improve math solver
This commit is contained in:
parent
1f4ded31c7
commit
a63f063a05
194
Cargo.lock
generated
194
Cargo.lock
generated
@ -1,3 +1,11 @@
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[[package]]
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name = "aho-corasick"
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version = "0.6.9"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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dependencies = [
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"memchr 2.1.3 (registry+https://github.com/rust-lang/crates.io-index)",
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]
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[[package]]
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name = "alga"
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version = "0.7.2"
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@ -17,6 +25,16 @@ dependencies = [
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"num-traits 0.2.6 (registry+https://github.com/rust-lang/crates.io-index)",
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]
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[[package]]
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dependencies = [
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[[package]]
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name = "bitflags"
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version = "1.0.4"
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@ -27,9 +45,17 @@ name = "cad_rs"
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version = "0.1.0"
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dependencies = [
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"approx 0.3.1 (registry+https://github.com/rust-lang/crates.io-index)",
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[[package]]
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name = "cfg-if"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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[[package]]
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name = "cloudabi"
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version = "0.0.3"
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@ -38,6 +64,23 @@ dependencies = [
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[[package]]
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[[package]]
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name = "env_logger"
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version = "0.6.0"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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dependencies = [
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[[package]]
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name = "fuchsia-cprng"
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version = "0.1.0"
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@ -51,6 +94,27 @@ dependencies = [
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[[package]]
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dependencies = [
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[[package]]
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name = "itertools"
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version = "0.8.0"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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dependencies = [
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[[package]]
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name = "lazy_static"
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version = "1.2.0"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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[[package]]
