From c4e439f7aff0b8ceb6e342159d2b1175fac4a828 Mon Sep 17 00:00:00 2001
From: L <457124+liborty@users.noreply.github.com>
Date: Tue, 23 Apr 2024 16:11:16 +1000
Subject: [PATCH] v 2.0.10

---
 Cargo.toml       |  4 ++--
 README.md        |  2 ++
 src/triangmat.rs | 25 ++++++++++++++++++++++---
 tests/tests.rs   | 10 +++++-----
 4 files changed, 31 insertions(+), 10 deletions(-)

diff --git a/Cargo.toml b/Cargo.toml
index 0dfeca1..6854e36 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -1,9 +1,9 @@
 [package]
 name = "rstats"
-version = "2.0.9"
+version = "2.0.10"
 authors = ["Libor Spacek"]
 edition = "2021"
-description = "Statistics, Information Measures, Data Analysis, Linear Algebra, Clifford Algebra, Machine Learning, Geometric Median, Matrix Decompositions, Mahalanobis Distance, Hulls, Multithreading.."
+description = "Statistics, Information Measures, Data Analysis, Linear Algebra, Clifford Algebra, Machine Learning, Geometric Median, Matrix Decompositions, PCA, Mahalanobis Distance, Hulls, Multithreading.."
 readme = "README.md"
 homepage = "https://github.com/liborty/rstats"
 repository = "https://github.com/liborty/rstats"
diff --git a/README.md b/README.md
index dc4e0af..61b2ae5 100644
--- a/README.md
+++ b/README.md
@@ -332,6 +332,8 @@ Methods which take an additional generic vector argument, such as a vector of we
 
 ## Appendix: Recent Releases
 
+* **Version 2.0.10** - Added to struct TriangMat `eigenvectors` (enabling PCA) and `variances` which compute variances of the data cloud along the original axes, by projecting on them and summing the eigenvalue weighted principal components.
+
 * **Version 2.0.9** - Pruned some rarely used methods, simplified `gmparts` and `gmerror`, updated dependencies.
 
 * **Version 2.0.8**' - Changed initial guess in iterative weighted gm methods to weighted mean. This, being more accurate than plain mean, leads to fewer iterations. Updated some dependencies.
diff --git a/src/triangmat.rs b/src/triangmat.rs
index d32046d..13da3ee 100644
--- a/src/triangmat.rs
+++ b/src/triangmat.rs
@@ -1,4 +1,4 @@
-use crate::{re_error, sumn, RError, Stats, TriangMat, Vecg, RE}; // MStats, MinMax, MutVecg, Stats, VecVec };
+use crate::{re_error, sumn, RError, Stats, TriangMat, Vecg, MutVecg, RE}; // MStats, MinMax, MutVecg, Stats, VecVec };
 pub use indxvec::{printing::*, Printing, Vecops};
 
 /// Meanings of 'kind' field. Note that 'Upper Symmetric' would represent the same full matrix as
@@ -83,14 +83,33 @@ impl TriangMat {
         }
         TriangMat { kind: 2, data }
     }
-    /// Eigenvalues (obtainable from Cholesky L matrix)
+    /// Eigenvalues from Cholesky L matrix
     pub fn eigenvalues(&self) -> Vec<f64> {
         self.diagonal().iter().map(|&x| x * x).collect::<Vec<f64>>()
     }
-    /// Determinant (obtainable from Cholesky L matrix)
+    /// Determinant from Cholesky L matrix
     pub fn determinant(&self) -> f64 {
         self.diagonal().iter().map(|&x| x * x).product()
     }
+    /// 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 eigenvectors(&self) -> Vec<Vec<f64>> {
+        let mut fullcov = self.to_full(); 
+        fullcov.iter_mut().for_each(|eigenvector| eigenvector.munit());
+        fullcov
+    }
+    /// Independent variances along the original axes (dimensions),  
+    /// from triangular covariance matrix. 
+    pub fn variances(&self) -> Result< Vec<f64>, RE > {
+        let eigenvalues = self.cholesky()?.eigenvalues();
+        let eigenvectors = self.eigenvectors();
+        let mut result = vec![0_f64;eigenvalues.len()];
+        eigenvectors.iter().zip(eigenvalues).for_each(
+            |(eigenvector, eigenvalue)| result.mutvadd(&eigenvector.smult(eigenvalue)));
+        Ok(result)
+    }
 
     /// Translates subscripts to a 1d vector, i.e. natural numbers, to a pair of
     /// (row,column) coordinates within a lower/upper triangular matrix.
diff --git a/tests/tests.rs b/tests/tests.rs
index 89ce60c..646c4dc 100644
--- a/tests/tests.rs
+++ b/tests/tests.rs
@@ -242,8 +242,7 @@ fn triangmat() -> Result<(), RE> {
     println!("Diagonal: {}",TriangMat::unit(7).diagonal().gr());
     let d = 10_usize;
     let n = 90_usize;
-    println!("Testing on a random set of {n} points in {d} dimensional space");
-    // set_seeds(1133);
+    println!("Testing on a random set of {n} points in {d} dimensional space"); 
     let pts = ranvv_f64_range(n,d, 0.0..=4.0)?;
     // println!("\nTest data:\n{}",pts.gr());
     // let transppt = pts.transpose();
@@ -251,9 +250,10 @@ fn triangmat() -> Result<(), RE> {
     println!("Comediance matrix:\n{cov}");
     let chol = cov.cholesky()?;
     println!("Cholesky L matrix:\n{chol}");
-    println!("Sorted eigenvalues of the comediance matrix from Cholesky decomposition:\n{}",
-        chol.eigenvalues().sortm(false).gr());
-    println!("Determinant of the comediance matrix (their product): {}",chol.determinant().gr());
+    println!("Eigenvalues by Cholesky decomposition:\n{}",
+        chol.eigenvalues().gr());
+    println!("Determinant (their product): {}",chol.determinant().gr());
+    println!("Variances of the original data by summing principal components:\n{}",cov.variances()?.gr());
     let d = ranv_f64(d)?;
     let dmag = d.vmag();
     let mahamag = chol.mahalanobis(&d)?;