m_bVerticalVectors = true;
m_NumVectors = a.Columns;
m_VectorLen = a.Rows;
m_Array = new double[m_NumVectors][];
for (int i = 0; i < m_NumVectors; i++)
{
m_Array[i] = new double[m_VectorLen];
}
MatrixMath.Copy(a, this);
}
else if (this.m_bVerticalVectors == true)
{
double [][] newArray = new double[m_NumVectors + a.Columns][];
for (int i = 0; i < m_NumVectors; i++)
{
newArray[i] = m_Array[i];
}
for (int i = m_NumVectors; i < m_NumVectors + a.Columns; i++)
{
newArray[i] = new double[m_VectorLen];
}
m_Array = newArray;
m_NumVectors += a.Columns;
MatrixMath.Copy(a, this, 0, this.Columns - a.Columns);
}
else
{
throw new System.NotImplementedException("This worst case is not implemented yet.");
}
}
public void AppendBottom(IROMatrix <double> a)
{
if (m_NumVectors == 0 && m_VectorLen == 0)
{
m_bVerticalVectors = false;
m_NumVectors = a.RowCount;
m_VectorLen = a.ColumnCount;
m_Array = new double[m_NumVectors][];
for (int i = 0; i < m_NumVectors; i++)
{
m_Array[i] = new double[m_VectorLen];
}
MatrixMath.Copy(a, this);
}
else if (m_bVerticalVectors == false)
{
double[][] newArray = new double[m_NumVectors + a.RowCount][];
for (int i = 0; i < m_NumVectors; i++)
{
newArray[i] = m_Array[i];
}
for (int i = m_NumVectors; i < m_NumVectors + a.RowCount; i++)
{
newArray[i] = new double[m_VectorLen];
}
m_Array = newArray;
m_NumVectors += a.RowCount;
MatrixMath.Copy(a, this, RowCount - a.RowCount, 0);
}
else
{
throw new System.NotImplementedException("This worst case is not implemented yet.");
}
}
public void Decompose(IROMatrix <double> A)
{
// Initialize.
if (m == A.RowCount && n == A.ColumnCount)
{
MatrixMath.Copy(A, new JaggedArrayMatrix(QR, m, n));
//JaggedArrayMath.Copy(A, QR);
}
else
{
QR = JaggedArrayMath.GetMatrixCopy(A);
m = A.RowCount;
n = A.ColumnCount;
Rdiag = new double[n];
}
// Main loop.
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 = RMath.Hypot(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];
}
}
}
Rdiag[k] = -nrm;
}
}
/// <summary>Solves system of linear equations Ax = b using Gaussian elimination with partial pivoting.</summary>
/// <param name="A">Elements of matrix 'A'. This array is modified during solution!</param>
/// <param name="b">Right part 'b'. This array is also modified during solution!</param>
/// <param name="x">Vector to store the result, i.e. the solution to the problem a x = b.</param>
public void Solve(IROMatrix <double> A, IReadOnlyList <double> b, IVector <double> x)
{
if (_temp_A.RowCount != A.RowCount || _temp_A.ColumnCount != A.ColumnCount)
{
_temp_A = new MatrixWrapperStructForLeftSpineJaggedArray <double>(A.RowCount, A.ColumnCount);
}
if (b.Count != _temp_b?.Length)
{
_temp_b = new double[b.Count];
}
if (b.Count != _temp_x?.Length)
{
_temp_x = new double[b.Count];
}
MatrixMath.Copy(A, _temp_A);
VectorMath.Copy(b, _temp_b);
SolveDestructive(_temp_A, _temp_b, _temp_x);
VectorMath.Copy(_temp_x, x);
}
/** Least squares solution of A*X = B
* @param B A Matrix with as many rows as A and any number of columns.
* @return X that minimizes the two norm of Q*R*X-B.
* @exception IllegalArgumentException Matrix row dimensions must agree.
* @exception RuntimeException Matrix is rank deficient.
