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Adapt BLAS tests to complex numbers.

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This commit is contained in:
sebcrozet 2019-03-26 18:02:03 +01:00
parent 4ef4001836
commit 3b6cd04a80
1 changed files with 187 additions and 66 deletions
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253
src/base/blas.rs
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@ -11,7 +11,7 @@ use crate::base::constraint::{
};
use crate::base::dimension::{Dim, Dynamic, U1, U2, U3, U4};
use crate::base::storage::{Storage, StorageMut};
use crate::base::{DefaultAllocator, Matrix, Scalar, SquareMatrix, Vector, DVectorSlice};
use crate::base::{DefaultAllocator, Matrix, Scalar, SquareMatrix, Vector, DVectorSlice, VectorSliceN};
// FIXME: find a way to avoid code duplication just for complex number support.
@ -368,6 +368,9 @@ where N: Scalar + Zero + ClosedAdd + ClosedMul
/// The dot product between two vectors or matrices (seen as vectors).
///
/// This is equal to `self.transpose() * rhs`. For the sesquilinear complex dot product, use
/// `self.dotc(rhs)`.
///
/// Note that this is **not** the matrix multiplication as in, e.g., numpy. For matrix
/// multiplication, use one of: `.gemm`, `.mul_to`, `.mul`, the `*` operator.
///
@ -385,6 +388,7 @@ where N: Scalar + Zero + ClosedAdd + ClosedMul
/// 0.4, 0.5, 0.6);
/// assert_eq!(mat1.dot(&mat2), 9.1);
/// ```
///
#[inline]
pub fn dot<R2: Dim, C2: Dim, SB>(&self, rhs: &Matrix<N, R2, C2, SB>) -> N
where
@ -394,24 +398,24 @@ where N: Scalar + Zero + ClosedAdd + ClosedMul
self.dotx(rhs, |e| e)
}
/// The dot product between two vectors or matrices (seen as vectors).
/// The conjugate-linear dot product between two vectors or matrices (seen as vectors).
///
/// This is equal to `self.adjoint() * rhs`.
/// For real vectors, this is identical to `self.dot(&rhs)`.
/// Note that this is **not** the matrix multiplication as in, e.g., numpy. For matrix
/// multiplication, use one of: `.gemm`, `.mul_to`, `.mul`, the `*` operator.
///
/// # Examples:
///
/// ```
/// # use nalgebra::{Vector3, Matrix2x3};
/// let vec1 = Vector3::new(1.0, 2.0, 3.0);
/// let vec2 = Vector3::new(0.1, 0.2, 0.3);
/// assert_eq!(vec1.dot(&vec2), 1.4);
/// # use nalgebra::{Vector2, Complex};
/// let vec1 = Vector2::new(Complex::new(1.0, 2.0), Complex::new(3.0, 4.0));
/// let vec2 = Vector2::new(Complex::new(0.4, 0.3), Complex::new(0.2, 0.1));
/// assert_eq!(vec1.dotc(&vec2), Complex::new(2.0, -1.0));
///
/// let mat1 = Matrix2x3::new(1.0, 2.0, 3.0,
/// 4.0, 5.0, 6.0);
/// let mat2 = Matrix2x3::new(0.1, 0.2, 0.3,
/// 0.4, 0.5, 0.6);
/// assert_eq!(mat1.dot(&mat2), 9.1);
/// // Note that for complex vectors, we generally have:
/// // vec1.dotc(&vec2) != vec2.dot(&vec2)
/// assert_ne!(vec1.dotc(&vec2), vec1.dot(&vec2));
/// ```
#[inline]
pub fn dotc<R2: Dim, C2: Dim, SB>(&self, rhs: &Matrix<N, R2, C2, SB>) -> N
@ -579,7 +583,7 @@ where
#[inline(always)]
fn xgemv<D2: Dim, D3: Dim, SB, SC>(
fn xxgemv<D2: Dim, D3: Dim, SB, SC>(
&mut self,
alpha: N,
a: &SquareMatrix<N, D2, SB>,
@ -651,6 +655,7 @@ where
/// Computes `self = alpha * a * x + beta * self`, where `a` is a **symmetric** matrix, `x` a
/// vector, and `alpha, beta` two scalars.
