gorgonia: gorgonia.org/gorgonia Index | Examples | Files

package gorgonia

import "gorgonia.org/gorgonia"

Package gorgonia is a library that helps facilitate machine learning in Go. Write and evaluate mathematical equations involving multidimensional arrays easily. Do differentiation with them just as easily.

Autodiff showcases automatic differentiation

Code:

g := NewGraph()

var x, y, z *Node
var err error

// define the expression
x = NewScalar(g, Float64, WithName("x"))
y = NewScalar(g, Float64, WithName("y"))
if z, err = Add(x, y); err != nil {
    log.Fatal(err)
}

// set initial values then run
Let(x, 2.0)
Let(y, 2.5)

// by default, LispMachine performs forward mode and backwards mode execution
m := NewLispMachine(g)
defer m.Close()
if err = m.RunAll(); err != nil {
    log.Fatal(err)
}

fmt.Printf("z: %v\n", z.Value())

if xgrad, err := x.Grad(); err == nil {
    fmt.Printf("dz/dx: %v\n", xgrad)
}

if ygrad, err := y.Grad(); err == nil {
    fmt.Printf("dz/dy: %v\n", ygrad)
}

Output:

z: 4.5
dz/dx: 1
dz/dy: 1

Basic example of representing mathematical equations as graphs.

In this example, we want to represent the following equation

z = x + y

Code:

g := NewGraph()

var x, y, z *Node
var err error

// define the expression
x = NewScalar(g, Float64, WithName("x"))
y = NewScalar(g, Float64, WithName("y"))
if z, err = Add(x, y); err != nil {
    log.Fatal(err)
}

// create a VM to run the program on
machine := NewTapeMachine(g)
defer machine.Close()

// set initial values then run
Let(x, 2.0)
Let(y, 2.5)
if err = machine.RunAll(); err != nil {
    log.Fatal(err)
}

fmt.Printf("%v", z.Value())

Output:

4.5

Code:

xV, yV, bs := prep()
concurrentTraining(xV, yV, bs, epochs)

fmt.Printf("x:\n%1.1v", xV)
fmt.Printf("y:\n%1.1v", yV)

Output:

x:
⎡    6      7      8      9  ... 5e+01  5e+01  5e+01  5e+01⎤
⎢7e+01  7e+01  7e+01  7e+01  ... 1e+02  1e+02  1e+02  1e+02⎥
⎢1e+02  1e+02  1e+02  1e+02  ... 2e+02  2e+02  2e+02  2e+02⎥
⎢2e+02  2e+02  2e+02  2e+02  ... 2e+02  2e+02  2e+02  2e+02⎥
.
.
.
⎢4e+07  4e+07  4e+07  4e+07  ... 4e+07  4e+07  4e+07  4e+07⎥
⎢4e+07  4e+07  4e+07  4e+07  ... 4e+07  4e+07  4e+07  4e+07⎥
⎢4e+07  4e+07  4e+07  4e+07  ... 4e+07  4e+07  4e+07  4e+07⎥
⎣4e+07  4e+07  4e+07  4e+07  ... 4e+07  4e+07  4e+07  4e+07⎦
y:
[-1e+02  -4e+02  -7e+02  -9e+02  ... -2e+08  -2e+08  -2e+08  -2e+08]

Linear Regression Example

The formula for a straight line is

y = mx + c

We want to find an `m` and a `c` that fits the equation well. We'll do it in both float32 and float64 to showcase the extensibility of Gorgonia

Code:

package main

import (
    "fmt"
    "log"
    "math/rand"
    "runtime"

    . "gorgonia.org/gorgonia"
    "gorgonia.org/tensor"
)

const (
    vecSize = 1000000
)

// manually generate a fake dataset which is y=2x+random
func xy(dt tensor.Dtype) (x tensor.Tensor, y tensor.Tensor) {
    var xBack, yBack interface{}
    switch dt {
    case Float32:
        xBack = tensor.Range(tensor.Float32, 1, vecSize+1).([]float32)
        yBackC := tensor.Range(tensor.Float32, 1, vecSize+1).([]float32)

        for i, v := range yBackC {
            yBackC[i] = v*2 + rand.Float32()
        }
        yBack = yBackC
    case Float64:
        xBack = tensor.Range(tensor.Float64, 1, vecSize+1).([]float64)
        yBackC := tensor.Range(tensor.Float64, 1, vecSize+1).([]float64)

        for i, v := range yBackC {
            yBackC[i] = v*2 + rand.Float64()
        }
        yBack = yBackC
    }

    x = tensor.New(tensor.WithBacking(xBack), tensor.WithShape(vecSize))
    y = tensor.New(tensor.WithBacking(yBack), tensor.WithShape(vecSize))
    return
}

func random(dt tensor.Dtype) interface{} {
    rand.Seed(13370)
    switch dt {
    case tensor.Float32:
        return rand.Float32()
    case tensor.Float64:
        return rand.Float64()
    default:
        panic("Unhandled dtype")
    }
}

func linregSetup(Float tensor.Dtype) (m, c *Node, machine VM) {
    var xT, yT Value
    xT, yT = xy(Float)

    g := NewGraph()
    x := NewVector(g, Float, WithShape(vecSize), WithName("x"), WithValue(xT))
    y := NewVector(g, Float, WithShape(vecSize), WithName("y"), WithValue(yT))
    m = NewScalar(g, Float, WithName("m"), WithValue(random(Float)))
    c = NewScalar(g, Float, WithName("c"), WithValue(random(Float)))

    pred := Must(Add(Must(Mul(x, m)), c))
    se := Must(Square(Must(Sub(pred, y))))
    cost := Must(Mean(se))

    if _, err := Grad(cost, m, c); err != nil {
        log.Fatalf("Failed to backpropagate: %v", err)
    }

    // machine := NewLispMachine(g)  // you can use a LispMachine, but it'll be VERY slow.
    machine = NewTapeMachine(g, BindDualValues(m, c))
    return m, c, machine
}

func linregRun(m, c *Node, machine VM, iter int, autoCleanup bool) (retM, retC Value) {
    if autoCleanup {
        defer machine.Close()
    }
    model := []ValueGrad{m, c}
    solver := NewVanillaSolver(WithLearnRate(0.001), WithClip(5)) // good idea to clip

    if CUDA {
        runtime.LockOSThread()
        defer runtime.UnlockOSThread()
    }
    var err error
    for i := 0; i < iter; i++ {
        if err = machine.RunAll(); err != nil {
            fmt.Printf("Error during iteration: %v: %v\n", i, err)
            break
        }

        if err = solver.Step(model); err != nil {
            log.Fatal(err)
        }

        machine.Reset() // Reset is necessary in a loop like this
    }
    return m.Value(), c.Value()

}

func linearRegression(Float tensor.Dtype, iter int) (retM, retC Value) {
    defer runtime.GC()
    m, c, machine := linregSetup(Float)
    return linregRun(m, c, machine, iter, true)
}

// Linear Regression Example
//
// The formula for a straight line is
//		y = mx + c
// We want to find an `m` and a `c` that fits the equation well. We'll do it in both float32 and float64 to showcase the extensibility of Gorgonia
func main() {
    var m, c Value
    // Float32
    m, c = linearRegression(Float32, 500)
    fmt.Printf("float32: y = %3.3fx + %3.3f\n", m, c)

    // Float64
    m, c = linearRegression(Float64, 500)
    fmt.Printf("float64: y = %3.3fx + %3.3f\n", m, c)

}

Code:

xV, yV, _ := prep()
nonConcurrentTraining(xV, yV, epochs)

fmt.Printf("x:\n%1.1v", xV)
fmt.Printf("y:\n%1.1v", yV)

Output:

x:
⎡    6      7      8      9  ... 5e+01  5e+01  5e+01  5e+01⎤
⎢7e+01  7e+01  7e+01  7e+01  ... 1e+02  1e+02  1e+02  1e+02⎥
⎢1e+02  1e+02  1e+02  1e+02  ... 2e+02  2e+02  2e+02  2e+02⎥
⎢2e+02  2e+02  2e+02  2e+02  ... 2e+02  2e+02  2e+02  2e+02⎥
.
.
.
⎢4e+07  4e+07  4e+07  4e+07  ... 4e+07  4e+07  4e+07  4e+07⎥
⎢4e+07  4e+07  4e+07  4e+07  ... 4e+07  4e+07  4e+07  4e+07⎥
⎢4e+07  4e+07  4e+07  4e+07  ... 4e+07  4e+07  4e+07  4e+07⎥
⎣4e+07  4e+07  4e+07  4e+07  ... 4e+07  4e+07  4e+07  4e+07⎦
y:
[-1e+02  -4e+02  -7e+02  -9e+02  ... -2e+08  -2e+08  -2e+08  -2e+08]

SymbolicDiff showcases symbolic differentiation

Code:

g := NewGraph()

var x, y, z *Node
var err error

// define the expression
x = NewScalar(g, Float64, WithName("x"))
y = NewScalar(g, Float64, WithName("y"))
if z, err = Add(x, y); err != nil {
    log.Fatal(err)
}

// symbolically differentiate z with regards to x and y
// this adds the gradient nodes to the graph g
var grads Nodes
if grads, err = Grad(z, x, y); err != nil {
    log.Fatal(err)
}

// create a VM to run the program on
machine := NewTapeMachine(g)
defer machine.Close()

// set initial values then run
Let(x, 2.0)
Let(y, 2.5)
if err = machine.RunAll(); err != nil {
    log.Fatal(err)
}

fmt.Printf("z: %v\n", z.Value())
if xgrad, err := x.Grad(); err == nil {
    fmt.Printf("dz/dx: %v | %v\n", xgrad, grads[0].Value())
}

if ygrad, err := y.Grad(); err == nil {
    fmt.Printf("dz/dy: %v | %v\n", ygrad, grads[1].Value())
}

Output:

z: 4.5
dz/dx: 1 | 1
dz/dy: 1 | 1

Index

Examples

Package Files

analysis.go api_gen.go batch.go bitmap.go blas.go broadcast.go collections.go compile.go const.go device.go differentiation.go doc.go dual.go engine.go equalities.go errors.go execution.go formatter.go gorgonia.go graph.go interfaces.go math.go math_nooptim.go mathutils.go nn.go node.go node_set.go noextern.go op.go op_infidel.go op_math.go op_math_noextern.go op_nn.go op_reduction.go op_tensor.go operations.go operatorLinAlg.go operatorLinAlg_const.go operatorPointwise_binary.go operatorPointwise_binary_const.go operatorPointwise_unary.go operatorPointwise_unary_const.go opt.go perf.go regalloc.go release.go shape.go slice.go solvers.go stabilization.go templates.go type.go typeSystem.go utils.go values.go values_primitives.go values_utils.go vm.go vm_genera.go vm_genera_nocuda.go vm_tape.go vm_tape_nocuda.go walker.go weights.go

Constants

const CUDA = false

CUDA indicates if this build is using CUDA

const DEBUG = false

DEBUG indicates if this build is in debug mode. It is not.

