public void TestMulNonSquare()
{
// Arrange
SafeMatrix <Rational> a = new SafeMatrix <Rational>(
new Rational[, ] {
{ R(1), R(2), R(3) },
{ R(2), R(3), R(4) },
{ R(3), R(4), R(5) },
{ R(4), R(5), R(6) }
});
SafeMatrix <Rational> b = new SafeMatrix <Rational>(
new Rational[, ] {
{ R(5), R(6), R(7), R(6) },
{ R(6), R(7), R(8), R(9) },
{ R(7), R(8), R(9), R(10) }
});
// Act
SafeMatrix <Rational> actual = a * b;
// Assert
SafeMatrix <Rational> expected = new SafeMatrix <Rational>(
new Rational[, ] {
{ R(38), R(44), R(50), R(54) },
{ R(56), R(65), R(74), R(79) },
{ R(74), R(86), R(98), R(104) },
{ R(92), R(107), R(122), R(129) }
});
Assert.AreEqual(actual, expected);
}
public void TestSetBlock()
{
// Arrange
SafeMatrix <Rational> a = new SafeMatrix <Rational>(
new Rational[, ] {
{ R(1), R(2), R(3) },
{ R(2), R(3), R(4) },
{ R(3), R(4), R(5) },
{ R(4), R(5), R(6) }
});
SafeMatrix <Rational> block = new SafeMatrix <Rational>(
new Rational[, ] {
{ R(0), R(0) },
{ R(0), R(0) }
});
// Act
a.SetBlock(2, 1, block);
// Assert
SafeMatrix <Rational> expected = new SafeMatrix <Rational>(
new Rational[, ] {
{ R(1), R(2), R(3) },
{ R(2), R(3), R(4) },
{ R(3), R(0), R(0) },
{ R(4), R(0), R(0) }
});
Assert.AreEqual(a, expected);
}
public void TestAdd()
{
// Arrange
SafeMatrix <Rational> a = new SafeMatrix <Rational>(
new Rational[, ] {
{ R(1), R(2), R(3) },
{ R(2), R(3), R(4) },
{ R(3), R(4), R(5) }
});
SafeMatrix <Rational> b = new SafeMatrix <Rational>(
new Rational[, ] {
{ R(4), R(5), R(6) },
{ R(5), R(6), R(7) },
{ R(6), R(7), R(8) }
});
// Act
SafeMatrix <Rational> actual = a + b;
// Assert
SafeMatrix <Rational> expected = new SafeMatrix <Rational>(
new Rational[, ] {
{ R(5), R(7), R(9) },
{ R(7), R(9), R(11) },
{ R(9), R(11), R(13) }
});
Assert.AreEqual(actual, expected);
Assert.AreEqual(actual - b, a);
}
/// <summary>
/// Warning: This method is not thread safe!
/// </summary>
public static SafeMatrix SolveLinearSystemFast(SafeMatrix A, SafeMatrix X)
{
if (A.RowCount > 35 * 35)
{
throw new InvalidOperationException("Not a PSF fitting linear system.");
}
if (s_NumVariables != A.ColumnCount)
{
LinearSystemFastInitialiseSolution(A.ColumnCount, 35 * 35);
s_NumVariables = A.ColumnCount;
}
double[] a = A.GetElements();
double[] x = X.GetElements();
double[] y = new double[A.ColumnCount * X.ColumnCount];
SolveLinearSystemFast(a, x, A.RowCount, y);
SafeMatrix rv = new SafeMatrix(X.RowCount, X.ColumnCount);
rv.SetElements(y);
return(rv);
}
public void Calibrate()
{
if (m_PixelPos.Count < 3)
{
throw new InvalidOperationException("Cannot get a fit from less than 3 points.");
}
var A = new SafeMatrix(m_PixelPos.Count, 2);
var X = new SafeMatrix(m_PixelPos.Count, 1);
for (int i = 0; i < m_PixelPos.Count; i++)
{
A[i, 0] = m_Wavelengths[i];
A[i, 1] = 1;
X[i, 0] = m_PixelPos[i];
}
SafeMatrix a_T = A.Transpose();
SafeMatrix aa = a_T * A;
SafeMatrix aa_inv = aa.Inverse();
SafeMatrix bx = (aa_inv * a_T) * X;
m_A = (float)bx[0, 0];
m_B = (float)bx[1, 0];
}
protected override void ConfigureObservation(SafeMatrix A, SafeMatrix AReverse, int i)
{
A[i, 0] = m_StarPairs[i].x;
A[i, 1] = m_StarPairs[i].y;
A[i, 2] = 1;
AReverse[i, 0] = m_StarPairs[i].ExpectedXTang;
AReverse[i, 1] = m_StarPairs[i].ExpectedYTang;
AReverse[i, 2] = 1;
}
private void CalibrateNonLinearMagModelInternal(List <AbsFluxSpectra> standards)
{
m_MagnitudeCoefficients.Clear();
m_ExtinctionCoefficients.Clear();
m_SensitivityCoefficients.Clear();
m_Wavelengths.Clear();
for (int i = 0; i < standards[0].DeltaMagnitiudes.Count; i++)
{
var A = new SafeMatrix(standards.Count, 3);
var X = new SafeMatrix(standards.Count, 1);
bool containsNaNs = false;
// MagAbs = A * MagInst + B * X + C = Km * MagInst + Ke * X + Ks
for (int j = 0; j < standards.Count; j++)
{
A[j, 0] = -2.5 * Math.Log10(standards[j].ObservedFluxes[i] / standards[j].InputFile.Exposure);
A[j, 1] = standards[j].InputFile.AirMass;
A[j, 2] = 1;
double absMag = -2.5 * Math.Log10(standards[j].AbsoluteFluxes[i]);
X[j, 0] = absMag;
if (double.IsNaN(absMag) || double.IsNaN(A[j, 0]))
{
containsNaNs = true;
}
}
m_Wavelengths.Add(standards[0].ResolvedWavelengths[i]);
if (!containsNaNs)
{
SafeMatrix a_T = A.Transpose();
SafeMatrix aa = a_T * A;
SafeMatrix aa_inv = aa.Inverse();
SafeMatrix bx = (aa_inv * a_T) * X;
float km = (float)bx[0, 0];
float ke = (float)bx[1, 0];
float ks = (float)bx[2, 0];
m_MagnitudeCoefficients.Add(km);
