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Add description and equation for all matrix-vector operations
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@bluss
bluss committed Feb 28, 2016
1 parent cdca602 commit 27398c4
Showing 1 changed file with 66 additions and 0 deletions.
66 changes: 66 additions & 0 deletions src/matrix_vector/ops.rs
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Expand Up @@ -12,6 +12,9 @@ use pointer::CPtr;
use scalar::Scalar;
use vector::Vector;

/// General multiply with vector
///
/// A ← αA<sup>OP</sup>x + βy
pub trait Gemv: Sized {
fn gemv<V: ?Sized + Vector<Self>, W: ?Sized + Vector<Self>>(trans: Transpose, alpha: &Self, a: &Matrix<Self>, x: &V, beta: &Self, y: &mut W);
}
Expand Down Expand Up @@ -86,10 +89,16 @@ mod gemv_tests {
}
}

/// Symmetric multiply with vector
///
/// A ← αAx + βy
pub trait Symv: Sized {
fn symv<V: ?Sized + Vector<Self>, W: ?Sized + Vector<Self>>(symmetry: Symmetry, alpha: &Self, a: &Matrix<Self>, x: &V, beta: &Self, y: &mut W);
}

/// Hermitian multiply with vector
///
/// A ← αAx + βy
pub trait Hemv: Sized {
fn hemv<V: ?Sized + Vector<Self>, W: ?Sized + Vector<Self>>(symmetry: Symmetry, alpha: &Self, a: &Matrix<Self>, x: &V, beta: &Self, y: &mut W);
}
Expand Down Expand Up @@ -158,10 +167,16 @@ mod symv_tests {
}
}

/// General rank-1 update
///
/// A ← A + αxy<sup>T</sup>
pub trait Ger: Sized {
fn ger<V: ?Sized + Vector<Self>, W: ?Sized + Vector<Self>>(alpha: &Self, x: &V, y: &W, a: &mut Matrix<Self>);
}

/// General rank-1 update (using hermitian conjugate)
///
/// A ← A + αxy<sup>H</sup>
pub trait Gerc: Ger {
fn gerc<V: ?Sized + Vector<Self>, W: ?Sized + Vector<Self>>(alpha: &Self, x: &V, y: &W, a: &mut Matrix<Self>) {
Ger::ger(alpha, x, y, a);
Expand Down Expand Up @@ -214,10 +229,16 @@ mod ger_tests {
}
}

/// Symmetric rank-1 update
///
/// A ← A + αxx<sup>T</sup>
pub trait Syr: Sized {
fn syr<V: ?Sized + Vector<Self>>(symmetry: Symmetry, alpha: &Self, x: &V, a: &mut Matrix<Self>);
}

/// Hermitian rank-1 update
///
/// A ← A + αxx<sup>H</sup>
pub trait Her: Sized {
fn her<V: ?Sized + Vector<Complex<Self>>>(symmetry: Symmetry, alpha: &Self, x: &V, a: &mut Matrix<Complex<Self>>);
}
Expand Down Expand Up @@ -258,10 +279,16 @@ macro_rules! syr_impl(($($t: ident), +) => (

syr_impl!(f32, f64);

/// Symmetric rank-2 update
///
/// A ← A + αxy<sup>T</sup> + αyx<sup>T</sup>
pub trait Syr2: Sized {
fn syr2<V: ?Sized + Vector<Self>, W: ?Sized + Vector<Self>>(symmetry: Symmetry, alpha: &Self, x: &V, y: &W, a: &mut Matrix<Self>);
}

/// Hermitian rank-2 update
///
/// A ← A + αxy<sup>H</sup> + y(αx)<sup>H</sup>
pub trait Her2: Sized {
fn her2<V: ?Sized + Vector<Self>, W: ?Sized + Vector<Self>>(symmetry: Symmetry, alpha: &Self, x: &V, y: &W, a: &mut Matrix<Self>);
}
Expand All @@ -286,6 +313,9 @@ macro_rules! syr2_impl(($trait_name: ident, $fn_name: ident, $($t: ident), +) =>
syr2_impl!(Syr2, syr2, f32, f64);
syr2_impl!(Her2, her2, Complex32, Complex64);

/// General band matrix multiply with vector.
///
/// A ← αA<sup>OP</sup>x + βy
pub trait Gbmv: Sized {
fn gbmv<V: ?Sized + Vector<Self>, W: ?Sized + Vector<Self>>(trans: Transpose, alpha: &Self, a: &BandMatrix<Self>, x: &V, beta: &Self, y: &mut W);
}
Expand All @@ -311,10 +341,16 @@ macro_rules! gbmv_impl(($($t: ident), +) => (

gbmv_impl!(f32, f64, Complex32, Complex64);

/// Symmetric band matrix multiply with vector
///
/// A ← αAx + βy
pub trait Sbmv: Sized {
fn sbmv<V: ?Sized + Vector<Self>, W: ?Sized + Vector<Self>>(symmetry: Symmetry, alpha: &Self, a: &BandMatrix<Self>, x: &V, beta: &Self, y: &mut W);
}

