WIP use Complex instead of Real whenever possible on the linalg module.

Cargo.toml

@@ -26,7 +26,7 @@ arbitrary       = [ "quickcheck" ]
 serde-serialize = [ "serde", "serde_derive", "num-complex/serde" ]
 abomonation-serialize = [ "abomonation" ]
 sparse = [ ]
-debug = [ ]
+debug = [ "approx/num-complex", "rand/std" ]
 alloc = [ ]
 io = [ "pest", "pest_derive" ]
 
@@ -53,3 +53,6 @@ rand_xorshift = "0.1"
 
 [workspace]
 members = [ "nalgebra-lapack", "nalgebra-glm" ]
+
+[patch.crates-io]
+alga = { path = "../alga/alga" }

src/base/blas.rs

@@ -13,6 +13,39 @@ use base::dimension::{Dim, Dynamic, U1, U2, U3, U4};
 use base::storage::{Storage, StorageMut};
 use base::{DefaultAllocator, Matrix, Scalar, SquareMatrix, Vector};
 
+
+// FIXME: find a way to avoid code duplication just for complex number support.
+impl<N: Complex, D: Dim, S: Storage<N, D>> Vector<N, D, S> {
+    /// Computes the index of the vector component with the largest complex or real absolute value.
+    ///
+    /// # Examples:
+    ///
+    /// ```
+    /// # use num_complex::Complex;
+    /// # use nalgebra::Vector3;
+    /// let vec = Vector3::new(Complex::new(11.0, 3.0), Complex::new(-15.0, 0.0), Complex::new(13.0, 5.0));
+    /// assert_eq!(vec.icamax(), 2);
+    /// ```
+    #[inline]
+    pub fn icamax(&self) -> usize {
+        assert!(!self.is_empty(), "The input vector must not be empty.");
+
+        let mut the_max = unsafe { self.vget_unchecked(0).asum() };
+        let mut the_i = 0;
+
+        for i in 1..self.nrows() {
+            let val = unsafe { self.vget_unchecked(i).asum() };
+
+            if val > the_max {
+                the_max = val;
+                the_i = i;
+            }
+        }
+
+        the_i
+    }
+}
+
 impl<N: Scalar + PartialOrd, D: Dim, S: Storage<N, D>> Vector<N, D, S> {
     /// Computes the index and value of the vector component with the largest value.
     ///
@@ -157,6 +190,41 @@ impl<N: Scalar + PartialOrd, D: Dim, S: Storage<N, D>> Vector<N, D, S> {
     }
 }
 
+// FIXME: find a way to avoid code duplication just for complex number support.
+impl<N: Complex, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
+    /// Computes the index of the matrix component with the largest absolute value.
+    ///
+    /// # Examples:
+    ///
+    /// ```
+    /// # use nalgebra::Matrix2x3;
+    /// let mat = Matrix2x3::new(Complex::new(11.0, 1.0), Complex::new(-12.0, 2.0), Complex::new(13.0, 3.0),
+    ///                          Complex::new(21.0, 43.0), Complex::new(22.0, 5.0), Complex::new(-23.0, 0.0);
+    /// assert_eq!(mat.iamax_full(), (1, 0));
+    /// ```
+    #[inline]
+    pub fn icamax_full(&self) -> (usize, usize) {
+        assert!(!self.is_empty(), "The input matrix must not be empty.");
+
+        let mut the_max = unsafe { self.get_unchecked((0, 0)).asum() };
+        let mut the_ij = (0, 0);
+
+        for j in 0..self.ncols() {
+            for i in 0..self.nrows() {
+                let val = unsafe { self.get_unchecked((i, j)).asum() };
+
+                if val > the_max {
+                    the_max = val;
+                    the_ij = (i, j);
+                }
+            }
+        }
+
+        the_ij
+    }
+}
+
+
 impl<N: Scalar + PartialOrd + Signed, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     /// Computes the index of the matrix component with the largest absolute value.
     ///
@@ -705,6 +773,56 @@ where
     }
 }
 
