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scalar.go
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/* Copyright (C) 2015-2020 Philipp Benner
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
package autodiff
/* -------------------------------------------------------------------------- */
import "fmt"
import "reflect"
import "encoding/json"
/* -------------------------------------------------------------------------- */
type ConstScalar interface {
// clone methods
CloneConstScalar() ConstScalar
// read access
GetInt8 () int8
GetInt16 () int16
GetInt32 () int32
GetInt64 () int64
GetInt () int
GetFloat32 () float32
GetFloat64 () float64
// magic access
GetOrder () int
GetDerivative (int) float64
GetHessian (int, int) float64
GetN () int
// type reflections
Type () ScalarType
ConvertConstScalar(ScalarType) ConstScalar
// simple math
Equals (ConstScalar, float64) bool
Greater (ConstScalar) bool
Smaller (ConstScalar) bool
Sign () int
// nice printing
fmt.Stringer
// json
json.Marshaler
}
/* -------------------------------------------------------------------------- */
type Scalar interface {
ConstScalar
// clone methods
CloneScalar () Scalar
// write access
Reset ()
Set (ConstScalar)
SetInt8 (int8)
SetInt16 (int16)
SetInt32 (int32)
SetInt64 (int64)
SetInt (int)
SetFloat32 (float32)
SetFloat64 (float64)
setInt8 (int8)
setInt16 (int16)
setInt32 (int32)
setInt64 (int64)
setInt (int)
setFloat32 (float32)
setFloat64 (float64)
// type reflections
ConvertScalar(ScalarType) Scalar
// some basic operations on scalars
Min (ConstScalar, ConstScalar) Scalar
Max (ConstScalar, ConstScalar) Scalar
Abs (ConstScalar) Scalar
Neg (ConstScalar) Scalar
Add (ConstScalar, ConstScalar) Scalar
Sub (ConstScalar, ConstScalar) Scalar
Mul (ConstScalar, ConstScalar) Scalar
Div (ConstScalar, ConstScalar) Scalar
// add/substract the first two variables on log-scale,
// take the third argument as a temporary variable
LogAdd (ConstScalar, ConstScalar, Scalar) Scalar
LogSub (ConstScalar, ConstScalar, Scalar) Scalar
Log1pExp (ConstScalar) Scalar
Sigmoid (ConstScalar, Scalar) Scalar
Pow (ConstScalar, ConstScalar) Scalar
Sqrt (ConstScalar) Scalar
Sin (ConstScalar) Scalar
Sinh (ConstScalar) Scalar
Cos (ConstScalar) Scalar
Cosh (ConstScalar) Scalar
Tan (ConstScalar) Scalar
Tanh (ConstScalar) Scalar
Exp (ConstScalar) Scalar
Log (ConstScalar) Scalar
Log1p (ConstScalar) Scalar
Logistic (ConstScalar) Scalar
Erf (ConstScalar) Scalar
Erfc (ConstScalar) Scalar
LogErfc (ConstScalar) Scalar
Gamma (ConstScalar) Scalar
Lgamma (ConstScalar) Scalar
Mlgamma (ConstScalar, int) Scalar // multivariate log gamma
GammaP (float64, ConstScalar) Scalar // regularized lower incomplete gamma
BesselI (float64, ConstScalar) Scalar // modified bessel function of the first kind
// vector operations
SmoothMax (x ConstVector, alpha ConstFloat64, t [2]Scalar) Scalar
LogSmoothMax (x ConstVector, alpha ConstFloat64, t [3]Scalar) Scalar
Vmean (a ConstVector) Scalar
VdotV (a, b ConstVector) Scalar
Vnorm (a ConstVector) Scalar
Mnorm (a ConstMatrix) Scalar
Mtrace (a ConstMatrix) Scalar
}
/* -------------------------------------------------------------------------- */
type MagicScalar interface {
Scalar
CloneMagicScalar() MagicScalar
// magic write access
ResetDerivatives()
SetDerivative (int, float64)
SetHessian (int, int, float64)
SetVariable (int, int, int) error
// allocate memory for derivatives of n variables
Alloc (int, int)
// allocate enough memory for the derivatives of the given