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name = "libc"
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version = "0.2.48"
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@ -61,6 +125,14 @@ name = "libm"
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version = "0.1.2"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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[[package]]
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name = "log"
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[[package]]
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name = "matrixmultiply"
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version = "0.1.15"
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@ -69,6 +141,15 @@ dependencies = [
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[[package]]
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name = "memchr"
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version = "2.1.3"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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dependencies = [
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[[package]]
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name = "nalgebra"
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version = "0.16.13"
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@ -97,6 +178,11 @@ name = "num-traits"
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version = "0.2.6"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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[[package]]
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name = "quick-error"
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version = "1.2.2"
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[[package]]
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name = "rand"
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version = "0.5.6"
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@ -127,11 +213,80 @@ name = "rawpointer"
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version = "0.1.0"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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version = "0.1.51"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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[[package]]
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[[package]]
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name = "ucd-util"
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version = "0.1.3"
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@ -146,29 +301,68 @@ name = "winapi-i686-pc-windows-gnu"
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|
||||
"checksum wincolor 1.0.1 (registry+https://github.com/rust-lang/crates.io-index)" = "561ed901ae465d6185fa7864d63fbd5720d0ef718366c9a4dc83cf6170d7e9ba"
|
||||
|
||||
@ -7,3 +7,6 @@ edition = "2018"
|
||||
[dependencies]
|
||||
nalgebra = "0.16"
|
||||
approx = "0.3"
|
||||
itertools = "0.8"
|
||||
log = "0.4"
|
||||
env_logger = "0.6"
|
||||
10
src/main.rs
10
src/main.rs
@ -1,8 +1,16 @@
|
||||
#![feature(drain_filter)]
|
||||
#![feature(box_patterns)]
|
||||
#![feature(slice_patterns)]
|
||||
#![feature(bind_by_move_pattern_guards)]
|
||||
#![feature(vec_remove_item)]
|
||||
|
||||
extern crate nalgebra;
|
||||
#[macro_use]
|
||||
extern crate approx;
|
||||
extern crate itertools;
|
||||
#[macro_use]
|
||||
extern crate log;
|
||||
extern crate env_logger;
|
||||
|
||||
mod entity;
|
||||
mod math;
|
||||
@ -13,6 +21,8 @@ fn main() {
|
||||
use math::Point2;
|
||||
use relation::{Relation, ResolveResult};
|
||||
|
||||
env_logger::init();
|
||||
|
||||
println!("Hello, world!");
|
||||
let origin = Point::new_ref(Var::new_single(Point2::new(0., 0.)));
