func ExampleCholFact_Solve() {
// A = V' V, with V = [1, 1; 2, 1]
v := cmat.NewRows([][]complex128{
{1, 1},
{2, 1},
})
a := cmat.Mul(cmat.H(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 := []complex128{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.Println(formatSlice(x, 'f', 3))
// Output:
// [(1.000+0.000i) (2.000+0.000i)]
}
func ExampleQRFact_Solve() {
a := cmat.NewRows([][]complex128{
{4, 2},
{1, 1},
{2, 0},
})
b_over := []complex128{6, 7, 4}
b_under := []complex128{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.Println(formatSlice(x_over, 'f', 3))
x_under, err := qr.Solve(true, b_under)
if err != nil {
fmt.Println(err)
return
}
fmt.Println(formatSlice(x_under, 'f', 3))
// Output:
// [(1.000+0.000i) (2.000+0.000i)]
// [(8.000+0.000i) (3.000+0.000i) (2.000+0.000i)]
}
func ExampleSolveHerm() {
a := cmat.NewRows([][]complex128{
{1, 2},
{2, -3},
})
// x = [1; 2]
// b = A x = [5; -4]
b := []complex128{5, -4}
x, err := SolveHerm(a, b)
if err != nil {
fmt.Println(err)
return
}
fmt.Println(formatSlice(x, 'f', 3))
// Output:
// [(1.000+0.000i) (2.000+0.000i)]
}
func ExampleSolveSquare() {
a := cmat.NewRows([][]complex128{
{-1, 2},
{3, 1},
})
// x = [1; 2]
// b = A x = [3; 5]
b := []complex128{3, 5}
x, err := SolveSquare(a, b)
if err != nil {
fmt.Println(err)
return
}
fmt.Println(formatSlice(x, 'f', 3))
// Output:
// [(1.000+0.000i) (2.000+0.000i)]
}
func ExampleSolve_underdetermined() {
// Find minimum-norm solution to
// x + z = 6,
// y + z = 9.
a := cmat.NewRows([][]complex128{
{1, 0, 1},
{0, 1, 1},
})
b := []complex128{6, 9}
x, err := Solve(a, b)
if err != nil {
fmt.Println(err)
return
}
fmt.Println(formatSlice(x, 'f', 3))
// Output:
// [(1.000+0.000i) (4.000+0.000i) (5.000+0.000i)]
}
func ExampleSolve_overdetermined() {
// Find minimum-error solution to
// x = 3,
// y = 6,
// x + y = 3.
a := cmat.NewRows([][]complex128{
{1, 0},
{0, 1},
{1, 1},
})
b := []complex128{3, 6, 3}
x, err := Solve(a, b)
if err != nil {
fmt.Println(err)
return
}
fmt.Println(formatSlice(x, 'f', 3))
// Output:
// [(1.000+0.000i) (4.000+0.000i)]
}
func ExampleLDLFact_Solve() {
a := cmat.NewRows([][]complex128{
{1, 2},
{2, -3},
})
// x = [1; 2]
// b = A x = [5; -4]
b := []complex128{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.Println(formatSlice(x, 'f', 3))
// Output:
// [(1.000+0.000i) (2.000+0.000i)]
}
func ExampleLUFact_Solve() {
a := cmat.NewRows([][]complex128{
{-1, 2},
{3, 1},
})
// x = [1; 2]
// b = A x = [3; 5]
b := []complex128{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.Println(formatSlice(x, 'f', 3))
// Output:
// [(1.000+0.000i) (2.000+0.000i)]
}