Package jline.solvers.fluid.moments

Class MvnRectangle

java.lang.Object

jline.solvers.fluid.moments.MvnRectangle

public final class MvnRectangle
extends Object

Rectangle probability of a multivariate normal, the cell integral behind SolverFluid.getProbAggr under the moment-closure methods. Java twin of the MATLAB fluid_mvn_rectangle and of the Python mvn_rectangle.

The integral has no closed form beyond one dimension, so it is evaluated by the separation-of-variables transformation of Genz (1992): the Cholesky factor of C turns the rectangle into an iterated integral over the unit cube whose integrand is a product of normal-CDF differences, and the first coordinate is integrated exactly. The remaining cube is integrated with a DETERMINISTIC Richtmyer lattice rule, frac(k*sqrt(p_j)) over the first primes, averaged with its antithetic reflection. Determinism is required here, not merely convenient: the MATLAB, Java and Python twins must return the same number, and a randomized rule would make them agree only in distribution.

C may be SINGULAR, which is the common case: a closed population fixes the sum of the station coordinates, so the covariance of a station holding a whole class is rank deficient. A coordinate whose CONDITIONAL variance vanishes is not integrated; it is a hard constraint, contributing 1 when the conditional mean falls inside its interval and 0 otherwise.

See Also:

• FluidLyapunov

Field Summary

Fields

Modifier and Type	Field	Description
static final int	DEFAULT_POINTS	Lattice points per antithetic pair.

Method Summary

Modifier and Type	Method	Description
static double	logProbability(double[] m, double[][] C, double[] a, double[] b)	Natural logarithm of probability(double[], double[][], double[], double[]), negative infinity when the probability is zero.
static double	probability(double[] m, double[][] C, double[] a, double[] b)	Probability that a normal vector falls in the rectangle [a,b].
static double	probability(double[] m, double[][] C, double[] a, double[] b, int npoints)	Probability that a normal vector falls in the rectangle [a,b].

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Details

DEFAULT_POINTS

public static final int DEFAULT_POINTS

Lattice points per antithetic pair.

See Also:

• Constant Field Values

Method Details

probability

public static double probability(double[] m,
 double[][] C,
 double[] a,
 double[] b)

Probability that a normal vector falls in the rectangle [a,b].

Parameters:

m - mean vector, length d

C - covariance matrix, d-by-d, symmetric positive semi-definite

a - lower corner, -infinity allowed

b - upper corner, +infinity allowed

Returns:

the probability in [0,1]

probability

public static double probability(double[] m,
 double[][] C,
 double[] a,
 double[] b,
 int npoints)

Probability that a normal vector falls in the rectangle [a,b].

Parameters:

m - mean vector, length d

C - covariance matrix, d-by-d, symmetric positive semi-definite

a - lower corner, -infinity allowed

b - upper corner, +infinity allowed

npoints - lattice points per antithetic pair

Returns:

the probability in [0,1]

logProbability

public static double logProbability(double[] m,
 double[][] C,
 double[] a,
 double[] b)

Natural logarithm of probability(double[], double[][], double[], double[]), negative infinity when the probability is zero.

Parameters:

m - mean vector

C - covariance matrix

a - lower corner

b - upper corner

Returns:

log of the rectangle probability