// SpectralCompose recreates tensor m from its spectral decomposition
// m -- 2nd order tensor in Mandel basis
// λ -- eigenvalues
// n -- eigenvectors [ncp][nvecs]
// tmp -- temporary matrix [3][3]
func SpectralCompose(m, λ []float64, n, tmp [][]float64) {
for i := 0; i < 3; i++ {
for j := 0; j < 3; j++ {
tmp[i][j] = λ[0]*n[i][0]*n[j][0] + λ[1]*n[i][1]*n[j][1] + λ[2]*n[i][2]*n[j][2]
}
}
tsr.Ten2Man(m, tmp)
}
// spectral_decomp computes the spectral decomposition of b := F*tr(F) tensor
func (o *Ogden) b_and_spectral_decomp(F [][]float64) (err error) {
// determinant of F
o.J, err = tsr.Inv(o.Fi, F)
if err != nil {
return
}
// left Cauchy-Green tensor
tsr.LeftCauchyGreenDef(o.b, F)
// eigenvalues and eigenprojectors
tsr.Ten2Man(o.bm, o.b)
err = tsr.M_EigenValsProjsNum(o.P, o.λ, o.bm)
if err != nil {
return
}
o.λ[0] = math.Sqrt(o.λ[0])
o.λ[1] = math.Sqrt(o.λ[1])
o.λ[2] = math.Sqrt(o.λ[2])
return
}