code: def sample_inputs_linalg_pinv_singular(
      op_info, device, dtype, requires_grad=False, **kwargs
  ):
      """
      This function produces factors `a` and `b` to generate inputs of the form `a @ b.t()` to
      test the backward method of `linalg_pinv`. That way we always preserve the rank of the
      input no matter the perturbations applied to it by the gradcheck.
      Note that `pinv` is Frechet-differentiable in a rank-preserving neighborhood.
      """
      batches = [(), (0,), (2,), (1, 1)]
      # the size of at least 30 is required to cause failures for the previous implicit implementation
      # of the pinv's backward method, albeit it is slow.
      size = [0, 3, 50]
  
      for batch, m, n in product(batches, size, size):
          for k in range(min(3, m, n)):
              # Note that by making the columns of `a` and `b` orthonormal we make sure that
              # the product matrix `a @ b.t()` has condition number 1 when restricted to its image
              a = (
                  torch.rand(*batch, m, k, device=device, dtype=dtype)
                  .qr()
                  .Q.requires_grad_(requires_grad)
              )
              b = (
                  torch.rand(*batch, n, k, device=device, dtype=dtype)
                  .qr()
                  .Q.requires_grad_(requires_grad)
              )
              yield SampleInput(a, args=(b,))
  
imports: import itertools
  import random
  import unittest
  from functools import partial
  from itertools import chain, product
  from typing import Iterable, List, Tuple
  import numpy
  from numpy import inf
  import torch
  from torch.testing import make_tensor
  from torch.testing._internal.common_cuda import _get_magma_version, _get_torch_cuda_version, with_tf32_off
  from torch.testing._internal.common_device_type import has_cusolver, skipCPUIfNoLapack, skipCUDAIf, skipCUDAIfNoCusolver, skipCUDAIfNoMagma, skipCUDAIfNoMagmaAndNoCusolver, skipCUDAIfNoMagmaAndNoLinalgsolver, skipCUDAIfRocm, tol, toleranceOverride
  from torch.testing._internal.common_dtype import all_types_and_complex, all_types_and_complex_and, floating_and_complex_types, floating_and_complex_types_and, get_all_complex_dtypes
  from torch.testing._internal.common_utils import GRADCHECK_NONDET_TOL, IS_MACOS, make_fullrank_matrices_with_distinct_singular_values, skipIfSlowGradcheckEnv, slowTest, TEST_WITH_ROCM
  from torch.testing._internal.opinfo.core import clone_sample, DecorateInfo, ErrorInput, gradcheck_wrapper_hermitian_input, L, M, OpInfo, ReductionOpInfo, S, SampleInput
  from torch.testing._internal.opinfo.refs import PythonRefInfo, ReductionPythonRefInfo
label_desc: Use image node_id 16 for calling a global function with example usage: sample_inputs_linalg_pinv_singular(op_info, device, dtype, requires_grad) without return types