func (n *InnerNormal) SetScale(data *mat64.Dense) error {
rows, dim := data.Dims()
if rows < 2 {
return errors.New("scale: less than two inputs")
}
means := make([]float64, dim)
stds := make([]float64, dim)
for i := 0; i < dim; i++ {
// Filter out the extremes
r := data.Col(nil, i)
if len(r) != rows {
panic("bad lengths")
}
sort.Float64s(r)
lowerIdx := int(math.Floor(float64(rows) * n.LowerQuantile))
upperIdx := int(math.Ceil(float64(rows) * n.UpperQuantile))
trimmed := r[lowerIdx:upperIdx]
mean, std := stat.MeanStdDev(trimmed, nil)
//std := stat.StdDev(trimmed, mean, nil)
means[i] = mean
stds[i] = std
}
n.Mu = means
n.Sigma = stds
fmt.Println(n.Mu, n.Sigma)
n.Dim = dim
n.Scaled = true
return nil
}
func (nb *NaiveBayes) Predict(X *mat64.Dense) []Prediction {
nSamples, _ := X.Dims()
prediction := []Prediction{}
for i := 0; i < nSamples; i++ {
scores := map[int]float64{}
for langIdx, _ := range nb.params.LangsCount {
scores[langIdx] = nb.tokensProba(X.Row(nil, i), langIdx) + nb.langProba(langIdx)
}
bestScore := scores[0]
bestLangIdx := 0
for langIdx, score := range scores {
if score > bestScore {
bestScore = score
bestLangIdx = langIdx
}
}
prediction = append(prediction, Prediction{
Label: bestLangIdx,
Language: "TODO: PENDING",
Score: bestScore,
})
}
return prediction
}
// GcvInitCameraMatrix2D takes one 3-by-N matrix and one 2-by-N Matrix as input.
// Each column in the input matrix represents a point in real world (objPts) or
// in image (imgPts).
// Return: the camera matrix.
func GcvInitCameraMatrix2D(objPts, imgPts *mat64.Dense, dims [2]int,
aspectRatio float64) (camMat *mat64.Dense) {
objDim, nObjPts := objPts.Dims()
imgDim, nImgPts := imgPts.Dims()
if objDim != 3 || imgDim != 2 || nObjPts != nImgPts {
panic("Invalid dimensions for objPts and imgPts")
}
objPtsVec := NewGcvPoint3f32Vector(int64(nObjPts))
imgPtsVec := NewGcvPoint2f32Vector(int64(nObjPts))
for j := 0; j < nObjPts; j++ {
objPtsVec.Set(j, NewGcvPoint3f32(mat64.Col(nil, j, objPts)...))
}
for j := 0; j < nObjPts; j++ {
imgPtsVec.Set(j, NewGcvPoint2f32(mat64.Col(nil, j, imgPts)...))
}
_imgSize := NewGcvSize2i(dims[0], dims[1])
camMat = GcvMatToMat64(GcvInitCameraMatrix2D_(
objPtsVec, imgPtsVec, _imgSize, aspectRatio))
return camMat
}
func StackConstr(low, A, up *mat64.Dense) (stackA, b *mat64.Dense, ranges []float64) {
neglow := &mat64.Dense{}
neglow.Scale(-1, low)
b = &mat64.Dense{}
b.Stack(up, neglow)
negA := &mat64.Dense{}
negA.Scale(-1, A)
stackA = &mat64.Dense{}
stackA.Stack(A, negA)
// capture the range of each constraint from A because this information is
// lost when converting from "low <= Ax <= up" via stacking to "Ax <= up".
m, _ := A.Dims()
ranges = make([]float64, m, 2*m)
for i := 0; i < m; i++ {
ranges[i] = up.At(i, 0) - low.At(i, 0)
if ranges[i] == 0 {
if up.At(i, 0) == 0 {
ranges[i] = 1
} else {
ranges[i] = up.At(i, 0)
}
}
}
ranges = append(ranges, ranges...)
