// 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.ColView(j))...))
}
for j := 0; j < nObjPts; j++ {
imgPtsVec.Set(j, NewGcvPoint2f32(mat64.Col(nil, j, imgPts.ColView(j))...))
}
_imgSize := NewGcvSize2i(dims[0], dims[1])
camMat = GcvMatToMat64(GcvInitCameraMatrix2D_(
objPtsVec, imgPtsVec, _imgSize, aspectRatio))
return camMat
}
// 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 DivideData(data *mat64.Dense, start, size int) (*mat64.Dense, []float64) {
_x := []float64{}
y := []float64{}
for i := start; i < (start + size); i++ {
_x = append(_x, data.ColView(0).At(i, 0)) // x1
_x = append(_x, data.ColView(1).At(i, 0)) // x2
y = append(y, data.ColView(2).At(i, 0)) // label
}
x := mat64.NewDense(size, 2, _x) // x1 and x2
return x, y
}
func Accuracy(y_true, y_pred *mat64.Dense) float64 {
y1 := y_true.ColView(0).RawVector().Data
y2 := y_pred.ColView(0).RawVector().Data
total := 0.0
correct := 0.0
for i := 0; i < len(y1); i++ {
if y1[i] == y2[i] {
correct++
}
total++
}
return correct / total
}
func Grad(x *mat64.Dense, y, w []float64, b float64, s int) (w_grad, b_grad []float64) {
errs := []float64{}
yhat := P_y_given_x(x, w, b, s)
for i := 0; i < len(y); i++ {
errs = append(errs, y[i]-yhat[i]) // error = label - pred
}
e := mat64.NewDense(s, 1, errs)
w_grad = append(w_grad, -1*mat64.Dot(x.ColView(0), e))
w_grad = append(w_grad, -1*mat64.Dot(x.ColView(1), e))
b_grad = append(b_grad, -1*Mean(errs))
return w_grad, b_grad
}
// StdDevBatch predicts the standard deviation at a set of locations of x.
func (g *GP) StdDevBatch(std []float64, x mat64.Matrix) []float64 {
r, c := x.Dims()
if c != g.inputDim {
panic(badInputLength)
}
if std == nil {
std = make([]float64, r)
}
if len(std) != r {
panic(badStorage)
}
// For a single point, the stddev is
// sigma = k(x,x) - k_*^T * K^-1 * k_*
// where k is the vector of kernels between the input points and the output points
// For many points, the formula is:
// nu_* = k(x_*, k_*) - k_*^T * K^-1 * k_*
// This creates the full covariance matrix which is an rxr matrix. However,
// the standard deviations are just the diagonal of this matrix. Instead, be
// smart about it and compute the diagonal terms one at a time.
kStar := g.formKStar(x)
var tmp mat64.Dense
tmp.SolveCholesky(g.cholK, kStar)
// set k(x_*, x_*) into std then subtract k_*^T K^-1 k_* , computed one row at a time
var tmp2 mat64.Vector
row := make([]float64, c)
for i := range std {
for k := 0; k < c; k++ {
row[k] = x.At(i, k)
}
std[i] = g.kernel.Distance(row, row)
tmp2.MulVec(kStar.ColView(i).T(), tmp.ColView(i))
rt, ct := tmp2.Dims()
if rt != 1 && ct != 1 {
panic("bad size")
}
std[i] -= tmp2.At(0, 0)
std[i] = math.Sqrt(std[i])
}
// Need to scale the standard deviation to be in the same units as y.
floats.Scale(g.std, std)
return std
}
func mulMulti(a *mat64.Dense, b []float64, rows int) (r []float64) {
var m, m2 mat64.Dense
b1 := mat64.NewDense(1, 1, []float64{b[0]})
b2 := mat64.NewDense(1, 1, []float64{b[1]})
m.Mul(a.ColView(0), b1)
m2.Mul(a.ColView(1), b2)
for i := 0; i < rows; i++ {
r = append(r, m.ColView(0).At(i, 0)+m2.ColView(0).At(i, 0))
}
return r
}
func GcvCalibrateCamera(objPts, imgPts, camMat, distCoeffs *mat64.Dense,
dims [2]int, flags int) (calCamMat, rvec, tvec *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.ColView(j))...))
}
for j := 0; j < nObjPts; j++ {
imgPtsVec.Set(j, NewGcvPoint2f32(mat64.Col(nil, j, imgPts.ColView(j))...))
}
_camMat := Mat64ToGcvMat(camMat)
_distCoeffs := Mat64ToGcvMat(distCoeffs)
_rvec := NewGcvMat()
_tvec := NewGcvMat()
_imgSize := NewGcvSize2i(dims[0], dims[1])
GcvCalibrateCamera_(
objPtsVec, imgPtsVec,
_imgSize, _camMat, _distCoeffs,
_rvec, _tvec, flags)
calCamMat = GcvMatToMat64(_camMat)
rvec = GcvMatToMat64(_rvec)
tvec = GcvMatToMat64(_tvec)
return calCamMat, rvec, tvec
}
// Wrapper for the `train` function in liblinear.
//
// `model* train(const struct problem *prob, const struct parameter *param);`
//
// The explanation of parameters are:
//
// solverType:
//
// for multi-class classification
// 0 -- L2-regularized logistic regression (primal)
// 1 -- L2-regularized L2-loss support vector classification (dual)
// 2 -- L2-regularized L2-loss support vector classification (primal)
// 3 -- L2-regularized L1-loss support vector classification (dual)
// 4 -- support vector classification by Crammer and Singer
// 5 -- L1-regularized L2-loss support vector classification
// 6 -- L1-regularized logistic regression
// 7 -- L2-regularized logistic regression (dual)
// for regression
// 11 -- L2-regularized L2-loss support vector regression (primal)
// 12 -- L2-regularized L2-loss support vector regression (dual)
// 13 -- L2-regularized L1-loss support vector regression (dual)
//
// eps is the stopping criterion.
//
// C_ is the cost of constraints violation.
//
// p is the sensitiveness of loss of support vector regression.
//
// classWeights is a map from int to float64, with the key be the class and the
// value be the weight. For example, {1: 10, -1: 0.5} means giving weight=10 for
// class=1 while weight=0.5 for class=-1
//
// If you do not want to change penalty for any of the classes, just set
// classWeights to nil.
func Train(X, y *mat64.Dense, bias float64, solverType int, c_, p, eps float64, classWeights map[int]float64) *Model {
var weightLabelPtr *C.int
var weightPtr *C.double
nRows, nCols := X.Dims()
cX := mapCDouble(X.RawMatrix().Data)
cY := mapCDouble(y.ColView(0).RawVector().Data)
nrWeight := len(classWeights)
weightLabel := []C.int{}
weight := []C.double{}
for key, val := range classWeights {
weightLabel = append(weightLabel, (C.int)(key))
weight = append(weight, (C.double)(val))
}
if nrWeight > 0 {
weightLabelPtr = &weightLabel[0]
weightPtr = &weight[0]
} else {
weightLabelPtr = nil
weightPtr = nil
}
model := C.call_train(
&cX[0], &cY[0],
C.int(nRows), C.int(nCols), C.double(bias),
C.int(solverType), C.double(c_), C.double(p), C.double(eps),
C.int(nrWeight), weightLabelPtr, weightPtr)
return &Model{
cModel: model,
}
}