Package ffx.numerics.integrate

Class Integrate1DNumeric

java.lang.Object

ffx.numerics.integrate.Integrate1DNumeric

public class Integrate1DNumeric
extends Object

This program integrates using four methods: rectangular integration, the trapezoidal method, Simpson's Three Point Integration, and Boole's Five Point Integration. Of these, Simpson's and Boole's integration methods generally perform the best. Parallelized methods exist and seem to function, but the performance of a parallelized method should not be necessary, and the parallelization introduces some complexity and inefficiency.

Primary methods: integrateData and integrateByBins, using some DataSet, which is often a DoublesDataSet.

Author:

Claire O'Connell, Jacob M. Litman

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static enum	Integrate1DNumeric.IntegrationSide	Left vs right-hand integration; left-hand integration will start from the first available point, run right as far as possible, and then clean up any remaining points using finishIntegration, while right-hand integration will start from the last available point, run left as far as possible, and then clean up any remaining points using finishIntegration.
static enum	Integrate1DNumeric.IntegrationType	Enumeration of implemented integration methods, and the number of points required by them.

Method Summary

Modifier and Type	Method	Description
static double	booles(DataSet data, Integrate1DNumeric.IntegrationSide side)	Numerically integrates a data set using Boole's rule.
static double	booles(DataSet data, Integrate1DNumeric.IntegrationSide side, int lb, int ub)	Numerically integrates a data set, in bounds lb-ub inclusive, using Boole's rule.
static double	boolesParallel(DataSet data, Integrate1DNumeric.IntegrationSide side)	Numerically integrates a data set using Boole's rule.
static double	boolesParallel(DataSet data, Integrate1DNumeric.IntegrationSide side, int lb, int ub)	Numerically integrates a data set, in bounds lb-ub inclusive, using Boole's rule.
static double[]	generateXPoints(double lb, double ub, int nPoints, boolean halfWidthEnds)	Generates a set of points along x.
static double[]	integrateByBins(DataSet data, Integrate1DNumeric.IntegrationSide side, Integrate1DNumeric.IntegrationType maxType)	Returns the contribution of each bin to the overall integral as an array; will be most accurate at break-points for the integration type.
static double	integrateData(DataSet data, Integrate1DNumeric.IntegrationSide side, Integrate1DNumeric.IntegrationType type)	Generic caller for 1D integration schemes given an IntegrationType.
static double	rectangular(DataSet data, Integrate1DNumeric.IntegrationSide side)	Numerically integrates a data set using rectangular integration.
static double	rectangular(DataSet data, Integrate1DNumeric.IntegrationSide side, int lb, int ub)	Numerically integrates a data set, in bounds lb-ub inclusive, using rectangular integration.
static double	rectangularEnds(DataSet data, Integrate1DNumeric.IntegrationSide side)	Treats half-width bins at the ends of a DataSet using rectangular integration.
static double	rectangularParallel(DataSet data, Integrate1DNumeric.IntegrationSide side)	Numerically integrates a data set using parallelized rectangular integration.
static double	rectangularParallel(DataSet data, Integrate1DNumeric.IntegrationSide side, int lb, int ub)	Numerically integrates a data set, in bounds lb-ub inclusive, using rectangular integration.
static double	simpsons(DataSet data, Integrate1DNumeric.IntegrationSide side)	Numerically integrates a data set using Simpson's rule.
static double	simpsons(DataSet data, Integrate1DNumeric.IntegrationSide side, int lb, int ub)	Numerically integrates a data set, in bounds lb-ub inclusive, using Simpson's rule.
static double	simpsonsParallel(DataSet data, Integrate1DNumeric.IntegrationSide side)	Numerically integrates a data set using Boole's rule.
static double	simpsonsParallel(DataSet data, Integrate1DNumeric.IntegrationSide side, int lb, int ub)	Numerically integrates a data set, in bounds lb-ub inclusive, using Simpson's rule.
static double	trapezoidal(DataSet data, Integrate1DNumeric.IntegrationSide side)	Numerically integrates a data set using trapezoidal integration.
static double	trapezoidal(DataSet data, Integrate1DNumeric.IntegrationSide side, int lb, int ub)	Numerically integrates a data set, in bounds lb-ub inclusive, using trapezoidal integration.
static double	trapezoidalEnds(DataSet data, Integrate1DNumeric.IntegrationSide side)	Treats half-width bins at the ends of a DataSet using trapezoidal integration.
static double	trapezoidalParallel(DataSet data, Integrate1DNumeric.IntegrationSide side)	Numerically integrates a data set using trapezoidal integration.
static double	trapezoidalParallel(DataSet data, Integrate1DNumeric.IntegrationSide side, int lb, int ub)	Numerically integrates a data set, in bounds lb-ub inclusive, using trapezoidal integration.

