/// <summary> /// Calculates the position /// </summary> /// <param name="BlindNode">The BlindNode to be positioned</param> /// <param name="filterMethod">The filter to use on the RSS values</param> /// <param name="RangingMethod">The ranging method</param> /// <param name="multihop">use multihop or not</param> /// <returns>The position of the blind node</returns> public static Point CalculatePosition(Node BlindNode, Node.FilterMethod filterMethod, Node.RangingMethod rangingMethod, bool multihop) { Point position = new Point(); List<AnchorNode> AllAnchors = new List<AnchorNode>(); double[][] y = new double[BlindNode.Anchors.Count-1][]; double[][] x = new double[BlindNode.Anchors.Count-1][]; foreach (AnchorNode an in BlindNode.Anchors) { an.fRSS = filterMethod(an.RSS); an.range = rangingMethod(an.fRSS); } if (!multihop) { if (BlindNode.Anchors.Count >= 3) { for (int i = 1; i < BlindNode.Anchors.Count; i++) { y[i - 1] = new double[] { Math.Pow(BlindNode.Anchors[i].posx, 2) - Math.Pow(BlindNode.Anchors[0].posx, 2) + Math.Pow(BlindNode.Anchors[i].posy, 2) - Math.Pow(BlindNode.Anchors[0].posy, 2) - Math.Pow(BlindNode.Anchors[i].range, 2) + Math.Pow(BlindNode.Anchors[0].range, 2) }; x[i - 1] = new double[] { BlindNode.Anchors[i].posx - BlindNode.Anchors[0].posx, BlindNode.Anchors[i].posy - BlindNode.Anchors[0].posy }; } } else position = null; } else { foreach (AnchorNode an in BlindNode.Anchors) AllAnchors.Add(an); foreach (AnchorNode van in BlindNode.VirtualAnchors) AllAnchors.Add(van); for (int i = 1; i < AllAnchors.Count; i++) { if (AllAnchors[i].posx == AllAnchors[0].posx) AllAnchors[i].posx += 0.1; if (AllAnchors[i].posy == AllAnchors[0].posy) AllAnchors[i].posy += 0.1; y[i - 1] = new double[] { Math.Pow(AllAnchors[i].posx, 2) - Math.Pow(AllAnchors[0].posx, 2) + Math.Pow(AllAnchors[i].posy, 2) - Math.Pow(AllAnchors[0].posy, 2) - Math.Pow(AllAnchors[i].range, 2) + Math.Pow(AllAnchors[0].range, 2) }; x[i - 1] = new double[] { AllAnchors[i].posx - AllAnchors[0].posx, AllAnchors[i].posy - AllAnchors[0].posy }; } } GeneralMatrix Y = new GeneralMatrix(y); GeneralMatrix X = new GeneralMatrix(x); GeneralMatrix XT = X.Transpose(); GeneralMatrix haakjes = XT.Multiply(X); GeneralMatrix inverted = haakjes.Inverse(); // 2 * 2 GeneralMatrix XTY = XT.Multiply(Y); // 2 * 1 GeneralMatrix sol = inverted.Multiply(XTY); GeneralMatrix SOL2 = sol.Multiply(0.5); position.x = SOL2.Array[0][0]; position.y = SOL2.Array[1][0]; return position; }
/// <summary>QR Decomposition, computed by Householder reflections.</summary> /// <param name="A"> Rectangular matrix /// </param> /// <returns> Structure to access R and the Householder vectors and compute Q. /// </returns> public QRDecomposition(GeneralMatrix A) { // Initialize. QR = A.ArrayCopy; m = A.RowDimension; n = A.ColumnDimension; 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 = Maths.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>Cholesky algorithm for symmetric and positive definite matrix.</summary> /// <param name="Arg"> Square, symmetric matrix. /// </param> /// <returns> Structure to access L and isspd flag. /// </returns> public CholeskyDecomposition(GeneralMatrix Arg) { // Initialize. double[][] A = Arg.Array; n = Arg.RowDimension; L = new double[n][]; for (int i = 0; i < n; i++) { L[i] = new double[n]; } isspd = (Arg.ColumnDimension == n); // Main loop. for (int j = 0; j < n; j++) { double[] Lrowj = L[j]; double d = 0.0; for (int k = 0; k < j; k++) { double[] Lrowk = L[k]; double s = 0.0; for (int i = 0; i < k; i++) { s += Lrowk[i] * Lrowj[i]; } Lrowj[k] = s = (A[j][k] - s) / L[k][k]; d = d + s * s; isspd = isspd & (A[k][j] == A[j][k]); } d = A[j][j] - d; isspd = isspd & (d > 0.0); L[j][j] = System.Math.Sqrt(System.Math.Max(d, 0.0)); for (int k = j + 1; k < n; k++) { L[j][k] = 0.0; } } }
