nalgebra/src/structs/mat_macros.rs

#![macro_use]

macro_rules! mat_impl(
  ($t: ident, $($compN: ident),+) => (
    impl<N> $t<N> {
        #[inline]
        pub fn new($($compN: N ),+) -> $t<N> {
            $t {
                $($compN: $compN ),+
            }
        }
    }
  )
);

macro_rules! as_array_impl(
    ($t: ident, $dim: expr) => (
        impl<N> $t<N> {
            /// View this matrix as a column-major array of arrays.
            #[inline]
            pub fn as_array(&self) -> &[[N; $dim]; $dim] {
                unsafe {
                    mem::transmute(self)
                }
            }

            /// View this matrix as a column-major mutable array of arrays.
            #[inline]
            pub fn as_array_mut<'a>(&'a mut self) -> &'a mut [[N; $dim]; $dim] {
                unsafe {
                    mem::transmute(self)
                }
            }

            // FIXME: because of https://github.com/rust-lang/rust/issues/16418 we cannot do the
            // array-to-mat conversion by-value:
            //
            // pub fn from_array(array: [N; $dim]) -> $t<N>

            /// View a column-major array of array as a vector.
            #[inline]
            pub fn from_array_ref(array: &[[N; $dim]; $dim]) -> &$t<N> {
                unsafe {
                    mem::transmute(array)
                }
            }

            /// View a column-major array of array as a mutable vector.
            #[inline]
            pub fn from_array_mut(array: &mut [[N; $dim]; $dim]) -> &mut $t<N> {
                unsafe {
                    mem::transmute(array)
                }
            }
        }
    )
);

macro_rules! at_fast_impl(
    ($t: ident, $dim: expr) => (
        impl<N: Copy> $t<N> {
            #[inline]
            pub unsafe fn at_fast(&self, (i, j): (usize, usize)) -> N {
                (*mem::transmute::<&$t<N>, &[N; $dim * $dim]>(self)
                 .get_unchecked(i + j * $dim))
            }

            #[inline]
            pub unsafe fn set_fast(&mut self, (i, j): (usize, usize), val: N) {
                (*mem::transmute::<&mut $t<N>, &mut [N; $dim * $dim]>(self)
                 .get_unchecked_mut(i + j * $dim)) = val
            }
        }
    )
);

macro_rules! mat_cast_impl(
    ($t: ident, $($compN: ident),+) => (
        impl<Nin: Copy, Nout: Copy + Cast<Nin>> Cast<$t<Nin>> for $t<Nout> {
            #[inline]
            fn from(v: $t<Nin>) -> $t<Nout> {
                $t::new($(Cast::from(v.$compN)),+)
            }
        }
    )
);

macro_rules! add_impl(
    ($t: ident, $($compN: ident),+) => (
        impl<N: Add<N, Output = N>> Add<$t<N>> for $t<N> {
            type Output = $t<N>;

            #[inline]
            fn add(self, right: $t<N>) -> $t<N> {
                $t::new($(self.$compN + right.$compN),+)
            }
        }
    )
);

macro_rules! sub_impl(
    ($t: ident, $($compN: ident),+) => (
        impl<N: Sub<N, Output = N>> Sub<$t<N>> for $t<N> {
            type Output = $t<N>;

            #[inline]
            fn sub(self, right: $t<N>) -> $t<N> {
                $t::new($(self.$compN - right.$compN),+)
            }
        }
    )
);

macro_rules! mat_mul_scalar_impl(
    ($t: ident, $($compN: ident),+) => (
        impl<N: Mul<N, Output = N>> Mul<N> for N {
            type Output = $t<N>;

            #[inline]
            fn mul(self, right: N) -> $t<N> {
                $t::new($(self.$compN * *right),+)
            }
        }
    )
);

macro_rules! mat_div_scalar_impl(
    ($t: ident, $($compN: ident),+) => (
        impl<N: Div<N, Output = N>> Div<N> for $t<N> {
            type Output = $t<N>;

            #[inline]
            fn div(self, right: N) -> $t<N> {
                $t::new($(self.$compN / *right),+)
            }
        }
    )
);

macro_rules! mat_add_scalar_impl(
    ($t: ident, $($compN: ident),+) => (
        impl<N: Add<N, Output = N>> Add<N> for $t<N> {
            type Output = $t<N>;