m_ExtinctionCoefficients.Add(ke);
m_SensitivityCoefficients.Add(ks);
}
else
{
m_MagnitudeCoefficients.Add(double.NaN);
m_ExtinctionCoefficients.Add(double.NaN);
m_SensitivityCoefficients.Add(double.NaN);
}
}
}
private void CalibrateLinearModelInternal(List <AbsFluxSpectra> standards)
{
m_MagnitudeCoefficients.Clear();
m_ExtinctionCoefficients.Clear();
m_SensitivityCoefficients.Clear();
m_Wavelengths.Clear();
for (int i = 0; i < standards[0].DeltaMagnitiudes.Count; i++)
{
var A = new SafeMatrix(standards.Count, 2);
var X = new SafeMatrix(standards.Count, 1);
bool containsNaNs = false;
// Delta_Mag = A * X + B = Ke * X + Ks
for (int j = 0; j < standards.Count; j++)
{
A[j, 0] = standards[j].InputFile.AirMass;
A[j, 1] = 1;
double deltaMag = standards[j].DeltaMagnitiudes[i];
X[j, 0] = deltaMag;
if (double.IsNaN(deltaMag))
{
containsNaNs = true;
}
}
m_Wavelengths.Add(standards[0].ResolvedWavelengths[i]);
if (!containsNaNs)
{
SafeMatrix a_T = A.Transpose();
SafeMatrix aa = a_T * A;
SafeMatrix aa_inv = aa.Inverse();
SafeMatrix bx = (aa_inv * a_T) * X;
float ke = (float)bx[0, 0];
float ks = (float)bx[1, 0];
m_MagnitudeCoefficients.Add(1);
m_ExtinctionCoefficients.Add(ke);
m_SensitivityCoefficients.Add(ks);
}
else
{
m_MagnitudeCoefficients.Add(double.NaN);
m_ExtinctionCoefficients.Add(double.NaN);
m_SensitivityCoefficients.Add(double.NaN);
}
}
}
public static SafeMatrix SolveLinearSystem(SafeMatrix A, SafeMatrix X)
{
double[] a = A.GetElements();
double[] x = X.GetElements();
double[] y = new double[A.ColumnCount * X.ColumnCount];
SolveLinearSystem(a, A.RowCount, A.ColumnCount, x, X.RowCount, X.ColumnCount, y);
SafeMatrix rv = new SafeMatrix(X.RowCount, X.ColumnCount);
rv.SetElements(y);
return(rv);
}
public void TestGetBlockShouldFailIndexOutOfBounds()
{
// Arrange
SafeMatrix <Rational> a = new SafeMatrix <Rational>(
new Rational[, ] {
{ R(1), R(2), R(3) },
{ R(2), R(3), R(4) },
{ R(3), R(4), R(5) },
{ R(4), R(5), R(6) }
});
// Act & Assert
Assert.ThrowsException <IndexOutOfRangeException>(() => a.GetBlock(2, 1, 3, 3));
}
// Third Order (10 params): Z = A * x * x * x + B * x * x * y + C * y * y * x + D * y * y * y + E * x * x + F * x * y + G * y * y + H * x + I * y + J
private void SolveThirdOrderFit()
{
SafeMatrix A = new SafeMatrix(m_ZValues.Count, 10);
SafeMatrix X = new SafeMatrix(m_ZValues.Count, 1);
for (int i = 0; i < m_ZValues.Count; i++)
{
A[i, 0] = m_XXXValues[i];
A[i, 1] = m_XXYValues[i];
A[i, 2] = m_XYYValues[i];
A[i, 3] = m_YYYValues[i];
A[i, 4] = m_XXValues[i];
A[i, 5] = m_XYValues[i];
A[i, 6] = m_YYValues[i];
A[i, 7] = m_XValues[i];
A[i, 8] = m_YValues[i];
A[i, 9] = 1;
X[i, 0] = m_ZValues[i];
}
SafeMatrix a_T = A.Transpose();
SafeMatrix aa = a_T * A;
SafeMatrix aa_inv = aa.Inverse();
SafeMatrix bx = (aa_inv * a_T) * X;
m_ThirdA = bx[0, 0];
m_ThirdB = bx[1, 0];
m_ThirdC = bx[2, 0];
m_ThirdD = bx[3, 0];
m_ThirdE = bx[4, 0];
m_ThirdF = bx[5, 0];
m_ThirdG = bx[6, 0];
m_ThirdH = bx[7, 0];
m_ThirdI = bx[8, 0];
m_ThirdJ = bx[9, 0];
m_Residuals.Clear();
double sumResidualsSQ = 0;
for (int i = 0; i < m_ZValues.Count; i++)
{
double res = m_ZValues[i] - ComputeThirdOrderValue(m_XValues[i], m_YValues[i]);
m_Residuals.Add(res);
sumResidualsSQ += res * res;
}
m_ThirdVariance = Math.Sqrt(sumResidualsSQ / (m_ZValues.Count - 1));
}
protected override void ReadSolvedReversedConstants(SafeMatrix bx, SafeMatrix by)
{
Const_A1 = bx[0, 0];
Const_B1 = bx[1, 0];
Const_C1 = bx[2, 0];
Const_D1 = bx[3, 0];
Const_E1 = bx[4, 0];
Const_F1 = bx[5, 0];
Const_G1 = by[0, 0];
Const_H1 = by[1, 0];
Const_K1 = by[2, 0];
Const_L1 = by[3, 0];
Const_M1 = by[4, 0];
Const_N1 = by[5, 0];
}
protected override bool ReadSolvedConstants(SafeMatrix bx, SafeMatrix by)
{
Const_A = bx[0, 0];
Const_B = bx[1, 0];
Const_C = bx[2, 0];
Const_D = bx[3, 0];
Const_E = bx[4, 0];
Const_F = bx[5, 0];
Const_G = by[0, 0];
Const_H = by[1, 0];
Const_K = by[2, 0];
Const_L = by[3, 0];
Const_M = by[4, 0];
Const_N = by[5, 0];
return(true);
}
public void TestMulShouldFailIncompatibleDimensions()
{
// Arrange
SafeMatrix <Rational> a = new SafeMatrix <Rational>(
new Rational[, ] {
{ R(1), R(2), R(3) },
{ R(2), R(3), R(4) },
{ R(3), R(4), R(5) }
});
SafeMatrix <Rational> b = new SafeMatrix <Rational>(
new Rational[, ] {
{ R(5), R(6), R(7), R(6) },
{ R(6), R(7), R(8), R(9) }
});
// Act & Assert
Assert.ThrowsException <ArgumentException>(() => a * b);
}
public void TestSubShouldFailDifferentDimensions()
