//gnEigen wraps the matrix.DenseMatrix.Eigen() function in order to guarantee
//That the eigenvectors and eigenvalues are sorted according to the eigenvalues
//It also guarantees orthonormality and handness. I don't know how many of
//these are already guaranteed by Eig(). Will delete the unneeded parts
//And even this whole function when sure. The main reason for this function
//Is the compatibiliy with go.matrix. This function should dissapear when we
//have a pure Go blas.
func EigenWrap(in *Matrix, epsilon float64) (*Matrix, []float64, error) {
if epsilon < 0 {
epsilon = appzero
}
efacs := mat64.Eigen(mat64.DenseCopyOf(in.Dense), epsilon)
evecsprev := &Matrix{efacs.V}
evalsmat := efacs.D()
d, _ := evalsmat.Dims()
evals := make([]float64, d, d)
for k, _ := range evals {
evals[k] = evalsmat.At(k, k)
}
evecs := Zeros(3)
fn := func() { evecs.Copy(evecsprev.T()) }
err := mat64.Maybe(fn)
if err != nil {
return nil, nil, Error{err.Error(), []string{"mat64.Copy/math64.T", "EigenWrap"}, true}
}
//evecs.TCopy(evecs.Dense)
eig := eigenpair{evecs, evals[:]}
sort.Sort(eig)
//Here I should orthonormalize vectors if needed instead of just complaining.
//I think orthonormality is guaranteed by DenseMatrix.Eig() If it is, Ill delete all this
//If not I'll add ortonormalization routines.
eigrows, _ := eig.evecs.Dims()
for i := 0; i < eigrows; i++ {
vectori := eig.evecs.VecView(i)
for j := i + 1; j < eigrows; j++ {
vectorj := eig.evecs.VecView(j)
if math.Abs(vectori.Dot(vectorj)) > epsilon && i != j {
reterr := Error{fmt.Sprintln("Eigenvectors ", i, "and", j, " not orthogonal. v", i, ":", vectori, "\nv", j, ":", vectorj, "\nDot:", math.Abs(vectori.Dot(vectorj)), "eigmatrix:", eig.evecs), []string{"EigenWrap"}, true}
return eig.evecs, evals[:], reterr
}
}
if math.Abs(vectori.Norm(0)-1) > epsilon {
//Of course I could just normalize the vectors instead of complaining.
//err= fmt.Errorf("Vectors not normalized %s",err.Error())
}
}
//Checking and fixing the handness of the matrix.This if-else is Jannes idea,
//I don't really know whether it works.
// eig.evecs.TCopy(eig.evecs)
if det(eig.evecs) < 0 { //Right now, this will fail if the matrix is not 3x3 (30/10/2013)
eig.evecs.Scale(-1, eig.evecs) //SSC
} else {
/*
eig.evecs.TransposeInPlace()
eig.evecs.ScaleRow(0,-1)
eig.evecs.ScaleRow(2,-1)
eig.evecs.TransposeInPlace()
*/
}
// eig.evecs.TCopy(eig.evecs)
return eig.evecs, eig.evals, nil //Returns a slice of evals
}
// erro no ask -> não devo passar loc.X como x
func (c *CMAES) ask() []float64 {
lenC, _ := c.C.Dims()
if float64(c.CountEval-c.EigenEval) > float64(c.Lambda)/(c.C1+c.Cmu)/float64(lenC)/10.0 {
c.EigenEval = c.CountEval
c.C.Add(c.C, c.C.T())
c.C.Scale(0.5, c.C)
eig := mat64.Eigen(c.C, 0.000001)
// fmt.Println("here")
c.D = eig.D()
c.B = eig.V
// fmt.Println("# Entrou no loop")
// fmt.Println("# ask c.B", c.B)
// fmt.Println("# ask c.D", c.D)
