#:include "common.fypp"
#:set RANKS = range(2, MAXRANK + 1)
module stdlib_specialfunctions
use stdlib_kinds, only: int8, int16, int32, int64, sp, dp, xdp, qp
implicit none
private
interface legendre
!! version: experimental
!!
!! Legendre polynomial
pure elemental module function legendre_fp64(n,x) result(leg)
integer, intent(in) :: n
real(dp), intent(in) :: x
real(dp) :: leg
end function
end interface
public :: legendre
interface dlegendre
!! version: experimental
!!
!! First derivative Legendre polynomial
pure elemental module function dlegendre_fp64(n,x) result(dleg)
integer, intent(in) :: n
real(dp), intent(in) :: x
real(dp) :: dleg
end function
end interface
public :: dlegendre
interface gaussian
!! Version: experimental
!!
!! gaussian function
!> ([Specification](../page/specs/stdlib_specialfunctions.html#gaussian))
#:for rk, rt in REAL_KINDS_TYPES
elemental module function gaussian_${rk}$( x ) result( y )
${rt}$, intent(in) :: x
${rt}$ :: y
end function
#:endfor
end interface
public :: gaussian
interface gaussian_grad
!! Version: experimental
!!
!! gradient of the gaussian function
!> ([Specification](../page/specs/stdlib_specialfunctions.html#gaussian_grad))
#:for rk, rt in REAL_KINDS_TYPES
elemental module function gaussian_grad_${rk}$( x ) result( y )
${rt}$, intent(in) :: x
${rt}$ :: y
end function
#:endfor
end interface
public :: gaussian_grad
interface elu
!! Version: experimental
!!
!! exponential linear unit function
!> ([Specification](../page/specs/stdlib_specialfunctions.html#elu))
#:for rk, rt in REAL_KINDS_TYPES
elemental module function elu_${rk}$( x , a ) result( y )
${rt}$, intent(in) :: x
${rt}$, intent(in) :: a
${rt}$ :: y
end function
#:endfor
end interface
public :: elu
interface elu_grad
!! Version: experimental
!!
!! gradient of the exponential linear unit function
!> ([Specification](../page/specs/stdlib_specialfunctions.html#elu_grad))
#:for rk, rt in REAL_KINDS_TYPES
elemental module function elu_grad_${rk}$( x , a ) result( y )
${rt}$, intent(in) :: x
${rt}$, intent(in) :: a
${rt}$ :: y
end function
#:endfor
end interface
public :: elu_grad
interface relu
!! Version: experimental
!!
!! Rectified linear unit function
!> ([Specification](../page/specs/stdlib_specialfunctions.html#relu))
#:for rk, rt in REAL_KINDS_TYPES
elemental module function relu_${rk}$( x ) result( y )
${rt}$, intent(in) :: x
${rt}$ :: y
end function
#:endfor
end interface
public :: relu
interface relu_grad
!! Version: experimental
!!
!! Gradient rectified linear unit function
!> ([Specification](../page/specs/stdlib_specialfunctions.html#relu_grad))
#:for rk, rt in REAL_KINDS_TYPES
elemental module function relu_grad_${rk}$( x ) result( y )
${rt}$, intent(in) :: x
${rt}$ :: y
end function
#:endfor
end interface
public :: relu_grad
interface leaky_relu
!! Version: experimental
!!
!! leaky Rectified linear unit function
!> ([Specification](../page/specs/stdlib_specialfunctions.html#leaky_relu))
#:for rk, rt in REAL_KINDS_TYPES
elemental module function leaky_relu_${rk}$( x , a ) result( y )
${rt}$, intent(in) :: x
${rt}$, intent(in) :: a
${rt}$ :: y
end function
#:endfor
end interface
public :: leaky_relu
interface leaky_relu_grad
!! Version: experimental
!!
!! Gradient of the leaky Rectified linear unit function
!> ([Specification](../page/specs/stdlib_specialfunctions.html#leaky_relu_grad))
#:for rk, rt in REAL_KINDS_TYPES
elemental module function leaky_relu_grad_${rk}$( x , a ) result( y )
${rt}$, intent(in) :: x
${rt}$, intent(in) :: a
${rt}$ :: y
end function
#:endfor
end interface
public :: leaky_relu_grad
interface gelu
!! Version: experimental
!!
