Struct gad::graph::Graph

pub struct Graph<C: Config> { /* fields omitted */ }

Main structure holding the computational graph (aka “tape”) used for automatic differentiation. In practice, the configuration is instantiated to build either Graph1 or GraphN, depending if higher-order differentials are needed or not.

Implementations

impl<C: Config> Graph<C>

pub fn new() -> Self

Create a new graph.

pub fn eval(&mut self) -> &mut C::EvalAlgebra

impl<C: Config> Graph<C>

pub fn make_node<D, G, F, Dims>(
    &mut self,
    data: D,
    inputs: Vec<Option<Id>>,
    update_func: F
) -> Value<D> where
    C::GradientAlgebra: CoreAlgebra<D, Value = G>,
    C::GradientStore: GradientStore<GradientId<D>, G>,
    D: HasDims<Dims = Dims>,
    G: HasDims<Dims = Dims> + Clone + 'static,
    Dims: PartialEq + Debug + Clone + 'static + Send + Sync,
    F: Fn(&mut C::GradientAlgebra, &mut C::GradientStore, G) -> Result<()> + 'static + Send + Sync, 

Create a computation node (used to define operators). During back-propagation, update_func must call store.add_gradient to propagate the gradient of each (non-constant) input.

pub fn make_generic_node<S, D, GS, GD, F, Dims>(
    &mut self,
    data: D,
    inputs: Vec<Option<Id>>,
    update_func: F
) -> Value<D> where
    C::GradientAlgebra: CoreAlgebra<S, Value = GS>,
    C::GradientAlgebra: CoreAlgebra<D, Value = GD>,
    C::GradientStore: GradientStore<GradientId<D>, GD>,
    C::GradientStore: GradientStore<GradientId<S>, GS>,
    D: HasDims<Dims = Dims>,
    GD: HasDims<Dims = Dims> + Clone + 'static,
    Dims: PartialEq + Debug + Clone + 'static + Send + Sync,
    F: Fn(&mut C::GradientAlgebra, &mut C::GradientStore, GD) -> Result<()> + 'static + Send + Sync, 

Create a computation node where the source type S may be different than the target type D.

impl<E: Default + Clone> Graph<Config1<E>>

First order only (this is the most common case)

pub fn evaluate_gradients<T>(
    &self,
    id: GradientId<T>,
    gradient: T
) -> Result<GenericGradientMap1> where
    E: CoreAlgebra<T, Value = T>,
    T: 'static, 

Propagate gradients backward, starting with the node id.

• Allow the graph to be re-used.
• Gradients are stored as pure data.

pub fn evaluate_gradients_once<T>(
    self,
    id: GradientId<T>,
    gradient: T
) -> Result<GenericGradientMap1> where
    E: CoreAlgebra<T, Value = T>,
    T: 'static, 

Propagate gradients backward, starting with the node id.

• Clean up memory when possible and consume the graph.
• Gradients are stored as pure data.

impl<E: Default + Clone> Graph<ConfigN<E>>

Higher order differentials.

pub fn compute_gradients<D>(
    &mut self,
    id: GradientId<D>,
    gradient: Value<D>
) -> Result<GenericGradientMapN> where
    Self: CoreAlgebra<D, Value = Value<D>>,
    D: 'static, 

Propagate gradients backward, starting with the node id.

• Gradients are computed as graph values that can be differentiated later.
• The graph is augmented with the nodes corresponding to gradient computations.

