/// <summary>
/// Creating a new document using the specified map, route, laps, initial transformation matrix, projection origin and document settings, and adding one new session with the specified route and laps.
/// </summary>
/// <param name="map"></param>
/// <param name="route"></param>
/// <param name="laps"></param>
/// <param name="initialTransformationMatrix"></param>
/// <param name="projectionOrigin"></param>
/// <param name="settings"></param>
public Document(Map map, Route route, LapCollection laps, GeneralMatrix initialTransformationMatrix, LongLat projectionOrigin, DocumentSettings settings)
{
Map = map;
sessions.Add(new Session(route, laps, map.Image.Size, initialTransformationMatrix, projectionOrigin, settings.DefaultSessionSettings));
this.settings = settings;
UpdateDocumentToCurrentVersion(this);
}
/// <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>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>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>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>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>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>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>Set 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>
/// <param name="X"> A(r(:),j0:j1)
/// </param>
/// <exception cref="System.IndexOutOfRangeException"> Submatrix indices
/// </exception>
public virtual void SetMatrix(int[] r, int j0, int j1, GeneralMatrix X)
{
try
{
for (int i = 0; i < r.Length; i++)
{
for (int j = j0; j <= j1; j++)
{
a[r[i]][j] = X.GetElement(i, j - j0);
}
}
}
catch (System.IndexOutOfRangeException e)
{
throw new System.IndexOutOfRangeException("Submatrix indices", e);
}
}
/// <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>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>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>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>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>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>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>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>Set 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>
/// <param name="X"> A(i0:i1,c(:))
/// </param>
/// <exception cref="System.IndexOutOfRangeException"> Submatrix indices
/// </exception>
public virtual void SetMatrix(int i0, int i1, int[] c, GeneralMatrix X)
{
try
{
for (int i = i0; i <= i1; i++)
{
for (int j = 0; j < c.Length; j++)
{
a[i][c[j]] = X.GetElement(i - i0, j);
}
}
}
catch (System.IndexOutOfRangeException e)
{
throw new System.IndexOutOfRangeException("Submatrix indices", e);
}
}
/// <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;
}
private byte[] CreateSessionData(Session session)
{
var sessionStream = new MemoryStream();
var sessionWriter = new BinaryWriter(sessionStream);
// route
var routeStream = new MemoryStream();
var routeWriter = new BinaryWriter(routeStream);
// which attributes to include for each waypoint
var attributes = WaypointAttribute.Position | WaypointAttribute.Time;
if (session.Route.ContainsWaypointAttribute(BusinessEntities.WaypointAttribute.HeartRate))
attributes |= WaypointAttribute.HeartRate;
if (session.Route.ContainsWaypointAttribute(BusinessEntities.WaypointAttribute.Altitude))
attributes |= WaypointAttribute.Altitude;
routeWriter.Write((UInt16)attributes);
// any extra length in bytes for future elements for each waypoint
routeWriter.Write((UInt16)0);
// number of route segments in this route
routeWriter.Write((UInt32)session.Route.Segments.Count);
foreach (var routeSegment in session.Route.Segments)
{
// number of waypoints in this route segment
routeWriter.Write((UInt32)routeSegment.Waypoints.Count);
var lastTime = DateTime.MinValue;
foreach (var waypoint in routeSegment.Waypoints)
{
// position: 8 bytes
WriteLongLat(waypoint.LongLat, routeWriter);
// time and tome type: 1 + 2-8 bytes
WriteTimeTypeAndTime(waypoint.Time, lastTime, routeWriter);
lastTime = waypoint.Time;
// heart rate: 1 byte
if ((((UInt16)attributes) & ((UInt16)WaypointAttribute.HeartRate)) == (UInt16)WaypointAttribute.HeartRate)
{
routeWriter.Write((byte)(waypoint.HeartRate.HasValue ? Math.Min(Math.Max(waypoint.HeartRate.Value, byte.MinValue), byte.MaxValue) : byte.MinValue));
}
// altitude: 2 bytes
if ((((UInt16)attributes) & ((UInt16)WaypointAttribute.Altitude)) == (UInt16)WaypointAttribute.Altitude)
{
routeWriter.Write((Int16)(waypoint.Altitude.HasValue ? Math.Min(Math.Max(waypoint.Altitude.Value, Int16.MinValue), Int16.MaxValue) : 0));
}
}
}
sessionWriter.Write((byte)Tags.Route);
sessionWriter.Write((UInt32)routeStream.Length);
sessionWriter.Write(routeStream.ToArray());
routeWriter.Close();
routeStream.Close();
