Add rot! to BLAS in stdlib/LinearAlgebra, add generic rotate! and reflect! (#35124)

Author: amontoison

NEWS.md

@@ -115,6 +115,8 @@ Standard library changes
 * `normalize` now supports multidimensional arrays ([#34239])
 * `lq` factorizations can now be used to compute the minimum-norm solution to under-determined systems ([#34350]).
 * The BLAS submodule now supports the level-2 BLAS subroutine `spmv!` ([#34320]).
+* The BLAS submodule now supports the level-1 BLAS subroutine `rot!` ([#35124]).
+* New generic `rotate!(x, y, c, s)` and `reflect!(x, y, c, s)` functions ([#35124]).
 
 #### Markdown
 

stdlib/LinearAlgebra/src/LinearAlgebra.jl

@@ -124,6 +124,8 @@ export
     opnorm,
     rank,
     rdiv!,
+    reflect!,
+    rotate!,
     schur,
     schur!,
     svd,

stdlib/LinearAlgebra/src/blas.jl

@@ -17,6 +17,7 @@ export
     blascopy!,
     dotc,
     dotu,
+    rot!,
     scal!,
     scal,
     nrm2,
@@ -198,6 +199,37 @@ for (fname, elty) in ((:dcopy_,:Float64),
     end
 end
 
+
+## rot
+
+"""
+    rot!(n, X, incx, Y, incy, c, s)
+
+Overwrite `X` with `c*X + s*Y` and `Y` with `-conj(s)*X + c*Y` for the first `n` elements of array `X` with stride `incx` and
+first `n` elements of array `Y` with stride `incy`. Returns `X` and `Y`.
+
+!!! compat "Julia 1.5"
+    `rot!` requires at least Julia 1.5.
+"""
+function rot! end
+
+for (fname, elty, cty, sty, lib) in ((:drot_, :Float64, :Float64, :Float64, libblas),
+                                     (:srot_, :Float32, :Float32, :Float32, libblas),
+                                     (:zdrot_, :ComplexF64, :Float64, :Float64, libblas),
+                                     (:csrot_, :ComplexF32, :Float32, :Float32, libblas),
+                                     (:zrot_, :ComplexF64, :Float64, :ComplexF64, liblapack),
+                                     (:crot_, :ComplexF32, :Float32, :ComplexF32, liblapack))
+    @eval begin
+        # SUBROUTINE DROT(N,DX,INCX,DY,INCY,C,S)
+        function rot!(n::Integer, DX::Union{Ptr{$elty},AbstractArray{$elty}}, incx::Integer, DY::Union{Ptr{$elty},AbstractArray{$elty}}, incy::Integer, C::$cty, S::$sty)
+            ccall((@blasfunc($fname), $lib), Cvoid,
+                (Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ptr{$elty}, Ref{BlasInt}, Ref{$cty}, Ref{$sty}),
+                 n, DX, incx, DY, incy, C, S)
+            DX, DY
+        end
+    end
+end
+
 ## scal
 
 """

stdlib/LinearAlgebra/src/generic.jl

@@ -1416,6 +1416,51 @@ function axpby!(α, x::AbstractArray, β, y::AbstractArray)
     y
 end
 
+"""
+    rotate!(x, y, c, s)
+
+Overwrite `x` with `c*x + s*y` and `y` with `-conj(s)*x + c*y`.
+Returns `x` and `y`.
+
+!!! compat "Julia 1.5"
+    `rotate!` requires at least Julia 1.5.
+"""
+function rotate!(x::AbstractVector, y::AbstractVector, c, s)
+    require_one_based_indexing(x, y)
+    n = length(x)
+    if n != length(y)
+        throw(DimensionMismatch("x has length $(length(x)), but y has length $(length(y))"))
+    end
+    @inbounds for i = 1:n
+        xi, yi = x[i], y[i]
+        x[i] =       c *xi + s*yi
+        y[i] = -conj(s)*xi + c*yi
+    end
+    return x, y
+end
+
+"""
+    reflect!(x, y, c, s)
+
+Overwrite `x` with `c*x + s*y` and `y` with `conj(s)*x - c*y`.
+Returns `x` and `y`.
+
+!!! compat "Julia 1.5"
+    `reflect!` requires at least Julia 1.5.
+"""
+function reflect!(x::AbstractVector, y::AbstractVector, c, s)
+    require_one_based_indexing(x, y)
+    n = length(x)
+    if n != length(y)
+        throw(DimensionMismatch("x has length $(length(x)), but y has length $(length(y))"))
+    end
+    @inbounds for i = 1:n
+        xi, yi = x[i], y[i]
+        x[i] =      c *xi + s*yi
+        y[i] = conj(s)*xi - c*yi
+    end
+    return x, y
+end
 
 # Elementary reflection similar to LAPACK. The reflector is not Hermitian but
 # ensures that tridiagonalization of Hermitian matrices become real. See lawn72

stdlib/LinearAlgebra/test/blas.jl

@@ -78,6 +78,32 @@ Random.seed!(100)
                 @test BLAS.iamax(z) == argmax(map(x -> abs(real(x)) + abs(imag(x)), z))
             end
         end
+        @testset "rot!" begin
+            if elty <: Real
+                x = convert(Vector{elty}, randn(n))
+                y = convert(Vector{elty}, randn(n))
+                c = rand(elty)
+                s = rand(elty)
+                x2 = copy(x)
+                y2 = copy(y)
+                BLAS.rot!(n, x, 1, y, 1, c, s)
+                @test x ≈ c*x2 + s*y2
+                @test y ≈ -s*x2 + c*y2
+            else
+                x = convert(Vector{elty}, complex.(randn(n),rand(n)))
+                y = convert(Vector{elty}, complex.(randn(n),rand(n)))
+                cty = (elty == ComplexF32) ? Float32 : Float64
+                c = rand(cty)
+                for sty in [cty, elty]
+                    s = rand(sty)
+                    x2 = copy(x)
+                    y2 = copy(y)
+                    BLAS.rot!(n, x, 1, y, 1, c, s)
+                    @test x ≈ c*x2 + s*y2
+                    @test y ≈ -conj(s)*x2 + c*y2
+                end
+            end
+        end
         @testset "axp(b)y" begin
             if elty <: Real
                 x1 = convert(Vector{elty}, randn(n))

stdlib/LinearAlgebra/test/generic.jl

@@ -217,6 +217,25 @@ end
     @test norm(x, 3) ≈ cbrt(5^3  +sqrt(5)^3)
 end
 
+@testset "rotate! and reflect!" begin
+    x = rand(ComplexF64, 10)
+    y = rand(ComplexF64, 10)
+    c = rand(Float64)
+    s = rand(ComplexF64)
+
+    x2 = copy(x)
+    y2 = copy(y)
+    rotate!(x, y, c, s)
+    @test x ≈ c*x2 + s*y2
+    @test y ≈ -conj(s)*x2 + c*y2
+
+    x3 = copy(x)
+    y3 = copy(y)
+    reflect!(x, y, c, s)
+    @test x ≈ c*x3 + s*y3
+    @test y ≈ conj(s)*x3 - c*y3
+end
+
 @testset "LinearAlgebra.axp(b)y! for element type without commutative multiplication" begin
     α = [1 2; 3 4]
     β = [5 6; 7 8]