org.jscience.mathematics.analysis.expressions
Interface NumericalDifferentiable

All Superinterfaces:

java.io.Serializable

All Known Implementing Classes:

Acos, Addition, Asin, Atan, Constant, Cos, Division, Exp, Log, Minus, Multiplication, NamedDataExpression, Parameter, Pow, Sin, Sqrt, Subtraction, Tan, Variable

public interface NumericalDifferentiable
extends java.io.Serializable

The interface specifies the methods that must be supplied for a class to be able to perform automatic differentiation in the reverse mode.
Example of use:
The example uses the classes from the symbolic computation package org.jscience.mathematics.analysis.expressions.symbolic that supports automatic differentiation. Note that since all classes do not implement the NumericalDifferentiable interface some class castings are necessary. In the example x, y, and z are independent variables/parameters, and e and f are dependent variables. All other expressions are auxiliaries.

 Variable x = new Variable( "x" );
 Variable y = new Variable( "y" );
 Parameter z = new Parameter( "z" );
 Expression a = new Sin( x );
 Expression b = new Multiplication( new Constant( 1.0 ), x );
 Expression c = new Division( y, a );
 Expression d = new Multiplication( a, z );
 Expression e = new Subtraction( b, c );
 Expression f = new Addition( c, d );
 for(int k = 0; k < 10; k++) f = new Sin( f );
 x.setIndex( 1 );
 y.setIndex( 2 );
 z.setIndex( 3 );
 ((NumericalDifferentiable)e).setNumberOfIndependents( 3 );
 ((NumericalDifferentiable)f).setNumberOfIndependents( 3 );
 x.setValue( 0.13 );
 y.setValue( 0.46 );
 z.setValue( 0.73 );
 ((NumericalDifferentiable)e).resetNumEval();
 ((NumericalDifferentiable)f).resetNumEval();
 ((NumericalDifferentiable)e).resetNumDiff( 1 );
 ((NumericalDifferentiable)f).resetNumDiff( 1 );
 double dedx = ((NumericalDifferentiable)e).numDiff( 1 );
 double dfdx = ((NumericalDifferentiable)f).numDiff( 1 );
 ((NumericalDifferentiable)e).resetNumDiff( 2 );
 ((NumericalDifferentiable)f).resetNumDiff( 2 );
 double dedy = ((NumericalDifferentiable)e).numDiff( 2 );
 double dfdy = ((NumericalDifferentiable)f).numDiff( 2 );
 ((NumericalDifferentiable)e).resetNumDiff( 3 );
 ((NumericalDifferentiable)f).resetNumDiff( 3 );
 double dedz = ((NumericalDifferentiable)e).numDiff( 3 );
 double dfdz = ((NumericalDifferentiable)f).numDiff( 3 );
 










Method Summary




 double
numDiff(int i)



          Returns the derivative of an Expression with respect to a
 NamedDataExpression whose index is the parameter.



 double
numEval()



          Compute the numerical value of the function expression.



 void
resetNumDiff(int i)



          Reset the computational tree for derivative calculation for the
 indexed independent variable.



 void
resetNumEval()



          Reset the function evaluation such that the next invocation of
 numEval() carries out the full computation.



 void
setIndex(int i)



          Sets the index of an independent variable.



 void
setNumberOfIndependents(int n)



          Sets the number of independent variables in the computational
 tree.


 





Method Detail



numDiff
double numDiff(int i)

Returns the derivative of an Expression with respect to a
 NamedDataExpression whose index is the parameter.





Parameters:
i - DOCUMENT ME!
Returns:
DOCUMENT ME!





resetNumDiff
void resetNumDiff(int i)

Reset the computational tree for derivative calculation for the
 indexed independent variable.





Parameters:
i - DOCUMENT ME!





setNumberOfIndependents
void setNumberOfIndependents(int n)

Sets the number of independent variables in the computational
 tree.





Parameters:
n - DOCUMENT ME!





setIndex
void setIndex(int i)

Sets the index of an independent variable. The index should be
 used to identify an independent variable





Parameters:
i - DOCUMENT ME!





numEval
double numEval()

Compute the numerical value of the function expression.






Returns:
DOCUMENT ME!





resetNumEval
void resetNumEval()

Reset the function evaluation such that the next invocation of
 numEval() carries out the full computation.