Support \ for SVD factorization

Author: timholy

src/StaticArrays.jl

@@ -18,7 +18,7 @@ using LinearAlgebra
 import LinearAlgebra: transpose, adjoint, dot, eigvals, eigen, lyap, tr,
                       kron, diag, norm, dot, diagm, lu, svd, svdvals,
                       factorize, ishermitian, issymmetric, isposdef, normalize,
-                      normalize!, Eigen, det, logdet, cross, diff, qr
+                      normalize!, Eigen, det, logdet, cross, diff, qr, \
 
 # import eye for deprecation warnings
 @static if isdefined(LinearAlgebra, :eye)

src/svd.jl

@@ -55,3 +55,8 @@ function _svd(A, full::Val{true})
     SVD(U,S,Vt)
 end
 
+function \(F::SVD, B::StaticVecOrMat)
+    sthresh = eps(F.S[1])
+    Sinv = map(s->s < sthresh ? zero(1/sthresh) : 1/s, F.S)
+    return F.Vt' * (Diagonal(Sinv) * (F.U'*B))
+end

test/svd.jl

@@ -4,6 +4,8 @@ using StaticArrays, Test, LinearAlgebra
     m3 = @SMatrix Float64[3 9 4; 6 6 2; 3 7 9]
     m3c = ComplexF64.(m3)
     m23 = @SMatrix Float64[3 9 4; 6 6 2]
+    m_sing = @SMatrix [2.0 3.0 5.0; 4.0 9.0 10.0; 1.0 1.0 1.0]
+    v = @SVector [1, 2, 3]
 
     @testset "svd" begin
         @testinf svdvals(@SMatrix [2 0; 0 0])::StaticVector ≊ [2, 0]
@@ -51,5 +53,10 @@ using StaticArrays, Test, LinearAlgebra
         @testinf svd(m3c).U  isa SMatrix{3,3,ComplexF64}
         @testinf svd(m3c).S  isa SVector{3,Float64}
         @testinf svd(m3c).Vt isa SMatrix{3,3,ComplexF64}
+
+        @testinf svd(m3) \ v ≈ svd(Matrix(m3)) \ Vector(v)
+        @testinf svd(m_sing) \ v ≈ svd(Matrix(m_sing)) \ Vector(v)
+        @testinf svd(m3) \ m23' ≈ svd(Matrix(m3)) \ Matrix(m23')
+        @testinf svd(m_sing) \ m23' ≈ svd(Matrix(m_sing)) \ Matrix(m23')
     end
 end