Merge branch 'fight_the_power' into 'master'

replace ** with clearer operators where possible

See merge request !149

nifty/minimization/line_searching/line_search_strong_wolfe.py

@@ -23,29 +23,29 @@ from .line_search import LineSearch
 
 class LineSearchStrongWolfe(LineSearch):
     """Class for finding a step size that satisfies the strong Wolfe conditions.
-    
-    Algorithm contains two stages. It begins whit a trial step length and it 
+
+    Algorithm contains two stages. It begins whit a trial step length and it
     keeps increasing the it until it finds an acceptable step length or an
-    interval. If it does not satisfy the Wolfe conditions it performs the Zoom 
-    algorithm (second stage). By interpolating it decreases the size of the 
-    interval until an acceptable step length is found.  
-    
+    interval. If it does not satisfy the Wolfe conditions it performs the Zoom
+    algorithm (second stage). By interpolating it decreases the size of the
+    interval until an acceptable step length is found.
+
     Parameters
     ----------
-    c1 : float 
+    c1 : float
         Parameter for Armijo condition rule. (Default: 1e-4)
     c2 : float
         Parameter for curvature condition rule. (Default: 0.9)
     max_step_size : float
-        Maximum step allowed in to be made in the descent direction. 
+        Maximum step allowed in to be made in the descent direction.
         (Default: 50)
     max_iterations : integer
         Maximum number of iterations performed by the line search algorithm.
         (Default: 10)
     max_zoom_iterations : integer
-        Maximum number of iterations performed by the zoom algorithm. 
+        Maximum number of iterations performed by the zoom algorithm.
         (Default: 10)
-        
+
     Attributes
     ----------
     c1 : float
@@ -53,19 +53,18 @@ class LineSearchStrongWolfe(LineSearch):
     c2 : float
         Parameter for curvature condition rule.
     max_step_size : float
-        Maximum step allowed in to be made in the descent direction. 
+        Maximum step allowed in to be made in the descent direction.
     max_iterations : integer
         Maximum number of iterations performed by the line search algorithm.
     max_zoom_iterations : integer
         Maximum number of iterations performed by the zoom algorithm.
-        
+
     """
 
     def __init__(self, c1=1e-4, c2=0.9,
                  max_step_size=50, max_iterations=10,
                  max_zoom_iterations=10):
 
-
         super(LineSearchStrongWolfe, self).__init__()
 
         self.c1 = np.float(c1)
@@ -76,11 +75,11 @@ class LineSearchStrongWolfe(LineSearch):
 