Variables

var (
    Float64 = tensor.Float64
    Float32 = tensor.Float32
    Int     = tensor.Int
    Int64   = tensor.Int64
    Int32   = tensor.Int32
    Byte    = tensor.Uint8
    Bool    = tensor.Bool

    Ptr = tensor.UnsafePointer // equivalent to interface{}. Ugh Ugh Ugh

)

func BatchNorm Uses

func BatchNorm(x, scale, bias *Node, momentum, epsilon float64) (retVal, γ, β *Node, op *BatchNormOp, err error)

func Binomial32 Uses

func Binomial32(trials, prob float64, s ...int) []float32

Binomial32 returns a []float32 drawn from a binomial distribution given the trial and probability parameters.

func Binomial64 Uses

func Binomial64(trials, prob float64, s ...int) []float64

Binomial64 returns a []float64 drawn from a binomial distribution given the trial and probability parameters.

func Compile Uses

func Compile(g *ExprGraph) (prog *program, locMap map[*Node]register, err error)

Compile takes a graph and outputs a program suitable for *tapeMachine to run

func CompileFunction Uses

func CompileFunction(g *ExprGraph, inputs, outputs Nodes) (prog *program, locMap map[*Node]register, err error)

CompileFunction takes a graph, subsets it based on the input and output nodes provided and outputs a program suitable for *tapeMachine to run. It is analogous to theano.Function(). If some input nodes are not used or is not reachable, this function will return an error

func DebugDerives Uses

func DebugDerives()

DebugDerives turns on the derivation debug option when printing a graph

func DimSizersToShapes Uses

func DimSizersToShapes(ds []DimSizer) ([]tensor.Shape, error)

DimSizersToShapes is a convenience function to convert a slice of DimSizer to a slice of tensor.Shape. It will return an error if any of them isn't a tensor.Shape

func DontDebugDerives Uses

func DontDebugDerives()

DontDebugDerives turns off derivation debug option when printing a graph. It is off by default

func FmtNodeMap Uses

func FmtNodeMap(m interface{}) mapFmt

FmtNodeMap is a convenience function to print map[*Node]<T>

The fmt flag that makes it all nicely formatted is "-". Because a map consists of two types (key's type and val's type), and the Go fmt verb doesn't quite allow us to do something like "%ds", a hack is introduced to enable nicer printing of map[*Node]<T>

Here's the hack: The "#" flag is used to indicate if the map will use the Node's ID or Name when formatting the map.

%-v 	nodeName:%v
%-#v	nodeID:%v
%-d 	nodeName:%x
%-#d 	nodeID: %x
%-p 	nodeName:%p
%-#p	nodeID:%p

If the "-" flag is not found, then the formatter returns the default Go format for map[<T>]<T2>

func Gaussian32 Uses

func Gaussian32(mean, stdev float64, s ...int) []float32

Gaussian32 returns a []float32 drawn from a gaussian distribution as defined by the mean and stdev

func Gaussian64 Uses

func Gaussian64(mean, stdev float64, s ...int) []float64

Gaussian64 returns a []float64 drawn from a gaussian distribution as defined by the mean and stdev

func GlorotEtAlN32 Uses

func GlorotEtAlN32(gain float64, s ...int) []float32

GlorotEtAlN32 returns float32 weights sampled from a normal distribution using the methods specified in Glorot et. al (2010). See also: http://jmlr.org/proceedings/papers/v9/glorot10a/glorot10a.pdf

func GlorotEtAlN64 Uses

func GlorotEtAlN64(gain float64, s ...int) []float64

GlorotEtAlN64 returns float64 weights sampled from a normal distribution using the methods specified in Glorot et. al (2010). See also: http://jmlr.org/proceedings/papers/v9/glorot10a/glorot10a.pdf

func GlorotEtAlU32 Uses

func GlorotEtAlU32(gain float64, s ...int) []float32

GlorotEtAlU32 returns float32 weights sampled from a uniform distribution using the methods specified in Glorot et. al (2010). See also: http://jmlr.org/proceedings/papers/v9/glorot10a/glorot10a.pdf

For best results, use:

1.0 for gain for weights that will be used in linear and/or sigmoid units
math.Sqrt(2.0) for gain for weights that will be used in ReLU units
math.Sqrt(2.0 / (1+alpha*alpha)) for ReLU that are leaky with alpha

func GlorotEtAlU64 Uses

func GlorotEtAlU64(gain float64, s ...int) []float64

GlorotEtAlU64 returns float64 weights sampled from a uniform distribution using the methods specified in Glorot et. al (2010). See also: http://jmlr.org/proceedings/papers/v9/glorot10a/glorot10a.pdf

For best results, use:

1.0 for gain for weights that will be used in linear and/or sigmoid units
math.Sqrt(2.0) for gain for weights that will be used in ReLU units
math.Sqrt(2.0 / (1+alpha*alpha)) for ReLU that are leaky with alpha

func GraphCollisionStats Uses

func GraphCollisionStats() (int, int, int)

Graph Collision related debugging code

func HeEtAlN64 Uses

func HeEtAlN64(gain float64, s ...int) []float64

HeEtAlN64 returns float64 weights sampled from a normal distro, using the methods described in He et al (2015). The formula is:

randn(n) * sqrt(2/n)

See also https://arxiv.org/abs/1502.01852

For best results, use:

1.0 for gain for weights that will be used in linear and/or sigmoid units
math.Sqrt(2.0) for gain for weights that will be used in ReLU units
math.Sqrt(2.0 / (1+alpha*alpha)) for ReLU that are leaky with alpha

func HeEtAlU64 Uses

func HeEtAlU64(gain float64, s ...int) []float64

HeEtAlU64 returns float64 weights sampled from a uniform distro, using the methods described in He et al (2015). The formula is:

randn(n) * sqrt(2/n)

See also https://arxiv.org/abs/1502.01852

For best results, use:

1.0 for gain for weights that will be used in linear and/or sigmoid units
math.Sqrt(2.0) for gain for weights that will be used in ReLU units
math.Sqrt(2.0 / (1+alpha*alpha)) for ReLU that are leaky with alpha

func Let Uses

func Let(n *Node, be interface{}) error

Let binds a Value to a node that is a variable. A variable is represented as a *Node with no Op. It is equivalent to :

x = 2

func NewLispMachine Uses

func NewLispMachine(g *ExprGraph, opts ...VMOpt) *lispMachine

NewLispMachine creates a VM that executes the graph as it is traversed. Depending on the VMOpts passed in this VM is also capable of performing automatic differentiation.

func NewTapeMachine Uses

func NewTapeMachine(g *ExprGraph, opts ...VMOpt) *tapeMachine

NewTapeMachine creates a VM that compiles a graph into a prog.

func ReturnNode Uses

func ReturnNode(n *Node)

ReturnNode returns a node to the pool. It does not check that the *Node has been removed from the graph. USE WITH CAUTION.

func ReturnType Uses

func ReturnType(t hm.Type)

ReturnType

func S Uses

func S(start int, opt ...int) tensor.Slice

S creates a tensor.Slice. end is optional. It should be passed in as the first param of the optionals. step is optional. It should be passed in as the second param of the optionals.

Default end is start+1. Default step is 1, unless end == step+1, then it defaults to 0

func SetDerivOf Uses

func SetDerivOf(deriv, of *Node)

SetDerivOf is used to hack around the fundamental limitations of Gorgonia.

Specifically it is used to set a node as the derivative of another node, used in the cuDNN version of batch norm.

The cuDNN BatchNorm operation produces the derivatives for the scale and bias as a side effect of calculating the derivative of the input. Because Gorgonia's Ops are modelled as pure functions (and no tuples) this causes a bit of trouble. With the clever use of scratch space ops multireturn can be simulated. But this causes derivatives to not be set correctly.

func SetOptimizationLevel Uses

func SetOptimizationLevel(i int)

SetOptimizationLevel sets the fast math optimization level. By default, fast math is turned off, and this function is a no-op.

Use the `fastmath` build tag to use fast math

func TypeOf Uses

func TypeOf(v Value) hm.Type

TypeOf returns the Type of the value

func Uniform32 Uses

func Uniform32(low, high float64, s ...int) []float32

Uniform32 returns a []float64 drawn from a uniform distribution between [low, high) that is provided

func Uniform64 Uses

func Uniform64(low, high float64, s ...int) []float64

Uniform64 returns a []float64 drawn from a uniform distribution between [low, high) that is provided

func UnsafeLet Uses

func UnsafeLet(n *Node, be interface{}) error

UnsafeLet binds a Value to any node, not just a variable node. This means that you can use it to change any node's value at the runtime of the graph. UNSAFE!

Additional notes: if `be` is a tensor.Slice, and the node's op is a sliceOp or sliceIncrOp, the op's slice will be replaced with the new slice.

func Use Uses

func Use(b BLAS)

Use defines which BLAS implementation gorgonia should use. The default is Gonum's Native. These are the other options:

Use(blastoise.Implementation())
Use(cubone.Implementation())
Use(cgo.Implementation)

Note the differences in the brackets. The blastoise and cubone ones are functions.

func UseNonStable Uses

func UseNonStable()

UseNonStable turns off the stabilization functions when building graphs.

func UseStabilization Uses

func UseStabilization()

UseStabilization sets the global option to invoke stabilization functions when building the graph. Numerical stabilization is on by default

func ValueClose Uses

func ValueClose(a, b Value) bool

ValueClose checks whether two values are close to one another. It's predominantly used as an alternative equality test for floats

func ValueEq Uses

func ValueEq(a, b Value) bool

ValueEq is the equality function for values

func WalkGraph Uses

func WalkGraph(start *Node) <-chan *Node

WalkGraph walks a graph. It returns a channel of *Nodes, so be sure to consume the channel or there may be a deadlock

func WithGraphName Uses

func WithGraphName(name string) graphconopt

WithGraphName is a ExprGraph construction option that provides a name.

type ADOp Uses

type ADOp interface {
    Op

    DoDiff(ctx ExecutionContext, inputs Nodes, output *Node) error
}

An ADOp is an Op that supports automatic differentiation.

type AdaGradSolver Uses

type AdaGradSolver struct {
    // contains filtered or unexported fields
}

AdaGradSolver is the solver that does adaptive gradient descent. Read the paper: http://jmlr.org/papers/v12/duchi11a.html

func NewAdaGradSolver Uses

func NewAdaGradSolver(opts ...SolverOpt) *AdaGradSolver

NewAdaGradSolver creates a new AdaGradSolver with sane-ish default values

func (*AdaGradSolver) Step Uses

func (s *AdaGradSolver) Step(model []ValueGrad) (err error)

Step steps through each node in the model and applies the Adaptive Gradient gradient descent algorithm on the value.

This function will error out if the nodes do not have an associated Grad value.

type AdamSolver Uses

type AdamSolver struct {
    // contains filtered or unexported fields
}

AdamSolver is the Adaptive Moment Estimation solver (basically RMSProp on steroids). Paper: http://arxiv.org/abs/1412.6980

We overload the purpose of existing data structure of a *dualValue. However, instead of just holding a value and its derivative, the cache's *dualValues hold the Means of gradients (in .Value) and the variances of the gradients (in .d)

func NewAdamSolver Uses

func NewAdamSolver(opts ...SolverOpt) *AdamSolver

NewAdamSolver creates an Adam solver with these default values:

eta (learn rate)	  	: 0.001
eps (smoothing factor)		: 1e-8
beta1				: 0.9
beta2 				: 0.999
batch				: 1

func (*AdamSolver) Step Uses

func (s *AdamSolver) Step(model []ValueGrad) (err error)

Step steps through each node in the model and applies the Adaptive Moment Estimation gradient descent algorithm on the value.