*/
public void Solve(IROMatrix <double> B, IMatrix <double> result)
{
if (B.RowCount != m)
{
throw new ArgumentException("Matrix row dimensions must agree.");
}
if (!IsFullRank())
{
throw new Exception("Matrix is rank deficient.");
}
// Copy right hand side
int nx = B.ColumnCount;
double[][] X;
if (_solveMatrixWorkspace != null && _solveMatrixWorkspace.RowCount == B.RowCount && _solveMatrixWorkspace.ColumnCount == B.ColumnCount)
{
X = _solveMatrixWorkspace.Array;
MatrixMath.Copy(B, _solveMatrixWorkspace);
}
else
{
X = JaggedArrayMath.GetMatrixCopy(B);
_solveMatrixWorkspace = new JaggedArrayMatrix(X, B.RowCount, B.ColumnCount);
}
// Compute Y = transpose(Q)*B
for (int k = 0; k < n; k++)
{
for (int j = 0; j < nx; 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 < nx; j++)
{
X[k][j] /= Rdiag[k];
}
for (int i = 0; i < k; i++)
{
for (int j = 0; j < nx; j++)
{
X[i][j] -= X[k][j] * QR[i][k];
}
}
}
MatrixMath.Submatrix(_solveMatrixWorkspace, result, 0, 0);
}
/// <summary>
/// Execution of the fast nonnegative least squares algorithm. The algorithm finds a vector x with all elements xi>=0 which minimizes |X*x-y|.
/// </summary>
/// <param name="XtX">X transposed multiplied by X, thus a square matrix.</param>
/// <param name="Xty">X transposed multiplied by Y, thus a matrix with one column and same number of rows as X.</param>
/// <param name="isRestrictedToPositiveValues">Function that takes the parameter index as argument and returns true if the parameter at this index is restricted to positive values; otherwise the return value must be false.</param>
/// <param name="tolerance">Used to decide if a solution element is less than or equal to zero. If this is null, a default tolerance of tolerance = MAX(SIZE(XtX)) * NORM(XtX,1) * EPS is used.</param>
/// <param name="x">Output: solution vector (matrix with one column and number of rows according to dimension of X.</param>
/// <param name="w">Output: Lagrange vector. Elements which take place in the fit are set to 0. Elements fixed to zero contain a negative number.</param>
/// <remarks>
/// <para>
/// Literature: Rasmus Bro and Sijmen De Jong, 'A fast non-negativity-constrained least squares algorithm', Journal of Chemometrics, Vol. 11, 393-401 (1997)
/// </para>
/// <para>
/// Algorithm modified by Dirk Lellinger 2015 to allow a mixture of restricted and unrestricted parameters.
/// </para>
/// </remarks>
public static void Execution(IROMatrix <double> XtX, IROMatrix <double> Xty, Func <int, bool> isRestrictedToPositiveValues, double?tolerance, out IMatrix <double> x, out IMatrix <double> w)
{
if (null == XtX)
{
throw new ArgumentNullException(nameof(XtX));
}
if (null == Xty)
{
throw new ArgumentNullException(nameof(Xty));
}
if (null == isRestrictedToPositiveValues)
{
throw new ArgumentNullException(nameof(isRestrictedToPositiveValues));
}
if (XtX.RowCount != XtX.ColumnCount)
{
throw new ArgumentException("Matrix should be a square matrix", nameof(XtX));
}
if (Xty.ColumnCount != 1)
{
throw new ArgumentException(nameof(Xty) + " should be a column vector (number of columns should be equal to 1)", nameof(Xty));
}
if (Xty.RowCount != XtX.ColumnCount)
{
throw new ArgumentException("Number of rows in " + nameof(Xty) + " should match number of columns in " + nameof(XtX), nameof(Xty));