// variable(s) and copy the order
AllocForOne (ConstScalar)
AllocForTwo (ConstScalar, ConstScalar)
// type reflections
ConvertMagicScalar(ScalarType) MagicScalar
}
/* -------------------------------------------------------------------------- */
// this allows to idenfity the type of a scalar
type ScalarType reflect.Type
/* keep a map of valid scalar implementations and a reference
* to the constructors
* -------------------------------------------------------------------------- */
type rtype1 map[ScalarType]func(float64) Scalar
type rtype2 map[ScalarType]func(float64) MagicScalar
type rtype3 map[ScalarType]func(float64) ConstScalar
// initialize empty registry
var scalarRegistry rtype1 = make(rtype1)
var magicScalarRegistry rtype2 = make(rtype2)
var constScalarRegistry rtype3 = make(rtype3)
// scalar types can be registered so that the constructors below can be used for
// all types
func RegisterConstScalar(t ScalarType, constructor func(float64) ConstScalar) {
constScalarRegistry[t] = constructor
}
func RegisterMagicScalar(t ScalarType, constructor func(float64) MagicScalar) {
magicScalarRegistry[t] = constructor
}
func RegisterScalar(t ScalarType, constructor func(float64) Scalar) {
scalarRegistry[t] = constructor
}
/* scalar constructors
* -------------------------------------------------------------------------- */
func NewScalar(t ScalarType, value float64) Scalar {
f, ok := scalarRegistry[t]
if !ok {
panic(fmt.Sprintf("invalid scalar type `%v'", t))
}
return f(value)
}
func NullScalar(t ScalarType) Scalar {
return NewScalar(t, 0.0)
}
/* const scalar constructors
* -------------------------------------------------------------------------- */
func NewConstScalar(t ScalarType, value float64) ConstScalar {
f, ok := scalarRegistry[t]
if !ok {
panic(fmt.Sprintf("invalid scalar type `%v'", t))
}
return f(value)
}
func NullConstScalar(t ScalarType) ConstScalar {
return NewConstScalar(t, 0.0)
}
/* magic scalar constructors
* -------------------------------------------------------------------------- */
func NewMagicScalar(t ScalarType, value float64) MagicScalar {
f, ok := magicScalarRegistry[t]
if !ok {
panic(fmt.Sprintf("invalid scalar type `%v'", t))
}
return f(value)
}
func NullMagicScalar(t ScalarType) MagicScalar {
return NewMagicScalar(t, 0.0)
}
/* -------------------------------------------------------------------------- */
func Variables(order int, reals ...MagicScalar) error {
for i, _ := range reals {
if err := reals[i].SetVariable(i, len(reals), order); err != nil {
return err
}
}
return nil
}
/* -------------------------------------------------------------------------- */
func CopyGradient(g Vector, x ConstScalar) error {
n := x.GetN()
if g.Dim() != n {
return fmt.Errorf("vector has invalid length")
}
for i := 0; i < n; i++ {
g.At(i).SetFloat64(x.GetDerivative(i))
}
return nil
}
func CopyHessian(H Matrix, x ConstScalar) error {
n := x.GetN()
if n1, n2 := H.Dims(); n1 != n || n2 != n {
return fmt.Errorf("matrix has invalid dimensions")
}
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
H.At(i, j).SetFloat64(x.GetHessian(i,j))
}
}
return nil
}
func GetGradient(t ScalarType, x ConstScalar) Vector {
n := x.GetN()
g := NullDenseVector(t, n)
for i := 0; i < n; i++ {
g.At(i).SetFloat64(x.GetDerivative(i))
}
return g
}
func GetHessian(t ScalarType, x ConstScalar) Matrix {
n := x.GetN()
H := NullDenseMatrix(t, n, n)
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
H.At(i, j).SetFloat64(x.GetHessian(i,j))
}
}
return H
}