autodiff package¶

Submodules¶

autodiff.operations module¶

Collection of tools to make new elementary operations

autodiff.operations.acos(x)¶

Arccos

Parameters:	x (Number) – Value
Returns:	acos(x)
Return type:	Number

autodiff.operations.acos_deriv(x)¶

Derivative of arccos

Parameters:	x (Number) – Value
Returns:	Partial derivatives w.r.t. everything x had a partial w.r.t.
Return type:	dict

autodiff.operations.add(x, y)¶

add two numbers together, one of x and y has to be a Number object

Parameters:	x – a Number object or an int/float y – a Number object or an int/float to be added
Returns:	value of the sum

autodiff.operations.add_deriv(x, y)¶

Derivative of additions, one of x and y has to be a Number object

Parameters:	x – a Number y – a Number object or an int/float to be added
Returns:	The derivative of the sum of x and y

autodiff.operations.asin(x)¶

Arcsin

Parameters:	x (Number) – Value
Returns:	asin(x)
Return type:	Number

autodiff.operations.asin_deriv(x)¶

Arcsin derivative

Parameters:	x (Number) – Value
Returns:	Partial derivatives w.r.t. everything x had a partial w.r.t.
Return type:	dict

autodiff.operations.atan(x)¶

Arctan

Parameters:	x (Number) – Value
Returns:	atan(x)
Return type:	Number

autodiff.operations.atan_deriv(x)¶

Derivative of atan

Parameters:	x (Number) – Value
Returns:	Partial derivatives w.r.t. everything x had a partial w.r.t.
Return type:	dict

autodiff.operations.cos(x)¶

Take the cos(x)

Parameters:	x (Number) – Number to take the cos of
Returns:	cos(x.val)
Return type:	float

autodiff.operations.cos_deriv(x)¶

Derivative of cos(x)

Parameters:	x (structures.Number()) – Number to take the cos of. Must have a `deriv` attribute
Returns:	dictionary of partial derivatives
Return type:	dict

autodiff.operations.cosh(x)¶

Hyperbolic cosine

Parameters:	x (Number) – Value
Returns:	cosh(x)
Return type:	Number

autodiff.operations.cosh_deriv(x)¶

Hyperbolic cosine

Parameters:	x (Number) – Value
Returns:	Partial derivatives w.r.t. everything x had a partial w.r.t.
Return type:	dict

autodiff.operations.div(x, y)¶

Subtract one number from another, one of x and y has to be a Number object

Parameters:	x – a Number object y – a Number object or an int/float to be subtracted
Returns:	value of the difference

autodiff.operations.div_deriv(x, y)¶

Derivative of division, one of x and y has to be a Number object

Parameters:	x – a Number y – a Number object or an int/float to be divided
Returns:	The derivative of the quotient of x and y

autodiff.operations.elementary(deriv_func)¶

Decorator to create an elementary operation

This takes as an argument a function that calculates the derivative of the function the user is calculating. When the decorated function is called, @elementary also calls deriv_func and stores both the value and derivative in a new Number() object

Example

>>> import numpy as np
>>> def sin_deriv(x):
...     return {x: np.cos(x.val) * x.deriv[x]}
>>> @elementary(sin_deriv)
... def sin(x):
...     return np.sin(x.val)
>>> a = Number(np.pi / 2)
>>> sina = sin(a)
>>> sina.val
1.0
>>> sina.deriv[a]
0.0

Parameters:	deriv_func (function) – Function specifying the derivative of this function. Must return a dictionary where each key-value pair is the partial derivative of the decorated function
Returns:	Decorated function
Return type:	function

autodiff.operations.exp(x)¶

Take the exp(x)

Parameters:	x (Number) – Number to take the exp of
Returns:	exp(x.val)
Return type:	float

autodiff.operations.exp_deriv(x)¶

Derivative of exp(x)

Parameters:	x (structures.Number()) – Number to take the exp of. Must have a `deriv` attribute
Returns:	dictionary of partial derivatives
Return type:	dict

autodiff.operations.log(x, y=2.718281828459045)¶

Take the log(x) at base y

Parameters:	x (Number) – Number to take the log of y (a Number object or an int/float) – Base of the logarithm.
Returns:	log(x.val)
Return type:	float

autodiff.operations.log_deriv(x, y=2.718281828459045)¶

Derivative of log(x) at base y

Parameters:	x (structures.Number()) – Number to take the log of. Must have a `deriv` attribute y (a Number object or an int/float) – Base of the logarithm.
Returns:	dictionary of partial derivatives
Return type:	dict

autodiff.operations.logistic(x)¶

Take the logistic(x)

Parameters:	x (Number) – Number to the natural exponential in the logistic
Returns:	logistic(x.val)
Return type:	float

autodiff.operations.logistic_deriv(x)¶

Derivative of logistic(x)

