Specialized inv(F::SVD) (#32126)

* inv(F::SVD)

* throw SingularException

* SingularException test

* truncate

stdlib/LinearAlgebra/src/svd.jl

@@ -238,6 +238,14 @@ function ldiv!(A::SVD{T}, B::StridedVecOrMat) where T
     view(A.Vt,1:k,:)' * (view(A.S,1:k) .\ (view(A.U,:,1:k)' * B))
 end
 
+function inv(F::SVD{T}) where T
+    @inbounds for i in eachindex(F.S)
+        iszero(F.S[i]) && throw(SingularException(i))
+    end
+    k = searchsortedlast(F.S, eps(T)*F.S[1], rev=true)
+    @views (F.S[1:k] .\ F.Vt[1:k, :])' * F.U[:,1:k]'
+end
+
 size(A::SVD, dim::Integer) = dim == 1 ? size(A.U, dim) : size(A.Vt, dim)
 size(A::SVD) = (size(A, 1), size(A, 2))
 

stdlib/LinearAlgebra/test/svd.jl

@@ -31,6 +31,10 @@ using LinearAlgebra: BlasComplex, BlasFloat, BlasReal, QRPivoted
     @test sf2.U*Diagonal(sf2.S)*sf2.Vt' ≊ m2
 
     @test ldiv!([0., 0.], svd(Matrix(I, 2, 2)), [1., 1.]) ≊ [1., 1.]
+    @test inv(svd(Matrix(I, 2, 2))) ≈ I
+    @test inv(svd([1 2; 3 4])) ≈ [-2.0 1.0; 1.5 -0.5]
+    @test inv(svd([1 0 1; 0 1 0])) ≈ [0.5 0.0; 0.0 1.0; 0.5 0.0]
+    @test_throws SingularException inv(svd([0 0; 0 0]))
 end
 
 n = 10