+// FIXME: duplicate code
+impl<N, R1: Dim, C1: Dim, S: StorageMut<N, R1, C1>> Matrix<N, R1, C1, S>
+    where N: Complex + Zero + ClosedAdd + ClosedMul
+{
+    /// Computes `self = alpha * x * y.transpose() + beta * self`.
+    ///
+    /// If `beta` is zero, `self` is never read.
+    ///
+    /// # Examples:
+    ///
+    /// ```
+    /// # use nalgebra::{Matrix2x3, Vector2, Vector3};
+    /// let mut mat = Matrix2x3::repeat(4.0);
+    /// let vec1 = Vector2::new(1.0, 2.0);
+    /// let vec2 = Vector3::new(0.1, 0.2, 0.3);
+    /// let expected = vec1 * vec2.transpose() * 10.0 + mat * 5.0;
+    ///
+    /// mat.ger(10.0, &vec1, &vec2, 5.0);
+    /// assert_eq!(mat, expected);
+    /// ```
+    #[inline]
+    pub fn gerc<D2: Dim, D3: Dim, SB, SC>(
+        &mut self,
+        alpha: N,
+        x: &Vector<N, D2, SB>,
+        y: &Vector<N, D3, SC>,
+        beta: N,
+    ) where
+        N: One,
+        SB: Storage<N, D2>,
+        SC: Storage<N, D3>,
+        ShapeConstraint: DimEq<R1, D2> + DimEq<C1, D3>,
+    {
+        let (nrows1, ncols1) = self.shape();
+        let dim2 = x.nrows();
+        let dim3 = y.nrows();
+
+        assert!(
+            nrows1 == dim2 && ncols1 == dim3,
+            "ger: dimensions mismatch."
+        );
+
+        for j in 0..ncols1 {
+            // FIXME: avoid bound checks.
+            let val = unsafe { y.vget_unchecked(j).conjugate() };
+            self.column_mut(j).axpy(alpha * val, x, beta);
+        }
+    }
+}
+
 impl<N, R1: Dim, C1: Dim, S: StorageMut<N, R1, C1>> Matrix<N, R1, C1, S>
 where N: Scalar + Zero + ClosedAdd + ClosedMul
 {

src/base/matrix.rs

@@ -944,6 +944,47 @@ impl<N: Complex, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
             res
         }
     }
+
+    /// The conjugate of `self`.
+    #[inline]
+    pub fn conjugate(&self) -> MatrixMN<N, R, C>
+        where DefaultAllocator: Allocator<N, R, C> {
+        self.map(|e| e.conjugate())
+    }
+
+    /// Divides each component of `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.
+    #[inline]
+    pub fn scale(&self, real: N::Real) -> MatrixMN<N, R, C>
+        where DefaultAllocator: Allocator<N, R, C> {
+        self.map(|e| e.scale(real))
+    }
+}
+
+impl<N: Complex, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
+    /// The conjugate of `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.
+    #[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.
+    #[inline]
+    pub fn scale_mut(&mut self, real: N::Real) {
+        self.apply(|e| e.scale(real))
+    }
 }
 
 impl<N: Complex, D: Dim, S: StorageMut<N, D, D>> Matrix<N, D, D, S> {
@@ -975,7 +1016,7 @@ impl<N: Scalar, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S> {
     /// Creates a square matrix with its diagonal set to `diag` and all other entries set to 0.
     #[inline]
     pub fn diagonal(&self) -> VectorN<N, D>
-    where DefaultAllocator: Allocator<N, D> {
+        where DefaultAllocator: Allocator<N, D> {
         assert!(
             self.is_square(),
             "Unable to get the diagonal of a non-square matrix."
@@ -996,7 +1037,7 @@ impl<N: Scalar, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S> {
     /// Computes a trace of a square matrix, i.e., the sum of its diagonal elements.
     #[inline]
     pub fn trace(&self) -> N
-    where N: Ring {
+        where N: Ring {
         assert!(
             self.is_square(),
             "Cannot compute the trace of non-square matrix."
@@ -1013,6 +1054,34 @@ impl<N: Scalar, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S> {
     }
 }
 
+impl<N: Complex, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S> {
+    /// The symmetric part of `self`, i.e., `0.5 * (self + self.transpose())`.
+    #[inline]
+    pub fn symmetric_part(&self) -> MatrixMN<N, D, D>
+        where DefaultAllocator: Allocator<N, D, D> {
+        assert!(self.is_square(), "Cannot compute the symmetric part of a non-square matrix.");
+        let mut tr = self.transpose();
+        tr += self;
+        tr *= ::convert::<_, N>(0.5);
+        tr
+    }
+
+    /// The hermitian part of `self`, i.e., `0.5 * (self + self.conjugate_transpose())`.
+    #[inline]
+    pub fn hermitian_part(&self) -> MatrixMN<N, D, D>
+        where DefaultAllocator: Allocator<N, D, D> {
+        assert!(self.is_square(), "Cannot compute the hermitian part of a non-square matrix.");
+        let nrows = self.data.shape().0;
+
+        unsafe {
+            let mut tr = self.conjugate_transpose();
+            tr += self;
+            tr *= ::convert::<_, N>(0.5);
+            tr
+        }
+    }
+}
+
 impl<N: Scalar + One + Zero, D: DimAdd<U1> + IsNotStaticOne, S: Storage<N, D, D>> Matrix<N, D, D, S> {
 
     /// Yields the homogeneous matrix for this matrix, i.e., appending an additional dimension and

src/base/ops.rs

@@ -5,7 +5,7 @@ use std::ops::{
     Add, AddAssign, Div, DivAssign, Index, IndexMut, Mul, MulAssign, Neg, Sub, SubAssign,
 };
 
