| Line | Branch | Exec | Source |
|---|---|---|---|
| 1 | !!!############################################################################# | ||
| 2 | !!! Code written by Ned Thaddeus Taylor | ||
| 3 | !!! Code part of the ATHENA library - a feedforward neural network library | ||
| 4 | !!!############################################################################# | ||
| 5 | !!! module contains implementation of the Gaussian activation function | ||
| 6 | !!!############################################################################# | ||
| 7 | module activation_gaussian | ||
| 8 | use constants, only: real12, pi | ||
| 9 | use custom_types, only: activation_type | ||
| 10 | implicit none | ||
| 11 | |||
| 12 | type, extends(activation_type) :: gaussian_type | ||
| 13 | real(real12) :: sigma | ||
| 14 | contains | ||
| 15 | procedure, pass(this) :: activate_1d => gaussian_activate_1d | ||
| 16 | procedure, pass(this) :: activate_2d => gaussian_activate_2d | ||
| 17 | procedure, pass(this) :: activate_3d => gaussian_activate_3d | ||
| 18 | procedure, pass(this) :: activate_4d => gaussian_activate_4d | ||
| 19 | procedure, pass(this) :: activate_5d => gaussian_activate_5d | ||
| 20 | procedure, pass(this) :: differentiate_1d => gaussian_differentiate_1d | ||
| 21 | procedure, pass(this) :: differentiate_2d => gaussian_differentiate_2d | ||
| 22 | procedure, pass(this) :: differentiate_3d => gaussian_differentiate_3d | ||
| 23 | procedure, pass(this) :: differentiate_4d => gaussian_differentiate_4d | ||
| 24 | procedure, pass(this) :: differentiate_5d => gaussian_differentiate_5d | ||
| 25 | end type gaussian_type | ||
| 26 | |||
| 27 | interface gaussian_setup | ||
| 28 | procedure initialise | ||
| 29 | end interface gaussian_setup | ||
| 30 | |||
| 31 | |||
| 32 | private | ||
| 33 | |||
| 34 | public :: gaussian_setup | ||
| 35 | |||
| 36 | |||
| 37 | contains | ||
| 38 | |||
| 39 | !!!############################################################################# | ||
| 40 | !!! initialisation | ||
| 41 | !!!############################################################################# | ||
| 42 | 5 | pure function initialise(threshold, scale, sigma) | |
| 43 | implicit none | ||
| 44 | type(gaussian_type) :: initialise | ||
| 45 | real(real12), optional, intent(in) :: threshold | ||
| 46 | real(real12), optional, intent(in) :: scale | ||
| 47 | real(real12), optional, intent(in) :: sigma | ||
| 48 | |||
| 49 | 5 | initialise%name = "gaussian" | |
| 50 | |||
| 51 |
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5 | if(present(scale))then |
| 52 | 4 | initialise%scale = scale | |
| 53 | else | ||
| 54 | 1 | initialise%scale = 1._real12 | |
| 55 | end if | ||
| 56 | |||
| 57 |
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5 | if(present(sigma))then |
| 58 | 1 | initialise%sigma = sigma | |
| 59 | else | ||
| 60 | 4 | initialise%sigma = 1.5_real12 | |
| 61 | end if | ||
| 62 | |||
| 63 |
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5 | if(present(threshold))then |
| 64 | 1 | initialise%threshold = threshold | |
| 65 | else | ||
| 66 | initialise%threshold = min(huge(1._real12),16._real12) * & | ||
| 67 | 4 | initialise%sigma | |
| 68 | end if | ||
| 69 | |||
| 70 | 5 | end function initialise | |
| 71 | !!!############################################################################# | ||
| 72 | |||
| 73 | |||
| 74 | !!!############################################################################# | ||
| 75 | !!! gaussian transfer function | ||
| 76 | !!! f = 1/(1+exp(-x)) | ||
| 77 | !!!############################################################################# | ||
| 78 |
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2 | pure function gaussian_activate_1d(this, val) result(output) |
| 79 | implicit none | ||
| 80 | class(gaussian_type), intent(in) :: this | ||
| 81 | real(real12), dimension(:), intent(in) :: val | ||
| 82 |
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2 | real(real12), dimension(size(val,dim=1)) :: output |
| 83 | |||
| 84 |
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4 | output = 0._real12 |
| 85 |
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4 | where(abs(val).le.this%threshold) |
| 86 |
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2 | output = this%scale * 1._real12/(sqrt(2*pi)*this%sigma) * & |
| 87 |
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2 | exp(-0.5_real12 * (val/this%sigma)**2._real12) |
| 88 | end where | ||
| 89 |
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2 | end function gaussian_activate_1d |
| 90 | !!!----------------------------------------------------------------------------- | ||