/// <summary>Check for symmetry, then construct the eigenvalue decomposition</summary> /// <param name="Arg"> Square matrix /// </param> /// <returns> Structure to access D and V. /// </returns> public EigenvalueDecomposition(GeneralMatrix Arg) { double[][] A = Arg.Array; n = Arg.ColumnDimension; V = new double[n][]; for (int i = 0; i < n; i++) { V[i] = new double[n]; } d = new double[n]; e = new double[n]; issymmetric = true; for (int j = 0; (j < n) & issymmetric; j++) { for (int i = 0; (i < n) & issymmetric; i++) { issymmetric = (A[i][j] == A[j][i]); } } if (issymmetric) { for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { V[i][j] = A[i][j]; } } // Tridiagonalize. tred2(); // Diagonalize. tql2(); } else { H = new double[n][]; for (int i2 = 0; i2 < n; i2++) { H[i2] = new double[n]; } ort = new double[n]; for (int j = 0; j < n; j++) { for (int i = 0; i < n; i++) { H[i][j] = A[i][j]; } } // Reduce to Hessenberg form. orthes(); // Reduce Hessenberg to real Schur form. hqr2(); } }
/// <summary>Solve A*X = B</summary> /// <param name="B"> A Matrix with as many rows as A and any number of columns. /// </param> /// <returns> X so that L*U*X = B(piv,:) /// </returns> /// <exception cref="System.ArgumentException"> Matrix row dimensions must agree. /// </exception> /// <exception cref="System.SystemException"> Matrix is singular. /// </exception> public virtual GeneralMatrix Solve(GeneralMatrix B) { if (B.RowDimension != m) { throw new System.ArgumentException("Matrix row dimensions must agree."); } if (!this.IsNonSingular) { throw new System.SystemException("Matrix is singular."); } // Copy right hand side with pivoting int nx = B.ColumnDimension; GeneralMatrix Xmat = B.GetMatrix(piv, 0, nx - 1); double[][] X = Xmat.Array; // Solve L*Y = B(piv,:) for (int k = 0; k < n; k++) { for (int i = k + 1; i < n; i++) { for (int j = 0; j < nx; j++) { X[i][j] -= X[k][j] * LU[i][k]; } } } // Solve U*X = Y; for (int k = n - 1; k >= 0; k--) { for (int j = 0; j < nx; j++) { X[k][j] /= LU[k][k]; } for (int i = 0; i < k; i++) { for (int j = 0; j < nx; j++) { X[i][j] -= X[k][j] * LU[i][k]; } } } return Xmat; }
/// <summary>Solve X*A = B, which is also A'*X' = B'</summary> /// <param name="B"> right hand side /// </param> /// <returns> solution if A is square, least squares solution otherwise. /// </returns> public virtual GeneralMatrix SolveTranspose(GeneralMatrix B) { return(Transpose().Solve(B.Transpose())); }
/// <summary>Set a submatrix.</summary> /// <param name="r"> Array of row indices. /// </param> /// <param name="c"> Array of column indices. /// </param> /// <param name="X"> A(r(:),c(:)) /// </param> /// <exception cref="System.IndexOutOfRangeException"> Submatrix indices /// </exception> public virtual void SetMatrix(int[] r, int[] c, GeneralMatrix X) { try { for (int i = 0; i < r.Length; i++) { for (int j = 0; j < c.Length; j++) { A[r[i]][c[j]] = X.GetElement(i, j); } } } catch (System.IndexOutOfRangeException e) { throw new System.IndexOutOfRangeException("Submatrix indices", e); } }
/// <summary>Linear algebraic matrix multiplication, A * B</summary> /// <param name="B"> another matrix /// </param> /// <returns> Matrix product, A * B /// </returns> /// <exception cref="System.ArgumentException"> Matrix inner dimensions must agree. /// </exception> public virtual GeneralMatrix Multiply(GeneralMatrix B) { if (B.m != n) { throw new System.ArgumentException("GeneralMatrix inner dimensions must agree."); } GeneralMatrix X = new GeneralMatrix(m, B.n); double[][] C = X.Array; double[] Bcolj = new double[n]; for (int j = 0; j < B.n; j++) { for (int k = 0; k < n; k++) { Bcolj[k] = B.A[k][j]; } for (int i = 0; i < m; i++) { double[] Arowi = A[i]; double s = 0; for (int k = 0; k < n; k++) { s += Arowi[k] * Bcolj[k]; } C[i][j] = s; } } return X; }
