updates
This commit is contained in:
William Ball
parent
359c25e031
commit
6fd0257f4d
5 changed files with 214 additions and 426 deletions
0
fractal_dimension/bai_finch_rust/.projectile
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fractal_dimension/bai_finch_rust/.projectile
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fractal_dimension/bai_finch_rust/Cargo.lock
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381
fractal_dimension/bai_finch_rust/Cargo.lock
generated
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@ -1,25 +1,12 @@
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|
||||
checksum = "c3d0b9745dc2debf507c8422de05d7226cc1f0644216dfdfead988f9b1ab32a7"
|
||||
dependencies = [
|
||||
"proc-macro2",
|
||||
]
|
||||
|
||||
[[package]]
|
||||
name = "rand"
|
||||
version = "0.8.4"
|
||||
version = "0.7.3"
|
||||
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||
checksum = "2e7573632e6454cf6b99d7aac4ccca54be06da05aca2ef7423d22d27d4d4bcd8"
|
||||
checksum = "6a6b1679d49b24bbfe0c803429aa1874472f50d9b363131f0e89fc356b544d03"
|
||||
dependencies = [
|
||||
"getrandom",
|
||||
"libc",
|
||||
"rand_chacha",
|
||||
"rand_core",
|
||||
"rand_hc",
|
||||
"rand_pcg",
|
||||
]
|
||||
|
||||
[[package]]
|
||||
name = "rand_chacha"
|
||||
version = "0.3.1"
|
||||
version = "0.2.2"
|
||||
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||
checksum = "e6c10a63a0fa32252be49d21e7709d4d4baf8d231c2dbce1eaa8141b9b127d88"
|
||||
checksum = "f4c8ed856279c9737206bf725bf36935d8666ead7aa69b52be55af369d193402"
|
||||
dependencies = [
|
||||
"ppv-lite86",
|
||||
"rand_core",
|
||||
|
|
@ -400,18 +260,18 @@ dependencies = [
|
|||
|
||||
[[package]]
|
||||
name = "rand_core"
|
||||
version = "0.6.3"
|
||||
version = "0.5.1"
|
||||
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||
checksum = "d34f1408f55294453790c48b2f1ebbb1c5b4b7563eb1f418bcfcfdbb06ebb4e7"
|
||||
checksum = "90bde5296fc891b0cef12a6d03ddccc162ce7b2aff54160af9338f8d40df6d19"
|
||||
dependencies = [
|
||||
"getrandom",
|
||||
]
|
||||
|
||||
[[package]]
|
||||
name = "rand_distr"
|
||||
version = "0.4.1"
|
||||
version = "0.3.0"
|
||||
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||
checksum = "051b398806e42b9cd04ad9ec8f81e355d0a382c543ac6672c62f5a5b452ef142"
|
||||
checksum = "c9e9532ada3929fb8b2e9dbe28d1e06c9b2cc65813f074fcb6bd5fbefeff9d56"
|
||||
dependencies = [
|
||||
"num-traits",
|
||||
"rand",
|
||||
|
|
@ -419,9 +279,18 @@ dependencies = [
|
|||
|
||||
[[package]]
|
||||
name = "rand_hc"
|
||||
version = "0.3.1"
|
||||
version = "0.2.0"
|
||||
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||
checksum = "d51e9f596de227fda2ea6c84607f5558e196eeaf43c986b724ba4fb8fdf497e7"
|
||||
checksum = "ca3129af7b92a17112d59ad498c6f81eaf463253766b90396d39ea7a39d6613c"
|
||||
dependencies = [
|
||||
"rand_core",
|
||||
]
|
||||
|
||||
[[package]]
|
||||
name = "rand_pcg"
|
||||
version = "0.2.1"
|
||||
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||
checksum = "16abd0c1b639e9eb4d7c50c0b8100b0d0f849be2349829c740fe8e6eb4816429"
|
||||
dependencies = [
|
||||
"rand_core",
|
||||
]
|
||||
|
|
@ -432,37 +301,11 @@ version = "0.2.1"
|
|||
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||
checksum = "60a357793950651c4ed0f3f52338f53b2f809f32d83a07f72909fa13e4c6c1e3"
|
||||
|
||||
[[package]]
|
||||
