Module elemwise_unary 

Structs

ElemwiseAbsBackward

Backward: dx = sign(x) * dy where sign = 1 if x>0, -1 if x<0, 0 if x==0

ElemwiseAbsForward

Forward: y = |x|

ElemwiseAcosBackward

Backward: dx = -dy / sqrt(1 - x^2)

ElemwiseAcosForward

Forward: y = acos(x) = pi/2 - atan(x / sqrt(1 - x^2))

ElemwiseAcoshBackward

Backward: dx = dy / sqrt(x^2 - 1)

ElemwiseAcoshForward

Forward: y = acosh(x) = log(x + sqrt(x^2 - 1))

ElemwiseAsinBackward

Backward: dx = dy / sqrt(1 - x^2)

ElemwiseAsinForward

Forward: y = asin(x) = atan(x / sqrt(1 - x^2))

ElemwiseAsinhBackward

Backward: dx = dy / sqrt(x^2 + 1)

ElemwiseAsinhForward

Forward: y = asinh(x) = log(x + sqrt(x^2 + 1))

ElemwiseAtanBackward

Backward: dx = dy / (1 + x^2)

ElemwiseAtanForward

Forward: y = atan(x)

ElemwiseAtanhBackward

Backward: dx = dy / (1 - x^2)

ElemwiseAtanhForward

Forward: y = atanh(x) = log((1+x)/(1-x)) / 2

ElemwiseCeilForward

Forward: y = ceil(x)

ElemwiseCosBackward

Backward: dx = -sin(x) * dy

ElemwiseCosForward

Forward: y = cos(x)

ElemwiseCoshBackward

Backward: dx = sinh(x) * dy

ElemwiseCoshForward

Forward: y = cosh(x) = (exp(x) + exp(-x)) / 2

ElemwiseErfBackward

Backward: dx = 2/sqrt(pi) * exp(-x^2) * dy where 2/sqrt(pi) ~= 1.1283791670955126

ElemwiseErfForward

Forward: y = erf(x)

ElemwiseExpBackward

Backward: dx = exp(x) * dy

ElemwiseExpForward

Forward: y = exp(x)

ElemwiseFloorForward

Forward: y = floor(x)

ElemwiseIsnanForward

Forward: y = 1.0 if x is NaN else 0.0

ElemwiseLogBackward

Backward: dx = dy / x

ElemwiseLogForward

Forward: y = log(x)

ElemwiseNegBackward

Backward: dx = -dy

ElemwiseNegForward

Forward: y = -x

ElemwiseReciprocalBackward

Backward: dx = -dy / x^2

ElemwiseReciprocalForward

Forward: y = 1 / x

ElemwiseSignForward

Forward: y = 1 if x > 0, -1 if x < 0, 0 if x == 0

ElemwiseSinBackward

Backward: dx = cos(x) * dy

ElemwiseSinForward

Forward: y = sin(x)

ElemwiseSinhBackward

Backward: dx = cosh(x) * dy

ElemwiseSinhForward

Forward: y = sinh(x) = (exp(x) - exp(-x)) / 2

ElemwiseSqrtBackward

Backward: dx = dy / (2 * sqrt(x))

ElemwiseSqrtForward

Forward: y = sqrt(x)

ElemwiseTanBackward

Backward: dx = (1 + tan^2(x)) * dy

ElemwiseTanForward

Forward: y = tan(x) = sin(x) / cos(x)

Functions

elemwise_abs_backward

Backward: dx = sign(x) * dy where sign = 1 if x>0, -1 if x<0, 0 if x==0

elemwise_abs_forward

Forward: y = |x|

elemwise_acos_backward

Backward: dx = -dy / sqrt(1 - x^2)

elemwise_acos_forward

Forward: y = acos(x) = pi/2 - atan(x / sqrt(1 - x^2))

elemwise_acosh_backward

Backward: dx = dy / sqrt(x^2 - 1)

elemwise_acosh_forward

Forward: y = acosh(x) = log(x + sqrt(x^2 - 1))

elemwise_asin_backward

Backward: dx = dy / sqrt(1 - x^2)

elemwise_asin_forward

Forward: y = asin(x) = atan(x / sqrt(1 - x^2))

elemwise_asinh_backward

Backward: dx = dy / sqrt(x^2 + 1)

elemwise_asinh_forward

Forward: y = asinh(x) = log(x + sqrt(x^2 + 1))

elemwise_atan_backward

Backward: dx = dy / (1 + x^2)

elemwise_atan_forward

Forward: y = atan(x)

elemwise_atanh_backward

Backward: dx = dy / (1 - x^2)

elemwise_atanh_forward

Forward: y = atanh(x) = log((1+x)/(1-x)) / 2

elemwise_ceil_forward

Forward: y = ceil(x)

elemwise_cos_backward

Backward: dx = -sin(x) * dy

elemwise_cos_forward

Forward: y = cos(x)

elemwise_cosh_backward

Backward: dx = sinh(x) * dy

elemwise_cosh_forward

Forward: y = cosh(x) = (exp(x) + exp(-x)) / 2

elemwise_erf_backward

Backward: dx = 2/sqrt(pi) * exp(-x^2) * dy where 2/sqrt(pi) ~= 1.1283791670955126

elemwise_erf_forward

Forward: y = erf(x)

elemwise_exp_backward

Backward: dx = exp(x) * dy

elemwise_exp_forward

Forward: y = exp(x)

elemwise_floor_forward

Forward: y = floor(x)

elemwise_isnan_forward

Forward: y = 1.0 if x is NaN else 0.0

elemwise_log_backward

Backward: dx = dy / x

elemwise_log_forward

Forward: y = log(x)

elemwise_neg_backward

Backward: dx = -dy

elemwise_neg_forward

Forward: y = -x

elemwise_reciprocal_backward

Backward: dx = -dy / x^2

elemwise_reciprocal_forward

Forward: y = 1 / x

elemwise_sign_forward

Forward: y = 1 if x > 0, -1 if x < 0, 0 if x == 0

elemwise_sin_backward

Backward: dx = cos(x) * dy

elemwise_sin_forward

Forward: y = sin(x)

elemwise_sinh_backward

Backward: dx = cosh(x) * dy

elemwise_sinh_forward

Forward: y = sinh(x) = (exp(x) - exp(-x)) / 2

elemwise_sqrt_backward

Backward: dx = dy / (2 * sqrt(x))

elemwise_sqrt_forward

Forward: y = sqrt(x)

elemwise_tan_backward

Backward: dx = (1 + tan^2(x)) * dy

elemwise_tan_forward

Forward: y = tan(x) = sin(x) / cos(x)