This function will error out if the nodes do not have an associated Grad value.

type Arena Uses

type Arena interface {
    Get(dev Device, size int64) (tensor.Memory, error)       // Get returns a NoOpError when it cannot get a memory. Please allocate
    GetFromValue(dev Device, v Value) (tensor.Memory, error) // Gets a memory and copies the values into the memory and returns it.
    Put(dev Device, mem tensor.Memory, size int64)           // puts the memory back into the arena
    PutValue(dev Device, v Value)                            // puts the memory back into the arena

    // Transfers memory from device to device
    Transfer(toDev, fromDev Device, v Value, synchronous bool) (retVal Value, err error)
}

Arena is a representation of a pool of tensor.Memory

type AutoDiffError Uses

type AutoDiffError struct{}

AutoDiffError is an error which should be passed if the function is not differentiable. This is useful for Op implementations

func (AutoDiffError) Error Uses

func (err AutoDiffError) Error() string

type B Uses

type B bool

B represents a bool value.

func (*B) Data Uses

func (v *B) Data() interface{}

Data returns the original representation of the Value

func (*B) Dtype Uses

func (v *B) Dtype() tensor.Dtype

Dtype returns the Dtype of the value

func (*B) Format Uses

func (v *B) Format(s fmt.State, c rune)

Format implements fmt.Formatter

func (*B) MemSize Uses

func (v *B) MemSize() uintptr

MemSize satisfies the tensor.Memory interface

func (*B) Pointer Uses

func (v *B) Pointer() unsafe.Pointer

Pointer returns the pointer as an unsafe.Pointer. Satisfies the tensor.Memory interface

func (*B) Shape Uses

func (v *B) Shape() tensor.Shape

Shape returns a scalar shape for all scalar values

func (*B) Size Uses

func (v *B) Size() int

Size returns 0 for all scalar Values

func (*B) Uintptr Uses

func (v *B) Uintptr() uintptr

Uintptr satisfies the tensor.Memory interface

type BLAS Uses

type BLAS interface {
    blas.Float32
    blas.Float64
}

BLAS represents all the possible implementations of BLAS. The default is Gonum's Native

func WhichBLAS Uses

func WhichBLAS() BLAS

WhichBLAS returns the BLAS that gorgonia uses.

type BarzilaiBorweinSolver Uses

type BarzilaiBorweinSolver struct {
    // contains filtered or unexported fields
}

Barzilai-Borwein performs Gradient Descent in steepest descend direction Solves 0 = F(x), by x_{i+1} = x_i - eta * Grad(F)(x_i) Where the learn rate eta is calculated by the Barzilai-Borwein method: eta(x_i) = <(x_i - x_{i-1}), (Grad(F)(x_i) - Grad(F)(x_{i-1}))> /

||(Grad(F)(x_i) - Grad(F)(x_{i-1}))||^2

The input learn rate is used for the first iteration. TODO: Check out stochastic implementations, e.g. "Barzilai-Borwein Step Size for Stochastic Gradient Descent" https://arxiv.org/abs/1605.04131

func NewBarzilaiBorweinSolver Uses

func NewBarzilaiBorweinSolver(opts ...SolverOpt) *BarzilaiBorweinSolver

func (*BarzilaiBorweinSolver) Step Uses

func (s *BarzilaiBorweinSolver) Step(model []ValueGrad) (err error)

Step steps through each node in the model and applies the Barzilai-Borwein gradient descent algorithm on the value.

This function will error out if the nodes do not have an associated Grad value.

type BatchNormOp Uses

type BatchNormOp struct {
    // contains filtered or unexported fields
}

BatchNormOp is a batch normalization process as described by Ioffe and Szegedy (2015) - http://arxiv.org/abs/1502.03167

Normalization is done as:

γ(x - μ) / σ + β

γ is the scaling factor and β is the offset factor. These are created by BatchNorm()

func (*BatchNormOp) Arity Uses

func (op *BatchNormOp) Arity() int

func (*BatchNormOp) CallsExtern Uses

func (op *BatchNormOp) CallsExtern() bool

func (*BatchNormOp) DiffWRT Uses

func (op *BatchNormOp) DiffWRT(inputs int) []bool

func (*BatchNormOp) Do Uses

func (op *BatchNormOp) Do(values ...Value) (retVal Value, err error)

func (*BatchNormOp) DoDiff Uses

func (op *BatchNormOp) DoDiff(ctx ExecutionContext, inputs Nodes, output *Node) error

func (*BatchNormOp) Hashcode Uses

func (op *BatchNormOp) Hashcode() uint32

func (*BatchNormOp) InferShape Uses

func (op *BatchNormOp) InferShape(ns ...DimSizer) (tensor.Shape, error)

func (*BatchNormOp) OverwritesInput Uses

func (op *BatchNormOp) OverwritesInput() int

func (*BatchNormOp) Reset Uses

func (op *BatchNormOp) Reset() error

func (*BatchNormOp) ReturnsPtr Uses

func (op *BatchNormOp) ReturnsPtr() bool

func (*BatchNormOp) SetTesting Uses

func (op *BatchNormOp) SetTesting()

func (*BatchNormOp) SetTraining Uses

func (op *BatchNormOp) SetTraining()

func (*BatchNormOp) String Uses

func (op *BatchNormOp) String() string

func (*BatchNormOp) SymDiff Uses

func (op *BatchNormOp) SymDiff(inputs Nodes, output *Node, grad *Node) (retVal Nodes, err error)

func (*BatchNormOp) Type Uses

func (op *BatchNormOp) Type() hm.Type

func (*BatchNormOp) UsePreallocDo Uses

func (op *BatchNormOp) UsePreallocDo(prealloc Value, inputs ...Value) (retVal Value, err error)

func (*BatchNormOp) WriteHash Uses

func (op *BatchNormOp) WriteHash(h hash.Hash)

type Batched Uses

type Batched interface {
    WorkAvailable() <-chan struct{}
    DoWork()
}

type BatchedBLAS Uses

type BatchedBLAS interface {
    Batched
    BLAS
}

type BatchedDevice Uses

type BatchedDevice interface {
    Batched
    Retval() interface{}
    Errors() error
}

type BestDoer Uses

type BestDoer interface {
    Op

    BestDo(prealloc Value, vals ...Value) (Value, error)
}

type BinaryOp Uses

type BinaryOp interface {
    Op

    IsBinary() bool
}

A BinaryOp is an Op that takes only two inputs

type BroadcastPattern Uses

type BroadcastPattern byte

BroadcastPattern is actually a bit array. It's split into 2 nibbles - the left nibble represents the left operand, the right nibble represents the right operand:

xxxx|xxxx

The least significant bit of each nibble is elem 0. Concrete examples:

00000010 (0x02) = broadcast axis 1 of the right operand
00000001 (0x01) = broadcast axis 0 of the right operand
00000101 (0x09) = broadcast axis 0 AND axis 2 of the right operand
00010000 (0x10) = broadcast axis 0 of the left operand
00110000 (0x30) = broadcast axis 0 and axis 1 of the lef operand

You get the drill.

Do note that the current limitation of the BroadcastPattern allows only up to 4 dimensions per operand.

func NewBroadcastPattern Uses

func NewBroadcastPattern(leftAxes, rightAxes []byte) BroadcastPattern

NewBroadcastPattern is a helper function to create broadcast patterns

type CLDoer Uses

type CLDoer interface {
    CLDo(inputs ...Value) (Value, error)
}

CLDoer uses OpenCL to perform the Op. As of now, there are NO Ops that support OpenCL

type CUDAADOp Uses

type CUDAADOp interface {
    ADOp
    CUDADoDiff(extern External, dev Device, inputs Nodes, output *Node) error
}

type CUDADoer Uses

type CUDADoer interface {
    CUDADo(extern External, dev Device, prealloc Value, inputs ...Value) (retVal Value, err error)
}

CUDADoer uses CUDA to perform the Op.

type CloneErrorer Uses

type CloneErrorer interface {
    Clone() (interface{}, error)
}

CloneErrorer represents any type that can clone itself and return an error if necessary

type Cloner Uses

type Cloner interface {
    Clone() interface{}
}

Cloner represents any type that can clone itself.

type CopierFrom Uses

type CopierFrom interface {
    CopyFrom(src interface{}) error
}

CopierFrom represents any type that can copy data from the source provided.

type CopierTo Uses

type CopierTo interface {
    CopyTo(dest interface{}) error
}

CopierTo represents any type that can copy data to the destination.

type Device Uses

type Device int

Device represents the device where the code will be executed on. In this build, all code will run on the CPU

const (
    CPU Device = 0 // CPU the only device the graph will be executed on
)

func (Device) Alloc Uses

func (d Device) Alloc(extern External, size int64) (tensor.Memory, error)

Alloc allocates memory on the device. This is currently a NO-OP in this build

func (Device) Free Uses

func (d Device) Free(extern External, mem tensor.Memory, sie uint) error

Free frees the memory on the device. This is currently a NO-OP in this build

func (Device) IsGPU Uses

func (d Device) IsGPU() bool

IsGPU will always return false in this build

func (Device) String Uses

func (d Device) String() string

String implements fmt.Stringer and runtime.Stringer

type DimSizer Uses

type DimSizer interface {
    DimSize(int) (int, error)
}

DimSizer is any type (typically a tensor.Shape) that allows querying for a dimension size given an input dimension.

func ShapesToDimSizers Uses

func ShapesToDimSizers(shapes []tensor.Shape) []DimSizer

ShapesToDimSizers is a convenience function to convert a slice of tensor.Shape to a slice of DimSizer

type Dtyper Uses

type Dtyper interface {
    Dtype() tensor.Dtype
}

Dtyper represents any type (typically a Value) that knows its own Dtype

type ExecutionContext Uses

type ExecutionContext struct {
    External
    Device
}

ExecutionContext informs how an op should be executed

type ExprGraph Uses

type ExprGraph struct {
    // contains filtered or unexported fields
}

ExprGraph is a data structure for a directed acyclic graph (of expressions). This structure is the main entry point for Gorgonia.

func NewGraph Uses

func NewGraph(opts ...graphconopt) *ExprGraph

NewGraph creates a new graph. Duh

func (*ExprGraph) AddNode Uses

func (g *ExprGraph) AddNode(n *Node) (retVal *Node)

AddNode adds n to the graph. It panics if the added node ID matches an existing node ID.

func (*ExprGraph) AllNodes Uses

func (g *ExprGraph) AllNodes() Nodes

AllNodes is like Nodes, but returns Nodes instead of []graph.Node. Nodes() has been reserved for the graph.Directed interface, so this one is named AllNodes instead

func (*ExprGraph) ByName Uses

func (g *ExprGraph) ByName(name string) (retVal Nodes)

ByName returns nodes that have the name provided. Bear in mind that the name that is compared to is the internal name, not the result of calling node.Name(). The reason for doing this is for ease of finding only names that are user-supplied, instead of autogenerated names

func (*ExprGraph) Clone Uses

func (g *ExprGraph) Clone() interface{}

Clone clones the graph. All nodes gets cloned, and their values are cloned as well.

func (*ExprGraph) Constant Uses

func (g *ExprGraph) Constant(v Value) *Node

Constant returns a constant that may be found in the graph. If no constant were found, a new one is created instead

func (*ExprGraph) Edge Uses

func (g *ExprGraph) Edge(u, v int64) graph.Edge

Edge returns the edge from u to v if such an edge exists and nil otherwise. The node v must be directly reachable from u as defined by the From method.

func (*ExprGraph) ExactSubgraphRoots Uses

func (g *ExprGraph) ExactSubgraphRoots(ns ...*Node) *ExprGraph

ExactSubgraphRoots creates a subgraph from the roots provided. The difference between SubgraphRoots and ExactSubgraphRoots is that ExactSubGraphRoots will not attempt to discover if any nodes are missing.

