Golang Dense.RowView方法代码示例

// Creates the features from the inputs. Features must be nSamples x nFeatures or nil
func FeaturizeTrainable(t Trainable, inputs common.RowMatrix, featurizedInputs *mat64.Dense) *mat64.Dense {
	nSamples, nDim := inputs.Dims()
	if featurizedInputs == nil {
		nFeatures := t.NumFeatures()
		featurizedInputs = mat64.NewDense(nSamples, nFeatures, nil)
	}

	rowViewer, isRowViewer := inputs.(mat64.RowViewer)
	var f func(start, end int)
	if isRowViewer {
		f = func(start, end int) {
			featurizer := t.NewFeaturizer()
			for i := start; i < end; i++ {
				featurizer.Featurize(rowViewer.RowView(i), featurizedInputs.RowView(i))
			}
		}
	} else {
		f = func(start, end int) {
			featurizer := t.NewFeaturizer()
			input := make([]float64, nDim)
			for i := start; i < end; i++ {
				inputs.Row(input, i)
				featurizer.Featurize(input, featurizedInputs.RowView(i))
			}
		}
	}

	common.ParallelFor(nSamples, common.GetGrainSize(nSamples, minGrain, maxGrain), f)
	return featurizedInputs
}

// LinearLeastSquares computes the least squares fit for the function
//
//   f(x) = ╬њРѓђtermsРѓђ(x) + ╬њРѓЂtermsРѓЂ(x) + ...
//
// to the data (xs[i], ys[i]). It returns the parameters ╬њРѓђ, ╬њРѓЂ, ...
// that minimize the sum of the squares of the residuals of f:
//
//   РѕЉ (ys[i] - f(xs[i]))┬▓
//
// If weights is non-nil, it is used to weight these residuals:
//
//   РѕЉ weights[i] ├Ќ (ys[i] - f(xs[i]))┬▓
//
// The function f is specified by one Go function for each linear
// term. For efficiency, the Go function is vectorized: it will be
// passed a slice of x values in xs and must fill the slice termOut
// with the value of the term for each value in xs.
func LinearLeastSquares(xs, ys, weights []float64, terms ...func(xs, termOut []float64)) (params []float64) {
	// The optimal parameters are found by solving for ╬њ╠ѓ in the
	// "normal equations":
	//
	//    (­ЮљЌрхђ­Юљќ­ЮљЌ)╬њ╠ѓ = ­ЮљЌрхђ­Юљќ­Юљ▓
	//
	// where ­Юљќ is a diagonal weight matrix (or the identity matrix
	// for the unweighted case).

	// TODO: Consider using orthogonal decomposition.

	if len(xs) != len(ys) {
		panic("len(xs) != len(ys)")
	}
	if weights != nil && len(xs) != len(weights) {
		panic("len(xs) != len(weights")
	}

	// Construct ­ЮљЌрхђ. This is the more convenient representation
	// for efficiently calling the term functions.
	xTVals := make([]float64, len(terms)*len(xs))
	for i, term := range terms {
		term(xs, xTVals[i*len(xs):i*len(xs)+len(xs)])
	}
	XT := mat64.NewDense(len(terms), len(xs), xTVals)
	X := XT.T()

	// Construct ­ЮљЌрхђ­Юљќ.
	var XTW *mat64.Dense
	if weights == nil {
		// ­Юљќ is the identity matrix.
		XTW = XT
	} else {
		// Since ­Юљќ is a diagonal matrix, we do this directly.
		XTW = mat64.DenseCopyOf(XT)
		WDiag := mat64.NewVector(len(weights), weights)
		for row := 0; row < len(terms); row++ {
			rowView := XTW.RowView(row)
			rowView.MulElemVec(rowView, WDiag)
		}
	}

	// Construct ­Юљ▓.
	y := mat64.NewVector(len(ys), ys)

	// Compute ╬њ╠ѓ.
	lhs := mat64.NewDense(len(terms), len(terms), nil)
	lhs.Mul(XTW, X)

	rhs := mat64.NewVector(len(terms), nil)
	rhs.MulVec(XTW, y)

