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Mathematical methods.
Modules§
- assert
- Assertion helpers for comparing values.
- integrate
- Integration, ODEs, and DAEs.
- interpolate
- Interpolation schemes.
- optimize
- Optimization and root finding.
- random
- Random number generation.
- sparse
- Sparse data types.
- special
- Special functions.
Structs§
- Auxiliary
- A second intermediate configuration.
- Current
- The current configuration.
- Factor
- The shared index of a factorization.
- Flattened
- The second index of a flattened higher-rank tensor.
- FxHasher
- A non-cryptographic hasher (the FxHash algorithm).
- Graph
- A connected set of members or nodes.
- Intermediate
- An intermediate configuration.
- LdlDecomposition
- The LDLᵀ decomposition of a symmetric matrix.
- LuDecomposition
- The LU decomposition of a square matrix.
- Matrix
- A matrix.
- Projection
- The space a composite element projects onto.
- Quantity
- A scalar carrying a physical unit.
- Quantity
Sparse Vec - A sparse vector of quantities, storing only inserted entries.
- Reference
- The reference configuration.
- Set
- A collection of members with optional numbering.
- Sets
- A set of sets that optionally provides the converse.
- Square
Matrix - A square matrix.
- Tensor
List - A fixed-size collection of tensors.
- Tensor
Rank1 - A d-dimensional tensor of rank 1.
- Tensor
Rank2 - A d-dimensional tensor of rank 2.
- Tensor
Rank3 - A d-dimensional tensor of rank 3.
- Tensor
Rank4 - A d-dimensional tensor of rank 4.
- Tensor
Rank2 Sparse Vec - A sparse vector of rank-2 tensors, storing only inserted entries.
- Tensor
Rank2 Sparse Vec2D Symmetric - A vector of sparse vectors of rank-2 tensors, storing only the symmetric half.
- Tensor
Tuple - A fixed-size nested collection of different tensors.
- Tensor
Vector - A resizable collection of tensors.
- Transposed
- A
HessianBlockwith its rows and columns swapped. - Vector
- A vector.
Enums§
- Norm
- Different norms for tensors.
- Spectrum
- A cached eigendecomposition of a symmetric tensor, letting
Self::powm/Self::dpowmbe evaluated at several exponents while paying for only one cubic eigensolve. - Tensor
Error - Possible errors for tensors.
Constants§
- IDENTITY
- The 3D identity, configurations (1, 1).
- IDENTITY_
00 - The 3D identity, configurations (0, 0).
- IDENTITY_
10 - The 3D identity, configurations (1, 0).
- IDENTITY_
22 - The 3D identity, configurations (2, 2).
- IDENTITY_
1010 - The 3D rank-4 identity, configurations (1, 0, 1, 0).
- LEVI_
CIVITA - The 3D Levi-Civita permutation tensor, configurations (1, 1, 1).
- ZERO
- The 3D zero tensor, configurations (1, 1).
- ZERO_10
- The 3D zero tensor, configurations (1, 0).
Traits§
- Configuration
- The configuration a tensor index belongs to.
- Contract
AllWith First - Transforms all four indices of a rank-4 tensor.
- Contract
First Second With Second - Contract
First Third Fourth With First - Contract
Second Fourth With First - Contract
Second With First - Contract
Third Fourth With First Second - Contract
Third With First - Contract
With - The full contraction of two tensors whose units need not agree.
- Cross
Product - The cross product of two rank-1 tensors.
- Differentiable
- A tensor that can be differentiated with respect to a variable of unit
T. - Erase
- Views a tensor with its configurations and unit discarded.
- Hessian
- Common methods for Hessians.
- Hessian
Accumulate - Accumulates rank-2 blocks into a sparse Hessian-like structure.
- Hessian
Block - Common methods for blocks of a Hessian.
- Is
- Implemented only where the two types are the same, so that a unit may be named where it is discarded without allowing a different one.
- Jacobian
- Common methods for Jacobians.
- Rank2
- Common methods for rank-2 tensors.
- Solution
- Common methods for solutions.
- Tensor
- Common methods for tensors.
- Tensor
Array - Common methods for tensors derived from arrays.
- Tensor
Vec - Common methods for tensors derived from Vec.
Functions§
- levi_
civita - Returns the rank-3 Levi-Civita symbol.
- tensor_
rank_ 1_ zero - Returns the rank-1 zero tensor as a constant.
Type Aliases§
- Derivative
- The derivative of
Ywith respect to a variable of unitT. - FxHash
Map - A
HashMapusingFxHasherinstead of the default SipHash. - FxHash
Set - A
HashSetusingFxHasher. - Quantity
Sparse Vec2D - A vector of sparse vectors of quantities, storing only inserted entries.
- Quantity
Vector - A vector of quantities.
- Scalar
- A scalar.
- Scalar
List - A list of scalars.
- Scalar
List Vec - A vector of lists of scalars.
- Scalars
- A vector of scalars.
- Square
- The unit a quantity of unit
Ucarries once squared. - Tensor
Rank0 - A tensor of rank 0 (a scalar).
- Tensor
Rank0 List - A list of rank-0 tensors (scalars).
- Tensor
Rank0 List2D - A list of lists of rank-0 tensors (scalars).
- Tensor
Rank1 List - A list of rank-1 tensors.
- Tensor
Rank1 List2D - A list of lists of rank-1 tensors.
- Tensor
Rank1 RefVec - A vector of references to rank-1 tensors.
- Tensor
Rank1 Vec - A vector of rank-1 tensors.
- Tensor
Rank1 Vec2D - A vector of vectors of rank-1 tensors.
- Tensor
Rank2 List - A list of rank-2 tensors.
- Tensor
Rank2 List2D - A list of lists of rank-2 tensors.
- Tensor
Rank2 List Vec - A vector of lists of rank-2 tensors.
- Tensor
Rank2 Sparse Vec2D - A vector of sparse vectors of rank-2 tensors, storing only inserted entries.
- Tensor
Rank2 Vec - A vector of rank-2 tensors.
- Tensor
Rank2 Vec2D - A vector of vectors of rank-2 tensors.
- Tensor
Rank4 List - A list of rank-4 tensors.
- Tensor
Rank4 Vec - A vector of rank-4 tensors.
- Tensor
Tuple List - A list of tensor tuples.
- Tensor
Tuple List Vec - A vector of lists of tensor tuples.
- Tensor
Tuple List Vec2D - A vector of vectors of lists of tensor tuples.
- Tensor
Tuple Vec - A vector of tensor tuples.