Given a function like the following:

z = x + y
set(x, -x.Grad) // setting the value of x to the negative of the gradient

When SubgraphRoots is used on z, the `-x.Grad` will be included. When using ExactSubgraphRoots, only `x` and `y` are included in the subgraph

func (*ExprGraph) From Uses

func (g *ExprGraph) From(nodeid int64) graph.Nodes

From returns all nodes in g that can be reached directly from n.

func (*ExprGraph) Has Uses

func (g *ExprGraph) Has(nodeid int64) bool

Has returns whether the node exists within the graph.

func (*ExprGraph) HasEdgeBetween Uses

func (g *ExprGraph) HasEdgeBetween(x, y int64) bool

HasEdgeBetween returns whether an edge exists between nodes x and y without considering direction.

func (*ExprGraph) HasEdgeFromTo Uses

func (g *ExprGraph) HasEdgeFromTo(u, v int64) bool

HasEdgeFromTo returns whether an edge exists in the graph from u to v.

func (*ExprGraph) Inputs Uses

func (g *ExprGraph) Inputs() (retVal Nodes)

Inputs returns a list of nodes which are inputs (that is to say, the user is required to set a value in it)

func (*ExprGraph) Node Uses

func (g *ExprGraph) Node(id int64) graph.Node

Node returns the node in the graph with the given ID.

func (*ExprGraph) Nodes Uses

func (g *ExprGraph) Nodes() graph.Nodes

Nodes returns all the nodes in the graph.

func (*ExprGraph) RemoveNode Uses

func (g *ExprGraph) RemoveNode(node graph.Node)

RemoveNode removes n from the graph, as well as any edges attached to it. If the node is not in the graph it is a no-op.

func (*ExprGraph) Roots Uses

func (g *ExprGraph) Roots() (retVal Nodes)

Roots returns a list of nodes that are not children of any other nodes

func (*ExprGraph) SetEdge Uses

func (g *ExprGraph) SetEdge(e graph.Edge)

SetEdge adds e, an edge from one node to another. If the nodes do not exist, they are added. It will panic if the IDs of the e.From and e.To are equal.

func (*ExprGraph) String Uses

func (g *ExprGraph) String() string

func (*ExprGraph) Subgraph Uses

func (g *ExprGraph) Subgraph(ns ...*Node) *ExprGraph

Subgraph subsets a graph. This function has overloaded meanings - If only one node is passed in, it assumes that the one node is the root, otherwise, it treats ns as the subset of nodes to be included in the subgraph

func (*ExprGraph) SubgraphRoots Uses

func (g *ExprGraph) SubgraphRoots(ns ...*Node) *ExprGraph

SubgraphRoots creates a subgraph, assuming the provided nodes are roots to the new subgraph.

func (*ExprGraph) To Uses

func (g *ExprGraph) To(nid int64) graph.Nodes

To returns all nodes in g that can reach directly to n.

func (*ExprGraph) ToDot Uses

func (g *ExprGraph) ToDot() string

ToDot generates the graph in graphviz format. The use of this is to generate for the entire graph which may have multiple trees with different roots TODO: This is getting unwieldy. Perhaps refactor out into a ToDot(...Opt)?

func (*ExprGraph) UnbindAll Uses

func (g *ExprGraph) UnbindAll()

UnbindAll unbinds all the values from the nodes

func (*ExprGraph) UnbindAllNonInputs Uses

func (g *ExprGraph) UnbindAllNonInputs()

UnbindAllNonInputs unbinds all the values from nodes that aren't input nodes

type ExternMetadata Uses

type ExternMetadata struct {
    tensor.Engine
    // contains filtered or unexported fields
}

ExternMetadata is used to hold metadata about external execution devices. In this build, it's an empty struct because the default build doesn't use external devices to execute the graph on

func (*ExternMetadata) Cleanup Uses

func (m *ExternMetadata) Cleanup()

Cleanup cleans up the ancillary allocations made during the calling of batched external device function.

The reason for this method is due to the fact that there is currently no way to free memory while the context is still running without causing some weirdness to the CUDA calls.

This is a No-op in this build

func (*ExternMetadata) DoWork Uses

func (m *ExternMetadata) DoWork() error

DoWork flushes any batched cgo calls. In this build it only flushes the batched BLAS calls.

func (*ExternMetadata) Get Uses

func (m *ExternMetadata) Get(dev Device, size int64) (tensor.Memory, error)

Get allocates a memory of the size. In this build it returns a NoOpError.

func (*ExternMetadata) GetFromValue Uses

func (m *ExternMetadata) GetFromValue(dev Device, v Value) (tensor.Memory, error)

GetFromValue allocates a memory of the size of v. In this build it returns a NoOpError, and v itself

func (ExternMetadata) HasFunc Uses

func (m ExternMetadata) HasFunc(name string) bool

HasFunc will always return false in this build

func (*ExternMetadata) Put Uses

func (m *ExternMetadata) Put(dev Device, mem tensor.Memory, size int64)

Put puts a previously allocated memory slab of the provided size back into the pool. Currently this is a No-op in this build.

func (*ExternMetadata) PutValue Uses

func (m *ExternMetadata) PutValue(dev Device, v Value)

PutValue puts a previously allocated value into the pool. In this build, it is a noop.

func (*ExternMetadata) Reset Uses

func (m *ExternMetadata) Reset()

func (*ExternMetadata) Signal Uses

func (m *ExternMetadata) Signal()

Signal sends a signal down the workavailable channel, telling the VM to call the DoWork method. Signal is a synchronous method

func (*ExternMetadata) Sync Uses

func (m *ExternMetadata) Sync() chan struct{}

Sync returns the sync channel

func (*ExternMetadata) Transfer Uses

func (m *ExternMetadata) Transfer(toDev, fromDev Device, v Value, synchronous bool) (retVal Value, err error)

Transfer transfers a value from device to device. In this build, it's a noop, returning the input value, and a nil error

func (*ExternMetadata) WorkAvailable Uses

func (m *ExternMetadata) WorkAvailable() <-chan bool

WorkAvailable returns a channel of empty struct, which is used to signal to the VM when there is work available. The VM will then call the DoWork method.

type External Uses

type External interface {
    Arena
    Signal() // signals the machine to do work
    Sync() chan struct{}
}

External is a representation of an external device (cuda/cgo/openCL), conceptually modelled as a machine.

type ExternalOp Uses

type ExternalOp struct {
    Op
    ExecutionContext

    Prealloc  Value
    Incr      Value // is this a Incr? IncrDoers have higher precedence over PreallocDo
    UseUnsafe bool  // Is this an unsafe op? Lowest of all "special" Dos
}

ExternalOp is an op that contains an external context. This allows for ops to be run without needing a VM

func NewAddOp Uses

func NewAddOp(a, b *Node, ctx ExecutionContext) *ExternalOp

func NewExternalOp Uses

func NewExternalOp(op Op, ctx ExecutionContext, prealloc Value) *ExternalOp

NewExternalOp creates a new *ExternalOp.

func NewHadamardProdOp Uses

func NewHadamardProdOp(a, b *Node, ctx ExecutionContext) *ExternalOp

func NewSubOp Uses

func NewSubOp(a, b *Node, ctx ExecutionContext) *ExternalOp

NewSubOp creates a new *ExternalOp that wraps a sub op

func (*ExternalOp) DetermineDevice Uses

func (op *ExternalOp) DetermineDevice(inputs Nodes, output *Node) error

func (*ExternalOp) Do Uses

func (op *ExternalOp) Do(vals ...Value) (Value, error)

Do performs the op,

func (*ExternalOp) String Uses

func (op *ExternalOp) String() string

type F32 Uses

type F32 float32

F32 represents a float32 value.

func (*F32) Data Uses

func (v *F32) Data() interface{}

Data returns the original representation of the Value

func (*F32) Dtype Uses

func (v *F32) Dtype() tensor.Dtype

Dtype returns the Dtype of the value

func (*F32) Format Uses

func (v *F32) Format(s fmt.State, c rune)

Format implements fmt.Formatter

func (*F32) MemSize Uses

func (v *F32) MemSize() uintptr

MemSize satisfies the tensor.Memory interface

func (*F32) Pointer Uses

func (v *F32) Pointer() unsafe.Pointer

Pointer returns the pointer as an unsafe.Pointer. Satisfies the tensor.Memory interface

func (*F32) Shape Uses

func (v *F32) Shape() tensor.Shape

Shape returns a scalar shape for all scalar values

func (*F32) Size Uses

func (v *F32) Size() int

Size returns 0 for all scalar Values

func (*F32) Uintptr Uses

func (v *F32) Uintptr() uintptr

Uintptr satisfies the tensor.Memory interface

type F64 Uses

type F64 float64

F64 represents a float64 value.

func (*F64) Data Uses

func (v *F64) Data() interface{}

Data returns the original representation of the Value

func (*F64) Dtype Uses

func (v *F64) Dtype() tensor.Dtype

Dtype returns the Dtype of the value

func (*F64) Format Uses

func (v *F64) Format(s fmt.State, c rune)

Format implements fmt.Formatter

func (*F64) MemSize Uses

func (v *F64) MemSize() uintptr

MemSize satisfies the tensor.Memory interface

func (*F64) Pointer Uses

func (v *F64) Pointer() unsafe.Pointer

Pointer returns the pointer as an unsafe.Pointer. Satisfies the tensor.Memory interface

func (*F64) Shape Uses

func (v *F64) Shape() tensor.Shape

Shape returns a scalar shape for all scalar values

func (*F64) Size Uses

func (v *F64) Size() int

Size returns 0 for all scalar Values

func (*F64) Uintptr Uses

func (v *F64) Uintptr() uintptr

Uintptr satisfies the tensor.Memory interface

type I Uses

type I int

I represents a int value.

func (*I) Data Uses

func (v *I) Data() interface{}

Data returns the original representation of the Value

func (*I) Dtype Uses

func (v *I) Dtype() tensor.Dtype

Dtype returns the Dtype of the value

func (*I) Format Uses

func (v *I) Format(s fmt.State, c rune)

Format implements fmt.Formatter

func (*I) MemSize Uses

func (v *I) MemSize() uintptr

MemSize satisfies the tensor.Memory interface

func (*I) Pointer Uses

func (v *I) Pointer() unsafe.Pointer

Pointer returns the pointer as an unsafe.Pointer. Satisfies the tensor.Memory interface

func (*I) Shape Uses

func (v *I) Shape() tensor.Shape

Shape returns a scalar shape for all scalar values

func (*I) Size Uses

func (v *I) Size() int

Size returns 0 for all scalar Values

func (*I) Uintptr Uses

func (v *I) Uintptr() uintptr

Uintptr satisfies the tensor.Memory interface

type I32 Uses

type I32 int32

I32 represents a int32 value.

func (*I32) Data Uses

func (v *I32) Data() interface{}

Data returns the original representation of the Value

func (*I32) Dtype Uses

func (v *I32) Dtype() tensor.Dtype

Dtype returns the Dtype of the value

func (*I32) Format Uses

func (v *I32) Format(s fmt.State, c rune)

Format implements fmt.Formatter

func (*I32) MemSize Uses

func (v *I32) MemSize() uintptr

MemSize satisfies the tensor.Memory interface

func (*I32) Pointer Uses

func (v *I32) Pointer() unsafe.Pointer

Pointer returns the pointer as an unsafe.Pointer. Satisfies the tensor.Memory interface

func (*I32) Shape Uses

func (v *I32) Shape() tensor.Shape

Shape returns a scalar shape for all scalar values

func (*I32) Size Uses

func (v *I32) Size() int

Size returns 0 for all scalar Values

func (*I32) Uintptr Uses

func (v *I32) Uintptr() uintptr

Uintptr satisfies the tensor.Memory interface

type I64 Uses

type I64 int64

I64 represents a int64 value.

func (*I64) Data Uses

func (v *I64) Data() interface{}

Data returns the original representation of the Value

func (*I64) Dtype Uses

func (v *I64) Dtype() tensor.Dtype

Dtype returns the Dtype of the value

func (*I64) Format Uses

func (v *I64) Format(s fmt.State, c rune)

Format implements fmt.Formatter

func (*I64) MemSize Uses

func (v *I64) MemSize() uintptr

MemSize satisfies the tensor.Memory interface

func (*I64) Pointer Uses

func (v *I64) Pointer() unsafe.Pointer

Pointer returns the pointer as an unsafe.Pointer. Satisfies the tensor.Memory interface

func (*I64) Shape Uses

func (v *I64) Shape() tensor.Shape

Shape returns a scalar shape for all scalar values

func (*I64) Size Uses

func (v *I64) Size() int

Size returns 0 for all scalar Values

func (*I64) Uintptr Uses

func (v *I64) Uintptr() uintptr

Uintptr satisfies the tensor.Memory interface

type IncrDoer Uses

type IncrDoer interface {
    IncrDo(toIncr Value, inputs ...Value) error
}

IncrDoer increments the toIncr with the result of doing

type InitWFn Uses

type InitWFn func(dt tensor.Dtype, s ...int) interface{}

InitWFn is a type of helper function to help initialize weights vector/matrices. It generates the backing required for the tensors.

