Gridap.TensorValues

This module provides concrete implementations of Number that represent 1st, 2nd and general order tensors.

Why

The main feature of this module is that the provided types do not extend from AbstractArray, but from Number!

This allows one to work with them as if they were scalar values in broadcasted operations on arrays of VectorValue objects (also for TensorValue or MultiValue objects). For instance, one can perform the following manipulations:

# Assing a VectorValue to all the entries of an Array of VectorValues
A = zeros(VectorValue{2,Int}, (4,5))
v = VectorValue(12,31)
A .= v # This is posible since  VectorValue <: Number

# Broadcasting of tensor operations in arrays of TensorValues
t = TensorValue(13,41,53,17) # creates a 2x2 TensorValue
g = TensorValue(32,41,3,14) # creates another 2x2 TensorValue
B = fill(t,(1,5))
C = inner.(g,B) # inner product of g against all TensorValues in the array B
@show C
# C = [2494 2494 2494 2494 2494]

The exported names are:

• MultiValue
• SymFourthOrderTensorValue
• SymTensorValue
• TensorValue
• ThirdOrderTensorValue
• VectorValue
• change_eltype
• cross
• det
• diagonal_tensor
• dot
• double_contraction
• inner
• inv
• meas
• mutable
• n_components
• norm
• num_components
• outer
• symmetric_part
• tr
• ×
• ⊗
• ⊙
• ⊡
• ⋅
• ⋅²
• ⋅¹

Type representing a multi-dimensional value

Type representing a first-order tensor

Type representing a second-order tensor

outer(∇,f)

Equivalent to

gradient(f)

outer(f,∇)

Equivalent to

transpose(gradient(f))