|
||||
let p1 = Point::new_ref(Var::new_full(Point2::new(1., 1.)));
|
||||
|
||||
530
src/math.rs
530
src/math.rs
@ -214,9 +214,9 @@ impl Region2 {
|
||||
}
|
||||
}
|
||||
|
||||
mod solve {
|
||||
pub mod solve {
|
||||
|
||||
use std::collections::BTreeSet;
|
||||
use std::collections::{BTreeMap, BTreeSet};
|
||||
use std::fmt;
|
||||
use std::iter::FromIterator;
|
||||
|
||||
@ -268,10 +268,179 @@ mod solve {
|
||||
enum Expr {
|
||||
Unkn(Unknown),
|
||||
Const(Scalar),
|
||||
Plus(Box<Expr>, Box<Expr>),
|
||||
Sum(Exprs),
|
||||
Neg(Box<Expr>),
|
||||
Times(Box<Expr>, Box<Expr>),
|
||||
Inv(Box<Expr>),
|
||||
Product(Exprs),
|
||||
Div(Box<Expr>, Box<Expr>),
|
||||
}
|
||||
|
||||
type Exprs = Vec<Expr>;
|
||||
|
||||
impl Unknowns for Exprs {
|
||||
fn unknowns(&self) -> UnknownSet {
|
||||
self.iter().flat_map(|e: &Expr| e.unknowns()).collect()
|
||||
}
|
||||
fn has_unknowns(&self) -> bool {
|
||||
self.iter().any(|e: &Expr| e.has_unknowns())
|
||||
}
|
||||
fn has_unknown(&self, u: Unknown) -> bool {
|
||||
self.iter().any(|e: &Expr| e.has_unknown(u))
|
||||
}
|
||||
}
|
||||
|
||||
fn write_separated_exprs(es: &Exprs, f: &mut fmt::Formatter, sep: &str) -> fmt::Result {
|
||||
let mut is_first = true;
|
||||
for e in es {
|
||||
if is_first {
|
||||
is_first = false;
|
||||
} else {
|
||||
write!(f, "{}", sep)?
|
||||
}
|
||||
write!(f, "({})", e)?
|
||||
}
|
||||
Ok(())
|
||||
}
|
||||
|
||||
fn remove_common_terms(l: &mut Vec<Expr>, r: &mut Vec<Expr>) -> Vec<Expr> {
|
||||
let common: Vec<_> = l.drain_filter(|e| r.contains(e)).collect();
|
||||
common.iter().for_each(|e| {
|
||||
r.remove_item(e);
|
||||
});
|
||||
common
|
||||
}
|
||||
|
||||
fn remove_term(terms: &mut Vec<Expr>, term: &Expr) -> Option<Expr> {
|
||||
terms.remove_item(term)
|
||||
}
|
||||
|
||||
fn sum_fold(l: Expr, r: Expr) -> Expr {
|
||||
use itertools::Itertools;
|
||||
use Expr::*;
|
||||
match (l, r) {
|
||||
(Const(lc), Const(rc)) => Const(lc + rc),
|
||||
(Const(c), o) | (o, Const(c)) if relative_eq!(c, 0.) => o,
|
||||
(Product(mut l), Product(mut r)) => {
|
||||
let comm = remove_common_terms(&mut l, &mut r);
|
||||
Expr::new_product(Sum(comm), Expr::new_sum(Product(l), Product(r))).simplify()
|
||||
}
|
||||
(Product(mut l), r) | (r, Product(mut l)) => {
|
||||
let comm = remove_term(&mut l, &r);
|
||||
match comm {
|
||||
Some(_) => {
|
||||
Expr::new_product(r, Expr::new_sum(Product(l), Const(1.))).simplify()
|
||||
}
|
||||
None => Expr::new_sum(Product(l), r),
|
||||
}
|
||||
}
|
||||
(l, r) => Expr::new_sum(l, r),
|
||||
}
|
||||
}
|
||||
|
||||
fn group_sum(es: Exprs) -> Exprs {
|
||||
use Expr::*;
|
||||
let mut common: BTreeMap<UnknownSet, Expr> = BTreeMap::new();
|
||||
for e in es {
|
||||
let unkns = e.unknowns();
|
||||
match common.get_mut(&unkns) {
|
||||
None => {
|
||||
match e {
|
||||
Const(c) if relative_eq!(c, 0.) => (),
|
||||
e => {
|
||||
common.insert(unkns, e);
|
||||
}
|
||||
};
|
||||
}
|
||||
Some(existing) => {
|
||||
match existing {
|
||||
Sum(ref mut es) => {
|
||||
// already failed at merging, so just add it to the list
|
||||
es.push(e);
|
||||
}
|
||||
other => {
|
||||
*other = sum_fold(other.clone(), e);
|
||||
}
|
||||
};
|
||||
}
|
||||
};
|
||||
}
|
||||
common.into_iter().map(|(_, v)| v).collect()
|
||||
}
|
||||
|
||||
fn product_fold(l: Expr, r: Expr) -> Expr {
|
||||
use itertools::Itertools;
|
||||
use Expr::*;
|
||||
match (l, r) {
|
||||
(Const(lc), Const(rc)) => Const(lc * rc),
|
||||
(Const(c), o) | (o, Const(c)) if relative_eq!(c, 1.) => o,
|
||||
(Div(num, den), mul) | (mul, Div(num, den)) => {
|
||||
if mul == *den {
|
||||
*num
|
||||
} else {
|
||||
Expr::Div(Box::new(Expr::Product(vec![*num, mul])), den).simplify()
|
||||
}
|
||||
}
|
||||
(l, r) => Expr::new_product(l, r),
