Elementary Transcentental Functions¶
These types of activation functions where highly explored by Taehwan Kim and Tulay Adali, mainly in [CIT2001-KIM] and [CIT2003-KIM]. Please refer to them for further information. These functions are divided into 4 groups.
- Circular
- Inverse Circular
- Hyperbolic
- Inverse Hyperbolic
Circular¶
-
etf_circular_tan(z):
Computes tan of z element-wise.
\[tan(z) = \frac{e^{iz} - e^{-iz}}{i(e^{iz} + e^{-iz})}\]Parameters: z – A Tensor. Must be one of the following types: bfloat16, half, float32, float64, int8, int16, int32, int64, complex64, complex128.
-
etf_circular_sin(z):
Computes sine of z element-wise.
\[sin(z) = \frac{e^{iz} - e^{-iz}}{2i}\]Parameters: z – A Tensor. Must be one of the following types: bfloat16, half, float32, float64, int8, int16, int32, int64, complex64, complex128.
Inverse Circular¶
-
etf_inv_circular_atan(z):
Computes the trignometric inverse tangent of z element-wise.
\[atan(z) = \int_{0}^{z} \frac{dt}{1+t^2}\]Parameters: z – A Tensor. Must be one of the following types: bfloat16, half, float32, float64, int8, int16, int32, int64, complex64, complex128.
-
etf_inv_circular_asin(z):
Computes the trignometric inverse sine of z element-wise.
\[asin(z) = \int_{0}^{z} \frac{dt}{(1-t)^1/2}\]Parameters: z – A Tensor. Must be one of the following types: bfloat16, half, float32, float64, int8, int16, int32, int64, complex64, complex128.
-
etf_inv_circular_acos(z):
Computes acos of z element-wise.
\[acos(z) = \int_{z}^{1} \frac{dt}{(1-t^2)^1/2}\]Parameters: z – A Tensor. Must be one of the following types: bfloat16, half, float32, float64, int8, int16, int32, int64, complex64, complex128.
Hyperbolic¶
-
etf_circular_tanh(z):
Computes hyperbolic tangent of z element-wise.
\[tanh(z) = \frac{sinh(z)}{cosh(z)} = \frac{e^{z} - e^{-z}}{e^{z} + e^{-z}}\]Parameters: z – A Tensor. Must be one of the following types: bfloat16, half, float32, float64, int8, int16, int32, int64, complex64, complex128.
-
etf_circular_sinh(z):
Computes hyperbolic sine of z element-wise.
\[sinh(z) = \frac{e^{z} - e^{-z}}{2}\]Parameters: z – A Tensor. Must be one of the following types: bfloat16, half, float32, float64, int8, int16, int32, int64, complex64, complex128.
Inverse Hyperbolic¶
-
etf_inv_circular_atanh(z):
Computes inverse hyperbolic tangent of z element-wise.
\[atanh(z) = \int_{0}^{z} \frac{dt}{1-t^2}\]Parameters: z – A Tensor. Must be one of the following types: bfloat16, half, float32, float64, int8, int16, int32, int64, complex64, complex128.
-
etf_inv_circular_asinh(z):
Computes inverse hyperbolic sine of z element-wise.
\[asinh(z) = \int_{0}^{z} \frac{dt}{(1+t^2)^1/2}\]Parameters: z – A Tensor. Must be one of the following types: bfloat16, half, float32, float64, int8, int16, int32, int64, complex64, complex128.
[CIT2001-KIM] |
|
[CIT2003-KIM] |
|