Struct rstats::TriangMat

pub struct TriangMat {
    pub kind: usize,
    pub data: Vec<f64>,
}

Compact Triangular Matrix.
TriangMat stores and manipulates triangular matrices. It also compactly represents square symmetric and antisymmetric matrices. TriangMat is typically produced by some matrix calculations, so the end-type for its data is f64.
The actual length of its data is triangmat.len() = n*(n+1)/2.
The dimension of the implied nxn matrix is n = triangmat.dim().
The kind (field) of the TriangMat is encoded as 0..5. This enables trivial transpositions by: (kind+3) % 6.

Fields

kind: usize

Matrix kind encoding: 0=plain, 1=antisymmetric, 2=symmetric, +3=transposed

data: Vec<f64>

Packed 1d vector of triangular matrix data of size (n+1)*n/2

Implementations

impl TriangMat

Implementation of associated functions for struct TriangleMat. End type is f64, as triangular matrices will be mostly computed

pub fn len(&self) -> usize

Length of the data vec

pub fn dim(&self) -> usize

Dimension of the implied full (square) matrix from the quadratic equation: n^2 + n - 2l = 0

pub fn is_empty(&self) -> bool

Empty TriangMat test

pub fn magsq(&self) -> f64

Squared euclidian vector magnitude (norm) of the data vector

pub fn sum(&self) -> f64

Sum of the elements:
when applied to the wedge product a∧b, returns det(a,b)

pub fn diagonal(&self) -> Vec<f64>

Diagonal elements

pub fn unit(n: usize) -> Self

New unit (symmetric) TriangMat matrix with total data size n*(n+1)/2

pub fn eigenvalues(&self) -> Vec<f64>

Eigenvalues from Cholesky L matrix

pub fn determinant(&self) -> f64

Determinant from Cholesky L matrix

pub fn eigenvectors(&self) -> Vec<Vec<f64>>

Normalized full eigenvectors from triangular covariance matrix. Can be used together with eigenvalues for Principal Components Analysis.
Covariance matrix is symmetric, so we use its rows as eigenvectors (no need to transpose it)

pub fn rowcol(s: usize) -> (usize, usize)

Translates subscripts to a 1d vector, i.e. natural numbers, to a pair of (row,column) coordinates within a lower/upper triangular matrix. Enables memory efficient representation of triangular matrices as one flat vector.

pub fn project(&self, index: &[usize]) -> Self

Project symmetric/antisymmetric triangmat to a smaller one of the same kind, into a subspace specified by an ascending index of dimensions. Deletes all rows and columns of the missing dimensions.

pub fn row(&self, r: usize) -> Vec<f64>

Extract one row from TriangMat

pub fn to_triangle(&self) -> Vec<Vec<f64>>

Unpacks flat TriangMat Vec to triangular Vec form

pub fn transpose(&mut self)

TriangMat trivial implicit transposition

pub fn to_full(&self) -> Vec<Vec<f64>>

Unpacks TriangMat to ordinary full matrix

pub fn cholesky(&self) -> Result<Self, RE>

Efficient Cholesky-Banachiewicz matrix decomposition into LL', where L is the returned lower triangular matrix and L’ its upper triangular transpose. Expects as input a symmetric positive definite matrix in TriangMat compact form, such as a covariance matrix produced by covar. The computations are all done on the compact form, making this implementation memory efficient for large (symmetric) matrices. Reports errors if the above conditions are not satisfied.

pub fn mahalanobis<U>(&self, d: &[U]) -> Result<f64, RE>

where U: Copy + PartialOrd + Display, f64: From<U>,

Mahalanobis scaled magnitude m(d) of a (column) vector d. Self is the decomposed lower triangular matrix L, as returned by cholesky decomposition of covariance/comediance positive definite matrix: C = LL’, where ’ denotes transpose. Mahalanobis distance is defined as:
m(d) = sqrt(d'inv(C)d) = sqrt(d'inv(LL')d) = sqrt(d'inv(L')inv(L)d), where inv() denotes matrix inverse, which is not explicitly computed.
Let x = inv(L)d ( and therefore also x' = d'inv(L') ). Substituting x into the above definition: `m(d) = sqrt(x’x) = |x|.
We obtain x by setting Lx = d and solving by forward substitution. All the calculations are done in the compact triangular form.

pub fn house_uapply<T>(&self, m: &[Vec<T>]) -> Vec<Vec<f64>>

where T: Copy + PartialOrd + Display, f64: From<T>,

Householder’s Q*M matrix product without explicitly computing Q

Trait Implementations

impl Clone for TriangMat

fn clone(&self) -> TriangMat

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Default for TriangMat

fn default() -> TriangMat

Returns the “default value” for a type.

impl Display for TriangMat

Display implementation for TriangMat

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

Formats the value using the given formatter.