            #[inline]
            fn add(self, right: N) -> $t<N> {
                $t::new($(self.$compN + *right),+)
            }
        }
    )
);


macro_rules! eye_impl(
    ($t: ident, $dim: expr, $($comp_diagN: ident),+) => (
        impl<N: Zero + One> Eye for $t<N> {
            fn new_identity(dim: usize) -> $t<N> {
                assert!(dim == $dim);
                let mut eye: $t<N> = ::zero();
                $(eye.$comp_diagN = ::one();)+
                eye
            }
        }
    )
);

macro_rules! mat_sub_scalar_impl(
    ($t: ident, $($compN: ident),+) => (
        impl<N: Sub<N, Output = N> Sub<N> for $t<N> {
            type Output = $t<N>;

            #[inline]
            fn sub(self, right: &N) -> $t<N> {
                $t::new($(self.$compN - *right),+)
            }
        }
    )
);

macro_rules! absolute_impl(
  ($t: ident, $($compN: ident),+) => (
    impl<N: Absolute<N>> Absolute<$t<N>> for $t<N> {
        #[inline]
        fn abs(m: &$t<N>) -> $t<N> {
            $t::new($(::abs(&m.$compN) ),+)
        }
    }
  )
);

macro_rules! iterable_impl(
  ($t: ident, $dim: expr) => (
    impl<N> Iterable<N> for $t<N> {
        #[inline]
        fn iter<'l>(&'l self) -> Iter<'l, N> {
            unsafe {
                mem::transmute::<&'l $t<N>, &'l [N; $dim * $dim]>(self).iter()
            }
        }
    }
  )
);

macro_rules! iterable_mut_impl(
  ($t: ident, $dim: expr) => (
    impl<N> IterableMut<N> for $t<N> {
        #[inline]
        fn iter_mut<'l>(&'l mut self) -> IterMut<'l, N> {
            unsafe {
                mem::transmute::<&'l mut $t<N>, &'l mut [N; $dim * $dim]>(self).iter_mut()
            }
        }
    }
  )
);

macro_rules! one_impl(
  ($t: ident, $($valueN: expr),+ ) => (
    impl<N: Copy + BaseNum> One for $t<N> {
        #[inline]
        fn one() -> $t<N> {
            $t::new($($valueN() ),+)
        }
    }
  )
);

macro_rules! zero_impl(
  ($t: ident, $($compN: ident),+ ) => (
    impl<N: Zero> Zero for $t<N> {
        #[inline]
        fn zero() -> $t<N> {
            $t {
                $($compN: ::zero() ),+
            }
        }

        #[inline]
        fn is_zero(&self) -> bool {
            $(::is_zero(&self.$compN) )&&+
        }
    }
  )
);

macro_rules! dim_impl(
  ($t: ident, $dim: expr) => (
    impl<N> Dim for $t<N> {
        #[inline]
        fn dim(_: Option<$t<N>>) -> usize {
            $dim
        }
    }
  )
);

macro_rules! indexable_impl(
  ($t: ident, $dim: expr) => (
    impl<N> Shape<(usize, usize)> for $t<N> {
        #[inline]
        fn shape(&self) -> (usize, usize) {
            ($dim, $dim)
        }
    }

    impl<N: Copy> Indexable<(usize, usize), N> for $t<N> {
        #[inline]
        fn at(&self, (i, j): (usize, usize)) -> N {
            unsafe {
                mem::transmute::<&$t<N>, &[N; $dim * $dim]>(self)[i + j * $dim]
            }
        }

        #[inline]
        fn set(&mut self, (i, j): (usize, usize), val: N) {
            unsafe {
                mem::transmute::<&mut $t<N>, &mut [N; $dim * $dim]>(self)[i + j * $dim] = val
            }
        }

        #[inline]
        fn swap(&mut self, (i1, j1): (usize, usize), (i2, j2): (usize, usize)) {
            unsafe {
              mem::transmute::<&mut $t<N>, &mut [N; $dim * $dim]>(self)
                .swap(i1 + j1 * $dim, i2 + j2 * $dim)
            }
        }