|
||||
}
|
||||
}
|
||||
|
||||
fn group_product(es: Exprs) -> Exprs {
|
||||
use Expr::*;
|
||||
let mut common: BTreeMap<UnknownSet, Expr> = BTreeMap::new();
|
||||
for e in es {
|
||||
let unkns = e.unknowns();
|
||||
match common.get_mut(&unkns) {
|
||||
None => {
|
||||
match e {
|
||||
Const(c) if relative_eq!(c, 1.) => (),
|
||||
e => {
|
||||
common.insert(unkns, e);
|
||||
}
|
||||
};
|
||||
}
|
||||
Some(existing) => {
|
||||
match existing {
|
||||
Sum(ref mut es) => {
|
||||
// already failed at merging, so just add it to the list
|
||||
es.push(e);
|
||||
}
|
||||
other => *other = product_fold(other.clone(), e),
|
||||
};
|
||||
}
|
||||
};
|
||||
}
|
||||
common.into_iter().map(|(_, v)| v).collect()
|
||||
}
|
||||
|
||||
fn distribute_product_sums(mut es: Exprs) -> Expr {
|
||||
trace!("distribute_product_sums: {}", Product(es.clone()));
|
||||
use itertools::Itertools;
|
||||
use Expr::*;
|
||||
let sums = es
|
||||
.drain_filter(|e| match e {
|
||||
Sum(_) => true,
|
||||
_ => false,
|
||||
})
|
||||
.map(|e| {
|
||||
trace!("sum in product: {}", e);
|
||||
match e {
|
||||
Sum(es) => es,
|
||||
_ => unreachable!(),
|
||||
}
|
||||
});
|
||||
let products: Vec<_> = sums.multi_cartesian_product().collect();
|
||||
if products.is_empty() {
|
||||
trace!("no sums to distribute");
|
||||
return Product(es);
|
||||
}
|
||||
let sums = products
|
||||
.into_iter()
|
||||
.map(|mut prod| {
|
||||
prod.extend(es.clone());
|
||||
trace!("prod: {}", Product(prod.clone()));
|
||||
Product(prod)
|
||||
})
|
||||
.collect();
|
||||
Sum(sums)
|
||||
}
|
||||
|
||||
impl Unknowns for Expr {
|
||||
@ -280,8 +449,9 @@ mod solve {
|
||||
match self {
|
||||
Unkn(u) => u.unknowns(),
|
||||
Const(_) => UnknownSet::default(),
|
||||
Plus(l, r) | Times(l, r) => l.unknowns().union(&r.unknowns()).cloned().collect(),
|
||||
Neg(e) | Inv(e) => e.unknowns(),
|
||||
Sum(es) | Product(es) => es.unknowns(),
|
||||
Div(l, r) => l.unknowns().union(&r.unknowns()).cloned().collect(),
|
||||
Neg(e) => e.unknowns(),
|
||||
}
|
||||
}
|
||||
fn has_unknowns(&self) -> bool {
|
||||
@ -289,8 +459,9 @@ mod solve {
|
||||
match self {
|
||||
Unkn(u) => u.has_unknowns(),
|
||||
Const(_) => false,
|
||||
Plus(l, r) | Times(l, r) => l.has_unknowns() || r.has_unknowns(),
|
||||
Neg(e) | Inv(e) => e.has_unknowns(),
|
||||
Sum(es) | Product(es) => es.has_unknowns(),
|
||||
Div(l, r) => l.has_unknowns() || r.has_unknowns(),
|
||||
Neg(e) => e.has_unknowns(),
|
||||
}
|
||||
}
|
||||
fn has_unknown(&self, u: Unknown) -> bool {
|
||||
@ -298,30 +469,31 @@ mod solve {
|
||||
match self {
|
||||
Unkn(u1) => u1.has_unknown(u),
|
||||
Const(_) => false,
|
||||
Plus(l, r) | Times(l, r) => l.has_unknown(u) || r.has_unknown(u),
|
||||
Neg(e) | Inv(e) => e.has_unknown(u),
|
||||
Sum(es) | Product(es) => es.has_unknown(u),
|
||||
Div(l, r) => l.has_unknown(u) || r.has_unknown(u),
|
||||
Neg(e) => e.has_unknown(u),
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
impl Expr {
|
||||
fn new_plus(e1: Expr, e2: Expr) -> Expr {
|
||||
Expr::Plus(Box::new(e1), Box::new(e2))
|
||||
fn new_sum(e1: Expr, e2: Expr) -> Expr {
|
||||
Expr::Sum(vec![e1, e2])
|
||||
}
|
||||
fn new_times(e1: Expr, e2: Expr) -> Expr {
|
||||
Expr::Times(Box::new(e1), Box::new(e2))
|
||||
fn new_product(e1: Expr, e2: Expr) -> Expr {
|
||||
Expr::Product(vec![e1, e2])
|
||||
}
|
||||
fn new_neg(e1: Expr) -> Expr {
|
||||
Expr::Neg(Box::new(e1))
|
||||
}
|
||||
fn new_inv(e1: Expr) -> Expr {
|
||||
Expr::Inv(Box::new(e1))
|
||||
fn new_div(num: Expr, den: Expr) -> Expr {
|
||||
Expr::Div(Box::new(num), Box::new(den))
|
||||
}
|
||||
fn new_minus(e1: Expr, e2: Expr) -> Expr {
|
||||
Expr::Plus(Box::new(e1), Box::new(Expr::new_neg(e2)))
|
||||
Expr::Sum(vec![e1, Expr::new_neg(e2)])
|
||||
}
|
||||