It's typically used in closures

func Gaussian Uses

func Gaussian(mean, stdev float64) InitWFn

Gaussian creates a InitWFn with the specified parameters. Example Usage:

w := NewMatrix(g, Float64, WithName("w"), WithShape(2,2), WithInit(Gaussian(0, 1)))

This will create a backing slice of []float64, with the length of 4, and its values are drawn from a gaussian distro

func GlorotN Uses

func GlorotN(gain float64) InitWFn

GlorotN creates a InitWFn that populates a Value with weights normally sampled using Glorot et al.'s algorithm

func GlorotU Uses

func GlorotU(gain float64) InitWFn

GlorotU creates a InitWFn that populates a Value with weights uniformly sampled using Glorot et al.'s algorithm

func Ones Uses

func Ones() InitWFn

func RangedFrom Uses

func RangedFrom(start int) InitWFn

RangedFrom creates an InitWFn that populates a Value starting with the provided start, increamenting the number for each element in the value by 1

func Uniform Uses

func Uniform(low, high float64) InitWFn

Uniform creates a InitWFn with the specified parameters. Example Usage:

w := NewMatrix(g, Float64, WithName("w"), WithShape(2,2), WithInit(Uniform(-1, 1)))

This will create a backing slice of []float64, with the length of 4, and its values are drawn from a uniform distro

func ValuesOf Uses

func ValuesOf(val interface{}) InitWFn

func Zeroes Uses

func Zeroes() InitWFn

Zeroes creates an InitWfn that populates a Value with... zeroes. I don't know what you expected.

type Momentum Uses

type Momentum struct {
    // contains filtered or unexported fields
}

Momentum is the stochastic gradient descent optimizer with momentum item.

func NewMomentum Uses

func NewMomentum(opts ...SolverOpt) *Momentum

NewMomentum creates a new Momentum with sane-ish default values

func (*Momentum) Step Uses

func (s *Momentum) Step(model []ValueGrad) (err error)

Step steps through each node in the model and applies the Momentum stochastic gradient descent algorithm on the value.

This function will error out if the nodes do not have an associated Grad value.

type Namer Uses

type Namer interface {
    Name() string
}

Namer is anything that has a name

type NoOpError Uses

type NoOpError interface {
    NoOp() bool
}

NoOpError is an error returned when an operation does nothing.

type NoRetOp Uses

type NoRetOp interface {
    Op

    ReturnsNothing() bool
}

A NoRetOp is an Op that reads a value, but does not return any value. It's a representation of a not-pure function

type Node Uses

type Node struct {
    // contains filtered or unexported fields
}

A Node is a node in the computation graph

func Abs Uses

func Abs(a *Node) (*Node, error)

Abs performs a pointwise abs.

func Add Uses

func Add(a, b *Node) (*Node, error)

Add perfors a pointwise add operation.

func ApplyOp Uses

func ApplyOp(op Op, children ...*Node) (retVal *Node, err error)

ApplyOp is the generic function application - for when no specialization is required

func ApplyOpWithName Uses

func ApplyOpWithName(op Op, name string, children ...*Node) (retVal *Node, err error)

ApplyOpWithName applies the op, and then gives the node the given name

func At Uses

func At(a *Node, coords ...int) (retVal *Node, err error)

At is a symbolic operation for getting a value at the provided coordinates. If the input is a scalar, all the coordinates MUST be 0, or else an error will be returned.

func BatchedMatMul Uses

func BatchedMatMul(a, b *Node) (retVal *Node, err error)

BatchedMatMul returns a node representing the batched mat mul operation

func BinaryXent Uses

func BinaryXent(output, target *Node) (retVal *Node, err error)

BinaryXent is a convenience function for doing binary crossentropy stuff. The formula is as below:

-(y * logprob) +  (1-y)(1-logprob)

func BinomialRandomNode Uses

func BinomialRandomNode(g *ExprGraph, dt tensor.Dtype, trials, prob float64, shape ...int) *Node

BinomialRandomNode creates an input node that has a random op so that everytime the node is passed, random values will be plucked from a binomial distribution with the mean and stdev provided. The type of the node depends on the shape passed in. To get a scalar value at run time, don't pass in any shapes

Whilst technically the number of trials of a binomal distribution should be a discrete value (you can't have half a trial), to keep with API uniformity, trials is passed in as a float64, but will be truncated to an int at runtime.

func Broadcast Uses

func Broadcast(binOp ʘBinaryOperatorType, a, b *Node, pattern BroadcastPattern) (retVal *Node, err error)

Broadcast works somewhat like Numpy's broadcast, except it's now exposed as a function.

func Ceil Uses

func Ceil(a *Node) (*Node, error)

Ceil performs a pointwise ceil.

func Concat Uses

func Concat(axis int, ns ...*Node) (retVal *Node, err error)

Concat performs a concatenate on the provided axis and inputs.

func Conv1d Uses

func Conv1d(in, filter *Node, kernel, pad, stride, dilation int) (*Node, error)

Conv1d is a 1D convlution. It relies on Conv2D

func Conv2d Uses

func Conv2d(im, filter *Node, kernelShape tensor.Shape, pad, stride, dilation []int) (retVal *Node, err error)

Conv2d is a simple 2D convoution, to be used for CPU computation only. If CuDNN is used, use the CUDAConv2D function. These are the properties the inputs must fulfil:

im: must have 4D shape. Expected format is BCHW (batch, channel, height, width) filter: must have 4D shape: (batch, kernel, height, width) kernelShape: shape of the filter kernel pad: len(pad) == 2 stride: len(stride) == 2 dilation: len(dilation) == 2

func Cos Uses

func Cos(a *Node) (*Node, error)

Cos performs a pointwise cos.

func Cube Uses

func Cube(a *Node) (*Node, error)

Cube performs a pointwise cube.

func Div Uses

func Div(a, b *Node) (retVal *Node, err error)

Div is a shortcut function for HadamardDiv for scalar values. For matrix/tensor values, the matrix division operation is not yet handled, and will panic.

func Dropout Uses

func Dropout(x *Node, prob float64) (retVal *Node, err error)

Dropout is a convenience function to implement dropout. It uses randomly zeroes out a *Tensor with a probability drawn from a uniform distribution

func Eq Uses

func Eq(a, b *Node, retSame bool) (*Node, error)

Eq perfors a pointwise eq operation.

retSame indicates if the data type of the return value should be the same as the input data type. It defaults to Bool otherwise.

func Exp Uses

func Exp(a *Node) (*Node, error)

Exp performs a pointwise exp.

func Expm1 Uses

func Expm1(a *Node) (*Node, error)

Expm1 performs a pointwise expm1.

func Floor Uses

func Floor(a *Node) (*Node, error)

Floor performs a pointwise floor.

func GaussianRandomNode Uses

func GaussianRandomNode(g *ExprGraph, dt tensor.Dtype, mean, stdev float64, shape ...int) *Node

GaussianRandomNode creates an input node that has a random op so everytime the node is passed, random values will be plucked from a gaussian distribution with the mean and stdev provided. The type of the node depends on the shape passed in. To get a scalar value at run time, don't pass in any shapes

func Gt Uses

func Gt(a, b *Node, retSame bool) (*Node, error)

Gt perfors a pointwise gt operation.

retSame indicates if the data type of the return value should be the same as the input data type. It defaults to Bool otherwise.

func Gte Uses

func Gte(a, b *Node, retSame bool) (*Node, error)

Gte perfors a pointwise gte operation.

retSame indicates if the data type of the return value should be the same as the input data type. It defaults to Bool otherwise.

func HadamardDiv Uses

func HadamardDiv(a, b *Node) (*Node, error)

HadamardDiv perfors a pointwise hadamarddiv operation.

func HadamardProd Uses

func HadamardProd(a, b *Node) (*Node, error)

HadamardProd perfors a pointwise hadamardprod operation.

func Im2Col Uses

func Im2Col(n *Node, kernel, pad, stride, dilation tensor.Shape) (retVal *Node, err error)

Im2Col converts a BCHW image block to columns. The kernel, pad and stride parameter must be shape of size 2, no more no less This poor naming scheme clearly comes from matlab

func Inverse Uses

func Inverse(a *Node) (*Node, error)

Inverse performs a pointwise inverse.

func InverseSqrt Uses

func InverseSqrt(a *Node) (*Node, error)

InverseSqrt performs a pointwise inversesqrt.

func Log Uses

func Log(a *Node) (*Node, error)

Log performs a pointwise log.

func Log1p Uses

func Log1p(a *Node) (*Node, error)

Log1p performs a pointwise log1p.

func Log2 Uses

func Log2(a *Node) (*Node, error)

Log2 performs a pointwise log2.

func LogSumExp Uses

func LogSumExp(a *Node, axis int) (retVal *Node, err error)

LogSumExp performs addition in the log domain

func Lt Uses

func Lt(a, b *Node, retSame bool) (*Node, error)

Lt perfors a pointwise lt operation.

retSame indicates if the data type of the return value should be the same as the input data type. It defaults to Bool otherwise.

func Lte Uses

func Lte(a, b *Node, retSame bool) (*Node, error)

Lte perfors a pointwise lte operation.

retSame indicates if the data type of the return value should be the same as the input data type. It defaults to Bool otherwise.

func Max Uses

func Max(a *Node, along ...int) (retVal *Node, err error)

Max performs a max() on the input and the provided axes.

func MaxPool2D Uses

func MaxPool2D(x *Node, kernel tensor.Shape, pad, stride []int) (*Node, error)

func Mean Uses

func Mean(a *Node, along ...int) (retVal *Node, err error)

Mean performs a mean() on the input and the provided axes.

func Mul Uses

func Mul(a, b *Node) (retVal *Node, err error)

Mul is the general handler for multiplication of nodes. It is extremely overloaded. Only use if you know what you're doing

If any of the nodes are ScalarType, then it'll be redirected to HadamardProd() instead If the nodes are both vectors (that is, have a shape of (x, 1) or (1, x)), then the operator used will be a vectorDot If only one of the nodes is a vector, then the operator used will be a matrix-vector multiplication will be used, and most importantly, a transpose will be used (when necessary) If both nodes are matrices, then well, matrix multiplication will be done

func Must Uses

func Must(n *Node, err error, opts ...NodeConsOpt) *Node

Must indicates a node must be created. If there isn't a node created, or there was an error, it subsumes the error, and immediately panics

func Ne Uses

func Ne(a, b *Node, retSame bool) (*Node, error)

Ne perfors a pointwise ne operation.

retSame indicates if the data type of the return value should be the same as the input data type. It defaults to Bool otherwise.

func Neg Uses

func Neg(a *Node) (*Node, error)

Neg performs a pointwise neg.

func NegNegOptimization Uses

func NegNegOptimization(a *Node) (retVal *Node, err error)

NegNegOptimization optimizes away -(-x) to just return x place before neg

func NewConstant Uses

func NewConstant(v interface{}, opts ...NodeConsOpt) *Node

NewConstant takes in any reasonable value and makes it a constant node.

func NewMatrix Uses

func NewMatrix(g *ExprGraph, t tensor.Dtype, opts ...NodeConsOpt) *Node

NewMatrix creates a Node representing a variable that holds a matrix (nxm)

func NewScalar Uses

func NewScalar(g *ExprGraph, t tensor.Dtype, opts ...NodeConsOpt) *Node

NewScalar creates a Node representing a variable that holds a scalar value

func NewTensor Uses

func NewTensor(g *ExprGraph, t tensor.Dtype, dims int, opts ...NodeConsOpt) *Node

NewTensor creates a Node representing a variable that holds a tensor (any n-dimensional array with dimensions greater than 2)

func NewUniqueNode Uses

func NewUniqueNode(opts ...NodeConsOpt) *Node

NewUniqueNode creates a new unique node in a graph. If no graph was specified in the construction options then it will just return a graphless node.

func NewVector Uses

func NewVector(g *ExprGraph, t tensor.Dtype, opts ...NodeConsOpt) *Node

NewVector creates a Node representing a variable that holds a vector (nx1 matrix)

func NodeFromAny Uses

func NodeFromAny(g *ExprGraph, any interface{}, opts ...NodeConsOpt) *Node

NodeFromAny creates a Node from a tensor.Tensor, automatically filling in shape and type info

func Norm Uses

func Norm(a *Node, axis, p int) (retVal *Node, err error)

Norm returns the p-norm of a Value. Use p=2 if you want to use unordered norms.

