umontreal.iro.lecuyer.util

Class Misc

java.lang.Object

umontreal.iro.lecuyer.util.Misc

public class Misc
extends java.lang.Object

This class provides miscellaneous functions that are hard to classify. Some may be moved to another class in the future.

Method Summary

Modifier and Type	Method and Description
static double	evalPoly(double[] C, int n, double x) Evaluates the polynomial
static double	evalPoly(int n, double[] X, double[] C, double z) Given n, X and C as described in interpol(n, X, Y, C), this function returns the value of the interpolating polynomial P(z) evaluated at z (see eq.
static int	getTimeInterval(double[] times, int start, int end, double t) Returns the index of the time interval corresponding to time t.
static void	interpol(int n, double[] X, double[] Y, double[] C) Computes the Newton interpolating polynomial.
static double	quickSelect(double[] t, int n, int k) Returns the kth smallest item of the array t of size n.
static int	quickSelect(int[] t, int n, int k) Returns the kth smallest item of the array t of size n.

Methods inherited from class java.lang.Object

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

Method Detail

quickSelect

public static double quickSelect(double[] t,
                                 int n,
                                 int k)

Returns the k^th smallest item of the array t of size n. Array t is unchanged by the method.

Parameters:

t - the array which contain the items

n - the number of items in the array

k - the index of the smallest item

Returns:

the kth smallest item of the array t

quickSelect

public static int quickSelect(int[] t,
                              int n,
                              int k)

Returns the k^th smallest item of the array t of size n. Array t is unchanged by the method.

Parameters:

t - the array which contain the items

n - the number of items in the array

k - the index of the smallest item

Returns:

the kth smallest item of the array t

getTimeInterval

public static int getTimeInterval(double[] times,
                                  int start,
                                  int end,
                                  double t)

Returns the index of the time interval corresponding to time t. Let t₀ <= ^... <= t_n be simulation times stored in a subset of times. This method uses binary search to determine the smallest value i for which t_i <= t < t_i+1, and returns i. The value of t_i is stored in times[start+i] whereas n is defined as end - start. If t < t₀, this returns -1. If t >= t_n, this returns n. Otherwise, the returned value is greater than or equal to 0, and smaller than or equal to n - 1. start and end are only used to set lower and upper limits of the search in the times array; the index space of the returned value always starts at 0. Note that if the elements of times with indices start, ..., end are not sorted in non-decreasing order, the behavior of this method is undefined.

Parameters:

times - an array of simulation times.

start - the first index in the array to consider.

end - the last index (inclusive) in the array to consider.

t - the queried simulation time.

Returns:

the index of the interval.

Throws:

java.lang.NullPointerException - if times is null.

java.lang.IllegalArgumentException - if start is negative, or if end is smaller than start.

java.lang.ArrayIndexOutOfBoundsException - if start + end is greater than or equal to the length of times.

interpol

public static void interpol(int n,
                            double[] X,
                            double[] Y,
                            double[] C)

Computes the Newton interpolating polynomial. Given the n + 1 real distinct points (x₀, y₀), (x₁, y₁),…,(x_n, y_n), with X[i] = x_i, Y[i] = y_i, this function computes the n + 1 coefficients C[i] = c_i of the Newton interpolating polynomial P(x) of degree n passing through these points, i.e. such that y_i = P(x_i), given by

P(x) = c₀ + c₁(x - x₀) + c₂(x - x₀)(x - x₁) + ^... + c_n(x - x₀)(x - x₁) ^... (x - x_n-1).

Parameters:

n - degree of the interpolating polynomial

X - x-coordinates of points

Y - y-coordinates of points

C - Coefficients of the interpolating polynomial

evalPoly

public static double evalPoly(int n,
                              double[] X,
                              double[] C,
                              double z)

Given n, X and C as described in interpol(n, X, Y, C), this function returns the value of the interpolating polynomial P(z) evaluated at z (see eq. ).

Parameters:

n - degree of the interpolating polynomial

X - x-coordinates of points

C - Coefficients of the interpolating polynomial

z - argument where polynomial is evaluated

Returns:

Value of the interpolating polynomial P(z)

evalPoly

public static double evalPoly(double[] C,
                              int n,
                              double x)

Evaluates the polynomial

P(x) = c₀ + c₁x + c₂x² + ^... + c_nxⁿ

of degree n with coefficients c_j = C[j] at x.

Parameters:

C - Coefficients of the polynomial

n - degree of the polynomial

x - argument where polynomial is evaluated

Returns:

Value of the polynomial P(x)