Trait Implementations

impl<D, E, Dims> AnalyticAlgebra<Value<D>> for Graph<Config1<E>> where
    E: Default + Clone + CoreAlgebra<D, Value = D> + AnalyticAlgebra<D> + ArithAlgebra<D> + ConstArithAlgebra<D, i16> + LinkedAlgebra<Value<D>, D>,
    D: HasDims<Dims = Dims> + Clone + 'static + Send + Sync,
    Dims: PartialEq + Debug + Clone + 'static + Send + Sync, 

fn exp(&mut self, v: &Value<D>) -> Value<D>

Element-wise natural logarithm exp(x).

fn log(&mut self, v: &Value<D>) -> Value<D>

Element-wise natural logarithm log(x).

fn log1p(&mut self, v: &Value<D>) -> Value<D>

Element-wise natural logarithm shifted by one log(1 + x).

fn sin(&mut self, v: &Value<D>) -> Value<D>

Element-wise sinus sin(x).

fn cos(&mut self, v: &Value<D>) -> Value<D>

Element-wise cosinus cos(x).

fn tanh(&mut self, v: &Value<D>) -> Value<D>

Element-wise hyperbolic tangent tanh(x).

fn sigmoid(&mut self, v: &Value<D>) -> Value<D>

Element-wise sigmoid 1 / (1 + exp(-x)).

fn reciprocal(&mut self, v: &Value<D>) -> Value<D>

Element-wise reciprocal 1/x.

fn sqrt(&mut self, v: &Value<D>) -> Value<D>

Element-wise square root sqrt(x).

fn div(&mut self, v0: &Value<D>, v1: &Value<D>) -> Result<Value<D>>

Element-wise division x / y.

fn pow(&mut self, v: &Value, p: &Value) -> Result<Value> where
    Self: ArithAlgebra<Value>, 

Element-wise power x ^ p.

impl<D, E, Dims> AnalyticAlgebra<Value<D>> for Graph<ConfigN<E>> where
    E: Default + Clone + CoreAlgebra<D, Value = D> + AnalyticAlgebra<D> + ArithAlgebra<D> + ConstArithAlgebra<D, i16> + LinkedAlgebra<Value<D>, D>,
    D: HasDims<Dims = Dims> + Clone + 'static + Send + Sync,
    Dims: PartialEq + Debug + Clone + 'static + Send + Sync, 

fn exp(&mut self, v: &Value<D>) -> Value<D>

Element-wise natural logarithm exp(x).

fn log(&mut self, v: &Value<D>) -> Value<D>

Element-wise natural logarithm log(x).

fn log1p(&mut self, v: &Value<D>) -> Value<D>

Element-wise natural logarithm shifted by one log(1 + x).

fn sin(&mut self, v: &Value<D>) -> Value<D>

Element-wise sinus sin(x).

fn cos(&mut self, v: &Value<D>) -> Value<D>

Element-wise cosinus cos(x).

fn tanh(&mut self, v: &Value<D>) -> Value<D>

Element-wise hyperbolic tangent tanh(x).

fn sigmoid(&mut self, v: &Value<D>) -> Value<D>

Element-wise sigmoid 1 / (1 + exp(-x)).

fn reciprocal(&mut self, v: &Value<D>) -> Value<D>

Element-wise reciprocal 1/x.

fn sqrt(&mut self, v: &Value<D>) -> Value<D>

Element-wise square root sqrt(x).

fn div(&mut self, v0: &Value<D>, v1: &Value<D>) -> Result<Value<D>>

Element-wise division x / y.

fn pow(&mut self, v: &Value, p: &Value) -> Result<Value> where
    Self: ArithAlgebra<Value>, 

Element-wise power x ^ p.

impl<D, E, Dims> ArithAlgebra<Value<D>> for Graph<Config1<E>> where
    E: Default + Clone + CoreAlgebra<D, Value = D> + ArithAlgebra<D> + LinkedAlgebra<Value<D>, D>,
    D: HasDims<Dims = Dims> + Clone + 'static + Send + Sync,
    Dims: PartialEq + Debug + Clone + 'static + Send + Sync, 

fn zeros(&mut self, v: &Value<D>) -> Value<D>

Element-wise zero (same dimensions as v).

fn ones(&mut self, v: &Value<D>) -> Value<D>

Element-wise one (same dimensions as v).

