func (l *LBFGS) NextDirection(loc *Location, dir []float64) (stepSize float64) {
	// Uses two-loop correction as described in
	// Nocedal, J., Wright, S.: Numerical Optimization (2nd ed). Springer (2006), chapter 7, page 178.

	if len(loc.X) != l.dim {
		panic("lbfgs: unexpected size mismatch")
	}
	if len(loc.Gradient) != l.dim {
		panic("lbfgs: unexpected size mismatch")
	}
	if len(dir) != l.dim {
		panic("lbfgs: unexpected size mismatch")
	}

	y := l.y[l.oldest]
	floats.SubTo(y, loc.Gradient, l.grad)
	s := l.s[l.oldest]
	floats.SubTo(s, loc.X, l.x)
	sDotY := floats.Dot(s, y)
	l.rho[l.oldest] = 1 / sDotY

	l.oldest = (l.oldest + 1) % l.Store

	copy(l.x, loc.X)
	copy(l.grad, loc.Gradient)
	copy(dir, loc.Gradient)

	// Start with the most recent element and go backward,
	for i := 0; i < l.Store; i++ {
		idx := l.oldest - i - 1
		if idx < 0 {
			idx += l.Store
		}
		l.a[idx] = l.rho[idx] * floats.Dot(l.s[idx], dir)
		floats.AddScaled(dir, -l.a[idx], l.y[idx])
	}

	// Scale the initial Hessian.
	gamma := sDotY / floats.Dot(y, y)
	floats.Scale(gamma, dir)

	// Start with the oldest element and go forward.
	for i := 0; i < l.Store; i++ {
		idx := i + l.oldest
		if idx >= l.Store {
			idx -= l.Store
		}
		beta := l.rho[idx] * floats.Dot(l.y[idx], dir)
		floats.AddScaled(dir, l.a[idx]-beta, l.s[idx])
	}

	// dir contains H^{-1} * g, so flip the direction for minimization.
	floats.Scale(-1, dir)

	return 1
}

func (l *LBFGS) NextDirection(loc *Location, dir []float64) (stepSize float64) {
	if len(loc.X) != l.dim {
		panic("lbfgs: unexpected size mismatch")
	}
	if len(loc.Gradient) != l.dim {
		panic("lbfgs: unexpected size mismatch")
	}
	if len(dir) != l.dim {
		panic("lbfgs: unexpected size mismatch")
	}

	// Update direction. Uses two-loop correction as described in
	// Nocedal, Wright (2006), Numerical Optimization (2nd ed.). Chapter 7, page 178.
	copy(dir, loc.Gradient)
	floats.SubTo(l.y, loc.Gradient, l.grad)
	floats.SubTo(l.s, loc.X, l.x)
	copy(l.sHist[l.oldest], l.s)
	copy(l.yHist[l.oldest], l.y)
	sDotY := floats.Dot(l.y, l.s)
	l.rhoHist[l.oldest] = 1 / sDotY

	l.oldest++
	l.oldest = l.oldest % l.Store
	copy(l.x, loc.X)
	copy(l.grad, loc.Gradient)

	// two loop update. First loop starts with the most recent element
	// and goes backward, second starts with the oldest element and goes
	// forward. At the end have computed H^-1 * g, so flip the direction for
	// minimization.
	for i := 0; i < l.Store; i++ {
		idx := l.oldest - i - 1
		if idx < 0 {
			idx += l.Store
		}
		l.a[idx] = l.rhoHist[idx] * floats.Dot(l.sHist[idx], dir)
		floats.AddScaled(dir, -l.a[idx], l.yHist[idx])
	}

	// Scale the initial Hessian.
	gamma := sDotY / floats.Dot(l.y, l.y)
	floats.Scale(gamma, dir)

	for i := 0; i < l.Store; i++ {
		idx := i + l.oldest
		if idx >= l.Store {
			idx -= l.Store
		}
		beta := l.rhoHist[idx] * floats.Dot(l.yHist[idx], dir)
		floats.AddScaled(dir, l.a[idx]-beta, l.sHist[idx])
	}
	floats.Scale(-1, dir)

	return 1
}

func (ls *LinesearchMethod) initNextLinesearch(loc *Location, xNext []float64) (EvaluationType, IterationType, error) {
	copy(ls.x, loc.X)

