/// <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]; } } } }