fn neg(&mut self, v: &Value<D>) -> Value<D>

Element-wise negation -v

fn sub(&mut self, v0: &Value<D>, v1: &Value<D>) -> Result<Value<D>>

Element-wise subtraction v0 - v1

fn mul(&mut self, v0: &Value<D>, v1: &Value<D>) -> Result<Value<D>>

Element-wise multiplication v0 * v1

impl<D, E, Dims> ArithAlgebra<Value<D>> for Graph<ConfigN<E>> where
    E: Default + Clone + CoreAlgebra<D, Value = D> + ArithAlgebra<D> + LinkedAlgebra<Value<D>, D>,
    D: HasDims<Dims = Dims> + Clone + 'static + Send + Sync,
    Dims: PartialEq + Debug + Clone + 'static + Send + Sync, 

fn zeros(&mut self, v: &Value<D>) -> Value<D>

Element-wise zero (same dimensions as v).

fn ones(&mut self, v: &Value<D>) -> Value<D>

Element-wise one (same dimensions as v).

fn neg(&mut self, v: &Value<D>) -> Value<D>

Element-wise negation -v

fn sub(&mut self, v0: &Value<D>, v1: &Value<D>) -> Result<Value<D>>

Element-wise subtraction v0 - v1

fn mul(&mut self, v0: &Value<D>, v1: &Value<D>) -> Result<Value<D>>

Element-wise multiplication v0 * v1

impl<D, E, T, Dims> ArrayAlgebra<Value<D>> for Graph<Config1<E>> where
    E: Default + Clone + CoreAlgebra<D, Value = D> + CoreAlgebra<T, Value = T> + LinkedAlgebra<Value<D>, D> + LinkedAlgebra<Value<T>, T> + ArrayAlgebra<D, Scalar = T, Dims = Dims>,
    Dims: PartialEq + Clone + Copy + Debug + Default + 'static + Send + Sync,
    D: HasDims<Dims = Dims> + Clone + 'static + Send + Sync,
    T: Number, 

type Dims = Dims

type Scalar = Value<T>

fn flat(&mut self, v: &Value<D>) -> Value<D>

Re-shape the input into a single dimension array.

fn moddims(&mut self, v: &Value<D>, rdims: Dims) -> Result<Value<D>>

Re-shape the input into an array of the given dimensions.

fn tile_as(&mut self, v: &Value<D>, rdims: Dims) -> Result<Value<D>>

Repeats the input to match the given shape.

fn sum_as(&mut self, v: &Value<D>, rdims: Dims) -> Result<Value<D>>

Sums some of the dimension of the input to fit the given shape.

fn constant_as(&mut self, v: &Value<T>, dims: Dims) -> Value<D>

Fill an array of the given shape with the given scalar value.

fn as_scalar(&mut self, v: &Value<D>) -> Result<Value<T>>

Read the scalar value in a one-element array.

fn scale(&mut self, v1: &Value<T>, v2: &Value<D>) -> Value<D>

Multiply the array element-wise by the given scalar.

fn dot(&mut self, v1: &Value<D>, v2: &Value<D>) -> Result<Value<T>>

Compute the dot-product of two arrays of the same shape.

fn norm2(&mut self, v: &Value) -> Self::Scalar

Compute the L2-norm of an array.

impl<D, E, T, Dims> ArrayAlgebra<Value<D>> for Graph<ConfigN<E>> where
    E: Default + Clone + CoreAlgebra<D, Value = D> + CoreAlgebra<T, Value = T> + LinkedAlgebra<Value<D>, D> + LinkedAlgebra<Value<T>, T> + ArrayAlgebra<D, Scalar = T, Dims = Dims>,
    Dims: PartialEq + Clone + Copy + Debug + Default + 'static + Send + Sync,
    D: HasDims<Dims = Dims> + Clone + 'static + Send + Sync,
    T: Number, 

type Dims = Dims

type Scalar = Value<T>

fn flat(&mut self, v: &Value<D>) -> Value<D>

Re-shape the input into a single dimension array.

fn moddims(&mut self, v: &Value<D>, rdims: Dims) -> Result<Value<D>>

Re-shape the input into an array of the given dimensions.

fn tile_as(&mut self, v: &Value<D>, rdims: Dims) -> Result<Value<D>>

Repeats the input to match the given shape.