	var stepSize float64
	if ls.first {
		stepSize = ls.NextDirectioner.InitDirection(loc, ls.dir)
		ls.first = false
	} else {
		stepSize = ls.NextDirectioner.NextDirection(loc, ls.dir)
	}

	projGrad := floats.Dot(loc.Gradient, ls.dir)
	if projGrad >= 0 {
		ls.evalType = NoEvaluation
		ls.iterType = NoIteration
		return ls.evalType, ls.iterType, ErrNonNegativeStepDirection
	}

	ls.evalType = ls.Linesearcher.Init(loc.F, projGrad, stepSize)

	floats.AddScaledTo(xNext, ls.x, stepSize, ls.dir)
	// Compare the starting point for the current iteration with the next
	// evaluation point to make sure that rounding errors do not prevent progress.
	if floats.Equal(ls.x, xNext) {
		ls.evalType = NoEvaluation
		ls.iterType = NoIteration
		return ls.evalType, ls.iterType, ErrNoProgress
	}

	ls.iterType = MinorIteration
	return ls.evalType, ls.iterType, nil
}

// initNextLinesearch initializes the next linesearch using the previous
// complete location stored in loc. It fills loc.X and returns an evaluation
// to be performed at loc.X.
func (ls *LinesearchMethod) initNextLinesearch(loc *Location) (Operation, error) {
	copy(ls.x, loc.X)

	var step float64
	if ls.first {
		ls.first = false
		step = ls.NextDirectioner.InitDirection(loc, ls.dir)
	} else {
		step = ls.NextDirectioner.NextDirection(loc, ls.dir)
	}

	projGrad := floats.Dot(loc.Gradient, ls.dir)
	if projGrad >= 0 {
		return ls.error(ErrNonNegativeStepDirection)
	}

	op := ls.Linesearcher.Init(loc.F, projGrad, step)
	if !op.isEvaluation() {
		panic("linesearch: Linesearcher returned invalid operation")
	}

	floats.AddScaledTo(loc.X, ls.x, step, ls.dir)
	if floats.Equal(ls.x, loc.X) {
		// Step size is so small that the next evaluation point is
		// indistinguishable from the starting point for the current iteration
		// due to rounding errors.
		return ls.error(ErrNoProgress)
	}

	ls.lastStep = step
	ls.eval = NoOperation // Invalidate all fields of loc.

	ls.lastOp = op
	return ls.lastOp, nil
}

// Combine takes a weighted sum of the inputs with the weights set by parameters
// The last element of parameters is the bias term, so len(parameters) = len(inputs) + 1
func (s SumNeuron) Combine(parameters []float64, inputs []float64) (combination float64) {
	/*
		for i, val := range inputs {
			combination += parameters[i] * val
		}
	*/
	combination = floats.Dot(inputs, parameters[:len(inputs)])
	combination += parameters[len(parameters)-1]
	return
}

func (ls *LinesearchMethod) Iterate(loc *Location, xNext []float64) (EvaluationType, IterationType, error) {
	if ls.iterType == SubIteration {
		// We needed to evaluate invalid fields of Location. Now we have them
		// and can announce MajorIteration.
		copy(xNext, loc.X)
		ls.evalType = NoEvaluation
		ls.iterType = MajorIteration
		return ls.evalType, ls.iterType, nil
	}

	if ls.iterType == MajorIteration {
		// The linesearch previously signaled MajorIteration. Since we're here,
		// it means that the previous location is not good enough to converge,
		// so start the next linesearch.
		return ls.initNextLinesearch(loc, xNext)
	}

	projGrad := floats.Dot(loc.Gradient, ls.dir)
	if ls.Linesearcher.Finished(loc.F, projGrad) {
		copy(xNext, loc.X)
		// Check if the last evaluation evaluated all fields of Location.
		ls.evalType = complementEval(loc, ls.evalType)
		if ls.evalType == NoEvaluation {
			// Location is complete and MajorIteration can be announced directly.
			ls.iterType = MajorIteration
		} else {
			// Location is not complete, evaluate its invalid fields in SubIteration.
			ls.iterType = SubIteration
		}
		return ls.evalType, ls.iterType, nil
	}