     def perform_line_search(self, energy, pk, f_k_minus_1=None):
         """Performs the first stage of the algorithm.
-        
-        It starts with a trial step size and it keeps increasing it until it 
-        satisfy the strong Wolf conditions. It also performs the descent and 
+
+        It starts with a trial step size and it keeps increasing it until it
+        satisfy the strong Wolf conditions. It also performs the descent and
         returns the optimal step length and the new enrgy.
-        
+
         Parameters
         ----------
         energy : Energy object
@@ -89,9 +88,9 @@ class LineSearchStrongWolfe(LineSearch):
         pk : Field
             Unit vector pointing into the search direction.
         f_k_minus_1 : float
-            Value of the fuction (which is being minimized) at the k-1 
+            Value of the fuction (which is being minimized) at the k-1
             iteration of the line search procedure. (Default: None)
-        
+
         Returns
         -------
         alpha_star : float
@@ -100,9 +99,9 @@ class LineSearchStrongWolfe(LineSearch):
             Value of the energy after the performed descent.
         energy_star : Energy object
             The new Energy object on the new position.
-            
-        """        
-        
+
+        """
+
         self._set_line_energy(energy, pk, f_k_minus_1=f_k_minus_1)
         c1 = self.c1
         c2 = self.c2
@@ -195,11 +194,11 @@ class LineSearchStrongWolfe(LineSearch):
     def _zoom(self, alpha_lo, alpha_hi, phi_0, phiprime_0,
               phi_lo, phiprime_lo, phi_hi, c1, c2):
         """Performs the second stage of the line search algorithm.
-        
-        If the first stage was not successful then the Zoom algorithm tries to 
-        find a suitable step length by using bisection, quadratic, cubic 
+
+        If the first stage was not successful then the Zoom algorithm tries to
+        find a suitable step length by using bisection, quadratic, cubic
         interpolation.
-        
+
         Parameters
         ----------
         alpha_lo : float
@@ -207,24 +206,24 @@ class LineSearchStrongWolfe(LineSearch):
         alph_hi : float
             The upper boundary for the step length interval.
         phi_0 : float
-            Value of the energy at the starting point of the line search 
+            Value of the energy at the starting point of the line search
             algorithm.
         phiprime_0 : Field
             Gradient at the starting point of the line search algorithm.
         phi_lo : float
-            Value of the energy if we perform a step of length alpha_lo in 
+            Value of the energy if we perform a step of length alpha_lo in
             descent direction.
         phiprime_lo : Field
-            Gradient at the nwe position if we perform a step of length 
+            Gradient at the nwe position if we perform a step of length
             alpha_lo in descent direction.
         phi_hi : float
-            Value of the energy if we perform a step of length alpha_hi in 
+            Value of the energy if we perform a step of length alpha_hi in
             descent direction.
         c1 : float
             Parameter for Armijo condition rule.
         c2 : float
             Parameter for curvature condition rule.
-        
+
         Returns
         -------
         alpha_star : float
@@ -233,7 +232,7 @@ class LineSearchStrongWolfe(LineSearch):
             Value of the energy after the performed descent.
         energy_star : Energy object
             The new Energy object on the new position.
-        
+
         """
         max_iterations = self.max_zoom_iterations
         # define the cubic and quadratic interpolant checks
@@ -306,12 +305,13 @@ class LineSearchStrongWolfe(LineSearch):
 
     def _cubicmin(self, a, fa, fpa, b, fb, c, fc):
         """Estimating the minimum with cubic interpolation.
-        
+
         Finds the minimizer for a cubic polynomial that goes through the
-        points ( a,f(a) ), ( b,f(b) ), and ( c,f(c) ) with derivative at point a of fpa.
+        points ( a,f(a) ), ( b,f(b) ), and ( c,f(c) ) with derivative at point
+        a of fpa.
         f(x) = A *(x-a)^3 + B*(x-a)^2 + C*(x-a) + D
         If no minimizer can be found return None
-        
+
         Parameters
         ----------
         a : float
@@ -328,12 +328,12 @@ class LineSearchStrongWolfe(LineSearch):
             Selected point.
         fc : float
             Value of polynomial at point c.
-        
+
         Returns
         -------
         xmin : float
             Position of the approximated minimum.
-        
+
         """
 
         with np.errstate(divide='raise', over='raise', invalid='raise'):
@@ -341,12 +341,12 @@ class LineSearchStrongWolfe(LineSearch):
                 C = fpa
                 db = b - a
                 dc = c - a
-                denom = (db * dc) ** 2 * (db - dc)
+                denom = db * db * dc * dc * (db - dc)
                 d1 = np.empty((2, 2))
-                d1[0, 0] = dc ** 2
-                d1[0, 1] = -db ** 2
-                d1[1, 0] = -dc ** 3
-                d1[1, 1] = db ** 3
+                d1[0, 0] = dc * dc
+                d1[0, 1] = -(db*db)
+                d1[1, 0] = -(dc*dc*dc)
+                d1[1, 1] = db*db*db
                 [A, B] = np.dot(d1, np.asarray([fb - fa - C * db,
                                                 fc - fa - C * dc]).flatten())
                 A /= denom
@@ -361,11 +361,11 @@ class LineSearchStrongWolfe(LineSearch):
 