fn sum_as(&mut self, v: &Value<D>, rdims: Dims) -> Result<Value<D>>

Sums some of the dimension of the input to fit the given shape.

fn constant_as(&mut self, v: &Value<T>, dims: Dims) -> Value<D>

Fill an array of the given shape with the given scalar value.

fn as_scalar(&mut self, v: &Value<D>) -> Result<Value<T>>

Read the scalar value in a one-element array.

fn scale(&mut self, v1: &Value<T>, v2: &Value<D>) -> Value<D>

Multiply the array element-wise by the given scalar.

fn dot(&mut self, v1: &Value<D>, v2: &Value<D>) -> Result<Value<T>>

Compute the dot-product of two arrays of the same shape.

fn norm2(&mut self, v: &Value) -> Self::Scalar

Compute the L2-norm of an array.

impl<D, E, T, Dims> ArrayCompareAlgebra<Value<D>> for Graph<Config1<E>> where
    E: Default + Clone + CoreAlgebra<D, Value = D> + CoreAlgebra<T, Value = T> + CompareAlgebra<D> + ArrayCompareAlgebra<D> + ArrayAlgebra<D, Dims = Dims> + ArithAlgebra<D> + ArrayAlgebra<D, Scalar = T, Dims = Dims> + LinkedAlgebra<Value<D>, D> + LinkedAlgebra<Value<T>, T>,
    T: Number,
    D: HasDims<Dims = Dims> + Clone + 'static + Send + Sync,
    Dims: PartialEq + Debug + Default + Copy + Clone + 'static + Send + Sync, 

fn max_as(&mut self, v: &Value<D>, rdims: Dims) -> Result<Value<D>>

fn argmax_as(&mut self, v: &Value<D>, rdims: Dims) -> Result<Value<D>>

fn softmax_as(&mut self, v: &Value<D>, rdims: Dims) -> Result<Value<D>>

impl<D, E, T, Dims> ArrayCompareAlgebra<Value<D>> for Graph<ConfigN<E>> where
    E: Default + Clone + CoreAlgebra<D, Value = D> + CoreAlgebra<T, Value = T> + CompareAlgebra<D> + ArrayCompareAlgebra<D> + ArrayAlgebra<D, Dims = Dims> + ArithAlgebra<D> + ArrayAlgebra<D, Scalar = T, Dims = Dims> + LinkedAlgebra<Value<D>, D> + LinkedAlgebra<Value<T>, T>,
    T: Number,
    D: HasDims<Dims = Dims> + Clone + 'static + Send + Sync,
    Dims: PartialEq + Debug + Default + Copy + Clone + 'static + Send + Sync, 

fn max_as(&mut self, v: &Value<D>, rdims: Dims) -> Result<Value<D>>

fn argmax_as(&mut self, v: &Value<D>, rdims: Dims) -> Result<Value<D>>

fn softmax_as(&mut self, v: &Value<D>, rdims: Dims) -> Result<Value<D>>

impl<C: Config> Clone for Graph<C>

fn clone(&self) -> Self

Returns a copy of the value.

pub fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<D, E, Dims> CompareAlgebra<Value<D>> for Graph<Config1<E>> where
    E: Default + Clone + CoreAlgebra<D, Value = D> + CompareAlgebra<D> + LinkedAlgebra<Value<D>, D>,
    D: HasDims<Dims = Dims> + Clone + 'static + Send + Sync,
    Dims: PartialEq + Debug + Clone + 'static + Send + Sync, 

fn select_argmax(
    &mut self,
    v0: &Value<D>,
    v1: &Value<D>,
    r0: Option<&Value<D>>,
    r1: Option<&Value<D>>
) -> Result<Value<D>>

Element-wise selection by comparison: if v0 >= v1 then r0 else r1 None arguments are taken as zeroes.

fn min(&mut self, v0: &Value, v1: &Value) -> Result<Value>

Element-wise minimum min(v0, v1).