return stackA, b, ranges
}
func toFeatureNodes(X *mat64.Dense) []*C.struct_feature_node {
featureNodes := []*C.struct_feature_node{}
nRows, nCols := X.Dims()
for i := 0; i < nRows; i++ {
row := []C.struct_feature_node{}
for j := 0; j < nCols; j++ {
val := X.At(i, j)
if val != 0 {
row = append(row, C.struct_feature_node{
index: C.int(j + 1),
value: C.double(val),
})
}
}
row = append(row, C.struct_feature_node{
index: C.int(-1),
value: C.double(0),
})
featureNodes = append(featureNodes, &row[0])
}
return featureNodes
}
func (fm *FeatureMatrix) Mat64(header, transpose bool) *mat64.Dense {
var (
idx int
iter fmIt
dense *mat64.Dense
)
ncol := len(fm.Data)
nrow := len(fm.CaseLabels)
if !transpose {
iter = rowIter(fm, header)
dense = mat64.NewDense(nrow, ncol, nil)
} else {
iter = colIter(fm, header)
dense = mat64.NewDense(ncol, nrow+1, nil)
}
for row, ok := iter(); ok; idx++ {
for j, val := range row {
flt, _ := strconv.ParseFloat(val, 64)
dense.Set(idx, j, flt)
}
row, ok = iter()
}
return dense
}
// Batch gradient descent finds the local minimum of a function.
// See http://en.wikipedia.org/wiki/Gradient_descent for more details.
func BatchGradientDescent(x, y, theta *mat64.Dense, alpha float64, epoch int) *mat64.Dense {
m, _ := y.Dims()
for i := 0; i < epoch; i++ {
xFlat := mat64.DenseCopyOf(x)
xFlat.TCopy(xFlat)
temp := mat64.DenseCopyOf(x)
// Calculate our best prediction, given theta
temp.Mul(temp, theta)
// Calculate our error from the real values
temp.Sub(temp, y)
xFlat.Mul(xFlat, temp)
// Temporary hack to get around the fact there is no scalar division in mat64
xFlatRow, _ := xFlat.Dims()
gradient := make([]float64, 0)
for k := 0; k < xFlatRow; k++ {
row := xFlat.RowView(k)
for v := range row {
divd := row[v] / float64(m) * alpha
gradient = append(gradient, divd)
}
}
grows := len(gradient)
grad := mat64.NewDense(grows, 1, gradient)
theta.Sub(theta, grad)
}
return theta
}
// 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
}
func GradientDescent(X *mat64.Dense, y *mat64.Vector, alpha, tolerance float64, maxIters int) *mat64.Vector {
// m = Number of Training Examples
// n = Number of Features
m, n := X.Dims()
h := mat64.NewVector(m, nil)
partials := mat64.NewVector(n, nil)
new_theta := mat64.NewVector(n, nil)
Regression:
for i := 0; i < maxIters; i++ {
// Calculate partial derivatives
h.MulVec(X, new_theta)
for el := 0; el < m; el++ {
val := (h.At(el, 0) - y.At(el, 0)) / float64(m)
h.SetVec(el, val)
}
partials.MulVec(X.T(), h)
// Update theta values
for el := 0; el < n; el++ {
new_val := new_theta.At(el, 0) - (alpha * partials.At(el, 0))
new_theta.SetVec(el, new_val)
}
// Check the "distance" to the local minumum
dist := math.Sqrt(mat64.Dot(partials, partials))
if dist <= tolerance {
break Regression
}
}
return new_theta
}
//MassCenter centers in in the center of mass of oref. Mass must be
//A column vector. Returns the centered matrix and the displacement matrix.
func MassCenter(in, oref *v3.Matrix, mass *mat64.Dense) (*v3.Matrix, *v3.Matrix, error) {
or, _ := oref.Dims()
ir, _ := in.Dims()
if mass == nil { //just obtain the geometric center
tmp := ones(or)
mass = mat64.NewDense(or, 1, tmp) //gnOnes(or, 1)
}
ref := v3.Zeros(or)
ref.Copy(oref)
gnOnesvector := gnOnes(1, or)
f := func() { ref.ScaleByCol(ref, mass) }
if err := gnMaybe(gnPanicker(f)); err != nil {
return nil, nil, CError{err.Error(), []string{"v3.Matrix.ScaleByCol", "MassCenter"}}
}
ref2 := v3.Zeros(1)
g := func() { ref2.Mul(gnOnesvector, ref) }
if err := gnMaybe(gnPanicker(g)); err != nil {
return nil, nil, CError{err.Error(), []string{"v3.gOnesVector", "MassCenter"}}
}
ref2.Scale(1.0/mass.Sum(), ref2)
returned := v3.Zeros(ir)
returned.Copy(in)
returned.SubVec(returned, ref2)
/* for i := 0; i < ir; i++ {
if err := returned.GetRowVector(i).Subtract(ref2); err != nil {
return nil, nil, err
}
}
*/
return returned, ref2, nil
}
func (lr *LogisticRegression) Predict(X *mat64.Dense) []Prediction {
nSamples, _ := X.Dims()
prediction := []Prediction{}
for i := 0; i < nSamples; i++ {
scores := liblinear.PredictProba(lr.model, X)
_, nClasses := scores.Dims()
bestScore := scores.At(i, 0)
bestLangIdx := 0
for langIdx := 0; langIdx < nClasses; langIdx++ {
score := scores.At(i, langIdx)
if score > bestScore {
bestScore = score
bestLangIdx = langIdx
}
}
prediction = append(prediction, Prediction{
Label: bestLangIdx,
Language: "TODO: PENDING",
Score: bestScore,
})
}
return prediction
}
// MetropolisHastings generates rows(batch) samples using the Metropolis Hastings
// algorithm (http://en.wikipedia.org/wiki/Metropolis%E2%80%93Hastings_algorithm),
// with the given target and proposal distributions, starting at the intial location
// and storing the results in-place into samples. If src != nil, it will be used to generate random
// numbers, otherwise rand.Float64 will be used.