// fmt.Println("# ask c.C", c.C)
// fmt.Println("# ask c.InvSqrtC", c.InvSqrtC)
// fmt.Println("# here")
for i := 0; i < c.N; i++ {
if c.D.At(i, i) < 0 {
c.D.Set(i, i, -1*math.Sqrt(-1*c.D.At(i, i)))
} else {
c.D.Set(i, i, math.Sqrt(c.D.At(i, i)))
}
}
c.InvSqrtC.Inverse(c.D)
c.InvSqrtC.Mul(c.B, c.InvSqrtC)
c.InvSqrtC.Mul(c.InvSqrtC, c.B.T())
// fmt.Println("Entrou no loop")
// fmt.Println("ask c.B", c.B)
// fmt.Println("ask c.D", c.D)
// fmt.Println("ask c.C", c.C)
// fmt.Println("ask c.InvSqrtC", c.InvSqrtC)
}
randn := make([]float64, c.N)
for i := 0; i < c.N; i++ {
randn[i] = c.D.At(i, i) * rand.NormFloat64()
}
tmp := mat64.NewDense(c.N, 1, randn)
tmp.Mul(c.B, tmp)
newL := make([]float64, c.N)
for i := 0; i < c.N; i++ {
newL[i] = c.Xmean[i] + c.Sigma*tmp.At(i, 0)
}
// fmt.Println("ask tmp", tmp)
return newL
}
func (t Tournament) Ranks() []float64 {
m := t.Matrix()
eig := mat64.Eigen(m, 1e-10)
_, c := eig.V.Dims()
var ranks []float64
for i := 0; i < c; i++ {
ranks = eig.V.Col(nil, i)
sense := math.Copysign(1, ranks[0])
for _, val := range ranks {
if sense == 0 {
sense = math.Copysign(1, val)
}
if val*sense < 0 {
ranks = nil
break
}
}
if ranks != nil {
min := 1e100
max := 0.0
for i := range ranks {
col := t.Matrix().Col(nil, i)
row := t.Matrix().Row(nil, i)
tot := 0.0
for j := range col {
tot += col[j] + row[j]
}
ranks[i] = ranks[i] * sense / tot // normalize to # games
min = math.Min(ranks[i], min)
max = math.Max(ranks[i], max)
}
// uncomment this to make min score = 0 and max score = 1
//for i := range ranks {
// ranks[i] = (ranks[i] - min) / (max - min)
//}
break
}
}
return ranks
}
func main() {
flag.Parse()
log.SetFlags(0)
var tourn Tournament
if *demo {
tourn = Tournament{
{"bob-r", "joe-c"},
{"bob-r", "tim-c"},
{"bob-r", "tim-c"},
{"bob-r", "tim-c"},
{"joe-r", "tim-c"},
{"joe-r", "bob-c"},
{"tim-r", "joe-c"},
{"tim-r", "bob-c"},
{"bob-c", "joe-r"},
{"bob-c", "tim-r"},
{"joe-c", "tim-r"},
{"joe-c", "bob-r"},
{"tim-c", "joe-r"},
{"tim-c", "bob-r"},
}
} else {
matches, err := ParseMatches(os.Stdin)
if err != nil {
log.Fatal(err)
}
tourn = Tournament(matches)
}
if *graph {
tourn.Graph(os.Stdout)
return
} else if *matrix {
prefix := "tournmat = "
fmt.Printf("%v%v\n", prefix, mat64.Formatted(tourn.Matrix(), mat64.Prefix(strings.Repeat(" ", len(prefix)))))
return
} else if *eigvect {
eig := mat64.Eigen(tourn.Matrix(), 1e-10)
prefix := "eigvects = "
fmt.Printf("%v%.4v\n", prefix, mat64.Formatted(eig.V, mat64.Prefix(strings.Repeat(" ", len(prefix)))))
return
} else if *eigval {
eig := mat64.Eigen(tourn.Matrix(), 1e-10)
prefix := "eigvals = "
fmt.Printf("%v%.4v\n", prefix, mat64.Formatted(eig.D(), mat64.Prefix(strings.Repeat(" ", len(prefix)))))
return
}
ranks := tourn.Ranks()
if ranks == nil {
log.Fatalf("no valid eigenvector ranking found")
}
players := tourn.Players()
for i, rank := range ranks {
fmt.Printf("%v\t%.2v\n", players[i], rank)
}
}