fn max(&mut self, v0: &Value, v1: &Value) -> Result<Value>

Element-wise maximum max(v0, v1).

fn abs(&mut self, v: &Value) -> Value where
    Self: ArithAlgebra<Value>, 

Element-wise absolute value |v|.

fn sign(&mut self, v: &Value) -> Value where
    Self: ArithAlgebra<Value>, 

Element-wise sign value sign(v).

fn relu(&mut self, v: &Value) -> Value where
    Self: ArithAlgebra<Value>, 

Element-wise value relu(v) = max(v, 0).

impl<D, E, Dims> CompareAlgebra<Value<D>> for Graph<ConfigN<E>> where
    E: Default + Clone + CoreAlgebra<D, Value = D> + CompareAlgebra<D> + LinkedAlgebra<Value<D>, D>,
    D: HasDims<Dims = Dims> + Clone + 'static + Send + Sync,
    Dims: PartialEq + Debug + Clone + 'static + Send + Sync, 

fn select_argmax(
    &mut self,
    v0: &Value<D>,
    v1: &Value<D>,
    r0: Option<&Value<D>>,
    r1: Option<&Value<D>>
) -> Result<Value<D>>

Element-wise selection by comparison: if v0 >= v1 then r0 else r1 None arguments are taken as zeroes.

fn min(&mut self, v0: &Value, v1: &Value) -> Result<Value>

Element-wise minimum min(v0, v1).

fn max(&mut self, v0: &Value, v1: &Value) -> Result<Value>

Element-wise maximum max(v0, v1).

fn abs(&mut self, v: &Value) -> Value where
    Self: ArithAlgebra<Value>, 

Element-wise absolute value |v|.

fn sign(&mut self, v: &Value) -> Value where
    Self: ArithAlgebra<Value>, 

Element-wise sign value sign(v).

fn relu(&mut self, v: &Value) -> Value where
    Self: ArithAlgebra<Value>, 

Element-wise value relu(v) = max(v, 0).

impl<D, E, Dims, C> ConstArithAlgebra<Value<D>, C> for Graph<Config1<E>> where
    E: Default + Clone + CoreAlgebra<D, Value = D> + ArithAlgebra<D> + ConstArithAlgebra<D, C> + LinkedAlgebra<Value<D>, D>,
    C: Sub<C, Output = C> + One + Clone + 'static + Send + Sync,
    D: HasDims<Dims = Dims> + Clone + 'static + Send + Sync,
    Dims: PartialEq + Debug + Clone + 'static + Send + Sync, 

fn setc(&mut self, v: &Value<D>, c: C) -> Value<D>

Return a value with the same shape as v but filled with constant c.

fn addc(&mut self, v: &Value<D>, c: C) -> Value<D>

Element-wise addition of a constant v + c.

fn mulc(&mut self, v: &Value<D>, c: C) -> Value<D>

Element-wise multiplication by a constant v * c.

fn powc(&mut self, v: &Value<D>, c: C) -> Value<D>

Element-wise exponentiation by a constant v ^ c.

impl<D, E, Dims, C> ConstArithAlgebra<Value<D>, C> for Graph<ConfigN<E>> where
    E: Default + Clone + CoreAlgebra<D, Value = D> + ArithAlgebra<D> + ConstArithAlgebra<D, C> + LinkedAlgebra<Value<D>, D>,
    C: Sub<C, Output = C> + One + Clone + 'static + Send + Sync,
    D: HasDims<Dims = Dims> + Clone + 'static + Send + Sync,
    Dims: PartialEq + Debug + Clone + 'static + Send + Sync, 

fn setc(&mut self, v: &Value<D>, c: C) -> Value<D>

Return a value with the same shape as v but filled with constant c.

fn addc(&mut self, v: &Value<D>, c: C) -> Value<D>

Element-wise addition of a constant v + c.

fn mulc(&mut self, v: &Value<D>, c: C) -> Value<D>

Element-wise multiplication by a constant v * c.

fn powc(&mut self, v: &Value<D>, c: C) -> Value<D>

Element-wise exponentiation by a constant v ^ c.

