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translate the Cephes log_exp functions into pure Rust
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1,57 +1,148 @@ | ||
| /// Expit function, `1/(1 + exp(-x))` | ||
| use num_traits::Float; | ||
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| /// Expit (a.k.a. logistic sigmoid) function, $1 / (1 + e^{-x})$ | ||
| /// | ||
| /// Corresponds to [`scipy.special.expit`][expit]. Translated into pure Rust from xsf. | ||
| /// | ||
| /// [expit]: https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.expit.html | ||
| /// | ||
| /// # See also | ||
| /// - [`logit`] | ||
| #[must_use] | ||
| #[inline] | ||
| pub fn expit(x: f64) -> f64 { | ||
| unsafe { crate::ffi::xsf::expit(x) } | ||
| pub fn expit<T: Float>(x: T) -> T { | ||
| (T::one() + (-x).exp()).recip() | ||
| } | ||
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| /// Relative error exponential, `(exp(x) - 1)/x` | ||
| /// Relative error exponential, $(e^x - 1) / x$ | ||
| /// | ||
| /// Corresponds to [`scipy.special.exprel`][exprel]. Translated into pure Rust from xsf. | ||
| /// | ||
| /// [exprel]: https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.exprel.html | ||
| /// | ||
| /// # See also | ||
| /// - [`expm1`](crate::expm1) | ||
| #[must_use] | ||
| #[inline] | ||
| pub fn exprel(x: f64) -> f64 { | ||
| unsafe { crate::ffi::xsf::exprel(x) } | ||
| pub fn exprel<T: Float>(x: T) -> T { | ||
| if x.abs() < T::epsilon() { | ||
| T::one() | ||
| } else { | ||
| x.exp_m1() / x | ||
| } | ||
| } | ||
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| /// Logit function, `log(x / (1 - x))` | ||
| /// Logit function, $\ln(x / (1 - x))$ | ||
| /// | ||
| /// Corresponds to [`scipy.special.logit`][logit]. Translated into pure Rust from xsf. | ||
| /// | ||
| /// [logit]: https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.logit.html | ||
| /// | ||
| /// # See also | ||
| /// - [`expit`] | ||
| #[must_use] | ||
| #[inline] | ||
| pub fn logit(x: f64) -> f64 { | ||
| unsafe { crate::ffi::xsf::logit(x) } | ||
| #[allow(clippy::missing_panics_doc)] | ||
| pub fn logit<T: Float>(x: T) -> T { | ||
| // The standard formula is log(x/(1 - x)), but this expression | ||
| // loses precision near x=0.5, as does log(x) - log1p(-x). | ||
| // We use the standard formula away from p=0.5, and use | ||
| // log1p(2*(x - 0.5)) - log1p(-2*(x - 0.5)) around p=0.5, which | ||
| // provides very good precision in this interval. | ||
| let a = T::from(0.3).unwrap(); | ||
| let b = T::from(0.65).unwrap(); | ||
| if a <= x && x <= b { | ||
| let s = x + x - T::one(); | ||
| s.ln_1p() - (-s).ln_1p() | ||
| } else { | ||
| (x / (T::one() - x)).ln() | ||
| } | ||
| } | ||
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| /// Log of the expit function, `log(expit(x))` | ||
| /// Natural logarithm of [`expit`] | ||
| /// | ||
| /// Corresponds to [`scipy.special.log_expit`][log_expit]. Translated into pure Rust from xsf. | ||
| /// | ||
| /// [log_expit]: https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.log_expit.html | ||
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| #[must_use] | ||
| #[inline] | ||
| pub fn log_expit(x: f64) -> f64 { | ||
| unsafe { crate::ffi::xsf::log_expit(x) } | ||
| pub fn log_expit<T: Float>(x: T) -> T { | ||
| if x.is_sign_negative() { | ||
| x - x.exp().ln_1p() | ||
| } else { | ||
| -(-x).exp().ln_1p() | ||
| } | ||
| } | ||
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| /// Compute `log(1 - exp(x))` | ||
| /// Compute $\ln(1 - e^x)$ | ||
| /// | ||
| /// Translated into pure Rust from xsf. | ||
| /// This function has no analogue in `scipy.special`. | ||
| /// | ||
| /// # See also | ||
| /// - [`expm1`](crate::expm1) | ||
| #[must_use] | ||
| #[inline] | ||
| pub fn log1mexp(x: f64) -> f64 { | ||
| unsafe { crate::ffi::xsf::log1mexp(x) } | ||
| pub fn log1mexp<T: Float>(x: T) -> T { | ||
| if x > T::zero() { | ||
| T::nan() | ||
| } else if x.is_zero() { | ||
| T::neg_infinity() | ||
| } else if x < -T::one() { | ||
| (-x.exp()).ln_1p() | ||
| } else { | ||
| (-x.exp_m1()).ln() | ||
| } | ||
| } | ||
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| #[cfg(test)] | ||
| #[allow(clippy::cast_possible_truncation)] | ||
| mod tests { | ||
| use crate::np_assert_allclose; | ||
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| #[test] | ||
| fn test_expit() { | ||
| fn test_expit_f32() { | ||
| xsref::test("expit", "f-f", |x| crate::expit(x[0] as f32)); | ||
| } | ||
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| #[test] | ||
| fn test_expit_f64() { | ||
| xsref::test("expit", "d-d", |x| crate::expit(x[0])); | ||
| } | ||
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| #[test] | ||
| fn test_exprel() { | ||
| xsref::test("exprel", "d-d", |x| crate::exprel(x[0])); | ||
| fn test_logit_f32() { | ||
| xsref::test("logit", "f-f", |x| crate::logit(x[0] as f32)); | ||
| } | ||
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| #[test] | ||
| fn test_logit() { | ||
| fn test_logit_f64() { | ||
| xsref::test("logit", "d-d", |x| crate::logit(x[0])); | ||
| } | ||
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| #[test] | ||
| fn test_log_expit() { | ||
| fn test_log_expit_f32() { | ||
| xsref::test("log_expit", "f-f", |x| crate::log_expit(x[0] as f32)); | ||
| } | ||
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| #[test] | ||
| fn test_log_expit_f64() { | ||
| xsref::test("log_expit", "d-d", |x| crate::log_expit(x[0])); | ||
| } | ||
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| #[test] | ||
| fn test_exprel() { | ||
| xsref::test("exprel", "d-d", |x| crate::exprel(x[0])); | ||
| } | ||
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| #[test] | ||
| fn test_log1mexp() { | ||
| let xs: [f64; 5] = [-20.0, -5.0, -1.5, -1.0, -0.75]; | ||
| let expected = xs.map(|x| (-x.exp_m1()).ln()); | ||
| np_assert_allclose!(xs.map(crate::log1mexp), expected, atol = 1e-15); | ||
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| assert!(crate::log1mexp(0.5_f64).is_nan()); | ||
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| let zero_limit = crate::log1mexp(0.0_f64); | ||
| assert!(zero_limit.is_infinite() && zero_limit.is_sign_negative()); | ||
| } | ||
| } | ||
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