!! Gaussian error linear unit function
!> ([Specification](../page/specs/stdlib_specialfunctions.html#gelu))
#:for rk, rt in REAL_KINDS_TYPES
elemental module function gelu_${rk}$( x ) result( y )
${rt}$, intent(in) :: x
${rt}$ :: y
end function
#:endfor
end interface
public :: gelu
interface gelu_grad
!! Version: experimental
!!
!! Gradient of the gaussian error linear unit function
!> ([Specification](../page/specs/stdlib_specialfunctions.html#gelu_grad))
#:for rk, rt in REAL_KINDS_TYPES
elemental module function gelu_grad_${rk}$( x ) result( y )
${rt}$, intent(in) :: x
${rt}$ :: y
end function
#:endfor
end interface
public :: gelu_grad
interface gelu_approx
!! Version: experimental
!!
!! Approximated gaussian error linear unit function
!> ([Specification](../page/specs/stdlib_specialfunctions.html#gelu_approx))
#:for rk, rt in REAL_KINDS_TYPES
elemental module function gelu_approx_${rk}$( x ) result( y )
${rt}$, intent(in) :: x
${rt}$ :: y
end function
#:endfor
end interface
public :: gelu_approx
interface gelu_approx_grad
!! Version: experimental
!!
!! Gradient of the approximated gaussian error linear unit function
!> ([Specification](../page/specs/stdlib_specialfunctions.html#gelu_approx_grad))
#:for rk, rt in REAL_KINDS_TYPES
elemental module function gelu_approx_grad_${rk}$( x ) result( y )
${rt}$, intent(in) :: x
${rt}$ :: y
end function
#:endfor
end interface
public :: gelu_approx_grad
interface selu
!! Version: experimental
!!
!! Scaled Exponential Linear Unit
!> ([Specification](../page/specs/stdlib_specialfunctions.html#selu))
#:for rk, rt in REAL_KINDS_TYPES
elemental module function selu_${rk}$( x ) result( y )
${rt}$, intent(in) :: x
${rt}$ :: y
end function
#:endfor
end interface
public :: selu
interface selu_grad
!! Version: experimental
!!
!! Scaled Exponential Linear Unit
!> ([Specification](../page/specs/stdlib_specialfunctions.html#selu_grad))
#:for rk, rt in REAL_KINDS_TYPES
elemental module function selu_grad_${rk}$( x ) result( y )
${rt}$, intent(in) :: x
${rt}$ :: y
end function
#:endfor
end interface
public :: selu_grad
interface sigmoid
!! Version: experimental
!!
!! Sigmoid function
!> ([Specification](../page/specs/stdlib_specialfunctions.html#sigmoid))
#:for rk, rt in REAL_KINDS_TYPES
elemental module function sigmoid_${rk}$( x ) result( y )
${rt}$, intent(in) :: x
${rt}$ :: y
end function
#:endfor
end interface
public :: sigmoid
interface sigmoid_grad
!! Version: experimental
!!
!! Gradient of the sigmoid function
!> ([Specification](../page/specs/stdlib_specialfunctions.html#sigmoid_grad))
#:for rk, rt in REAL_KINDS_TYPES
elemental module function sigmoid_grad_${rk}$( x ) result( y )
${rt}$, intent(in) :: x
${rt}$ :: y
end function
#:endfor
end interface
public :: sigmoid_grad
interface silu
!! Version: experimental
!!
!! Sigmoid Linear Unit function
!> ([Specification](../page/specs/stdlib_specialfunctions.html#silu))
#:for rk, rt in REAL_KINDS_TYPES
elemental module function silu_${rk}$( x ) result( y )
${rt}$, intent(in) :: x
${rt}$ :: y
end function
#:endfor
end interface
public :: silu
interface silu_grad
!! Version: experimental
!!
!! Gradient of the Sigmoid Linear Unit function
!> ([Specification](../page/specs/stdlib_specialfunctions.html#silu_grad))
#:for rk, rt in REAL_KINDS_TYPES
elemental module function silu_grad_${rk}$( x ) result( y )
${rt}$, intent(in) :: x
${rt}$ :: y
end function
#:endfor
end interface
public :: silu_grad
interface step
!! Version: experimental
!!
!! Step function
!> ([Specification](../page/specs/stdlib_specialfunctions.html#step))
#:for rk, rt in REAL_KINDS_TYPES
elemental module function step_${rk}$( x ) result( y )
${rt}$, intent(in) :: x
${rt}$ :: y
end function
#:endfor
end interface
public :: step
interface step_grad
!! Version: experimental
!!