///
/// For hermitian matrices, use `.hegemv` instead.
/// If `beta` is zero, `self` is never read. If `self` is read, only its lower-triangular part
/// (including the diagonal) is actually read.
///
@ -688,7 +693,7 @@ where
SC: Storage<N, D3>,
ShapeConstraint: DimEq<D, D2> + AreMultipliable<D2, D2, D3, U1>,
{
self.xgemv(alpha, a, x, beta, |a, b| a.dot(b))
self.xxgemv(alpha, a, x, beta, |a, b| a.dot(b))
}
/// Computes `self = alpha * a * x + beta * self`, where `a` is an **hermitian** matrix, `x` a
@ -700,23 +705,25 @@ where
/// # Examples:
///
/// ```
/// # use nalgebra::{Matrix2, Vector2};
/// let mat = Matrix2::new(1.0, 2.0,
/// 2.0, 4.0);
/// let mut vec1 = Vector2::new(1.0, 2.0);
/// let vec2 = Vector2::new(0.1, 0.2);
/// vec1.sygemv(10.0, &mat, &vec2, 5.0);
/// assert_eq!(vec1, Vector2::new(10.0, 20.0));
/// # use nalgebra::{Matrix2, Vector2, Complex};
/// let mat = Matrix2::new(Complex::new(1.0, 0.0), Complex::new(2.0, -0.1),
/// Complex::new(2.0, 1.0), Complex::new(4.0, 0.0));
/// let mut vec1 = Vector2::new(Complex::new(1.0, 2.0), Complex::new(3.0, 4.0));
/// let vec2 = Vector2::new(Complex::new(0.1, 0.2), Complex::new(0.3, 0.4));
/// vec1.sygemv(Complex::new(10.0, 20.0), &mat, &vec2, Complex::new(5.0, 15.0));
/// assert_eq!(vec1, Vector2::new(Complex::new(-48.0, 44.0), Complex::new(-75.0, 110.0)));
///
///
/// // The matrix upper-triangular elements can be garbage because it is never
/// // read by this method. Therefore, it is not necessary for the caller to
/// // fill the matrix struct upper-triangle.
/// let mat = Matrix2::new(1.0, 9999999.9999999,
/// 2.0, 4.0);
/// let mut vec1 = Vector2::new(1.0, 2.0);
/// vec1.sygemv(10.0, &mat, &vec2, 5.0);
/// assert_eq!(vec1, Vector2::new(10.0, 20.0));
///
/// let mat = Matrix2::new(Complex::new(1.0, 0.0), Complex::new(99999999.9, 999999999.9),
/// Complex::new(2.0, 1.0), Complex::new(4.0, 0.0));
/// let mut vec1 = Vector2::new(Complex::new(1.0, 2.0), Complex::new(3.0, 4.0));
/// let vec2 = Vector2::new(Complex::new(0.1, 0.2), Complex::new(0.3, 0.4));
/// vec1.sygemv(Complex::new(10.0, 20.0), &mat, &vec2, Complex::new(5.0, 15.0));
/// assert_eq!(vec1, Vector2::new(Complex::new(-48.0, 44.0), Complex::new(-75.0, 110.0)));
/// ```
#[inline]
pub fn hegemv<D2: Dim, D3: Dim, SB, SC>(
@ -731,9 +738,51 @@ where
SC: Storage<N, D3>,
ShapeConstraint: DimEq<D, D2> + AreMultipliable<D2, D2, D3, U1>,
{
self.xgemv(alpha, a, x, beta, |a, b| a.dotc(b))
self.xxgemv(alpha, a, x, beta, |a, b| a.dotc(b))
}
#[inline(always)]
fn gemv_xx<R2: Dim, C2: Dim, D3: Dim, SB, SC>(
&mut self,
alpha: N,
a: &Matrix<N, R2, C2, SB>,
x: &Vector<N, D3, SC>,
beta: N,
dot: impl Fn(&VectorSliceN<N, R2, SB::RStride, SB::CStride>, &Vector<N, D3, SC>) -> N,
) where
N: One,
SB: Storage<N, R2, C2>,
SC: Storage<N, D3>,
ShapeConstraint: DimEq<D, C2> + AreMultipliable<C2, R2, D3, U1>,
{
let dim1 = self.nrows();
let (nrows2, ncols2) = a.shape();
let dim3 = x.nrows();
assert!(
nrows2 == dim3 && dim1 == ncols2,
"Gemv: dimensions mismatch."