{
// Arrange
SafeMatrix <Rational> a = new SafeMatrix <Rational>(
new Rational[, ] {
{ R(1), R(2), R(3) },
{ R(2), R(3), R(4) },
{ R(3), R(4), R(5) }
});
SafeMatrix <Rational> b = new SafeMatrix <Rational>(
new Rational[, ] {
{ R(4), R(5), R(6) },
{ R(5), R(6), R(7) }
});
// Act & Assert
Assert.ThrowsException <ArgumentException>(() => a - b);
}
protected override bool ReadSolvedConstants(SafeMatrix bx, SafeMatrix by)
{
Const_A = bx[0, 0];
Const_B = bx[1, 0];
Const_C = bx[2, 0];
Const_D = by[0, 0];
Const_E = by[1, 0];
Const_F = by[2, 0];
Const_A1 = Const_E / (Const_E * Const_A - Const_B * Const_D);
Const_B1 = -Const_B / (Const_E * Const_A - Const_B * Const_D);
Const_C1 = (Const_B * Const_F - Const_C * Const_E) / (Const_E * Const_A - Const_B * Const_D);
Const_D1 = Const_D / (Const_B * Const_D - Const_A * Const_E);
Const_E1 = -Const_A / (Const_B * Const_D - Const_A * Const_E);
Const_F1 = (Const_A * Const_F - Const_C * Const_D) / (Const_B * Const_D - Const_A * Const_E);
return(false);
}
private static void SafeMatrixDemo()
{
Console.WriteLine("-------MATRIX OF COMPLEX NUMBERS DEMO-------");
SafeMatrix <Complex> A = Utils.RandomMatrix(3, 3, Utils.RandomComplex);
SafeMatrix <Complex> B = Utils.RandomMatrix(3, 3, Utils.RandomComplex);
Console.WriteLine("A:");
Console.WriteLine(A);
Console.WriteLine();
Console.WriteLine("B:");
Console.WriteLine(B);
Console.WriteLine();
Console.WriteLine("A + B:");
Console.WriteLine(A + B);
Console.WriteLine();
Console.WriteLine("A - B:");
Console.WriteLine(A - B);
Console.WriteLine();
Console.WriteLine("A * B:");
Console.WriteLine(A * B);
Console.WriteLine();
Complex scalar = Utils.RandomComplex(9, 9);
Console.WriteLine($"A * {scalar}:");
Console.WriteLine(A * scalar);
Console.WriteLine();
Console.WriteLine($"B * {scalar}:");
Console.WriteLine(B * scalar);
Console.WriteLine();
Console.WriteLine("A transpose:");
Console.WriteLine(A.Transpose());
Console.WriteLine();
Console.WriteLine("B transpose:");
Console.WriteLine(B.Transpose());
Console.WriteLine();
}
public void TestGetBlock()
{
// Arrange
SafeMatrix <Rational> a = new SafeMatrix <Rational>(
new Rational[, ] {
{ R(1), R(2), R(3) },
{ R(2), R(3), R(4) },
{ R(3), R(4), R(5) },
{ R(4), R(5), R(6) }
});
// Act
SafeMatrix <Rational> actual = a.GetBlock(2, 1, 2, 2);
// Assert
SafeMatrix <Rational> expected = new SafeMatrix <Rational>(
new Rational[, ] {
{ R(4), R(5) },
{ R(5), R(6) }
});
Assert.AreEqual(actual, expected);
}
// First Order (3 params): Z = A * x + B * y + C
private void SolveFirstOrderFit()
{
SafeMatrix A = new SafeMatrix(m_ZValues.Count, 3);
SafeMatrix X = new SafeMatrix(m_ZValues.Count, 1);
for (int i = 0; i < m_ZValues.Count; i++)
{
A[i, 0] = m_XValues[i];
A[i, 1] = m_YValues[i];
A[i, 2] = 1;
X[i, 0] = m_ZValues[i];
}
SafeMatrix a_T = A.Transpose();
SafeMatrix aa = a_T * A;
SafeMatrix aa_inv = aa.Inverse();
SafeMatrix bx = (aa_inv * a_T) * X;
m_FirstA = bx[0, 0];
m_FirstB = bx[1, 0];
m_FirstC = bx[2, 0];
m_Residuals.Clear();
double sumResidualsSQ = 0;
for (int i = 0; i < m_ZValues.Count; i++)
{
double res = m_ZValues[i] - ComputeFirstOrderValue(m_XValues[i], m_YValues[i]);
m_Residuals.Add(res);
sumResidualsSQ += res * res;
}
m_FirstVariance = Math.Sqrt(sumResidualsSQ / (m_ZValues.Count - 1));
}
internal void GenerateBackgroundModelParameters(int order, double depth)
{
Random rnd = new Random((int)DateTime.Now.Ticks);
if (order == 1)
{
// z = ax + by + c
int dist = rnd.Next(m_X0, m_X0 + (int)(1.2 * m_Radius));
int d2 = rnd.Next((int)depth / 2, (int)depth);
SafeMatrix A = new SafeMatrix(3, 3);
SafeMatrix X = new SafeMatrix(3, 1);
A[0, 0] = m_X0; A[0, 1] = m_Y0; A[0, 2] = 1; X[0, 0] = depth;
A[1, 0] = m_X0 + dist / 2; A[1, 1] = m_Y0 + dist / 3; A[1, 2] = 1; X[1, 0] = d2;
A[2, 0] = m_X0 + dist; A[2, 1] = m_Y0 + dist / 2; A[2, 2] = 1; X[2, 0] = 0;
SafeMatrix a_T = A.Transpose();
SafeMatrix aa = a_T * A;
SafeMatrix aa_inv = aa.Inverse();
SafeMatrix bx = (aa_inv * a_T) * X;
this.A = bx[0, 0];
B = bx[1, 0];
C = bx[2, 0];
}
else if (order == 2)
{
// z = axx + bxy + cyy + dx + ey + f
int[] xArr = new int[6];
int[] yArr = new int[6];
double[] zArr = new double[6];
xArr[0] = m_X0; yArr[0] = m_Y0; zArr[0] = depth;
xArr[1] = m_X0 + m_Radius; yArr[1] = m_Y0 + m_Radius / 3; zArr[1] = 0;
for (int i = 2; i < 6; i++)
{
xArr[i] = rnd.Next(m_X0, m_X0 + (int)(1.2 * m_Radius));
yArr[i] = rnd.Next(m_Y0, m_Y0 + (int)(0.6 * m_Radius));
