// M_EigenValsProjsNum computes the eigenvalues and eigenprojectors of tensor 'a' (2nd order symmetric tensor in Mandel's basis)
// using Jacobi rotation.
func M_EigenValsProjsNum(P [][]float64, λ, a []float64) (err error) {
Q := Alloc2()
A := Alloc2()
Man2Ten(A, a)
_, err = la.Jacobi(Q, λ, A)
if err != nil {
return
}
P[0][0] = Q[0][0] * Q[0][0]
P[0][1] = Q[1][0] * Q[1][0]
P[0][2] = Q[2][0] * Q[2][0]
P[0][3] = Q[0][0] * Q[1][0] * SQ2
P[1][0] = Q[0][1] * Q[0][1]
P[1][1] = Q[1][1] * Q[1][1]
P[1][2] = Q[2][1] * Q[2][1]
P[1][3] = Q[0][1] * Q[1][1] * SQ2
P[2][0] = Q[0][2] * Q[0][2]
P[2][1] = Q[1][2] * Q[1][2]
P[2][2] = Q[2][2] * Q[2][2]
P[2][3] = Q[0][2] * Q[1][2] * SQ2
if len(a) == 6 {
P[0][4] = Q[1][0] * Q[2][0] * SQ2
P[0][5] = Q[2][0] * Q[0][0] * SQ2
P[1][4] = Q[1][1] * Q[2][1] * SQ2
P[1][5] = Q[2][1] * Q[0][1] * SQ2
P[2][4] = Q[1][2] * Q[2][2] * SQ2
P[2][5] = Q[2][2] * Q[0][2] * SQ2
}
return
}
// M_EigenValsNum returns the eigenvalues of tensor 'a' (2nd order symmetric tensor in Mandel's basis)
// using Jacobi rotation
func M_EigenValsNum(λ, a []float64) (err error) {
Q := Alloc2()
A := Alloc2()
Man2Ten(A, a)
_, err = la.Jacobi(Q, λ, A)
return
}
// M_PrincValsNum returns the (sorted, ascending) eigenvalues of tensor 'a' (2nd order symmetric tensor in Mandel's basis)
// using Jacobi rotation.
func M_PrincValsNum(a []float64) (λ0, λ1, λ2 float64, err error) {
Q := Alloc2()
A := Alloc2()
v := make([]float64, 3)
Man2Ten(A, a)
_, err = la.Jacobi(Q, v, A)
if err != nil {
return
}
λ0, λ1, λ2 = v[0], v[1], v[2]
utl.DblSort3(&λ0, &λ1, &λ2)
return
}
// M_EigenValsVecs returns the eigenvalues and eigenvectors of tensor 'a' (2nd order symmetric tensor in Mandel's basis)
// using Jacobi rotation.
func M_EigenValsVecsNum(Q [][]float64, λ, a []float64) (err error) {
A := Alloc2()
Man2Ten(A, a)
_, err = la.Jacobi(Q, λ, A)
return
}
// M_EigenProjsDerivNum returns the derivatives of the eigenprojectors w.r.t its defining tensor
// using the finite differences method.
// Input:
// a -- tensor in Mandel basis
// h -- step size for finite differences
// Output:
// dPda -- derivatives [3][ncp][ncp]
func M_EigenProjsDerivNum(dPda [][][]float64, a []float64, h float64) (err error) {
ncp := len(a)
λ := make([]float64, 3)
P := la.MatAlloc(3, ncp)
Q := Alloc2()
A := Alloc2()
q2p := func(k int) {
switch k {
case 0:
P[0][0] = Q[0][0] * Q[0][0]
P[0][1] = Q[1][0] * Q[1][0]
P[0][2] = Q[2][0] * Q[2][0]
P[0][3] = Q[0][0] * Q[1][0] * SQ2
if ncp == 6 {
P[0][4] = Q[1][0] * Q[2][0] * SQ2
P[0][5] = Q[2][0] * Q[0][0] * SQ2
}
case 1:
P[1][0] = Q[0][1] * Q[0][1]
P[1][1] = Q[1][1] * Q[1][1]
P[1][2] = Q[2][1] * Q[2][1]
P[1][3] = Q[0][1] * Q[1][1] * SQ2
if ncp == 6 {
P[1][4] = Q[1][1] * Q[2][1] * SQ2
P[1][5] = Q[2][1] * Q[0][1] * SQ2
}
case 2:
P[2][0] = Q[0][2] * Q[0][2]
P[2][1] = Q[1][2] * Q[1][2]
P[2][2] = Q[2][2] * Q[2][2]
P[2][3] = Q[0][2] * Q[1][2] * SQ2
if ncp == 6 {
P[2][4] = Q[1][2] * Q[2][2] * SQ2
P[2][5] = Q[2][2] * Q[0][2] * SQ2
}
}
}
var tmp float64
failed := false
for k := 0; k < 3; k++ {
for i := 0; i < ncp; i++ {
for j := 0; j < ncp; j++ {
dPda[k][i][j], _ = num.DerivCentral(func(x float64, args ...interface{}) float64 {
tmp, a[j] = a[j], x
defer func() { a[j] = tmp }()
Man2Ten(A, a)
_, err = la.Jacobi(Q, λ, A)
if err != nil {
failed = true
return 0
}
q2p(k)
return P[k][i]
}, a[j], h)
if failed {
return
}
}
}
}
return
}