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Fix quadratic form computation.

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For the moment only the version that does not make any assumption regarding symmetry is
implemented.
This commit is contained in:
Sébastien Crozet 2018-02-02 12:26:09 +01:00
parent 39d20306f1
commit 1ee8a702ea
2 changed files with 40 additions and 39 deletions
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61
src/core/blas.rs
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@ -462,36 +462,41 @@ impl<N, D1: Dim, S: StorageMut<N, D1, D1>> SquareMatrix<N, D1, S>
where N: Scalar + Zero + One + ClosedAdd + ClosedMul { where N: Scalar + Zero + One + ClosedAdd + ClosedMul {
/// Computes the quadratic form `self = alpha * lrs * mid * lhs.transpose() + beta * self`. /// Computes the quadratic form `self = alpha * lrs * mid * lhs.transpose() + beta * self`.
pub fn quadform_symm<D2, S2, R3, C3, S3, S4>(&mut self, pub fn quadform_with_workspace<D2, S2, R3, C3, S3, D4, S4>(&mut self,
scratch: &mut Vector<N, D1, S2>, work: &mut Vector<N, D2, S2>,
alpha: N, alpha: N,
mid: &SquareMatrix<N, D2, S3>, lhs: &Matrix<N, R3, C3, S3>,
rhs: &Matrix<N, R3, C3, S4>, mid: &SquareMatrix<N, D4, S4>,
beta: N) beta: N)
where D2: Dim, R3: Dim, C3: Dim, where D2: Dim, R3: Dim, C3: Dim, D4: Dim,
S2: StorageMut<N, D1>, S2: StorageMut<N, D2>,
S3: Storage<N, D2, D2>, S3: Storage<N, R3, C3>,
S4: Storage<N, R3, C3>, S4: Storage<N, D4, D4>,
ShapeConstraint: DimEq<D1, D2> + DimEq<D2, R3> + DimEq<D1, C3>, // FIXME: why is this one necessary? ShapeConstraint: DimEq<D1, D2> +
DimEq<D1, R3> +
DimEq<D2, R3> +
DimEq<C3, D4> {
work.gemv(N::one(), lhs, &mid.column(0), N::zero());
self.ger(alpha, work, &lhs.column(0), beta);
for j in 1 .. mid.ncols() {
work.gemv(N::one(), lhs, &mid.column(j), N::zero());
self.ger(alpha, work, &lhs.column(j), N::one());
}
}
/// Computes the quadratic form `self = alpha * lrs * mid * lhs.transpose() + beta * self`.
pub fn quadform<R3, C3, S3, D4, S4>(&mut self,
alpha: N,
lhs: &Matrix<N, R3, C3, S3>,
mid: &SquareMatrix<N, D4, S4>,
beta: N)
where R3: Dim, C3: Dim, D4: Dim,
S3: Storage<N, R3, C3>,
S4: Storage<N, D4, D4>,
ShapeConstraint: DimEq<D1, D1> + DimEq<D1, R3> + DimEq<C3, D4>,
DefaultAllocator: Allocator<N, D1> { DefaultAllocator: Allocator<N, D1> {
let mut work = unsafe { Vector::new_uninitialized_generic(self.data.shape().0, U1) };
self.quadform_with_workspace(&mut work, alpha, lhs, mid, beta)
/*
scratch.gemv(N::one(), lhs, &mid.column(0), N::zero());
self.ger_symm(alpha, &scratch, &lhs.column(0), beta);
for j in 1 .. mid.ncols() {
scratch.gemv(N::one(), lhs, &mid.column(j), N::zero());
self.ger_symm(alpha, &scratch, &lhs.column(j), N::one());
}
*/
scratch.gemv_symm(N::one(), mid, &rhs.column(0), N::zero());
self.column_mut(0).gemv(alpha, rhs, &scratch, beta);
for j in 1 .. mid.ncols() {
scratch.gemv_symm(N::one(), mid, &rhs.column(j), N::zero());
self.slice_range_mut(j .., j).gemv(alpha, &rhs.rows_range(j ..), &scratch, N::one());
}
} }
} }

12
tests/core/blas.rs
View File

@ -53,22 +53,18 @@ quickcheck! {
relative_eq!(a1.lower_triangle(), a2) relative_eq!(a1.lower_triangle(), a2)
} }
fn quadform_symm(n: usize, alpha: f64, beta: f64) -> bool { fn quadform(n: usize, alpha: f64, beta: f64) -> bool {
let n = cmp::max(1, cmp::min(n, 50)); let n = cmp::max(1, cmp::min(n, 50));
let lhs = DMatrix::<f64>::new_random(6, n); let lhs = DMatrix::<f64>::new_random(6, n);
let mut mid = DMatrix::<f64>::new_random(n, n); let mid = DMatrix::<f64>::new_random(n, n);
let mut res = DMatrix::new_random(6, 6); let mut res = DMatrix::new_random(6, 6);
let mut scratch = Vector6::zeros();
mid.fill_upper_triangle_with_lower_triangle();
let expected = &res * beta + &lhs * &mid * lhs.transpose() * alpha; let expected = &res * beta + &lhs * &mid * lhs.transpose() * alpha;
res.quadform_symm(&mut scratch, alpha, &lhs, &mid, beta); res.quadform(alpha, &lhs, &mid , beta);
res.fill_upper_triangle_with_lower_triangle();
println!("{}{}", res, expected); println!("{}{}", res, expected);
relative_eq!(res.lower_triangle(), expected.lower_triangle(), epsilon = 1.0e-7) relative_eq!(res, expected, epsilon = 1.0e-7)
} }
} }