ENH: reimplement bijection checks from 10bf4cd

Author: phmbressan

rocketpy/Function.py

@@ -2411,20 +2411,99 @@ def integralFunction(self, lower=None, upper=None, datapoints=100):
                 outputs=[o + " Integral" for o in self.__outputs__],
             )
 
+    def isBijective(self):
+        """Checks whether the Function is bijective. Only applicable to
+        Functions whose source is a list of points, raises an error otherwise.
+
+        Returns
+        -------
+        result : bool
+            True if the Function is bijective, False otherwise.
+        """
+        if isinstance(self.source, np.ndarray):
+            xDataDistinct = set(self.xArray)
+            yDataDistinct = set(self.yArray)
+            distinctMap = set(zip(xDataDistinct, yDataDistinct))
+            return len(distinctMap) == len(xDataDistinct) == len(yDataDistinct)
+        else:
+            raise TypeError(
+                "Only Functions whose source is a list of points can be "
+                "checked for bijectivity."
+            )
+
+    def isStrictlyBijective(self):
+        """Checks whether the Function is "strictly" bijective.
+        Only applicable to Functions whose source is a list of points,
+        raises an error otherwise.
+
+        Notes
+        -----
+        By "strictly" bijective, this implementation considers the
+        list-of-points-defined Function bijective between each consecutive pair
+        of points. Therefore, the Function may be flagged as not bijective even
+        if the mapping between the set of points which define the Function is
+        bijective.
+
+        Returns
+        -------
+        result : bool
+            True if the Function is "strictly" bijective, False otherwise.
+
+        Examples
+        --------
+        >>> f = Function([[0, 0], [1, 1], [2, 4]])
+        >>> f.isBijective()
+        True
+        >>> f.isStrictlyBijective()
+        True
+
+        >>> f = Function([[-1, 1], [0, 0], [1, 1], [2, 4]])
+        >>> f.isBijective()
+        False
+        >>> f.isStrictlyBijective()
+        False
+
+        A Function which is not "strictly" bijective, but is bijective, can be
+        constructed as x^2 defined at -1, 0 and 2.
+
+        >>> f = Function([[-1, 1], [0, 0], [2, 4]])
+        >>> f.isBijective()
+        True
+        >>> f.isStrictlyBijective()
+        False
+        """
+        if isinstance(self.source, np.ndarray):
+            # Assuming domain is sorted, range must also be
+            yData = self.yArray
+            # Both ascending and descending order means Function is bijective
+            yDataDiff = np.diff(yData)
+            return np.all(yDataDiff >= 0) or np.all(yDataDiff <= 0)
+        else:
+            raise TypeError(
+                "Only Functions whose source is a list of points can be "
+                "checked for bijectivity."
+            )
+
     def inverseFunction(self, approxFunc=None, tol=1e-4):
         """
         Returns the inverse of the Function. The inverse function of F is a
         function that undoes the operation of F. The inverse of F exists if
         and only if F is bijective. Makes the domain the range and the range
         the domain.
 
+        If the Function is given by a list of points, its bijectivity is
+        checked and an error is raised if it is not bijective.
+        If the Function is given by a function, its bijection is not
+        checked and may lead to innacuracies outside of its bijective region.
+
         Parameters
         ----------
         approxFunc : callable, optional
             A function that approximates the inverse of the Function. This
             function is used to find the starting guesses for the inverse
             root finding algorithm. This is better used when the inverse
-            in complex but has a simple approximation.
+            in complex but has a simple approximation or when the root
+            finding algorithm performs poorly due to default start point.
             The default is None in which case the starting point is zero.
 
         tol : float, optional
@@ -2437,10 +2516,15 @@ def inverseFunction(self, approxFunc=None, tol=1e-4):
             A Function whose domain and range have been inverted.
         """
         if isinstance(self.source, np.ndarray):
-            # Swap the columns
-            source = np.flip(self.source, axis=1)
+            if self.isStrictlyBijective():
+                # Swap the columns
+                source = np.flip(self.source, axis=1)
+            else:
+                raise ValueError(
+                    "Function is not bijective, so it does not have an inverse."
+                )
         else:
-            if approxFunc:
+            if approxFunc is not None:
                 source = lambda x: self.findInput(x, start=approxFunc(x), tol=tol)
             else:
                 source = lambda x: self.findInput(x, start=0, tol=tol)