//
// Metropolis-Hastings is a Markov-chain Monte Carlo algorithm that generates
// samples according to the distribution specified by target by using the Markov
// chain implicitly defined by the proposal distribution. At each
// iteration, a proposal point is generated randomly from the current location.
// This proposal point is accepted with probability
// p = min(1, (target(new) * proposal(current|new)) / (target(current) * proposal(new|current)))
// If the new location is accepted, it is stored into batch and becomes the
// new current location. If it is rejected, the current location remains and
// is stored into samples. Thus, a location is stored into batch at every iteration.
//
// The samples in Metropolis Hastings are correlated with one another through the
// Markov chain. As a result, the initial value can have a significant influence
// on the early samples, and so, typically, the first samples generated by the chain
// are ignored. This is known as "burn-in", and can be accomplished with slicing.
// The best choice for burn-in length will depend on the sampling and target
// distributions.
//
// Many choose to have a sampling "rate" where a number of samples
// are ignored in between each kept sample. This helps decorrelate
// the samples from one another, but also reduces the number of available samples.
// A sampling rate can be implemented with successive calls to MetropolisHastings.
func MetropolisHastings(batch *mat64.Dense, initial []float64, target distmv.LogProber, proposal MHProposal, src *rand.Rand) {
f64 := rand.Float64
if src != nil {
f64 = src.Float64
}
if len(initial) == 0 {
panic("metropolishastings: zero length initial")
}
r, _ := batch.Dims()
current := make([]float64, len(initial))
copy(current, initial)
proposed := make([]float64, len(initial))
currentLogProb := target.LogProb(initial)
for i := 0; i < r; i++ {
proposal.ConditionalRand(proposed, current)
proposedLogProb := target.LogProb(proposed)
probTo := proposal.ConditionalLogProb(proposed, current)
probBack := proposal.ConditionalLogProb(current, proposed)
accept := math.Exp(proposedLogProb + probBack - probTo - currentLogProb)
if accept > f64() {
copy(current, proposed)
currentLogProb = proposedLogProb
}
batch.SetRow(i, current)
}
}
// InnerProduct computes the inner product through a kernel trick
// K(x, y) = (x^T y + 1)^d
func (p *PolyKernel) InnerProduct(vectorX *mat64.Dense, vectorY *mat64.Dense) float64 {
subVectorX := vectorX.ColView(0)
subVectorY := vectorY.ColView(0)
result := mat64.Dot(subVectorX, subVectorY)
result = math.Pow(result+1, float64(p.degree))
return result
}
func DfFromMat(mat *mat64.Dense) *DataFrame {
rows, cols := mat.Dims()
return &DataFrame{
data: mat,
rows: rows,
cols: cols,
}
}
func rowSum(matrix *mat64.Dense, rowId int) float64 {
_, col := matrix.Dims()
sum := float64(0)
for c := 0; c < col; c++ {
sum += matrix.At(rowId, c)
}
return sum
}
func colSum(matrix *mat64.Dense, colId int) float64 {
row, _ := matrix.Dims()
sum := float64(0)
for r := 0; r < row; r++ {
sum += matrix.At(r, colId)
}
return sum
}
func ExampleCholesky() {
// Construct a symmetric positive definite matrix.
tmp := mat64.NewDense(4, 4, []float64{
2, 6, 8, -4,
1, 8, 7, -2,
2, 2, 1, 7,
8, -2, -2, 1,
})
var a mat64.SymDense
a.SymOuterK(1, tmp)
fmt.Printf("a = %0.4v\n", mat64.Formatted(&a, mat64.Prefix(" ")))
// Compute the cholesky factorization.
var chol mat64.Cholesky
if ok := chol.Factorize(&a); !ok {
fmt.Println("a matrix is not positive semi-definite.")