/// <summary>Get a submatrix.</summary> /// <param name="r"> Array of row indices. /// </param> /// <param name="j0"> Initial column index /// </param> /// <param name="j1"> Final column index /// </param> /// <returns> A(r(:),j0:j1) /// </returns> /// <exception cref="System.IndexOutOfRangeException"> Submatrix indices /// </exception> public virtual GeneralMatrix GetMatrix(int[] r, int j0, int j1) { GeneralMatrix X = new GeneralMatrix(r.Length, j1 - j0 + 1); double[][] B = X.Array; try { for (int i = 0; i < r.Length; i++) { for (int j = j0; j <= j1; j++) { B[i][j - j0] = A[r[i]][j]; } } } catch (System.IndexOutOfRangeException e) { throw new System.IndexOutOfRangeException("Submatrix indices", e); } return X; }
/// <summary>Element-by-element right division in place, A = A./B</summary> /// <param name="B"> another matrix /// </param> /// <returns> A./B /// </returns> public virtual GeneralMatrix ArrayRightDivideEquals(GeneralMatrix B) { CheckMatrixDimensions(B); for (int i = 0; i < m; i++) { for (int j = 0; j < n; j++) { A[i][j] = A[i][j] / B.A[i][j]; } } return this; }
/// <summary>Solve A*X = B</summary> /// <param name="B"> right hand side /// </param> /// <returns> solution if A is square, least squares solution otherwise /// </returns> public virtual GeneralMatrix Solve(GeneralMatrix B) { return (m == n ? (new LUDecomposition(this)).Solve(B):(new QRDecomposition(this)).Solve(B)); }
/// <summary>Construct the singular value decomposition</summary> /// <param name="Arg"> Rectangular matrix /// </param> /// <returns> Structure to access U, S and V. /// </returns> public SingularValueDecomposition(GeneralMatrix Arg) { // Derived from LINPACK code. // Initialize. double[][] A = Arg.ArrayCopy; m = Arg.RowDimension; n = Arg.ColumnDimension; int nu = System.Math.Min(m, n); s = new double[System.Math.Min(m + 1, n)]; U = new double[m][]; for (int i = 0; i < m; i++) { U[i] = new double[nu]; } V = new double[n][]; for (int i2 = 0; i2 < n; i2++) { V[i2] = new double[n]; } double[] e = new double[n]; double[] work = new double[m]; bool wantu = true; bool wantv = true; // Reduce A to bidiagonal form, storing the diagonal elements // in s and the super-diagonal elements in e. int nct = System.Math.Min(m - 1, n); int nrt = System.Math.Max(0, System.Math.Min(n - 2, m)); for (int k = 0; k < System.Math.Max(nct, nrt); k++) { if (k < nct) { // Compute the transformation for the k-th column and // place the k-th diagonal in s[k]. // Compute 2-norm of k-th column without under/overflow. s[k] = 0; for (int i = k; i < m; i++) { s[k] = Maths.Hypot(s[k], A[i][k]); } if (s[k] != 0.0) { if (A[k][k] < 0.0) { s[k] = - s[k]; } for (int i = k; i < m; i++) { A[i][k] /= s[k]; } A[k][k] += 1.0; } s[k] = - s[k]; } for (int j = k + 1; j < n; j++) { if ((k < nct) & (s[k] != 0.0)) { // Apply the transformation. double t = 0; for (int i = k; i < m; i++) { t += A[i][k] * A[i][j]; } t = (- t) / A[k][k]; for (int i = k; i < m; i++) { A[i][j] += t * A[i][k]; } } // Place the k-th row of A into e for the // subsequent calculation of the row transformation. e[j] = A[k][j]; } if (wantu & (k < nct)) { // Place the transformation in U for subsequent back // multiplication. for (int i = k; i < m; i++) { U[i][k] = A[i][k]; } } if (k < nrt) { // Compute the k-th row transformation and place the // k-th super-diagonal in e[k]. // Compute 2-norm without under/overflow. e[k] = 0; for (int i = k + 1; i < n; i++) { e[k] = Maths.Hypot(e[k], e[i]); } if (e[k] != 0.0) { if (e[k + 1] < 0.0) { e[k] = - e[k]; } for (int i = k + 1; i < n; i++) { e[i] /= e[k]; } e[k + 1] += 1.0; } e[k] = - e[k]; if ((k + 1 < m) & (e[k] != 0.0)) { // Apply the transformation. for (int i = k + 1; i < m; i++) { work[i] = 0.0; } for (int j = k + 1; j < n; j++) { for (int i = k + 1; i < m; i++) { work[i] += e[j] * A[i][j]; } } for (int j = k + 1; j < n; j++) { double t = (- e[j]) / e[k + 1]; for (int i = k + 1; i < m; i++) { A[i][j] += t * work[i]; } } } if (wantv) { // Place the transformation in V for subsequent // back multiplication. for (int i = k + 1; i < n; i++) { V[i][k] = e[i]; } } } } // Set up the final bidiagonal matrix or order p. int p = System.Math.Min(n, m + 1); if (nct < n) { s[nct] = A[nct][nct]; } if (m < p) { s[p - 1] = 0.0; } if (nrt + 1 < p) { e[nrt] = A[nrt][p - 1]; } e[p - 1] = 0.0; // If required, generate U. if (wantu) { for (int j = nct; j < nu; j++) { for (int i = 0; i < m; i++) { U[i][j] = 0.0; } U[j][j] = 1.0; } for (int k = nct - 1; k >= 0; k--) { if (s[k] != 0.0) { for (int j = k + 1; j < nu; j++) { double t = 0; for (int i = k; i < m; i++) { t += U[i][k] * U[i][j]; } t = (- t) / U[k][k]; for (int i = k; i < m; i++) { U[i][j] += t * U[i][k]; } } for (int i = k; i < m; i++) { U[i][k] = - U[i][k]; } U[k][k] = 1.0 + U[k][k]; for (int i = 0; i < k - 1; i++) { U[i][k] = 0.0; } } else { for (int i = 0; i < m; i++) { U[i][k] = 0.0; } U[k][k] = 1.0; } } } // If required, generate V. if (wantv) { for (int k = n - 1; k >= 0; k--) { if ((k < nrt) & (e[k] != 0.0)) { for (int j = k + 1; j < nu; j++) { double t = 0; for (int i = k + 1; i < n; i++) { t += V[i][k] * V[i][j]; } t = (- t) / V[k + 1][k]; for (int i = k + 1; i < n; i++) { V[i][j] += t * V[i][k]; } } } for (int i = 0; i < n; i++) { V[i][k] = 0.0; } V[k][k] = 1.0; } } // Main iteration loop for the singular values. int pp = p - 1; int iter = 0; double eps = System.Math.Pow(2.0, - 52.0); while (p > 0) { int k, kase; // Here is where a test for too many iterations would go. // This section of the program inspects for // negligible elements in the s and e arrays. On // completion the variables kase and k are set as follows. // kase = 1 if s(p) and e[k-1] are negligible and k<p // kase = 2 if s(k) is negligible and k<p // kase = 3 if e[k-1] is negligible, k<p, and // s(k), ..., s(p) are not negligible (qr step). // kase = 4 if e(p-1) is negligible (convergence). for (k = p - 2; k >= - 1; k--) { if (k == - 1) { break; } if (System.Math.Abs(e[k]) <= eps * (System.Math.Abs(s[k]) + System.Math.Abs(s[k + 1]))) { e[k] = 0.0; break; } } if (k == p - 2) { kase = 4; } else { int ks; for (ks = p - 1; ks >= k; ks--) { if (ks == k) { break; } double t = (ks != p?System.Math.Abs(e[ks]):0.0) + (ks != k + 1?System.Math.Abs(e[ks - 1]):0.0); if (System.Math.Abs(s[ks]) <= eps * t) { s[ks] = 0.0; break; } } if (ks == k) { kase = 3; } else if (ks == p - 1) { kase = 1; } else { kase = 2; k = ks; } } k++; // Perform the task indicated by kase. switch (kase) { // Deflate negligible s(p). case 1: { double f = e[p - 2]; e[p - 2] = 0.0; for (int j = p - 2; j >= k; j--) { double t = Maths.Hypot(s[j], f); double cs = s[j] / t; double sn = f / t; s[j] = t; if (j != k) { f = (- sn) * e[j - 1]; e[j - 1] = cs * e[j - 1]; } if (wantv) { for (int i = 0; i < n; i++) { t = cs * V[i][j] + sn * V[i][p - 1]; V[i][p - 1] = (- sn) * V[i][j] + cs * V[i][p - 1]; V[i][j] = t; } } } } break; // Split at negligible s(k). case 2: { double f = e[k - 1]; e[k - 1] = 0.0; for (int j = k; j < p; j++) { double t = Maths.Hypot(s[j], f); double cs = s[j] / t; double sn = f / t; s[j] = t; f = (- sn) * e[j]; e[j] = cs * e[j]; if (wantu) { for (int i = 0; i < m; i++) { t = cs * U[i][j] + sn * U[i][k - 1]; U[i][k - 1] = (- sn) * U[i][j] + cs * U[i][k - 1]; U[i][j] = t; } } } } break; // Perform one qr step. case 3: { // Calculate the shift. double scale = System.Math.Max(System.Math.Max(System.Math.Max(System.Math.Max(System.Math.Abs(s[p - 1]), System.Math.Abs(s[p - 2])), System.Math.Abs(e[p - 2])), System.Math.Abs(s[k])), System.Math.Abs(e[k])); double sp = s[p - 1] / scale; double spm1 = s[p - 2] / scale; double epm1 = e[p - 2] / scale; double sk = s[k] / scale; double ek = e[k] / scale; double b = ((spm1 + sp) * (spm1 - sp) + epm1 * epm1) / 2.0; double c = (sp * epm1) * (sp * epm1); double shift = 0.0; if ((b != 0.0) | (c != 0.0)) { shift = System.Math.Sqrt(b * b + c); if (b < 0.0) { shift = - shift; } shift = c / (b + shift); } double f = (sk + sp) * (sk - sp) + shift; double