A 3x3 covariance matrix, backed by an Nx tensor.
Used to express uncertainty over a 3-vector quantity such as an accelerometer reading, an angular velocity, or a position. The matrix is mathematically expected to be symmetric and positive semi-definite; this module does not enforce those invariants on construction (zero matrices, in particular, are legitimate "unknown variance" placeholders and must remain constructible).
Follows the same typed-Nx-wrapper pattern as BB.Math.Vec3,
BB.Math.Quaternion, and BB.Math.Transform.
Examples
iex> c = BB.Math.Covariance3.diagonal([0.01, 0.01, 0.02])
iex> BB.Math.Covariance3.get(c, 0, 0)
0.01Summary
Functions
Builds a diagonal covariance from a list of three variances or a
{3} tensor.
Wraps an existing {3, 3} tensor without validation. Convenience
alias for new/1 matching the convention used by BB.Math.Transform.
Reads a scalar element at row/column (i, j).
Returns the 3x3 identity matrix as a covariance.
Creates a covariance from a {3, 3} tensor.
Returns the underlying tensor.
Returns the zero covariance - all variances and correlations zero.
Types
@type t() :: %BB.Math.Covariance3{tensor: Nx.Tensor.t()}
Functions
@spec diagonal([number()] | Nx.Tensor.t()) :: t()
Builds a diagonal covariance from a list of three variances or a
{3} tensor.
Examples
iex> c = BB.Math.Covariance3.diagonal([0.1, 0.2, 0.3])
iex> {BB.Math.Covariance3.get(c, 0, 0), BB.Math.Covariance3.get(c, 1, 1), BB.Math.Covariance3.get(c, 2, 2)}
{0.1, 0.2, 0.3}@spec from_tensor(Nx.Tensor.t()) :: t()
Wraps an existing {3, 3} tensor without validation. Convenience
alias for new/1 matching the convention used by BB.Math.Transform.
Reads a scalar element at row/column (i, j).
Examples
iex> c = BB.Math.Covariance3.diagonal([0.5, 1.5, 2.5])
iex> BB.Math.Covariance3.get(c, 2, 2)
2.5@spec identity() :: t()
Returns the 3x3 identity matrix as a covariance.
Examples
iex> c = BB.Math.Covariance3.identity()
iex> {BB.Math.Covariance3.get(c, 0, 0), BB.Math.Covariance3.get(c, 0, 1)}
{1.0, 0.0}@spec new(Nx.Tensor.t()) :: t()
Creates a covariance from a {3, 3} tensor.
Examples
iex> tensor = Nx.tensor([[1.0, 0.0, 0.0], [0.0, 2.0, 0.0], [0.0, 0.0, 3.0]])
iex> c = BB.Math.Covariance3.new(tensor)
iex> BB.Math.Covariance3.get(c, 1, 1)
2.0@spec to_tensor(t()) :: Nx.Tensor.t()
Returns the underlying tensor.
@spec zero() :: t()
Returns the zero covariance - all variances and correlations zero.
Examples
iex> c = BB.Math.Covariance3.zero()
iex> BB.Math.Covariance3.get(c, 0, 0)
0.0