name = "rustc-demangle"
|
||||
version = "0.1.20"
|
||||
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||
checksum = "dead70b0b5e03e9c814bcb6b01e03e68f7c57a80aa48c72ec92152ab3e818d49"
|
||||
|
||||
[[package]]
|
||||
name = "serde"
|
||||
version = "1.0.126"
|
||||
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||
checksum = "ec7505abeacaec74ae4778d9d9328fe5a5d04253220a85c4ee022239fc996d03"
|
||||
dependencies = [
|
||||
"serde_derive",
|
||||
]
|
||||
|
||||
[[package]]
|
||||
name = "serde_derive"
|
||||
version = "1.0.126"
|
||||
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||
checksum = "963a7dbc9895aeac7ac90e74f34a5d5261828f79df35cbed41e10189d3804d43"
|
||||
dependencies = [
|
||||
"proc-macro2",
|
||||
"quote",
|
||||
"syn",
|
||||
]
|
||||
|
||||
[[package]]
|
||||
name = "simba"
|
||||
version = "0.5.1"
|
||||
version = "0.3.1"
|
||||
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||
checksum = "8e82063457853d00243beda9952e910b82593e4b07ae9f721b9278a99a0d3d5c"
|
||||
checksum = "17bfe642b1728a6e89137ad428ef5d4738eca4efaba9590f9e110b8944028621"
|
||||
dependencies = [
|
||||
"approx",
|
||||
"num-complex",
|
||||
|
|
@ -471,44 +314,10 @@ dependencies = [
|
|||
]
|
||||
|
||||
[[package]]
|
||||
name = "syn"
|
||||
version = "1.0.73"
|
||||
name = "siphasher"
|
||||
version = "0.3.5"
|
||||
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||
checksum = "f71489ff30030d2ae598524f61326b902466f72a0fb1a8564c001cc63425bcc7"
|
||||
dependencies = [
|
||||
"proc-macro2",
|
||||
"quote",
|
||||
"unicode-xid",
|
||||
]
|
||||
|
||||
[[package]]
|
||||
name = "thiserror"
|
||||
version = "1.0.25"
|
||||
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||
checksum = "fa6f76457f59514c7eeb4e59d891395fab0b2fd1d40723ae737d64153392e9c6"
|
||||
dependencies = [
|
||||
"thiserror-impl",
|
||||
]
|
||||
|
||||
[[package]]
|
||||
name = "thiserror-impl"
|
||||
version = "1.0.25"
|
||||
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||
checksum = "8a36768c0fbf1bb15eca10defa29526bda730a2376c2ab4393ccfa16fb1a318d"
|
||||
dependencies = [
|
||||
"proc-macro2",
|
||||
"quote",
|
||||
"syn",
|
||||
]
|
||||
|
||||
[[package]]
|
||||
name = "thread-tree"
|
||||
version = "0.3.2"
|
||||
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||
checksum = "dd15110864dc0eccbd281d13c15a5863f7739a6fbcf710190a6d13e797aa1a57"
|
||||
dependencies = [
|
||||
"crossbeam-channel",
|
||||
]
|
||||
checksum = "cbce6d4507c7e4a3962091436e56e95290cb71fa302d0d270e32130b75fbff27"
|
||||
|
||||
[[package]]
|
||||
name = "typenum"
|
||||
|
|
@ -517,13 +326,13 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
|
|||
checksum = "879f6906492a7cd215bfa4cf595b600146ccfac0c79bcbd1f3000162af5e8b06"
|
||||
|
||||
[[package]]
|
||||
name = "unicode-xid"
|
||||
version = "0.2.2"
|
||||
name = "version_check"
|
||||
version = "0.9.3"
|
||||
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||
checksum = "8ccb82d61f80a663efe1f787a51b16b5a51e3314d6ac365b08639f52387b33f3"
|
||||
checksum = "5fecdca9a5291cc2b8dcf7dc02453fee791a280f3743cb0905f8822ae463b3fe"
|
||||
|
||||
[[package]]
|
||||
name = "wasi"
|
||||
version = "0.10.2+wasi-snapshot-preview1"
|
||||
version = "0.9.0+wasi-snapshot-preview1"
|
||||
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||
checksum = "fd6fbd9a79829dd1ad0cc20627bf1ed606756a7f77edff7b66b7064f9cb327c6"