fn new_div(e1: Expr, e2: Expr) -> Expr {
|
||||
Expr::Times(Box::new(e1), Box::new(Expr::new_inv(e2)))
|
||||
fn new_inv(den: Expr) -> Expr {
|
||||
Expr::new_div(Expr::Const(1.), den)
|
||||
}
|
||||
|
||||
fn is_zero(&self) -> bool {
|
||||
@ -343,90 +515,132 @@ mod solve {
|
||||
fn simplify(self) -> Expr {
|
||||
use Expr::*;
|
||||
match self {
|
||||
Plus(l, r) => match (l.simplify(), r.simplify()) {
|
||||
(Const(lc), Const(rc)) => Const(lc + rc),
|
||||
(Const(c), ref o) | (ref o, Const(c)) if relative_eq!(c, 0.) => o.clone(),
|
||||
(Times(l1, l2), Times(r1, r2)) => {
|
||||
if l2 == r2 {
|
||||
Expr::new_times(Expr::Plus(l1, r1), *l2).simplify()
|
||||
} else if l1 == r1 {
|
||||
Expr::new_times(Expr::Plus(l2, r2), *l1).simplify()
|
||||
} else if l1 == r2 {
|
||||
Expr::new_times(Expr::Plus(l2, r1), *l1).simplify()
|
||||
} else if l2 == r1 {
|
||||
Expr::new_times(Expr::Plus(l1, r2), *l2).simplify()
|
||||
Sum(es) => {
|
||||
let mut new_es: Vec<_> = es
|
||||
.into_iter()
|
||||
.map(|e| e.simplify())
|
||||
.flat_map(|e| match e {
|
||||
Sum(more_es) => more_es,
|
||||
other => vec![other],
|
||||
})
|
||||
.collect();
|
||||
let pre_new_es = new_es.clone();
|
||||
new_es = group_sum(new_es);
|
||||
trace!(
|
||||
"simplify sum {} => {}",
|
||||
Sum(pre_new_es),
|
||||
Sum(new_es.clone())
|
||||
);
|
||||
|
||||
match new_es.len() {
|
||||
0 => Const(0.), // none
|
||||
1 => new_es.into_iter().next().unwrap(), // one
|
||||
_ => Sum(new_es), // many
|
||||
}
|
||||
}
|
||||
Product(es) => {
|
||||
let new_es: Vec<_> = es
|
||||
.into_iter()
|
||||
.map(|e| e.simplify())
|
||||
.flat_map(|e| match e {
|
||||
Product(more_es) => more_es,
|
||||
other => vec![other],
|
||||
})
|
||||
.collect();
|
||||
let pre_new_es = new_es.clone();
|
||||
let new_es = group_product(new_es);
|
||||
trace!(
|
||||
"simplify product {} => {}",
|
||||
Product(pre_new_es),
|
||||
Product(new_es.clone())
|
||||
);
|
||||
match new_es.len() {
|
||||
0 => Const(1.), // none
|
||||
1 => new_es.into_iter().next().unwrap(), // one
|
||||
_ => Product(new_es), // many
|
||||
}
|
||||
}
|
||||
Neg(mut v) => {
|
||||
*v = v.simplify();
|
||||
trace!("simplify neg {}", Neg(v.clone()));
|
||||
match v {
|
||||
box Const(c) => Const(-c),
|
||||
box Neg(v) => *v,
|
||||
e => Product(vec![Const(-1.), *e]),
|
||||
}
|
||||
}
|
||||
Div(mut num, mut den) => {
|
||||
*num = num.simplify();
|
||||
*den = den.simplify();
|
||||
trace!("simplify div {}", Div(num.clone(), den.clone()));
|
||||
match (num, den) {
|
||||
(box Const(num), box Const(den)) => Const(num / den),
|
||||
(num, box Const(den)) => {
|
||||
if relative_eq!(den, 1.) {
|
||||
*num
|
||||
} else {
|
||||
Expr::new_plus(Times(l1, l2), Times(r1, r2))
|
||||
Expr::new_product(*num, Const(1. / den))
|
||||
}
|
||||
}
|
||||
(l, r) => Self::new_plus(l, r),
|
||||
},
|
||||
Times(l, r) => match (l.simplify(), r.simplify()) {
|
||||
(Const(lc), Const(rc)) => Const(lc * rc),
|
||||
(Const(c), ref o) | (ref o, Const(c)) if relative_eq!(c, 1.) => o.clone(),
|
||||
(Inv(ref den), ref num) | (ref num, Inv(ref den)) if *num == **den => Const(1.),
|
||||
(l, r) => Self::new_times(l, r),
|
||||
},
|
||||
Neg(v) => match v.simplify() {
|
||||
Const(c) => Const(-c),
|
||||
Neg(v) => *v,
|
||||
e => Self::new_times(Const(-1.), e),
|
||||
},
|
||||
Inv(v) => match v.simplify() {
|
||||
Const(c) => Const(1. / c),
|
||||
Inv(v) => *v,
|
||||
e => Self::new_inv(e),
|
||||
(num, box Div(dennum, denden)) => {
|
||||
Div(Box::new(Product(vec![*num, *denden])), dennum).simplify()
|
||||
}
|
||||
(box Product(mut es), box den) => match es.remove_item(&den) {
|
||||
Some(_) => Product(es),
|
||||
None => Expr::new_div(Product(es), den),
|
||||
},
|
||||
(num, den) => {
|
||||
if num == den {
|
||||
Expr::Const(1.)
