diff --git a/argmin_testfunctions/all.html b/argmin_testfunctions/all.html index 386927806..0b0afcbba 100644 --- a/argmin_testfunctions/all.html +++ b/argmin_testfunctions/all.html @@ -1 +1 @@ -List of all items in this crate

List of all items

Functions

\ No newline at end of file +List of all items in this crate

List of all items

Functions

\ No newline at end of file diff --git a/argmin_testfunctions/easom/fn.easom_derivative.html b/argmin_testfunctions/easom/fn.easom_derivative.html new file mode 100644 index 000000000..a6855479d --- /dev/null +++ b/argmin_testfunctions/easom/fn.easom_derivative.html @@ -0,0 +1,11 @@ + + + + + Redirection + + +

Redirecting to ../../argmin_testfunctions/fn.easom_derivative.html...

+ + + \ No newline at end of file diff --git a/argmin_testfunctions/easom/fn.easom_hessian.html b/argmin_testfunctions/easom/fn.easom_hessian.html new file mode 100644 index 000000000..5ecab62b7 --- /dev/null +++ b/argmin_testfunctions/easom/fn.easom_hessian.html @@ -0,0 +1,11 @@ + + + + + Redirection + + +

Redirecting to ../../argmin_testfunctions/fn.easom_hessian.html...

+ + + \ No newline at end of file diff --git a/argmin_testfunctions/fn.easom_derivative.html b/argmin_testfunctions/fn.easom_derivative.html new file mode 100644 index 000000000..e9f6a5357 --- /dev/null +++ b/argmin_testfunctions/fn.easom_derivative.html @@ -0,0 +1,3 @@ +easom_derivative in argmin_testfunctions - Rust

Function argmin_testfunctions::easom_derivative

source · 
pub fn easom_derivative<T>(param: &[T; 2]) -> [T; 2]where
+    T: Float + FromPrimitive,
Expand description

Derivative of Easom test function

+
\ No newline at end of file diff --git a/argmin_testfunctions/fn.easom_hessian.html b/argmin_testfunctions/fn.easom_hessian.html new file mode 100644 index 000000000..612ac0387 --- /dev/null +++ b/argmin_testfunctions/fn.easom_hessian.html @@ -0,0 +1,3 @@ +easom_hessian in argmin_testfunctions - Rust

Function argmin_testfunctions::easom_hessian

source · 
pub fn easom_hessian<T>(param: &[T; 2]) -> [[T; 2]; 2]where
+    T: Float + FromPrimitive,
Expand description

Hessian of Easom test function

+
\ No newline at end of file diff --git a/argmin_testfunctions/index.html b/argmin_testfunctions/index.html index fed319e91..c2f3c2fb8 100644 --- a/argmin_testfunctions/index.html +++ b/argmin_testfunctions/index.html @@ -1,2 +1,2 @@ argmin_testfunctions - Rust

Crate argmin_testfunctions

source ·
Expand description

Test functions for optimization algorithms

Functions

\ No newline at end of file +
  • All Items

    • Crate argmin_testfunctions

    source ·
    Expand description

    Test functions for optimization algorithms

    Functions

    \ No newline at end of file diff --git a/argmin_testfunctions/sidebar-items.js b/argmin_testfunctions/sidebar-items.js index f533a2bcb..359fc558a 100644 --- a/argmin_testfunctions/sidebar-items.js +++ b/argmin_testfunctions/sidebar-items.js @@ -1 +1 @@ -window.SIDEBAR_ITEMS = 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a/src/argmin_testfunctions/easom.rs.html b/src/argmin_testfunctions/easom.rs.html index 325208911..734d9130d 100644 --- a/src/argmin_testfunctions/easom.rs.html +++ b/src/argmin_testfunctions/easom.rs.html @@ -48,6 +48,98 @@ 48 49 50 +51 +52 +53 +54 +55 +56 +57 +58 +59 +60 +61 +62 +63 +64 +65 +66 +67 +68 +69 +70 +71 +72 +73 +74 +75 +76 +77 +78 +79 +80 +81 +82 +83 +84 +85 +86 +87 +88 +89 +90 +91 +92 +93 +94 +95 +96 +97 +98 +99 +100 +101 +102 +103 +104 +105 +106 +107 +108 +109 +110 +111 +112 +113 +114 +115 +116 +117 +118 +119 +120 +121 +122 +123 +124 +125 +126 +127 +128 +129 +130 +131 +132 +133 +134 +135 +136 +137 +138 +139 +140 +141 +142 
    // Copyright 2018-2024 argmin developers
 //
 // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
@@ -86,16 +178,108 @@
     -x1.cos() * x2.cos() * (-(x1 - pi).powi(2) - (x2 - pi).powi(2)).exp()
 }
 
