diff options
Diffstat (limited to 'tensorflow/core/api_def/base_api/api_def_MatrixSolveLs.pbtxt')
| -rw-r--r-- | tensorflow/core/api_def/base_api/api_def_MatrixSolveLs.pbtxt | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/tensorflow/core/api_def/base_api/api_def_MatrixSolveLs.pbtxt b/tensorflow/core/api_def/base_api/api_def_MatrixSolveLs.pbtxt index 51d91399f8..e667c328ae 100644 --- a/tensorflow/core/api_def/base_api/api_def_MatrixSolveLs.pbtxt +++ b/tensorflow/core/api_def/base_api/api_def_MatrixSolveLs.pbtxt @@ -49,14 +49,14 @@ in the batch: If `fast` is `True`, then the solution is computed by solving the normal equations using Cholesky decomposition. Specifically, if \\(m \ge n\\) then \\(X = (A^H A + \lambda I)^{-1} A^H B\\), which solves the least-squares -problem \\(X = \mathrm{argmin}_{Z \in \Re^{n \times k} } ||A Z - B||_F^2 + -\lambda ||Z||_F^2\\). If \\(m \lt n\\) then `output` is computed as +problem \\(X = \mathrm{argmin}_{Z \in \Re^{n \times k} } ||A Z - B||_F^2 + \lambda ||Z||_F^2\\). +If \\(m \lt n\\) then `output` is computed as \\(X = A^H (A A^H + \lambda I)^{-1} B\\), which (for \\(\lambda = 0\\)) is the minimum-norm solution to the under-determined linear system, i.e. \\(X = \mathrm{argmin}_{Z \in \mathbb{C}^{n \times k} } ||Z||_F^2 \\), subject to \\(A Z = B\\). Notice that the fast path is only numerically stable when \\(A\\) is numerically full rank and has a condition number -\\(\mathrm{cond}(A) \lt \frac{1}{\sqrt{\epsilon_{mach} } }\\) or\\(\lambda\\) is +\\(\mathrm{cond}(A) \lt \frac{1}{\sqrt{\epsilon_{mach} } }\\) or \\(\lambda\\) is sufficiently large. If `fast` is `False` an algorithm based on the numerically robust complete |