|
||||
} else {
|
||||
Div(num, den)
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
e => e,
|
||||
}
|
||||
}
|
||||
|
||||
fn distrubute(self) -> Expr {
|
||||
fn distribute(self) -> Expr {
|
||||
use Expr::*;
|
||||
trace!("distribute {}", self);
|
||||
match self {
|
||||
Plus(l, r) => Expr::new_plus(l.distrubute(), r.distrubute()),
|
||||
Times(l, r) => match (*l, *r) {
|
||||
(Plus(l, r), o) | (o, Plus(l, r)) => Expr::new_plus(
|
||||
Expr::Times(Box::new(o.clone()), l),
|
||||
Expr::Times(Box::new(o), r),
|
||||
)
|
||||
.distrubute(),
|
||||
(l, r) => Expr::new_times(l, r),
|
||||
},
|
||||
Neg(v) => match *v {
|
||||
Plus(l, r) => Expr::new_plus(Neg(l).distrubute(), Neg(r).distrubute()),
|
||||
Times(l, r) => Expr::new_times(Neg(l).distrubute(), *r),
|
||||
Neg(v) => v.distrubute(),
|
||||
Inv(v) => Expr::new_inv(Neg(v).distrubute()),
|
||||
e => Expr::new_neg(e),
|
||||
},
|
||||
Inv(v) => match *v {
|
||||
Plus(l, r) => Expr::new_plus(Inv(l).distrubute(), Inv(r).distrubute()),
|
||||
Times(l, r) => Expr::new_times(Inv(l).distrubute(), Inv(r).distrubute()),
|
||||
Inv(v) => v.distrubute(),
|
||||
e => Expr::new_inv(e),
|
||||
},
|
||||
e => e,
|
||||
Sum(mut es) => {
|
||||
for e in &mut es {
|
||||
*e = e.clone().distribute();
|
||||
}
|
||||
Sum(es)
|
||||
}
|
||||
Product(es) => distribute_product_sums(es),
|
||||
Div(mut num, mut den) => {
|
||||
*num = num.distribute();
|
||||
*den = den.distribute();
|
||||
match (num, den) {
|
||||
(box Sum(es), box den) => Sum(es
|
||||
.into_iter()
|
||||
.map(|e| Expr::new_div(e, den.clone()))
|
||||
.collect()),
|
||||
(mut num, mut den) => Div(num, den),
|
||||
}
|
||||
}
|
||||
|
||||
fn reduce(self, for_u: Unknown) -> Expr {
|
||||
use Expr::*;
|
||||
match self {
|
||||
Plus(l, r) => match (l.reduce(for_u), r.reduce(for_u)) {
|
||||
(Const(lc), Const(rc)) => Const(lc + rc),
|
||||
(l, r) => Self::new_plus(l, r),
|
||||
},
|
||||
Times(l, r) => match (l.reduce(for_u), r.reduce(for_u)) {
|
||||
(Const(lc), Const(rc)) => Const(lc * rc),
|
||||
(l, r) => Self::new_times(l, r),
|
||||
},
|
||||
Neg(v) => match v.reduce(for_u) {
|
||||
Unkn(u) if u == for_u => Expr::new_times(Const(-1.), Unkn(u)),
|
||||
e => Self::new_neg(e),
|
||||
},
|
||||
Inv(v) => match v.reduce(for_u) {
|
||||
e => Self::new_inv(e),
|
||||
Neg(v) => match v {
|
||||
// box Sum(mut l, mut r) => {
|
||||
// *l = Neg(l.clone()).distribute();
|
||||
// *r = Neg(r.clone()).distribute();
|
||||
// Sum(l, r)
|
||||
// }
|
||||
// box Product(mut l, r) => {
|
||||
// *l = Neg(l.clone()).distribute();
|
||||
// Product(l, r)
|
||||
// }
|
||||
box Neg(v) => v.distribute(),
|
||||
box Div(mut num, mut den) => {
|
||||
*num = Neg(num.clone()).distribute();
|
||||
*den = Neg(den.clone()).distribute();
|
||||
Div(num, den)
|
||||
}
|
||||
e => Neg(e),
|
||||
},
|
||||
e => e,
|
||||
}
|
||||
@ -439,10 +653,10 @@ mod solve {
|
||||
match self {
|
||||
Unkn(u) => write!(f, "{}", u),
|
||||
Const(c) => write!(f, "{}", c),
|
||||
Plus(l, r) => write!(f, "({}) + ({})", l, r),
|
||||
Times(l, r) => write!(f, "({}) * ({})", l, r),
|
||||
Sum(es) => write_separated_exprs(es, f, " + "),