| 91 | !!!----------------------------------------------------------------------------- | ||
| 92 |
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2 | pure function gaussian_activate_2d(this, val) result(output) |
| 93 | implicit none | ||
| 94 | class(gaussian_type), intent(in) :: this | ||
| 95 | real(real12), dimension(:,:), intent(in) :: val | ||
| 96 |
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4 | real(real12), dimension(size(val,1),size(val,2)) :: output |
| 97 | |||
| 98 |
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6 | output = 0._real12 |
| 99 |
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6 | where(abs(val).le.this%threshold) |
| 100 |
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2 | output = this%scale * 1._real12/(sqrt(2*pi)*this%sigma) * & |
| 101 |
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2 | exp(-0.5_real12 * (val/this%sigma)**2._real12) |
| 102 | end where | ||
| 103 |
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4 | end function gaussian_activate_2d |
| 104 | !!!----------------------------------------------------------------------------- | ||
| 105 | !!!----------------------------------------------------------------------------- | ||
| 106 |
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2 | pure function gaussian_activate_3d(this, val) result(output) |
| 107 | implicit none | ||
| 108 | class(gaussian_type), intent(in) :: this | ||
| 109 | real(real12), dimension(:,:,:), intent(in) :: val | ||
| 110 |
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6 | real(real12), dimension(size(val,1),size(val,2),size(val,3)) :: output |
| 111 | |||
| 112 |
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|
8 | output = 0._real12 |
| 113 |
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8 | where(abs(val).le.this%threshold) |
| 114 |
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2 | output = this%scale * 1._real12/(sqrt(2*pi)*this%sigma) * & |
| 115 |
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2 | exp(-0.5_real12 * (val/this%sigma)**2._real12) |
| 116 | end where | ||
| 117 |
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6 | end function gaussian_activate_3d |
| 118 | !!!----------------------------------------------------------------------------- | ||
| 119 | !!!----------------------------------------------------------------------------- | ||
| 120 |
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2 | pure function gaussian_activate_4d(this, val) result(output) |
| 121 | implicit none | ||
| 122 | class(gaussian_type), intent(in) :: this | ||
| 123 | real(real12), dimension(:,:,:,:), intent(in) :: val | ||
| 124 | real(real12), dimension(& | ||
| 125 |
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8 | size(val,1),size(val,2),size(val,3),size(val,4)) :: output |
| 126 | |||
| 127 |
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|
10 | output = 0._real12 |
| 128 |
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10 | where(abs(val).le.this%threshold) |
| 129 |
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|
2 | output = this%scale * 1._real12/(sqrt(2*pi)*this%sigma) * & |
| 130 |
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|
2 | exp(-0.5_real12 * (val/this%sigma)**2._real12) |
| 131 | end where | ||
| 132 |
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|
8 | end function gaussian_activate_4d |
| 133 | !!!----------------------------------------------------------------------------- | ||
| 134 | !!!----------------------------------------------------------------------------- | ||
| 135 |
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2 | pure function gaussian_activate_5d(this, val) result(output) |
| 136 | implicit none | ||
| 137 | class(gaussian_type), intent(in) :: this | ||
| 138 | real(real12), dimension(:,:,:,:,:), intent(in) :: val | ||
| 139 | real(real12), dimension(& | ||
| 140 |
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|
10 | size(val,1),size(val,2),size(val,3),size(val,4),size(val,5)) :: output |
| 141 | |||
| 142 |
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|
12 | output = 0._real12 |
| 143 |
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|
12 | where(abs(val).le.this%threshold) |
| 144 |
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|
2 | output = this%scale * 1._real12/(sqrt(2*pi)*this%sigma) * & |
| 145 |
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|
2 | exp(-0.5_real12 * (val/this%sigma)**2._real12) |
| 146 | end where | ||
| 147 |
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|
10 | end function gaussian_activate_5d |