/// Hermitian band matrix multiply with vector
///
/// A ← αAx + βy
pub trait Hbmv: Sized {
fn hbmv<V: ?Sized + Vector<Self>, W: ?Sized + Vector<Self>>(symmetry: Symmetry, alpha: &Self, a: &BandMatrix<Self>, x: &V, beta: &Self, y: &mut W);
}
Expand All @@ -340,10 +376,16 @@ macro_rules! sbmv_impl(($trait_name: ident, $fn_name: ident, $($t: ident), +) =>
sbmv_impl!(Sbmv, sbmv, f32, f64);
sbmv_impl!(Hbmv, hbmv, Complex32, Complex64);

/// Triangular band matrix multiply with vector
///
/// A ← A<sup>OP</sup>x
pub trait Tbmv: Sized {
fn tbmv<V: ?Sized + Vector<Self>>(symmetry: Symmetry, trans: Transpose, diagonal: Diagonal, a: &BandMatrix<Self>, x: &mut V);
}

/// Solve triangular band matrix system
///
/// A ← A<sup>-1 OP</sup>x
pub trait Tbsv: Sized {
fn tbsv<V: ?Sized + Vector<Self>>(symmetry: Symmetry, trans: Transpose, diagonal: Diagonal, a: &BandMatrix<Self>, x: &mut V);
}
Expand All @@ -367,10 +409,16 @@ macro_rules! tbmv_impl(($trait_name: ident, $fn_name: ident, $($t: ident), +) =>
tbmv_impl!(Tbmv, tbmv, f32, f64, Complex32, Complex64);
tbmv_impl!(Tbsv, tbsv, f32, f64, Complex32, Complex64);

/// Symmetric packed matrix multiply with vector
///
/// A ← αAx + βy
pub trait Spmv: Sized {
fn spmv<V: ?Sized + Vector<Self>, W: ?Sized + Vector<Self>>(symmetry: Symmetry, alpha: &Self, a: &Matrix<Self>, x: &V, beta: &Self, y: &mut W);
}

/// Hermitian packed matrix multiply with vector
///
/// A ← αAx + βy
pub trait Hpmv: Sized {
fn hpmv<V: ?Sized + Vector<Self>, W: ?Sized + Vector<Self>>(symmetry: Symmetry, alpha: &Self, a: &Matrix<Self>, x: &V, beta: &Self, y: &mut W);
}
Expand All @@ -396,10 +444,16 @@ macro_rules! spmv_impl(($trait_name: ident, $fn_name: ident, $($t: ident), +) =>
spmv_impl!(Spmv, spmv, f32, f64);
spmv_impl!(Hpmv, hpmv, Complex32, Complex64);

/// Triangular packed matrix multiply with vector
///
/// A ← A<sup>OP</sup>x
pub trait Tpmv: Sized {
fn tpmv<V: ?Sized + Vector<Self>>(symmetry: Symmetry, trans: Transpose, diagonal: Diagonal, a: &Matrix<Self>, x: &mut V);
}

/// Solve triangular packed matrix system
///
/// A ← A<sup>-1 OP</sup>x
pub trait Tpsv: Sized {
fn tpsv<V: ?Sized + Vector<Self>>(symmetry: Symmetry, trans: Transpose, diagonal: Diagonal, a: &Matrix<Self>, x: &mut V);
}
Expand All @@ -423,6 +477,9 @@ macro_rules! tpmv_impl(($trait_name: ident, $fn_name: ident, $($t: ident), +) =>
tpmv_impl!(Tpmv, tpmv, f32, f64, Complex32, Complex64);
tpmv_impl!(Tpsv, tpsv, f32, f64, Complex32, Complex64);

/// Hermitian packed matrix rank-1 update
///
/// A ← A + αxx<sup>H</sup>
pub trait Hpr: Sized {
fn hpr<V: ?Sized + Vector<Complex<Self>>>(symmetry: Symmetry, alpha: &Self, x: &V, a: &mut Matrix<Complex<Self>>);
}
Expand All @@ -445,6 +502,9 @@ macro_rules! hpr_impl(($($t: ident), +) => (

hpr_impl!(f32, f64);

/// Symmetric packed matrix rank-1 update
///
/// A ← A + αxx<sup>T</sup>
pub trait Spr: Sized {
fn spr<V: ?Sized + Vector<Self>>(symmetry: Symmetry, alpha: &Self, x: &V, a: &mut Matrix<Self>);
}
Expand All @@ -467,10 +527,16 @@ macro_rules! spr_impl(($($t: ident), +) => (

spr_impl!(f32, f64);

/// Symmetric packed matrix rank-2 update
///
/// A ← A + αxy<sup>T</sup> + αyx<sup>T</sup>
pub trait Spr2: Sized {
fn spr2<V: ?Sized + Vector<Self>, W: ?Sized + Vector<Self>>(symmetry: Symmetry, alpha: &Self, x: &V, y: &W, a: &mut Matrix<Self>);
}

/// Hermitian packed matrix rank-2 update
///
/// A ← A + αxy<sup>H</sup> + y(αx)<sup>H</sup>
pub trait Hpr2: Sized {
fn hpr2<V: ?Sized + Vector<Self>, W: ?Sized + Vector<Self>>(symmetry: Symmetry, alpha: &Self, x: &V, y: &W, a: &mut Matrix<Self>);
}
Expand Down

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