Init

Vektorrechnung.py

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+import math
+import decimal
+decimal.getcontext().prec = 30
+
+
+class Vector(object):
+      CANNOT_NORMALIZE_ZERO_VECTOR_MSG = 'Cannot normalize the zero vector'
+
+      def __init__(self, coordinates):
+        try:
+            if not coordinates:
+                raise ValueError
+            self.coordinates = tuple([decimal.Decimal(x) for x in coordinates])
+            self.dimension = len(coordinates)
+
+        except ValueError:
+            raise ValueError('The coordinates must be nonempty')
+
+        except TypeError:
+            raise TypeError('The coordinates must be an iterable')
+
+      def __str__(self):
+        return 'Vector: {}'.format(self.coordinates)
+
+      def __eq__(self, v):
+          return self.coordinates == v.coordinates
+
+     # LINEAR ALGEBRA METHODS
+      def plus(self, v):
+          new_coordinates = [x+y for x,
+              y in zip(self.coordinates, v.coordinates)]
+          return Vector(new_coordinates)
+      
+      def minus(self, v):
+          new_coordinates = [x-y for x,y in zip(self.coordinates, v.coordinates)]
+          return Vector(new_coordinates)
+      
+      def times_scalar(self,c):
+          new_coordinates = [c*x for x in self.coordinates]
+          return Vector(new_coordinates)
+      
+      def magnitude(self):
+          coordinates_squared = [x**2 for x in self.coordinates]     
+          return decimal.Decimal(math.sqrt(sum(coordinates_squared)))
+      
+      def normalized(self):
+          try:         
+              magnitude = self.magnitude()
+              return self.times_scalar(decimal.Decimal('1.0')/magnitude)
+          except ZeroDivisionError:
+              raise Exception(self.CANNOT_NORMALIZE_ZERO_VECTOR_MSG)
+              
+      def dot(self,v):
+          return sum([x*y for x,y in zip(self.coordinates, v.coordinates)])  
+      
+      def angle_inner_with(self, v, in_degrees = False):
+          try:
+              u1 = self.normalized()
+              u2 = v.normalized()
+              #Capture within range of dot product to be within 1 & -1
+              u1u2dot = replace_if_within_tolerance(u1.dot(u2),1)
+              u1u2dot = replace_if_within_tolerance(u1.dot(u2),-1)
+              angle_in_radians = math.acos(u1u2dot)
+                     
+          if in_degrees:
+              return math.degrees(angle_in_radians)         
+          else:
+              return angle_in_radians
+          except Exception as e:
+              if str(e) == self.CANNOT_NORMALIZE_ZERO_VECTOR_MSG:
+                  raise Exception('Cannot compute an angle with the zero vector')
+              else:
+                  raise e  def is_zero(self, tolerance = 1e-10):
+                      #returns true if magnitude is less than tolerance     
+                      return self.magnitude() < tolerance   
+          
+      def is_parallel_to(self, v):     
+          return ( self.is_zero() or
+          v.is_zero() or              
+          self.angle_inner_with(v) == 0 or              
+          self.angle_inner_with(v) == math.pi )  
+      
+      def is_orthogonal_to(self, v, tolerance = 1e-10):     
+        return abs(self.dot(v)) < tolerance  
+      
+      def replace_if_within_tolerance(val, compared_against, tolerance = 1e-10): 
+        if abs(val - compared_against) < tolerance: 
+          return compared_against 
+        else: 
+          return val  
+        
+    #Values from Parallel Orthogonal Quiz, math domain error 
+
+    v = Vector([’-7.579’, ‘-7.88’]) 
+    w = Vector([‘22.737’, ‘23.64’]) 
+    print(v.is_parallel_to(w)) print(v.is_orthogonal_to(w))  
+    #v = Vector([’-2.029’, ‘9.97’, ‘4.172’]) w = Vector([’-9.231’, ‘-6.639’, ‘-7.245’]) print(v.is_parallel_to(w)) print(v.is_orthogonal_to(w))  v = Vector([’-2.328’, ‘-7.284’, ‘-1.214’]) w = Vector([’-1.821’, ‘1.072’, ‘-2.94’]) print(v.is_parallel_to(w)) print(v.is_orthogonal_to(w))  v = Vector([‘2.118’, ‘4.827’]) w = Vector([‘0’, ‘0’]) print(v.is_parallel_to(w)) print(v.is_orthogonal_to(w))