|
||||
checksum = "cccddf32554fecc6acb585f82a32a72e28b48f8c4c1883ddfeeeaa96f7d8e519"
|
||||
|
|
|
|||
|
|
@ -7,7 +7,8 @@ edition = "2018"
|
|||
# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
|
||||
|
||||
[dependencies]
|
||||
num = "0.4.0"
|
||||
nalgebra = "0.27.1"
|
||||
peroxide = "0.30"
|
||||
gad = "0.2.0"
|
||||
num = "0.3.1"
|
||||
nalgebra = "0.24.1"
|
||||
bacon-sci = "*"
|
||||
simba = "0.3.1"
|
||||
num-complex = "0.3.1"
|
||||
|
|
|
|||
57
fractal_dimension/bai_finch_rust/src/diff.rs
Normal file
57
fractal_dimension/bai_finch_rust/src/diff.rs
Normal file
|
|
@ -0,0 +1,57 @@
|
|||
use num_complex::Complex64;
|
||||
use simba::scalar::ComplexField;
|
||||
use std::f64::consts::PI;
|
||||
|
||||
pub type CFunction<'a> = &'a dyn Fn(Complex64) -> Complex64;
|
||||
pub type Path<'a> = &'a dyn Fn(f64) -> Complex64;
|
||||
pub type Rule<'a> = &'a dyn Fn(CFunction, Complex64, Complex64) -> Complex64;
|
||||
|
||||
pub fn unit_circle(t: f64) -> Complex64 {
|
||||
num::Complex::new((2.0 * PI * t).cos(), (2.0 * PI * t).sin())
|
||||
}
|
||||
|
||||
pub fn trapezoid(f: CFunction, a: Complex64, b: Complex64) -> Complex64 {
|
||||
0.5 * (b - a) * (f(a) + f(b))
|
||||
}
|
||||
|
||||
fn factorial(n: i32) -> i32 {
|
||||
(1..=n).product()
|
||||
}
|
||||
|
||||
fn test(t: f64) -> Complex64 {
|
||||
1.0 / unit_circle(t)
|
||||
}
|
||||
|
||||
// pub fn diff(fun: CFunction, a: Complex64, n: i32) -> Result<Complex64, String> {
|
||||
// let f = |t: f64| -> Complex64 {
|
||||
// let z = unit_circle(t);
|
||||
// fun(z) / (z - a).powi(n + 1)
|
||||
// };
|
||||
// let integral = bacon_sci::integrate::integrate_fixed(0f64, 1f64, f, 10)?;
|
||||
// Ok(integral * Complex64::new(factorial(n) as f64, 0.0) / Complex64::new(0.0, 2.0 * PI))
|
||||
// }
|
||||
|
||||
pub fn diff(fun: CFunction, a: Complex64, n: i32) -> Result<Complex64, String> {
|
||||
let f = |z: Complex64| -> Complex64 {
|
||||
fun(z) / (z - a).powi(n + 1)
|
||||
};
|
||||
let integral = integrate(&f, &unit_circle, &trapezoid);
|
||||
Ok(integral * Complex64::new(factorial(n) as f64, 0.0) / Complex64::new(0.0, 2.0 * PI))
|
||||
}
|
||||
|
||||
pub fn integrate(f: CFunction, path: Path, rule: Rule) -> Complex64 {
|
||||
let increment = 0.00001;
|
||||
let mut integral = Complex64::new(0.0, 0.0);
|
||||
|
||||
let mut i = increment;
|
||||
let mut previous_point = path(0.0);
|
||||
while i <= 1.0 {
|
||||
let point = path(i);
|
||||
integral += rule(f, previous_point, point);
|
||||
previous_point = point;
|
||||
|
||||
i += increment;
|
||||
}
|
||||
|
||||
integral
|
||||
}
|
||||
|
|
@ -1,143 +1,32 @@
|
|||
use gad::prelude::*;
|
||||
use nalgebra::{SMatrix, SVector};
|
||||
use num::Complex;
|
||||
#![allow(dead_code)]
|
||||
|
||||
mod diff;
|
||||
|
||||
use diff::*;
|
||||
use num_complex::Complex64;
|
||||
use std::f64::consts::PI;
|
||||
// use nalgebra::{SMatrix, SVector};
|
||||
|
||||
type F = f64;
|
||||
type Matrix2x2 = SMatrix<Complex<F>, 2, 2>;
|
||||
// type NComplex = num::Complex<F>;
|
||||
// type Matrix2x2 = SMatrix<num::Complex<F>, 2, 2>;
|
||||
// type Complex = Complex64;
|
||||
|
||||
fn sum(
|
||||
g: &mut GraphN,
|
||||
ar: &Value<F>,
|
||||
ai: &Value<F>,
|
||||
br: &Value<F>,
|
||||
bi: &Value<F>,
|
||||
) -> Result<(Value<F>, Value<F>)> {
|
||||
Ok((g.add(ar, br)?, g.add(ai, bi)?))
