func solveUT(r, b *matrix.DenseMatrix) *matrix.DenseMatrix {
n := r.Cols()
x := matrix.Zeros(n, 1)
for k := n - 1; k >= 0; k-- {
sum := 0.
for j := k + 1; j < n; j++ {
sum += r.Get(k, j) * x.Get(j, 0)
}
x.Set(k, 0, (b.Get(k, 0)-sum)/r.Get(k, k))
}
return x
}
func polyfit(x, y *matrix.DenseMatrix, n int) *matrix.DenseMatrix {
m := x.Cols()
a := matrix.Zeros(m, n+1)
for i := 0; i < m; i++ {
for j := 0; j <= n; j++ {
a.Set(i, j, math.Pow(x.Get(0, i), float64(j)))
}
}
return lsqr(a, y.Transpose())
}
func householder(a *matrix.DenseMatrix) *matrix.DenseMatrix {
m := a.Rows()
s := sign(a.Get(0, 0))
e := unitVector(m)
u := matrix.Sum(a, matrix.Scaled(e, a.TwoNorm()*s))
v := matrix.Scaled(u, 1/u.Get(0, 0))
// (error checking skipped in this solution)
prod, _ := v.Transpose().TimesDense(v)
β := 2 / prod.Get(0, 0)
prod, _ = v.TimesDense(v.Transpose())
return matrix.Difference(matrix.Eye(m), matrix.Scaled(prod, β))
}
func qr(a *matrix.DenseMatrix) (q, r *matrix.DenseMatrix) {
m := a.Rows()
n := a.Cols()
q = matrix.Eye(m)
last := n - 1
if m == n {
last--
}
for i := 0; i <= last; i++ {
// (copy is only for compatibility with an older version of gomatrix)
b := a.GetMatrix(i, i, m-i, n-i).Copy()
x := b.GetColVector(0)
h := matrix.Eye(m)
h.SetMatrix(i, i, householder(x))
q, _ = q.TimesDense(h)
a, _ = h.TimesDense(a)
}
return q, a
}