func randmatmul(n int) matrix.MatrixRO {
a := matrix.Zeros(n, n)
b := matrix.Zeros(n, n)
for i := 0; i < n; i++ {
for k := 0; k < n; k++ {
a.Set(i, k, rand.Float64())
b.Set(i, k, rand.Float64())
}
}
return matrix.Product(a, b)
}
func randmatstat(t int) (float64, float64) {
n := 5
var v stats.Stats
var w stats.Stats
for i := 0; i < t; i++ {
a := matrix.Zeros(n, n)
b := matrix.Zeros(n, n)
c := matrix.Zeros(n, n)
d := matrix.Zeros(n, n)
for j := 0; j < n; j++ {
for k := 0; k < n; k++ {
a.Set(j, k, rand.NormFloat64())
b.Set(j, k, rand.NormFloat64())
c.Set(j, k, rand.NormFloat64())
d.Set(j, k, rand.NormFloat64())
}
}
P := matrix.Zeros(n, 4*n)
for j := 0; j < n; j++ {
for k := 0; k < n; k++ {
P.Set(j, k, a.Get(j, k))
P.Set(j, n+k, b.Get(j, k))
P.Set(j, 2*n+k, c.Get(j, k))
P.Set(j, 3*n+k, d.Get(j, k))
}
}
Q := matrix.Zeros(2*n, 2*n)
for j := 0; j < n; j++ {
for k := 0; k < n; k++ {
Q.Set(j, k, a.Get(j, k))
Q.Set(j, n+k, b.Get(j, k))
Q.Set(n+j, k, c.Get(j, k))
Q.Set(n+j, n+k, d.Get(j, k))
}
}
P = matrix.Product(matrix.Transpose(P), P)
P = matrix.Product(P, P)
P = matrix.Product(P, P)
Q = matrix.Product(matrix.Transpose(Q), Q)
Q = matrix.Product(Q, Q)
Q = matrix.Product(Q, Q)
v.Update(P.Trace())
w.Update(Q.Trace())
}
return v.PopulationStandardDeviation() / float64(v.Count()) / v.Mean(), w.PopulationStandardDeviation() / float64(w.Count()) / w.Mean()
}
func shiftMatrix(A *matrix.DenseMatrix, x int, y int) *matrix.DenseMatrix {
result := A
// fmt.Println("Shift x: ", x)
// fmt.Println("Shift y: ", y)
// A*shiftRightOrUp will shift A right
// shiftRightOrUp*A will shift A up
shiftRightOrUp := matrix.MakeDenseMatrix([]float64{
0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
}, 15, 15)
// A*shiftLeftOrDown will shift A left
// shiftLeftOrDown*A will shift A down
shiftLeftOrDown := matrix.MakeDenseMatrix([]float64{
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
}, 15, 15)
// fmt.Println("Start Matrix: ", result.String(), "\n\n")
if x < 0 {
for i := x; i < 0; i++ {
// fmt.Print("<")
result = matrix.Product(result, shiftLeftOrDown)
// fmt.Println("Shifted Matrix ", i, ": ", result.String(), "\n\n")
}
} else if x > 0 {
for i := 0; i < x; i++ {
// fmt.Print(">")
result = matrix.Product(result, shiftRightOrUp)
// fmt.Println("Shifted Matrix ", i, ": ", result.String(), "\n\n")
}
}
// fmt.Println()
if y < 0 {
for i := y; i < 0; i++ {
result = matrix.Product(shiftLeftOrDown, result)
// fmt.Println("Shifted Matrix ", i, ": ", result.String(), "\n\n")
}
} else if y > 0 {
for i := 0; i < y; i++ {
result = matrix.Product(shiftRightOrUp, result)
// fmt.Println("Shifted Matrix ", i, ": ", result.String(), "\n\n")
}
}
// fmt.Println("Shifted Matrix: ", result.String())
return result
}