);
if ncols2 == 0 {
return;
}
if beta.is_zero() {
for j in 0..ncols2 {
let val = unsafe { self.vget_unchecked_mut(j) };
*val = alpha * dot(&a.column(j), x)
}
} else {
for j in 0..ncols2 {
let val = unsafe { self.vget_unchecked_mut(j) };
*val = alpha * dot(&a.column(j), x) + beta * *val;
}
}
}
/// Computes `self = alpha * a.transpose() * x + beta * self`, where `a` is a matrix, `x` a vector, and
/// `alpha, beta` two scalars.
///
@ -765,30 +814,42 @@ where
SC: Storage<N, D3>,
ShapeConstraint: DimEq<D, C2> + AreMultipliable<C2, R2, D3, U1>,
{
let dim1 = self.nrows();
let (nrows2, ncols2) = a.shape();
let dim3 = x.nrows();
self.gemv_xx(alpha, a, x, beta, |a, b| a.dot(b))
}
assert!(
nrows2 == dim3 && dim1 == ncols2,
"Gemv: dimensions mismatch."
);
if ncols2 == 0 {
return;
}
if beta.is_zero() {
for j in 0..ncols2 {
let val = unsafe { self.vget_unchecked_mut(j) };
*val = alpha * a.column(j).dot(x)
}
} else {
for j in 0..ncols2 {
let val = unsafe { self.vget_unchecked_mut(j) };
*val = alpha * a.column(j).dot(x) + beta * *val;
}
}
/// Computes `self = alpha * a.adjoint() * x + beta * self`, where `a` is a matrix, `x` a vector, and
/// `alpha, beta` two scalars.
///
/// For real matrices, this is the same as `.gemv_tr`.
/// If `beta` is zero, `self` is never read.
///
/// # Examples:
///
/// ```
/// # use nalgebra::{Matrix2, Vector2, Complex};
/// let mat = Matrix2::new(Complex::new(1.0, 2.0), Complex::new(3.0, 4.0),
/// Complex::new(5.0, 6.0), Complex::new(7.0, 8.0));
/// let mut vec1 = Vector2::new(Complex::new(1.0, 2.0), Complex::new(3.0, 4.0));
/// let vec2 = Vector2::new(Complex::new(0.1, 0.2), Complex::new(0.3, 0.4));
/// let expected = mat.adjoint() * vec2 * Complex::new(10.0, 20.0) + vec1 * Complex::new(5.0, 15.0);
///
/// vec1.gemv_ad(Complex::new(10.0, 20.0), &mat, &vec2, Complex::new(5.0, 15.0));
/// assert_eq!(vec1, expected);
/// ```
#[inline]
pub fn gemv_ad<R2: Dim, C2: Dim, D3: Dim, SB, SC>(
&mut self,
alpha: N,
a: &Matrix<N, R2, C2, SB>,
x: &Vector<N, D3, SC>,
beta: N,
) where
N: ComplexField,
SB: Storage<N, R2, C2>,
SC: Storage<N, D3>,
ShapeConstraint: DimEq<D, C2> + AreMultipliable<C2, R2, D3, U1>,
{
self.gemv_xx(alpha, a, x, beta, |a, b| a.dotc(b))
}
}
@ -857,20 +918,21 @@ where N: Scalar + Zero + ClosedAdd + ClosedMul
self.gerx(alpha, x, y, beta, |e| e)
}
/// Computes `self = alpha * x * y.transpose() + beta * self`.
