kalix 0.2.1

Declarative Kalman filtering from dynamics expressions. Write the physics, derive the filter.
Documentation 
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#[cfg(test)]
mod tests {
    use kalix::expr::diff::diff;
    use kalix::expr::eval::eval;
    use kalix::expr::parser::parse;

    fn diff_and_eval(expr_str: &str, var: &str, bindings: &[(&str, f64)]) -> f64 {
        let expr = parse(expr_str).unwrap();
        let d = diff(&expr, var);
        eval(&d, bindings).unwrap()
    }

    #[test]
    fn test_diff_pos_independent_of_bindings() {
        let expr = "pos + vel*dt + 0.5*acc*dt^2";

        let v = diff_and_eval(
            expr,
            "pos",
            &[("pos", 0.0), ("vel", 0.0), ("acc", 0.0), ("dt", 1.0)],
        );
        assert!((v - 1.0).abs() < 1e-15);

        let v = diff_and_eval(
            expr,
            "pos",
            &[("pos", 5.0), ("vel", 3.0), ("acc", 1.0), ("dt", 0.5)],
        );
        assert!((v - 1.0).abs() < 1e-15);
    }

    #[test]
    fn test_diff_vel_equals_dt() {
        let expr = "pos + vel*dt + 0.5*acc*dt^2";

        let v = diff_and_eval(
            expr,
            "vel",
            &[("pos", 0.0), ("vel", 0.0), ("acc", 0.0), ("dt", 1.0)],
        );
        assert!((v - 1.0).abs() < 1e-15);

        let v = diff_and_eval(
            expr,
            "vel",
            &[("pos", 0.0), ("vel", 0.0), ("acc", 0.0), ("dt", 0.5)],
        );
        assert!((v - 0.5).abs() < 1e-15);
    }

    #[test]
    fn test_diff_acc_equals_half_dt_squared() {
        let expr = "pos + vel*dt + 0.5*acc*dt^2";

        // d/d(acc) = 0.5 * dt^2
        let v = diff_and_eval(
            expr,
            "acc",
            &[("pos", 0.0), ("vel", 0.0), ("acc", 0.0), ("dt", 1.0)],
        );
        assert!((v - 0.5).abs() < 1e-15);

        // 0.5 * (0.5)^2 = 0.5 * 0.25 = 0.125
        let v = diff_and_eval(
            expr,
            "acc",
            &[("pos", 0.0), ("vel", 0.0), ("acc", 0.0), ("dt", 0.5)],
        );
        assert!((v - 0.125).abs() < 1e-15);
    }

    #[test]
    fn test_diff_pos_simplifies_to_lit_one() {
        use kalix::expr::ast::Expr;
        let expr = parse("pos").unwrap();
        let d = diff(&expr, "pos");
        assert!(matches!(d, Expr::Lit(v) if v == 1.0));
    }

    #[test]
    fn test_diff_vel_and_acc_in_vel_plus_acc_dt() {
        let expr = "vel + acc*dt";

        let v = diff_and_eval(expr, "vel", &[("vel", 0.0), ("acc", 0.0), ("dt", 1.0)]);
        assert!((v - 1.0).abs() < 1e-15);

        let v = diff_and_eval(expr, "acc", &[("vel", 0.0), ("acc", 0.0), ("dt", 1.0)]);
        assert!((v - 1.0).abs() < 1e-15);

        let v = diff_and_eval(expr, "acc", &[("vel", 0.0), ("acc", 0.0), ("dt", 0.5)]);
        assert!((v - 0.5).abs() < 1e-15);
    }

    #[test]
    fn test_diff_sin_x_is_cos_x() {
        // d/dx(sin(x)) = cos(x)
        let v = diff_and_eval("sin(x)", "x", &[("x", 0.0)]);
        assert!((v - 1.0).abs() < 1e-15);

        let v = diff_and_eval("sin(x)", "x", &[("x", std::f64::consts::FRAC_PI_3)]);
        assert!((v - 0.5).abs() < 1e-10);
    }

