numal.lowprecision.test
Class TestMarquardt

java.lang.Object
  numal.lowprecision.test.TestMarquardt

All Implemented Interfaces:

Function

public class TestMarquardt
extends Object
implements Function

Test the least-square fit method AnalyticProblems.marquardt(int, int, float[], float[], float[][], numal.lowprecision.Function, float[]). Should return the following results : Parameters: 5.23219E2 -1.56833E2 -1.99784E-1 OUT: 7.22065E7 1.15716E2 1.74713E-3 1.65459E2 2.30000E1 2.20000E1 0.00000E0 Last residual vector: -29.6 86.6 -47.3 -26.2 -22.9 39.5

Constructor Summary

TestMarquardt(float[] x, float[] y)

Method Summary

void	computeJacobian(int m, int n, float[] parameter, float[] rv, float[][] jac) Get the partial derivatives jac[i][j] = drv[i]/dpar[j], obtained with the current values of the parameters.
boolean	computeResidualVector(int m, int n, float[] parameter, float[] rv) Get residual vector rv[i] = f(x[i],par) - y[i].
static float	f(float x, float[] parameter) Get the value of this function for a given abcissa and parameters.
float	getAbsoluteTolerance() Absolute tolerance for the difference between the Euclidian norm of the ultimate and penultimate residual vector (value of epsilon_a) the process is terminated if the improvement of the sum of the squares is less than relativeTolerance*(sum of the squares)+absoluteTolerance*absoluteTolerance
float[]	getAnalyticValues(int m, float[] parameter) Get the analytic values of the function for the given set of parameters and for all abcissa.
int	getInvocations() Maximum allowed number of invocations of Function.computeResidualVector(int, int, float[], float[])
float	getMachinePrecision() Machine precision
float	getRelativeTolerance() Relative tolerance for the difference between the Euclidian norm of the ultimate and penultimate residual vector (value of epsilon_re) (see absoluteTolerance)
float	getStartingValue() Starting value used for the relation between the gradient and the Gauss-Newton direction (value of ξ); if the problem is well conditioned then a suitable value for startingValue will be 0.01; if the problem is ill conditioned then startingValue should be greater, but the value of startingValue must satisfy : machinePrecision < startingValue ≤ 1 / machinePrecision
static void	main(String[] args)

Methods inherited from class java.lang.Object

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

Constructor Detail

TestMarquardt

public TestMarquardt(float[] x,
                     float[] y)

Method Detail

main

public static void main(String[] args)

f

public static float f(float x,
                      float[] parameter)

Get the value of this function for a given abcissa and parameters.

Parameters:

x - the abcissa at which this function is to be evaluated

parameter - an array of function parameters

Returns:

the value of this function for the given x and parameters

getAnalyticValues

public float[] getAnalyticValues(int m,
                                 float[] parameter)

Description copied from interface: Function

Get the analytic values of the function for the given set of parameters and for all abcissa.

Specified by:

getAnalyticValues in interface Function

Parameters:

m - number of sample points used in the fitting

parameter - an array of function parameters

Returns:

the value of this function for all abcissa and parameters

computeResidualVector

public boolean computeResidualVector(int m,
                                     int n,
                                     float[] parameter,
                                     float[] rv)

Description copied from interface: Function

Get residual vector rv[i] = f(x[i],par) - y[i]. POSTCONDITION: parameter array must not be altered.

Specified by:

computeResidualVector in interface Function

Parameters:

m - number of sample points used in the fitting

n - number of parameters, must be less than or equal to m

parameter - input: current values of parameters (shouldn't be altered by funct)

rv - output: residual vector obtained with current value of parameters; i.e f(x[i],par) - y[i]

Returns:

true when successful, false if current estimates of parameters lie outside a feasible region (invoker can avoid residual vector calculations on values which may make no sense or even cause overflow)

computeJacobian

public void computeJacobian(int m,
                            int n,
                            float[] parameter,
                            float[] rv,
                            float[][] jac)

Description copied from interface: Function

Get the partial derivatives jac[i][j] = drv[i]/dpar[j], obtained with the current values of the parameters. The precision of this method in computing the elements of jac must be at least the precision defined by in[3] and in[4] of AnalyticProblems.marquardt(int, int, float[], float[], float[][], numal.lowprecision.Function, float[]). POSTCONDITION: parameter array must not be altered.

Specified by:

computeJacobian in interface Function

Parameters:

m - number of sample points used in the fitting

n - number of parameters, must be less than or equal to the number of sample points

parameter - input: current values of parameters

rv - output: residual vector obtained with current value of parameters; i.e f(x[i],parameter) - y[i]

jac - output: partial derivatives drv[i]/dparameter[j], obtained with the current values of the parameters

getInvocations

public int getInvocations()

Description copied from interface: Function

Maximum allowed number of invocations of Function.computeResidualVector(int, int, float[], float[])

Specified by:

getInvocations in interface Function

getMachinePrecision

public float getMachinePrecision()

Description copied from interface: Function

Machine precision

Specified by:

getMachinePrecision in interface Function

getRelativeTolerance

public float getRelativeTolerance()

Description copied from interface: Function

Relative tolerance for the difference between the Euclidian norm of the ultimate and penultimate residual vector (value of epsilon_re) (see absoluteTolerance)

Specified by:

getRelativeTolerance in interface Function

getAbsoluteTolerance

public float getAbsoluteTolerance()

Description copied from interface: Function

Absolute tolerance for the difference between the Euclidian norm of the ultimate and penultimate residual vector (value of epsilon_a) the process is terminated if the improvement of the sum of the squares is less than relativeTolerance*(sum of the squares)+absoluteTolerance*absoluteTolerance

Specified by:

getAbsoluteTolerance in interface Function

getStartingValue

public float getStartingValue()

Description copied from interface: Function

Starting value used for the relation between the gradient and the Gauss-Newton direction (value of ξ); if the problem is well conditioned then a suitable value for startingValue will be 0.01; if the problem is ill conditioned then startingValue should be greater, but the value of startingValue must satisfy : machinePrecision < startingValue ≤ 1 / machinePrecision

Specified by:

getStartingValue in interface Function