/// <summary>
/// Inverts square matrix as long as det != 0.
/// </summary>
/// <returns>Inverse of matrix.</returns>
public SafeMatrix Inverse()
{
if (!this.IsSquare())
{
throw new InvalidOperationException("Cannot invert non-square matrix.");
}
double det = this.Determinant();
if (det == 0)
{
throw new InvalidOperationException("Cannot invert (nearly) singular matrix.");
}
SafeMatrix buf = new SafeMatrix(m_ColumnCount, m_ColumnCount);
for (int i = 0; i < m_ColumnCount; i++)
{
for (int j = 0; j < m_ColumnCount; j++)
{
buf.m_Elements[i * buf.m_ColumnCount + j] = (Math.Pow(-1, i + j) * this.Minor(j, i).Determinant()) / det;
}
}
return(buf);
}
public SafeMatrix Minor(int row, int col)
{
// THIS IS THE LOW-LEVEL SOLUTION ~ O(n^2)
SafeMatrix buf = new SafeMatrix(m_RowCount - 1, m_ColumnCount - 1);
int r = 0;
int c = 0;
for (int i = 0; i < m_RowCount; i++)
{
if (i != row)
{
for (int j = 0; j < m_ColumnCount; j++)
{
if (j != col)
{
buf.m_Elements[r * buf.m_ColumnCount + c] = m_Elements[i * m_ColumnCount + j];
c++;
}
}
c = 0;
r++;
}
}
return(buf);
}
public double Determinant()
{
if (!this.IsSquare())
{
throw new InvalidOperationException("Cannot calc determinant of non-square matrix.");
}
if (this.m_ColumnCount == 1)
{
return(this[0, 0]);
}
// perform LU-decomposition & return product of diagonal elements of U
SafeMatrix X = this.Clone();
// for speed concerns, use this
try
{
X.LU();
return(X.DiagProd());
}
catch (DivideByZeroException)
{
// this is slower and needs more memory... .
//Matrix P = X.LUSafe();
//return (double)P.Signum() * X.DiagProd();
throw;
}
}
public SafeMatrix Clone()
{
SafeMatrix A = new SafeMatrix(m_RowCount, m_ColumnCount);
for (int i = 0; i < m_MatrixSize; i++)
{
A.m_Elements[i] = m_Elements[i];
}
return(A);
}
public static SafeMatrix operator *(double x, SafeMatrix A)
{
SafeMatrix B = new SafeMatrix(A.RowCount, A.ColumnCount);
for (int i = 0; i < A.m_MatrixSize; i++)
{
B.m_Elements[i] = A.m_Elements[i] * x;
}
return(B);
}
public SafeMatrix Transpose()
{
SafeMatrix M = new SafeMatrix(m_ColumnCount, m_RowCount);
for (int i = 0; i < m_ColumnCount; i++)
{
for (int j = 0; j < m_RowCount; j++)
{
M.m_Elements[i * M.m_ColumnCount + j] = m_Elements[j * m_ColumnCount + i];
}
}
return(M);
}
public static double Dot(SafeMatrix v, int vRow, SafeMatrix w, int wCol)
{
if (v.ColumnCount != w.RowCount)
{
throw new ArgumentException("Vectors must be of the same length.");
}
double buf = 0;
for (int i = 0; i < v.ColumnCount; i++)
{
buf += v.m_Elements[vRow * v.m_ColumnCount + i] * w.m_Elements[i * w.m_ColumnCount + wCol];
}
return(buf);
}
public static SafeMatrix operator *(SafeMatrix A, SafeMatrix B)
{
if (A.ColumnCount != B.RowCount)
{
throw new ArgumentException("Inner matrix dimensions must agree.");
}
SafeMatrix C = new SafeMatrix(A.RowCount, B.ColumnCount);