g = sk * ek; // Chase zeros. for (int j = k; j < p - 1; j++) { double t = Maths.Hypot(f, g); double cs = f / t; double sn = g / t; if (j != k) { e[j - 1] = t; } f = cs * s[j] + sn * e[j]; e[j] = cs * e[j] - sn * s[j]; g = sn * s[j + 1]; s[j + 1] = cs * s[j + 1]; if (wantv) { for (int i = 0; i < n; i++) { t = cs * V[i][j] + sn * V[i][j + 1]; V[i][j + 1] = (- sn) * V[i][j] + cs * V[i][j + 1]; V[i][j] = t; } } t = Maths.Hypot(f, g); cs = f / t; sn = g / t; s[j] = t; f = cs * e[j] + sn * s[j + 1]; s[j + 1] = (- sn) * e[j] + cs * s[j + 1]; g = sn * e[j + 1]; e[j + 1] = cs * e[j + 1]; if (wantu && (j < m - 1)) { for (int i = 0; i < m; i++) { t = cs * U[i][j] + sn * U[i][j + 1]; U[i][j + 1] = (- sn) * U[i][j] + cs * U[i][j + 1]; U[i][j] = t; } } } e[p - 2] = f; iter = iter + 1; } break; // Convergence. case 4: { // Make the singular values positive. if (s[k] <= 0.0) { s[k] = (s[k] < 0.0?- s[k]:0.0); if (wantv) { for (int i = 0; i <= pp; i++) { V[i][k] = - V[i][k]; } } } // Order the singular values. while (k < pp) { if (s[k] >= s[k + 1]) { break; } double t = s[k]; s[k] = s[k + 1]; s[k + 1] = t; if (wantv && (k < n - 1)) { for (int i = 0; i < n; i++) { t = V[i][k + 1]; V[i][k + 1] = V[i][k]; V[i][k] = t; } } if (wantu && (k < m - 1)) { for (int i = 0; i < m; i++) { t = U[i][k + 1]; U[i][k + 1] = U[i][k]; U[i][k] = t; } } k++; } iter = 0; p--; } break; } } }
/// <summary>Solve A*X = B</summary> /// <param name="B"> A Matrix with as many rows as A and any number of columns. /// </param> /// <returns> X so that L*L'*X = B /// </returns> /// <exception cref="System.ArgumentException"> Matrix row dimensions must agree. /// </exception> /// <exception cref="System.SystemException"> Matrix is not symmetric positive definite. /// </exception> public virtual GeneralMatrix Solve(GeneralMatrix B) { if (B.RowDimension != n) { throw new System.ArgumentException("Matrix row dimensions must agree."); } if (!isspd) { throw new System.SystemException("Matrix is not symmetric positive definite."); } // Copy right hand side. double[][] X = B.ArrayCopy; int nx = B.ColumnDimension; // Solve L*Y = B; for (int k = 0; k < n; k++) { for (int i = k + 1; i < n; i++) { for (int j = 0; j < nx; j++) { X[i][j] -= X[k][j] * L[i][k]; } } for (int j = 0; j < nx; j++) { X[k][j] /= L[k][k]; } } // Solve L'*X = Y; for (int k = n - 1; k >= 0; k--) { for (int j = 0; j < nx; j++) { X[k][j] /= L[k][k]; } for (int i = 0; i < k; i++) { for (int j = 0; j < nx; j++) { X[i][j] -= X[k][j] * L[k][i]; } } } return new GeneralMatrix(X, n, nx); }
/// <summary>Least squares solution of A*X = B</summary> /// <param name="B"> A Matrix with as many rows as A and any number of columns. /// </param> /// <returns> X that minimizes the two norm of Q*R*X-B. /// </returns> /// <exception cref="System.ArgumentException"> Matrix row dimensions must agree. /// </exception> /// <exception cref="System.SystemException"> Matrix is rank deficient. /// </exception> public virtual GeneralMatrix Solve(GeneralMatrix B) { if (B.RowDimension != m) { throw new System.ArgumentException("GeneralMatrix row dimensions must agree."); } if (!this.FullRank) { throw new System.SystemException("Matrix is rank deficient."); } // Copy right hand side int nx = B.ColumnDimension; double[][] X = B.ArrayCopy; // 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]; } } } return (new GeneralMatrix(X, n, nx).GetMatrix(0, n - 1, 0, nx - 1)); }
/// <summary>Solve X*A = B, which is also A'*X' = B'</summary> /// <param name="B"> right hand side /// </param> /// <returns> solution if A is square, least squares solution otherwise. /// </returns> public virtual GeneralMatrix SolveTranspose(GeneralMatrix B) { return Transpose().Solve(B.Transpose()); }