     def _quadmin(self, a, fa, fpa, b, fb):
         """Estimating the minimum with quadratic interpolation.
-        
+
         Finds the minimizer for a quadratic polynomial that goes through
         the points ( a,f(a) ), ( b,f(b) ) with derivative at point a of fpa.
         f(x) = B*(x-a)^2 + C*(x-a) + D
-        
+
         Parameters
         ----------
         a : float
@@ -378,11 +378,11 @@ class LineSearchStrongWolfe(LineSearch):
             Selected point.
         fb : float
             Value of polynomial at point b.
-        
+
         Returns
         -------
         xmin : float
-            Position of the approximated minimum.       
+            Position of the approximated minimum.
         """
         # f(x) = B*(x-a)^2 + C*(x-a) + D
         with np.errstate(divide='raise', over='raise', invalid='raise'):

nifty/operators/fft_operator/transformations/rgrgtransformation.py

@@ -118,7 +118,7 @@ class RGRGTransformation(Transformation):
             np.absolute(np.array(domain.shape) *
                         np.array(domain.distances) *
                         np.array(codomain.distances) - 1) <
-                10**-7):
+                1e-7):
             raise AttributeError("The grid-distances of domain and codomain "
                                  "do not match.")
 

nifty/spaces/hp_space/hp_space.py

@@ -93,11 +93,11 @@ class HPSpace(Space):
 
     @property
     def shape(self):
-        return (np.int(12 * self.nside ** 2),)
+        return (np.int(12 * self.nside * self.nside),)
 
     @property
     def dim(self):
-        return np.int(12 * self.nside ** 2)
+        return np.int(12 * self.nside * self.nside)
 
     @property
     def total_volume(self):
@@ -108,7 +108,7 @@ class HPSpace(Space):
 
     def weight(self, x, power=1, axes=None, inplace=False):
 
-        weight = ((4 * np.pi) / (12 * self.nside**2)) ** np.float(power)
+        weight = ((4*np.pi) / (12*self.nside*self.nside)) ** np.float(power)
 
         if inplace:
             x *= weight

nifty/spaces/lm_space/lm_space.py

@@ -130,7 +130,7 @@ class LMSpace(Space):
         # dim = (((2*(l+1)-1)+1)**2/4 - 2 * (l-m)(l-m+1)/2
         # dim = np.int((l+1)**2 - (l-m)*(l-m+1.))
         # We fix l == m
-        return np.int((l+1)**2)
+        return np.int((l+1)*(l+1))
 
     @property
     def total_volume(self):
@@ -166,7 +166,7 @@ class LMSpace(Space):
 
     def get_fft_smoothing_kernel_function(self, sigma):
         # FIXME why x(x+1) ? add reference to paper!
-        return lambda x: np.exp(-0.5 * x * (x + 1) * sigma**2)
+        return lambda x: np.exp(-0.5 * x * (x + 1) * sigma*sigma)
 
     # ---Added properties and methods---
 

nifty/spaces/rg_space/rg_space.py

@@ -267,14 +267,16 @@ class RGSpace(Space):
 
         cords = np.ogrid[inds]
 
-        dists = ((cords[0] - shape[0]//2)*dk[0])**2
+        dists = (cords[0] - shape[0]//2)*dk[0]
+        dists *= dists
         # apply zerocenterQ shift
         if not self.zerocenter[0]:
             dists = np.fft.ifftshift(dists)
         # only save the individual slice
         dists = dists[slice_of_first_dimension]
         for ii in range(1, len(shape)):
-            temp = ((cords[ii] - shape[ii] // 2) * dk[ii])**2
+            temp = (cords[ii] - shape[ii] // 2) * dk[ii]
+            temp *= temp
             if not self.zerocenter[ii]:
                 temp = np.fft.ifftshift(temp)
             dists = dists + temp
@@ -282,7 +284,7 @@ class RGSpace(Space):
         return dists
 
     def get_fft_smoothing_kernel_function(self, sigma):
-        return lambda x: np.exp(-0.5 * np.pi**2 * x**2 * sigma**2)
+        return lambda x: np.exp(-0.5 * np.pi*np.pi * x*x * sigma*sigma)
 
     # ---Added properties and methods---