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Remove all spurious allocation introduced by complex number support on decompositions.

This commit is contained in:
sebcrozet 2019-03-23 14:13:00 +01:00
parent 921a05d523
commit ce24ea972e
16 changed files with 87 additions and 135 deletions
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2
nalgebra-lapack/src/lu.rs
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@ -253,7 +253,7 @@ where
/// be determined.
///
/// Returns `false` if no solution was found (the decomposed matrix is singular).
pub fn solve_conjugate_transpose_mut<R2: Dim, C2: Dim>(
pub fn solve_adjoint_mut<R2: Dim, C2: Dim>(
&self,
b: &mut MatrixMN<N, R2, C2>,
) -> bool

12
src/base/blas.rs
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@ -585,7 +585,7 @@ where
a: &SquareMatrix<N, D2, SB>,
x: &Vector<N, D3, SC>,
beta: N,
dotc: impl Fn(&DVectorSlice<N, SB::RStride, SB::CStride>, &DVectorSlice<N, SC::RStride, SC::CStride>) -> N,
dot: impl Fn(&DVectorSlice<N, SB::RStride, SB::CStride>, &DVectorSlice<N, SC::RStride, SC::CStride>) -> N,
) where
N: One,
SB: Storage<N, D2, D2>,
@ -613,11 +613,11 @@ where
let col2 = a.column(0);
let val = unsafe { *x.vget_unchecked(0) };
self.axpy(alpha * val, &col2, beta);
self[0] += alpha * dotc(&a.slice_range(1.., 0), &x.rows_range(1..));
self[0] += alpha * dot(&a.slice_range(1.., 0), &x.rows_range(1..));
for j in 1..dim2 {
let col2 = a.column(j);
let dot = dotc(&col2.rows_range(j..), &x.rows_range(j..));
let dot = dot(&col2.rows_range(j..), &x.rows_range(j..));
let val;
unsafe {
@ -1083,7 +1083,7 @@ impl<N, R1: Dim, C1: Dim, S: StorageMut<N, R1, C1>> Matrix<N, R1, C1, S>
where N: Scalar + Zero + ClosedAdd + ClosedMul
{
#[inline(always)]
fn sygerx<D2: Dim, D3: Dim, SB, SC>(
fn xxgerx<D2: Dim, D3: Dim, SB, SC>(
&mut self,
alpha: N,
x: &Vector<N, D2, SB>,
@ -1186,7 +1186,7 @@ where N: Scalar + Zero + ClosedAdd + ClosedMul
SC: Storage<N, D3>,
ShapeConstraint: DimEq<R1, D2> + DimEq<C1, D3>,
{
self.sygerx(alpha, x, y, beta, |e| e)
self.xxgerx(alpha, x, y, beta, |e| e)
}
/// Computes `self = alpha * x * y.transpose() + beta * self`, where `self` is a **symmetric**
@ -1221,7 +1221,7 @@ where N: Scalar + Zero + ClosedAdd + ClosedMul
SC: Storage<N, D3>,
ShapeConstraint: DimEq<R1, D2> + DimEq<C1, D3>,
{
self.sygerx(alpha, x, y, beta, Complex::conjugate)
self.xxgerx(alpha, x, y, beta, Complex::conjugate)
}
}