	// Line search not done, just iterate.
	stepSize, evalType, err := ls.Linesearcher.Iterate(loc.F, projGrad)
	if err != nil {
		ls.evalType = NoEvaluation
		ls.iterType = NoIteration
		return ls.evalType, ls.iterType, err
	}

	floats.AddScaledTo(xNext, ls.x, stepSize, ls.dir)
	// Compare the starting point for the current iteration with the next
	// evaluation point to make sure that rounding errors do not prevent progress.
	if floats.Equal(ls.x, xNext) {
		ls.evalType = NoEvaluation
		ls.iterType = NoIteration
		return ls.evalType, ls.iterType, ErrNoProgress
	}

	ls.evalType = evalType
	ls.iterType = MinorIteration
	return ls.evalType, ls.iterType, nil
}

func (cg *CG) Iterate(ctx *Context) Operation {
	switch cg.resume {
	case 1:
		cg.resume = 2
		return SolvePreconditioner
		// Solve M z = r_{i-1}
	case 2:
		// ρ_i = r_{i-1} · z
		cg.rho = floats.Dot(ctx.Residual, ctx.Z)
		if !cg.first {
			// β = ρ_i / ρ_{i-1}
			beta := cg.rho / cg.rho1
			// z = z + β p_{i-1}
			floats.AddScaled(ctx.Z, beta, ctx.P)
		}
		cg.first = false
		// p_i = z
		copy(ctx.P, ctx.Z)

		cg.resume = 3
		return ComputeAp
		// Compute Ap
	case 3:
		// α = ρ_i / (p_i · Ap_i)
		alpha := cg.rho / floats.Dot(ctx.P, ctx.Ap)
		// x_i = x_{i-1} + α p_i
		floats.AddScaled(ctx.X, alpha, ctx.P)
		// r_i = r_{i-1} - α Ap_i
		floats.AddScaled(ctx.Residual, -alpha, ctx.Ap)

		cg.rho1 = cg.rho

		cg.resume = 1
		return CheckConvergence
	}
	panic("unreachable")
}

func isOrthogonal(a *Dense) bool {
	rows, cols := a.Dims()
	col1 := make([]float64, rows)
	col2 := make([]float64, rows)
	for i := 0; i < cols-1; i++ {
		for j := i + 1; j < cols; j++ {
			a.Col(col1, i)
			a.Col(col2, j)
			dot := floats.Dot(col1, col2)
			if math.Abs(dot) > 1e-14 {
				return false
			}
		}
	}
	return true
}

// LogProb computes the log of the pdf of the point x.
func (n *Normal) LogProb(x []float64) float64 {
	dim := n.dim
	if len(x) != dim {
		panic(badSizeMismatch)
	}
	// Compute the normalization constant
	c := -0.5*float64(dim)*logTwoPi - n.logSqrtDet

	// Compute (x-mu)'Sigma^-1 (x-mu)
	xMinusMu := make([]float64, dim)
	floats.SubTo(xMinusMu, x, n.mu)
	d := mat64.NewVector(dim, xMinusMu)
	tmp := make([]float64, dim)
	tmpVec := mat64.NewVector(dim, tmp)
	tmpVec.SolveCholeskyVec(n.chol, d)
	return c - 0.5*floats.Dot(tmp, xMinusMu)
}

// Mean returns the gaussian process prediction of the mean at the location x.
func (g *GP) Mean(x []float64) float64 {
	// y_mean = k_*^T K^-1 y
	// where k_* is the vector of the kernel between the new location and all
	// of the data points
	// y are the outputs at all the data points
	// K^-1 is the full covariance of the data points
	// (K^-1y is stored)

	if len(x) != g.inputDim {
		panic(badInputLength)
	}
	nSamples, _ := g.inputs.Dims()

	covariance := make([]float64, nSamples)
	for i := range covariance {
		covariance[i] = g.kernel.Distance(x, g.inputs.RawRowView(i))
	}
	y := floats.Dot(g.sigInvY.RawVector().Data, covariance)
	return y*g.std + g.mean
}

func (l *linesearchFun) ObjGrad(step float64) (f float64, g float64, err error) {
	// Take the step (need to add back in the scaling)
	for i, val := range l.direction {
		l.currLoc[i] = val*step + l.initLoc[i]
	}
	// Copy the location (in case the user-defined function modifies it)
	copy(l.currLocCopy, l.currLoc)
	f, gVec, err := l.fun.ObjGrad(l.currLocCopy)
	if err != nil {
		return f, g, errors.New("linesearch: error during user defined function")
	}
	// Add the function to the history so that it isn't thrown out
	// Copy the gradient vector (in case Fun modifies it)
	n := copy(l.currGrad, gVec)
	if n != len(l.currLocCopy) {
		return f, g, errors.New("linesearch: user defined function returned incorrect gradient length")
	}