}
// Find the determinant.
fmt.Printf("\nThe determinant of a is %0.4g\n\n", chol.Det())
// Use the factorization to solve the system of equations a * x = b.
b := mat64.NewVector(4, []float64{1, 2, 3, 4})
var x mat64.Vector
if err := x.SolveCholeskyVec(&chol, b); err != nil {
fmt.Println("Matrix is near singular: ", err)
}
fmt.Println("Solve a * x = b")
fmt.Printf("x = %0.4v\n", mat64.Formatted(&x, mat64.Prefix(" ")))
// Extract the factorization and check that it equals the original matrix.
var t mat64.TriDense
t.LFromCholesky(&chol)
var test mat64.Dense
test.Mul(&t, t.T())
fmt.Println()
fmt.Printf("L * L^T = %0.4v\n", mat64.Formatted(&a, mat64.Prefix(" ")))
// Output:
// a = ⎡120 114 -4 -16⎤
// ⎢114 118 11 -24⎥
// ⎢ -4 11 58 17⎥
// ⎣-16 -24 17 73⎦
//
// The determinant of a is 1.543e+06
//
// Solve a * x = b
// x = ⎡ -0.239⎤
// ⎢ 0.2732⎥
// ⎢-0.04681⎥
// ⎣ 0.1031⎦
//
// L * L^T = ⎡120 114 -4 -16⎤
// ⎢114 118 11 -24⎥
// ⎢ -4 11 58 17⎥
// ⎣-16 -24 17 73⎦
}
// TODO(ariw): Delete any matrix creation in layer operations.
func (self *Layer) Forward(previous *Layer) {
self.resetForExamples(previous)
self.Input = previous.Output
var inputAndBias mat64.Dense
inputAndBias.Augment(self.Input, self.Ones) // Add bias to input.
self.Output.Mul(&inputAndBias, self.Weight)
self.DActivationFunction(self.Output.T(), self.Derivatives)
self.ActivationFunction(self.Output, self.Output)
}
// double predict(const struct model *model_, const struct feature_node *x);
func Predict(model *Model, X *mat64.Dense) *mat64.Dense {
nRows, nCols := X.Dims()
cX := mapCDouble(X.RawMatrix().Data)
y := mat64.NewDense(nRows, 1, nil)
result := doubleToFloats(C.call_predict(
model.cModel, &cX[0], C.int(nRows), C.int(nCols)), nRows)
y.SetCol(0, result)
return y
}
// 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
}
// Generate generates a list of n random features given an input dimension d
func (iso IsoSqExp) Generate(n int, dim int, features *mat64.Dense) {
scale := math.Exp(iso.LogScale)
for i := 0; i < n; i++ {
for j := 0; j < dim; j++ {
features.Set(i, j, rand.NormFloat64()*scale)
}
}
}
// double predict(const struct model *model_, const struct feature_node *x);
func Predict(model *Model, X *mat64.Dense) *mat64.Dense {
nRows, _ := X.Dims()
cXs := toFeatureNodes(X)
y := mat64.NewDense(nRows, 1, nil)
for i, cX := range cXs {
y.Set(i, 0, float64(C.predict(model.cModel, cX)))
}
return y
}
// SetScale sets a linear scale between 0 and 1. If no data
// points. If the minimum and maximum value are identical in
// a dimension, the minimum and maximum values will be set to
// that value +/- 0.5 and a
func (l *Linear) SetScale(data *mat64.Dense) error {
rows, dim := data.Dims()
if rows < 2 {
return errors.New("scale: less than two inputs")
}
// Generate data for min and max if they don't already exist
if len(l.Min) < dim {
l.Min = make([]float64, dim)
} else {
l.Min = l.Min[0:dim]
}
if len(l.Max) < dim {
l.Max = make([]float64, dim)
} else {
l.Max = l.Max[0:dim]
}
for i := range l.Min {
l.Min[i] = math.Inf(1)
}
for i := range l.Max {
l.Max[i] = math.Inf(-1)
}
// Find the minimum and maximum in each dimension
for i := 0; i < rows; i++ {
for j := 0; j < dim; j++ {
val := data.At(i, j)
if val < l.Min[j] {
l.Min[j] = val
}
if val > l.Max[j] {
l.Max[j] = val
}
}
}
l.Scaled = true
l.Dim = dim
var unifError *UniformDimension
// Check that the maximum and minimum values are not identical
for i := range l.Min {
if l.Min[i] == l.Max[i] {
if unifError == nil {
unifError = &UniformDimension{}
}
unifError.Dims = append(unifError.Dims, i)
l.Min[i] -= 0.5
l.Max[i] += 0.5
}
}
if unifError != nil {
return unifError
}
return nil
}
// SampleWeighted generates rows(batch) samples from the embedded Sampler type
// and sets all of the weights equal to 1. If rows(batch) and len(weights)
// of weights are not equal, SampleWeighted will panic.