23
src/base/edition.rs
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@ -137,10 +137,10 @@ impl<N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
/// Fills the diagonal of this matrix with the content of the given vector.
#[inline]
pub fn set_diagonal<R2: Dim, S2>(&mut self, diag: &Vector<N, R2, S2>)
where
R: DimMin<C>,
S2: Storage<N, R2>,
ShapeConstraint: DimEq<DimMinimum<R, C>, R2>,
where
R: DimMin<C>,
S2: Storage<N, R2>,
ShapeConstraint: DimEq<DimMinimum<R, C>, R2>,
{
let (nrows, ncols) = self.shape();
let min_nrows_ncols = cmp::min(nrows, ncols);
@ -151,6 +151,21 @@ impl<N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
}
}
/// Fills the diagonal of this matrix with the content of the given iterator.
///
/// This will fill as many diagonal elements as the iterator yields, up to the
/// minimum of the number of rows and columns of `self`, and starting with the
/// diagonal element at index (0, 0).
#[inline]
pub fn set_partial_diagonal(&mut self, diag: impl Iterator<Item = N>) {
let (nrows, ncols) = self.shape();
let min_nrows_ncols = cmp::min(nrows, ncols);
for (i, val) in diag.enumerate().take(min_nrows_ncols) {
unsafe { *self.get_unchecked_mut((i, i)) = val }
}
}
/// Fills the selected row of this matrix with the content of the given vector.
#[inline]
pub fn set_row<C2: Dim, S2>(&mut self, i: usize, row: &RowVector<N, C2, S2>)

37
src/base/matrix.rs
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@ -981,14 +981,14 @@ impl<N: Complex, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
self.map(|e| e.conjugate())
}
/// Divides each component of `self` by the given real.
/// Divides each component of the complex matrix `self` by the given real.
#[inline]
pub fn unscale(&self, real: N::Real) -> MatrixMN<N, R, C>
where DefaultAllocator: Allocator<N, R, C> {
self.map(|e| e.unscale(real))
}
/// Multiplies each component of `self` by the given real.
/// Multiplies each component of the complex matrix `self` by the given real.
#[inline]
pub fn scale(&self, real: N::Real) -> MatrixMN<N, R, C>
where DefaultAllocator: Allocator<N, R, C> {
@ -997,19 +997,19 @@ impl<N: Complex, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
}
impl<N: Complex, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
/// The conjugate of `self` computed in-place.
/// The conjugate of the complex matrix `self` computed in-place.
#[inline]
pub fn conjugate_mut(&mut self) {
self.apply(|e| e.conjugate())
}
/// Divides each component of `self` by the given real.
/// Divides each component of the complex matrix `self` by the given real.
#[inline]
pub fn unscale_mut(&mut self, real: N::Real) {
self.apply(|e| e.unscale(real))
}
/// Multiplies each component of `self` by the given real.
/// Multiplies each component of the complex matrix `self` by the given real.
#[inline]
pub fn scale_mut(&mut self, real: N::Real) {
self.apply(|e| e.scale(real))
@ -1017,8 +1017,14 @@ impl<N: Complex, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
}
impl<N: Complex, D: Dim, S: StorageMut<N, D, D>> Matrix<N, D, D, S> {
/// Sets `self` to its conjugate transpose.
pub fn conjugate_transpose_mut(&mut self) {
/// Sets `self` to its adjoint.
#[deprecated(note = "Renamed to `self.adjoint_mut()`.")]
pub fn conjugate_transform_mut(&mut self) {
self.adjoint_mut()
}
/// Sets `self` to its adjoint (aka. conjugate-transpose).
pub fn adjoint_mut(&mut self) {
assert!(
self.is_square(),
"Unable to transpose a non-square matrix in-place."
@ -1027,11 +1033,6 @@ impl<N: Complex, D: Dim, S: StorageMut<N, D, D>> Matrix<N, D, D, S> {
let dim = self.shape().0;
for i in 0..dim {
{
let diag = unsafe { self.get_unchecked_mut((i, i)) };
*diag = diag.conjugate();
}
for j in 0..i {
unsafe {
let ref_ij = self.get_unchecked_mut((i, j)) as *mut N;
@ -1042,6 +1043,11 @@ impl<N: Complex, D: Dim, S: StorageMut<N, D, D>> Matrix<N, D, D, S> {
*ref_ji = conj_ij;
}
}
{
let diag = unsafe { self.get_unchecked_mut((i, i)) };
*diag = diag.conjugate();
}
}
}
}
@ -1614,10 +1620,10 @@ impl<N: Complex, D: Dim, S: Storage<N, D>> Unit<Vector<N, D, S>> {
where
DefaultAllocator: Allocator<N, D>,
{
let c_hang = self.dotc(rhs).real();
let (c_hang, c_hang_sign) = self.dotc(rhs).to_exp();
// self == other
if c_hang.abs() >= N::Real::one() {
if c_hang >= N::Real::one() {
return Some(Unit::new_unchecked(self.clone_owned()));
}
@ -1630,7 +1636,8 @@ impl<N: Complex, D: Dim, S: Storage<N, D>> Unit<Vector<N, D, S>> {
} else {
let ta = ((N::Real::one() - t) * hang).sin() / s_hang;
let tb = (t * hang).sin() / s_hang;
let res = &**self * N::from_real(ta) + &**rhs * N::from_real(tb);
let mut res = self.scale(ta);
res.axpy(c_hang_sign.scale(tb), &**rhs, N::one());
Some(Unit::new_unchecked(res))
}