|
||||
}
|
||||
// fn power_method<const N: usize>(
|
||||
// vec: SVector<NComplex, N>,
|
||||
// mat: SMatrix<NComplex, N, N>,
|
||||
// iterations: usize,
|
||||
// ) -> NComplex {
|
||||
// let mut current = vec;
|
||||
// let mut previous = vec;
|
||||
// for _ in 0..iterations {
|
||||
// previous = current;
|
||||
// current = mat * current;
|
||||
// println!("current guess: {}", current[0] / previous[0]);
|
||||
// }
|
||||
|
||||
fn product(
|
||||
g: &mut GraphN,
|
||||
ar: &Value<F>,
|
||||
ai: &Value<F>,
|
||||
br: &Value<F>,
|
||||
bi: &Value<F>,
|
||||
) -> Result<(Value<F>, Value<F>)> {
|
||||
let t1 = g.mul(ar, br)?;
|
||||
let t2 = g.mul(ai, bi)?;
|
||||
let t3 = g.sub(&t1, &t2)?;
|
||||
|
||||
let s1 = g.mul(ar, bi)?;
|
||||
let s2 = g.mul(ai, br)?;
|
||||
let s3 = g.add(&s1, &s2)?;
|
||||
|
||||
Ok((t3, s3))
|
||||
}
|
||||
|
||||
fn division(
|
||||
g: &mut GraphN,
|
||||
ar: &Value<F>,
|
||||
ai: &Value<F>,
|
||||
br: &Value<F>,
|
||||
bi: &Value<F>,
|
||||
) -> Result<(Value<F>, Value<F>)> {
|
||||
let numerator1 = {
|
||||
let t1 = g.mul(ar, br)?;
|
||||
let t2 = g.mul(ai, bi)?;
|
||||
g.add(&t1, &t2)?
|
||||
};
|
||||
let denominator1 = {
|
||||
let t1 = g.mul(br, br)?;
|
||||
let t2 = g.mul(bi, bi)?;
|
||||
g.add(&t1, &t2)?
|
||||
};
|
||||
|
||||
let numerator2 = {
|
||||
let t1 = g.mul(ar, bi)?;
|
||||
let t2 = g.mul(ai, br)?;
|
||||
g.sub(&t1, &t2)?
|
||||
};
|
||||
let denominator2 = {
|
||||
let t1 = g.mul(br, br)?;
|
||||
let t2 = g.mul(bi, bi)?;
|
||||
g.add(&t1, &t2)?
|
||||
};
|
||||
|
||||
let f1 = g.div(&numerator1, &denominator1)?;
|
||||
let f2 = g.div(&numerator2, &denominator2)?;
|
||||
|
||||
Ok((f1, f2))
|
||||
}
|
||||
|
||||
fn mobius_derivative(mat: Matrix2x2) -> Result<(Value<F>, Value<F>)> {
|
||||
let mut g = GraphN::new();
|
||||
let x = g.variable(0.0);
|
||||
let y = g.variable(0.0);
|
||||
let a11r = g.constant(mat[(0, 0)].re);
|
||||
let a12r = g.constant(mat[(0, 1)].re);
|
||||
let a21r = g.constant(mat[(1, 0)].re);
|
||||
let a22r = g.constant(mat[(1, 1)].re);
|
||||
|
||||
let a11i = g.constant(mat[(0, 0)].im);
|
||||
let a12i = g.constant(mat[(0, 1)].im);
|
||||
let a21i = g.constant(mat[(1, 0)].im);
|
||||
let a22i = g.constant(mat[(1, 1)].im);
|
||||
|
||||
let (numeratorr, numeratori) = {
|
||||
let (prodr, prodi) = product(&mut g, &x, &y, &a11r, &a11i)?;
|
||||
sum(&mut g, &a12r, &a12i, &prodr, &prodi)?