| 148 | !!!############################################################################# | ||
| 149 | |||
| 150 | |||
| 151 | !!!############################################################################# | ||
| 152 | !!! derivative of gaussian function | ||
| 153 | !!! df/dx = f * (1 - f) | ||
| 154 | !!!############################################################################# | ||
| 155 |
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|
1 | pure function gaussian_differentiate_1d(this, val) result(output) |
| 156 | implicit none | ||
| 157 | class(gaussian_type), intent(in) :: this | ||
| 158 | real(real12), dimension(:), intent(in) :: val | ||
| 159 |
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1 | real(real12), dimension(size(val,dim=1)) :: output |
| 160 | |||
| 161 |
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|
2 | output = -val/this%sigma**2._real12 * this%activate_1d(val) |
| 162 |
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1 | end function gaussian_differentiate_1d |
| 163 | !!!----------------------------------------------------------------------------- | ||
| 164 | !!!----------------------------------------------------------------------------- | ||
| 165 |
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1 | pure function gaussian_differentiate_2d(this, val) result(output) |
| 166 | implicit none | ||
| 167 | class(gaussian_type), intent(in) :: this | ||
| 168 | real(real12), dimension(:,:), intent(in) :: val | ||
| 169 |
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2 | real(real12), dimension(size(val,1),size(val,2)) :: output |
| 170 | |||
| 171 |
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|
3 | output = -val/this%sigma**2._real12 * this%activate_2d(val) |
| 172 |
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2 | end function gaussian_differentiate_2d |
| 173 | !!!----------------------------------------------------------------------------- | ||
| 174 | !!!----------------------------------------------------------------------------- | ||
| 175 |
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1 | pure function gaussian_differentiate_3d(this, val) result(output) |
| 176 | implicit none | ||
| 177 | class(gaussian_type), intent(in) :: this | ||
| 178 | real(real12), dimension(:,:,:), intent(in) :: val | ||
| 179 |
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|
3 | real(real12), dimension(size(val,1),size(val,2),size(val,3)) :: output |
| 180 | |||
| 181 |
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|
4 | output = -val/this%sigma**2._real12 * this%activate_3d(val) |
| 182 |
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|
3 | end function gaussian_differentiate_3d |
| 183 | !!!----------------------------------------------------------------------------- | ||
| 184 | !!!----------------------------------------------------------------------------- | ||
| 185 |
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1 | pure function gaussian_differentiate_4d(this, val) result(output) |
| 186 | implicit none | ||
| 187 | class(gaussian_type), intent(in) :: this | ||
| 188 | real(real12), dimension(:,:,:,:), intent(in) :: val | ||
| 189 | real(real12), dimension(& | ||
| 190 |
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|
4 | size(val,1),size(val,2),size(val,3),size(val,4)) :: output |
| 191 | |||
| 192 |
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|
5 | output = -val/this%sigma**2._real12 * this%activate_4d(val) |
| 193 |
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4 | end function gaussian_differentiate_4d |
| 194 | !!!----------------------------------------------------------------------------- | ||
| 195 | !!!----------------------------------------------------------------------------- | ||
| 196 |
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1 | pure function gaussian_differentiate_5d(this, val) result(output) |
| 197 | implicit none | ||
| 198 | class(gaussian_type), intent(in) :: this | ||
| 199 | real(real12), dimension(:,:,:,:,:), intent(in) :: val | ||
| 200 | real(real12), dimension(& | ||
| 201 |
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|
5 | size(val,1),size(val,2),size(val,3),size(val,4),size(val,5)) :: output |
| 202 | |||
| 203 |
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|
6 | output = -val/this%sigma**2._real12 * this%activate_5d(val) |
| 204 |
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|
5 | end function gaussian_differentiate_5d |
| 205 | !!!############################################################################# | ||
| 206 | |||
| 207 | 12 | end module activation_gaussian | |
| 208 |