/// <summary>Solves a set of equation systems of type <c>A * X = B</c>.</summary> /// <param name="value">Right hand side matrix with as many rows as <c>A</c> and any number of columns.</param> /// <returns>Matrix <c>X</c> so that <c>L * U * X = B</c>.</returns> public MatrixField Solve(MatrixField value) { if (value == null) { throw new ArgumentNullException("value"); } if (value.Rows != this.LU.Rows) { throw new ArgumentException("Invalid matrix dimensions.", "value"); } if (!this.NonSingular) { throw new InvalidOperationException("Matrix is singular"); } // Copy right hand side with pivoting int count = value.Columns; MatrixField X = value.Submatrix(pivotVector, 0, count - 1); int rows = LU.Rows; int columns = LU.Columns; Field[][] lu = LU.Array; // Solve L*Y = B(piv,:) for (int k = 0; k < columns; k++) { for (int i = k + 1; i < columns; i++) { for (int j = 0; j < count; j++) { X[i, j] -= X[k, j] * lu[i][k]; } } } // Solve U*X = Y; for (int k = columns - 1; k >= 0; k--) { for (int j = 0; j < count; j++) { X[k, j] /= lu[k][k]; } for (int i = 0; i < k; i++) { for (int j = 0; j < count; j++) { X[i, j] -= X[k, j] * lu[i][k]; } } } return(X); }
/// <summary>Least squares solution of <c>A * X = B</c></summary> /// <param name="value">Right-hand-side matrix with as many rows as <c>A</c> and any number of columns.</param> /// <returns>A matrix that minimized the two norm of <c>Q * R * X - B</c>.</returns> /// <exception cref="T:System.ArgumentException">Matrix row dimensions must be the same.</exception> /// <exception cref="T:System.InvalidOperationException">Matrix is rank deficient.</exception> public MatrixField Solve(MatrixField value) { if (value == null) { throw new ArgumentNullException("value"); } if (value.Rows != QR.Rows) { 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.Columns; MatrixField X = value.Clone(); int m = QR.Rows; int n = QR.Columns; Field[][] qr = QR.Array; // Compute Y = transpose(Q)*B for (int k = 0; k < n; k++) { for (int j = 0; j < count; j++) { Field s = new Field(0); for (int i = k; i < m; i++) { s += qr[i][k] * X[i, j]; } s = (s - 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)); }