/// Computes `self = alpha * x * y.adjoint() + 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;
/// # #[macro_use] extern crate approx;
/// # use nalgebra::{Matrix2x3, Vector2, Vector3, Complex};
/// let mut mat = Matrix2x3::repeat(Complex::new(4.0, 5.0));
/// let vec1 = Vector2::new(Complex::new(1.0, 2.0), Complex::new(3.0, 4.0));
/// let vec2 = Vector3::new(Complex::new(0.6, 0.5), Complex::new(0.4, 0.5), Complex::new(0.2, 0.1));
/// let expected = vec1 * vec2.adjoint() * Complex::new(10.0, 20.0) + mat * Complex::new(5.0, 15.0);
///
/// mat.ger(10.0, &vec1, &vec2, 5.0);
/// mat.gerc(Complex::new(10.0, 20.0), &vec1, &vec2, Complex::new(5.0, 15.0));
/// assert_eq!(mat, expected);
/// ```
#[inline]
@ -1041,7 +1103,7 @@ where N: Scalar + Zero + ClosedAdd + ClosedMul
/// let expected = mat2.transpose() * mat3 * 10.0 + mat1 * 5.0;
///
/// mat1.gemm_tr(10.0, &mat2, &mat3, 5.0);
/// assert_relative_eq!(mat1, expected);
/// assert_eq!(mat1, expected);
/// ```
#[inline]
pub fn gemm_tr<R2: Dim, C2: Dim, R3: Dim, C3: Dim, SB, SC>(
@ -1077,6 +1139,64 @@ where N: Scalar + Zero + ClosedAdd + ClosedMul
self.column_mut(j1).gemv_tr(alpha, a, &b.column(j1), beta);
}
}
/// Computes `self = alpha * a.adjoint() * b + beta * self`, where `a, b, self` are matrices.
/// `alpha` and `beta` are scalar.
///
/// If `beta` is zero, `self` is never read.
///
/// # Examples:
///
/// ```
/// # #[macro_use] extern crate approx;
/// # use nalgebra::{Matrix3x2, Matrix3x4, Matrix2x4, Complex};
/// let mut mat1 = Matrix2x4::identity();
/// let mat2 = Matrix3x2::new(Complex::new(1.0, 4.0), Complex::new(7.0, 8.0),
/// Complex::new(2.0, 5.0), Complex::new(9.0, 10.0),
/// Complex::new(3.0, 6.0), Complex::new(11.0, 12.0));
/// let mat3 = Matrix3x4::new(Complex::new(0.1, 1.3), Complex::new(0.2, 1.4), Complex::new(0.3, 1.5), Complex::new(0.4, 1.6),
/// Complex::new(0.5, 1.7), Complex::new(0.6, 1.8), Complex::new(0.7, 1.9), Complex::new(0.8, 2.0),
/// Complex::new(0.9, 2.1), Complex::new(1.0, 2.2), Complex::new(1.1, 2.3), Complex::new(1.2, 2.4));
/// let expected = mat2.adjoint() * mat3 * Complex::new(10.0, 20.0) + mat1 * Complex::new(5.0, 15.0);
///
/// mat1.gemm_ad(Complex::new(10.0, 20.0), &mat2, &mat3, Complex::new(5.0, 15.0));
/// assert_eq!(mat1, expected);
/// ```
#[inline]
pub fn gemm_ad<R2: Dim, C2: Dim, R3: Dim, C3: Dim, SB, SC>(
&mut self,
alpha: N,
a: &Matrix<N, R2, C2, SB>,
b: &Matrix<N, R3, C3, SC>,
beta: N,
) where
N: ComplexField,
SB: Storage<N, R2, C2>,
SC: Storage<N, R3, C3>,
ShapeConstraint: SameNumberOfRows<R1, C2>
+ SameNumberOfColumns<C1, C3>
+ AreMultipliable<C2, R2, R3, C3>,
{
let (nrows1, ncols1) = self.shape();
let (nrows2, ncols2) = a.shape();
let (nrows3, ncols3) = b.shape();
assert_eq!(
nrows2, nrows3,
"gemm: dimensions mismatch for multiplication."
