From ce24ea972ef51d0319b3e0b08c39716d8ab4c1f9 Mon Sep 17 00:00:00 2001
From: sebcrozet <developer@crozet.re>
Date: Sat, 23 Mar 2019 14:13:00 +0100
Subject: [PATCH] Remove all spurious allocation introduced by complex number
 support on decompositions.

---
 nalgebra-lapack/src/lu.rs           |  2 +-
 src/base/blas.rs                    | 12 +++---
 src/base/edition.rs                 | 23 ++++++++--
 src/base/matrix.rs                  | 37 +++++++++-------
 src/base/matrix_alga.rs             |  2 +-
 src/base/norm.rs                    | 14 ++++---
 src/geometry/reflection.rs          |  4 +-
 src/geometry/unit_complex_ops.rs    | 65 ++---------------------------
 src/linalg/bidiagonal.rs            | 10 +----
 src/linalg/cholesky.rs              |  3 +-
 src/linalg/hessenberg.rs            | 13 +++---
 src/linalg/qr.rs                    |  8 +---
 src/linalg/schur.rs                 |  8 ++--
 src/linalg/svd.rs                   | 10 ++---
 src/linalg/symmetric_eigen.rs       |  8 ++--
 src/linalg/symmetric_tridiagonal.rs |  3 +-
 16 files changed, 87 insertions(+), 135 deletions(-)

diff --git a/nalgebra-lapack/src/lu.rs b/nalgebra-lapack/src/lu.rs
index dc21c12b..21fdfb41 100644
--- a/nalgebra-lapack/src/lu.rs
+++ b/nalgebra-lapack/src/lu.rs
@@ -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
diff --git a/src/base/blas.rs b/src/base/blas.rs
index 210db8cd..9f919e11 100644
--- a/src/base/blas.rs
+++ b/src/base/blas.rs
@@ -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)
     }
 }
 
diff --git a/src/base/edition.rs b/src/base/edition.rs
index 32e2c1aa..b95e0fcf 100644
--- a/src/base/edition.rs
+++ b/src/base/edition.rs
@@ -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>)
diff --git a/src/base/matrix.rs b/src/base/matrix.rs
index 6a89e945..77d49f42 100644
--- a/src/base/matrix.rs
+++ b/src/base/matrix.rs
@@ -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))
         }
diff --git a/src/base/matrix_alga.rs b/src/base/matrix_alga.rs
index 4d540f46..43774f17 100644
--- a/src/base/matrix_alga.rs
+++ b/src/base/matrix_alga.rs
@@ -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]]);
diff --git a/src/base/norm.rs b/src/base/norm.rs
index 2a50f4ec..b3d695e6 100644
--- a/src/base/norm.rs
+++ b/src/base/norm.rs
@@ -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)
         }
     }
diff --git a/src/geometry/reflection.rs b/src/geometry/reflection.rs
index 653a9bdc..45e6381c 100644
--- a/src/geometry/reflection.rs
+++ b/src/geometry/reflection.rs
@@ -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);
     }
 }
diff --git a/src/geometry/unit_complex_ops.rs b/src/geometry/unit_complex_ops.rs
index 75b45eda..28c9a9c3 100644
--- a/src/geometry/unit_complex_ops.rs
+++ b/src/geometry/unit_complex_ops.rs
@@ -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;
-            }
-        }
-    }
-}
+}
\ No newline at end of file
diff --git a/src/linalg/bidiagonal.rs b/src/linalg/bidiagonal.rs
index 7de0b887..9bf3cd12 100644
--- a/src/linalg/bidiagonal.rs
+++ b/src/linalg/bidiagonal.rs
@@ -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
     }
 
diff --git a/src/linalg/cholesky.rs b/src/linalg/cholesky.rs
index d4973df1..4ffacc97 100644
--- a/src/linalg/cholesky.rs
+++ b/src/linalg/cholesky.rs
@@ -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;
         }
 
diff --git a/src/linalg/hessenberg.rs b/src/linalg/hessenberg.rs
index a73ee5b5..bde3d325 100644
--- a/src/linalg/hessenberg.rs
+++ b/src/linalg/hessenberg.rs
@@ -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
     }
 
diff --git a/src/linalg/qr.rs b/src/linalg/qr.rs
index e48c057c..12e72463 100644
--- a/src/linalg/qr.rs
+++ b/src/linalg/qr.rs
@@ -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
     }
 
diff --git a/src/linalg/schur.rs b/src/linalg/schur.rs
index 9c877d92..a6521f72 100644
--- a/src/linalg/schur.rs
+++ b/src/linalg/schur.rs
@@ -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>
diff --git a/src/linalg/svd.rs b/src/linalg/svd.rs
index 12ee0469..0b5d0509 100644
--- a/src/linalg/svd.rs
+++ b/src/linalg/svd.rs
@@ -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);
 
diff --git a/src/linalg/symmetric_eigen.rs b/src/linalg/symmetric_eigen.rs
index 87b08dc2..acdf956e 100644
--- a/src/linalg/symmetric_eigen.rs
+++ b/src/linalg/symmetric_eigen.rs
@@ -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
     }
 }
diff --git a/src/linalg/symmetric_tridiagonal.rs b/src/linalg/symmetric_tridiagonal.rs
index d652ce4c..76267554 100644
--- a/src/linalg/symmetric_tridiagonal.rs
+++ b/src/linalg/symmetric_tridiagonal.rs
@@ -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());