Misc Class Reference

This class provides miscellaneous functions that are hard to classify. More...

Static Public Member Functions
static double	quickSelect (double[] A, int n, int k)
	Returns the \(k^{th}\) smallest item of the array \(A\) of size \(n\). More...
static int	quickSelect (int[] A, int n, int k)
	Returns the \(k^{th}\) smallest item of the array \(A\) of size \(n\). More...
static double	getMedian (double[] A, int n)
	Returns the median of the first \(n\) elements of array \(A\). More...
static double	getMedian (int[] A, int n)
	Returns the median of the first \(n\) elements of array \(A\). More...
static int	getTimeInterval (double[] times, int start, int end, double t)
	Returns the index of the time interval corresponding to time t. More...
static void	interpol (int n, double[] X, double[] Y, double[] C)
	Computes the Newton interpolating polynomial. More...
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. More...
static double	evalPoly (double[] C, int n, double x)
	Evaluates the polynomial \(P(x)\) of degree \(n\) with coefficients \(c_j =\) C[j] at \(x\): More...

Detailed Description

This class provides miscellaneous functions that are hard to classify.

Some may be moved to another class in the future.

Member Function Documentation

evalPoly() [1/2]

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

static

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.

eq.newton.interpol ).

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() [2/2]

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

static

Evaluates the polynomial \(P(x)\) of degree \(n\) with coefficients \(c_j =\) C[j] at \(x\):

\[ \qquad P(x) = c_0 + c_1 x + c_2 x^2 + \cdots+ c_n x^n \tag{eq.horner} \]

Parameters

C	Coefficients of the polynomial
n	degree of the polynomial
x	argument where polynomial is evaluated

Returns

Value of the polynomial \(P(x)\)

getMedian() [1/2]

static double getMedian ( double []  A, int  n  )

static

Returns the median of the first \(n\) elements of array \(A\).

Parameters

A	the array
n	the number of used elements

Returns

the median of \(A\)

getMedian() [2/2]

static double getMedian ( int []  A, int  n  )

static

Returns the median of the first \(n\) elements of array \(A\).

Parameters

A	the array
n	the number of used elements

Returns

the median of \(A\)

getTimeInterval()

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

static

Returns the index of the time interval corresponding to time t.

Let \(t_0\le\cdots\le t_n\) be simulation times stored in a subset of times. This method uses binary search to determine the smallest value \(i\) for which \(t_i\le t < t_{i+1}\), and returns \(i\). The value of \(t_i\) is stored in times[start+i] whereas \(n\) is defined as end - start. If \(t<t_0\), this returns \(-1\). If \(t\ge t_n\), 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.

Exceptions

NullPointerException	if times is null.
IllegalArgumentException	if start is negative, or if end is smaller than start.
ArrayIndexOutOfBoundsException	if start + end is greater than or equal to the length of times.

interpol()

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

static

Computes the Newton interpolating polynomial.

Given the \(n+1\) real distinct points \((x_0, y_0),\) \((x_1, y_1),…, (x_n, y_n)\), 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

\[ \qquad P(x) = c_0 + c_1(x-x_0) + c_2(x-x_0)(x-x_1) + \cdots+ c_n(x-x_0)(x-x_1) \cdots(x-x_{n-1}). \tag{eq.newton.interpol} \]

Parameters

n	degree of the interpolating polynomial
X	\(x\)-coordinates of points
Y	\(y\)-coordinates of points
C	Coefficients of the interpolating polynomial

quickSelect() [1/2]

static double quickSelect ( double []  A, int  n, int  k  )

static

Returns the \(k^{th}\) smallest item of the array \(A\) of size \(n\).

Array \(A\) is unchanged by the method. Restriction: \(1 \le k \le n\).

Parameters

A	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 \(A\)

quickSelect() [2/2]

static int quickSelect ( int []  A, int  n, int  k  )

static

Returns the \(k^{th}\) smallest item of the array \(A\) of size \(n\).

Array \(A\) is unchanged by the method. Restriction: \(1 \le k \le n\).

Parameters

A	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 \(A\)

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The documentation for this class was generated from the following file:

• Misc.java