);
assert_eq!(
(nrows1, ncols1),
(ncols2, ncols3),
"gemm: dimensions mismatch for addition."
);
for j1 in 0..ncols1 {
// FIXME: avoid bound checks.
self.column_mut(j1).gemv_ad(alpha, a, &b.column(j1), beta);
}
}
}
impl<N, R1: Dim, C1: Dim, S: StorageMut<N, R1, C1>> Matrix<N, R1, C1, S>
@ -1157,6 +1277,7 @@ where N: Scalar + Zero + ClosedAdd + ClosedMul
/// Computes `self = alpha * x * y.transpose() + beta * self`, where `self` is a **symmetric**
/// matrix.
///
/// For hermitian complex matrices, use `.hegerc` instead.
/// If `beta` is zero, `self` is never read. The result is symmetric. Only the lower-triangular
/// (including the diagonal) part of `self` is read/written.
///
@ -1170,7 +1291,7 @@ where N: Scalar + Zero + ClosedAdd + ClosedMul
/// let expected = vec1 * vec2.transpose() * 10.0 + mat * 5.0;
/// mat.m12 = 99999.99999; // This component is on the upper-triangular part and will not be read/written.
///
/// mat.ger_symm(10.0, &vec1, &vec2, 5.0);
/// mat.syger(10.0, &vec1, &vec2, 5.0);
/// assert_eq!(mat.lower_triangle(), expected.lower_triangle());
/// assert_eq!(mat.m12, 99999.99999); // This was untouched.
#[inline]
@ -1189,7 +1310,7 @@ where N: Scalar + Zero + ClosedAdd + ClosedMul
self.xxgerx(alpha, x, y, beta, |e| e)
}
/// Computes `self = alpha * x * y.transpose() + beta * self`, where `self` is a **symmetric**
/// Computes `self = alpha * x * y.adjoint() + beta * self`, where `self` is an **hermitian**
/// matrix.
///
/// If `beta` is zero, `self` is never read. The result is symmetric. Only the lower-triangular
@ -1198,16 +1319,16 @@ where N: Scalar + Zero + ClosedAdd + ClosedMul
/// # Examples:
///
/// ```
/// # use nalgebra::{Matrix2, Vector2};
/// # use nalgebra::{Matrix2, Vector2, Complex};
/// let mut mat = Matrix2::identity();
/// let vec1 = Vector2::new(1.0, 2.0);
/// let vec2 = Vector2::new(0.1, 0.2);
/// let expected = vec1 * vec2.transpose() * 10.0 + mat * 5.0;
/// mat.m12 = 99999.99999; // This component is on the upper-triangular part and will not be read/written.
/// let vec1 = Vector2::new(Complex::new(1.0, 3.0), Complex::new(2.0, 4.0));
/// let vec2 = Vector2::new(Complex::new(0.2, 0.4), Complex::new(0.1, 0.3));
/// let expected = vec1 * vec2.adjoint() * Complex::new(10.0, 20.0) + mat * Complex::new(5.0, 15.0);
/// mat.m12 = Complex::new(99999.99999, 88888.88888); // This component is on the upper-triangular part and will not be read/written.
///
/// mat.ger_symm(10.0, &vec1, &vec2, 5.0);
/// mat.hegerc(Complex::new(10.0, 20.0), &vec1, &vec2, Complex::new(5.0, 15.0));
/// assert_eq!(mat.lower_triangle(), expected.lower_triangle());
/// assert_eq!(mat.m12, 99999.99999); // This was untouched.
/// assert_eq!(mat.m12, Complex::new(99999.99999, 88888.88888)); // This was untouched.
#[inline]
pub fn hegerc<D2: Dim, D3: Dim, SB, SC>(
&mut self,