	// Find the gradient in the direction of the search vector
	g = floats.Dot(l.direction, l.currGrad)
	l.wolfe.SetCurrState(f, g, step)
	return f, g, nil
}

// Explicitly forms vectors and computes normalized dot product.
func cosCorrMultiNaive(f, g *rimg64.Multi) *rimg64.Image {
	h := rimg64.New(f.Width-g.Width+1, f.Height-g.Height+1)
	n := g.Width * g.Height * g.Channels
	a := make([]float64, n)
	b := make([]float64, n)
	for i := 0; i < h.Width; i++ {
		for j := 0; j < h.Height; j++ {
			a = a[:0]
			b = b[:0]
			for u := 0; u < g.Width; u++ {
				for v := 0; v < g.Height; v++ {
					for p := 0; p < g.Channels; p++ {
						a = append(a, f.At(i+u, j+v, p))
						b = append(b, g.At(u, v, p))
					}
				}
			}
			floats.Scale(1/floats.Norm(a, 2), a)
			floats.Scale(1/floats.Norm(b, 2), b)
			h.Set(i, j, floats.Dot(a, b))
		}
	}
	return h
}

// Linesearch performs a linesearch. Optimizer should turn off all non-wolfe status patterns for the gradient and step
func Linesearch(multifun common.MultiObjGrad, method LinesearchMethod, settings univariate.GradSettings, wolfe WolfeConditioner, searchVector []float64, initLoc []float64, initObj float64, initGrad []float64) (*LinesearchResult, error) {

	// Linesearch modifies the values of the slices, but should revert the changes by the end

	// Find the norm of the search direction
	normSearchVector := floats.Norm(searchVector, 2)

	// Find the search direction (replace this with an input to avoid make?)
	direction := make([]float64, len(searchVector))
	copy(direction, searchVector)
	floats.Scale(1/normSearchVector, direction)

	// Find the initial projection of the gradient into the search direction
	initDirectionalGrad := floats.Dot(direction, initGrad)

	if initDirectionalGrad > 0 {
		return &LinesearchResult{}, errors.New("initial directional gradient must be negative")
	}

	// Set wolfe constants
	wolfe.SetInitState(initObj, initDirectionalGrad)
	wolfe.SetCurrState(initObj, initDirectionalGrad, 1.0)
	fun := &linesearchFun{
		fun:         multifun,
		wolfe:       wolfe,
		direction:   direction,
		initLoc:     initLoc,
		currLoc:     make([]float64, len(initLoc)),
		currLocCopy: make([]float64, len(initLoc)),
		currGrad:    make([]float64, len(initLoc)),
	}

	settings.Gradient.Initial = initDirectionalGrad
	settings.Objective.Initial = initObj

	stepSettings := method.GetStepSettings()
	stepSettings.InitialStepSize = normSearchVector

	// Run optimization, initial location is zero
	optVal, optLoc, result, err := univariate.OptimizeGrad(fun, 0, settings, method)
	//status, err := common.OptimizeOpter(method, fun)

	// Regerate results structure (do this before returning error in case optimizer can recover from it)
	// need to scale alpha_k because linesearch is x_k + alpha_k p_k
	r := &LinesearchResult{
		Loc:  fun.currLoc,
		Obj:  optVal,
		Grad: fun.currGrad,
		Step: optLoc / normSearchVector,
	}

	if err != nil {
		fmt.Println("Error in linsearch")
		return r, errors.New("linesearch: error during linesearch optimization: " + err.Error())
	}
	stat := result.Status
	// Check to make sure that the status due to wolfe status
	if stat != common.WolfeConditionsMet {
		// If the status wasn't because of wolfe conditions, see if they are met anyway
		c := wolfe.Status()
		if c == common.WolfeConditionsMet {
			// Conditions met, no problem
			return r, nil
		}
		// Conditions not met
		return r, errors.New("linesearch: status not because of wolfe conditions.")
	}
	return r, nil
}