zArr[i] = rnd.Next(0, (int)depth);
}
// Start with an approximation
// z = axx + + cyy + + f
SafeMatrix A = new SafeMatrix(3, 3);
SafeMatrix X = new SafeMatrix(3, 1);
for (int i = 0; i < 3; i++)
{
A[i, 0] = xArr[i] * xArr[i];
A[i, 1] = yArr[i] * yArr[i];
A[i, 2] = 1;
X[i, 0] = zArr[i];
}
SafeMatrix a_T = A.Transpose();
SafeMatrix aa = a_T * A;
SafeMatrix aa_inv = aa.Inverse();
SafeMatrix bx = (aa_inv * a_T) * X;
this.A = bx[0, 0];
C = bx[1, 0];
F = bx[2, 0];
B = 0;
D = 0;
E = 0;
/*
* A = new SafeMatrix(6, 6);
* X = new SafeMatrix(6, 1);
*
* for (int i = 0; i < 6; i++)
* {
* A[i, 0] = xArr[i] * xArr[i];
* A[i, 1] = xArr[i] * yArr[i];
* A[i, 2] = yArr[i] * yArr[i];
* A[i, 3] = xArr[i];
* A[i, 4] = yArr[i];
* A[i, 5] = 1;
* X[i, 0] = zArr[i];
* }
*
* a_T = A.Transpose();
* aa = a_T * A;
* aa_inv = aa.Inverse();
* bx = (aa_inv * a_T) * X;
*
* m_A = bx[0, 0];
* m_B = bx[1, 0];
* m_C = bx[2, 0];
* m_D = bx[3, 0];
* m_E = bx[4, 0];
* m_F = bx[5, 0];
*/
}
else if (order == 3)
{
// z = axxx + bxxy + cxyy + dyyy + exx + fxy + gyy + hx + iy + j
int[] xArr = new int[10];
int[] yArr = new int[10];
double[] zArr = new double[10];
xArr[0] = m_X0; yArr[0] = m_Y0; zArr[0] = depth;
xArr[1] = m_X0 + m_Radius; yArr[1] = m_Y0 + m_Radius / 3; zArr[1] = 0;
for (int i = 2; i < 6; i++)
{
xArr[i] = rnd.Next(m_X0, m_X0 + (int)(1.2 * m_Radius));
yArr[i] = rnd.Next(m_Y0, m_Y0 + (int)(0.6 * m_Radius));
zArr[i] = rnd.Next(0, (int)depth);
}
// Start with an approximation
// z = axxx + + dyyy + + fxy + + j
SafeMatrix A = new SafeMatrix(4, 4);
SafeMatrix X = new SafeMatrix(4, 1);
for (int i = 0; i < 4; i++)
{
A[i, 0] = xArr[i] * xArr[i] * xArr[i];
A[i, 1] = yArr[i] * yArr[i] * yArr[i];
A[i, 2] = xArr[i] * yArr[i];
A[i, 3] = 1;
X[i, 0] = zArr[i];
}
SafeMatrix a_T = A.Transpose();
SafeMatrix aa = a_T * A;
SafeMatrix aa_inv = aa.Inverse();
SafeMatrix bx = (aa_inv * a_T) * X;
this.A = bx[0, 0];
D = bx[1, 0];
F = bx[2, 0];
J = bx[3, 0];
B = 0;
C = 0;
E = 0;
G = 0;
H = 0;
I = 0;
}
}
private void CalculateGagnitudeFit(Dictionary <IStar, double> measurements, double fixedColourCoeff)
{
List <MagFitEntry> datapoints = new List <MagFitEntry>();
foreach (IStar star in measurements.Keys)
{
UCAC4Entry ucac4 = (UCAC4Entry)star;
if (!double.IsNaN(ucac4.Mag_r) && Math.Abs(ucac4.Mag_r) > 0.00001 && !double.IsNaN(ucac4.MagB) && !double.IsNaN(ucac4.MagV))
{
datapoints.Add(new MagFitEntry()
{
APASS_Sloan_r = ucac4.Mag_r,
APASS_BV_Colour = ucac4.MagB - ucac4.MagV,
MedianIntensity = measurements[star],
MedianIntensityError = 0.05 * measurements[star]
});
}
}
float FIXED_COLOUR_COEFF = (float)fixedColourCoeff;
for (int i = 0; i < datapoints.Count; i++)
{
datapoints[i].InstrMag = -2.5 * Math.Log10(datapoints[i].MedianIntensity) + 32 - datapoints[i].APASS_BV_Colour * FIXED_COLOUR_COEFF;
datapoints[i].InstrMagErr = Math.Abs(-2.5 * Math.Log10((datapoints[i].MedianIntensity + datapoints[i].MedianIntensityError) / datapoints[i].MedianIntensity));
}
datapoints = datapoints.Where(x => !double.IsNaN(x.InstrMag) && x.InstrMagErr < 0.2).ToList();
if (datapoints.Count < 4)
{
return;
}
double variance = 0;
double Ka = 0;
double Kb = 0;
int MAX_ITTER = 2;
for (int itt = 0; itt <= MAX_ITTER; itt++)
{
SafeMatrix A = new SafeMatrix(datapoints.Count, 2);
SafeMatrix X = new SafeMatrix(datapoints.Count, 1);
int idx = 0;
for (int i = 0; i < datapoints.Count; i++)
{
A[idx, 0] = datapoints[i].InstrMag;
A[idx, 1] = 1;
X[idx, 0] = datapoints[i].APASS_Sloan_r;
idx++;
}
SafeMatrix a_T = A.Transpose();
SafeMatrix aa = a_T * A;
SafeMatrix aa_inv = aa.Inverse();
SafeMatrix bx = (aa_inv * a_T) * X;
Ka = bx[0, 0];
Kb = bx[1, 0];
double resSum = 0;
for (int i = 0; i < datapoints.Count; i++)
{
double computedMag = Ka * datapoints[i].InstrMag + Kb;
double diff = computedMag - datapoints[i].APASS_Sloan_r;
resSum += diff * diff;
datapoints[i].Residual = diff;
}
variance = Math.Sqrt(resSum / datapoints.Count);
if (itt < MAX_ITTER)
{
datapoints.RemoveAll(x => Math.Abs(x.Residual) > 2 * variance || Math.Abs(x.Residual) > 0.2);
}
}
Trace.WriteLine(string.Format("r' + {3} * (B-V) + = {0} * M + {1} +/- {2}", Ka.ToString("0.0000"), Kb.ToString("0.0000"), variance.ToString("0.00"), FIXED_COLOUR_COEFF.ToString("0.00000")));
}
protected abstract void ConfigureObservation(SafeMatrix A, SafeMatrix AReverse, int i);
private bool LeastSquareSolve(double ra0Deg, double de0Deg, int minNumberOfStars)
