public Matrix <double> Update(Matrix <double> E, double[,] HE, double[] observations, double[,] obsCoVar, double inflationFactor, double dampning)
{
Matrix <double> XXX = E;
int m_ensembleMembers = XXX.ColumnCount;
int n_elementsinStateVector = XXX.RowCount;
int p_DA_obs = observations.Length;
double tolerance = 1.5;
var M = Matrix <double> .Build;
Vector <double> x = XXX.RowSums().Divide(m_ensembleMembers); //ensemble mean
//substract ensemble mean to get ensemble anomelis (XXX = A)
//MB: a faster way?
for (int i = 0; i < m_ensembleMembers; i++)
{
for (int n = 0; n < n_elementsinStateVector; n++)
{
XXX[n, i] -= x[n];
}
}
//get HA
//double[,] HE = new double[p_DA_obs, m_ensembleMembers];
double[] hx = new double[p_DA_obs]; //mean of y
double[] dytemp = new double[p_DA_obs]; //innovation, dy = y - Hx(p x 1)
for (int i = 0; i < p_DA_obs; i++)
{
for (int j = 0; j < m_ensembleMembers; j++)
{
hx[i] += HE[i, j];
}
hx[i] = hx[i] / m_ensembleMembers;
dytemp[i] = observations[i] - hx[i];
}
Vector <double> dy = Vector <double> .Build.Dense(dytemp);
for (int i = 0; i < p_DA_obs; i++)
{
for (int j = 0; j < m_ensembleMembers; j++)
{
HE[i, j] -= hx[i];// substract mean to get anomalies at h
}
}
Matrix <double> HA = M.DenseOfArray(HE);
for (int i = 0; i < p_DA_obs; i++)
{
double stdObs = Math.Sqrt(obsCoVar[i, i]);//Does not take covar into account.
double uplim = dy[i] + tolerance * stdObs;
double downlim = dy[i] - tolerance * stdObs;
for (int j = 0; j < m_ensembleMembers; j++)
{
if (HE[i, j] > uplim)
{
HE[i, j] -= uplim;
}
else if (HE[i, j] < downlim)
{
HE[i, j] -= downlim;
}
else
{
HE[i, j] = 0;
}
}
}
Matrix <double> HAx = M.DenseOfArray(HE);
Matrix <double> ObsCoVar = M.DenseOfArray(obsCoVar);
KK = new KalmanGain(n_elementsinStateVector, p_DA_obs);
KK.CaclulateGain(XXX, HA, ObsCoVar);
XXX = XXX.Subtract((KK.K.Multiply(HAx)).Multiply(dampning)); //XXX contains updated A
XXX = XXX.Multiply(inflationFactor);
// XXX = XXX.Subtract(KK.K.Multiply(HA));
//Vector<double> Obs = Vector<double>.Build.Dense(observations);
Vector <double> dx = KK.K.Multiply(dampning) * dy;
//add ensemble mean to ensemble anomelis (XXX = A + dx + x)
//MB: a faster way?
for (int i = 0; i < m_ensembleMembers; i++)
{
for (int n = 0; n < n_elementsinStateVector; n++)
{
XXX[n, i] += (x[n] + dx[n]);
}
}
return(XXX);
}
public Matrix <double> Update(Matrix <double> E, double[,] HE, double[] observations, double[,] obsCoVar, double rFactor, double dampning)
{
Matrix <double> XXX = E;
int m_ensembleMembers = XXX.ColumnCount;
int n_elementsinStateVector = XXX.RowCount;
int p_DA_obs = observations.Length;
var M = Matrix <double> .Build;
Vector <double> x = XXX.RowSums().Divide(m_ensembleMembers); //ensemble mean
//substract ensemble mean to get ensemble anomelis (XXX = A)
//MB: a faster way?
for (int i = 0; i < m_ensembleMembers; i++)
{
for (int n = 0; n < n_elementsinStateVector; n++)
{
XXX[n, i] -= x[n];
}
}
//get HA
//double[,] HE = new double[p_DA_obs, m_ensembleMembers];
double[] hx = new double[p_DA_obs]; //mean of y
double[] dytemp = new double[p_DA_obs]; //innovation, dy = y - Hx(p x 1)
for (int i = 0; i < p_DA_obs; i++)
{
for (int j = 0; j < m_ensembleMembers; j++)
{
hx[i] += HE[i, j];
}
hx[i] = hx[i] / m_ensembleMembers;
dytemp[i] = observations[i] - hx[i];
}
Vector <double> dy = Vector <double> .Build.Dense(dytemp);
for (int i = 0; i < p_DA_obs; i++)
{
for (int j = 0; j < m_ensembleMembers; j++)
{
HE[i, j] -= hx[i]; // substract mean to get anomalies at h
}
}
Matrix <double> HA = M.DenseOfArray(HE);
double[] dd = new double[HA.RowCount * HA.ColumnCount];
MathNet.Numerics.Distributions.Normal.Samples(dd, 0, 1.0);
Matrix <double> D = (M.Dense(HA.RowCount, HA.ColumnCount, dd));
Matrix <double> ObsCoVar = M.DenseOfArray(obsCoVar);
D = D.TransposeThisAndMultiply((ObsCoVar.PointwiseSqrt()).Multiply(rFactor)).Transpose();
// from SAKOV's assimilate.m
// D = randn(p, m) * sqrt(r * rfactor);
// % Subtract the ensemble mean from D to ensure that update of the
// % anomalies does not perturb the ensemble mean. This reduces the
// % variance of each sample by a factor of 1 - 1 / m(I think).