2
src/base/matrix_alga.rs
View File

@ -269,7 +269,7 @@ where DefaultAllocator: Allocator<N, R, C>
let v = &vs[0];
let mut a;
if v[0].modulus() > v[1].modulus() {
if v[0].norm1() > v[1].norm1() {
a = Self::from_column_slice(&[v[2], N::zero(), -v[0]]);
} else {
a = Self::from_column_slice(&[N::zero(), -v[2], v[1]]);

14
src/base/norm.rs
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@ -33,7 +33,7 @@ impl<N: Complex> Norm<N> for EuclideanNorm {
#[inline]
fn norm<R, C, S>(&self, m: &Matrix<N, R, C, S>) -> N::Real
where R: Dim, C: Dim, S: Storage<N, R, C> {
m.dotc(m).real().sqrt()
m.norm_squared().sqrt()
}
#[inline]
@ -43,7 +43,7 @@ impl<N: Complex> Norm<N> for EuclideanNorm {
ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
m1.zip_fold(m2, N::Real::zero(), |acc, a, b| {
let diff = a - b;
acc + (diff.conjugate() * diff).real()
acc + diff.modulus_squared()
}).sqrt()
}
}
@ -73,6 +73,8 @@ impl<N: Complex> Norm<N> for UniformNorm {
#[inline]
fn norm<R, C, S>(&self, m: &Matrix<N, R, C, S>) -> N::Real
where R: Dim, C: Dim, S: Storage<N, R, C> {
// NOTE: we don't use `m.amax()` here because for the complex
// numbers this will return the max norm1 instead of the modulus.
m.fold(N::Real::zero(), |acc, a| acc.max(a.modulus()))
}
@ -187,7 +189,7 @@ impl<N: Complex, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
#[inline]
pub fn normalize(&self) -> MatrixMN<N, R, C>
where DefaultAllocator: Allocator<N, R, C> {
self.map(|e| e.unscale(self.norm()))
self.unscale(self.norm())
}
/// Returns a normalized version of this matrix unless its norm as smaller or equal to `eps`.
@ -199,7 +201,7 @@ impl<N: Complex, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
if n <= min_norm {
None
} else {
Some(self.map(|e| e.unscale(n)))
Some(self.unscale(n))
}
}
@ -216,7 +218,7 @@ impl<N: Complex, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
#[inline]
pub fn normalize_mut(&mut self) -> N::Real {
let n = self.norm();
self.apply(|e| e.unscale(n));
self.unscale_mut(n);
n
}
@ -231,7 +233,7 @@ impl<N: Complex, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
if n <= min_norm {
None
} else {
self.apply(|e| e.unscale(n));
self.unscale_mut(n);
Some(n)
}
}