!! Gradient of the step function
!> ([Specification](../page/specs/stdlib_specialfunctions.html#step_grad))
#:for rk, rt in REAL_KINDS_TYPES
elemental module function step_grad_${rk}$( x ) result( y )
${rt}$, intent(in) :: x
${rt}$ :: y
end function
#:endfor
end interface
public :: step_grad
interface softmax
!! Version: experimental
!!
!! softmax function. Available for ranks 1 to 4
!> ([Specification](../page/specs/stdlib_specialfunctions.html#softmax))
#:for rk, rt in REAL_KINDS_TYPES
pure module function softmax_r1_${rk}$( x ) result( y )
${rt}$, intent(in) :: x(:)
${rt}$ :: y(size(x))
end function
#:for rank in RANKS
pure module function softmax_r${rank}$_${rk}$( x , dim ) result( y )
${rt}$, intent(in) :: x${ranksuffix(rank)}$
${rt}$ :: y${shape_from_array_size('x', rank)}$
integer, intent(in), optional :: dim
end function
#:endfor
#:endfor
end interface
public :: softmax
interface softmax_grad
!! Version: experimental
!!
!! Gradient of the softmax function. Available for ranks 1 to 4
!> ([Specification](../page/specs/stdlib_specialfunctions.html#softmax_grad))
#:for rk, rt in REAL_KINDS_TYPES
pure module function softmax_grad_r1_${rk}$( x ) result( y )
${rt}$, intent(in) :: x(:)
${rt}$ :: y(size(x))
end function
#:for rank in RANKS
pure module function softmax_grad_r${rank}$_${rk}$( x , dim ) result( y )
${rt}$, intent(in) :: x${ranksuffix(rank)}$
${rt}$ :: y${shape_from_array_size('x', rank)}$
integer, intent(in), optional :: dim
end function
#:endfor
#:endfor
end interface
public :: softmax_grad
interface logsoftmax
!! Version: experimental
!!
!! softmax function. Available for ranks 1 to 4
!> ([Specification](../page/specs/stdlib_specialfunctions.html#logsoftmax))
#:for rk, rt in REAL_KINDS_TYPES
pure module function logsoftmax_r1_${rk}$( x ) result( y )
${rt}$, intent(in) :: x(:)
${rt}$ :: y(size(x))
end function
#:for rank in RANKS
pure module function logsoftmax_r${rank}$_${rk}$( x , dim ) result( y )
${rt}$, intent(in) :: x${ranksuffix(rank)}$
${rt}$ :: y${shape_from_array_size('x', rank)}$
integer, intent(in), optional :: dim
end function
#:endfor
#:endfor
end interface
public :: logsoftmax
interface softplus
!! Version: experimental
!!
!! softplus function
!> ([Specification](../page/specs/stdlib_specialfunctions.html#softplus))
#:for rk, rt in REAL_KINDS_TYPES
elemental module function softplus_${rk}$( x ) result( y )
${rt}$, intent(in) :: x
${rt}$ :: y
end function
#:endfor
end interface
public :: softplus
interface softplus_grad
!! Version: experimental
!!
!! Gradient of the softplus function
!> ([Specification](../page/specs/stdlib_specialfunctions.html#softplus_grad))
#:for rk, rt in REAL_KINDS_TYPES
elemental module function softplus_grad_${rk}$( x ) result( y )
${rt}$, intent(in) :: x
${rt}$ :: y
end function
#:endfor
end interface
public :: softplus_grad
interface fast_tanh
!! Version: experimental
!!
!! Fast approximation of the tanh function
#:for rk, rt in REAL_KINDS_TYPES
elemental module function fast_tanh_${rk}$( x ) result( y )
${rt}$, intent(in) :: x
${rt}$ :: y
end function
#:endfor
end interface
public :: fast_tanh
interface fast_tanh_grad
!! Version: experimental
!!
!! gradient of the hyperbolic tangent function
#:for rk, rt in REAL_KINDS_TYPES
elemental module function fast_tanh_grad_${rk}$( x ) result( y )
${rt}$, intent(in) :: x
${rt}$ :: y
end function
#:endfor
end interface
public :: fast_tanh_grad
interface fast_erf
!! Version: experimental
!!
!! Fast approximation of the erf function
#:for rk, rt in REAL_KINDS_TYPES
elemental module function fast_erf_${rk}$( x ) result( y )
${rt}$, intent(in) :: x
${rt}$ :: y
end function
#:endfor
end interface
public :: fast_erf
end module stdlib_specialfunctions