This is a simpler version of the norms found in the Tensor package, which specializes and optimizes even more (well, given it's adapted from Numpy, it is clearly way more optimized)

func OneHotVector Uses

func OneHotVector(id, classes int, t tensor.Dtype, opts ...NodeConsOpt) *Node

OneHotVector creates a node representing a one hot vector

func OuterProd Uses

func OuterProd(a, b *Node) (retVal *Node, err error)

OuterProd returns a Node representing the outer product of two vectors. This function will return an error if both input nodes are not vectors

func Pow Uses

func Pow(a, b *Node) (*Node, error)

Pow perfors a pointwise pow operation.

func Read Uses

func Read(n *Node, into *Value) (retVal *Node)

Read is one of those special snowflake tumblrina *Nodes. It allows for extraction of the value of the *Node at runtime into a Value. Note that a *Value (a pointer to a Value) is passed into this function, not a Value.

func Rectify Uses

func Rectify(x *Node) (retVal *Node, err error)

Rectify is a convenience function for creating rectified linear units activation functions. This function uses >=, which is the canonical version. If you want to use >, you can create your own by just following this.

func ReduceAdd Uses

func ReduceAdd(nodes Nodes, opts ...NodeConsOpt) (retVal *Node, err error)

ReduceAdd takes a slice of *Nodes, and folds them into one by adding

func ReduceMul Uses

func ReduceMul(nodes Nodes, opts ...NodeConsOpt) (retVal *Node, err error)

ReduceMul is like foldl(*, nodes)

func Reshape Uses

func Reshape(n *Node, to tensor.Shape) (retVal *Node, err error)

Reshape reshapes a node and returns a new node with the new shape

func Set Uses

func Set(a, b *Node) (retVal *Node)

Set is the equivalent of doing this:

a = b

where a and b are both variables

func Sigmoid Uses

func Sigmoid(a *Node) (*Node, error)

Sigmoid performs a pointwise sigmoid.

func Sign Uses

func Sign(a *Node) (*Node, error)

Sign performs a pointwise sign.

func Sin Uses

func Sin(a *Node) (*Node, error)

Sin performs a pointwise sin.

func SizeOf Uses

func SizeOf(axis int, x *Node) (retVal *Node, err error)

SizeOf returns the size of a value along an axis

func Slice Uses

func Slice(n *Node, slices ...tensor.Slice) (retVal *Node, err error)

Slice slices a *Node. For T[:] slices, pass in nil. Will error out if node's type is not a Tensor

func SoftMax Uses

func SoftMax(a *Node) (retVal *Node, err error)

SoftMax performs softmax on the input. Specifically this is used:

e^(a[i]) / sum((e^(a[i])))

For a more numerically stable SoftMax, use StableSoftMax.

func Softplus Uses

func Softplus(a *Node) (*Node, error)

Softplus performs a pointwise softplus.

func Sqrt Uses

func Sqrt(a *Node) (*Node, error)

Sqrt performs a pointwise sqrt.

func Square Uses

func Square(a *Node) (*Node, error)

Square performs a pointwise square.

func StableSoftMax Uses

func StableSoftMax(a *Node) (retVal *Node, err error)

StableSoftMax performs a numerically stable softmax on the input. Specifically this is the formula used:

e^(a - max(a)) / sum(e^(a - max(a)))

func Sub Uses

func Sub(a, b *Node) (*Node, error)

Sub perfors a pointwise sub operation.

func Sum Uses

func Sum(a *Node, along ...int) (retVal *Node, err error)

Sum performs a sum() on the input and the provided axes.

func Tanh Uses

func Tanh(a *Node) (*Node, error)

Tanh performs a pointwise tanh.

func Tensordot Uses

func Tensordot(aAxes []int, bAxes []int, a, b *Node) (retVal *Node, err error)

Tensordot performs a tensor contraction of a and b along specified axes.

func Transpose Uses

func Transpose(n *Node, axes ...int) (retVal *Node, err error)

Transpose performs a transpose on the input and provided permutation axes.

func UniformRandomNode Uses

func UniformRandomNode(g *ExprGraph, dt tensor.Dtype, low, high float64, shape ...int) *Node

UniformRandomNode creates an input node that has a random op so everytime the node is passed, random values will be plucked from a uniform distribution. The type of the node depends on the shape passed in. To get a scalar value at run time, don't pass in any shapes

func (*Node) Clone Uses

func (n *Node) Clone() (retVal interface{})

Clone clones the node. There are some caveats:

- the graph is not copied over - the node essentially does not belong to a collection
- there is no ID
- the children are not cloned

func (*Node) CloneTo Uses

func (n *Node) CloneTo(g *ExprGraph) *Node

CloneTo clones the node into a new graph. If CloneTo() is called on the same graph as the n, it will return n. The reason this is done is because at any given time, every node should be unique in the *ExprGraph.

TODO: clone children as well (this means that CloneTo() is only currently suitable fo input nodes)

func (*Node) Device Uses

func (n *Node) Device() Device

Device returns the device the data will be on

func (*Node) Dims Uses

func (n *Node) Dims() int

Dims indicates how many dimensions the node's result has

func (*Node) Dtype Uses

func (n *Node) Dtype() tensor.Dtype

Dtype returns the dtype of the node

func (*Node) Grad Uses

func (n *Node) Grad() (Value, error)

Grad returns the gradient if there is one.

func (*Node) GradOnDevice Uses

func (n *Node) GradOnDevice(dev Device, extern External) (retVal Value, allocOnExtern bool, err error)

GradOnDevice gets the gradient value of the node as a Value but on the desired device. In this build the device is always CPU, so it's equivalent to calling .Grad()

func (*Node) Graph Uses

func (n *Node) Graph() *ExprGraph

Graph returns the graph of the node

func (*Node) Hashcode Uses

func (n *Node) Hashcode() uint32

Hashcode provides the hash for the tree, assuming that the node is the root of the tree. Original implementation was here by Vatine (who's apparently 80 years old and using SO!?!):

http://stackoverflow.com/questions/1988665/hashing-a-tree-structure

func (*Node) ID Uses

func (n *Node) ID() int64

ID returns the ID of the node. This satisfies the gonum/graph.Node interface

func (*Node) IsColVec Uses

func (n *Node) IsColVec() bool

IsColVec indicates if a node represents a Column Vector. This is based on the type of the node, not the actual value associated with the node

func (*Node) IsMatrix Uses

func (n *Node) IsMatrix() bool

IsMatrix indicates if a node represents a matrix. This is based on the type of the node, not the actual value associated with the node

func (*Node) IsRowVec Uses

func (n *Node) IsRowVec() bool

IsRowVec indicates if a node represents a Row Vector. This is based on the type of the node, not the actual value associated with the node

func (*Node) IsScalar Uses

func (n *Node) IsScalar() bool

IsScalar indicates if a node represents a a scalar value. This is based on the type of the node, not the actual value associated with the node

func (*Node) IsVar Uses

func (n *Node) IsVar() bool

IsVar returns true if the node represents a differentiable variable (i.e. it's an argument to the function that is not a statement)

func (*Node) IsVec Uses

func (n *Node) IsVec() bool

IsVec returns whether this node is a vector

func (*Node) IsVector Uses

func (n *Node) IsVector() bool

IsVector indicates if a node represents a vector value. This is based on the type of the node, not the actual value associated with the node

func (*Node) Name Uses

func (n *Node) Name() string

Name returns the name of the node. If a name was specified and it is too long, the short name will be used instead (except in inputs)

The short name is typically of the form: OpName(%1, %2 ...), making it read more like a function call

func (*Node) Op Uses

func (n *Node) Op() Op

Op returns the Op of the node

func (*Node) RestrictedToDot Uses

func (n *Node) RestrictedToDot(up, down int) string

RestrictedToDot prints the graphviz compatible string but does not print the entire tree up and down indicates how many levels to look up, and how many levels to look down

func (*Node) Shape Uses

func (n *Node) Shape() tensor.Shape

Shape returns the shape of the node

func (*Node) Strides Uses

func (n *Node) Strides() []int

Strides returns the strides of the value of the node

func (*Node) String Uses

func (n *Node) String() string

String() implements the fmt.Stringer interface

func (*Node) ToDot Uses

func (n *Node) ToDot() string

ToDot returns the graph as a graphviz compatible string

func (*Node) Type Uses

func (n *Node) Type() hm.Type

Type returns the type of the node

func (*Node) Value Uses

func (n *Node) Value() Value

Value returns the valuse bound to the node. May return nil

func (*Node) ValueOnDevice Uses

func (n *Node) ValueOnDevice(dev Device, extern External) (retVal Value, allocOnExtern bool, err error)

ValueOnDevice gets the value of the node as a Value but on the desired device. In this build the device is always CPU, so it's equivalent to calling .Value()

func (*Node) WriteHash Uses

func (n *Node) WriteHash(h hash.Hash32)

WriteHash writes the hash to the provided Hash32.

type NodeConsOpt Uses

type NodeConsOpt func(*Node)

NodeConsOpt is a function that provides construction options for any Node.

func In Uses

func In(g *ExprGraph) NodeConsOpt

In is a node construction option to set a node's graph. A `*Node`'s graph is immutable. If the graph has already been set, a check will be made that the specifiec *Graph and the *Graph set in *Node are the same. If they are not, the function will panic/

func WithChildren Uses

func WithChildren(children Nodes) NodeConsOpt

WithChildren sets the children of a node to the specified chidren. This construction option does NOT check if existing children exists, and will overwrite the existing children.

func WithGrad Uses

func WithGrad(any interface{}) NodeConsOpt

WithGrad is a node construction option that binds the value to the *Node. This function may panic if:

- There isn't already a value associated with the node (.boundTo == nil)
- The type of the Value does not match the value of the node.

func WithGroupName Uses

func WithGroupName(name string) NodeConsOpt

WithGroupName is a node construction option to group a *Node within a particular group. This option is useful for debugging with graphs.

func WithInit Uses

func WithInit(fn InitWFn) NodeConsOpt

WithInit is a node construction option to initialize a *Node with the InitWFn provided.

func WithName Uses

func WithName(name string) NodeConsOpt

WithName is a node construction option that gives the *Node the provided name. This is especially useful in debugging graphs.

func WithOp Uses

func WithOp(op Op) NodeConsOpt

WithOp is a node construction option to set a node's Op to the specified Op. `Op`s in `*Node`s are immutable once set and cannot be changed. If the node already has an Op specified a check will be made to see if the provided Op and the one already specified in the `*Node` is the same - do note that comparison of Ops is done using the `Hashcode()` method of Ops, and hash collisions MAY occur - If both ops are different, this function will panic.

func WithShape Uses

func WithShape(shp ...int) NodeConsOpt

WithShape is a node construction option to initialize a *Node with a particular shape. This function panics if the shape's dimensions do not match the specified dimensions of the *Node.

func WithType Uses

func WithType(t hm.Type) NodeConsOpt

WithType is a node construction option to set a node to the specified type. Types in *Node are immutable once set. If the type has already been specified in the node, a check will be made to see if the both types are the same. If it isn't, it will panic.

func WithValue Uses

func WithValue(any interface{}) NodeConsOpt

WithValue is a node construction option that binds the value to the *Node. This function may panic if:

- Gorgonia was unable to convert interface{} into a Value.
- The type of the Value does not match the type of the nodes.

type NodeSet Uses

type NodeSet map[*Node]struct{}

NodeSet is the primary type that represents a set

func NewNodeSet Uses

func NewNodeSet(a ...*Node) NodeSet

NewNodeSet creates and returns a reference to an empty set.

