fixed dependencies

vendor/gonum.org/v1/gonum/optimize/backtracking.go

@@ -0,0 +1,84 @@
+// Copyright ©2014 The Gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package optimize
+
+const (
+	defaultBacktrackingContraction = 0.5
+	defaultBacktrackingDecrease    = 1e-4
+	minimumBacktrackingStepSize    = 1e-20
+)
+
+var _ Linesearcher = (*Backtracking)(nil)
+
+// Backtracking is a Linesearcher that uses backtracking to find a point that
+// satisfies the Armijo condition with the given decrease factor. If the Armijo
+// condition has not been met, the step size is decreased by ContractionFactor.
+//
+// The Armijo condition only requires the gradient at the beginning of each
+// major iteration (not at successive step locations), and so Backtracking may
+// be a good linesearch for functions with expensive gradients. Backtracking is
+// not appropriate for optimizers that require the Wolfe conditions to be met,
+// such as BFGS.
+//
+// Both DecreaseFactor and ContractionFactor must be between zero and one, and
+// Backtracking will panic otherwise. If either DecreaseFactor or
+// ContractionFactor are zero, it will be set to a reasonable default.
+type Backtracking struct {
+	DecreaseFactor    float64 // Constant factor in the sufficient decrease (Armijo) condition.
+	ContractionFactor float64 // Step size multiplier at each iteration (step *= ContractionFactor).
+
+	stepSize float64
+	initF    float64
+	initG    float64
+
+	lastOp Operation
+}
+
+func (b *Backtracking) Init(f, g float64, step float64) Operation {
+	if step <= 0 {
+		panic("backtracking: bad step size")
+	}
+	if g >= 0 {
+		panic("backtracking: initial derivative is non-negative")
+	}
+
+	if b.ContractionFactor == 0 {
+		b.ContractionFactor = defaultBacktrackingContraction
+	}
+	if b.DecreaseFactor == 0 {
+		b.DecreaseFactor = defaultBacktrackingDecrease
+	}
+	if b.ContractionFactor <= 0 || b.ContractionFactor >= 1 {
+		panic("backtracking: ContractionFactor must be between 0 and 1")
+	}
+	if b.DecreaseFactor <= 0 || b.DecreaseFactor >= 1 {
+		panic("backtracking: DecreaseFactor must be between 0 and 1")
+	}
+
+	b.stepSize = step
+	b.initF = f
+	b.initG = g
+
+	b.lastOp = FuncEvaluation
+	return b.lastOp
+}
+
+func (b *Backtracking) Iterate(f, _ float64) (Operation, float64, error) {
+	if b.lastOp != FuncEvaluation {
+		panic("backtracking: Init has not been called")
+	}
+
+	if ArmijoConditionMet(f, b.initF, b.initG, b.stepSize, b.DecreaseFactor) {
+		b.lastOp = MajorIteration
+		return b.lastOp, b.stepSize, nil
+	}
+	b.stepSize *= b.ContractionFactor
+	if b.stepSize < minimumBacktrackingStepSize {
+		b.lastOp = NoOperation
+		return b.lastOp, b.stepSize, ErrLinesearcherFailure
+	}
+	b.lastOp = FuncEvaluation
+	return b.lastOp, b.stepSize, nil
+}