{
int[] NUM_CONSTANTS = new int[] { 3, 6, 10 };
SafeMatrix A = new SafeMatrix(m_StarPairs.Count, NUM_CONSTANTS[(int)m_FitOrder]);
SafeMatrix X = new SafeMatrix(m_StarPairs.Count, 1);
SafeMatrix Y = new SafeMatrix(m_StarPairs.Count, 1);
SafeMatrix AReverse = new SafeMatrix(m_StarPairs.Count, NUM_CONSTANTS[(int)m_FitOrder]);
SafeMatrix XReverse = new SafeMatrix(m_StarPairs.Count, 1);
SafeMatrix YReverse = new SafeMatrix(m_StarPairs.Count, 1);
int numStars = 0;
for (int i = 0; i < m_StarPairs.Count; i++)
{
m_StarPairs[i].FitInfo.UsedInSolution = false;
if (m_StarPairs[i].FitInfo.ExcludedForHighResidual)
{
continue;
}
numStars++;
m_StarPairs[i].FitInfo.UsedInSolution = true;
ConfigureObservation(A, AReverse, i);
X[i, 0] = m_StarPairs[i].ExpectedXTang;
Y[i, 0] = m_StarPairs[i].ExpectedYTang;
XReverse[i, 0] = m_StarPairs[i].x;
YReverse[i, 0] = m_StarPairs[i].y;
}
// Insufficient stars to solve the plate
if (numStars < minNumberOfStars)
{
if (TangraConfig.Settings.TraceLevels.PlateSolving.TraceVerbose())
{
Debug.WriteLine(string.Format("Insufficient number of stars to do a fit. At least {0} stars requested.", minNumberOfStars));
}
return(false);
}
SafeMatrix a_T = A.Transpose();
SafeMatrix aa = a_T * A;
SafeMatrix aa_inv = aa.Inverse();
SafeMatrix bx = (aa_inv * a_T) * X;
SafeMatrix by = (aa_inv * a_T) * Y;
if (ReadSolvedConstants(bx, by))
{
a_T = AReverse.Transpose();
aa = a_T * AReverse;
aa_inv = aa.Inverse();
bx = (aa_inv * a_T) * XReverse;
by = (aa_inv * a_T) * YReverse;
ReadSolvedReversedConstants(bx, by);
}
double residualSum = 0;
double residualSumArcSecRA = 0;
double residualSumArcSecDE = 0;
int numResiduals = 0;
var absResRAArcSec = new List <double>();
var absResDEArcSec = new List <double>();
for (int i = 0; i < m_StarPairs.Count; i++)
{
double computedXTang, computedYTang;
GetTangentCoordsFromImageCoords(m_StarPairs[i].x, m_StarPairs[i].y, out computedXTang, out computedYTang);
m_StarPairs[i].FitInfo.ResidualXTang = m_StarPairs[i].ExpectedXTang - computedXTang;
m_StarPairs[i].FitInfo.ResidualYTang = m_StarPairs[i].ExpectedYTang - computedYTang;
double raComp, deComp;
TangentPlane.TangentToCelestial(computedXTang, computedYTang, ra0Deg, de0Deg, out raComp, out deComp);
m_StarPairs[i].FitInfo.ResidualRAArcSec = 3600.0 * AngleUtility.Elongation(m_StarPairs[i].RADeg, 0, raComp, 0);
m_StarPairs[i].FitInfo.ResidualDEArcSec = 3600.0 * AngleUtility.Elongation(0, m_StarPairs[i].DEDeg, 0, deComp);
if (!m_StarPairs[i].FitInfo.UsedInSolution)
{
continue;
}
numResiduals++;
residualSum += Math.Abs(m_StarPairs[i].FitInfo.ResidualXTang * m_StarPairs[i].FitInfo.ResidualYTang);
residualSumArcSecRA += m_StarPairs[i].FitInfo.ResidualRAArcSec * m_StarPairs[i].FitInfo.ResidualRAArcSec;
residualSumArcSecDE += m_StarPairs[i].FitInfo.ResidualDEArcSec * m_StarPairs[i].FitInfo.ResidualDEArcSec;
absResRAArcSec.Add(Math.Abs(m_StarPairs[i].FitInfo.ResidualRAArcSec));
absResDEArcSec.Add(Math.Abs(m_StarPairs[i].FitInfo.ResidualDEArcSec));
}
Variance = residualSum / (numResiduals - 1);
VarianceArcSecRA = residualSumArcSecRA / (numResiduals - 1);
VarianceArcSecDE = residualSumArcSecDE / (numResiduals - 1);
// Uncertainty based on Astrometrica's formula of median residual devided by SQRT(num stars)
UncertaintyArcSecRA = absResRAArcSec.Median() / Math.Sqrt(numResiduals);
UncertaintyArcSecDE = absResDEArcSec.Median() / Math.Sqrt(numResiduals);
return(true);
}
protected abstract void ReadSolvedReversedConstants(SafeMatrix bx, SafeMatrix by);
private void RecalculateFit()
{
int totalMeasuredFrames = m_Exports.SelectMany(x => x.Entries).Select(x => x.MeasuredFrames).ToList().Median();
List <TangraExportEntry> datapoints = m_Exports
.SelectMany(x => x.Entries)
.Where(x =>
!float.IsNaN(x.APASS_Sloan_r) && Math.Abs(x.APASS_Sloan_r) > 0.00001 && !float.IsNaN(x.MedianIntensity) &&
!float.IsNaN(x.MedianIntensity) && !float.IsNaN(x.APASS_BV_Colour) && x.MeasuredFrames > 0.95 * totalMeasuredFrames && x.SaturatedFrames == 0)
.ToList();
for (int i = 0; i < datapoints.Count; i++)
{
datapoints[i].InstrMag = -2.5 * Math.Log10(datapoints[i].MedianIntensity) + 32;
datapoints[i].InstrMagErr = Math.Abs(-2.5 * Math.Log10((datapoints[i].MedianIntensity + datapoints[i].MedianIntensityError) / datapoints[i].MedianIntensity));
}
datapoints = datapoints.Where(x => x.InstrMagErr < 0.2).ToList();
if (datapoints.Count < 4)
{
return;
}
double variance = 0;