// %
// d = mean(D')';
// D = sqrt(m / (m - 1)) * (D - repmat(d, 1, m));
// A = A + K * (D - HA);
KK = new KalmanGain(n_elementsinStateVector, p_DA_obs);
KK.CaclulateGain(XXX, HA, ObsCoVar);
//XXX = XXX.Subtract(KK.K.Multiply(HA.Subtract(D)));//XXX contains updated A
// XXX = XXX.Multiply(inflationFactor);
// XXX = XXX.Subtract(KK.K.Multiply(HA));
//Vector<double> Obs = Vector<double>.Build.Dense(observations);
Vector <double> dx = KK.K.Multiply(dampning) * dy;
for (int i = 0; i < m_ensembleMembers; i++)
{
for (int n = 0; n < n_elementsinStateVector; n++)
{
XXX[n, i] = XXX[n, i] * (x[n] + dx[n]) / x[n];//XXX contains updated A (scaled by change (unchanged std/mean)
}
}
//add ensemble mean to ensemble anomelis (XXX = A + dx + x)
//MB: a faster way?
//Calculate var and K at observed locations h
// double[] VarAtH = new double[p_DA_obs];
//double[] KAtH = new double[p_DA_obs];
/* for (int i = 0; i < p_DA_obs; i++)
* {
* for (int j = 0; j < m_ensembleMembers; j++)
* {
* VarAtH[i] += HE[i, j]* HE[i, j];// substract mean to get anomalies at h . beeeregn var
* }
* VarAtH[i] = VarAtH[i] / (m_ensembleMembers-1);
* //KAtH[i] = VarAtH[i] / (VarAtH[i] + obsCoVar[i,i]);
* }
*/
//sektion for ekstra inflationsstoej.
// double[] dd2 = new double[HA.RowCount * HA.ColumnCount];
// MathNet.Numerics.Distributions.Normal.Samples(dd2, 0, 1.0);
// Matrix<double> D2 = (M.Dense(HA.RowCount, HA.ColumnCount, dd));
//D2 = D2.TransposeThisAndMultiply(ObsCoVar.PointwiseSqrt()).Transpose();lkj
//XXX = XXX.Subtract(KK.K.Multiply(D2));//hvor D2 er støj der fordeles med K som en slags inflation der IKKE påvirker K.
for (int n = 0; n < n_elementsinStateVector; n++)
{
//double tempInflate = (1 + (inflationFactor - 1) * (Math.Abs((KK.K[n, 0] / (KAtH[0]+1)) * dy[0] / (Math.Sqrt(VarAtH[0])+Math.Sqrt(obsCoVar[0, 0])))));//mangler af justify addition of obs std (perhabs som sum of variances) til sidst og Kalman konstanten 1
// tempInflate = 1;
for (int i = 0; i < m_ensembleMembers; i++)
{
//inflate first
//double tempInflate = (1 + (inflationFactor - 1) * (KK.K[n, 0] / KAtH[0]) * (dy[0] / Math.Sqrt(VarAtH[0])));
// XXX[n, i] = XXX[n, i] * tempInflate; // virker kun med en obs .Skift 100 ud med custom factor.
//then recontruct ensamble
XXX[n, i] += (x[n] + dx[n]);
}
}
return(XXX);
}
public Matrix <double> Update(Matrix <double> E, double[,] HE, double[] observations, double[,] obsCoVar, double inflationFactor, double dampning)
{
Matrix <double> XXX = E;
int m_ensembleMembers = XXX.ColumnCount;
int n_elementsinStateVector = XXX.RowCount;
int p_DA_obs = observations.Length;
double stdObs = Math.Sqrt(obsCoVar[0, 0]);// only implemented for a single obs
double tolerance = 1.5;
var M = Matrix <double> .Build;
Vector <double> x = XXX.RowSums().Divide(m_ensembleMembers); //ensemble mean
//substract ensemble mean to get ensemble anomelis (XXX = A)
//MB: a faster way?
