377 lines
11 KiB
Rust
377 lines
11 KiB
Rust
#[cfg(feature = "serde-serialize")]
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use serde;
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use num::Zero;
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use num_complex::Complex;
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use alga::general::Real;
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use ComplexHelper;
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use na::{DefaultAllocator, Matrix, MatrixN, Scalar, VectorN};
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use na::dimension::{Dim, U1};
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use na::storage::Storage;
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use na::allocator::Allocator;
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use lapack::fortran as interface;
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/// Eigendecomposition of a real square matrix with real eigenvalues.
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#[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
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#[cfg_attr(feature = "serde-serialize",
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serde(bound(serialize = "DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
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VectorN<N, D>: serde::Serialize,
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MatrixN<N, D>: serde::Serialize")))]
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#[cfg_attr(feature = "serde-serialize",
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serde(bound(deserialize = "DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
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VectorN<N, D>: serde::Serialize,
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MatrixN<N, D>: serde::Deserialize<'de>")))]
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#[derive(Clone, Debug)]
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pub struct Eigen<N: Scalar, D: Dim>
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where
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DefaultAllocator: Allocator<N, D> + Allocator<N, D, D>,
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{
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/// The eigenvalues of the decomposed matrix.
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pub eigenvalues: VectorN<N, D>,
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/// The (right) eigenvectors of the decomposed matrix.
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pub eigenvectors: Option<MatrixN<N, D>>,
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/// The left eigenvectors of the decomposed matrix.
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pub left_eigenvectors: Option<MatrixN<N, D>>,
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}
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impl<N: Scalar, D: Dim> Copy for Eigen<N, D>
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where
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DefaultAllocator: Allocator<N, D> + Allocator<N, D, D>,
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VectorN<N, D>: Copy,
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MatrixN<N, D>: Copy,
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{
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}
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impl<N: EigenScalar + Real, D: Dim> Eigen<N, D>
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where
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DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
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{
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/// Computes the eigenvalues and eigenvectors of the square matrix `m`.
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///
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/// If `eigenvectors` is `false` then, the eigenvectors are not computed explicitly.
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pub fn new(
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mut m: MatrixN<N, D>,
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left_eigenvectors: bool,
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eigenvectors: bool,
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) -> Option<Eigen<N, D>> {
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assert!(
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m.is_square(),
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"Unable to compute the eigenvalue decomposition of a non-square matrix."
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);
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let ljob = if left_eigenvectors { b'V' } else { b'N' };
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let rjob = if eigenvectors { b'V' } else { b'N' };
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let (nrows, ncols) = m.data.shape();
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let n = nrows.value();
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let lda = n as i32;
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let mut wr = unsafe { Matrix::new_uninitialized_generic(nrows, U1) };
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// FIXME: Tap into the workspace.
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let mut wi = unsafe { Matrix::new_uninitialized_generic(nrows, U1) };
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let mut info = 0;
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let mut placeholder1 = [N::zero()];
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let mut placeholder2 = [N::zero()];
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let lwork = N::xgeev_work_size(
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ljob,
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rjob,
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n as i32,
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m.as_mut_slice(),
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lda,
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wr.as_mut_slice(),
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wi.as_mut_slice(),
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&mut placeholder1,
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n as i32,
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&mut placeholder2,
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n as i32,
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&mut info,
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);
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lapack_check!(info);
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let mut work = unsafe { ::uninitialized_vec(lwork as usize) };
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match (left_eigenvectors, eigenvectors) {
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(true, true) => {
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let mut vl = unsafe { Matrix::new_uninitialized_generic(nrows, ncols) };
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let mut vr = unsafe { Matrix::new_uninitialized_generic(nrows, ncols) };
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N::xgeev(
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ljob,
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rjob,
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n as i32,
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m.as_mut_slice(),
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lda,
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wr.as_mut_slice(),
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wi.as_mut_slice(),
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&mut vl.as_mut_slice(),
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n as i32,
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&mut vr.as_mut_slice(),
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n as i32,
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&mut work,
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lwork,
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&mut info,
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);
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lapack_check!(info);
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if wi.iter().all(|e| e.is_zero()) {
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return Some(Eigen {
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eigenvalues: wr,
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left_eigenvectors: Some(vl),
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eigenvectors: Some(vr),
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});
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}
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}
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(true, false) => {
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let mut vl = unsafe { Matrix::new_uninitialized_generic(nrows, ncols) };
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N::xgeev(
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ljob,
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rjob,
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n as i32,
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m.as_mut_slice(),
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lda,
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wr.as_mut_slice(),
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wi.as_mut_slice(),
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&mut vl.as_mut_slice(),
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n as i32,
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&mut placeholder2,
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1 as i32,
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&mut work,
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lwork,
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&mut info,
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);
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lapack_check!(info);
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if wi.iter().all(|e| e.is_zero()) {
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return Some(Eigen {
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eigenvalues: wr,
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left_eigenvectors: Some(vl),
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eigenvectors: None,
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});
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}
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}
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(false, true) => {
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let mut vr = unsafe { Matrix::new_uninitialized_generic(nrows, ncols) };
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N::xgeev(
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ljob,
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rjob,
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n as i32,
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m.as_mut_slice(),
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lda,
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wr.as_mut_slice(),
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wi.as_mut_slice(),
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&mut placeholder1,
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1 as i32,
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&mut vr.as_mut_slice(),
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n as i32,
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&mut work,
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lwork,
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&mut info,
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);
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lapack_check!(info);
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if wi.iter().all(|e| e.is_zero()) {
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return Some(Eigen {
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eigenvalues: wr,
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left_eigenvectors: None,
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eigenvectors: Some(vr),
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});
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}
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}
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(false, false) => {
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N::xgeev(
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ljob,
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rjob,
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n as i32,
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m.as_mut_slice(),
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lda,
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wr.as_mut_slice(),
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wi.as_mut_slice(),
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&mut placeholder1,
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1 as i32,
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&mut placeholder2,
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1 as i32,
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&mut work,
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lwork,
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&mut info,
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);
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lapack_check!(info);
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if wi.iter().all(|e| e.is_zero()) {
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return Some(Eigen {
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eigenvalues: wr,
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left_eigenvectors: None,
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eigenvectors: None,
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});
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}
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}
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}
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None
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}
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/// The complex eigenvalues of the given matrix.
