Struct Tensor 

pub struct Tensor {
    pub xx: f64,
    pub xy: f64,
    pub xz: f64,
    pub yx: f64,
    pub yy: f64,
    pub yz: f64,
    pub zx: f64,
    pub zy: f64,
    pub zz: f64,
}

Full (non-symmetric) 3×3 tensor stored row-major. Component order: xx, xy, xz, yx, yy, yz, zx, zy, zz. Maps to Foam::tensor (Foam::Tensor<scalar>).

Fields

xx: f64

xy: f64

xz: f64

yx: f64

yy: f64

yz: f64

zx: f64

zy: f64

zz: f64

Implementations

impl Tensor

pub const ZERO: Self

The zero tensor (all nine components 0).

pub const IDENTITY: Self

The identity tensor (unit diagonal, zero off-diagonal).

pub fn new( xx: f64, xy: f64, xz: f64, yx: f64, yy: f64, yz: f64, zx: f64, zy: f64, zz: f64, ) -> Self

Construct a tensor from its nine components in row-major order.

pub fn from_rows(x: Vector3, y: Vector3, z: Vector3) -> Self

Construct from three row vectors.

pub fn from_cols(x: Vector3, y: Vector3, z: Vector3) -> Self

Construct from three column vectors.

pub fn row_x(self) -> Vector3

First (x) row as a vector: (xx, xy, xz).

pub fn row_y(self) -> Vector3

Second (y) row as a vector: (yx, yy, yz).

pub fn row_z(self) -> Vector3

Third (z) row as a vector: (zx, zy, zz).

pub fn col_x(self) -> Vector3

First (x) column as a vector: (xx, yx, zx).

pub fn col_y(self) -> Vector3

Second (y) column as a vector: (xy, yy, zy).

pub fn col_z(self) -> Vector3

Third (z) column as a vector: (xz, yz, zz).

pub fn diag(self) -> Vector3

Diagonal as a vector

pub fn tr(self) -> f64

Trace

pub fn diag_sqr(self) -> f64

Sum of squared diagonal entries (not Frobenius)

pub fn transpose(self) -> Self

Transpose. C++ .T().

pub fn det(self) -> f64

Determinant

pub fn adjunct(self) -> Self

Adjunct (transpose of cofactor matrix)

pub fn cof(self) -> Self

Cofactor matrix = adjunct().T()

pub fn inv(self) -> Self

Inverse = adjunct / det. Panics (debug) if singular.

pub fn safe_inv(self) -> Self

Inverse with 2-D fallback: returns ZERO if nearly singular.

pub fn mat_mul(self, t: Self) -> Self

Matrix multiply: self & rhs. C++ operator&(Tensor, Tensor) / .inner(t2).

pub fn schur(self, t: Self) -> Self

Element-wise product (Schur/Hadamard product).

pub fn mat_vec(self, v: Vector3) -> Vector3

Matrix-vector multiply: T · v. C++ operator&(Tensor, Vector).

pub fn vec_mat(v: Vector3, t: Self) -> Vector3

Vector-matrix multiply: v · T. C++ operator&(Vector, Tensor).

pub fn double_inner(self, t: Self) -> f64

Double contraction (full Frobenius inner product). C++ operator&&(Tensor, Tensor).

pub fn symm(self) -> SymmTensor

Symmetric part: 0.5*(T + T^T). Returns SymmTensor.

pub fn two_symm(self) -> SymmTensor

Twice the symmetric part: T + T^T. Returns SymmTensor.

pub fn skew(self) -> Self

Skew-symmetric (antisymmetric) part: 0.5*(T - T^T).

pub fn dev(self) -> Self

Deviatoric part: T - (tr/3)*I.

pub fn dev2(self) -> Self

Two-thirds deviatoric: T - (2*tr/3)*I.

pub fn dev_symm(self) -> SymmTensor

Deviatoric of symmetric part: symm(T) - (tr/3)*I. Returns SymmTensor.

pub fn dev_two_symm(self) -> SymmTensor

Deviatoric of twice the symmetric part: twoSymm(T) - (2*tr/3)*I. Returns SymmTensor.

pub fn hodge_dual(self) -> Vector3

Hodge dual as a Vector. C++ operator*(Tensor).