4
src/geometry/reflection.rs
View File

@ -96,7 +96,7 @@ impl<N: Complex, D: Dim, S: Storage<N, D>> Reflection<N, D, S> {
}
let m_two: N = ::convert(-2.0f64);
lhs.ger(m_two, &work, &self.axis.conjugate(), N::one());
lhs.gerc(m_two, &work, &self.axis, N::one());
}
/// Applies the reflection to the rows of `lhs`.
@ -118,6 +118,6 @@ impl<N: Complex, D: Dim, S: Storage<N, D>> Reflection<N, D, S> {
}
let m_two = sign.scale(::convert(-2.0f64));
lhs.ger(m_two, &work, &self.axis.conjugate(), sign);
lhs.gerc(m_two, &work, &self.axis, sign);
}
}

65
src/geometry/unit_complex_ops.rs
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@ -2,10 +2,9 @@ use std::ops::{Div, DivAssign, Mul, MulAssign};
use alga::general::Real;
use base::allocator::Allocator;
use base::constraint::{DimEq, ShapeConstraint};
use base::dimension::{Dim, U1, U2};
use base::storage::{Storage, StorageMut};
use base::{DefaultAllocator, Matrix, Unit, Vector, Vector2};
use base::dimension::{U1, U2};
use base::storage::Storage;
use base::{DefaultAllocator, Unit, Vector, Vector2};
use geometry::{Isometry, Point2, Rotation, Similarity, Translation, UnitComplex};
/*
@ -404,60 +403,4 @@ where DefaultAllocator: Allocator<N, U2, U2>
fn div_assign(&mut self, rhs: &'b UnitComplex<N>) {
self.div_assign(rhs.to_rotation_matrix())
}
}
// Matrix = UnitComplex * Matrix
impl<N: Real> UnitComplex<N> {
/// Performs the multiplication `rhs = self * rhs` in-place.
pub fn rotate<R2: Dim, C2: Dim, S2: StorageMut<N, R2, C2>>(
&self,
rhs: &mut Matrix<N, R2, C2, S2>,
) where
ShapeConstraint: DimEq<R2, U2>,
{
assert_eq!(
rhs.nrows(),
2,
"Unit complex rotation: the input matrix must have exactly two rows."
);
let i = self.as_ref().im;
let r = self.as_ref().re;
for j in 0..rhs.ncols() {
unsafe {
let a = *rhs.get_unchecked((0, j));
let b = *rhs.get_unchecked((1, j));
*rhs.get_unchecked_mut((0, j)) = r * a - i * b;
*rhs.get_unchecked_mut((1, j)) = i * a + r * b;
}
}
}
/// Performs the multiplication `lhs = lhs * self` in-place.
pub fn rotate_rows<R2: Dim, C2: Dim, S2: StorageMut<N, R2, C2>>(
&self,
lhs: &mut Matrix<N, R2, C2, S2>,
) where
ShapeConstraint: DimEq<C2, U2>,
{
assert_eq!(
lhs.ncols(),
2,
"Unit complex rotation: the input matrix must have exactly two columns."
);
let i = self.as_ref().im;
let r = self.as_ref().re;
// FIXME: can we optimize that to iterate on one column at a time ?
for j in 0..lhs.nrows() {
unsafe {
let a = *lhs.get_unchecked((j, 0));
let b = *lhs.get_unchecked((j, 1));
*lhs.get_unchecked_mut((j, 0)) = r * a + i * b;
*lhs.get_unchecked_mut((j, 1)) = -i * a + r * b;
}
}
}
}
}

