[NDTensorsCUDAExt] Fix QR-based SVD for some rectangular matrices

NDTensors/ext/NDTensorsCUDAExt/NDTensorsCUDAExt.jl

@@ -18,6 +18,7 @@ else
 end
 
 include("imports.jl")
+include("default_kwargs.jl")
 include("set_types.jl")
 include("iscu.jl")
 include("adapt.jl")

NDTensors/ext/NDTensorsCUDAExt/default_kwargs.jl

@@ -0,0 +1 @@
+NDTensors.default_svd_alg(::Type{<:CuArray}, a) = "qr_algorithm"

NDTensors/ext/NDTensorsCUDAExt/linearalgebra.jl

@@ -1,13 +1,43 @@
-function NDTensors.svd_catch_error(A::CuMatrix; alg="JacobiAlgorithm")
-  if alg == "JacobiAlgorithm"
+function NDTensors.svd_catch_error(A::CuMatrix; alg::String="jacobi_algorithm")
+  if alg == "jacobi_algorithm"
     alg = CUDA.CUSOLVER.JacobiAlgorithm()
-  else
+  elseif alg == "qr_algorithm"
     alg = CUDA.CUSOLVER.QRAlgorithm()
+  else
+    error(
+      "svd algorithm $alg is not currently supported. Please see the documentation for currently supported algorithms.",
+    )
   end
+  return NDTensors.svd_catch_error(A, alg)
+end
+
+function NDTensors.svd_catch_error(A::CuMatrix, ::CUDA.CUSOLVER.JacobiAlgorithm)
   USV = try
-    svd(expose(A); alg=alg)
+    svd(A; alg=CUDA.CUSOLVER.JacobiAlgorithm())
   catch
     return nothing
   end
   return USV
 end
+
+function NDTensors.svd_catch_error(A::CuMatrix, ::CUDA.CUSOLVER.QRAlgorithm)
+  s = size(A)
+  if s[1] < s[2]
+    At = copy(Adjoint(A))
+
+    USV = try
+      svd(At; alg=CUDA.CUSOLVER.QRAlgorithm())
+    catch
+      return nothing
+    end
+    MV, MS, MU = USV
+    USV = (MU, MS, MV)
+  else
+    USV = try
+      svd(A; alg=CUDA.CUSOLVER.QRAlgorithm())
+    catch
+      return nothing
+    end
+  end
+  return USV
+end

NDTensors/src/default_kwargs.jl

@@ -4,6 +4,7 @@ replace_nothing(value, replacement) = value
 default_maxdim(a) = minimum(size(a))
 default_mindim(a) = true
 default_cutoff(a) = zero(eltype(a))
-default_svd_alg(a) = "divide_and_conquer"
+default_svd_alg(a) = default_svd_alg(unwrap_type(a), a)
+default_svd_alg(::Type{<:AbstractArray}, a) = "divide_and_conquer"
 default_use_absolute_cutoff(a) = false
 default_use_relative_cutoff(a) = true

NDTensors/src/linearalgebra/linearalgebra.jl

@@ -81,8 +81,8 @@ function lapack_svd_error_message(alg)
          "   ``A^{\\dagger} A`` is used to compute `U` and then a `qr` of\n" *
          "   ``A^{\\dagger} U`` is used to compute `V`. This is performed\n" *
          "   recursively to compute small singular values.\n" *
-         " - `\"QRAlgorithm\"` is a CUDA.jl implemented SVD algorithm using QR.\n" *
-         " - `\"JacobiAlgorithm\"` is a CUDA.jl implemented SVD algorithm.\n\n" *
+         " - `\"qr_algorithm\"` is a CUDA.jl implemented SVD algorithm using QR.\n" *
+         " - `\"jacobi_algorithm\"` is a CUDA.jl implemented SVD algorithm.\n\n" *
          "Returning `nothing`. For an output `F = svd(A, ...)` you can check if\n" *
          "`isnothing(F)` in your code and try a different algorithm.\n\n" *
          "To suppress this message in the future, you can wrap the `svd` call in the\n" *
@@ -127,7 +127,7 @@ function svd(
     end
   elseif alg == "recursive"
     MUSV = svd_recursive(matrix(T))
-  elseif alg == "QRAlgorithm" || alg == "JacobiAlgorithm"
+  elseif alg == "qr_algorithm" || alg == "jacobi_algorithm"
     MUSV = svd_catch_error(matrix(T); alg)
   else
     error(