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///
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/// Panics if the eigenvalue computation does not converge.
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pub fn complex_eigenvalues(mut m: MatrixN<N, D>) -> VectorN<Complex<N>, D>
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where
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DefaultAllocator: Allocator<Complex<N>, D>,
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{
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assert!(
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m.is_square(),
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"Unable to compute the eigenvalue decomposition of a non-square matrix."
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);
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let nrows = m.data.shape().0;
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let n = nrows.value();
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let lda = n as i32;
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let mut wr = unsafe { Matrix::new_uninitialized_generic(nrows, U1) };
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let mut wi = unsafe { Matrix::new_uninitialized_generic(nrows, U1) };
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let mut info = 0;
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let mut placeholder1 = [N::zero()];
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let mut placeholder2 = [N::zero()];
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let lwork = N::xgeev_work_size(
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b'N',
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b'N',
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n as i32,
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m.as_mut_slice(),
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lda,
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wr.as_mut_slice(),
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wi.as_mut_slice(),
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&mut placeholder1,
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n as i32,
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&mut placeholder2,
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n as i32,
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&mut info,
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);
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lapack_panic!(info);
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let mut work = unsafe { ::uninitialized_vec(lwork as usize) };
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N::xgeev(
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b'N',
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b'N',
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n as i32,
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m.as_mut_slice(),
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lda,
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wr.as_mut_slice(),
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wi.as_mut_slice(),
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&mut placeholder1,
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1 as i32,
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&mut placeholder2,
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1 as i32,
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&mut work,
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lwork,
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&mut info,
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);
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lapack_panic!(info);
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let mut res = unsafe { Matrix::new_uninitialized_generic(nrows, U1) };
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for i in 0..res.len() {
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res[i] = Complex::new(wr[i], wi[i]);
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}
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res
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}
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/// The determinant of the decomposed matrix.
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#[inline]
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pub fn determinant(&self) -> N {
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let mut det = N::one();
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for e in self.eigenvalues.iter() {
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det *= *e;
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}
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det
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}
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}
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/*
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*
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* Lapack functions dispatch.
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*
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*/
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/// Trait implemented by scalar type for which Lapack funtion exist to compute the
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/// eigendecomposition.
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pub trait EigenScalar: Scalar {
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#[allow(missing_docs)]
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fn xgeev(
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jobvl: u8,
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jobvr: u8,
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n: i32,
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a: &mut [Self],
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lda: i32,
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wr: &mut [Self],
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wi: &mut [Self],
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vl: &mut [Self],
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ldvl: i32,
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vr: &mut [Self],
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ldvr: i32,
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work: &mut [Self],
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lwork: i32,
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info: &mut i32,
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);
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#[allow(missing_docs)]
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fn xgeev_work_size(
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jobvl: u8,
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jobvr: u8,
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n: i32,
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a: &mut [Self],
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lda: i32,
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wr: &mut [Self],
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wi: &mut [Self],
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vl: &mut [Self],
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ldvl: i32,
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vr: &mut [Self],
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ldvr: i32,
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info: &mut i32,
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) -> i32;
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}
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macro_rules! real_eigensystem_scalar_impl (
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($N: ty, $xgeev: path) => (
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impl EigenScalar for $N {
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#[inline]
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fn xgeev(jobvl: u8, jobvr: u8, n: i32, a: &mut [Self], lda: i32,
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wr: &mut [Self], wi: &mut [Self],
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vl: &mut [Self], ldvl: i32, vr: &mut [Self], ldvr: i32,
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work: &mut [Self], lwork: i32, info: &mut i32) {
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$xgeev(jobvl, jobvr, n, a, lda, wr, wi, vl, ldvl, vr, ldvr, work, lwork, info)
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}
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#[inline]
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fn xgeev_work_size(jobvl: u8, jobvr: u8, n: i32, a: &mut [Self], lda: i32,
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wr: &mut [Self], wi: &mut [Self], vl: &mut [Self], ldvl: i32,
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vr: &mut [Self], ldvr: i32, info: &mut i32) -> i32 {
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let mut work = [ Zero::zero() ];
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let lwork = -1 as i32;
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$xgeev(jobvl, jobvr, n, a, lda, wr, wi, vl, ldvl, vr, ldvr, &mut work, lwork, info);
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ComplexHelper::real_part(work[0]) as i32
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}
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}
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)
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);
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real_eigensystem_scalar_impl!(f32, interface::sgeev);
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real_eigensystem_scalar_impl!(f64, interface::dgeev);
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//// FIXME: decomposition of complex matrix and matrices with complex eigenvalues.
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// eigensystem_complex_impl!(f32, interface::cgeev);
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// eigensystem_complex_impl!(f64, interface::zgeev);
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