double Ka = 0;
double Kb = 0;
double Kc = 0;
int MAX_ITTER = 2;
for (int itt = 0; itt <= MAX_ITTER; itt++)
{
SafeMatrix A = new SafeMatrix(datapoints.Count, 3);
SafeMatrix X = new SafeMatrix(datapoints.Count, 1);
int idx = 0;
for (int i = 0; i < datapoints.Count; i++)
{
A[idx, 0] = datapoints[i].InstrMag;
A[idx, 1] = datapoints[i].APASS_BV_Colour;
A[idx, 2] = 1;
X[idx, 0] = datapoints[i].APASS_Sloan_r;
idx++;
}
SafeMatrix a_T = A.Transpose();
SafeMatrix aa = a_T * A;
SafeMatrix aa_inv = aa.Inverse();
SafeMatrix bx = (aa_inv * a_T) * X;
Ka = bx[0, 0];
Kb = bx[1, 0];
Kc = bx[2, 0];
double resSum = 0;
for (int i = 0; i < datapoints.Count; i++)
{
double computedMag = Ka * datapoints[i].InstrMag + Kb * datapoints[i].APASS_BV_Colour + Kc;
double diff = computedMag - datapoints[i].APASS_Sloan_r;
resSum += diff * diff;
datapoints[i].Residual = diff;
}
variance = Math.Sqrt(resSum / datapoints.Count);
if (itt < MAX_ITTER)
{
datapoints.RemoveAll(x => Math.Abs(x.Residual) > 2 * variance || Math.Abs(x.Residual) > 0.2);
}
}
Trace.WriteLine(string.Format("r' = {0} * M + {1} * (B-V) + {2} +/- {3}", Ka.ToString("0.0000"), Kb.ToString("0.0000"), Kc.ToString("0.00"), variance.ToString("0.00")));
if (miColourPlot.Checked)
{
PlotColourFitData(datapoints, Ka, Kb, Kc, variance);
}
}
public FocalLengthFit ComputeFocalLengthFit()
{
if (m_FocalLengthFit != null)
{
return(m_FocalLengthFit);
}
List <DistSolveEntry> entries = new List <DistSolveEntry>();
for (int i = 0; i < m_Pairs.Count; i++)
{
if (!m_Pairs[i].FitInfo.UsedInSolution)
{
continue;
}
if (m_Pairs[i].FitInfo.ExcludedForHighResidual)
{
continue;
}
for (int j = 0; j < m_Pairs.Count; j++)
{
if (i == j)
{
continue;
}
if (!m_Pairs[j].FitInfo.UsedInSolution)
{
continue;
}
if (m_Pairs[j].FitInfo.ExcludedForHighResidual)
{
continue;
}
DistSolveEntry entry = new DistSolveEntry();
entry.DX = Math.Abs(m_Pairs[i].x - m_Pairs[j].x);
entry.DY = Math.Abs(m_Pairs[i].y - m_Pairs[j].y);
entry.StarNo1 = m_Pairs[i].StarNo;
entry.StarNo2 = m_Pairs[j].StarNo;
// NOTE: two ways of computing distances - by vx,vy,vz and Elongation()
//entry.DistRadians = Math.Acos(m_Pairs[i].VX * m_Pairs[j].VX + m_Pairs[i].VY * m_Pairs[j].VY + m_Pairs[i].VZ * m_Pairs[j].VZ);
double elong = AngleUtility.Elongation(m_Pairs[i].RADeg, m_Pairs[i].DEDeg, m_Pairs[j].RADeg, m_Pairs[j].DEDeg);
entry.DistRadians = elong * Math.PI / 180.0;
if (entry.DX == 0 || entry.DY == 0)
{
continue;
}
entries.Add(entry);
}
}
SafeMatrix A = new SafeMatrix(entries.Count, 2);
SafeMatrix X = new SafeMatrix(entries.Count, 1);
int numStars = 0;
foreach (DistSolveEntry entry in entries)
{
A[numStars, 0] = entry.DX * entry.DX;
A[numStars, 1] = entry.DY * entry.DY;
X[numStars, 0] = entry.DistRadians * entry.DistRadians;
numStars++;
}
// Insufficient stars to solve the plate
if (numStars < 3)
{
return(null);
}
SafeMatrix a_T = A.Transpose();
SafeMatrix aa = a_T * A;
SafeMatrix aa_inv = aa.Inverse();
SafeMatrix bx = (aa_inv * a_T) * X;
double a = bx[0, 0];
double b = bx[1, 0];
double residualSum = 0;
int numResiduals = 0;
foreach (DistSolveEntry entry in entries)
{
entry.ResidualRadians = entry.DistRadians - Math.Sqrt(a * entry.DX * entry.DX + b * entry.DY * entry.DY);
entry.ResidualPercent = entry.ResidualRadians * 100.0 / entry.DistRadians;
entry.ResidualArcSec = 3600.0 * entry.ResidualRadians * 180.0 / Math.PI;
numResiduals++;
residualSum += entry.ResidualRadians * entry.ResidualRadians;
}
double variance = Math.Sqrt(residualSum / (numResiduals - 1));
return(new FocalLengthFit(a, b, variance, entries));
}
public static StarMagnitudeFit PerformFit(
IAstrometryController astrometryController,
IVideoController videoController,
int bitPix,
uint maxSignalValue,
FitInfo astrometricFit,
TangraConfig.PhotometryReductionMethod photometryReductionMethod,
TangraConfig.PsfQuadrature psfQuadrature,
TangraConfig.PsfFittingMethod psfFittingMethod,
TangraConfig.BackgroundMethod photometryBackgroundMethod,
TangraConfig.PreProcessingFilter filter,
List <IStar> catalogueStars,
Guid magnitudeBandId,
float encodingGamma,
TangraConfig.KnownCameraResponse reverseCameraResponse,
float?aperture,
float?annulusInnerRadius,
int?annulusMinPixels,
ref float empericalPSFR0)
{
uint saturatedValue = TangraConfig.Settings.Photometry.Saturation.GetSaturationForBpp(bitPix, maxSignalValue);
MeasurementsHelper measurer = new MeasurementsHelper(
bitPix,
photometryBackgroundMethod,
