func TestLUFact_Solve_t(t *testing.T) {
n := 100
// Random square matrix.
a := randMat(n, n)
// Random vector.
want := randVec(n)
// Factorize.
lu, err := LU(a)
if err != nil {
t.Fatal(err)
}
// Solve un-transposed system.
b := cmat.MulVec(a, want)
got, err := lu.Solve(false, b)
if err != nil {
t.Fatal(err)
}
testSliceEq(t, want, got)
// Then solve conjugate-transpose system.
b = cmat.MulVec(cmat.H(a), want)
got, err = lu.Solve(true, b)
if err != nil {
t.Fatal(err)
}
testSliceEq(t, want, got)
}
func TestSolveSquare(t *testing.T) {
n := 100
a := randMat(n, n)
want := randVec(n)
b := cmat.MulVec(a, want)
got, err := SolveSquare(a, b)
if err != nil {
t.Fatal(err)
}
testSliceEq(t, want, got)
}
func TestSolvePosDef(t *testing.T) {
n := 100
// Random symmetric positive definite matrix.
a := randMat(2*n, n)
a = cmat.Mul(cmat.H(a), a)
// Random vector.
want := randVec(n)
b := cmat.MulVec(a, want)
got, err := SolvePosDef(a, b)
if err != nil {
t.Fatal(err)
}
testSliceEq(t, want, got)
}
func overDetProb(m, n int) (a *cmat.Mat, b, x []complex128, err error) {
if m < n {
panic("expect m >= n")
}
a = randMat(m, n)
b = randVec(m)
// Compute pseudo-inverse explicitly.
// y <- (A' A) \ b
x, err = SolveHerm(cmat.Mul(cmat.H(a), a), cmat.MulVec(cmat.H(a), b))
if err != nil {
return nil, nil, nil, err
}
return
}
func underDetProb(m, n int) (a *cmat.Mat, b, x []complex128, err error) {
if m > n {
panic("expect m <= n")
}
a = randMat(m, n)
b = randVec(m)
// Compute pseudo-inverse explicitly.
// y <- (A A') \ b
y, err := SolveHerm(cmat.Mul(a, cmat.H(a)), b)
if err != nil {
return nil, nil, nil, err
}
// x <- A' y
x = cmat.MulVec(cmat.H(a), y)
return
}
func TestLUFact_Solve(t *testing.T) {
n := 100
// Random square matrix.
a := randMat(n, n)
// Random vector.
want := randVec(n)
b := cmat.MulVec(a, want)
lu, err := LU(a)
if err != nil {
t.Fatal(err)
}
got, err := lu.Solve(false, b)
if err != nil {
t.Fatal(err)
}
testSliceEq(t, want, got)
}
func TestLDLFact_Solve(t *testing.T) {
n := 100
// Random symmetric matrix.
a := randMat(n, n)
a = cmat.Plus(a, cmat.H(a))
// Random vector.
want := randVec(n)
b := cmat.MulVec(a, want)
ldl, err := LDL(a)
if err != nil {
t.Fatal(err)
}
got, err := ldl.Solve(b)
if err != nil {
t.Fatal(err)
}
testSliceEq(t, want, got)
}
func TestCholFact_Solve(t *testing.T) {
n := 100
// Random symmetric positive definite matrix.
a := randMat(2*n, n)
a = cmat.Mul(cmat.H(a), a)
// Random vector.
want := randVec(n)
b := cmat.MulVec(a, want)
// Factorize matrix.
chol, err := Chol(a)
if err != nil {
t.Fatal(err)
}
got, err := chol.Solve(b)
if err != nil {
t.Fatal(err)
}
testSliceEq(t, want, got)
}