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Update ops-related pbtxt files.
PiperOrigin-RevId: 165747467
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TensorFlower Gardener
parent
64e54423bb
commit
57b0276cf9
@@ -12978,6 +12978,44 @@ op {
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}
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}
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}
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op {
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name: "MatrixSolveLs"
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input_arg {
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name: "matrix"
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type_attr: "T"
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}
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input_arg {
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name: "rhs"
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type_attr: "T"
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}
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input_arg {
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name: "l2_regularizer"
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type: DT_DOUBLE
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}
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output_arg {
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name: "output"
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type_attr: "T"
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}
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attr {
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name: "T"
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type: "type"
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allowed_values {
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list {
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type: DT_DOUBLE
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type: DT_FLOAT
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type: DT_COMPLEX64
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type: DT_COMPLEX128
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}
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}
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}
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attr {
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name: "fast"
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type: "bool"
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default_value {
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b: true
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}
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}
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}
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op {
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name: "MatrixTriangularSolve"
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input_arg {
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@@ -12296,6 +12296,8 @@ op {
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list {
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type: DT_DOUBLE
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type: DT_FLOAT
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type: DT_COMPLEX64
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type: DT_COMPLEX128
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}
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}
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}
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@@ -12307,7 +12309,7 @@ op {
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}
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}
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summary: "Solves one or more linear least-squares problems."
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description: "`matrix` is a tensor of shape `[..., M, N]` whose inner-most 2 dimensions\nform matrices of size `[M, N]`. Rhs is a tensor of shape `[..., M, K]`.\nThe output is a tensor shape `[..., N, K]` where each output matrix solves\neach of the equations matrix[..., :, :] * output[..., :, :] = rhs[..., :, :]\nin the least squares sense.\n\nmatrix and right-hand sides in the batch:\n\n`matrix`=\\\\(A \\in \\Re^{m \\times n}\\\\),\n`rhs`=\\\\(B \\in \\Re^{m \\times k}\\\\),\n`output`=\\\\(X \\in \\Re^{n \\times k}\\\\),\n`l2_regularizer`=\\\\(\\lambda\\\\).\n\nIf `fast` is `True`, then the solution is computed by solving the normal\nequations using Cholesky decomposition. Specifically, if \\\\(m \\ge n\\\\) then\n\\\\(X = (A^T A + \\lambda I)^{-1} A^T B\\\\), which solves the least-squares\nproblem \\\\(X = \\mathrm{argmin}_{Z \\in \\Re^{n \\times k} } ||A Z - B||_F^2 +\n\\lambda ||Z||_F^2\\\\). If \\\\(m \\lt n\\\\) then `output` is computed as\n\\\\(X = A^T (A A^T + \\lambda I)^{-1} B\\\\), which (for \\\\(\\lambda = 0\\\\)) is the\nminimum-norm solution to the under-determined linear system, i.e.\n\\\\(X = \\mathrm{argmin}_{Z \\in \\Re^{n \\times k} } ||Z||_F^2 \\\\), subject to\n\\\\(A Z = B\\\\). Notice that the fast path is only numerically stable when\n\\\\(A\\\\) is numerically full rank and has a condition number\n\\\\(\\mathrm{cond}(A) \\lt \\frac{1}{\\sqrt{\\epsilon_{mach} } }\\\\) or\\\\(\\lambda\\\\) is\nsufficiently large.\n\nIf `fast` is `False` an algorithm based on the numerically robust complete\northogonal decomposition is used. This computes the minimum-norm\nleast-squares solution, even when \\\\(A\\\\) is rank deficient. This path is\ntypically 6-7 times slower than the fast path. If `fast` is `False` then\n`l2_regularizer` is ignored."
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description: "`matrix` is a tensor of shape `[..., M, N]` whose inner-most 2 dimensions\nform real or complex matrices of size `[M, N]`. `Rhs` is a tensor of the same\ntype as `matrix` and shape `[..., M, K]`.\nThe output is a tensor shape `[..., N, K]` where each output matrix solves\neach of the equations\n`matrix[..., :, :]` * `output[..., :, :]` = `rhs[..., :, :]`\nin the least squares sense.\n\nWe use the following notation for (complex) matrix and right-hand sides\nin the batch:\n\n`matrix`=\\\\(A \\in \\mathbb{C}^{m \\times n}\\\\),\n`rhs`=\\\\(B \\in \\mathbb{C}^{m \\times k}\\\\),\n`output`=\\\\(X \\in \\mathbb{C}^{n \\times k}\\\\),\n`l2_regularizer`=\\\\(\\lambda \\in \\mathbb{R}\\\\).\n\nIf `fast` is `True`, then the solution is computed by solving the normal\nequations using Cholesky decomposition. Specifically, if \\\\(m \\ge n\\\\) then\n\\\\(X = (A^H A + \\lambda I)^{-1} A^H B\\\\), which solves the least-squares\nproblem \\\\(X = \\mathrm{argmin}_{Z \\in \\Re^{n \\times k} } ||A Z - B||_F^2 +\n\\lambda ||Z||_F^2\\\\). If \\\\(m \\lt n\\\\) then `output` is computed as\n\\\\(X = A^H (A A^H + \\lambda I)^{-1} B\\\\), which (for \\\\(\\lambda = 0\\\\)) is the\nminimum-norm solution to the under-determined linear system, i.e.\n\\\\(X = \\mathrm{argmin}_{Z \\in \\mathbb{C}^{n \\times k} } ||Z||_F^2 \\\\),\nsubject to \\\\(A Z = B\\\\). Notice that the fast path is only numerically stable\nwhen \\\\(A\\\\) is numerically full rank and has a condition number\n\\\\(\\mathrm{cond}(A) \\lt \\frac{1}{\\sqrt{\\epsilon_{mach} } }\\\\) or\\\\(\\lambda\\\\) is\nsufficiently large.\n\nIf `fast` is `False` an algorithm based on the numerically robust complete\northogonal decomposition is used. This computes the minimum-norm\nleast-squares solution, even when \\\\(A\\\\) is rank deficient. This path is\ntypically 6-7 times slower than the fast path. If `fast` is `False` then\n`l2_regularizer` is ignored."
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}
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op {
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name: "MatrixTriangularSolve"
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