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Update asvoigt.md
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adtzlr committed Jan 3, 2024
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Expand Up @@ -10,8 +10,52 @@ grand_parent: API Reference

Converts a `Tensor2` or `Tensor4` data type to a reduced Voigt-storage `Tensor2s` or `Tensor4s`.

- `asvoigt(T)`

Aliases:
- `voigt(T)`
- `symstore(T)`
- `symstore(T)`

$$
\begin{align}
\boldsymbol{C} = \begin{bmatrix}
C_{11} & C_{12} & C_{13} \\
C_{12} & C_{22} & C_{23} \\
C_{13} & C_{23} & C_{33}
\end{bmatrix} \longrightarrow
\begin{bmatrix}
C_{11} \\ C_{22} \\ C_{33} \\ C_{12} \\ C_{23} \\ C_{13}
\end{bmatrix}
\end{align}
$$

$$
\begin{align}
\mathbb{A} &= \begin{bmatrix}
A_{1111} & A_{1112} & A_{1113} &
A_{1121} & A_{1122} & A_{1123} &
A_{1131} & A_{1132} & A_{1133} \\
A_{1211} & A_{1212} & A_{1213} &
A_{1221} & A_{1222} & A_{1223} &
A_{1231} & A_{1232} & A_{1233} \\
\dots & \dots & \dots & \dots & \dots & \dots & \dots & \dots & \dots \\
A_{3111} & A_{3112} & A_{3113} &
A_{3121} & A_{3122} & A_{3123} &
A_{3131} & A_{3132} & A_{3133}
\end{bmatrix} \nonumber \\
&\longrightarrow
\begin{bmatrix}
A_{1111} & A_{1122} & A_{1133} & A_{1112} & A_{1123} & A_{1113} \\
A_{2211} & A_{2222} & A_{2233} & A_{2212} & A_{2223} & A_{2213} \\
\dots & \dots & \dots & \dots & \dots & \dots \\
A_{1311} & A_{1322} & A_{1333} & A_{1312} & A_{1323} & A_{1313}
\end{bmatrix}
\end{align}
$$

### Example

```fortran
type(Tensor2) :: T
type(Tensor2s) :: U
U = asvoigt(T)
```

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