func calculate_even_fib_until(limit int64) (m []float64) {
if limit <= 2 { // base case: This cannot be determined by the recurrence relation
m = []float64{2, 0}
return
}
done := false
var a, b, c *matrix.DenseMatrix
a = relation_mat // a holds older b before multiplication
b = relation_mat // b holds result of matrix multiplication
c = relation_mat // c holds matrix that is to be multiplied in current iteration
dict[float64(1)] = relation_mat
for !done {
a = b
b, _ = b.TimesDense(c)
t, _ := b.TimesDense(init_mat) // calculate resultant vector for a certain power of a matrix
if t.ColCopy(0)[1] < float64(limit) {
if pow[1] == -1 { // pow[1] = -1 means we are exponentiating the matrix (first mode).
pow[0] = 2 * pow[0]
c = b
dict[pow[0]] = b
} else {
pow[0] = math.Ceil((pow[1] + pow[0]) / float64(2))
c = dict[math.Ceil((pow[1]-pow[0])/float64(2))]
}
} else {
if pow[1] == -1 {
pow[1] = pow[0]
pow[0] = pow[0] / 2
dict[pow[1]] = b
if pow[1]-pow[0] < 2 {
c = dict[float64(1)]
} else {
c = dict[math.Ceil((pow[1]-pow[0])/float64(2))]
}
b = a
} else {
pow[1] = math.Ceil((pow[1] + pow[0]) / float64(2))
c = dict[math.Ceil((pow[1]-pow[0])/float64(2))]
b = a
}
}
t, _ = b.TimesDense(init_mat)
if pow[1] != -1 && t.ColCopy(0)[1] < float64(limit) && t.ColCopy(0)[0] >= float64(limit) {
done = true
m = t.ColCopy(0)
}
}
return
}
func (this *KnownVarianceLRPosterior) Remove(x, y *mx.DenseMatrix) {
xxt, _ := x.TimesDense(x.Transpose())
this.XXt.Subtract(xxt)
yxt, _ := y.TimesDense(x.Transpose())
this.YXt.Subtract(yxt)
}
func (this *KnownVarianceLRPosterior) Insert(x, y *mx.DenseMatrix) {
xxt, _ := x.TimesDense(x.Transpose())
this.XXt.Add(xxt)
yxt, _ := y.TimesDense(x.Transpose())
this.YXt.Add(yxt)
}
/*
If Y ~ N(AX, Sigma, I)
and A ~ N(M, Sigma, Phi)
this returns a sampler for P(A|X,Y,Sigma,M,Phi)
*/
func KnownVariancePosterior(Y, X, Sigma, M, Phi *mx.DenseMatrix) func() (A *mx.DenseMatrix) {
o := Y.Rows()
i := X.Rows()
n := Y.Cols()
if n != X.Cols() {
panic("X and Y don't have the same number of columns")
}
if o != M.Rows() {
panic("Y.Rows != M.Rows")
}
if i != M.Cols() {
panic("Y.Rows != M.Cols")
}
if o != Sigma.Rows() {
panic("Y.Rows != Sigma.Rows")
}
if Sigma.Cols() != Sigma.Rows() {
panic("Sigma is not square")
}
if i != Phi.Rows() {
panic("X.Rows != Phi.Rows")
}
if Phi.Cols() != Phi.Rows() {
panic("Phi is not square")
}
Xt := X.Transpose()
PhiInv, err := Phi.Inverse()
if err != nil {
panic(err)
}
XXt, err := X.TimesDense(Xt)
if err != nil {
panic(err)
}
XXtpPhiInv, err := XXt.PlusDense(PhiInv)
if err != nil {
panic(err)
}
Omega, err := XXtpPhiInv.Inverse()
if err != nil {
panic(err)
}
YXtpMPhiInv, err := Y.TimesDense(Xt)
if err != nil {
panic(err)
}
MPhiInv, err := M.TimesDense(PhiInv)
if err != nil {
panic(err)
}
err = YXtpMPhiInv.AddDense(MPhiInv)
if err != nil {
panic(err)
}
Mxy, err := YXtpMPhiInv.TimesDense(Omega)
if err != nil {
panic(err)
}
if false {
fmt.Printf("Mxy:\n%v\n", Mxy)
fmt.Printf("Sigma:\n%v\n", Sigma)
fmt.Printf("Omega:\n%v\n", Omega)
}
return dst.MatrixNormal(Mxy, Sigma, Omega)
}