func ExampleCholFact_Solve() {
// A = V' V, with V = [1, 1; 2, 1]
v := mat.NewRows([][]float64{
{1, 1},
{2, 1},
})
a := mat.Mul(mat.T(v), v)
// x = [1; 2]
// b = V' V x
// = V' [1, 1; 2, 1] [1; 2]
// = [1, 2; 1, 1] [3; 4]
// = [11; 7]
b := []float64{11, 7}
chol, err := Chol(a)
if err != nil {
fmt.Println(err)
return
}
x, err := chol.Solve(b)
if err != nil {
fmt.Println(err)
return
}
fmt.Printf("%.6g", x)
// Output:
// [1 2]
}
func ExampleInvertPosDef() {
// A = V' V, with V = [1, 1; 2, 1]
v := mat.NewRows([][]float64{
{1, 1},
{2, 1},
})
a := mat.Mul(mat.T(v), v)
b, err := InvertPosDef(a)
if err != nil {
fmt.Println(err)
return
}
for j := 0; j < 2; j++ {
for i := 0; i < 2; i++ {
if i > 0 {
fmt.Printf(" ")
}
fmt.Printf("%.3g", b.At(i, j))
}
fmt.Println()
}
// Output:
// 2 -3
// -3 5
}
func ExampleQRFact_Solve() {
a := mat.NewRows([][]float64{
{4, 2},
{1, 1},
{2, 0},
})
b_over := []float64{6, 7, 4}
b_under := []float64{39, 19}
qr, err := QR(a)
if err != nil {
fmt.Println(err)
return
}
x_over, err := qr.Solve(false, b_over)
if err != nil {
fmt.Println(err)
return
}
fmt.Printf("%.6g\n", x_over)
x_under, err := qr.Solve(true, b_under)
if err != nil {
fmt.Println(err)
return
}
fmt.Printf("%.6g\n", x_under)
// Output:
// [1 2]
// [8 3 2]
}
// Find minimum-norm solution to
// x + z = 6,
// y + z = 9.
func ExampleSolve_underdetermined() {
a := mat.NewRows([][]float64{
{1, 0, 1},
{0, 1, 1},
})
b := []float64{6, 9}
x, err := Solve(a, b)
if err != nil {
fmt.Println(err)
return
}
fmt.Printf("%.6g\n", x)
// Output:
// [1 4 5]
}
func ExampleEigSymm() {
a := mat.NewRows([][]float64{
{7, -2, 0},
{-2, 6, -2},
{0, -2, 5},
})
_, d, err := EigSymm(a)
if err != nil {
fmt.Println(err)
return
}
sort.Sort(sort.Float64Slice(d))
fmt.Printf("%.6g\n", d)
// Output:
// [3 6 9]
}
func ExampleSolveSymm() {
a := mat.NewRows([][]float64{
{1, 2},
{2, -3},
})
// x = [1; 2]
// b = A x = [5; -4]
b := []float64{5, -4}
x, err := SolveSymm(a, b)
if err != nil {
fmt.Println(err)
return
}
fmt.Printf("%.6g", x)
// Output:
// [1 2]
}
func ExampleSolveSquare() {
a := mat.NewRows([][]float64{
{-1, 2},
{3, 1},
})
// x = [1; 2]
// b = A x = [3; 5]
b := []float64{3, 5}
x, err := SolveSquare(a, b)
if err != nil {
fmt.Println(err)
return
}
fmt.Printf("%.6g", x)
// Output:
// [1 2]
}
func ExampleSolveFullRank_underdetermined() {
// Find minimum-norm solution to
// x + z = 6,
// y + z = 9.
a := mat.NewRows([][]float64{
{1, 0, 1},
{0, 1, 1},
})
b := []float64{6, 9}
x, err := SolveFullRank(a, b)
if err != nil {
fmt.Println(err)
return
}
fmt.Printf("%.6g", x)
// Output:
// [1 4 5]
}
func ExampleSolveFullRank_overdetermined() {
// Find minimum-error solution to
// x = 3,
// y = 6,
// x + y = 3.
a := mat.NewRows([][]float64{
{1, 0},
{0, 1},
{1, 1},
})
b := []float64{3, 6, 3}
x, err := SolveFullRank(a, b)
if err != nil {
fmt.Println(err)
return
}
fmt.Printf("%.6g", x)
// Output:
// [1 4]
}
func ExampleLDLFact_Solve() {
a := mat.NewRows([][]float64{
{1, 2},
{2, -3},
})
// x = [1; 2]
// b = A x = [5; -4]
b := []float64{5, -4}
ldl, err := LDL(a)
if err != nil {
fmt.Println(err)
return
}
x, err := ldl.Solve(b)
if err != nil {
fmt.Println(err)
return
}
fmt.Printf("%.6g", x)
// Output:
// [1 2]
}
func ExampleLUFact_Solve() {
a := mat.NewRows([][]float64{
{-1, 2},
{3, 1},
})
// x = [1; 2]
// b = A x = [3; 5]
b := []float64{3, 5}
lu, err := LU(a)
if err != nil {
fmt.Println(err)
return
}
x, err := lu.Solve(false, b)
if err != nil {
fmt.Println(err)
return
}
fmt.Printf("%.6g", x)
// Output:
// [1 2]
}