1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161

//! Construction of givens rotations.

use alga::general::ComplexField;
use num::{Zero, One};

use crate::base::dimension::{Dim, U2};
use crate::base::constraint::{ShapeConstraint, DimEq};
use crate::base::storage::{Storage, StorageMut};
use crate::base::{Vector, Matrix};


/// A Givens rotation.
#[derive(Debug, Clone, Copy)]
pub struct GivensRotation<N: ComplexField> {
    c: N::RealField,
    s: N
}

// Matrix = UnitComplex * Matrix
impl<N: ComplexField> GivensRotation<N> {
    /// The Givents rotation that does nothing.
    pub fn identity() -> Self {
        Self {
            c: N::RealField::one(),
            s: N::zero()
        }
    }

    /// Initializes a Givens rotation from its components.
    ///
    /// The components are copies as-is. It is not checked whether they describe
    /// an actually valid Givens rotation.
    pub fn new_unchecked(c: N::RealField, s: N) -> Self {
       Self {
           c, s
       }
    }

    /// Initializes a Givens rotation from its non-normalized cosine an sine components.
    pub fn new(c: N, s: N) -> (Self, N) {
        Self::try_new(c, s, N::RealField::zero()).unwrap()
    }

    /// Initializes a Givens rotation form its non-normalized cosine an sine components.
    pub fn try_new(c: N, s: N, eps: N::RealField) -> Option<(Self, N)> {
        let (mod0, sign0) = c.to_exp();
        let denom = (mod0 * mod0 + s.modulus_squared()).sqrt();

        if denom > eps {
            let norm = sign0.scale(denom);
            let c = mod0 / denom;
            let s = s / norm;
            Some((Self { c, s }, norm))
        } else {
            None
        }
    }

    /// Computes the rotation `R` required such that the `y` component of `R * v` is zero.
    ///
    /// Returns `None` if no rotation is needed (i.e. if `v.y == 0`). Otherwise, this returns the norm
    /// of `v` and the rotation `r` such that `R * v = [ |v|, 0.0 ]^t` where `|v|` is the norm of `v`.
    pub fn cancel_y<S: Storage<N, U2>>(v: &Vector<N, U2, S>) -> Option<(Self, N)> {
        if !v[1].is_zero() {
            let (mod0, sign0) = v[0].to_exp();
            let denom = (mod0 * mod0 + v[1].modulus_squared()).sqrt();
            let c = mod0 / denom;
            let s = -v[1] / sign0.scale(denom);
            let r = sign0.scale(denom);
            Some((Self { c, s }, r))
        } else {
            None
        }
    }

    /// Computes the rotation `R` required such that the `x` component of `R * v` is zero.
    ///
    /// Returns `None` if no rotation is needed (i.e. if `v.x == 0`). Otherwise, this returns the norm
    /// of `v` and the rotation `r` such that `R * v = [ 0.0, |v| ]^t` where `|v|` is the norm of `v`.
    pub fn cancel_x<S: Storage<N, U2>>(v: &Vector<N, U2, S>) -> Option<(Self, N)> {
        if !v[0].is_zero() {
            let (mod1, sign1) = v[1].to_exp();
            let denom = (mod1 * mod1 + v[0].modulus_squared()).sqrt();
            let c = mod1 / denom;
            let s = (v[0].conjugate() * sign1).unscale(denom);
            let r = sign1.scale(denom);
            Some((Self { c, s }, r))
        } else {
            None
        }
    }

    /// The cos part of this roration.
    pub fn c(&self) -> N::RealField {
        self.c
    }

    /// The sin part of this roration.
    pub fn s(&self) -> N {
        self.s
    }

    /// The inverse of this givens rotation.
    pub fn inverse(&self) -> Self {
        Self { c: self.c, s: -self.s }
    }

    /// 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 s = self.s;
        let c = self.c;

        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)) = a.scale(c) - s.conjugate() * b;
                *rhs.get_unchecked_mut((1, j)) = s * a + b.scale(c);
            }
        }
    }

    /// 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 s = self.s;
        let c = self.c;

        // 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)) = a.scale(c) + s * b;
                *lhs.get_unchecked_mut((j, 1)) = -s.conjugate() * a + b.scale(c);
            }
        }
    }
}