Parameters:	x (structures.Number()) – Number to the natural exponential in the logistic function. have a deriv attribute (Must) –
Returns:	dictionary of partial derivatives
Return type:	dict

autodiff.operations.mul(x, y)¶

Subtract one number from another, one of x and y has to be a Number object

Parameters:	x – a Number object y – a Number object or an int/float to be subtracted
Returns:	value of the difference

autodiff.operations.mul_deriv(x, y)¶

Derivative of multiplication, one of x and y has to be a Number object

Parameters:	x – a Number y – a Number object or an int/float to be multiplied
Returns:	The derivative of the product of x and y

autodiff.operations.negate(x)¶

Negate

Parameters:	x (Number) – Negate a number
Returns:	-x
Return type:	Number

autodiff.operations.negate_deriv(x)¶

Derivatives of the elementary negation function

Parameters:	x (Number) – Number to be negated
Returns:	the partial derivatives of the negated Number
Return type:	dictionary

autodiff.operations.pow_deriv(x, a)¶

Derivative of power of a Number

Parameters:	x – a Number a – a Number
Returns:	The derivative of the power

autodiff.operations.power(x, y)¶

power of one number by another, one of x and y has to be a Number object

Parameters:	x – a Number object or an int/float to be powered y – a Number object or an int/float to be the exponential
Returns:	value of the difference

autodiff.operations.sin(x)¶

Take the sin(x)

Parameters:	x (Number) – Number to take the sin of
Returns:	sin(x.val)
Return type:	float

autodiff.operations.sin_deriv(x)¶

Derivative of sin(x)

Parameters:	x (structures.Number()) – Number to take the sin of. Must have a `deriv` attribute
Returns:	dictionary of partial derivatives
Return type:	dict

autodiff.operations.sinh(x)¶

Hyperbolic sine

Parameters:	x (Number) – Value
Returns:	sinh(x)
Return type:	Number

autodiff.operations.sinh_deriv(x)¶

Hyperbolic sin derivative

Parameters:	x (Number) – Value
Returns:	Partial derivatives w.r.t. everything x had a partial w.r.t.
Return type:	dict

autodiff.operations.sqrt(x)¶

Square root of a number

Parameters:	x (Number) – Number to take the square root of
Returns:	the square root of Number x’s value
Return type:	float

autodiff.operations.sqrt_deriv(x)¶

Derivative of the square root function

Parameters:	x (Number) – Number to take the square root of
Returns:	the partial derivatives of the square root of number
Return type:	dictionary

autodiff.operations.subtract(x, y)¶

Subtract one number from another, one of x and y has to be a Number object

Parameters:	x – a Number object y – a Number object or an int/float to be subtracted
Returns:	value of the difference

autodiff.operations.subtract_deriv(x, y)¶

Derivative of subtractions, one of x and y has to be a Number object

Parameters:	x – a Number y – a Number object or an int/float to be subtracted
Returns:	The derivative of the difference of x and y

autodiff.operations.tan(x)¶

Take the tan(x)

Parameters:	x (Number) – Number to take the tan of
Returns:	tan(x.val)
Return type:	float

autodiff.operations.tan_deriv(x)¶

Derivative of tan(x)

Parameters:	x (structures.Numbers()) – Number to take the tan of. Must have a `deriv` attribute
Returns:	dictionary of partial derivatives
Return type:	dict

autodiff.operations.tanh(x)¶

Hyperbolic tan

Parameters:	x (Number) – Value
Returns:	tanh(x)
Return type:	Number

autodiff.operations.tanh_deriv(x)¶

Hyperbolic tan derivative

Parameters:	x (Number) – Value
Returns:	Partial derivatives w.r.t. everything x had a partial w.r.t.
Return type:	dict

autodiff.structures module¶

Data structures for autodiff

class autodiff.structures.Array(iterable)¶

Bases: object

Array class is another core data structure for ‘autodiff’. It instantiates an Array object as a list of Number objects. It holds the list internally as an np.ndarray

Parameters:	iterable – a iterable objects of Numbers to be held in Array. If lists of are passed, it will convert them to Number objects first (ints/floats) –
Returns:	Array, an object to perform automatic differentiation on.

Example

>>> import autodiff
>>> x = autodiff.structures.Number(3)
>>> a = autodiff.structures.Number(3,2)
>>> arr = autodiff.structures.Array([x, a])
Array([Number(val=3) Number(val=3)])
>>> arr.jacobian(a)
array([0, 2])

dot(other)¶

Defines the dot product on two Array objects.

Returns:	a Number object, which is the dot product.

jacobian(order)¶

Returns the jacobian matrix by the order specified.

Parameters:	order – the order to return the jacobian matrix in. Has to be not null
Returns:	a np.ndarray of partial derivatives specified by the order. Each row is an element in the original array, each column is the order specified. When order is a single element, it returns a flat array.

class autodiff.structures.Number(val, deriv=None)¶

Bases: object

Number class is the core data structure for ‘autodiff’. It instantiates a Number object by specifying a value and a derivative. Derivative with respect to itself is automatically instantiated to 1.

Parameters:	val – value of the Number deriv – a dictionary of partial derivatives. It is automatically instantiated to {self: 1} unless otherwise specified.
Returns:	Number, an object to perform automatic differentiation on.

Example

>>> import autodiff
>>> x = autodiff.structures.Number(3)
>>> x.value
3
>>> x.jacobian(x)
1
>>> a = autodiff.structures.Number(3,2)
>>> a.value
3
>>> a.jacobian(x)
2

jacobian(order)¶

Returns the jacobian matrix by the order specified.

Parameters:	order – the order to return the jacobian matrix in. Has to be not null
Returns:	a np.ndarray of partial derivatives specified by the order. When order is a single element, it returns a scaler

autodiff package¶

Submodules¶

autodiff.operations module¶

autodiff.structures module¶

Module contents¶