/// <summary>Element-by-element right division, C = A./B</summary> /// <param name="B"> another matrix /// </param> /// <returns> A./B /// </returns> public virtual GeneralMatrix ArrayRightDivide(GeneralMatrix B) { CheckMatrixDimensions(B); GeneralMatrix X = new GeneralMatrix(m, n); double[][] C = X.Array; for (int i = 0; i < m; i++) { for (int j = 0; j < n; j++) { C[i][j] = A[i][j] / B.A[i][j]; } } return X; }
/// <summary>A = A - B</summary> /// <param name="B"> another matrix /// </param> /// <returns> A - B /// </returns> public virtual GeneralMatrix SubtractEquals(GeneralMatrix B) { CheckMatrixDimensions(B); for (int i = 0; i < m; i++) { for (int j = 0; j < n; j++) { A[i][j] = A[i][j] - B.A[i][j]; } } return this; }
/// <summary>Get a submatrix.</summary> /// <param name="i0"> Initial row index /// </param> /// <param name="i1"> Final row index /// </param> /// <param name="c"> Array of column indices. /// </param> /// <returns> A(i0:i1,c(:)) /// </returns> /// <exception cref="System.IndexOutOfRangeException"> Submatrix indices /// </exception> public virtual GeneralMatrix GetMatrix(int i0, int i1, int[] c) { GeneralMatrix X = new GeneralMatrix(i1 - i0 + 1, c.Length); double[][] B = X.Array; try { for (int i = i0; i <= i1; i++) { for (int j = 0; j < c.Length; j++) { B[i - i0][j] = A[i][c[j]]; } } } catch (System.IndexOutOfRangeException e) { throw new System.IndexOutOfRangeException("Submatrix indices", e); } return X; }
/// <summary>Matrix transpose.</summary> /// <returns> A' /// </returns> public virtual GeneralMatrix Transpose() { GeneralMatrix X = new GeneralMatrix(n, m); double[][] C = X.Array; for (int i = 0; i < m; i++) { for (int j = 0; j < n; j++) { C[j][i] = A[i][j]; } } return X; }
/// <summary>Multiply a matrix by a scalar, C = s*A</summary> /// <param name="s"> scalar /// </param> /// <returns> s*A /// </returns> public virtual GeneralMatrix Multiply(double s) { GeneralMatrix X = new GeneralMatrix(m, n); double[][] C = X.Array; for (int i = 0; i < m; i++) { for (int j = 0; j < n; j++) { C[i][j] = s * A[i][j]; } } return X; }
/// <summary>Unary minus</summary> /// <returns> -A /// </returns> public virtual GeneralMatrix UnaryMinus() { GeneralMatrix X = new GeneralMatrix(m, n); double[][] C = X.Array; for (int i = 0; i < m; i++) { for (int j = 0; j < n; j++) { C[i][j] = -A[i][j]; } } return X; }
/// <summary>Set a submatrix.</summary> /// <param name="i0"> Initial row index /// </param> /// <param name="i1"> Final row index /// </param> /// <param name="j0"> Initial column index /// </param> /// <param name="j1"> Final column index /// </param> /// <param name="X"> A(i0:i1,j0:j1) /// </param> /// <exception cref="System.IndexOutOfRangeException"> Submatrix indices /// </exception> public virtual void SetMatrix(int i0, int i1, int j0, int j1, GeneralMatrix X) { try { for (int i = i0; i <= i1; i++) { for (int j = j0; j <= j1; j++) { A[i][j] = X.GetElement(i - i0, j - j0); } } } catch (System.IndexOutOfRangeException e) { throw new System.IndexOutOfRangeException("Submatrix indices", e); } }
/// <summary>Check if size(A) == size(B) *</summary> private void CheckMatrixDimensions(GeneralMatrix B) { if (B.m != m || B.n != n) { throw new System.ArgumentException("GeneralMatrix dimensions must agree."); } }
/// <summary>Solve A*X = B</summary> /// <param name="B"> right hand side /// </param> /// <returns> solution if A is square, least squares solution otherwise /// </returns> public virtual GeneralMatrix Solve(GeneralMatrix B) { return(m == n ? (new LUDecomposition(this)).Solve(B):(new QRDecomposition(this)).Solve(B)); }
/// <summary>Construct a matrix from a copy of a 2-D array.</summary> /// <param name="A"> Two-dimensional array of doubles. /// </param> /// <exception cref="System.ArgumentException"> All rows must have the same length /// </exception> public static GeneralMatrix Create(double[][] A) { int m = A.Length; int n = A[0].Length; GeneralMatrix X = new GeneralMatrix(m, n); double[][] C = X.Array; for (int i = 0; i < m; i++) { if (A[i].Length != n) { throw new System.ArgumentException("All rows must have the same length."); } for (int j = 0; j < n; j++) { C[i][j] = A[i][j]; } } return X; }
