func randmatstat(t int) (float64, float64) {
n := 5
v := make([]float64, t)
w := make([]float64, t)
ad := make([]float64, n*n)
bd := make([]float64, n*n)
cd := make([]float64, n*n)
dd := make([]float64, n*n)
P := mat64.NewDense(n, 4*n, nil)
Q := mat64.NewDense(2*n, 2*n, nil)
pTmp := mat64.NewDense(4*n, 4*n, nil)
qTmp := mat64.NewDense(2*n, 2*n, nil)
for i := 0; i < t; i++ {
for i := range ad {
ad[i] = rnd.NormFloat64()
bd[i] = rnd.NormFloat64()
cd[i] = rnd.NormFloat64()
dd[i] = rnd.NormFloat64()
}
a := mat64.NewDense(n, n, ad)
b := mat64.NewDense(n, n, bd)
c := mat64.NewDense(n, n, cd)
d := mat64.NewDense(n, n, dd)
P.Copy(a)
P.View(0, n, n, n).(*mat64.Dense).Copy(b)
P.View(0, 2*n, n, n).(*mat64.Dense).Copy(c)
P.View(0, 3*n, n, n).(*mat64.Dense).Copy(d)
Q.Copy(a)
Q.View(0, n, n, n).(*mat64.Dense).Copy(b)
Q.View(n, 0, n, n).(*mat64.Dense).Copy(c)
Q.View(n, n, n, n).(*mat64.Dense).Copy(d)
pTmp.Mul(P.T(), P)
pTmp.Pow(pTmp, 4)
qTmp.Mul(Q.T(), Q)
qTmp.Pow(qTmp, 4)
v[i] = mat64.Trace(pTmp)
w[i] = mat64.Trace(qTmp)
}
mv, stdv := stat.MeanStdDev(v, nil)
mw, stdw := stat.MeanStdDev(v, nil)
return stdv / mv, stdw / mw
}
func (g *GP) marginalLikelihoodDerivative(x, grad []float64, trainNoise bool, mem *margLikeMemory) {
// d/dTheta_j log[(p|X,theta)] =
// 1/2 * y^T * K^-1 dK/dTheta_j * K^-1 * y - 1/2 * tr(K^-1 * dK/dTheta_j)
// 1/2 * α^T * dK/dTheta_j * α - 1/2 * tr(K^-1 dK/dTheta_j)
// Multiply by the same -2
// -α^T * K^-1 * α + tr(K^-1 dK/dTheta_j)
// This first computation is an inner product.
n := len(g.outputs)
nHyper := g.kernel.NumHyper()
k := mem.k
chol := mem.chol
alpha := mem.alpha
dKdTheta := mem.dKdTheta
kInvDK := mem.kInvDK
y := mat64.NewVector(n, g.outputs)
var noise float64
if trainNoise {
noise = math.Exp(x[len(x)-1])
} else {
noise = g.noise
}
// If x is the same, then reuse what has been computed in the function.
if !floats.Equal(mem.lastX, x) {
copy(mem.lastX, x)
g.kernel.SetHyper(x[:nHyper])
g.setKernelMat(k, noise)
//chol.Cholesky(k, false)
chol.Factorize(k)
alpha.SolveCholeskyVec(chol, y)
}
g.setKernelMatDeriv(dKdTheta, trainNoise, noise)
for i := range dKdTheta {
kInvDK.SolveCholesky(chol, dKdTheta[i])
inner := mat64.Inner(alpha, dKdTheta[i], alpha)
grad[i] = -inner + mat64.Trace(kInvDK)
}
floats.Scale(1/float64(n), grad)
bounds := g.kernel.Bounds()
if trainNoise {
bounds = append(bounds, Bound{minLogNoise, maxLogNoise})
}
barrierGrad := make([]float64, len(grad))
for i, v := range x {
// Quadratic barrier penalty.
if v < bounds[i].Min {
diff := bounds[i].Min - v
barrierGrad[i] = -(barrierPow) * math.Pow(diff, barrierPow-1)
}
if v > bounds[i].Max {
diff := v - bounds[i].Max
barrierGrad[i] = (barrierPow) * math.Pow(diff, barrierPow-1)
}
}
fmt.Println("noise, minNoise", x[len(x)-1], bounds[len(x)-1].Min)
fmt.Println("barrier Grad", barrierGrad)
floats.Add(grad, barrierGrad)
//copy(grad, barrierGrad)
}