// ComputeZ computes the value of z with the given feature vector and b value.
// Sqrt2OverD = math.Sqrt(2.0 / len(nFeatures))
func computeZ(featurizedInput, feature []float64, b float64, sqrt2OverD float64) float64 {
	dot := floats.Dot(featurizedInput, feature)
	return sqrt2OverD * (math.Cos(dot + b))
}

func (ls *LinesearchMethod) Iterate(loc *Location) (Operation, error) {
	switch ls.lastOp {
	case NoOperation:
		// TODO(vladimir-ch): Either Init has not been called, or the caller is
		// trying to resume the optimization run after Iterate previously
		// returned with an error. Decide what is the proper thing to do. See also #125.

	case MajorIteration:
		// The previous updated location did not converge the full
		// optimization. Initialize a new Linesearch.
		return ls.initNextLinesearch(loc)

	default:
		// Update the indicator of valid fields of loc.
		ls.eval |= ls.lastOp

		if ls.nextMajor {
			ls.nextMajor = false

			// Linesearcher previously finished, and the invalid fields of loc
			// have now been validated. Announce MajorIteration.
			ls.lastOp = MajorIteration
			return ls.lastOp, nil
		}
	}

	// Continue the linesearch.

	f := math.NaN()
	if ls.eval&FuncEvaluation != 0 {
		f = loc.F
	}
	projGrad := math.NaN()
	if ls.eval&GradEvaluation != 0 {
		projGrad = floats.Dot(loc.Gradient, ls.dir)
	}
	op, step, err := ls.Linesearcher.Iterate(f, projGrad)
	if err != nil {
		return ls.error(err)
	}

	switch op {
	case MajorIteration:
		// Linesearch has been finished.

		ls.lastOp = complementEval(loc, ls.eval)
		if ls.lastOp == NoOperation {
			// loc is complete, MajorIteration can be declared directly.
			ls.lastOp = MajorIteration
		} else {
			// Declare MajorIteration on the next call to Iterate.
			ls.nextMajor = true
		}

	case FuncEvaluation, GradEvaluation, FuncEvaluation | GradEvaluation:
		if step != ls.lastStep {
			// We are moving to a new location, and not, say, evaluating extra
			// information at the current location.

			// Compute the next evaluation point and store it in loc.X.
			floats.AddScaledTo(loc.X, ls.x, step, ls.dir)
			if floats.Equal(ls.x, loc.X) {
				// Step size has become so small that the next evaluation point is
				// indistinguishable from the starting point for the current
				// iteration due to rounding errors.
				return ls.error(ErrNoProgress)
			}
			ls.lastStep = step
			ls.eval = NoOperation // Indicate all invalid fields of loc.
		}
		ls.lastOp = op

	default:
		panic("linesearch: Linesearcher returned invalid operation")
	}

	return ls.lastOp, nil
}

func main() {
	fmt.Println(floats.Dot(v, v))
}

//.........这里部分代码省略.........
	r := make([]float64, n-m)
	move := make([]float64, m)

	// Solve the linear program starting from the initial feasible set. This is
	// the "Phase 2" problem.
	//
	// Algorithm:
	// 1) Compute the "reduced costs" for the non-basic variables. The reduced
	// costs are the lagrange multipliers of the constraints.
	// 	 r = cn - an^T * ab^-T * cb
	// 2) If all of the reduced costs are positive, no improvement is possible,
	// and the solution is optimal (xn can only increase because of
	// non-negativity constraints). Otherwise, the solution can be improved and
	// one element will be exchanged in the basic set.
	// 3) Choose the x_n with the most negative value of r. Call this value xe.
	// This variable will be swapped into the basic set.
	// 4) Increase xe until the next constraint boundary is met. This will happen
	// when the first element in xb becomes 0. The distance xe can increase before
	// a given element in xb becomes negative can be found from
	//	xb = Ab^-1 b - Ab^-1 An xn
	//     = Ab^-1 b - Ab^-1 Ae xe
	//     = bhat + d x_e
	//  xe = bhat_i / - d_i
	// where Ae is the column of A corresponding to xe.
	// The constraining basic index is the first index for which this is true,
	// so remove the element which is min_i (bhat_i / -d_i), assuming d_i is negative.
	// If no d_i is less than 0, then the problem is unbounded.
	// 5) If the new xe is 0 (that is, bhat_i == 0), then this location is at
	// the intersection of several constraints. Use the Bland rule instead
	// of the rule in step 4 to avoid cycling.
	for {
		// Compute reduced costs -- r = cn - an^T ab^-T cb
		var tmp mat64.Vector
		err = tmp.SolveVec(ab.T(), cbVec)
		if err != nil {
			break
		}
		data := make([]float64, n-m)
		tmp2 := mat64.NewVector(n-m, data)
		tmp2.MulVec(an.T(), &tmp)
		floats.SubTo(r, cn, data)