    #[test]
    fn test_diff_cos_x_is_neg_sin_x() {
        // d/dx(cos(x)) = -sin(x)
        let v = diff_and_eval("cos(x)", "x", &[("x", 0.0)]);
        assert!((v - 0.0).abs() < 1e-15);

        let v = diff_and_eval("cos(x)", "x", &[("x", std::f64::consts::FRAC_PI_6)]);
        assert!((v + 0.5).abs() < 1e-10);
    }

    #[test]
    fn test_diff_sin_of_linear_uses_chain_rule() {
        // d/dx(sin(a*x + b)) = cos(a*x + b) * a
        let expr = "sin(2.0*x + 1.0)";

        let v = diff_and_eval(expr, "x", &[("x", 0.0)]);
        let expected = 2.0 * 1.0_f64.cos();
        assert!((v - expected).abs() < 1e-10);
    }

    #[test]
    fn test_diff_sin_pos_is_cos_pos() {
        // d/dx(sin(x)) when 'pos' is the variable name
        let v = diff_and_eval("sin(pos)", "pos", &[("pos", 0.0)]);
        assert!((v - 1.0).abs() < 1e-15);

        let v = diff_and_eval("sin(pos)", "pos", &[("pos", std::f64::consts::FRAC_PI_6)]);
        let expected = (std::f64::consts::FRAC_PI_6).cos();
        assert!((v - expected).abs() < 1e-10);
    }

    #[test]
    fn test_diff_trig_wrt_other_var_is_zero() {
        // d/dy(sin(x)) = cos(x) * 0 = 0
        let v = diff_and_eval("sin(x)", "y", &[("x", 1.0), ("y", 0.0)]);
        assert!((v - 0.0).abs() < 1e-15);
    }

    // ── log / exp differentiation ──────────────────────────────────

    #[test]
    fn test_diff_log_x_is_one_over_x() {
        // d/dx(log(x)) = 1/x
        let v = diff_and_eval("log(x)", "x", &[("x", 2.0)]);
        assert!((v - 0.5).abs() < 1e-15);

        let v = diff_and_eval("log(x)", "x", &[("x", 1.0)]);
        assert!((v - 1.0).abs() < 1e-15);
    }

    #[test]
    fn test_diff_exp_x_is_exp_x() {
        // d/dx(exp(x)) = exp(x)
        let v = diff_and_eval("exp(x)", "x", &[("x", 0.0)]);
        assert!((v - 1.0).abs() < 1e-15);

        let v = diff_and_eval("exp(x)", "x", &[("x", 1.0)]);
        let expected = 1.0_f64.exp();
        assert!((v - expected).abs() < 1e-10);
    }

    #[test]
    fn test_diff_log_of_linear_uses_chain_rule() {
        // d/dx(log(a*x + b)) = a / (a*x + b)
        let expr = "log(3.0*x + 2.0)";

        let v = diff_and_eval(expr, "x", &[("x", 1.0)]);
        let expected = 3.0 / 5.0; // 3 / (3*1 + 2)
        assert!((v - expected).abs() < 1e-10);
    }

    #[test]
    fn test_diff_exp_of_linear_uses_chain_rule() {
        // d/dx(exp(a*x + b)) = exp(a*x + b) * a
        let expr = "exp(2.0*x + 1.0)";

        let v = diff_and_eval(expr, "x", &[("x", 0.0)]);
        let expected = 2.0 * 1.0_f64.exp();
        assert!((v - expected).abs() < 1e-10);
    }

    #[test]
    fn test_diff_log_wrt_other_var_is_zero() {
        let v = diff_and_eval("log(x)", "y", &[("x", 2.0), ("y", 0.0)]);
        assert!((v - 0.0).abs() < 1e-15);
    }

    #[test]
    fn test_eval_log_of_negative_rejected() {
        use kalix::expr::eval::eval;
        use kalix::expr::parser::parse;

        let expr = parse("log(x)").unwrap();
        let result = eval(&expr, &[("x", -1.0)]);
        assert!(result.is_err());
        assert!(result.unwrap_err().contains("log of non-positive"));
    }
}