Methods inherited from class java.lang.Object

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

Method Details

booles

public static double booles(DataSet data,
 Integrate1DNumeric.IntegrationSide side)

Numerically integrates a data set using Boole's rule.

Parameters:

data - Data set to integrate

side - Side to integrate from

Returns:

Area of integral

booles

public static double booles(DataSet data,
 Integrate1DNumeric.IntegrationSide side,
 int lb,
 int ub)

Numerically integrates a data set, in bounds lb-ub inclusive, using Boole's rule.

Parameters:

data - Data set to integrate

side - Side to integrate from

lb - First index to integrate over

ub - Last index to integrate over

Returns:

Area of integral

boolesParallel

public static double boolesParallel(DataSet data,
 Integrate1DNumeric.IntegrationSide side)

Numerically integrates a data set using Boole's rule. The sequential version is preferred unless necessary.

Parameters:

data - Data set to integrate

side - Side to integrate from

Returns:

Area of integral

boolesParallel

public static double boolesParallel(DataSet data,
 Integrate1DNumeric.IntegrationSide side,
 int lb,
 int ub)

Numerically integrates a data set, in bounds lb-ub inclusive, using Boole's rule. The sequential version is preferred unless necessary.

Parameters:

data - Data set to integrate

side - Side to integrate from

lb - First index to integrate over

ub - Last index to integrate over

Returns:

Area of integral

generateXPoints

public static double[] generateXPoints(double lb,
 double ub,
 int nPoints,
 boolean halfWidthEnds)

Generates a set of points along x.

Parameters:

lb - Beginning value, inclusive

ub - Ending value, inclusive

nPoints - Total number of points

halfWidthEnds - If ends should have 1/2 regular separation

Returns:

an array of

invalid reference

double

objects.

integrateByBins

public static double[] integrateByBins(DataSet data,
 Integrate1DNumeric.IntegrationSide side,
 Integrate1DNumeric.IntegrationType maxType)

Returns the contribution of each bin to the overall integral as an array; will be most accurate at break-points for the integration type. Overall integral is the sum of the array of doubles, plus or minus minor rounding errors.

If N is a breakpoint for Boole's rule: N+1 is a trapezoid from N to N+1. N+2 is Simpson's from N to N+2, minus the prior trapezoid (N+1). N+3 is 4-point integration from N to N+3, minus the N to N+2 parabola. N+4 is the full Boole's Rule from N to N+4, minus the N to N+3 4-point integral.

Parameters:

data - Data to integrate

side - Side to integrate from

maxType - Maximum rule to be used

Returns:

Per-bin contributions to integral.

integrateData

public static double integrateData(DataSet data,
 Integrate1DNumeric.IntegrationSide side,
 Integrate1DNumeric.IntegrationType type)

Generic caller for 1D integration schemes given an IntegrationType.

Parameters:

data - To integrate

side - Integrate from side

type - Scheme to use

Returns:

Numeric integral

rectangular

public static double rectangular(DataSet data,
 Integrate1DNumeric.IntegrationSide side)

Numerically integrates a data set using rectangular integration. Not recommended; preferably use at least trapezoidal integration.

Parameters:

data - Data set to integrate

side - Side to integrate from

Returns:

Area of integral

rectangular

public static double rectangular(DataSet data,
 Integrate1DNumeric.IntegrationSide side,
 int lb,
 int ub)

Numerically integrates a data set, in bounds lb-ub inclusive, using rectangular integration. Not recommended; preferably use at least trapezoidal integration.

Parameters:

data - Data set to integrate

side - Side to integrate from

lb - First index to integrate over

ub - Last index to integrate over

Returns:

Area of integral

rectangularEnds

public static double rectangularEnds(DataSet data,
 Integrate1DNumeric.IntegrationSide side)

Treats half-width bins at the ends of a DataSet using rectangular integration. Not recommended, preferably use trapezoidal integration.

