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December 2, 2022 05:05
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Commonly used functions
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| ################################## | |
| ### Commonly-used functions | |
| ################################## | |
| """ | |
| Regular Hill function | |
| """ | |
| hill(x, k=one(x)) = x / (x + k) | |
| hill(x, k, n) = hill(x^n, k^n) | |
| """ | |
| Repressive Hill function | |
| """ | |
| hillr(x, k=one(x)) = hill(k, x) | |
| hillr(x, k, n) = hill(k, x, n) | |
| """ | |
| expit(x) | |
| Logistic sigmoid function. `expit(x) = 1 / (1 + exp(-x))` | |
| """ | |
| expit(x) = hillr(exp(-x)) | |
| """ | |
| exprel(x, em1 = expm1(x)) | |
| Returns `x / (exp(x)-1)` | |
| """ | |
| exprel(x, em1=expm1(x)) = x / em1 | |
| """ | |
| Signed sqare root | |
| """ | |
| sqrt_s(x) = sign(x) * sqrt(abs(x)) | |
| """ | |
| Signed power | |
| """ | |
| pow_s(x, n) = sign(x) * (abs(x)^n) | |
| """ | |
| Signed Hill function | |
| """ | |
| hill_s(x, k, n) = hill(pow_s(x, n), pow_s(k, n)) |
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