-use alga::general::{ClosedAdd, ClosedDiv, ClosedMul, ClosedNeg, ClosedSub};
+use alga::general::{Complex, ClosedAdd, ClosedDiv, ClosedMul, ClosedNeg, ClosedSub};
 
 use base::allocator::{Allocator, SameShapeAllocator, SameShapeC, SameShapeR};
 use base::constraint::{
@@ -760,6 +760,25 @@ where
     }
 }
 
+// XXX: avoid code duplication.
+impl<N: Complex, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
+    /// Returns the absolute value of the component with the largest absolute value.
+    #[inline]
+    pub fn camax(&self) -> N::Real {
+        let mut max = N::Real::zero();
+
+        for e in self.iter() {
+            let ae = e.asum();
+
+            if ae > max {
+                max = ae;
+            }
+        }
+
+        max
+    }
+}
+
 impl<N: Scalar + PartialOrd + Signed, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     /// Returns the absolute value of the component with the largest absolute value.
     #[inline]

src/base/properties.rs

@@ -2,7 +2,7 @@
 use approx::RelativeEq;
 use num::{One, Zero};
 
-use alga::general::{ClosedAdd, ClosedMul, Real};
+use alga::general::{ClosedAdd, ClosedMul, Real, Complex};
 
 use base::allocator::Allocator;
 use base::dimension::{Dim, DimMin};
@@ -82,20 +82,23 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
 
         true
     }
+}
 
+impl<N: Complex, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     /// Checks that `Mᵀ × M = Id`.
     ///
     /// In this definition `Id` is approximately equal to the identity matrix with a relative error
     /// equal to `eps`.
     #[inline]
     pub fn is_orthogonal(&self, eps: N::Epsilon) -> bool
-    where
-        N: Zero + One + ClosedAdd + ClosedMul + RelativeEq,
-        S: Storage<N, R, C>,
-        N::Epsilon: Copy,
-        DefaultAllocator: Allocator<N, C, C>,
+        where
+            N: Zero + One + ClosedAdd + ClosedMul + RelativeEq,
+            S: Storage<N, R, C>,
+            N::Epsilon: Copy,
+            DefaultAllocator: Allocator<N, R, C> + Allocator<N, C, C>,
     {
-        (self.tr_mul(self)).is_identity(eps)
+        // FIXME: add a conjugate-transpose-mul
+        (self.conjugate().tr_mul(self)).is_identity(eps)
     }
 }
 

src/geometry/reflection.rs

@@ -1,4 +1,4 @@
-use alga::general::Real;
+use alga::general::Complex;
 use base::allocator::Allocator;
 use base::constraint::{AreMultipliable, DimEq, SameNumberOfRows, ShapeConstraint};
 use base::{DefaultAllocator, Matrix, Scalar, Unit, Vector};
@@ -13,15 +13,15 @@ pub struct Reflection<N: Scalar, D: Dim, S: Storage<N, D>> {
     bias: N,
 }
 
-impl<N: Real, D: Dim, S: Storage<N, D>> Reflection<N, D, S> {
+impl<N: Complex, D: Dim, S: Storage<N, D>> Reflection<N, D, S> {
     /// Creates a new reflection wrt the plane orthogonal to the given axis and bias.
     ///
     /// The bias is the position of the plane on the axis. In particular, a bias equal to zero
     /// represents a plane that passes through the origin.
     pub fn new(axis: Unit<Vector<N, D, S>>, bias: N) -> Self {
         Self {
             axis: axis.into_inner(),
-            bias: bias,
+            bias,
         }
     }
 
@@ -35,7 +35,7 @@ impl<N: Real, D: Dim, S: Storage<N, D>> Reflection<N, D, S> {
         D: DimName,
         DefaultAllocator: Allocator<N, D>,
     {
-        let bias = pt.coords.dot(axis.as_ref());
+        let bias = axis.cdot(&pt.coords);
         Self::new(axis, bias)
     }
 
@@ -56,7 +56,7 @@ impl<N: Real, D: Dim, S: Storage<N, D>> Reflection<N, D, S> {
             // dot product, and then mutably. Somehow, this allows significantly
             // better optimizations of the dot product from the compiler.
             let m_two: N = ::convert(-2.0f64);
-            let factor = (rhs.column(i).dot(&self.axis) - self.bias) * m_two;
+            let factor = (self.axis.cdot(&rhs.column(i)) - self.bias) * m_two;
             rhs.column_mut(i).axpy(factor, &self.axis, N::one());
         }
     }
@@ -70,8 +70,9 @@ impl<N: Real, D: Dim, S: Storage<N, D>> Reflection<N, D, S> {
         S2: StorageMut<N, R2, C2>,
         S3: StorageMut<N, R2>,
         ShapeConstraint: DimEq<C2, D> + AreMultipliable<R2, C2, D, U1>,
+        DefaultAllocator: Allocator<N, D>
     {
-        rhs.mul_to(&self.axis, work);
+        rhs.mul_to(&self.axis.conjugate(), work);
 
         if !self.bias.is_zero() {
             work.add_scalar_mut(-self.bias);