Parameters:

data - Data set to integrate

side - Side to integrate from

Returns:

Estimate of area in half-width start/end bins.

rectangularParallel

public static double rectangularParallel(DataSet data,
 Integrate1DNumeric.IntegrationSide side)

Numerically integrates a data set using parallelized rectangular integration. Not recommended; preferably use at least trapezoidal integration, and avoid parallelized versions unless necessary.

Parameters:

data - Data set to integrate

side - Side to integrate from

Returns:

Area of integral

rectangularParallel

public static double rectangularParallel(DataSet data,
 Integrate1DNumeric.IntegrationSide side,
 int lb,
 int ub)

Numerically integrates a data set, in bounds lb-ub inclusive, using rectangular integration. Not recommended; preferably use at least trapezoidal integration. Also, prefer parallelized versions unless necessary.

Parameters:

data - Data set to integrate

side - Side to integrate from

lb - First index to integrate over

ub - Last index to integrate over

Returns:

Area of integral

simpsons

public static double simpsons(DataSet data,
 Integrate1DNumeric.IntegrationSide side)

Numerically integrates a data set using Simpson's rule.

Parameters:

data - Data set to integrate

side - Side to integrate from

Returns:

Area of integral

simpsons

public static double simpsons(DataSet data,
 Integrate1DNumeric.IntegrationSide side,
 int lb,
 int ub)

Numerically integrates a data set, in bounds lb-ub inclusive, using Simpson's rule.

Parameters:

data - Data set to integrate

side - Side to integrate from

lb - First index to integrate over

ub - Last index to integrate over

Returns:

Area of integral

simpsonsParallel

public static double simpsonsParallel(DataSet data,
 Integrate1DNumeric.IntegrationSide side)

Numerically integrates a data set using Boole's rule. The sequential version is preferred unless necessary.

Parameters:

data - Data set to integrate

side - Side to integrate from

Returns:

Area of integral

simpsonsParallel

public static double simpsonsParallel(DataSet data,
 Integrate1DNumeric.IntegrationSide side,
 int lb,
 int ub)

Numerically integrates a data set, in bounds lb-ub inclusive, using Simpson's rule. The sequential version is preferred unless necessary.

Parameters:

data - Data set to integrate

side - Side to integrate from

lb - First index to integrate over

ub - Last index to integrate over

Returns:

Area of integral

trapezoidal

public static double trapezoidal(DataSet data,
 Integrate1DNumeric.IntegrationSide side)

Numerically integrates a data set using trapezoidal integration. For most data sets, Simpson's rule or Boole's rule will out-perform trapezoidal integration.

Parameters:

data - Data set to integrate

side - Side to integrate from

Returns:

Area of integral

trapezoidal

public static double trapezoidal(DataSet data,
 Integrate1DNumeric.IntegrationSide side,
 int lb,
 int ub)

Numerically integrates a data set, in bounds lb-ub inclusive, using trapezoidal integration. For most data sets, Simpson's rule or Boole's rule will out-perform trapezoidal integration.

Parameters:

data - Data set to integrate

side - Side to integrate from

lb - First index to integrate over

ub - Last index to integrate over

Returns:

Area of integral

trapezoidalEnds

public static double trapezoidalEnds(DataSet data,
 Integrate1DNumeric.IntegrationSide side)

Treats half-width bins at the ends of a DataSet using trapezoidal integration.

Parameters:

data - Data set to integrate

side - Side to integrate from

Returns:

Estimate of area in half-width start/end bins.

trapezoidalParallel

public static double trapezoidalParallel(DataSet data,
 Integrate1DNumeric.IntegrationSide side)

Numerically integrates a data set using trapezoidal integration. For most data sets, Simpson's rule or Boole's rule will out-perform trapezoidal integration. Prefer use of the sequential version unless necessary.

Parameters:

data - Data set to integrate

side - Side to integrate from

Returns:

Area of integral

trapezoidalParallel

public static double trapezoidalParallel(DataSet data,
 Integrate1DNumeric.IntegrationSide side,
 int lb,
 int ub)

Numerically integrates a data set, in bounds lb-ub inclusive, using trapezoidal integration. For most data sets, Simpson's rule or Boole's rule will out-perform trapezoidal integration. Prefer use of the sequential version unless necessary.

Parameters:

data - Data set to integrate

side - Side to integrate from

lb - First index to integrate over

ub - Last index to integrate over

Returns:

Area of integral