Package Scientific :: Package Functions :: Module FirstDerivatives
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Module FirstDerivatives



Automatic differentiation for functions with any number of variables

Instances of the class DerivVar represent the values of a function and its partial derivatives with respect to a list of variables. All common mathematical operations and functions are available for these numbers. There is no restriction on the type of the numbers fed into the code; it works for real and complex numbers as well as for any Python type that implements the necessary operations.

This module is as far as possible compatible with the n-th order derivatives module Derivatives. If only first-order derivatives are required, this module is faster than the general one.

Example:
 print sin(DerivVar(2))
produces the output:
 (0.909297426826, [-0.416146836547])

The first number is the value of sin(2); the number in the following list is the value of the derivative of sin(x) at x=2, i.e. cos(2).

When there is more than one variable, DerivVar must be called with an integer second argument that specifies the number of the variable.

Example:
   >>>x = DerivVar(7., 0)
   >>>y = DerivVar(42., 1)
   >>>z = DerivVar(pi, 2)
   >>>print (sqrt(pow(x,2)+pow(y,2)+pow(z,2)))

   produces the output

   >>>(42.6950770511, [0.163953328662, 0.98371997197, 0.0735820818365])

The numbers in the list are the partial derivatives with respect to x, y, and z, respectively.

Note: It doesn't make sense to use DerivVar with different values for the same variable index in one calculation, but there is no check for this. I.e.:
   >>>print DerivVar(3, 0)+DerivVar(5, 0)

   produces

   >>>(8, [2])
but this result is meaningless.

Classes [hide private]
  DerivVar
Numerical variable with automatic derivatives of first order

Functions [hide private]
Scientific.Geometry.Vector DerivVector(x, y, z, index=0)
Returns a vector whose components are DerivVar objects
  _mapderiv(func, a, b)
bool isDerivVar(x)
Returns True if x is a DerivVar object, False otherwise

Function Details [hide private]

DerivVector(x, y, z, index=0)

 
Parameters:
  • x (number) - x component of the vector
  • y (number) - y component of the vector
  • z (number) - z component of the vector
  • index (int) - the DerivVar index for the x component. The y and z components receive consecutive indices.
Returns: Scientific.Geometry.Vector
a vector whose components are DerivVar objects

_mapderiv(func, a, b)

 

isDerivVar(x)

 
Parameters:
  • x - an arbitrary object
Returns: bool
True if x is a DerivVar object, False otherwise