for (int i = 0; i < A.RowCount; i++)
{
for (int j = 0; j < B.ColumnCount; j++)
{
C.m_Elements[i * C.m_ColumnCount + j] = Dot(A, i, B, j);
}
}
return(C);
}
public static SafeMatrix operator *(double x, SafeMatrix A)
{
SafeMatrix B = new SafeMatrix(A.RowCount, A.ColumnCount);
for (int i = 0; i < A.m_MatrixSize; i++)
{
B.m_Elements[i] = A.m_Elements[i] * x;
}
return B;
}
public SafeMatrix Transpose()
{
SafeMatrix M = new SafeMatrix(m_ColumnCount, m_RowCount);
for (int i = 0; i < m_ColumnCount; i++)
{
for (int j = 0; j < m_RowCount; j++)
{
M.m_Elements[i * M.m_ColumnCount + j] = m_Elements[j * m_ColumnCount + i];
}
}
return M;
}
public SafeMatrix Minor(int row, int col)
{
// THIS IS THE LOW-LEVEL SOLUTION ~ O(n^2)
SafeMatrix buf = new SafeMatrix(m_RowCount - 1, m_ColumnCount - 1);
int r = 0;
int c = 0;
for (int i = 0; i < m_RowCount; i++)
{
if (i != row)
{
for (int j = 0; j < m_ColumnCount; j++)
{
if (j != col)
{
buf.m_Elements[r * buf.m_ColumnCount + c] = m_Elements[i * m_ColumnCount + j];
c++;
}
}
c = 0;
r++;
}
}
return buf;
}
/// <summary>
/// Inverts square matrix as long as det != 0.
/// </summary>
/// <returns>Inverse of matrix.</returns>
public SafeMatrix Inverse()
{
if (!this.IsSquare())
throw new InvalidOperationException("Cannot invert non-square matrix.");
double det = this.Determinant();
if (det == 0)
throw new InvalidOperationException("Cannot invert (nearly) singular matrix.");
SafeMatrix buf = new SafeMatrix(m_ColumnCount, m_ColumnCount);
for (int i = 0; i < m_ColumnCount; i++)
{
for (int j = 0; j < m_ColumnCount; j++)
{
buf.m_Elements[i * buf.m_ColumnCount + j] = (Math.Pow(-1, i + j) * this.Minor(j, i).Determinant()) / det;
}
}
return buf;
}
public SafeMatrix Clone()
{
SafeMatrix A = new SafeMatrix(m_RowCount, m_ColumnCount);
for (int i = 0; i < m_MatrixSize; i++)
A.m_Elements[i] = m_Elements[i];
return A;
}
public static double Dot(SafeMatrix v, int vRow, SafeMatrix w, int wCol)
{
if (v.ColumnCount != w.RowCount)
throw new ArgumentException("Vectors must be of the same length.");
double buf = 0;
for (int i = 0; i < v.ColumnCount; i++)
{
buf += v.m_Elements[vRow * v.m_ColumnCount + i] * w.m_Elements[i * w.m_ColumnCount + wCol];
}
return buf;
}
public void Solve(bool useNormalisation, double t0_initialVal)
{
var varTimes = new List<double>();
var varMagnitudes = new List<double>();
double constNorm = double.NaN;
if (!useNormalisation)
{
List<double> medianCalcList = new List<double>(m_CompData);
medianCalcList.Sort();
constNorm = medianCalcList[medianCalcList.Count/2];
}
C = 1; // Fix C to 1
M0 = FitM0ForT0(t0_initialVal, constNorm) - 1; // Get from known max magnitude of star
for (int i = 0; i < m_NumObs; i++)
{
double mag = M0 - 2.5 * Math.Log10(m_VarData[i] / (!useNormalisation ? constNorm : m_CompData[i]));
if (IsOutlier(i, mag)) continue;