/// <summary>Generate identity matrix</summary> /// <param name="m"> Number of rows. /// </param> /// <param name="n"> Number of colums. /// </param> /// <returns> An m-by-n matrix with ones on the diagonal and zeros elsewhere. /// </returns> public static GeneralMatrix Identity(int m, int n) { GeneralMatrix A = new GeneralMatrix(m, n); double[][] X = A.Array; for (int i = 0; i < m; i++) { for (int j = 0; j < n; j++) { X[i][j] = (i == j ? 1.0 : 0.0); } } return A; }
/// <summary>LU Decomposition</summary> /// <param name="A"> Rectangular matrix /// </param> /// <returns> Structure to access L, U and piv. /// </returns> public LUDecomposition(GeneralMatrix A) { // Use a "left-looking", dot-product, Crout/Doolittle algorithm. LU = A.ArrayCopy; m = A.RowDimension; n = A.ColumnDimension; piv = new int[m]; for (int i = 0; i < m; i++) { piv[i] = i; } pivsign = 1; double[] LUrowi; double[] LUcolj = new double[m]; // Outer loop. for (int j = 0; j < n; j++) { // Make a copy of the j-th column to localize references. for (int i = 0; i < m; i++) { LUcolj[i] = LU[i][j]; } // Apply previous transformations. for (int i = 0; i < m; i++) { LUrowi = LU[i]; // Most of the time is spent in the following dot product. int kmax = System.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 < m; i++) { if (System.Math.Abs(LUcolj[i]) > System.Math.Abs(LUcolj[p])) { p = i; } } if (p != j) { for (int k = 0; k < n; k++) { double t = LU[p][k]; LU[p][k] = LU[j][k]; LU[j][k] = t; } int k2 = piv[p]; piv[p] = piv[j]; piv[j] = k2; pivsign = - pivsign; } // Compute multipliers. if (j < m & LU[j][j] != 0.0) { for (int i = j + 1; i < m; i++) { LU[i][j] /= LU[j][j]; } } } }
/// <summary>Generate matrix with random elements</summary> /// <param name="m"> Number of rows. /// </param> /// <param name="n"> Number of colums. /// </param> /// <returns> An m-by-n matrix with uniformly distributed random elements. /// </returns> public static GeneralMatrix Random(int m, int n) { System.Random random = new System.Random(); GeneralMatrix A = new GeneralMatrix(m, n); double[][] X = A.Array; for (int i = 0; i < m; i++) { for (int j = 0; j < n; j++) { X[i][j] = random.NextDouble(); } } return A; }
/// <summary> /// Calibrates the pathloss parameter with information of the anchor nodes using Least Squares /// </summary> /// <param name="AnchorNodes">The anchor nodes giving the calibration information</param> /// <param name="filterMethod">Method to filter the RSS</param> public static void CalibratePathlossLS(List<Node> CalibrationNodes, Node.FilterMethod filterMethod) { double pathlossExponent = 0; List<Node> AllAnchors = new List<Node>(); TwoAnchors twoAnchors1 = new TwoAnchors(); TwoAnchors twoAnchors2 = new TwoAnchors(); List<TwoAnchors> AllCalAnchors = new List<TwoAnchors>(); AllAnchors = CalibrationNodes; for (int j = 0; j < CalibrationNodes.Count; j++) { twoAnchors1.a1 = CalibrationNodes[j].WsnId; twoAnchors2.a2 = CalibrationNodes[j].WsnId; //CalibrationNodes[j].SetOwnPosition(); for (int i = 0; i < CalibrationNodes[j].Anchors.Count; i++) { twoAnchors1.a2 = CalibrationNodes[j].Anchors[i].nodeid; twoAnchors2.a1 = CalibrationNodes[j].Anchors[i].nodeid; if (!AllCalAnchors.Contains(twoAnchors1) && !AllCalAnchors.Contains(twoAnchors2)) { AllCalAnchors.Add(twoAnchors1); AllCalAnchors.Add(twoAnchors2); } else { foreach (Node mote in AllAnchors) { if (mote.WsnId == CalibrationNodes[j].Anchors[i].nodeid) foreach (AnchorNode an in mote.Anchors) if (an.nodeid == CalibrationNodes[j].WsnId) { foreach (double d in CalibrationNodes[j].Anchors[i].RSS) { an.RSS.Enqueue(d); } // mote.Anchors.Remove(CalibrationNodes[j].Anchors[i]); } } foreach (Node mote in AllAnchors) if (mote.WsnId == CalibrationNodes[j].WsnId) mote.Anchors.Remove(CalibrationNodes[j].Anchors[i]); } } } int