autodiff.Dual¶

class autodiff.Dual(val, der=1)¶

Primary data structure for forward mode automatic differentiation.

Dual numbers can be used as a data structure to store the value and derivative of a function. The value and derivative can be stored as the real and “dual” part of a dual number, respectively. The properties of a dual number lend itself nicely to a straightforward implementation of forward mode automatic differentiation.

Parameters

valfloat: The value of the Dual number.
derndarray: The derivative of the Dual number.

See also

Dual.constant
Dual.from_array

Examples

Construct a Dual number for a univariate function:

>>> x = ad.Dual(42)
>>> x
Dual(42, array([1]))

Construct a Dual number for a multivariate function with user-defined seed vector:

>>> x = ad.Dual(42, [1, 2])
>>> x
Dual(42, array([1, 2]))

Construct multiple Dual numbers from array of scalars:

>>> x, y, z = ad.Dual.from_array([1, 2, 4])
>>> x
Dual(1, array([1, 0, 0]))
>>> y
Dual(2, array([0, 1, 0]))

Create a function from multiple Dual numbers:

>>> x, y, z = ad.Dual.from_array([1, 2, 4])
>>> f = (x * y)/z
>>> f.val
0.5
>>> f.der
array([0.5, 0.25, -0.125])

Attributes

ndim: Return the number of dimensions of the Dual number.

Methods

`constant`(val[, ndim])	Create a Dual number representing a constant.
`from_array`(X)	Generate Dual numbers for a multivariable function.

property ndim¶

Return the number of dimensions of the Dual number.

Parameters

selfDual

Returns

outint: Number of dimensions.

Examples

>>> ad.Dual(-5, [6.2]).ndim
1

More than one dimension:

>>> ad.Dual(42, [1, 2]).ndim
2

static constant(val, ndim=1)¶

Create a Dual number representing a constant.

Parameters

valint or float: Value of dual number.
ndimint, optional: ndim is the number of dimensions of the zero derivative vector.

Returns

outDual: Dual number of value val with zero derivative vector.

Notes

Derivative vector of length ndim will be filled with zeros.

Examples

>>> ad.Dual.constant(42)
Dual(42, array([0.]))

Constant with more than one dimension:

>>> ad.Dual.constant(7, 2)
Dual(7, array([0., 0.]))

static from_array(X)¶

Generate Dual numbers for a multivariable function.

Parameters

Xarray: Array of numbers which will be values of Dual numbers.

Returns

outDual number generator: Dual numbers of value X[i] with zero derivative vector where the i-th element has a value of 1.

Examples

>>> x, y = ad.Dual.from_array([1, 42])
>>> x
Dual(1, array([1., 0.]))
>>> y
Dual(42, array([0., 1.]))

Dual

autodiff.Dual.__add__