Gradient for the singular value decomposition.
(op, grad_s, grad_u, grad_v)
| 345 | |
| 346 | @ops.RegisterGradient("Svd") |
| 347 | def _SvdGrad(op, grad_s, grad_u, grad_v): |
| 348 | """Gradient for the singular value decomposition.""" |
| 349 | |
| 350 | # The derivation for the compute_uv=False case, and most of |
| 351 | # the derivation for the full_matrices=True case, are in |
| 352 | # Giles' paper (see reference at top of file). A derivation for |
| 353 | # the full_matrices=False case is available at |
| 354 | # https://j-towns.github.io/papers/svd-derivative.pdf |
| 355 | a = op.inputs[0] |
| 356 | a_shape = a.get_shape().with_rank_at_least(2) |
| 357 | grad_s_mat = array_ops.matrix_diag(grad_s) |
| 358 | |
| 359 | if not op.get_attr("compute_uv"): |
| 360 | s, u, v = linalg_ops.svd(a, compute_uv=True) |
| 361 | grad_a = math_ops.matmul(u, math_ops.matmul(grad_s_mat, v, adjoint_b=True)) |
| 362 | grad_a.set_shape(a_shape) |
| 363 | return grad_a |
| 364 | |
| 365 | full_matrices = op.get_attr("full_matrices") |
| 366 | |
| 367 | # TODO(rmlarsen): Make this work with complex types. |
| 368 | if a.dtype.is_complex: |
| 369 | raise NotImplementedError( |
| 370 | "SVD gradient is not implemented for complex types and " |
| 371 | "compute_uv=True.") |
| 372 | grad_u_shape = grad_u.get_shape().with_rank_at_least(2) |
| 373 | grad_v_shape = grad_v.get_shape().with_rank_at_least(2) |
| 374 | m = a_shape.dims[-2].merge_with(grad_u_shape[-2]) |
| 375 | n = a_shape.dims[-1].merge_with(grad_v_shape[-2]) |
| 376 | batch_shape = a_shape[:-2].merge_with(grad_u_shape[:-2]).merge_with( |
| 377 | grad_v_shape[:-2]) |
| 378 | a_shape = batch_shape.concatenate([m, n]) |
| 379 | |
| 380 | m = a_shape.dims[-2].value |
| 381 | n = a_shape.dims[-1].value |
| 382 | # TODO(rmlarsen): Make this work with placeholders. |
| 383 | if m is None or n is None: |
| 384 | raise NotImplementedError( |
| 385 | "SVD gradient has not been implemented for input with unknown " |
| 386 | "inner matrix shape.") |
| 387 | |
| 388 | s = op.outputs[0] |
| 389 | u = op.outputs[1] |
| 390 | v = op.outputs[2] |
| 391 | |
| 392 | use_adjoint = False |
| 393 | if m > n: |
| 394 | # Compute the gradient for A^H = V * S^T * U^H, and (implicitly) take the |
| 395 | # Hermitian transpose of the gradient at the end. |
| 396 | use_adjoint = True |
| 397 | m, n = n, m |
| 398 | u, v = v, u |
| 399 | grad_u, grad_v = grad_v, grad_u |
| 400 | |
| 401 | with ops.control_dependencies([grad_s, grad_u, grad_v]): |
| 402 | if full_matrices and abs(m - n) > 1: |
| 403 | raise NotImplementedError( |
| 404 | "svd gradient is not implemented for abs(m - n) > 1 " |
nothing calls this directly
no test coverage detected