varTimes.Add(m_Times[i]);
varMagnitudes.Add(mag);
}
if (varMagnitudes.Count < 7)
{
// Not enought data points for solving 5 variables
IsSolved = false;
return;
}
// Starting values
C = 1;
T0 = t0_initialVal; // Get from Kwee van Worden
G = 0.5;
// Get D from solving the equation to D (with other starting values specified)
D = (varTimes[varMagnitudes.Count - 1] - T0) / Acosh(1 - Math.Log(1 - Math.Pow(1 - (varMagnitudes[varMagnitudes.Count - 1] - M0) / C, 1 / G)));
if (double.IsNaN(D) || double.IsInfinity(D)) D = 0.1;
NumberIterations = 100;
double[] minCorr = new double[] {double.MaxValue, double.MaxValue, double.MaxValue, double.MaxValue, double.MaxValue};
//// Our guess ot T0 is very close, so assume it is contant and solve for G and D
//for (int iter = NumberIterations; iter > 0; iter--)
//{
// var A = new SafeMatrix(varMagnitudes.Count, 2);
// var X = new SafeMatrix(varMagnitudes.Count, 1);
// for (int index = 0; index < varMagnitudes.Count; index++)
// {
// double t = varTimes[index];
// double difference = ComputeModelValue(t) - varMagnitudes[index];
// X[index, 0] = -difference;
// double GAMMA = 1 - Math.Exp(1 - Math.Cosh((t - T0) / D));
// double GAMMA_G = Math.Pow(GAMMA, G);
// A[index, 0] = GAMMA_G * Math.Log(G); // G
// A[index, 1] = -(G / D) * Math.Pow(GAMMA, G - 1) * Math.Exp(1 - Math.Cosh((t - T0) / D)) * Math.Sinh((t - T0) / D) * (t - T0) / D; // D
// }
// SafeMatrix a_T = A.Transpose();
// SafeMatrix aa = a_T * A;
// SafeMatrix aa_inv = aa.Inverse();
// SafeMatrix Y = (aa_inv * a_T) * X;
// D += Y[1, 0];
// if (D < 0) D = 0.001;
// // Enforce maximum correction for G of |0.1|. G > 0
// //if (Y[0, 0] > 0.01) Y[0, 0] = 0.01;
// //if (Y[0, 0] < -0.01) Y[0, 0] = -0.01;
// G += Y[0, 0];
// if (G < 0) G = 0.001;
// Trace.WriteLine(string.Format("D Corr: {0}\t\t G Corr: {1}", Y[1, 0], Y[0, 0]));
//}
for (int iter = NumberIterations; iter > 0; iter--)
{
var A = new SafeMatrix(varMagnitudes.Count, 3);
var X = new SafeMatrix(varMagnitudes.Count, 1);
for (int index = 0; index < varMagnitudes.Count; index++)
{
double t = varTimes[index];
double difference = ComputeModelValue(t) - varMagnitudes[index];
X[index, 0] = -difference;
double GAMMA = 1 - Math.Exp(1 - Math.Cosh((t - T0) / D));
double GAMMA_G = Math.Pow(GAMMA, G);
A[index, 0] = -GAMMA_G * Math.Log(G); // G
A[index, 1] = (G / D) * Math.Pow(GAMMA, G - 1) * Math.Exp(1 - Math.Cosh((t - T0) / D)) * Math.Sinh((t - T0) / D); // T0
A[index, 2] = A[index, 1] * (t - T0) / D; // D
}
SafeMatrix a_T = A.Transpose();
SafeMatrix aa = a_T * A;
SafeMatrix aa_inv = aa.Inverse();
SafeMatrix Y = (aa_inv * a_T) * X;
if (minCorr[0] > Math.Abs(Y[0, 0])) minCorr[0] = Y[0, 0];
if (minCorr[1] > Math.Abs(Y[1, 0])) minCorr[1] = Y[1, 0];
if (minCorr[2] > Math.Abs(Y[2, 0])) minCorr[2] = Y[2, 0];