        #[inline]
        unsafe fn unsafe_at(&self, (i, j): (usize, usize)) -> N {
            (*mem::transmute::<&$t<N>, &[N; $dim * $dim]>(self).get_unchecked(i + j * $dim))
        }

        #[inline]
        unsafe fn unsafe_set(&mut self, (i, j): (usize, usize), val: N) {
            (*mem::transmute::<&mut $t<N>, &mut [N; $dim * $dim]>(self).get_unchecked_mut(i + j * $dim)) = val
        }
    }
  )
);

macro_rules! index_impl(
    ($t: ident, $dim: expr) => (
        impl<N> Index<(usize, usize)> for $t<N> {
            type Output = N;

            fn index(&self, &(i, j): &(usize, usize)) -> &N {
                unsafe {
                    &mem::transmute::<&$t<N>, &mut [N; $dim * $dim]>(self)[i + j * $dim]
                }
            }
        }

        impl<N> IndexMut<(usize, usize)> for $t<N> {
            fn index_mut(&mut self, &(i, j): &(usize, usize)) -> &mut N {
                unsafe {
                    &mut mem::transmute::<&mut $t<N>, &mut [N; $dim * $dim]>(self)[i + j * $dim]
                }
            }
        }
    )
);

macro_rules! col_slice_impl(
    ($t: ident, $tv: ident, $slice: ident, $dim: expr) => (
        impl<N: Clone + Copy + Zero> ColSlice<$slice<N>> for $t<N> {
            fn col_slice(&self, cid: usize, rstart: usize, rend: usize) -> $slice<N> {
                let col = self.col(cid);

                $slice::from_slice(rend - rstart, &col.as_array()[rstart .. rend])
            }
        }
    )
);

macro_rules! row_impl(
  ($t: ident, $tv: ident, $dim: expr) => (
    impl<N: Copy + Zero> Row<$tv<N>> for $t<N> {
        #[inline]
        fn nrows(&self) -> usize {
            Dim::dim(None::<$t<N>>)
        }

        #[inline]
        fn set_row(&mut self, row: usize, v: $tv<N>) {
            for (i, e) in v.iter().enumerate() {
                self.set((row, i), *e);
            }
        }

        #[inline]
        fn row(&self, row: usize) -> $tv<N> {
            let mut res: $tv<N> = ::zero();

            for (i, e) in res.iter_mut().enumerate() {
                *e = self.at((row, i));
            }

            res
        }
    }
  )
);

macro_rules! row_slice_impl(
    ($t: ident, $tv: ident, $slice: ident, $dim: expr) => (
        impl<N: Clone + Copy + Zero> RowSlice<$slice<N>> for $t<N> {
            fn row_slice(&self, rid: usize, cstart: usize, cend: usize) -> $slice<N> {
                let row = self.row(rid);

                $slice::from_slice(cend - cstart, &row.as_array()[cstart .. cend])
            }
        }
    )
);

macro_rules! col_impl(
  ($t: ident, $tv: ident, $dim: expr) => (
    impl<N: Copy + Zero> Col<$tv<N>> for $t<N> {
        #[inline]
        fn ncols(&self) -> usize {
            Dim::dim(None::<$t<N>>)
        }

        #[inline]
        fn set_col(&mut self, col: usize, v: $tv<N>) {
            for (i, e) in v.iter().enumerate() {
                self.set((i, col), *e);
            }
        }

        #[inline]
        fn col(&self, col: usize) -> $tv<N> {
            let mut res: $tv<N> = ::zero();

            for (i, e) in res.iter_mut().enumerate() {
                *e = self.at((i, col));
            }

            res
        }
    }
  )
);

macro_rules! diag_impl(
    ($t: ident, $tv: ident, $dim: expr) => (
        impl<N: Copy + Zero> Diag<$tv<N>> for $t<N> {
            #[inline]
            fn from_diag(diag: &$tv<N>) -> $t<N> {
                let mut res: $t<N> = ::zero();

                res.set_diag(diag);

                res
            }

            #[inline]
            fn set_diag(&mut self, diag: &$tv<N>) {
                for i in 0..$dim {
                    unsafe { self.unsafe_set((i, i), diag.unsafe_at(i)) }
                }
            }

