update readme

Author: HugoMVale

README.md

@@ -1,31 +1,23 @@
-# odrpack
+# odrpack (-python)
 
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 ## Description
 
-`odrpack` is a package for weighted orthogonal distance regression (ODR), also known as [errors-in-variables regression]. 
-It is designed primarily for instances when both the explanatory and response variables have significant errors. 
-The package implements a highly efficient algorithm for minimizing the sum of the squares of the weighted orthogonal
-distances between each data point and the curve described by the model equation, subject to parameter bounds. The nonlinear
-model can be either explicit or implicit. Additionally, `odrpack` can be used to solve the ordinary least squares problem where all of
-the errors are attributed to the observations of the dependent variable.
+This Python package provides bindings for the well-known weighted orthogonal distance regression
+(ODR) solver [odrpack95]. This design ensures that users benefit from the performance and reliability
+of the original Fortran implementation, while working within the modern Python ecosystem.  
+
+ODR, also known as [errors-in-variables regression], is designed primarily for instances when both
+the explanatory and response variables have significant errors. 
 
 <p align="center">
   <img src="https://upload.wikimedia.org/wikipedia/commons/thumb/8/81/Total_least_squares.svg/220px-Total_least_squares.svg.png" width="200" alt="Deming regression; special case of ODR.">
 </p>
 
 [errors-in-variables regression]: https://en.wikipedia.org/wiki/Errors-in-variables_models
-
-## Python Bindings for Fortran Implementation
-
-The `odrpack` Python package provides convient bindings for the efficient ODR solver available
-in the Fortran [odrpack95] repository. This design ensures that users benefit from the performance
-and reliability of the original Fortran implementation, while working within the modern Python
-ecosystem.  
-
 [odrpack95]: https://github.com/HugoMVale/odrpack95
 
 
@@ -55,23 +47,13 @@ def f(beta: np.ndarray, x: np.ndarray) -> np.ndarray:
     return beta[0] * np.exp(beta[1]*x)
 
 
-def fjacb(beta: np.ndarray, x: np.ndarray) -> np.ndarray:
-    "Model jacobian w.r.t. the model parameters."
-    jac = np.zeros((beta.size, x.size))
-    jac[0, :] = np.exp(beta[1]*x)
-    jac[1, :] = beta[0]*x*np.exp(beta[1]*x)
-    return jac
-
-
-def fjacd(beta: np.ndarray, x: np.ndarray) -> np.ndarray:
-    "Model jacobian w.r.t. the error in the explanatory variable."
-    return beta[0] * beta[1] * np.exp(beta[1]*x)
-
-
-sol = odr(f, beta0, y, x, lower=lower, upper=upper,
-          fjacb=fjacb, fjacd=fjacd,
-          job=20, iprint=1001)
+sol = odr(f, beta0, y, x, lower=lower, upper=upper, iprint=1001)
 
 print("\n beta:", sol.beta)
 print("\n delta:", sol.delta)
+```
+
+```sh
+beta: [1.63337057 0.9       ]
+delta: [-0.36885787 -0.31272733  0.02928942  0.11031791]
 ```