func (w SampleUniformWeighted) SampleWeighted(batch *mat64.Dense, weights []float64) {
r, _ := batch.Dims()
if r != len(weights) {
panic(badLengthMismatch)
}
w.Sample(batch)
for i := range weights {
weights[i] = 1
}
}
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
}
}
}
func regionQuery(p int, ret *big.Int, dist *mat64.Dense, eps float64) *big.Int {
rows, _ := dist.Dims()
// Return any points within the Eps neighbourhood
for i := 0; i < rows; i++ {
if dist.At(p, i) <= eps {
ret = ret.SetBit(ret, i, 1) // Mark as neighbour
}
}
return ret
}
// UpdateBias computes B = B + l.E and updates the bias weights
// from a size * 1 back-propagated error vector.
func (n *Network) UpdateBias(err *mat64.Dense, learnRate float64) {
for i, b := range n.biases {
if i < n.input {
continue
}
n.biases[i] = b + err.At(i, 0)*learnRate
}
}
func (n *None) SetScale(data *mat64.Dense) error {
rows, cols := data.Dims()
if rows < 2 {
return errors.New("scale: less than two inputs")
}
n.Dim = cols
n.Scaled = true
return nil
}
// Add adds a new point to the gaussian process
func (gp *Trainer) Add(newInput []float64, newOutput []float64) {
gp.nData++
// See if we need to allocate new memory
var inputAtCap bool
if len(gp.inputData) == cap(gp.inputData) {
inputAtCap = true
}
/*
var outputAtCap bool
if len(gp.outputData) == cap(gp.outputData) {
outputAtCap = true
}
*/
gp.inputData = append(gp.inputData, newInput)
gp.outputData = append(gp.outputData, newOutput)
// If we had to allocate memory, allocate new memory for the kernel matrix
if gp.Implicit {
// If it's implicit, just need to update matrix size, because the kernel
// is computed on the fly
//gp.kernelMat =
panic("not coded")
}
var newKernelMatrix *mat64.Dense
if inputAtCap {
oldKernelMatrix := gp.kernelMatrix
// If we had to allocate new memory for the inputs, then need to expand
// the size of the matrix as well
newKernelData := make([]float64, cap(gp.inputData)*cap(gp.inputData))
panic("Need to use raw matrix")
//newKernelMatrix = mat64.NewDense(gp.nData, gp.nData, newKernelData)
// Copy the old kernel data into the new one. View and newKernelMatrix share
// the same underlying array
view := &mat64.Dense{}
view.View(newKernelMatrix, 0, 0, gp.nData-1, gp.nData-1)
view.Copy(oldKernelMatrix)
gp.kernelData = newKernelData
} else {
// We aren't at capacity, so just need to increase the size
newKernelMatrix = mat64.NewDense(nData, nData, gp.kernelData)
}
// Set the new values of the kernel matrix
for i := 0; i < nData; i++ {
oldInput := gp.inputData[i*gp.inputDim : (i+1)*gp.inputDim]
ker := gp.Kernel(oldData, newInput)
newKernelMatrix.Set(i, gp.nData, ker)
newKernelMatrix.Set(gp.nData, i, ker)
}
gp.kernelMatrix = newKernelMatrix
}
func main() {
// task 1: show qr decomp of wp example
a := mat64.NewDense(3, 3, []float64{
12, -51, 4,
6, 167, -68,
-4, 24, -41,
})
var qr mat64.QR
qr.Factorize(a)
var q, r mat64.Dense
q.QFromQR(&qr)
r.RFromQR(&qr)
fmt.Printf("q: %.3f\n\n", mat64.Formatted(&q, mat64.Prefix(" ")))
fmt.Printf("r: %.3f\n\n", mat64.Formatted(&r, mat64.Prefix(" ")))
// task 2: use qr decomp for polynomial regression example
x := []float64{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
y := []float64{1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321}
a = Vandermonde(x, 2)
b := mat64.NewDense(11, 1, y)
qr.Factorize(a)
var f mat64.Dense
f.SolveQR(&qr, false, b)
fmt.Printf("polyfit: %.3f\n",
mat64.Formatted(&f, mat64.Prefix(" ")))
}