package main

import (
    "fmt"
    "math"

    "github.com/skelterjohn/go.matrix"
)

func sign(s float64) float64 {
    if s > 0 {
        return 1
    } else if s < 0 {
        return -1
    }
    return 0
}

func unitVector(n int) *matrix.DenseMatrix {
    vec := matrix.Zeros(n, 1)
    vec.Set(0, 0, 1)
    return vec
}

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
}

func main() {
    // task 1: show qr decomp of wp example
    a := matrix.MakeDenseMatrixStacked([][]float64{
        {12, -51, 4},
        {6, 167, -68},
        {-4, 24, -41}})
    q, r := qr(a)
    fmt.Println("q:\n", q)
    fmt.Println("r:\n", r)

    // task 2: use qr decomp for polynomial regression example
    x := matrix.MakeDenseMatrixStacked([][]float64{
        {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}})
    y := matrix.MakeDenseMatrixStacked([][]float64{
        {1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321}})
    fmt.Println("\npolyfit:\n", polyfit(x, y, 2))
}

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 lsqr(a, b *matrix.DenseMatrix) *matrix.DenseMatrix {
    q, r := qr(a)
    n := r.Cols()
    prod, _ := q.Transpose().TimesDense(b)
    return solveUT(r.GetMatrix(0, 0, n, n), prod.GetMatrix(0, 0, n, 1))
}

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
}