	BVals := make([]float64, len(terms))
	B := mat64.NewVector(len(terms), BVals)
	B.SolveVec(lhs, rhs)
	return BVals
}

func predictFeaturized(featurizedInput []float64, featureWeights *mat64.Dense, output []float64) {
	for i := range output {
		output[i] = 0
	}
	for j, zval := range featurizedInput {
		for i, weight := range featureWeights.RowView(j) {
			output[i] += weight * zval
		}
	}
}

// Stochastic gradient descent updates the parameters of theta on a random row selection from a matrix.
// It is faster as it does not compute the cost function over the entire dataset every time.
// It instead calculates the error parameters over only one row of the dataset at a time.
// In return, there is a trade off for accuracy. This is minimised by running multiple SGD processes
// (the number of goroutines spawned is specified by the procs variable) in parallel and taking an average of the result.
func StochasticGradientDescent(x, y, theta *mat64.Dense, alpha float64, epoch, procs int) *mat64.Dense {
	m, _ := y.Dims()
	resultPipe := make(chan *mat64.Dense)
	results := make([]*mat64.Dense, 0)

	for p := 0; p < procs; p++ {
		go func() {
			// Is this just a pointer to theta?
			thetaCopy := mat64.DenseCopyOf(theta)
			for i := 0; i < epoch; i++ {
				for k := 0; k < m; k++ {
					datXtemp := x.RowView(k)
					datYtemp := y.RowView(k)
					datX := mat64.NewDense(1, len(datXtemp), datXtemp)
					datY := mat64.NewDense(1, 1, datYtemp)
					datXFlat := mat64.DenseCopyOf(datX)
					datXFlat.TCopy(datXFlat)
					datX.Mul(datX, thetaCopy)
					datX.Sub(datX, datY)
					datXFlat.Mul(datXFlat, datX)

					// Horrible hack to get around the fact there is no elementwise division in mat64
					xFlatRow, _ := datXFlat.Dims()
					gradient := make([]float64, 0)
					for i := 0; i < xFlatRow; i++ {
						row := datXFlat.RowView(i)
						for i := range row {
							divd := row[i] / float64(m) * alpha
							gradient = append(gradient, divd)
						}
					}
					grows := len(gradient)
					grad := mat64.NewDense(grows, 1, gradient)
					thetaCopy.Sub(thetaCopy, grad)
				}

			}
			resultPipe <- thetaCopy
		}()
	}

	for {
		select {
		case d := <-resultPipe:
			results = append(results, d)
			if len(results) == procs {
				return averageTheta(results)
			}
		}
	}
}

// wrapper for predict, assumes all inputs are correct
func predict(input []float64, features *mat64.Dense, b []float64, featureWeights *mat64.Dense, output []float64) {
	for i := range output {
		output[i] = 0
	}

	nFeatures, _ := features.Dims()
	_, outputDim := featureWeights.Dims()

	sqrt2OverD := math.Sqrt(2.0 / float64(nFeatures))
	//for i, feature := range features {
	for i := 0; i < nFeatures; i++ {
		z := computeZ(input, features.RowView(i), b[i], sqrt2OverD)
		for j := 0; j < outputDim; j++ {
			output[j] += z * featureWeights.At(i, j)
		}
	}
}

// UnscaleData is a wrapper for unscaling data in parallel.
// TODO: Make this work better so that if there is an error somewhere data isn't changed
func UnscaleData(scaler Scaler, data *mat64.Dense) error {
	m := &sync.Mutex{}
	var e ErrorList
	f := func(start, end int) {
		for r := start; r < end; r++ {
			errTmp := scaler.Unscale(data.RowView(r))
			if errTmp != nil {
				m.Lock()
				e = append(e, &SliceError{Header: "scale", Idx: r, Err: errTmp})
				m.Unlock()
			}
		}
	}

	nSamples, _ := data.Dims()
	grain := common.GetGrainSize(nSamples, 1, 500)
	common.ParallelFor(nSamples, grain, f)
	if len(e) != 0 {
		return e
	}
	return nil
}

func MultiHypothesis(x *mat64.Dense, theta *mat64.Vector) *mat64.Vector {
	var res mat64.Dense
	res.Mul(theta.T(), x)
	return res.RowView(0)
}