/**
* Converts source parameters to natural parameters.
*
* @param L source parameters \f$ \mathbf{\Lambda} = (p_1, \cdots, p_k)\f$
* @return natural parameters \f$ \mathbf{\Theta} = \left( \log \left( \frac{p_i}{p_k} \right)
* \right)_i \f$
*/
public PVector Lambda2Theta(PVector L) {
PVector theta = new PVector(L.getDimension() - 1);
theta.type = Parameter.TYPE.NATURAL_PARAMETER;
for (int i = 0; i < L.getDimension() - 1; i++)
theta.array[i] = Math.log(L.array[i] / L.array[L.getDimension() - 1]);
return theta;
}
/**
* Converts expectation parameters to source parameters.
*
* @param H natural parameters \f$ \mathbf{H} = (\eta_1, \cdots, \eta_{k-1})\f$
* @return source parameters \f$ \mathbf{\Lambda} = \begin{cases} p_i = \frac{\eta_i}{n} &
* \mbox{if $i<k$}\\ p_k = \frac{n - \sum_{j=1}^{k-1} \eta_j}{n} \end{cases}\f$
*/
public PVector Eta2Lambda(PVector H) {
PVector L = new PVector(H.getDimension() + 1);
L.type = Parameter.TYPE.SOURCE_PARAMETER;
double sum = 0;
for (int i = 0; i < H.getDimension(); i++) {
L.array[i] = H.array[i] / n;
sum += H.array[i];
}
L.array[H.getDimension()] = (n - sum) / n;
return L;
}
/**
* Computes \f$ \nabla G (\mathbf{H})\f$
*
* @param H expectation parameters \f$ \mathbf{H} = (\eta_1, \cdots, \eta_{k-1}) \f$
* @return \f$ \nabla G( \mathbf{H} ) = \left( \log \left( \frac{\eta_i}{n - \sum_{j=1}^{k-1}
* \eta_j} \right) \right)_i \f$
*/
public PVector gradG(PVector H) {
// Sum
double sum = 0;
for (int i = 0; i < H.getDimension(); i++) sum += H.array[i];
// Gradient
PVector gradient = new PVector(H.getDimension());
gradient.type = Parameter.TYPE.NATURAL_PARAMETER;
for (int i = 0; i < H.getDimension(); i++) gradient.array[i] = Math.log(H.array[i] / (n - sum));
// Return
return gradient;
}
/**
* Computes \f$ \nabla F ( \mathbf{\Theta} )\f$.
*
* @param T naturel parameters \f$ \mathbf{\Theta} = (\theta_1, \cdots, \theta_{k-1}) \f$
* @return \f$ \nabla F( \mathbf{\Theta} ) = \left( \frac{n \exp \theta_i}{1 + \sum_{j=1}^{k-1}
* \exp \theta_j} \right)_i \f$
*/
public PVector gradF(PVector T) {
// Sum
double sum = 0;
for (int i = 0; i < T.getDimension(); i++) sum += Math.exp(T.array[i]);
// Gradient
PVector gradient = new PVector(T.getDimension());
gradient.type = Parameter.TYPE.EXPECTATION_PARAMETER;
for (int i = 0; i < T.getDimension(); i++)
gradient.array[i] = (n * Math.exp(T.array[i])) / (1 + sum);
// Return
return gradient;
}
/**
* Converts natural parameters to source parameters.
*
* @param T natural parameters \f$ \mathbf{\Theta} = ( \theta_1, \cdots, \theta_{k-1} )\f$
* @return source parameters \f$ \mathbf{\Lambda} = \begin{cases} p_i = \frac{\exp \theta_i}{1 +
* \sum_{j=1}^{k-1}(\exp \theta_j)} & \mbox{if $i<k$}\\ p_k = \frac{1}{1 +
* \sum_{j=1}^{k-1}(\exp \theta_j)} \end{cases} \f$
*/
public PVector Theta2Lambda(PVector T) {
// Sums
double sum = 0;
for (int i = 0; i < T.getDimension(); i++) sum += Math.exp(T.array[i]);
// Conversion
PVector lambda = new PVector(T.getDimension() + 1);
lambda.type = Parameter.TYPE.SOURCE_PARAMETER;
for (int i = 0; i < T.getDimension(); i++) lambda.array[i] = Math.exp(T.array[i]) / (1.0 + sum);
lambda.array[T.getDimension()] = 1.0 / (1.0 + sum);
// Return
return lambda;
}
/**
* Converts source parameters to expectation parameters.
*
* @param L source parameters \f$ \mathbf{\Lambda} = p \f$
* @return expectation parameters \f$ \mathbf{H} = p \f$
*/
public PVector Lambda2Eta(PVector L) {
PVector H = new PVector(1);
H.array[0] = L.array[0];
H.type = Parameter.TYPE.EXPECTATION_PARAMETER;
return H;
}
/**
* Converts natural parameters to source parameters.
*
* @param T natural parameters \f$ \mathbf{\Theta} = \theta \f$
* @return source parameters \f$ \mathbf{\Lambda} = \frac{\exp\theta}{1+\exp\theta} \f$
*/
public PVector Theta2Lambda(PVector T) {
PVector L = new PVector(1);
L.array[0] = Math.exp(T.array[0]) / (1 + Math.exp(T.array[0]));
L.type = Parameter.TYPE.SOURCE_PARAMETER;
return L;
}
/**
* Converts source parameters to natural parameters.
