/// <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>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>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];
}
}