for (int i = 0; i < m_ensembleMembers; i++)
{
for (int n = 0; n < n_elementsinStateVector; n++)
{
XXX[n, i] -= x[n];
}
}
//get HA
//double[,] HE = new double[p_DA_obs, m_ensembleMembers];
double[] hx = new double[p_DA_obs]; //mean of y
double[] dytemp = new double[p_DA_obs]; //innovation, dy = y - Hx(p x 1)
for (int i = 0; i < p_DA_obs; i++)
{
for (int j = 0; j < m_ensembleMembers; j++)
{
hx[i] += HE[i, j];
}
hx[i] = hx[i] / m_ensembleMembers;
dytemp[i] = observations[i] - hx[i];
}
Vector <double> dy = Vector <double> .Build.Dense(dytemp);
double uplim = dy[0] + tolerance * stdObs;
double downlim = dy[0] - tolerance * stdObs;
for (int i = 0; i < p_DA_obs; i++)
{
for (int j = 0; j < m_ensembleMembers; j++)
{
HE[i, j] -= hx[i];// substract mean to get anomalies at h
}
}
Matrix <double> HA = M.DenseOfArray(HE);
for (int i = 0; i < p_DA_obs; i++)
{
for (int j = 0; j < m_ensembleMembers; j++)
{
if (HE[i, j] > uplim)
{
HE[i, j] -= uplim;
}
else if (HE[i, j] < downlim)
{
HE[i, j] -= downlim;
}
else
{
HE[i, j] = 0;
}
}
}
Matrix <double> HAx = M.DenseOfArray(HE);
Matrix <double> ObsCoVar = M.DenseOfArray(obsCoVar);
KK = new KalmanGain(n_elementsinStateVector, p_DA_obs);
KK.CaclulateGain(XXX, HA, ObsCoVar);
//calculate dampening from dy and std HE
double[] VarAtH = new double[p_DA_obs];
for (int i = 0; i < p_DA_obs; i++)
{
for (int j = 0; j < m_ensembleMembers; j++)
{
VarAtH[i] += HE[i, j] * HE[i, j]; // substract mean to get anomalies at h . beeeregn var
}
VarAtH[i] = VarAtH[i] / (m_ensembleMembers - 1);
}
double dy_std = Math.Abs(dy[0]) / Math.Sqrt(VarAtH[0]);
if (dy_std > tolerance)
{
// dampning = 1 / (1 + (dy_std - tolerance)*(dy_std - tolerance));// NOTE: Only implementet for single obs loc so far!
}
XXX = XXX.Subtract((KK.K.Multiply(HAx)).Multiply(dampning)); //XXX contains updated A
XXX = XXX.Multiply(inflationFactor);
// XXX = XXX.Subtract(KK.K.Multiply(HA));
//Vector<double> Obs = Vector<double>.Build.Dense(observations);
// Vector<double> dx = KK.K * dy;
//add ensemble mean to ensemble anomelis (XXX = A + dx + x)
//MB: a faster way?
for (int i = 0; i < m_ensembleMembers; i++)
{
for (int n = 0; n < n_elementsinStateVector; n++)
{
//XXX[n, i] += (x[n] + dx[n]);
XXX[n, i] += x[n];
}
}
return(XXX);
}
public Matrix <double> Update(Matrix <double> E, double[,] HE, double[] observations, double[,] obsCoVar, double inflationFactor, double dampning)
{
Matrix <double> XXX = E;
int m_ensembleMembers = XXX.ColumnCount;
int n_elementsinStateVector = XXX.RowCount;
int p_DA_obs = observations.Length;
var M = Matrix <double> .Build;
Vector <double> x = XXX.RowSums().Divide(m_ensembleMembers); //ensemble mean
//substract ensemble mean to get ensemble anomelis (XXX = A)
//MB: a faster way?
