merge

cxroots/ApproximateRoots.py

@@ -31,68 +31,68 @@ def approximate_roots(
     Parameters
     ----------
     C : :class:`~<cxroots.Contour.Contour>`
-            The contour which encloses the roots of f the user wishes to find.
+        The contour which encloses the roots of f the user wishes to find.
     N : int
-            The number of roots (counting multiplicties) of f within C.
-            This is the result of calling :meth:`~cxroots.Contour.Contour.count_roots`.
+        The number of roots (counting multiplicties) of f within C.
+        This is the result of calling :meth:`~cxroots.Contour.Contour.count_roots`.
     f : function
-            The function for which the roots are sought.  Must be a function
-            of a single complex variable, z, which is analytic within C and
-            has no poles or roots on the C.
+        The function for which the roots are sought.  Must be a function
+        of a single complex variable, z, which is analytic within C and
+        has no poles or roots on the C.
     df : function, optional
-            A function of a single complex variable which is the derivative
-            of the function f(z). If df is not given then it will be
-            approximated with a finite difference formula.
+        A function of a single complex variable which is the derivative
+        of the function f(z). If df is not given then it will be
+        approximated with a finite difference formula.
     absTol : float, optional
-            Absolute error tolerance for integration.
+        Absolute error tolerance for integration.
     relTol : float, optional
-            Relative error tolerance for integration.
+        Relative error tolerance for integration.
     errStop : float, optional
-            The number of distinct roots within a contour, n, is determined
-            by checking if all the elements of a list of contour integrals
-            involving formal orthogonal polynomials are sufficently close to
-            zero, ie. that the absolute value of each element is < errStop.
-            If errStop is too large/small then n may be smaller/larger than
-            it actually is.
+        The number of distinct roots within a contour, n, is determined
+        by checking if all the elements of a list of contour integrals
+        involving formal orthogonal polynomials are sufficently close to
+        zero, ie. that the absolute value of each element is < errStop.
+        If errStop is too large/small then n may be smaller/larger than
+        it actually is.
     divMin : int, optional
-            If the Romberg integration method is used then divMin is the
-            minimum number of divisions before the Romberg integration
-            routine is allowed to exit.
+        If the Romberg integration method is used then divMin is the
+        minimum number of divisions before the Romberg integration
+        routine is allowed to exit.
     divMax : int, optional
-            If the Romberg integration method is used then divMax is the
-            maximum number of divisions before the Romberg integration
-            routine exits.
+        If the Romberg integration method is used then divMax is the
+        maximum number of divisions before the Romberg integration
+        routine exits.
     m : int, optional
-            Only used if df=None and method='quad'.  The argument order=m is
-            passed to numdifftools.Derivative and is the order of the error
-            term in the Taylor approximation.  m must be even.
+        Only used if df=None and method='quad'.  The argument order=m is
+        passed to numdifftools.Derivative and is the order of the error
+        term in the Taylor approximation.  m must be even.
     rootTol : float, optional
-            If any roots are within rootTol of one another then they will be
-            treated as duplicates and removed.  This helps to alleviate the
-            problem of errStop being too small.
+        If any roots are within rootTol of one another then they will be
+        treated as duplicates and removed.  This helps to alleviate the
+        problem of errStop being too small.
     intMethod : {'quad', 'romb'}, optional
-            If 'quad' then :func:`scipy.integrate.quad` is used to perform
-            integration.  If 'romb' then Romberg integraion is performed
-            instead.
+        If 'quad' then :func:`scipy.integrate.quad` is used to perform
+        integration.  If 'romb' then Romberg integraion is performed
+        instead.
     callback : function, optional
-            Only used if intMethod is 'romb'.  Passed to :func:`~<cxroots.CountRoots.prod>`.
+        Only used if intMethod is 'romb'.  Passed to :func:`~<cxroots.CountRoots.prod>`.
 
     Returns
     -------
     tuple of complex
-            The distinct roots of f within the contour C.
+        The distinct roots of f within the contour C.
     tuple of float
-            The corresponding multiplicites of the roots within C.  Should
-            be integers but will not be automatically rounded here.
+        The corresponding multiplicites of the roots within C.  Should
+        be integers but will not be automatically rounded here.
 