func (NodeSet) Add Uses

func (set NodeSet) Add(i *Node) bool

Add adds an item to the current set if it doesn't already exist in the set.

func (NodeSet) Cardinality Uses

func (set NodeSet) Cardinality() int

Cardinality returns how many items are currently in the set.

func (*NodeSet) Clear Uses

func (set *NodeSet) Clear()

Clear clears the entire set to be the empty set.

func (NodeSet) Clone Uses

func (set NodeSet) Clone() NodeSet

Clone returns a clone of the set. Does NOT clone the underlying elements.

func (NodeSet) Contains Uses

func (set NodeSet) Contains(i *Node) bool

Contains determines if a given item is already in the set.

func (NodeSet) ContainsAll Uses

func (set NodeSet) ContainsAll(i ...*Node) bool

ContainsAll determines if the given items are all in the set

func (NodeSet) Difference Uses

func (set NodeSet) Difference(other NodeSet) NodeSet

Difference returns a new set with items in the current set but not in the other set

func (NodeSet) Equal Uses

func (set NodeSet) Equal(other NodeSet) bool

Equal determines if two sets are equal to each other. If they both are the same size and have the same items they are considered equal. Order of items is not relevent for sets to be equal.

func (NodeSet) Intersect Uses

func (set NodeSet) Intersect(other NodeSet) NodeSet

Intersect returns a new set with items that exist only in both sets.

func (NodeSet) IsSubset Uses

func (set NodeSet) IsSubset(other NodeSet) bool

IsSubset determines if every item in the other set is in this set.

func (NodeSet) IsSuperset Uses

func (set NodeSet) IsSuperset(other NodeSet) bool

IsSuperset determines if every item of this set is in the other set.

func (NodeSet) Iter Uses

func (set NodeSet) Iter() <-chan *Node

Iter returns a channel of type *Node that you can range over.

func (NodeSet) Remove Uses

func (set NodeSet) Remove(i *Node)

Remove allows the removal of a single item in the set.

func (NodeSet) SymmetricDifference Uses

func (set NodeSet) SymmetricDifference(other NodeSet) NodeSet

SymmetricDifference returns a new set with items in the current set or the other set but not in both.

func (NodeSet) ToSlice Uses

func (set NodeSet) ToSlice() Nodes

ToSlice returns the elements of the current set as a slice

func (NodeSet) Union Uses

func (set NodeSet) Union(other NodeSet) NodeSet

Union returns a new set with all items in both sets.

type Nodes Uses

type Nodes []*Node

Nodes is a slice of nodes, but it also acts as a set of nodes by implementing the Sort interface

func Backpropagate Uses

func Backpropagate(outputs, gradOutputs, wrt Nodes) (retVal Nodes, err error)

Backpropagate backpropagates errors by performing revers-emode symbolic differentiation, starting from the outputs, and working its way towads the inputs.

This is the rough algorithm:

1. Filter out nodes that are unreachable
2. Forwards analysis, where a list of nodes affecting the output is added to consideration
3. Backwards analysis, where a list of nodes affected by differentiating the output are added to the consideration
4. If there is a difference in both sets, it will cause an error (both sets should be the same)
5. Traverse the graph from output towards input. On each visit, perform the symbolic differentiation

For most cases, Grad() should be used instead of Backpropagate(), as Grad() performs several checks which would be the general use case, before calling Backpropagate()

func Grad Uses

func Grad(cost *Node, WRTs ...*Node) (retVal Nodes, err error)

Grad takes a scalar cost node and a list of with-regards-to, and returns the gradient

func Sort Uses

func Sort(g *ExprGraph) (sorted Nodes, err error)

Sort topologically sorts a ExprGraph: root of graph will be first

func UnstableSort Uses

func UnstableSort(g *ExprGraph) (sorted Nodes, err error)

func (Nodes) Add Uses

func (ns Nodes) Add(n *Node) Nodes

Add adds to set

func (Nodes) AllSameGraph Uses

func (ns Nodes) AllSameGraph() bool

AllSameGraph returns true if all the nodes in the slice belong to the same graph. Note that constants do not have to belong to the same graph.

func (Nodes) Contains Uses

func (ns Nodes) Contains(want *Node) bool

Contains checks if the wanted node is in the set

func (Nodes) Difference Uses

func (ns Nodes) Difference(other Nodes) Nodes

Difference is ns - other. Bear in mind it is NOT commutative

func (Nodes) Equals Uses

func (ns Nodes) Equals(other Nodes) bool

Equals returns true if two Nodes are the same

func (Nodes) Format Uses

func (ns Nodes) Format(s fmt.State, c rune)

Format implements fmt.Formatter, which allows Nodes to be differently formatted depending on the verbs

func (Nodes) Intersect Uses

func (ns Nodes) Intersect(other Nodes) Nodes

Intersect performs an intersection with other Nodes

func (Nodes) Len Uses

func (ns Nodes) Len() int

func (Nodes) Less Uses

func (ns Nodes) Less(i, j int) bool

func (Nodes) Set Uses

func (ns Nodes) Set() Nodes

Set returns a uniquifies slice. It mutates the slice.

func (Nodes) Swap Uses

func (ns Nodes) Swap(i, j int)

type Op Uses

type Op interface {

    // Arity returns the number of inputs the Op expects. -1 indicates that it's n-ary and will be determined at runtime
    Arity() int

    // Informs the type of the Op (not the node). This will be used by the type system to infer the final type of the node
    Type() hm.Type

    // returns the output shape as a function of the inputs
    InferShape(...DimSizer) (tensor.Shape, error)

    // executes the op
    Do(...Value) (Value, error)

    // indicates if the Op will return a pointer (allowing possible inplace edits) or by value
    // if it's false, the return value of the Op will be a copy of its input
    ReturnsPtr() bool

    // Does this op potentially call external (cgo or cuda) functions (thereby requiring extra overhead for Go's trampolining thing)
    CallsExtern() bool

    // overwriteInput() is a method which states which input the output will be overwriting.
    // This allows for some efficiency gains as the underlying arrays wouldn't have to be re-allocated.
    // The method returns an int instead of a bool because potentially different operations may be allowed
    // to overwrite certain inputs. For example, consider an operation to increment a value:
    // the IncrementOp would be a unary operator, and assuming we would like to overwrite the input,
    // the retVal of overwriteInput() will be 0 (inputs[0]).
    // -1 is returned if overwriting of input is disallowed
    OverwritesInput() int

    /* Other methods */
    WriteHash(h hash.Hash)
    Hashcode() uint32
    fmt.Stringer
}

An Op is a symbolic representation of an operation Think of them as functions, taking an input (or multiple), and outputting something

All Ops have type signatures that look like this:

OpName :: (Floats a) ⇒ Tensor a → Tensor a → Tensor a

type RMSPropSolver Uses

type RMSPropSolver struct {
    // contains filtered or unexported fields
}

RMSPropSolver is a solver that implements Geoffrey Hinton's RMSProp gradient descent optimization algorithm. http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf

func NewRMSPropSolver Uses

func NewRMSPropSolver(opts ...SolverOpt) *RMSPropSolver

NewRMSPropSolver creates an RMSProp solver with these default values:

eta (learn rate)	  : 0.001
eps (smoothing factor): 1e-8
rho (decay factor)    : 0.999

func (*RMSPropSolver) Step Uses

func (s *RMSPropSolver) Step(model []ValueGrad) (err error)

Step steps through each node in the model and applies the RMSProp gradient descent algorithm on the value.

This function will error out if the nodes do not have an associated Grad value.

type ReductionOp Uses

type ReductionOp interface {
    Op

    IsReduction() bool
}

ReductionOp changes the shape of the node

type SDOp Uses

type SDOp interface {
    Op

    // DiffWRT indicates if the op is differentiable with regards to the given number of inputs
    // returns []bool to indicate which input it is differentiable to
    DiffWRT(inputs int) []bool

    // SymDiff symbolically differentiates the op
    SymDiff(inputs Nodes, output, grad *Node) (retVal Nodes, err error)
}

A SDOp is an Op that supports symbolic differentiation

type Scalar Uses

type Scalar interface {
    Value
    // contains filtered or unexported methods
}

Scalar represents a scalar(non-array-based) value. Do note that it's the pointers of the scalar types (F64, F32, etc) that implement the Scalar interface. The main reason is primarily due to optimizations with regards to memory allocation and copying for device interoperability.

type Solver Uses

type Solver interface {
    Step([]ValueGrad) error
}

Solver is anything that does gradient updates. The name solvers is stolen from Caffe. A much shorter name than GradientUpdaters

type SolverOpt Uses

type SolverOpt func(s Solver)

SolverOpt is a function that provides construction options for a Solver

func WithBatchSize Uses

func WithBatchSize(batch float64) SolverOpt

WithBatchSize sets the batch size for the solver. Currently only Adam and Vanilla (basic SGD) has batch size support

func WithBeta1 Uses

func WithBeta1(beta1 float64) SolverOpt

WithBeta1 sets the beta1 param of the solver. Only works with Adam

func WithBeta2 Uses

func WithBeta2(beta2 float64) SolverOpt

WithBeta2 sets the beta1 param of the solver. Only works with Adam

func WithClip Uses

func WithClip(clip float64) SolverOpt

WithClip clips the gradient if it gets too crazy. By default all solvers do not have any clips attached

func WithEps Uses

func WithEps(eps float64) SolverOpt

WithEps sets the smoothing factor for the solver.

func WithL1Reg Uses

func WithL1Reg(l1reg float64) SolverOpt

WithL1Reg adds a L1 regularization parameter to the solver. By default, the solvers do not use any regularization param

func WithL2Reg Uses

func WithL2Reg(l2reg float64) SolverOpt

WithL2Reg adds a L2 regularization parameter to the solver. By default, the solvers do not use any regularization param

func WithLearnRate Uses

func WithLearnRate(eta float64) SolverOpt

WithLearnRate sets the learn rate or step size for the solver.

func WithMomentum Uses

func WithMomentum(momentum float64) SolverOpt

func WithRho Uses

func WithRho(rho float64) SolverOpt

WithRho sets the decay parameter of the RMSProp solver

type StandardEngine Uses

type StandardEngine struct {
    tensor.StdEng
}

StandardEngine is the default CPU engine for gorgonia

func (StandardEngine) Transpose Uses

func (e StandardEngine) Transpose(a tensor.Tensor, expStrides []int) error

type SymDiffError Uses

type SymDiffError struct {
    // contains filtered or unexported fields
}

SymDiffError provides the context at which an error occured

func (SymDiffError) Error Uses

func (err SymDiffError) Error() string

func (SymDiffError) Grad Uses

func (err SymDiffError) Grad() *Node

func (SymDiffError) Grads Uses

func (err SymDiffError) Grads() map[*Node]Nodes

func (SymDiffError) Node Uses

func (err SymDiffError) Node() *Node

func (SymDiffError) Nodes Uses

func (err SymDiffError) Nodes() Nodes

type SymbolicEngine Uses

type SymbolicEngine struct{}

type Tensor Uses

type Tensor interface {
    // info about the ndarrayN
    Shape() tensor.Shape
    Strides() []int
    Dtype() tensor.Dtype
    Dims() int
    Size() int
    DataSize() int

    // Data access related
    RequiresIterator() bool
    Iterator() tensor.Iterator

    // ops
    tensor.Slicer
    At(...int) (interface{}, error)
    SetAt(v interface{}, coord ...int) error
    Reshape(...int) error
    T(axes ...int) error
    UT()
    Transpose() error // Transpose actually moves the data
    Apply(fn interface{}, opts ...tensor.FuncOpt) (tensor.Tensor, error)

    // data related interface
    tensor.Zeroer
    tensor.MemSetter
    tensor.Dataer
    tensor.Eq
    tensor.Cloner

    // type overloading methods
    IsScalar() bool
    ScalarValue() interface{}

    // engine/memory related stuff
    // all Tensors should be able to be expressed of as a slab of memory
    // Note: the size of each element can be acquired by T.Dtype().Size()
    Engine() tensor.Engine      // Engine can be nil
    MemSize() uintptr           // the size in memory
    Uintptr() uintptr           // the pointer to the first element, as a uintptr
    Pointer() unsafe.Pointer    // the pointer to the first elemment as a unsafe.Ponter
    IsNativelyAccessible() bool // Can Go access the memory
    IsManuallyManaged() bool    // Must Go manage the memory

    // formatters
    fmt.Formatter
    fmt.Stringer

    // all Tensors are serializable to these formats
    WriteNpy(io.Writer) error
    ReadNpy(io.Reader) error
    gob.GobEncoder
    gob.GobDecoder
}

type TensorType Uses

type TensorType struct {
    Dims int // dims

    Of  hm.Type
}

TensorType is a type constructor for tensors.