for (int i = 0; i < m_ensembleMembers; i++)
{
for (int n = 0; n < n_elementsinStateVector; n++)
{
XXX[n, i] -= x[n];
}
}
//get HA
//double[,] HE = new double[p_DA_obs, m_ensembleMembers];
double[] hx = new double[p_DA_obs]; //mean of y
double[] dytemp = new double[p_DA_obs]; //innovation, dy = y - Hx(p x 1)
for (int i = 0; i < p_DA_obs; i++)
{
for (int j = 0; j < m_ensembleMembers; j++)
{
hx[i] += HE[i, j];
}
hx[i] = hx[i] / m_ensembleMembers;
dytemp[i] = observations[i] - hx[i];
}
Vector <double> dy = Vector <double> .Build.Dense(dytemp);
for (int i = 0; i < p_DA_obs; i++)
{
for (int j = 0; j < m_ensembleMembers; j++)
{
HE[i, j] -= hx[i];// substract mean to get anomalies at h
}
}
Matrix <double> HA = M.DenseOfArray(HE);
double[] dd = new double[HA.RowCount * HA.ColumnCount];
MathNet.Numerics.Distributions.Normal.Samples(dd, 0, 1.0);
Matrix <double> D = (M.Dense(HA.RowCount, HA.ColumnCount, dd));
Matrix <double> ObsCoVar = M.DenseOfArray(obsCoVar);
// A = A + 0.5*K * (HA);
KK = new KalmanGain(n_elementsinStateVector, p_DA_obs);
KK.CaclulateGain(XXX, HA, ObsCoVar);
XXX = XXX.Subtract((KK.K.Multiply(HA)).Multiply(0.5 * dampning));//XXX contains updated A
XXX = XXX.Multiply(inflationFactor);
// XXX = XXX.Subtract(KK.K.Multiply(HA));
//Vector<double> Obs = Vector<double>.Build.Dense(observations);
Vector <double> dx = KK.K.Multiply(dampning) * dy;
//add ensemble mean to ensemble anomelis (XXX = A + dx + x)
//MB: a faster way?
for (int i = 0; i < m_ensembleMembers; i++)
{
for (int n = 0; n < n_elementsinStateVector; n++)
{
XXX[n, i] += (x[n] + dx[n]);
}
}
return(XXX);
}
public Matrix <double> Update(Matrix <double> E, double[,] HE, double[] observations, double[,] obsCoVar, double inflationFactor, double dampning)
{
Matrix <double> XXX = E;
int m_ensembleMembers = XXX.ColumnCount;
int n_elementsinStateVector = XXX.RowCount;
int p_DA_obs = observations.Length;
var M = Matrix <double> .Build;
Vector <double> x = XXX.RowSums().Divide(m_ensembleMembers); //ensemble mean
//substract ensemble mean to get ensemble anomelis (XXX = A)
//MB: a faster way?
for (int i = 0; i < m_ensembleMembers; i++)
{
for (int n = 0; n < n_elementsinStateVector; n++)
{
XXX[n, i] -= x[n];
}
}
//get HA
//double[,] HE = new double[p_DA_obs, m_ensembleMembers];
double[] hx = new double[p_DA_obs]; //mean of y
double[] dytemp = new double[p_DA_obs]; //innovation, dy = y - Hx(p x 1)
for (int i = 0; i < p_DA_obs; i++)
{
for (int j = 0; j < m_ensembleMembers; j++)
{
hx[i] += HE[i, j];
}
hx[i] = hx[i] / m_ensembleMembers;
dytemp[i] = observations[i] - hx[i];
}
Vector <double> dy = Vector <double> .Build.Dense(dytemp);
for (int i = 0; i < p_DA_obs; i++)
{
for (int j = 0; j < m_ensembleMembers; j++)
{
HE[i, j] -= hx[i]; // substract mean to get anomalies at h
}
}
Matrix <double> HA = M.DenseOfArray(HE);
double[] dd = new double[HA.RowCount * HA.ColumnCount];
MathNet.Numerics.Distributions.Normal.Samples(dd, 0, 1.0);
Matrix <double> D = (M.Dense(HA.RowCount, HA.ColumnCount, dd));
Matrix <double> ObsCoVar = M.DenseOfArray(obsCoVar);
D = D.TransposeThisAndMultiply(ObsCoVar.PointwiseSqrt()).Transpose();
// from SAKOV's assimilate.m
// D = randn(p, m) * sqrt(r * rfactor);
// % Subtract the ensemble mean from D to ensure that update of the
// % anomalies does not perturb the ensemble mean. This reduces the
// % variance of each sample by a factor of 1 - 1 / m(I think).
// %
// d = mean(D')';
// D = sqrt(m / (m - 1)) * (D - repmat(d, 1, m));
// A = A + K * (D - HA);
KK = new KalmanGain(n_elementsinStateVector, p_DA_obs);
KK.CaclulateGain(XXX, HA, ObsCoVar);
XXX = XXX.Subtract(KK.K.Multiply(HA.Subtract(D)).Multiply(dampning)); //XXX contains updated A
XXX = XXX.Multiply(inflationFactor);
// XXX = XXX.Subtract(KK.K.Multiply(HA));
//Vector<double> Obs = Vector<double>.Build.Dense(observations);
Vector <double> dx = KK.K.Multiply(dampning) * dy;
//add ensemble mean to ensemble anomelis (XXX = A + dx + x)
//MB: a faster way?
for (int i = 0; i < m_ensembleMembers; i++)
{
for (int n = 0; n < n_elementsinStateVector; n++)
{
XXX[n, i] += (x[n] + dx[n]);
}
}
return(XXX);
}