10
src/linalg/bidiagonal.rs
View File

@ -179,9 +179,6 @@ where
DefaultAllocator: Allocator<N, DimMinimum<R, C>, DimMinimum<R, C>>
+ Allocator<N, R, DimMinimum<R, C>>
+ Allocator<N, DimMinimum<R, C>, C>,
// FIXME: the following bounds are ugly.
DimMinimum<R, C>: DimMin<DimMinimum<R, C>, Output = DimMinimum<R, C>>,
ShapeConstraint: DimEq<Dynamic, DimDiff<DimMinimum<R, C>, U1>>,
{
// FIXME: optimize by calling a reallocator.
(self.u(), self.d(), self.v_t())
@ -192,19 +189,16 @@ where
pub fn d(&self) -> MatrixN<N, DimMinimum<R, C>>
where
DefaultAllocator: Allocator<N, DimMinimum<R, C>, DimMinimum<R, C>>,
// FIXME: the following bounds are ugly.
DimMinimum<R, C>: DimMin<DimMinimum<R, C>, Output = DimMinimum<R, C>>,
ShapeConstraint: DimEq<Dynamic, DimDiff<DimMinimum<R, C>, U1>>,
{
let (nrows, ncols) = self.uv.data.shape();
let d = nrows.min(ncols);
let mut res = MatrixN::identity_generic(d, d);
res.set_diagonal(&self.diagonal.map(|e| N::from_real(e.modulus())));
res.set_partial_diagonal(self.diagonal.iter().map(|e| N::from_real(e.modulus())));
let start = self.axis_shift();
res.slice_mut(start, (d.value() - 1, d.value() - 1))
.set_diagonal(&self.off_diagonal.map(|e| N::from_real(e.modulus())));
.set_partial_diagonal(self.off_diagonal.iter().map(|e| N::from_real(e.modulus())));
res
}

3
src/linalg/cholesky.rs
View File

@ -70,11 +70,12 @@ where DefaultAllocator: Allocator<N, D, D>
let mut col = matrix.slice_range_mut(j + 1.., j);
col /= denom;
continue;
}
}
// The diagonal element is either zero or its square root could not
// be taken (e.g. for negative real numbers).
return None;
}

13
src/linalg/hessenberg.rs
View File

@ -92,8 +92,7 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D> + Allocator<N, DimD
/// Retrieves `(q, h)` with `q` the orthogonal matrix of this decomposition and `h` the
/// hessenberg matrix.
#[inline]
pub fn unpack(self) -> (MatrixN<N, D>, MatrixN<N, D>)
where ShapeConstraint: DimEq<Dynamic, DimDiff<D, U1>> {
pub fn unpack(self) -> (MatrixN<N, D>, MatrixN<N, D>) {
let q = self.q();
(q, self.unpack_h())
@ -101,13 +100,12 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D> + Allocator<N, DimD
/// Retrieves the upper trapezoidal submatrix `H` of this decomposition.
#[inline]
pub fn unpack_h(mut self) -> MatrixN<N, D>
where ShapeConstraint: DimEq<Dynamic, DimDiff<D, U1>> {
pub fn unpack_h(mut self) -> MatrixN<N, D> {
let dim = self.hess.nrows();
self.hess.fill_lower_triangle(N::zero(), 2);
self.hess
.slice_mut((1, 0), (dim - 1, dim - 1))
.set_diagonal(&self.subdiag.map(|e| N::from_real(e.modulus())));
.set_partial_diagonal(self.subdiag.iter().map(|e| N::from_real(e.modulus())));
self.hess
}
@ -116,13 +114,12 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D> + Allocator<N, DimD
///
/// This is less efficient than `.unpack_h()` as it allocates a new matrix.
#[inline]
pub fn h(&self) -> MatrixN<N, D>
where ShapeConstraint: DimEq<Dynamic, DimDiff<D, U1>> {
pub fn h(&self) -> MatrixN<N, D> {
let dim = self.hess.nrows();
let mut res = self.hess.clone();
res.fill_lower_triangle(N::zero(), 2);
res.slice_mut((1, 0), (dim - 1, dim - 1))
.set_diagonal(&self.subdiag.map(|e| N::from_real(e.modulus())));
.set_partial_diagonal(self.subdiag.iter().map(|e| N::from_real(e.modulus())));
res
}