Think of it as something like this:

data Tensor a = Tensor d a

The shape of the Tensor is not part of TensorType. Shape checking is relegated to the dynamic part of the program run

func (TensorType) Apply Uses

func (t TensorType) Apply(sub hm.Subs) hm.Substitutable

Apply applies the substitutions on the types. Satisfies the hm.Type interface.

func (TensorType) Eq Uses

func (t TensorType) Eq(other hm.Type) bool

Eq is the equality function of this type. The type of Tensor has to be the same, and for now, only the dimensions are compared. Shape may be compared in the future for tighter type inference. Satisfies the hm.Type interface.

func (TensorType) Format Uses

func (t TensorType) Format(state fmt.State, c rune)

Format implements fmt.Formatter. It is also required for the satisfication the hm.Type interface.

func (TensorType) FreeTypeVar Uses

func (t TensorType) FreeTypeVar() hm.TypeVarSet

FreeTypeVar returns any free (unbound) type variables in this type. Satisfies the hm.Type interface.

func (TensorType) Name Uses

func (t TensorType) Name() string

Name returns the name of the type, which will always be "Tensor". Satisfies the hm.Type interface.

func (TensorType) Normalize Uses

func (t TensorType) Normalize(k, v hm.TypeVarSet) (hm.Type, error)

Normalize normalizes the type variable names (if any) in the TensorType. Satisfies the hm.Type interface.

func (TensorType) String Uses

func (t TensorType) String() string

String implements fmt.Stringer and runtime.Stringer. Satisfies the hm.Type interface.

func (TensorType) Types Uses

func (t TensorType) Types() hm.Types

Types returns a list of types that TensorType contains - in this case, the type of Tensor (float64, float32, etc). Satisfies the hm.Type interface.

type Typer Uses

type Typer interface {
    Type() hm.Type
}

Typer represents any type (typically a Op) that knows its own Type

type U8 Uses

type U8 byte

U8 represents a byte value.

func (*U8) Data Uses

func (v *U8) Data() interface{}

Data returns the original representation of the Value

func (*U8) Dtype Uses

func (v *U8) Dtype() tensor.Dtype

Dtype returns the Dtype of the value

func (*U8) Format Uses

func (v *U8) Format(s fmt.State, c rune)

Format implements fmt.Formatter

func (*U8) MemSize Uses

func (v *U8) MemSize() uintptr

MemSize satisfies the tensor.Memory interface

func (*U8) Pointer Uses

func (v *U8) Pointer() unsafe.Pointer

Pointer returns the pointer as an unsafe.Pointer. Satisfies the tensor.Memory interface

func (*U8) Shape Uses

func (v *U8) Shape() tensor.Shape

Shape returns a scalar shape for all scalar values

func (*U8) Size Uses

func (v *U8) Size() int

Size returns 0 for all scalar Values

func (*U8) Uintptr Uses

func (v *U8) Uintptr() uintptr

Uintptr satisfies the tensor.Memory interface

type UnaryOp Uses

type UnaryOp interface {
    Op

    IsUnary() bool
}

A UnaryOp is an Op that takes only one input

type UnsafeDoer Uses

type UnsafeDoer interface {
    UnsafeDo(inputs ...Value) (Value, error)
}

UnsafeDoer is an op that will overwrite the underlying value.

type UsePreallocDoer Uses

type UsePreallocDoer interface {
    UsePreallocDo(prealloc Value, inputs ...Value) (Value, error)
}

UsePreallocDoer is an op that works when a preallocated value is provided

type VM Uses

type VM interface {
    RunAll() error
    Reset()

    // Close closes all the machine resources (CUDA, if any, loggers if any)
    Close() error
}

VM represents a structure that can execute a graph or program. There are two VMs (both unexported):

- *tapeMachine
- *lispMachine

The *tapeMachine pre-compiles a graph into a list of instructions, then executes the instructions linearly and sequentially. The main tradeoff is dynamism. Graphs cannot be dynamically created on the fly as a re-compilation process is required (and compilation is relatively expensive). However, graphs executed with the *tapeMachine run much faster as plenty of optimizations has been done in the code generation stage.

The *lispMachine allows for graphs to be dynamically built and executed upon. The tradeoff is that executing a graph on *lispMachine is generally slower than on *tapeMachine, given the same static "image" of a graph.

type VMOpt Uses

type VMOpt func(m VM)

VMOpt is a VM creation option

func BindDualValues Uses

func BindDualValues(nodes ...*Node) VMOpt

BindDualValues is an option for *tapeMachine only. This is useful to set when using a Solver

func ExecuteBwdOnly Uses

func ExecuteBwdOnly() VMOpt

ExecuteBwdOnly creates a VM that will execute a graph by doing back propagation only. The assumption is of course, that the forward graph has already been executed, and there are already values associated with the nodes. This option is only for *lispMachine. Try it on any other VMs and it will panic.

func ExecuteFwdOnly Uses

func ExecuteFwdOnly() VMOpt

ExecuteFwdOnly creates a VM that will execute a graph forwards only - it will not do back propagation. This option is only for *lispMachine. Try it on any other VMs and it will panic.

func LogBothDir Uses

func LogBothDir() VMOpt

LogBothDir logs both directions of the execution of the graph. This option is only available for *lispMachine.

func LogBwd Uses

func LogBwd() VMOpt

LogBwd logs the backwards execution of a graph. This option is only for *lispMachine. Try it on any other VMs and it will panic.

func LogFwd Uses

func LogFwd() VMOpt

LogFwd logs the forward execution of a graph. This option is only for *lispMachine. Try it on any other VMs and it will panic.

func TraceExec Uses

func TraceExec() VMOpt

TraceExec is an option for *tapeMachine only. It stores an immutable copy of the executed value into the node, instead of a mutable value, which may be clobbered

func UseCudaFor Uses

func UseCudaFor(ops ...string) VMOpt

UseCudaFor is an option for *tapeMachine. This function is NO-OP unless the program is built with the `cuda` tag.

func WithEngine Uses

func WithEngine(e tensor.Engine) VMOpt

func WithInfWatch Uses

func WithInfWatch() VMOpt

WithInfWatch creates a VM that will watch for Infs when executing. It watches for +Inf, -Inf and Inf. No choice there. This slows the execution down.

func WithLogger Uses

func WithLogger(logger *log.Logger) VMOpt

WithLogger creates a VM with the supplied logger. If the logger is nil, a default logger, writing to os.stderr will be created.

func WithManualGradient Uses

func WithManualGradient() VMOpt

WithManualGradient allows the user to set the gradient of the root, before backprop. The root gradients should be set using the SetDeriv method

func WithNaNWatch Uses

func WithNaNWatch() VMOpt

WithNaNWatch creates a VM that will watch for NaNs when executing. This slows the execution down.

func WithPrecompiled Uses

func WithPrecompiled(prog *program, locMap map[*Node]register) VMOpt

WithPrecompiled is an option to pass in compiled programs. This is useful for users who use the CompileFunction function

func WithValueFmt Uses

func WithValueFmt(format string) VMOpt

WithValueFmt defines how the logger will output the values. It defaults to "%3.3f"

func WithWatchlist Uses

func WithWatchlist(list ...interface{}) VMOpt

WithWatchlist creates a VM with a watchlist. When the execution touches the things in the watchlist, the VM's logger will the log it. This allows for watching and finetuning of the algorithm. When nothing is passed in, then the VM will default to watching and logging every single execution object.

The watchlist allows for different things to be watched, depending on VM type:

*lispMachine will ONLY take *Node
*tapeMachine will take int (for register IDs) or *Node.

type Value Uses

type Value interface {
    Shape() tensor.Shape // Shape  returns the shape of the Value. Scalar values return ScalarShape()
    Size() int           // Size represents the number of elements in the Value. Note that in cases such as a *tensor.Dense, the underlying slice MAY have more elements than the Size() reports. This is correct.
    Data() interface{}   // Data returns the original representation of the Value
    Dtype() tensor.Dtype // Dtype returns the Dtype of the value

    tensor.Memory
    fmt.Formatter
}

Value represents a value that Gorgonia accepts. At this point it is implemented by:

- all scalar value types (F64, F32... etc)
- *tensor.Dense
- *dualValue

A Value is essentially any thing that knows its own type and shape. Most importantly though, a Value is a pointer - and can be converted into a tensor.Memory. This is done for the sake of interoperability with external devices like cgo or CUDA or OpenCL. This also means for the most part most Values will be allocated on the heap. There are some performance tradeoffs made in this decision, but ultimately this is better than having to manually manage blocks of memory

func CloneValue Uses

func CloneValue(v Value) (Value, error)

CloneValue clones a value. For scalars, since Go copies scalars, it returns itself

func Copy Uses

func Copy(dest, src Value) (Value, error)

Copy copies the src values into dest values. For scalars, it just returns itself

func ScalarAsTensor Uses

func ScalarAsTensor(v Value, dims int, e tensor.Engine) Value

ScalarAsTensor returns the tensor representation of a scalar. It is particularly useful as a "reshape" of tensors of sorts

The Value passed in are either Scalar, tensor.Tensor, or *dualValue. Anything else will panic.

func ZeroValue Uses

func ZeroValue(v Value) Value

ZeroValue returns the zero value of a type

type ValueCloser Uses

type ValueCloser interface {
    ValueClose(interface{}) bool
}

ValueCloser represents any type that can perform a close-value check

type ValueEqualer Uses

type ValueEqualer interface {
    ValueEq(Value) bool
}

ValueEqualer represents any type that can perform a equal value check

type ValueGrad Uses

type ValueGrad interface {
    Valuer
    Grad() (Value, error)
}

ValueGrad is any type that has a value and a grad. This is used for Solvers

func NodesToValueGrads Uses

func NodesToValueGrads(in Nodes) (out []ValueGrad)

NodesToValueGrads is a utility function that converts a Nodes to a slice of ValueGrad for the solvers

type Valuer Uses

type Valuer interface {
    Value() Value
}

Valuer is any type that can return a Value

type VanillaSolver Uses

type VanillaSolver struct {
    // contains filtered or unexported fields
}

VanillaSolver is your bog standard stochastic gradient descent optimizer. There are no fancy features to this

func NewVanillaSolver Uses

func NewVanillaSolver(opts ...SolverOpt) *VanillaSolver

NewVanillaSolver creates a new VanillaSolver with sane-ish default values

func (*VanillaSolver) Step Uses

func (s *VanillaSolver) Step(model []ValueGrad) (err error)

Step steps through each node in the model and applies the most basic gradient descent algorithm on the value.

This function will error out if the nodes do not have an associated Grad value.

type ZeroValuer Uses

type ZeroValuer interface {
    Value
    ZeroValue() Value
}

ZeroValuer is a a Value that can provide the zero-value of its type

type Zeroer Uses

type Zeroer interface {
    Value
    Zero()
}

Zeroer is a Value that can zero itself

Package gorgonia imports 35 packages (graph) and is imported by 19 packages. Updated 2018-11-10. Refresh now. Tools for package owners.