|
||||
Product(es) => write_separated_exprs(es, f, " * "),
|
||||
Div(num, den) => write!(f, "({}) / ({})", num, den),
|
||||
Neg(e) => write!(f, "-({})", e),
|
||||
Inv(e) => write!(f, "1 / ({})", e),
|
||||
}
|
||||
}
|
||||
}
|
||||
@ -477,27 +691,62 @@ mod solve {
|
||||
}
|
||||
|
||||
impl Eqn {
|
||||
fn simplify(self) -> Eqn {
|
||||
Eqn(self.0.simplify(), self.1.simplify())
|
||||
}
|
||||
|
||||
fn solve(&self, for_u: Unknown) -> Option<Expr> {
|
||||
use Expr::*;
|
||||
if !self.has_unknown(for_u) {
|
||||
return None;
|
||||
}
|
||||
let (l, r) = (self.0.clone().simplify(), self.1.clone().simplify());
|
||||
let (l, r) = (
|
||||
self.0
|
||||
.clone() /*.distribute()*/
|
||||
.simplify(),
|
||||
self.1
|
||||
.clone() /*.distribute()*/
|
||||
.simplify(),
|
||||
);
|
||||
let (mut l, mut r) = ord_by_unkn(l, r, for_u)?;
|
||||
loop {
|
||||
trace!("solve: {} == {}", l, r);
|
||||
let (new_l, new_r): (Expr, Expr) = match l {
|
||||
Unkn(u) => return if u == for_u { Some(r.simplify()) } else { None },
|
||||
Plus(a, b) => {
|
||||
let (a, b) = ord_by_unkn(*a, *b, for_u)?;
|
||||
(a, Expr::new_minus(r, b))
|
||||
Sum(es) => {
|
||||
let (us, not_us): (Vec<_>, Vec<_>) =
|
||||
es.into_iter().partition(|e| e.has_unknown(for_u));
|
||||
if us.len() != 1 {
|
||||
return None;
|
||||
}
|
||||
Times(a, b) => {
|
||||
let (a, b) = ord_by_unkn(*a, *b, for_u)?;
|
||||
(a, Expr::new_div(r, b))
|
||||
(
|
||||
Sum(us).simplify(),
|
||||
Expr::new_minus(r, Sum(not_us)).simplify(),
|
||||
)
|
||||
}
|
||||
Product(es) => {
|
||||
let (us, not_us): (Vec<_>, Vec<_>) =
|
||||
es.into_iter().partition(|e| e.has_unknown(for_u));
|
||||
if us.len() != 1 {
|
||||
return None;
|
||||
}
|
||||
(
|
||||
Product(us).simplify(),
|
||||
Expr::new_div(r, Product(not_us)).simplify(),
|
||||
)
|
||||
}
|
||||
Neg(v) => (*v, Expr::new_neg(r)),
|
||||
Inv(v) => (*v, Expr::new_inv(r)),
|
||||
Div(num, den) => {
|
||||
let (nu, du) = (num.has_unknown(for_u), den.has_unknown(for_u));
|
||||
match (nu, du) {
|
||||
(true, false) => (*num, Expr::new_product(r, *den)),
|
||||
(false, true) => (Expr::new_product(r, *den), *num),
|
||||
(true, true) => return None, // TODO: simplify
|
||||
(false, false) => return None,
|
||||
}
|
||||
}
|
||||
Const(_) => return None,
|
||||
_ => return None,
|
||||
};
|
||||
l = new_l;
|
||||
r = new_r;
|
||||
@ -505,6 +754,12 @@ mod solve {
|
||||
}
|
||||
}
|
||||
|
||||
impl fmt::Display for Eqn {
|
||||
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
|
||||
write!(f, "{} == {}", self.0, self.1)
|
||||
}
|
||||
}
|
||||
|
||||
#[derive(Clone, Debug, PartialEq)]
|
||||
struct Eqns(Vec<Eqn>);
|
||||
|
||||
@ -554,6 +809,7 @@ mod solve {
|
||||
#[test]
|
||||
fn test_solve() {
|
||||
use Expr::*;
|
||||
let _ = env_logger::try_init();
|
||||
let u1 = Unknown(1);
|
||||
let e1 = Unkn(u1);
|
||||
let e2 = Const(1.);
|
||||
@ -563,9 +819,9 @@ mod solve {
|
||||
let eqn = Eqn(e2.clone(), e1.clone());
|
||||
assert_eq!(eqn.solve(u1), Some(Const(1.)));
|
||||
|
||||
let e3 = Expr::new_plus(Const(1.), Const(1.));
|
||||
let e3 = Expr::new_sum(Const(1.), Expr::new_sum(Const(1.), Const(2.)));