impl<D, E, Dims> CoreAlgebra<D> for Graph<Config1<E>> where
    E: Default + Clone + CoreAlgebra<D, Value = D>,
    D: HasDims<Dims = Dims> + Clone + 'static + Send + Sync,
    Dims: PartialEq + Debug + Clone + 'static + Send + Sync, 

type Value = Value<D>

Tracked values of underlying type Data.

fn variable(&mut self, data: D) -> Value<D>

A differential input to the computation.

fn constant(&mut self, data: D) -> Value<D>

A non-differential input to the computation.

fn add(&mut self, v1: &Value<D>, v2: &Value<D>) -> Result<Value<D>>

Compute the sum of two values v1 + v2.

fn add_all(&mut self, values: &[&Value<D>]) -> Result<Value<D>>

Compute the sum of several values.

impl<D, E, Dims> CoreAlgebra<D> for Graph<ConfigN<E>> where
    E: Default + Clone + CoreAlgebra<D, Value = D>,
    D: HasDims<Dims = Dims> + Clone + 'static + Send + Sync,
    Dims: PartialEq + Debug + Clone + 'static + Send + Sync, 

type Value = Value<D>

Tracked values of underlying type Data.

fn variable(&mut self, data: D) -> Value<D>

A differential input to the computation.

fn constant(&mut self, data: D) -> Value<D>

A non-differential input to the computation.

fn add(&mut self, v1: &Value<D>, v2: &Value<D>) -> Result<Value<D>>

Compute the sum of two values v1 + v2.

fn add_all(&mut self, values: &[&Value<D>]) -> Result<Value<D>>

Compute the sum of several values.

impl<C: Config> Debug for Graph<C>

fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

impl<C: Config> Default for Graph<C>

fn default() -> Self

Returns the “default value” for a type.

impl<C: Config> HasGradientReader for Graph<C>

type GradientReader = C::GradientStore

impl<V, C: Config> LinkedAlgebra<V, V> for Graph<C>

Assume that we link into a copy of the original graph.

fn link<'a>(&mut self, value: &'a V) -> &'a V

impl<D, E, Dims> MatrixAlgebra<Value<D>> for Graph<Config1<E>> where
    E: Default + Clone + CoreAlgebra<D, Value = D> + LinkedAlgebra<Value<D>, D> + MatrixAlgebra<D>,
    D: HasDims<Dims = Dims> + Clone + 'static + Send + Sync,
    Dims: PartialEq + Debug + Clone + 'static + Send + Sync, 

fn matmul(
    &mut self,
    v1: &Value<D>,
    v2: &Value<D>,
    prop1: MatProp,
    prop2: MatProp
) -> Result<Value<D>>

Multiplication of two matrices after some optional transpositions.

fn transpose(&mut self, v: &Value<D>, conjugate: bool) -> Result<Value<D>>

Transpose (and optionally conjuguate) a matrix.

fn matmul_nn(&mut self, v1: &Value, v2: &Value) -> Result<Value>

Non-transposed multiplication of two matrices.

impl<D, E, Dims> MatrixAlgebra<Value<D>> for Graph<ConfigN<E>> where
    E: Default + Clone + CoreAlgebra<D, Value = D> + LinkedAlgebra<Value<D>, D> + MatrixAlgebra<D>,
    D: HasDims<Dims = Dims> + Clone + 'static + Send + Sync,
    Dims: PartialEq + Debug + Clone + 'static + Send + Sync, 

fn matmul(
    &mut self,
    v1: &Value<D>,
    v2: &Value<D>,
    prop1: MatProp,
    prop2: MatProp
) -> Result<Value<D>>

Multiplication of two matrices after some optional transpositions.

fn transpose(&mut self, v: &Value<D>, conjugate: bool) -> Result<Value<D>>

Transpose (and optionally conjuguate) a matrix.

fn matmul_nn(&mut self, v1: &Value, v2: &Value) -> Result<Value>

Non-transposed multiplication of two matrices.