            #[inline]
            fn diag(&self) -> $tv<N> {
                let mut diag: $tv<N> = ::zero();

                for i in 0..$dim {
                    unsafe { diag.unsafe_set(i, self.unsafe_at((i, i))) }
                }

                diag
            }
        }
    )
);

macro_rules! mat_mul_mat_impl(
  ($t: ident, $dim: expr) => (
    impl<N: Copy + BaseNum> Mul<$t<N>> for $t<N> {
        type Output = $t<N>;
        #[inline]
        fn mul(self, right: $t<N>) -> $t<N> {
            // careful! we need to comute other * self here (self is the rhs).
            let mut res: $t<N> = ::zero();

            for i in 0..$dim {
                for j in 0..$dim {
                    let mut acc: N = ::zero();

                    unsafe {
                        for k in 0..$dim {
                            acc = acc + self.at_fast((i, k)) * right.at_fast((k, j));
                        }

                        res.set_fast((i, j), acc);
                    }
                }
            }

            res
        }
    }
  )
);

macro_rules! vec_mul_mat_impl(
  ($t: ident, $v: ident, $dim: expr, $zero: expr) => (
    impl<N: Copy + BaseNum> Mul<$t<N>> for $v<N> {
        type Output = $v<N>;

        #[inline]
        fn mul(self, right: $t<N>) -> $v<N> {
            let mut res : $v<N> = $zero();

            for i in 0..$dim {
                for j in 0..$dim {
                    unsafe {
                        let val = res.at_fast(i) + self.at_fast(j) * right.at_fast((j, i));
                        res.set_fast(i, val)
                    }
                }
            }

            res
        }
    }
  )
);

macro_rules! mat_mul_vec_impl(
  ($t: ident, $v: ident, $dim: expr, $zero: expr) => (
    impl<N: Copy + BaseNum> Mul<$v<N>> for $t<N> {
        type Output = $v<N>;

        #[inline]
        fn mul(self, right: $v<N>) -> $v<N> {
            let mut res : $v<N> = $zero();

            for i in 0..$dim {
                for j in 0..$dim {
                    unsafe {
                        let val = res.at_fast(i) + self.at_fast((i, j)) * right.at_fast(j);
                        res.set_fast(i, val)
                    }
                }
            }

            res
        }
    }
  )
);

macro_rules! pnt_mul_mat_impl(
  ($t: ident, $v: ident, $dim: expr, $zero: expr) => (
      vec_mul_mat_impl!($t, $v, $dim, $zero);
  )
);

macro_rules! mat_mul_pnt_impl(
  ($t: ident, $v: ident, $dim: expr, $zero: expr) => (
      mat_mul_vec_impl!($t, $v, $dim, $zero);
  )
);

macro_rules! inv_impl(
  ($t: ident, $dim: expr) => (
    impl<N: Copy + BaseNum>
    Inv for $t<N> {
        #[inline]
        fn inv(&self) -> Option<$t<N>> {
            let mut res : $t<N> = *self;
            if res.inv_mut() {
                Some(res)
            }
            else {
                None
            }
        }

        fn inv_mut(&mut self) -> bool {
            let mut res: $t<N> = ::one();

            // inversion using Gauss-Jordan elimination
            for k in 0..$dim {
                // search a non-zero value on the k-th column
                // FIXME: would it be worth it to spend some more time searching for the
                // max instead?

                let mut n0 = k; // index of a non-zero entry

                while n0 != $dim {
                    if self.at((n0, k)) != ::zero() {
                        break;
                    }

                    n0 = n0 + 1;
                }

                if n0 == $dim {
                    return false
                }

                // swap pivot line
                if n0 != k {
                    for j in 0..$dim {
                        self.swap((n0, j), (k, j));
                        res.swap((n0, j), (k, j));
                    }
                }

                let pivot = self.at((k, k));

                for j in k..$dim {
                    let selfval = self.at((k, j)) / pivot;
                    self.set((k, j), selfval);
                }

                for j in 0..$dim {
                    let resval = res.at((k, j)) / pivot;
                    res.set((k, j), resval);
                }

                for l in 0..$dim {
                    if l != k {
                        let normalizer = self.at((l, k));