}
var matrixGenerator = new Func <int, int, DoubleMatrix>((rows, cols) => new DoubleMatrix(rows, cols));
// if nargin < 3
// tol = 10 * eps * norm(XtX, 1) * length(XtX);
// end
double tol = tolerance.HasValue ? tolerance.Value : 10 * DoubleConstants.DBL_EPSILON * MatrixMath.Norm(XtX, MatrixNorm.M1Norm) * Math.Max(XtX.RowCount, XtX.ColumnCount);
// [m, n] = size(XtX);
int n = XtX.ColumnCount;
// P = zeros(1, n);
// Z = 1:n;
var P = new bool[n]; // POSITIVE SET: all indices which are currently not fixed are marked with TRUE (Negative set is simply this, but inverted)
bool initializationOfSolutionRequired = false;
for (int i = 0; i < n; ++i)
{
bool isNotRestricted = !isRestrictedToPositiveValues(i);
P[i] = isNotRestricted;
initializationOfSolutionRequired |= isNotRestricted;
}
// x = P';
x = matrixGenerator(n, 1);
// w = Xty-XtX*x;
w = matrixGenerator(n, 1);
MatrixMath.Copy(Xty, w);
var helper_n_1 = matrixGenerator(n, 1);
MatrixMath.Multiply(XtX, x, helper_n_1);
MatrixMath.Subtract(w, helper_n_1, w);
// set up iteration criterion
int iter = 0;
int itmax = 30 * n;
// outer loop to put variables into set to hold positive coefficients
// while any(Z) & any(w(ZZ) > tol)
while (initializationOfSolutionRequired || (P.Any(ele => false == ele) && w.Any((r, c, ele) => false == P[r] && ele > tol)))
{
if (initializationOfSolutionRequired)
{
initializationOfSolutionRequired = false;
}
else
{
// [wt, t] = max(w(ZZ));
// t = ZZ(t);
int t = -1; // INDEX
double wt = double.NegativeInfinity;
for (int i = 0; i < n; ++i)
{
if (!P[i])
{
if (w[i, 0] > wt)
{
wt = w[i, 0];
t = i;
}
}
}
// P(1, t) = t;
// Z(t) = 0;
P[t] = true;
}
// z(PP')=(Xty(PP)'/XtX(PP,PP)');
var subXty = Xty.SubMatrix(P, 0, matrixGenerator); // Xty(PP)'
var subXtX = XtX.SubMatrix(P, P, matrixGenerator);
var solver = new DoubleLUDecomp(subXtX);
var subSolution = solver.Solve(subXty);
var z = matrixGenerator(n, 1);
for (int i = 0, ii = 0; i < n; ++i)
{
z[i, 0] = P[i] ? subSolution[ii++, 0] : 0;
}
// C. Inner loop (to remove elements from the positive set which no longer belong to)
while (z.Any((r, c, ele) => true == P[r] && ele <= tol && isRestrictedToPositiveValues(r)) && iter < itmax)
{
++iter;
// QQ = find((z <= tol) & P');
//alpha = min(x(QQ)./ (x(QQ) - z(QQ)));
double alpha = double.PositiveInfinity;
for (int i = 0; i < n; ++i)
{
if ((z[i, 0] <= tol && true == P[i] && isRestrictedToPositiveValues(i)))
{
alpha = Math.Min(alpha, x[i, 0] / (x[i, 0] - z[i, 0]));
}
}
// x = x + alpha * (z - x);
for (int i = 0; i < n; ++i)
{
x[i, 0] += alpha * (z[i, 0] - x[i, 0]);
}
// ij = find(abs(x) < tol & P' ~= 0);
// Z(ij) = ij';
// P(ij) = zeros(1, length(ij));
for (int i = 0; i < n; ++i)
{
if (Math.Abs(x[i, 0]) < tol && P[i] == true && isRestrictedToPositiveValues(i))
{
P[i] = false;
}
}
//PP = find(P);
//ZZ = find(Z);
//nzz = size(ZZ);
//z(PP) = (Xty(PP)'/XtX(PP,PP)');
subXty = Xty.SubMatrix(P, 0, matrixGenerator);
subXtX = XtX.SubMatrix(P, P, matrixGenerator);
solver = new DoubleLUDecomp(subXtX);
subSolution = solver.Solve(subXty);
for (int i = 0, ii = 0; i < n; ++i)
{
z[i, 0] = P[i] ? subSolution[ii++, 0] : 0;
}
} // end inner loop
MatrixMath.Copy(z, x);
MatrixMath.Copy(Xty, w);
MatrixMath.Multiply(XtX, x, helper_n_1);
MatrixMath.Subtract(w, helper_n_1, w);
}
}
