diff options
author | 2017-05-01 12:30:30 -0800 | |
---|---|---|
committer | 2017-05-01 13:43:54 -0700 | |
commit | 54d78fdb9461111af31dc2c8d08db833a6402e17 (patch) | |
tree | e886d849c1ac681d8f797b092578a23c5002b712 /tensorflow | |
parent | 0388bb0e2d7c4ddeef7c51d1a1eafebfbd8f2ed4 (diff) |
Fixes latex in math ops' documentation.
Change: 154752402
Diffstat (limited to 'tensorflow')
-rw-r--r-- | tensorflow/core/ops/math_ops.cc | 47 | ||||
-rw-r--r-- | tensorflow/python/ops/special_math_ops.py | 15 |
2 files changed, 31 insertions, 31 deletions
diff --git a/tensorflow/core/ops/math_ops.cc b/tensorflow/core/ops/math_ops.cc index aafbd1b5cc..494358fec6 100644 --- a/tensorflow/core/ops/math_ops.cc +++ b/tensorflow/core/ops/math_ops.cc @@ -662,13 +662,12 @@ Compute the upper regularized incomplete Gamma function `Q(a, x)`. The upper regularized incomplete Gamma function is defined as: -``` -Q(a, x) = Gamma(a, x) / Gamma(a) = 1 - P(a, x) -``` +\\(Q(a, x) = Gamma(a, x) / Gamma(a) = 1 - P(a, x)\\) + where -``` -Gamma(a, x) = int_{x}^{\infty} t^{a-1} exp(-t) dt -``` + +\\(Gamma(a, x) = int_{x}^{\infty} t^{a-1} exp(-t) dt\\) + is the upper incomplete Gama function. Note, above `P(a, x)` (`Igamma`) is the lower regularized complete @@ -686,13 +685,13 @@ Compute the lower regularized incomplete Gamma function `Q(a, x)`. The lower regularized incomplete Gamma function is defined as: -``` -P(a, x) = gamma(a, x) / Gamma(a) = 1 - Q(a, x) -``` + +\\(P(a, x) = gamma(a, x) / Gamma(a) = 1 - Q(a, x)\\) + where -``` -gamma(a, x) = int_{0}^{x} t^{a-1} exp(-t) dt -``` + +\\(gamma(a, x) = int_{0}^{x} t^{a-1} exp(-t) dt\\) + is the lower incomplete Gamma function. Note, above `Q(a, x)` (`Igammac`) is the upper regularized complete @@ -710,9 +709,9 @@ Compute the Hurwitz zeta function \\(\zeta(x, q)\\). The Hurwitz zeta function is defined as: -``` -\zeta(x, q) = \sum_{n=0}^{\infty} (q + n)^{-x} -``` + +\\(\zeta(x, q) = \sum_{n=0}^{\infty} (q + n)^{-x}\\) + )doc"); REGISTER_OP("Polygamma") @@ -726,9 +725,9 @@ Compute the polygamma function \\(\psi^{(n)}(x)\\). The polygamma function is defined as: -``` -\psi^{(n)}(x) = \frac{d^n}{dx^n} \psi(x) -``` + +\\(\psi^{(n)}(x) = \frac{d^n}{dx^n} \psi(x)\\) + where \\(\psi(x)\\) is the digamma function. )doc"); @@ -775,14 +774,14 @@ Compute the regularized incomplete beta integral \\(I_x(a, b)\\). The regularized incomplete beta integral is defined as: -``` -I_x(a, b) = \frac{B(x; a, b)}{B(a, b)} -``` + +\\(I_x(a, b) = \frac{B(x; a, b)}{B(a, b)}\\) + where -``` -B(x; a, b) = \int_0^x t^{a-1} (1 - t)^{b-1} dt -``` + +\\(B(x; a, b) = \int_0^x t^{a-1} (1 - t)^{b-1} dt\\) + is the incomplete beta function and \\(B(a, b)\\) is the *complete* beta function. diff --git a/tensorflow/python/ops/special_math_ops.py b/tensorflow/python/ops/special_math_ops.py index e24246464e..851fba0beb 100644 --- a/tensorflow/python/ops/special_math_ops.py +++ b/tensorflow/python/ops/special_math_ops.py @@ -35,19 +35,20 @@ from tensorflow.python.platform import tf_logging as logging # TODO(b/27419586) Change docstring for required dtype of x once int allowed def lbeta(x, name='lbeta'): - r"""Computes `ln(|Beta(x)|)`, reducing along the last dimension. + r"""Computes \\(ln(|Beta(x)|)\\), reducing along the last dimension. Given one-dimensional `z = [z_0,...,z_{K-1}]`, we define - ```Beta(z) = \prod_j Gamma(z_j) / Gamma(\sum_j z_j)``` + $$Beta(z) = \prod_j Gamma(z_j) / Gamma(\sum_j z_j)$$ And for `n + 1` dimensional `x` with shape `[N1, ..., Nn, K]`, we define - `lbeta(x)[i1, ..., in] = Log(|Beta(x[i1, ..., in, :])|)`. In other words, - the last dimension is treated as the `z` vector. + $$lbeta(x)[i1, ..., in] = Log(|Beta(x[i1, ..., in, :])|)$$. + + In other words, the last dimension is treated as the `z` vector. Note that if `z = [u, v]`, then - `Beta(z) = int_0^1 t^{u-1} (1 - t)^{v-1} dt`, which defines the traditional - bivariate beta function. + \\(Beta(z) = int_0^1 t^{u-1} (1 - t)^{v-1} dt\\), which defines the + traditional bivariate beta function. If the last dimension is empty, we follow the convention that the sum over the empty set is zero, and the product is one. @@ -57,7 +58,7 @@ def lbeta(x, name='lbeta'): name: A name for the operation (optional). Returns: - The logarithm of `|Beta(x)|` reducing along the last dimension. + The logarithm of \\(|Beta(x)|\\) reducing along the last dimension. """ # In the event that the last dimension has zero entries, we return -inf. # This is consistent with a convention that the sum over the empty set 0, and |