//if (Y[1, 0] > 0.0001) Y[1, 0] = 0.0001;
//if (Y[1, 0] < -0.0001) Y[1, 0] = -0.0001;
T0 += Y[1, 0];
Trace.WriteLine(string.Format("T0 Corr: {0}; ", Y[1, 0]));
//if (Y[2, 0] > 0.01) Y[2, 0] = 0.01;
//if (Y[2, 0] < -0.01) Y[2, 0] = -0.01;
D += Y[2, 0];
if (D < 0) D = 0.001;
// Enforce maximum correction for G of |0.1|. G > 0
//if (Y[0, 0] > 0.01) Y[0, 0] = 0.01;
//if (Y[0, 0] < -0.01) Y[0, 0] = -0.01;
G += Y[0, 0];
if (G < 0) G = 0.001;
}
//Trace.WriteLine(string.Format("{0}; {1}; {2}; {3}; {4}", minCorr[0], minCorr[1], minCorr[2], minCorr[3], minCorr[4]));
Times.Clear();
NormIntensities.Clear();
var residuals = new List<double>();
for (int index = 0; index < varMagnitudes.Count; index++)
{
double t = varTimes[index];
Times.Add(t);
double magVal = ComputeModelValue(t);
double residual = magVal - varMagnitudes[index];
NormIntensities.Add(Math.Pow(10, (10 - magVal)/2.5));
residuals.Add(residual);
}
}
public void Solve(bool useNormalisation, double t0_initialVal)
{
var varTimes = new List <double>();
var varMagnitudes = new List <double>();
double constNorm = double.NaN;
if (!useNormalisation)
{
List <double> medianCalcList = new List <double>(m_CompData);
medianCalcList.Sort();
constNorm = medianCalcList[medianCalcList.Count / 2];
}
C = 1; // Fix C to 1
M0 = FitM0ForT0(t0_initialVal, constNorm) - 1; // Get from known max magnitude of star
for (int i = 0; i < m_NumObs; i++)
{
double mag = M0 - 2.5 * Math.Log10(m_VarData[i] / (!useNormalisation ? constNorm : m_CompData[i]));
if (IsOutlier(i, mag))
{
continue;
}
varTimes.Add(m_Times[i]);
varMagnitudes.Add(mag);
}
if (varMagnitudes.Count < 7)
{
// Not enought data points for solving 5 variables
IsSolved = false;
return;
}
// Starting values
C = 1;
T0 = t0_initialVal; // Get from Kwee van Worden
G = 0.5;
// Get D from solving the equation to D (with other starting values specified)
D = (varTimes[varMagnitudes.Count - 1] - T0) / Acosh(1 - Math.Log(1 - Math.Pow(1 - (varMagnitudes[varMagnitudes.Count - 1] - M0) / C, 1 / G)));
if (double.IsNaN(D) || double.IsInfinity(D))
{
D = 0.1;
}
NumberIterations = 100;
double[] minCorr = new double[] { double.MaxValue, double.MaxValue, double.MaxValue, double.MaxValue, double.MaxValue };
//// Our guess ot T0 is very close, so assume it is contant and solve for G and D
//for (int iter = NumberIterations; iter > 0; iter--)
//{
// var A = new SafeMatrix(varMagnitudes.Count, 2);
// var X = new SafeMatrix(varMagnitudes.Count, 1);
// for (int index = 0; index < varMagnitudes.Count; index++)
// {
// double t = varTimes[index];
// double difference = ComputeModelValue(t) - varMagnitudes[index];
// X[index, 0] = -difference;
// double GAMMA = 1 - Math.Exp(1 - Math.Cosh((t - T0) / D));
// double GAMMA_G = Math.Pow(GAMMA, G);
// A[index, 0] = GAMMA_G * Math.Log(G); // G