8
src/linalg/qr.rs
View File

@ -79,12 +79,10 @@ where DefaultAllocator: Allocator<N, R, C> + Allocator<N, R> + Allocator<N, DimM
pub fn r(&self) -> MatrixMN<N, DimMinimum<R, C>, C>
where
DefaultAllocator: Allocator<N, DimMinimum<R, C>, C>,
// FIXME: the following bound is ugly.
DimMinimum<R, C>: DimMin<C, Output = DimMinimum<R, C>>,
{
let (nrows, ncols) = self.qr.data.shape();
let mut res = self.qr.rows_generic(0, nrows.min(ncols)).upper_triangle();
res.set_diagonal(&self.diag.map(|e| N::from_real(e.modulus())));
res.set_partial_diagonal(self.diag.iter().map(|e| N::from_real(e.modulus())));
res
}
@ -95,13 +93,11 @@ where DefaultAllocator: Allocator<N, R, C> + Allocator<N, R> + Allocator<N, DimM
pub fn unpack_r(self) -> MatrixMN<N, DimMinimum<R, C>, C>
where
DefaultAllocator: Reallocator<N, R, C, DimMinimum<R, C>, C>,
// FIXME: the following bound is ugly (needed by `set_diagonal`).
DimMinimum<R, C>: DimMin<C, Output = DimMinimum<R, C>>,
{
let (nrows, ncols) = self.qr.data.shape();
let mut res = self.qr.resize_generic(nrows.min(ncols), ncols, N::zero());
res.fill_lower_triangle(N::zero(), 1);
res.set_diagonal(&self.diag.map(|e| N::from_real(e.modulus())));
res.set_partial_diagonal(self.diag.iter().map(|e| N::from_real(e.modulus())));
res
}

8
src/linalg/schur.rs
View File

@ -52,7 +52,6 @@ where
impl<N: Complex, D: Dim> Schur<N, D>
where
D: DimSub<U1>, // For Hessenberg.
ShapeConstraint: DimEq<Dynamic, DimDiff<D, U1>>, // For Hessenberg.
DefaultAllocator: Allocator<N, D, DimDiff<D, U1>>
+ Allocator<N, DimDiff<D, U1>>
+ Allocator<N, D, D>
@ -341,7 +340,7 @@ where
while n > 0 {
let m = n - 1;
if t[(n, m)].modulus() <= eps * (t[(n, n)].modulus() + t[(m, m)].modulus()) {
if t[(n, m)].norm1() <= eps * (t[(n, n)].norm1() + t[(m, m)].norm1()) {
t[(n, m)] = N::zero();
} else {
break;
@ -360,7 +359,7 @@ where
let off_diag = t[(new_start, m)];
if off_diag.is_zero()
|| off_diag.modulus() <= eps * (t[(new_start, new_start)].modulus() + t[(m, m)].modulus())
|| off_diag.norm1() <= eps * (t[(new_start, new_start)].norm1() + t[(m, m)].norm1())
{
t[(new_start, m)] = N::zero();
break;
@ -479,7 +478,7 @@ fn compute_2x2_basis<N: Complex, S: Storage<N, U2, U2>>(
// NOTE: Choose the one that yields a larger x component.
// This is necessary for numerical stability of the normalization of the complex
// number.
if x1.modulus() > x2.modulus() {
if x1.norm1() > x2.norm1() {
Some(GivensRotation::new(x1, h10).0)
} else {
Some(GivensRotation::new(x2, h10).0)
@ -492,7 +491,6 @@ fn compute_2x2_basis<N: Complex, S: Storage<N, U2, U2>>(
impl<N: Complex, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S>
where
D: DimSub<U1>, // For Hessenberg.
ShapeConstraint: DimEq<Dynamic, DimDiff<D, U1>>, // For Hessenberg.
DefaultAllocator: Allocator<N, D, DimDiff<D, U1>>
+ Allocator<N, DimDiff<D, U1>>
+ Allocator<N, D, D>