TangraConfig.Settings.Photometry.SubPixelSquareSize,
saturatedValue);
measurer.SetCoreProperties(
annulusInnerRadius ?? TangraConfig.Settings.Photometry.AnnulusInnerRadius,
annulusMinPixels ?? TangraConfig.Settings.Photometry.AnnulusMinPixels,
CorePhotometrySettings.Default.RejectionBackgroundPixelsStdDev,
2 /* TODO: This must be configurable */);
var bgProvider = new BackgroundProvider(videoController);
measurer.GetImagePixelsCallback += new MeasurementsHelper.GetImagePixelsDelegate(bgProvider.measurer_GetImagePixelsCallback);
List <double> intencities = new List <double>();
List <double> magnitudes = new List <double>();
List <double> colours = new List <double>();
List <double> residuals = new List <double>();
List <bool> saturatedFlags = new List <bool>();
List <IStar> stars = new List <IStar>();
List <PSFFit> gaussians = new List <PSFFit>();
List <MagFitRecord> fitRecords = new List <MagFitRecord>();
AstroImage currentAstroImage = videoController.GetCurrentAstroImage(false);
Rectangle osdRectToExclude = astrometryController.OSDRectToExclude;
Rectangle rectToInclude = astrometryController.RectToInclude;
bool limitByInclusion = astrometryController.LimitByInclusion;
int matSize = CorePhotometrySettings.Default.MatrixSizeForCalibratedPhotometry;
double a = double.NaN;
double b = double.NaN;
double c = double.NaN;
int excludedStars = 0;
double empericalFWHM = double.NaN;
try
{
foreach (PlateConstStarPair pair in astrometricFit.AllStarPairs)
{
if (limitByInclusion && !rectToInclude.Contains((int)pair.x, (int)pair.y))
{
continue;
}
if (!limitByInclusion && osdRectToExclude.Contains((int)pair.x, (int)pair.y))
{
continue;
}
IStar star = catalogueStars.Find(s => s.StarNo == pair.StarNo);
if (star == null || double.IsNaN(star.Mag) || star.Mag == 0)
{
continue;
}
uint[,] data = currentAstroImage.GetMeasurableAreaPixels((int)pair.x, (int)pair.y, matSize);
PSFFit fit = new PSFFit((int)pair.x, (int)pair.y);
fit.Fit(data, PSF_FIT_AREA_SIZE);
if (!fit.IsSolved)
{
continue;
}
MagFitRecord record = new MagFitRecord();
record.Star = star;
record.Pair = pair;
record.PsfFit = fit;
record.Saturation = IsSaturated(data, matSize, saturatedValue);
if (!EXCLUDE_SATURATED_STARS || !record.Saturation)
{
fitRecords.Add(record);
}
}
// We need the average R0 if it hasn't been determined yet
if (float.IsNaN(empericalPSFR0))
{
empericalPSFR0 = 0;
foreach (MagFitRecord rec in fitRecords)
{
empericalPSFR0 += (float)rec.PsfFit.R0;
}
empericalPSFR0 /= fitRecords.Count;
}
empericalFWHM = 2 * Math.Sqrt(Math.Log(2)) * empericalPSFR0;
foreach (MagFitRecord record in fitRecords)
{
ImagePixel center = new ImagePixel(255, record.Pair.x, record.Pair.y);
int areaSize = filter == TangraConfig.PreProcessingFilter.NoFilter ? 17 : 19;
int centerX = (int)Math.Round(center.XDouble);
int centerY = (int)Math.Round(center.YDouble);
uint[,] data = currentAstroImage.GetMeasurableAreaPixels(centerX, centerY, areaSize);
uint[,] backgroundPixels = currentAstroImage.GetMeasurableAreaPixels(centerX, centerY, 35);
measurer.MeasureObject(
center,
data,
backgroundPixels,
currentAstroImage.Pixelmap.BitPixCamera,
filter,
photometryReductionMethod,
psfQuadrature,
psfFittingMethod,
aperture != null ? aperture.Value : (float)Aperture(record.PsfFit.FWHM),
record.PsfFit.FWHM,
(float)empericalFWHM,
new FakeIMeasuredObject(record.PsfFit),
null,
null,
false);
double intensity = measurer.TotalReading - measurer.TotalBackground;
if (intensity > 0)
{
var mag = record.Star.GetMagnitudeForBand(magnitudeBandId);
var clr = record.Star.MagJ - record.Star.MagK;
if (!double.IsNaN(mag) && !double.IsNaN(clr) && !double.IsInfinity(mag) && !double.IsInfinity(clr))
{
intencities.Add(intensity);
magnitudes.Add(record.Star.GetMagnitudeForBand(magnitudeBandId));
colours.Add(record.Star.MagJ - record.Star.MagK);
gaussians.Add(record.PsfFit);
stars.Add(record.Star);
saturatedFlags.Add(measurer.HasSaturatedPixels || record.PsfFit.IMax >= measurer.SaturationValue);
}
}
}
// Remove stars with unusual PSF fit radii (once only)
double sum = 0;
for (int i = 0; i < gaussians.Count; i++)
{
sum += gaussians[i].R0;
}
double averageR = sum / gaussians.Count;
residuals.Clear();
sum = 0;
for (int i = 0; i < gaussians.Count; i++)
{
residuals.Add(averageR - gaussians[i].R0);
sum += (averageR - gaussians[i].R0) * (averageR - gaussians[i].R0);
}
double stdDev = Math.Sqrt(sum) / gaussians.Count;
if (EXCLUDE_BAD_RESIDUALS)