// A[index, 1] = -(G / D) * Math.Pow(GAMMA, G - 1) * Math.Exp(1 - Math.Cosh((t - T0) / D)) * Math.Sinh((t - T0) / D) * (t - T0) / D; // D
// }
// SafeMatrix a_T = A.Transpose();
// SafeMatrix aa = a_T * A;
// SafeMatrix aa_inv = aa.Inverse();
// SafeMatrix Y = (aa_inv * a_T) * X;
// D += Y[1, 0];
// if (D < 0) D = 0.001;
// // Enforce maximum correction for G of |0.1|. G > 0
// //if (Y[0, 0] > 0.01) Y[0, 0] = 0.01;
// //if (Y[0, 0] < -0.01) Y[0, 0] = -0.01;
// G += Y[0, 0];
// if (G < 0) G = 0.001;
// Trace.WriteLine(string.Format("D Corr: {0}\t\t G Corr: {1}", Y[1, 0], Y[0, 0]));
//}
for (int iter = NumberIterations; iter > 0; iter--)
{
var A = new SafeMatrix(varMagnitudes.Count, 3);
var X = new SafeMatrix(varMagnitudes.Count, 1);
for (int index = 0; index < varMagnitudes.Count; index++)
{
double t = varTimes[index];
double difference = ComputeModelValue(t) - varMagnitudes[index];
X[index, 0] = -difference;
double GAMMA = 1 - Math.Exp(1 - Math.Cosh((t - T0) / D));
double GAMMA_G = Math.Pow(GAMMA, G);
A[index, 0] = -GAMMA_G *Math.Log(G); // G
A[index, 1] = (G / D) * Math.Pow(GAMMA, G - 1) * Math.Exp(1 - Math.Cosh((t - T0) / D)) * Math.Sinh((t - T0) / D); // T0
A[index, 2] = A[index, 1] * (t - T0) / D; // D
}
SafeMatrix a_T = A.Transpose();
SafeMatrix aa = a_T * A;
SafeMatrix aa_inv = aa.Inverse();
SafeMatrix Y = (aa_inv * a_T) * X;
if (minCorr[0] > Math.Abs(Y[0, 0]))
{
minCorr[0] = Y[0, 0];
}
if (minCorr[1] > Math.Abs(Y[1, 0]))
{
minCorr[1] = Y[1, 0];
}
if (minCorr[2] > Math.Abs(Y[2, 0]))
{
minCorr[2] = Y[2, 0];
}
//if (Y[1, 0] > 0.0001) Y[1, 0] = 0.0001;
//if (Y[1, 0] < -0.0001) Y[1, 0] = -0.0001;
T0 += Y[1, 0];
Trace.WriteLine(string.Format("T0 Corr: {0}; ", Y[1, 0]));
//if (Y[2, 0] > 0.01) Y[2, 0] = 0.01;
//if (Y[2, 0] < -0.01) Y[2, 0] = -0.01;
D += Y[2, 0];
if (D < 0)
{
D = 0.001;
}
// Enforce maximum correction for G of |0.1|. G > 0
//if (Y[0, 0] > 0.01) Y[0, 0] = 0.01;
//if (Y[0, 0] < -0.01) Y[0, 0] = -0.01;
G += Y[0, 0];
if (G < 0)
{
G = 0.001;
}
}
//Trace.WriteLine(string.Format("{0}; {1}; {2}; {3}; {4}", minCorr[0], minCorr[1], minCorr[2], minCorr[3], minCorr[4]));
Times.Clear();
NormIntensities.Clear();
var residuals = new List <double>();
for (int index = 0; index < varMagnitudes.Count; index++)
{
double t = varTimes[index];
Times.Add(t);
double magVal = ComputeModelValue(t);
double residual = magVal - varMagnitudes[index];
NormIntensities.Add(Math.Pow(10, (10 - magVal) / 2.5));
residuals.Add(residual);
}
}
public static SafeMatrix operator *(SafeMatrix A, SafeMatrix B)
{
if (A.ColumnCount != B.RowCount)
throw new ArgumentException("Inner matrix dimensions must agree.");
SafeMatrix C = new SafeMatrix(A.RowCount, B.ColumnCount);
for (int i = 0; i < A.RowCount; i++)
{
for (int j = 0; j < B.ColumnCount; j++)
{
C.m_Elements[i * C.m_ColumnCount + j] = Dot(A, i, B, j);
}
}
return C;
}