routeStream.Dispose();
// handles
// TODO: adjust for zoom
var handleStream = new MemoryStream();
var handleWriter = new BinaryWriter(handleStream);
handleWriter.Write((UInt32)session.Handles.Length);
foreach (var handle in session.Handles)
{
// transformation matrix
var scaleMatrix = new GeneralMatrix(new[] {PercentualSize, 0, 0, 0, PercentualSize, 0, 0, 0, 1}, 3);
var scaledTM = scaleMatrix*handle.TransformationMatrix;
for (var i = 0; i < 3; i++)
{
for (var j = 0; j < 3; j++)
{
handleWriter.Write(scaledTM.GetElement(i, j));
}
}
// parameterized location
handleWriter.Write((UInt32)handle.ParameterizedLocation.SegmentIndex);
handleWriter.Write(handle.ParameterizedLocation.Value);
// pixel location
handleWriter.Write(PercentualSize * handle.Location.X);
handleWriter.Write(PercentualSize * handle.Location.Y);
// type
handleWriter.Write((Int16)handle.Type);
}
sessionWriter.Write((byte)Tags.Handles);
sessionWriter.Write((UInt32)handleStream.Length);
sessionWriter.Write(handleStream.ToArray());
handleWriter.Close();
handleStream.Close();
handleStream.Dispose();
// projection origin
sessionWriter.Write((byte)Tags.ProjectionOrigin);
sessionWriter.Write((UInt32)8);
WriteLongLat(session.ProjectionOrigin, sessionWriter);
// laps
var lapStream = new MemoryStream();
var lapWriter = new BinaryWriter(lapStream);
lapWriter.Write((UInt32)session.Laps.Count);
foreach (var lap in session.Laps)
{
// time
lapWriter.Write(lap.Time.ToUniversalTime().ToBinary());
// type
lapWriter.Write((byte)lap.LapType);
}
sessionWriter.Write((byte)Tags.Laps);
sessionWriter.Write((UInt32)lapStream.Length);
sessionWriter.Write(lapStream.ToArray());
lapWriter.Close();
lapStream.Close();
lapStream.Dispose();
// session info
var sessionInfoStream = new MemoryStream();
var sessionInfoWriter = new BinaryWriter(sessionInfoStream);
// never change the order or remove field that has already been added!
WriteString(session.SessionInfo.Person.Name, sessionInfoWriter);
WriteString(session.SessionInfo.Person.Club, sessionInfoWriter);
sessionInfoWriter.Write(session.SessionInfo.Person.Id);
WriteString(session.SessionInfo.Description, sessionInfoWriter);
sessionWriter.Write((byte)Tags.SessionInfo);
sessionWriter.Write((UInt32)sessionInfoStream.Length);
sessionWriter.Write(sessionInfoStream.ToArray());
sessionInfoWriter.Close();
sessionInfoStream.Close();
sessionInfoStream.Dispose();
// map reading info
var mapReadingsList = session.Route.GetMapReadingsList();
if(mapReadingsList != null)
{
var mapReadingInfoStream = new MemoryStream();
var mapReadingInfoWriter = new BinaryWriter(mapReadingInfoStream);
var lastTime = DateTime.MinValue;
foreach (var mapReading in mapReadingsList)
{
WriteTimeTypeAndTime(mapReading, lastTime, mapReadingInfoWriter);
}
sessionWriter.Write((byte)Tags.MapReadingInfo);
sessionWriter.Write((UInt32)mapReadingInfoStream.Length);
sessionWriter.Write(mapReadingInfoStream.ToArray());
mapReadingInfoWriter.Close();
mapReadingInfoStream.Close();
mapReadingInfoStream.Dispose();
}
var data = sessionStream.ToArray();
sessionWriter.Close();
sessionStream.Close();
sessionStream.Dispose();
return data;
}
/// <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>
/// Creating a new document using the specified map, route, laps, initial transformation matrix and document settings, and adding one new session with the specified route and laps.
/// </summary>
/// <param name="map"></param>
/// <param name="route"></param>
/// <param name="laps"></param>
/// <param name="initialTransformationMatrix"></param>
/// <param name="settings"></param>
public Document(Map map, Route route, LapCollection laps, GeneralMatrix initialTransformationMatrix, DocumentSettings settings)
: this(map, route, laps, initialTransformationMatrix, null, settings)
{
}
/// <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>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>
/// Converts a map image pixel coordinate to a longitude and latitude coordinate
/// </summary>
/// <param name="mapImagePosition">Map pixel coordinate, referring to unzoomed map without any borders and image header</param>
/// <returns></returns>
public LongLat GetLongLatForMapImagePosition(PointD mapImagePosition, GeneralMatrix averageTransformationMatrixInverse)
{
var projectedPosition = LinearAlgebraUtil.Transform(mapImagePosition, averageTransformationMatrixInverse);
return LongLat.Deproject(projectedPosition, ProjectionOrigin);
}
/// <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>C = A - B</summary>
/// <param name="B"> another matrix
/// </param>
/// <returns> A - B
/// </returns>
public virtual GeneralMatrix Subtract(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>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);
}