Add fidget::solver module (#129)

CHANGELOG.md

@@ -5,6 +5,11 @@
   type to match `Context::get_var`.
 - Added `impl From<i32> for Tree` to make writing tree expressions easier
 - Removed `Error::ReservedName` and `Error::DuplicateName`, which were unused
+- Add the `fidget::solver` module, which contains a simple solver for systems of
+  equations.  The solver requires the equations to implement Fidget's `Function`
+  trait.  It uses both point-wise and gradient evaluation to solve for a set of
+  `Var` values, using the Levenberg-Marquardt algorithm.
+- Add `Tree::var()` and `impl TryFrom<Tree> for Var`
 
 # 0.3.0
 - Major refactoring of core evaluation traits

fidget/Cargo.toml

@@ -40,7 +40,7 @@ windows = { version = "0.54.0", features = ["Win32_Foundation", "Win32_System_Me
 getrandom = { version = "0.2", features = ["js"] }
 
 [features]
-default = ["jit", "rhai", "render", "mesh"]
+default = ["jit", "rhai", "render", "mesh", "solver"]
 
 ## Enables fast evaluation via a JIT compiler.  This is exposed in the
 ## [`fidget::jit`](crate::jit) module, and is supported on macOS, Linux, and
@@ -60,13 +60,18 @@ render = []
 ## Enable 3D meshing, in the [`fidget::mesh`](crate::mesh) module
 mesh = ["dep:crossbeam-deque"]
 
+## Enable a system-of-equations solver, in the [`fidget::solver`](crate::solver)
+## module
+solver = []
+
 ## Enable `eval-tests` if you're writing your own evaluators and want to
 ## unit-test them.  When enabled, the crate exports a set of macros to test each
 ## evaluator type, e.g. `float_slice_tests!(...)`.
 eval-tests = []
 
 [dev-dependencies]
 criterion = { version = "0.5", features = ["html_reports"] }
+approx = "0.5.1"
 
 [[bench]]
 name = "render"

fidget/src/core/context/tree.rs

@@ -1,6 +1,6 @@
 //! Context-free math trees
 use super::op::{BinaryOpcode, UnaryOpcode};
-use crate::var::Var;
+use crate::{var::Var, Error};
 use std::sync::Arc;
 
 /// Opcode type for trees
@@ -159,6 +159,22 @@ impl Tree {
             z: z.0,
         }))
     }
+
+    /// Returns the inner [`Var`] if this is an input tree, or `None`
+    pub fn var(&self) -> Option<Var> {
+        if let TreeOp::Input(v) = &*self.0 {
+            Some(*v)
+        } else {
+            None
+        }
+    }
+}
+
+impl TryFrom<Tree> for Var {
+    type Error = Error;
+    fn try_from(t: Tree) -> Result<Var, Error> {
+        t.var().ok_or(Error::NotAVar)
+    }
 }
 
 /// See [`Context`](crate::Context) for documentation of these functions

fidget/src/error.rs

@@ -61,6 +61,10 @@ pub enum Error {
     #[error("variable index ({0}) exceeds max var index for this tape ({1})")]
     BadVarIndex(usize, usize),
 
+    /// Could not solve for matrix pseudo-inverse
+    #[error("could not solve for matrix pseudo-inverse: {0}")]
+    SingularMatrix(&'static str),
+
     /// io error; see inner code for details
     #[error("io error: {0}")]
     IoError(#[from] std::io::Error),

fidget/src/lib.rs

@@ -282,3 +282,6 @@ pub mod jit;
 
 #[cfg(feature = "mesh")]
 pub mod mesh;
+
+#[cfg(feature = "solver")]
+pub mod solver;