+/// Derivative of Easom test function
+pub fn easom_derivative<T>(param: &[T; 2]) -> [T; 2]
+where
+    T: Float + FromPrimitive,
+{
+    let [x1, x2] = *param;
+
+    let pi = T::from_f64(PI).unwrap();
+    let n2 = T::from_f64(2.0).unwrap();
+
+    let factor = (-(x1 - pi).powi(2) - (x2 - pi).powi(2)).exp();
+
+    [
+        factor * x2.cos() * (x1.sin() + n2 * x1 * x1.cos() - n2 * pi * x1.cos()),
+        factor * x1.cos() * (x2.sin() + n2 * x2 * x2.cos() - n2 * pi * x2.cos()),
+    ]
+}
+
+/// Hessian of Easom test function
+pub fn easom_hessian<T>(param: &[T; 2]) -> [[T; 2]; 2]
+where
+    T: Float + FromPrimitive,
+{
+    let [x1, x2] = *param;
+
+    let pi = T::from_f64(PI).unwrap();
+    let n2 = T::from_f64(2.0).unwrap();
+    let n4 = T::from_f64(4.0).unwrap();
+    let n3 = T::from_f64(3.0).unwrap();
+    let n8 = T::from_f64(8.0).unwrap();
+
+    let x1cos = x1.cos();
+    let x1sin = x1.sin();
+    let x2cos = x2.cos();
+    let x2sin = x2.sin();
+    let factor = (-(x1 - pi).powi(2) - (x2 - pi).powi(2)).exp();
+    let offdiag = factor * (x1sin + n2 * (x1 - pi) * x1cos) * (n2 * (pi - x2) * x2cos - x2sin);
+
+    [
+        [
+            factor
+                * x2cos
+                * (n4 * (pi - x1) * x1sin
+                    + (-n4 * x1.powi(2) + n8 * pi * x1 - n4 * pi.powi(2) + n3) * x1cos),
+            offdiag,
+        ],
+        [
+            offdiag,
+            factor
+                * x1cos
+                * (n4 * (pi - x2) * x2sin
+                    + (-n4 * x2.powi(2) + n8 * pi * x2 - n4 * pi.powi(2) + n3) * x2cos),
+        ],
+    ]
+}
+
 #[cfg(test)]
 mod tests {
     use super::*;
     use approx::assert_relative_eq;
+    use finitediff::FiniteDiff;
+    use proptest::prelude::*;
     use std::{f32, f32::consts::PI as PI32, f64, f64::consts::PI as PI64};
 
     #[test]
     fn test_easom_optimum() {
         assert_relative_eq!(easom(&[PI32, PI32]), -1.0_f32, epsilon = f32::EPSILON);
         assert_relative_eq!(easom(&[PI64, PI64]), -1.0_f64, epsilon = f64::EPSILON);
+
+        let deriv = easom_derivative(&[PI64, PI64]);
+        for i in 0..2 {
+            assert_relative_eq!(deriv[i], 0.0_f64, epsilon = f64::EPSILON);
+        }
+    }
+
+    proptest! {
+        #[test]
+        fn test_easom_derivative_finitediff(a in -100.0..100.0, b in -100.0..100.0) {
+            let param = [a, b];
+            let derivative = easom_derivative(&param);
+            let derivative_fd = Vec::from(param).central_diff(&|x| easom(&[x[0], x[1]]));
+            for i in 0..derivative.len() {
+                assert_relative_eq!(derivative[i], derivative_fd[i], epsilon = 1e-5);
+            }
+        }
+    }
+
+    proptest! {
+        #[test]
+        fn test_easom_hessian_finitediff(a in -100.0..100.0, b in -100.0..100.0) {
+            let param = [a, b];
+            let hessian = easom_hessian(&param);
+            let hessian_fd =
+                Vec::from(param).forward_hessian(&|x| easom_derivative(&[x[0], x[1]]).to_vec());
+            let n = hessian.len();
+            for i in 0..n {
+                assert_eq!(hessian[i].len(), n);
+                for j in 0..n {
+                    assert_relative_eq!(hessian[i][j], hessian_fd[i][j], epsilon = 1e-5);
+                }
+            }
+        }
     }
 }
    \ No newline at end of file