totalcountt = 0; foreach (Node nod in AllAnchors) totalcountt += nod.Anchors.Count; if (totalcountt >= 3) { int totalcount = 0; int count = 0; foreach (Node node in AllAnchors) totalcount += node.Anchors.Count; double[][] y = new double[totalcount][]; double[][] x = new double[totalcount][]; foreach (Node cal in AllAnchors) { for (int i = 0; i < cal.Anchors.Count; i++) { cal.Anchors[i].fRSS = filterMethod(cal.Anchors[i].RSS); double distance = Math.Pow((Math.Pow((cal.Position.x - cal.Anchors[i].posx), 2) + Math.Pow((cal.Position.y - cal.Anchors[i].posy), 2)), 0.5); if (distance == 0) distance = 0.1; y[count] = new double[1] { cal.Anchors[i].fRSS }; x[count] = new double[2] { 1, -10 * Math.Log10(distance) }; count++; } } GeneralMatrix Y = new GeneralMatrix(y); GeneralMatrix X = new GeneralMatrix(x); GeneralMatrix XT = X.Transpose(); GeneralMatrix haakjes = XT.Multiply(X); GeneralMatrix inverted = haakjes.Inverse(); GeneralMatrix XTY = XT.Multiply(Y); GeneralMatrix sol = inverted.Multiply(XTY); RangeBasedPositioning.baseLoss = -sol.Array[0][0]; RangeBasedPositioning.pathLossExponent = sol.Array[1][0]; } }
/// <summary> /// Calibrates the pathloss parameter with information of the anchor nodes using Least Squares /// </summary> /// <param name="AnchorNodes">The anchor nodes giving the calibration information</param> /// <param name="filterMethod">Method to filter the RSS</param> public static void CalibratePathlossLS(List <Node> CalibrationNodes, Node.FilterMethod filterMethod) { double pathlossExponent = 0; List <Node> AllAnchors = new List <Node>(); TwoAnchors twoAnchors1 = new TwoAnchors(); TwoAnchors twoAnchors2 = new TwoAnchors(); List <TwoAnchors> AllCalAnchors = new List <TwoAnchors>(); AllAnchors = CalibrationNodes; for (int j = 0; j < CalibrationNodes.Count; j++) { twoAnchors1.a1 = CalibrationNodes[j].WsnId; twoAnchors2.a2 = CalibrationNodes[j].WsnId; //CalibrationNodes[j].SetOwnPosition(); for (int i = 0; i < CalibrationNodes[j].Anchors.Count; i++) { twoAnchors1.a2 = CalibrationNodes[j].Anchors[i].nodeid; twoAnchors2.a1 = CalibrationNodes[j].Anchors[i].nodeid; if (!AllCalAnchors.Contains(twoAnchors1) && !AllCalAnchors.Contains(twoAnchors2)) { AllCalAnchors.Add(twoAnchors1); AllCalAnchors.Add(twoAnchors2); } else { foreach (Node mote in AllAnchors) { if (mote.WsnId == CalibrationNodes[j].Anchors[i].nodeid) { foreach (AnchorNode an in mote.Anchors) { if (an.nodeid == CalibrationNodes[j].WsnId) { foreach (double d in CalibrationNodes[j].Anchors[i].RSS) { an.RSS.Enqueue(d); } // mote.Anchors.Remove(CalibrationNodes[j].Anchors[i]); } } } } foreach (Node mote in AllAnchors) { if (mote.WsnId == CalibrationNodes[j].WsnId) { mote.Anchors.Remove(CalibrationNodes[j].Anchors[i]); } } } } } int totalcountt = 0; foreach (Node nod in AllAnchors) { totalcountt += nod.Anchors.Count; } if (totalcountt >= 3) { int totalcount = 0; int count = 0; foreach (Node node in AllAnchors) { totalcount += node.Anchors.Count; } double[][] y = new double[totalcount][]; double[][] x = new double[totalcount][]; foreach (Node cal in AllAnchors) { for (int i = 0; i < cal.Anchors.Count; i++) { cal.Anchors[i].fRSS = filterMethod(cal.Anchors[i].RSS); double distance = Math.Pow((Math.Pow((cal.Position.x - cal.Anchors[i].posx), 2) + Math.Pow((cal.Position.y - cal.Anchors[i].posy), 2)), 0.5); if (distance == 0) { distance = 0.1; } y[count] = new double[1] { cal.Anchors[i].fRSS }; x[count] = new double[2] { 1, -10 * Math.Log10(distance) }; count++; } } GeneralMatrix Y = new GeneralMatrix(y); GeneralMatrix X = new GeneralMatrix(x); GeneralMatrix XT = X.Transpose(); GeneralMatrix haakjes = XT.Multiply(X); GeneralMatrix inverted = haakjes.Inverse(); GeneralMatrix XTY = XT.Multiply(Y); GeneralMatrix sol = inverted.Multiply(XTY); RangeBasedPositioning.baseLoss = -sol.Array[0][0]; RangeBasedPositioning.pathLossExponent = sol.Array[1][0]; } }