|
||||
};
|
||||
|
||||
let (denominatorr, denominatori) = {
|
||||
let (prodr, prodi) = product(&mut g, &x, &y, &a21r, &a21i)?;
|
||||
sum(&mut g, &a22r, &a22i, &prodr, &prodi)?
|
||||
};
|
||||
|
||||
let (resultr, resulti) = division(
|
||||
&mut g,
|
||||
&numeratorr,
|
||||
&numeratori,
|
||||
&denominatorr,
|
||||
&denominatori,
|
||||
)?;
|
||||
|
||||
let x = x.gid()?;
|
||||
|
||||
let one = g.constant(1.0);
|
||||
let one2 = g.constant(1.0);
|
||||
let gradients1 = g.compute_gradients(resultr.gid()?, one)?;
|
||||
let gradients2 = g.compute_gradients(resulti.gid()?, one2)?;
|
||||
|
||||
let du_dx = gradients1.get(x).unwrap();
|
||||
let dv_dx = gradients2.get(x).unwrap();
|
||||
|
||||
Ok(Complex::new(*du_dx.data(), -*dv_dx.data()))
|
||||
}
|
||||
|
||||
fn next_order_derivative(
|
||||
g: &mut GraphN,
|
||||
expr: &GradientId<F>,
|
||||
var: &GradientId<F>,
|
||||
) -> Result<Value<F>> {
|
||||
let dz = g.constant(1.0);
|
||||
let dz_d = g.compute_gradients(*expr, dz)?;
|
||||
Ok(dz_d.get(*var).unwrap().clone())
|
||||
}
|
||||
|
||||
fn power_method<const N: usize>(
|
||||
vec: SVector<Complex<F>, N>,
|
||||
mat: SMatrix<Complex<F>, N, N>,
|
||||
iterations: usize,
|
||||
) -> Complex<F> {
|
||||
let mut current = vec;
|
||||
let mut previous = vec;
|
||||
for _ in 0..iterations {
|
||||
previous = current;
|
||||
current = mat * current;
|
||||
println!("current guess: {}", current[0] / previous[0]);
|
||||
}
|
||||
|
||||
current[0] / previous[0]
|
||||
}
|
||||
// current[0] / previous[0]
|
||||
// }
|
||||
|
||||
fn secant_method(f: fn(F) -> F, x0: F, x1: F, accuracy: F, iterations: usize) -> F {
|
||||
let mut x0 = x0;
|
||||
|
|
@ -158,6 +47,13 @@ fn secant_method(f: fn(F) -> F, x0: F, x1: F, accuracy: F, iterations: usize) ->
|
|||
x0
|
||||
}
|
||||
|
||||
fn dzdt(t: f64) -> Complex64 {
|
||||
Complex64::new(
|
||||
-2.0 * PI * (-2.0 * PI * t).sin(),
|
||||
2.0 * PI * ( 2.0 * PI * t).cos(),
|
||||
)
|
||||
}
|
||||
|
||||
fn main() {
|
||||
// let g = Matrix2x2::new(
|
||||
// Complex::new(2.0 / 12.0, -2.0 / 12.0),
|
||||
|
|
@ -172,4 +68,29 @@ fn main() {
|
|||
// Complex::new(0.0, 4.0 / 12.0),
|
||||
// Complex::new(-6.0 / 12.0, -8.0 / 12.0),
|
||||
// );
|
||||
|
||||
println!(
|
||||
"{}",
|
||||
diff(&|z: Complex64| z * z, Complex64::new(0.3, 0.3), 1).unwrap()
|
||||
);
|
||||
|
||||
// println!(
|
||||
// "{}",
|
||||
// bacon_sci::integrate::integrate(
|
||||
// 0.0,
|
||||
// 1.0,
|
||||
// &|t: f64| dzdt(t)
|
||||
// / Complex64::new(
|
||||
// (std::f64::consts::PI * 2.0 * t).cos(),
|
||||
// (std::f64::consts::PI * 2.0 * t).sin()
|
||||
// ),
|
||||
// 0.001
|
||||
// )
|
||||
// .unwrap()
|
||||
// );
|
||||
|
||||
println!(
|
||||
"{}",
|
||||
integrate(&|z: Complex64| 1.0 / z, &unit_circle, &trapezoid)
|
||||
);
|
||||
}
|
||||
|
|
|
|||
Loading…
Reference in a new issue