{
for (int i = residuals.Count - 1; i >= 0; i--)
{
if (Math.Abs(residuals[i]) > 6 * stdDev)
{
intencities.RemoveAt(i);
magnitudes.RemoveAt(i);
colours.RemoveAt(i);
stars.RemoveAt(i);
gaussians.RemoveAt(i);
saturatedFlags.RemoveAt(i);
}
}
}
double maxResidual = Math.Max(0.1, TangraConfig.Settings.Photometry.MaxResidualStellarMags);
for (int itter = 1; itter <= MAX_ITERR; itter++)
{
residuals.Clear();
SafeMatrix A = new SafeMatrix(intencities.Count, 3);
SafeMatrix X = new SafeMatrix(intencities.Count, 1);
int idx = 0;
for (int i = 0; i < intencities.Count; i++)
{
A[idx, 0] = magnitudes[i];
A[idx, 1] = colours[i];
A[idx, 2] = 1;
X[idx, 0] = -2.5 * Math.Log10(intencities[i]);
idx++;
}
SafeMatrix a_T = A.Transpose();
SafeMatrix aa = a_T * A;
SafeMatrix aa_inv = aa.Inverse();
SafeMatrix bx = (aa_inv * a_T) * X;
double Ka = bx[0, 0];
double Kb = bx[1, 0];
double Kc = bx[2, 0];
// -2.5 * a * Log(Median-Intensity) = A * Mv + B * Mjk + C - b
// -2.5 * Log(Median-Intensity) = Ka * Mv + Kb * Mjk + Kc
// Mv = -2.5 * a * Log(Median-Intensity) - b * Mjk - c
a = 1 / Ka;
b = -Kb / Ka;
c = -Kc / Ka;
int starsExcludedThisTime = 0;
if (EXCLUDE_BAD_RESIDUALS)
{
List <int> indexesToRemove = new List <int>();
for (int i = 0; i < intencities.Count; i++)
{
double computed = a * -2.5 * Math.Log10(intencities[i]) + b * colours[i] + c;
double diff = Math.Abs(computed - magnitudes[i]);
if (itter < MAX_ITERR)
{
if (Math.Abs(diff) > maxResidual)
{
indexesToRemove.Add(i);
}
}
else
{
residuals.Add(diff);
}
}
for (int i = indexesToRemove.Count - 1; i >= 0; i--)
{
int idxToRemove = indexesToRemove[i];
intencities.RemoveAt(idxToRemove);
magnitudes.RemoveAt(idxToRemove);
colours.RemoveAt(idxToRemove);
stars.RemoveAt(idxToRemove);
gaussians.RemoveAt(idxToRemove);
saturatedFlags.RemoveAt(idxToRemove);
excludedStars++;
starsExcludedThisTime++;
}
}
if (starsExcludedThisTime == 0)
{
break;
}
}
}
catch (Exception ex)
{
Trace.WriteLine(ex.ToString());
}
return(new StarMagnitudeFit(
currentAstroImage,
bitPix,
intencities, magnitudes, colours, stars, gaussians, new List <double>(),
saturatedFlags, a, b, c, encodingGamma, reverseCameraResponse, excludedStars, filter, empericalFWHM,
photometryReductionMethod, photometryBackgroundMethod, psfQuadrature, psfFittingMethod, measurer, aperture));
}
protected abstract bool ReadSolvedConstants(SafeMatrix bx, SafeMatrix by);
protected override void ReadSolvedReversedConstants(SafeMatrix bx, SafeMatrix by)
{
}
public ThreeStarAstrometry(AstroPlate image, Dictionary <ImagePixel, IStar> userStarIdentification, int tolerance)
{
if (userStarIdentification.Count != 3)
{
throw new InvalidOperationException();
}
Image = image;
UserStars = userStarIdentification.ToDictionary(kvp => kvp.Key, kvp => kvp.Value);
double a0 = userStarIdentification.Values.Average(x => x.RADeg) * DEG_TO_RAD;
double d0 = userStarIdentification.Values.Average(x => x.DEDeg) * DEG_TO_RAD;
double corr = double.MaxValue;
int attempts = 0;
do
{
SafeMatrix AX = new SafeMatrix(3, 3);
SafeMatrix X = new SafeMatrix(3, 1);
SafeMatrix AY = new SafeMatrix(3, 3);
SafeMatrix Y = new SafeMatrix(3, 1);
int i = 0;
foreach (var pixel in userStarIdentification.Keys)
{
IStar star = userStarIdentification[pixel];
double a = star.RADeg * DEG_TO_RAD;
double d = star.DEDeg * DEG_TO_RAD;
AX[i, 0] = pixel.XDouble;
AX[i, 1] = pixel.YDouble;
AX[i, 2] = 1;
AY[i, 0] = pixel.XDouble;
AY[i, 1] = pixel.YDouble;
AY[i, 2] = 1;
X[i, 0] = Math.Cos(d) * Math.Sin(a - a0) / (Math.Cos(d0) * Math.Cos(d) * Math.Cos(a - a0) + Math.Sin(d0) * Math.Sin(d));
Y[i, 0] = (Math.Cos(d0) * Math.Sin(d) - Math.Cos(d) * Math.Sin(d0) * Math.Cos(a - a0)) / (Math.Sin(d0) * Math.Sin(d) + Math.Cos(d0) * Math.Cos(d) * Math.Cos(a - a0));
i++;
}
SafeMatrix a_T = AX.Transpose();
SafeMatrix aa = a_T * AX;
SafeMatrix aa_inv = aa.Inverse();
SafeMatrix bx = (aa_inv * a_T) * X;
m_A = bx[0, 0];
m_B = bx[1, 0];
m_C = bx[2, 0];
a_T = AY.Transpose();
aa = a_T * AY;
aa_inv = aa.Inverse();
bx = (aa_inv * a_T) * Y;
m_D = bx[0, 0];
m_E = bx[1, 0];
m_F = bx[2, 0];
m_A0Rad = a0;
m_D0Rad = d0;
double ra_c, de_c;
GetRADEFromImageCoords(Image.CenterXImage, Image.CenterYImage, out ra_c, out de_c);
corr = AngleUtility.Elongation(ra_c, de_c, a0 * RAD_TO_DEG, d0 * RAD_TO_DEG) * 3600;
a0 = ra_c * DEG_TO_RAD;
d0 = de_c * DEG_TO_RAD;
attempts++;
}while (corr > tolerance && attempts < MAX_ATTEMPTS);
Success = corr <= tolerance;
}