		// Replace the most negative element in the simplex. If there are no
		// negative entries then the optimal solution has been found.
		minIdx := floats.MinIdx(r)
		if r[minIdx] >= -tol {
			break
		}

		for i, v := range r {
			if math.Abs(v) < rRoundTol {
				r[i] = 0
			}
		}

		// Compute the moving distance.
		err = computeMove(move, minIdx, A, ab, xb, nonBasicIdx)
		if err != nil {
			if err == ErrUnbounded {
				return math.Inf(-1), nil, nil, ErrUnbounded
			}
			break
		}

		// Replace the basic index along the tightest constraint.
		replace := floats.MinIdx(move)
		if move[replace] <= 0 {
			replace, minIdx, err = replaceBland(A, ab, xb, basicIdxs, nonBasicIdx, r, move)
			if err != nil {
				if err == ErrUnbounded {
					return math.Inf(-1), nil, nil, ErrUnbounded
				}
				break
			}
		}

		// Replace the constrained basicIdx with the newIdx.
		basicIdxs[replace], nonBasicIdx[minIdx] = nonBasicIdx[minIdx], basicIdxs[replace]
		cb[replace], cn[minIdx] = cn[minIdx], cb[replace]
		tmpCol1 := mat64.Col(nil, replace, ab)
		tmpCol2 := mat64.Col(nil, minIdx, an)
		ab.SetCol(replace, tmpCol2)
		an.SetCol(minIdx, tmpCol1)

		// Compute the new xb.
		xbVec := mat64.NewVector(len(xb), xb)
		err = xbVec.SolveVec(ab, bVec)
		if err != nil {
			break
		}
	}
	// Found the optimum successfully or died trying. The basic variables get
	// their values, and the non-basic variables are all zero.
	opt := floats.Dot(cb, xb)
	xopt := make([]float64, n)
	for i, v := range basicIdxs {
		xopt[v] = xb[i]
	}
	return opt, xopt, basicIdxs, err
}

func (b *BFGS) NextDirection(loc *Location, dir []float64) (stepSize float64) {
	if len(loc.X) != b.dim {
		panic("bfgs: unexpected size mismatch")
	}
	if len(loc.Gradient) != b.dim {
		panic("bfgs: unexpected size mismatch")
	}
	if len(dir) != b.dim {
		panic("bfgs: unexpected size mismatch")
	}

	// Compute the gradient difference in the last step
	// y = g_{k+1} - g_{k}
	floats.SubTo(b.y, loc.Gradient, b.grad)

	// Compute the step difference
	// s = x_{k+1} - x_{k}
	floats.SubTo(b.s, loc.X, b.x)

	sDotY := floats.Dot(b.s, b.y)
	sDotYSquared := sDotY * sDotY

	if b.first {
		// Rescale the initial hessian.
		// From: Numerical optimization, Nocedal and Wright, Page 143, Eq. 6.20 (second edition).
		yDotY := floats.Dot(b.y, b.y)
		scale := sDotY / yDotY
		for i := 0; i < len(loc.X); i++ {
			for j := 0; j < len(loc.X); j++ {
				if i == j {
					b.invHess.SetSym(i, i, scale)
				} else {
					b.invHess.SetSym(i, j, 0)
				}
			}
		}
		b.first = false
	}

	// Compute the update rule
	//     B_{k+1}^-1
	// First term is just the existing inverse hessian
	// Second term is
	//     (sk^T yk + yk^T B_k^-1 yk)(s_k sk_^T) / (sk^T yk)^2
	// Third term is
	//     B_k ^-1 y_k sk^T + s_k y_k^T B_k-1
	//
	// y_k^T B_k^-1 y_k is a scalar, and the third term is a rank-two update
	// where B_k^-1 y_k is one vector and s_k is the other. Compute the update
	// values then actually perform the rank updates.
	yBy := mat64.Inner(b.yVec, b.invHess, b.yVec)
	firstTermConst := (sDotY + yBy) / (sDotYSquared)
	b.tmpVec.MulVec(b.invHess, b.yVec)

	b.invHess.RankTwo(b.invHess, -1/sDotY, b.tmpVec, b.sVec)
	b.invHess.SymRankOne(b.invHess, firstTermConst, b.sVec)

