- replace ndarray-linalg matrix inverse by a function that does not require blas

src/error.rs

@@ -9,8 +9,6 @@ pub enum Error {
     #[error(transparent)]
     ShapeError(#[from] ndarray::ShapeError),
     #[error(transparent)]
-    LinAlg(#[from] ndarray_linalg::error::LinalgError),
-    #[error(transparent)]
     NpyError(#[from] ndarray_npy::WriteNpzError),
     #[error("number of dimensions is not defined")]
     NumberOfDimensionsNotDefined,

src/transform.rs

@@ -4,7 +4,6 @@ use crate::metric::FixedMu;
 use crate::register::{Registration, RegistrationResult, RegistrationStep};
 use itertools::Itertools;
 use ndarray::{Array, Array2, ArrayD, AsArray, Dimension, Ix2, s};
-use ndarray_linalg::Inverse;
 use num::cast::AsPrimitive;
 use serde::{Deserialize, Serialize};
 use serde_yaml::{from_reader, to_writer};
@@ -44,6 +43,63 @@ where
         .collect()
 }
 
+/// Calculate the inverse of a square matrix using LU factorization with partial pivoting.
+fn matrix_inverse(matrix: Array2<f64>) -> Array2<f64> {
+    let n = matrix.nrows();
+    debug_assert_eq!(n, matrix.ncols(), "matrix must be square");
+
+    // PA = LU factorization (Doolittle with partial pivoting)
+    let mut lu = matrix;
+    let mut perm: Vec<usize> = (0..n).collect();
+
+    for k in 0..n {
+        let mut pivot_row = k;
+        for i in (k + 1)..n {
+            if lu[[i, k]].abs() > lu[[pivot_row, k]].abs() {
+                pivot_row = i;
+            }
+        }
+        assert_ne!(lu[[pivot_row, k]], 0.0, "matrix is singular");
+        if pivot_row != k {
+            for j in 0..n {
+                lu.swap([k, j], [pivot_row, j]);
+            }
+            perm.swap(k, pivot_row);
+        }
+
+        for i in (k + 1)..n {
+            let factor = lu[[i, k]] / lu[[k, k]];
+            lu[[i, k]] = factor;
+            for j in (k + 1)..n {
+                lu[[i, j]] -= factor * lu[[k, j]];
+            }
+        }
+    }
+
+    // Solve A * inv = I column by column: first L*y = P*e_col, then U*x = y.
+    let mut inv = Array2::zeros((n, n));
+    for col in 0..n {
+        let mut y = vec![0.0; n];
+        for i in 0..n {
+            let rhs = if perm[i] == col { 1.0 } else { 0.0 };
+            let mut sum = rhs;
+            for j in 0..i {
+                sum -= lu[[i, j]] * y[j];
+            }
+            y[i] = sum;
+        }
+        for i in (0..n).rev() {
+            let mut sum = y[i];
+            for j in (i + 1)..n {
+                sum -= lu[[i, j]] * inv[[j, col]];
+            }
+            inv[[i, col]] = sum / lu[[i, i]];
+        }
+    }
+
+    inv
+}
+
 /// a struct describing the transform
 /// generic parameter N = # image dimensions
 #[derive(Clone, Debug, Deserialize, Serialize, PartialEq)]
@@ -428,7 +484,7 @@ impl<D: Dimension> Transform<D> {
     /// get the inverse transform
     pub fn inverse(&self) -> Result<Self, Error> {
         let matrix = self.matrix();
-        let inverse = matrix.inv()?;
+        let inverse = matrix_inverse(matrix);
         let parameters = inverse
             .slice(s![..self.ndim, ..self.ndim])
             .iter()
@@ -519,6 +575,7 @@ impl Transform<Ix2> {
 
 #[cfg(test)]
 mod tests {
+    use super::matrix_inverse;
     use crate::julia_image;
     use crate::transform::Transform;
     use itertools::Itertools;
@@ -528,7 +585,40 @@ mod tests {
     use std::path::Path;
     use tiff::decoder::{Decoder, DecodingResult};
     use tiff::tags::Tag;
-    use tiffwrite::IJTiffFile;
+
+    #[test]
+    fn matrix_inverse_test() -> Result<(), Box<dyn std::error::Error>> {
+        use ndarray::array;
+
+        let a = array![[4.0, 7.0], [2.0, 6.0]];
+        let expected = array![[0.6, -0.7], [-0.2, 0.4]];
+        let got = matrix_inverse(a.clone());
+        assert!(
+            got.iter()
+                .zip_eq(expected.iter())
+                .all(|(x, y)| (x - y).abs() < 1e-12)
+        );
+
+        let b = array![[0.0, 2.0], [3.0, 4.0]];
+        let expected = array![[-2.0 / 3.0, 1.0 / 3.0], [0.5, 0.0]];
+        let got = matrix_inverse(b.clone());
+        assert!(
+            got.iter()
+                .zip_eq(expected.iter())
+                .all(|(x, y)| (x - y).abs() < 1e-12)
+        );
+
+        let c = array![[1.0, 2.0, 3.0], [0.0, 1.0, 4.0], [5.0, 6.0, 0.0]];
+        let reference = array![[-24.0, 18.0, 5.0], [20.0, -15.0, -4.0], [-5.0, 4.0, 1.0]];
+        let got = matrix_inverse(c);
+        assert!(
+            got.iter()
+                .zip_eq(reference.iter())
+                .all(|(x, y)| (x - y).abs() < 1e-10)
+        );
+
+        Ok(())
+    }
 
     #[test]
     fn interpolate() -> Result<(), Box<dyn std::error::Error>> {