                        for j in k..$dim {
                            let selfval = self.at((l, j)) - self.at((k, j)) * normalizer;
                            self.set((l, j), selfval);
                        }

                        for j in 0..$dim {
                            let resval  = res.at((l, j)) - res.at((k, j)) * normalizer;
                            res.set((l, j), resval);
                        }
                    }
                }
            }

            *self = res;

            true
        }
    }
  )
);

macro_rules! transpose_impl(
  ($t: ident, $dim: expr) => (
    impl<N: Copy> Transpose for $t<N> {
        #[inline]
        fn transpose(&self) -> $t<N> {
            let mut res = *self;

            res.transpose_mut();
            res
        }

        #[inline]
        fn transpose_mut(&mut self) {
            for i in 1..$dim {
                for j in 0..i {
                    self.swap((i, j), (j, i))
                }
            }
        }
    }
  )
);

macro_rules! approx_eq_impl(
  ($t: ident) => (
    impl<N: ApproxEq<N>> ApproxEq<N> for $t<N> {
        #[inline]
        fn approx_epsilon(_: Option<$t<N>>) -> N {
            ApproxEq::approx_epsilon(None::<N>)
        }

        #[inline]
        fn approx_ulps(_: Option<$t<N>>) -> u32 {
            ApproxEq::approx_ulps(None::<N>)
        }

        #[inline]
        fn approx_eq_eps(&self, other: &$t<N>, epsilon: &N) -> bool {
            let mut zip = self.iter().zip(other.iter());
            zip.all(|(a, b)| ApproxEq::approx_eq_eps(a, b, epsilon))
        }

        #[inline]
        fn approx_eq_ulps(&self, other: &$t<N>, ulps: u32) -> bool {
            let mut zip = self.iter().zip(other.iter());
            zip.all(|(a, b)| ApproxEq::approx_eq_ulps(a, b, ulps))
        }
    }
  )
);

macro_rules! to_homogeneous_impl(
  ($t: ident, $t2: ident, $dim: expr, $dim2: expr) => (
    impl<N: BaseNum + Copy> ToHomogeneous<$t2<N>> for $t<N> {
        #[inline]
        fn to_homogeneous(&self) -> $t2<N> {
            let mut res: $t2<N> = ::one();

            for i in 0..$dim {
                for j in 0..$dim {
                    res.set((i, j), self.at((i, j)))
                }
            }

            res
        }
    }
  )
);

macro_rules! from_homogeneous_impl(
  ($t: ident, $t2: ident, $dim: expr, $dim2: expr) => (
    impl<N: BaseNum + Copy> FromHomogeneous<$t2<N>> for $t<N> {
        #[inline]
        fn from(m: &$t2<N>) -> $t<N> {
            let mut res: $t<N> = ::one();

            for i in 0..$dim2 {
                for j in 0..$dim2 {
                    res.set((i, j), m.at((i, j)))
                }
            }

            // FIXME: do we have to deal the lost components
            // (like if the 1 is not a 1… do we have to divide?)

            res
        }
    }
  )
);

macro_rules! outer_impl(
    ($t: ident, $m: ident) => (
        impl<N: Copy + Mul<N, Output = N> + Zero> Outer<$m<N>> for $t<N> {
            #[inline]
            fn outer(&self, other: &$t<N>) -> $m<N> {
                let mut res: $m<N> = ::zero();
                for i in 0..Dim::dim(None::<$t<N>>) {
                    for j in 0..Dim::dim(None::<$t<N>>) {
                        res.set((i, j), self.at(i) * other.at(j))
                    }
                }
                res
            }
        }
    )
);

macro_rules! eigen_qr_impl(
    ($t: ident, $v: ident) => (
        impl<N> EigenQR<N, $v<N>> for $t<N>
            where N: BaseFloat + ApproxEq<N> + Clone {
            fn eigen_qr(&self, eps: &N, niter: usize) -> ($t<N>, $v<N>) {
                linalg::eigen_qr(self, eps, niter)
            }
        }
    )
);