pub fn invariant_i(self) -> f64

First invariant: trace

pub fn invariant_ii(self) -> f64

Second invariant: (xxyy + yyzz + xxzz) - (xyyx + yzzy + xzzx)

pub fn invariant_iii(self) -> f64

Third invariant: determinant

pub fn is_identity(self, tol: f64) -> bool

True if approximately the identity.

pub fn lerp(a: Self, b: Self, t: f64) -> Self

Linear interpolation

Trait Implementations

impl Add for Tensor

type Output = Tensor

The resulting type after applying the + operator.

fn add(self, r: Self) -> Self

Performs the + operation.

impl Add<SphericalTensor> for Tensor

type Output = Tensor

The resulting type after applying the + operator.

fn add(self, st: SphericalTensor) -> Self

Performs the + operation.

impl Add<SymmTensor> for Tensor

type Output = Tensor

The resulting type after applying the + operator.

fn add(self, st: SymmTensor) -> Self

Performs the + operation.

impl Add<Tensor> for SphericalTensor

type Output = Tensor

The resulting type after applying the + operator.

fn add(self, t: Tensor) -> Tensor

Performs the + operation.

impl Add<Tensor> for SymmTensor

type Output = Tensor

The resulting type after applying the + operator.

fn add(self, t: Tensor) -> Tensor

Performs the + operation.

impl AddAssign for Tensor

fn add_assign(&mut self, r: Self)

Performs the += operation.

impl Clone for Tensor

fn clone(&self) -> Self

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Copy for Tensor

impl Debug for Tensor

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Default for Tensor

fn default() -> Self

Returns the “default value” for a type.

impl Div<f64> for Tensor

type Output = Tensor

The resulting type after applying the / operator.

fn div(self, s: f64) -> Self

Performs the / operation.

impl From<SphericalTensor> for Tensor

fn from(st: SphericalTensor) -> Self

Converts to this type from the input type.

impl From<SymmTensor> for Tensor

fn from(st: SymmTensor) -> Self

Converts to this type from the input type.

impl Mul<SphericalTensor> for Tensor

type Output = Tensor

The resulting type after applying the * operator.

fn mul(self, st: SphericalTensor) -> Self

Performs the * operation.

impl Mul<SymmTensor> for Tensor

type Output = Tensor

The resulting type after applying the * operator.

fn mul(self, st: SymmTensor) -> Self

Performs the * operation.

impl Mul<Tensor> for f64

type Output = Tensor

The resulting type after applying the * operator.

fn mul(self, t: Tensor) -> Tensor

Performs the * operation.

impl Mul<Tensor> for SphericalTensor

type Output = Tensor

The resulting type after applying the * operator.

fn mul(self, t: Tensor) -> Tensor

Performs the * operation.

impl Mul<Tensor> for SymmTensor

type Output = Tensor

The resulting type after applying the * operator.

fn mul(self, t: Tensor) -> Tensor

Performs the * operation.

impl Mul<f64> for Tensor

type Output = Tensor

The resulting type after applying the * operator.

fn mul(self, s: f64) -> Self

Performs the * operation.

impl MulAssign<f64> for Tensor

fn mul_assign(&mut self, s: f64)

Performs the *= operation.

impl Neg for Tensor

type Output = Tensor

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl PartialEq for Tensor

fn eq(&self, other: &Self) -> bool

Equality operator ==.

fn ne(&self, other: &Rhs) -> bool

Inequality operator !=.

impl StructuralPartialEq for Tensor

impl Sub for Tensor

type Output = Tensor

The resulting type after applying the - operator.

fn sub(self, r: Self) -> Self

Performs the - operation.

impl Sub<SphericalTensor> for Tensor

type Output = Tensor

The resulting type after applying the - operator.

fn sub(self, st: SphericalTensor) -> Self

Performs the - operation.

impl Sub<SymmTensor> for Tensor

type Output = Tensor

The resulting type after applying the - operator.

fn sub(self, st: SymmTensor) -> Self

Performs the - operation.

impl Sub<Tensor> for SphericalTensor

type Output = Tensor

The resulting type after applying the - operator.

fn sub(self, t: Tensor) -> Tensor

Performs the - operation.

impl Sub<Tensor> for SymmTensor

type Output = Tensor

The resulting type after applying the - operator.

fn sub(self, t: Tensor) -> Tensor

Performs the - operation.

impl SubAssign for Tensor

fn sub_assign(&mut self, r: Self)

Performs the -= operation.