/// <summary>Determines weather two instances are equal.</summary> public static bool Equals(MatrixField left, MatrixField right) { if (left == ((object)right)) { return(true); } if ((((object)left) == null) || (((object)right) == null)) { return(false); } if ((left.Rows != right.Rows) || (left.Columns != right.Columns)) { return(false); } for (int i = 0; i < left.Rows; i++) { for (int j = 0; j < left.Columns; j++) { if (left[i, j] != right[i, j]) { return(false); } } } return(true); }
/// <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)); }
/// <summary>Construct a QR decomposition.</summary> public QrDecompositionField(MatrixField value) { throw new InvalidOperationException("QrDecompositionField is not supported for Galois Fields for now :)"); if (value == null) { throw new ArgumentNullException("value"); } this.QR = value.Clone(); Field[][] qr = this.QR.Array; int m = value.Rows; int n = value.Columns; this.Rdiag = new Field[n]; //for (int k = 0; k < n; k++) //{ // // Compute 2-norm of k-th column without under/overflow. // Field nrm = new Field(0); // for (int i = k; i < m; i++) // { // nrm = Hypotenuse(nrm, qr[i][k]); // } // if (nrm.Value != 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>Construct a LU decomposition.</summary> public LuDecompositionField(MatrixField value) { if (value == null) { throw new ArgumentNullException("value"); } this.LU = value.Clone(); Field[][] 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; Field[] LUrowi; Field[] LUcolj = new Field[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); Field s = new Field(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 (LUcolj[i].Value > LUcolj[p].Value) { p = i; } } if (p != j) { for (int k = 0; k < columns; k++) { Field 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].Value != 0) { for (int i = j + 1; i < rows; i++) { lu[i][j] /= lu[j][j]; } } } }