|
||||
let eqn = Eqn(e1.clone(), e3.clone());
|
||||
assert_eq!(eqn.solve(u1), Some(Const(2.)));
|
||||
assert_eq!(eqn.solve(u1), Some(Const(4.)));
|
||||
let e3 = Expr::new_minus(Const(1.), Const(1.));
|
||||
let eqn = Eqn(e1.clone(), e3.clone());
|
||||
assert_eq!(eqn.solve(u1), Some(Const(0.)));
|
||||
@ -573,30 +829,74 @@ mod solve {
|
||||
let e1 = Expr::new_div(Const(2.), Expr::new_minus(Const(1.), Const(4.)));
|
||||
let e2 = Expr::new_minus(Const(1.), Unkn(u1));
|
||||
let eqn = Eqn(e1, e2);
|
||||
info!("eqn: {} => {}", eqn, eqn.clone().simplify());
|
||||
let e = eqn.solve(u1).unwrap();
|
||||
assert!(const_expr(e.clone()).is_some());
|
||||
assert!(relative_eq!(const_expr(e.clone()).unwrap(), 5. / 3.));
|
||||
|
||||
let e1 = Expr::new_times(Const(2.), Expr::new_minus(Const(1.), Const(4.)));
|
||||
let e2 = Expr::new_minus(Expr::new_times(Unkn(u1), Const(2.)), Unkn(u1));
|
||||
println!(
|
||||
let e1 = Expr::new_product(Const(2.), Expr::new_minus(Const(1.), Const(4.)));
|
||||
let e2 = Expr::new_minus(Expr::new_product(Unkn(u1), Const(2.)), Unkn(u1));
|
||||
info!(
|
||||
"e1==e2: {}=={} => {}=={}",
|
||||
e1,
|
||||
e2,
|
||||
e1.clone().simplify(),
|
||||
e2.clone().simplify()
|
||||
);
|
||||
println!(
|
||||
"e1==e2: {}=={} => {}=={}",
|
||||
e1,
|
||||
e2,
|
||||
e1.clone().distrubute(),
|
||||
e2.clone().distrubute()
|
||||
);
|
||||
let eqn = Eqn(e1, e2);
|
||||
let e = eqn.solve(u1).unwrap();
|
||||
assert!(const_expr(e.clone()).is_some());
|
||||
assert!(relative_eq!(const_expr(e.clone()).unwrap(), -6.));
|
||||
|
||||
let e1 = Expr::new_product(Const(2.), Expr::new_minus(Const(1.), Const(4.)));
|
||||
let e2 = Expr::new_div(
|
||||
Expr::new_sum(
|
||||
Expr::new_product(Unkn(u1), Const(2.)),
|
||||
Expr::new_product(Unkn(u1), Unkn(u1)),
|
||||
),
|
||||
Unkn(u1),
|
||||
);
|
||||
info!(
|
||||
"{}=={} distrib=> {}=={}",
|
||||
e1,
|
||||
e2,
|
||||
e1.clone().distribute(),
|
||||
e2.clone().distribute()
|
||||
);
|
||||
info!(
|
||||
"{}=={} simplify=> {}=={}",
|
||||
e1,
|
||||
e2,
|
||||
e1.clone().distribute().simplify(),
|
||||
e2.clone().distribute().simplify()
|
||||
);
|
||||
let eqn = Eqn(e1, e2);
|
||||
let e = eqn.solve(u1).unwrap();
|
||||
assert!(const_expr(e.clone()).is_some());
|
||||
assert!(relative_eq!(const_expr(e.clone()).unwrap(), -8.));
|
||||
|
||||
let e1 = Expr::new_product(Const(2.), Expr::new_minus(Const(1.), Const(4.)));
|
||||
let e2 = Expr::new_div(
|
||||
Expr::new_sum(
|
||||
Expr::new_product(Unkn(u1), Const(2.)),
|
||||
Expr::new_sum(
|
||||
Expr::new_sum(Expr::new_product(Unkn(u1), Unkn(u1)), Unkn(u1)),
|
||||
Expr::new_minus(Const(2.), Const(1. + 1.)),
|
||||
),
|
||||
),
|
||||
Unkn(u1),
|
||||
);
|
||||
info!(
|
||||
"e1==e2: {}=={} => {}=={}",
|
||||
e1,
|
||||
e2,
|
||||
e1.clone().distribute().simplify(),
|
||||
e2.clone().distribute().simplify().simplify()
|
||||
);
|
||||
let eqn = Eqn(e1, e2);
|
||||
let e = eqn.solve(u1).unwrap();
|
||||
assert!(const_expr(e.clone()).is_some());
|
||||
assert!(relative_eq!(const_expr(e.clone()).unwrap(), -9.));
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user