*
* @param L source parameters \f$ \mathbf{\Lambda} = p \f$
* @return natural parameters \f$ \mathbf{\Theta} = \log \left( \frac{p}{1-p} \right) \f$
*/
public PVector Lambda2Theta(PVector L) {
PVector T = new PVector(1);
T.array[0] = Math.log(L.array[0] / (1 - L.array[0]));
T.type = Parameter.TYPE.NATURAL_PARAMETER;
return T;
}
/**
* Computes the sufficient statistic \f$ t(x)\f$.
*
* @param x a point
* @return \f$ t(x) = x \f$
*/
public PVector t(PVector x) {
PVector t = (PVector) x.clone();
t.type = Parameter.TYPE.EXPECTATION_PARAMETER;
return t;
}
/**
* Computes \f$ \nabla G (\mathbf{H})\f$
*
* @param H expectation parameters \f$ \mathbf{H} = \eta \f$
* @return \f$ \nabla G(\mathbf{H}) = \eta \f$
*/
public PVector gradG(PVector H) {
PVector gradient = (PVector) H.clone();
gradient.type = Parameter.TYPE.NATURAL_PARAMETER;
return gradient;
}
/**
* Computes the sufficient statistic \f$ t(x)\f$.
*
* @param x a point
* @return \f$ t(x) = (x_1, \cdots, x_{k-1}) \f$
*/
public PVector t(PVector x) {
PVector t = new PVector(x.getDimension() - 1);
t.type = Parameter.TYPE.EXPECTATION_PARAMETER;
for (int i = 0; i < x.getDimension() - 1; i++) t.array[i] = x.array[i];
return t;
}
/**
* Computes \f$ \nabla G (\mathbf{H})\f$.
*
* @param H expectation parameters \f$ \mathbf{H} = \eta \f$
* @return \f$ \nabla G( \mathbf{H} ) = \log \left( \frac{\eta}{1-\eta} \right) \f$
*/
public PVector gradG(PVector H) {
PVector gradient = new PVector(1);
gradient.array[0] = Math.log(H.array[0] / (1 - H.array[0]));
gradient.type = Parameter.TYPE.NATURAL_PARAMETER;
return gradient;
}
/**
* Converts source parameters to expectation parameters.
*
* @param L source parameters \f$ \mathbf{\Lambda} = \mu \f$
* @return expectation parameters \f$ \mathbf{H} = \mu \f$
*/
public PVector Lambda2Eta(PVector L) {
PVector H = (PVector) L.clone();
H.type = Parameter.TYPE.EXPECTATION_PARAMETER;
return H;
}
/**
* Converts source parameters to natural parameters.
*
* @param L source parameters \f$ \mathbf{\Lambda} = \mu \f$
* @return natural parameters \f$ \mathbf{\Theta} = \mu \f$
*/
public PVector Lambda2Theta(PVector L) {
PVector T = (PVector) L.clone();
T.type = Parameter.TYPE.NATURAL_PARAMETER;
return T;
}
/**
* Converts source parameters to expectation parameters.
*
* @param L source parameters \f$ \mathbf{\Lambda} = ( p_1, \cdots, p_k )\f$
* @return expectation parameters \f$ \mathbf{H} = \left( n p_i \right)_i\f$
*/
public PVector Lambda2Eta(PVector L) {
PVector H = new PVector(L.getDimension() - 1);
H.type = Parameter.TYPE.EXPECTATION_PARAMETER;
for (int i = 0; i < L.getDimension() - 1; i++) H.array[i] = n * L.array[i];
return H;
}
/**
* Converts expectation parameters to source parameters.
*
* @param H expectation parameters \f$ \mathbf{H} = \eta\f$
* @return source parameters \f$ \mathbf{\Lambda} = \eta \f$
*/
public PVector Eta2Lambda(PVector H) {
PVector L = new PVector(1);
L.array[0] = H.array[0];
L.type = Parameter.TYPE.SOURCE_PARAMETER;
return L;
}
/**
* Computes \f$ \nabla F ( \mathbf{\Theta} )\f$.
*
* @param T natural parameters \f$ \mathbf{\Theta} = \theta \f$
* @return \f$ \nabla F( \mathbf{\Theta} ) = \frac{\exp \theta}{1 + \exp \theta} \f$
*/
public PVector gradF(PVector T) {
PVector gradient = new PVector(1);
gradient.array[0] = Math.exp(T.array[0]) / (1 + Math.exp(T.array[0]));
gradient.type = Parameter.TYPE.EXPECTATION_PARAMETER;
return gradient;
}
/**
* Converts expectation parameters to source parameters.
*
* @param H expectation parameters \f$ \mathbf{H} = \eta \f$
* @return source parameters \f$ \mathbf{\Lambda} = \eta \f$
*/
public PVector Eta2Lambda(PVector H) {
PVector L = (PVector) H.clone();
L.type = Parameter.TYPE.SOURCE_PARAMETER;
return L;
}
/**
* Computes the sufficient statistic \f$ t(x)\f$.
*
* @param x a point
* @return \f$ t(x) = x \f$
*/
public PVector t(PVector x) {
PVector t = new PVector(1);
t.array[0] = x.array[0];
t.type = Parameter.TYPE.EXPECTATION_PARAMETER;
return t;
}
/**
* Computes \f$ \nabla F ( \mathbf{\Theta} )\f$.
*
* @param T natural \f$ \mathbf{\Theta} = \theta \f$
* @return \f$ \nabla F( \mathbf{\Theta} ) = \theta \f$
*/
public PVector gradF(PVector T) {
PVector gradient = (PVector) T.clone();
gradient.type = Parameter.TYPE.EXPECTATION_PARAMETER;
return gradient;
}