     References
     ----------
     .. [KB] P. Kravanja and M. Van Barel. "Computing the Zeros of
-            Anayltic Functions". Springer (2000)
+        Anayltic Functions". Springer (2000)
     .. [SLV] E. Strakova, D. Lukas, P. Vodstrcil. "Finding Zeros of
-            Analytic Functions and Local Eigenvalue Analysis Using Contour
-            Integral Method in Examples". Mathematical Analysis and Numerical
-            Mathematics, Vol. 15, 2, (2017)
+        Analytic Functions and Local Eigenvalue Analysis Using Contour
+        Integral Method in Examples". Mathematical Analysis and Numerical
+        Mathematics, Vol. 15, 2, (2017)
     """
     logger = logging.getLogger(__name__)
     logger.info("Approximating the " + str(N) + " roots in: " + str(C))

cxroots/Contour.py

@@ -18,9 +18,9 @@ class Contour(object):
     Attributes
     ----------
     centralPoint : complex
-            The point at the center of the contour.
+        The point at the center of the contour.
     area : float
-            The surface area of the contour.
+        The surface area of the contour.
     """
 
     def __init__(self, segments):
@@ -34,19 +34,19 @@ def __call__(self, t):
         Parameters
         ----------
         t : float
-                A real number :math:`0\leq t \leq 1` which parameterises
-                the contour.
+            A real number :math:`0\leq t \leq 1` which parameterises
+            the contour.
 
         Returns
         -------
         complex
-                A point on the contour.
+            A point on the contour.
 
         Example
         -------
 
         >>> from cxroots.Paths import Circle
-        >>> c = Circle(0,1)	# Circle |z|=1 parameterised by e^{it}
+        >>> c = Circle(0,1) # Circle |z|=1 parameterised by e^{it}
         >>> c(0.25)
         (6.123233995736766e-17+1j)
         >>> c(0) == c(1)
@@ -85,7 +85,7 @@ def contains(self, z):
         Returns
         -------
         bool
-                True if z lies within the contour and false otherwise.
+            True if z lies within the contour and false otherwise.
         """
         raise NotImplementedError("contains() needs to be implemented in the subclass.")
 
@@ -118,10 +118,10 @@ def show(self, saveFile=None, **plotKwargs):
         Parameters
         ----------
         saveFile : str (optional)
-                If given then the plot will be saved to disk with name
-                'saveFile'.  If saveFile=None the plot is shown on-screen.
+            If given then the plot will be saved to disk with name
+            'saveFile'.  If saveFile=None the plot is shown on-screen.
         **plotKwargs
-                Key word arguments are as in :meth:`~cxroots.Contour.Contour.plot`.
+            Key word arguments are as in :meth:`~cxroots.Contour.Contour.plot`.
         """
         import matplotlib.pyplot as plt
 
@@ -140,18 +140,18 @@ def subdivisions(self, axis="alternating"):
         Parameters
         ----------
         axis : str, 'alternating' or any element of self.axisName.
-                The axis along which the line subdividing the contour is a
-                constant (eg. subdividing a circle along the radial axis
-                will give an outer annulus and an inner circle).  If
-                alternating then the dividing axis will always be different
-                to the dividing axis used to create the contour which is now
-                being divided.
+            The axis along which the line subdividing the contour is a
+            constant (eg. subdividing a circle along the radial axis
+            will give an outer annulus and an inner circle).  If
+            alternating then the dividing axis will always be different
+            to the dividing axis used to create the contour which is now
+            being divided.
 
         Yields
         ------
         tuple
-                A tuple with two contours which subdivide the original
-                contour.
+            A tuple with two contours which subdivide the original
+            contour.
         """
         if axis == "alternating":
             if hasattr(self, "_createdBySubdivisionAxis"):
@@ -170,14 +170,14 @@ def distance(self, z):
         Parameters
         ----------
         z : complex
-                The point from which to measure the distance to the closest
-                point on the contour to z.
+            The point from which to measure the distance to the closest
+            point on the contour to z.
 
         Returns
         -------
         float
-                The distance from z to the point on the contour which is
-                closest to z.
+            The distance from z to the point on the contour which is
+            closest to z.
         """
         return min(segment.distance(z) for segment in self.segments)