10
src/linalg/svd.rs
View File

@ -316,17 +316,17 @@ where
let m = n - 1;
if off_diagonal[m].is_zero()
|| off_diagonal[m].modulus() <= eps * (diagonal[n].modulus() + diagonal[m].modulus())
|| off_diagonal[m].norm1() <= eps * (diagonal[n].norm1() + diagonal[m].norm1())
{
off_diagonal[m] = N::Real::zero();
} else if diagonal[m].modulus() <= eps {
} else if diagonal[m].norm1() <= eps {
diagonal[m] = N::Real::zero();
Self::cancel_horizontal_off_diagonal_elt(diagonal, off_diagonal, u, v_t, is_upper_diagonal, m, m + 1);
if m != 0 {
Self::cancel_vertical_off_diagonal_elt(diagonal, off_diagonal, u, v_t, is_upper_diagonal, m - 1);
}
} else if diagonal[n].modulus() <= eps {
} else if diagonal[n].norm1() <= eps {
diagonal[n] = N::Real::zero();
Self::cancel_vertical_off_diagonal_elt(diagonal, off_diagonal, u, v_t, is_upper_diagonal, m);
} else {
@ -344,13 +344,13 @@ where
while new_start > 0 {
let m = new_start - 1;
if off_diagonal[m].modulus() <= eps * (diagonal[new_start].modulus() + diagonal[m].modulus())
if off_diagonal[m].norm1() <= eps * (diagonal[new_start].norm1() + diagonal[m].norm1())
{
off_diagonal[m] = N::Real::zero();
break;
}
// FIXME: write a test that enters this case.
else if diagonal[m].modulus() <= eps {
else if diagonal[m].norm1() <= eps {
diagonal[m] = N::Real::zero();
Self::cancel_horizontal_off_diagonal_elt(diagonal, off_diagonal, u, v_t, is_upper_diagonal, m, n);

8
src/linalg/symmetric_eigen.rs
View File

@ -184,7 +184,7 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N::Real, D>
}
}
if off_diag[m].modulus() <= eps * (diag[m].modulus() + diag[n].modulus()) {
if off_diag[m].norm1() <= eps * (diag[m].norm1() + diag[n].norm1()) {
end -= 1;
}
} else if subdim == 2 {
@ -240,7 +240,7 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N::Real, D>
while n > 0 {
let m = n - 1;
if off_diag[m].modulus() > eps * (diag[n].modulus() + diag[m].modulus()) {
if off_diag[m].norm1() > eps * (diag[n].norm1() + diag[m].norm1()) {
break;
}
@ -256,7 +256,7 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N::Real, D>
let m = new_start - 1;
if off_diag[m].is_zero()
|| off_diag[m].modulus() <= eps * (diag[new_start].modulus() + diag[m].modulus())
|| off_diag[m].norm1() <= eps * (diag[new_start].norm1() + diag[m].norm1())
{
off_diag[m] = N::Real::zero();
break;
@ -277,7 +277,7 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N::Real, D>
let val = self.eigenvalues[i];
u_t.column_mut(i).scale_mut(val);
}
u_t.conjugate_transpose_mut();
u_t.adjoint_mut();
&self.eigenvectors * u_t
}
}

3
src/linalg/symmetric_tridiagonal.rs
View File

@ -76,9 +76,8 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimDiff<D, U1>>
let mut p = p.rows_range_mut(i..);
p.hegemv(::convert(2.0), &m, &axis, N::zero());
let dot = axis.dotc(&p);
// p.axpy(-dot, &axis.conjugate(), N::one());
let dot = axis.dotc(&p);
m.hegerc(-N::one(), &p, &axis, N::one());
m.hegerc(-N::one(), &axis, &p, N::one());
m.hegerc(dot * ::convert(2.0), &axis, &axis, N::one());