	// update the bfgs stored data to the new iteration
	copy(b.x, loc.X)
	copy(b.grad, loc.Gradient)

	// Compute the new search direction
	d := mat64.NewVector(b.dim, dir)
	g := mat64.NewVector(b.dim, loc.Gradient)

	d.MulVec(b.invHess, g) // new direction stored in place
	floats.Scale(-1, dir)
	return 1
}

func (lbfgs *Lbfgs) Iterate(loc *multi.Location, obj *uni.Objective, grad *multi.Gradient, fun optimize.MultiObjGrad) (status.Status, error) {
	counter := lbfgs.counter
	q := lbfgs.q
	a := lbfgs.a
	b := lbfgs.b
	rhoHist := lbfgs.rhoHist
	sHist := lbfgs.sHist
	yHist := lbfgs.yHist
	gamma_k := lbfgs.gamma_k
	tmp := lbfgs.tmp
	p_k := lbfgs.p_k
	s_k := lbfgs.s_k
	y_k := lbfgs.y_k
	z := lbfgs.z

	// Calculate search direction
	for i, val := range grad.Curr() {
		q[i] = val
	}
	for i := counter - 1; i >= 0; i-- {
		a[i] = rhoHist[i] * floats.Dot(sHist[i], q)
		copy(tmp, yHist[i])
		floats.Scale(a[i], tmp)
		floats.Sub(q, tmp)
	}
	for i := lbfgs.NumStore - 1; i >= counter; i-- {
		a[i] = rhoHist[i] * floats.Dot(sHist[i], q)
		copy(tmp, yHist[i])
		floats.Scale(a[i], tmp)
		//fmt.Println(q)
		//fmt.Println(tmp)
		floats.Sub(q, tmp)
	}

	// Assume H_0 is the identity times gamma_k
	copy(z, q)
	floats.Scale(gamma_k, z)
	// Second loop for update, going oldest to newest
	for i := counter; i < lbfgs.NumStore; i++ {
		b[i] = rhoHist[i] * floats.Dot(yHist[i], z)
		copy(tmp, sHist[i])
		floats.Scale(a[i]-b[i], tmp)
		floats.Add(z, tmp)
	}
	for i := 0; i < counter; i++ {
		b[i] = rhoHist[i] * floats.Dot(yHist[i], z)
		copy(tmp, sHist[i])
		floats.Scale(a[i]-b[i], tmp)
		floats.Add(z, tmp)
	}

	lbfgs.a = a
	lbfgs.b = b

	copy(p_k, z)
	floats.Scale(-1, p_k)
	normP_k := floats.Norm(p_k, 2)

	// Perform line search -- need to find some way to implement this, especially bookkeeping function values
	linesearchResult, err := linesearch.Linesearch(fun, lbfgs.LinesearchMethod, lbfgs.LinesearchSettings, lbfgs.Wolfe, p_k, loc.Curr(), obj.Curr(), grad.Curr())

	// In the future add a check to switch to a different linesearcher?
	if err != nil {
		return status.LinesearchFailure, err
	}
	x_kp1 := linesearchResult.Loc
	f_kp1 := linesearchResult.Obj
	g_kp1 := linesearchResult.Grad
	alpha_k := linesearchResult.Step

	// Update hessian estimate
	copy(s_k, p_k)
	floats.Scale(alpha_k, s_k)

	copy(y_k, g_kp1)
	floats.Sub(y_k, grad.Curr())
	skDotYk := floats.Dot(s_k, y_k)

	// Bookkeep the results
	stepSize := alpha_k * normP_k
	lbfgs.step.AddToHist(stepSize)
	lbfgs.step.SetCurr(stepSize)
	loc.SetCurr(x_kp1)
	//lbfgs.loc.AddToHist(x_kp1)

	//fmt.Println(lbfgs.loc.GetHist())
	obj.SetCurr(f_kp1)
	grad.SetCurr(g_kp1)

	copy(sHist[counter], s_k)
	copy(yHist[counter], y_k)
	rhoHist[counter] = 1 / skDotYk

	lbfgs.gamma_k = skDotYk / floats.Dot(y_k, y_k)

	lbfgs.counter += 1
	if lbfgs.counter == lbfgs.NumStore {
		lbfgs.counter = 0
	}
	return status.Continue, nil
//.........这里部分代码省略.........