Implemented all single-objective functions (#6)

Please note that a merge conflict was resolved while committing
this change. Look at lines 283 to 308, specifically to the Matyas
function.

pyswarms/utils/functions/single_obj.py

@@ -156,9 +156,9 @@ def beale_func(x):
 
     x_ = x[:,0]
     y_ = x[:,1]
-    j = (1.5 - x_ + x_ * y_)**2.0 + \
-           (2.25 - x_ + x_ * y_**2.0)**2.0 + \
-           (2.625 - x_ + x_ * y_**3.0)**2.0
+    j = ((1.5 - x_ + x_ * y_)**2.0
+        + (2.25 - x_ + x_ * y_**2.0)**2.0
+        + (2.625 - x_ + x_ * y_**3.0)**2.0)
 
     return j
 
@@ -193,12 +193,14 @@ def goldstein_func(x):
     if not np.logical_and(x >= -2, x <= 2).all():
         raise ValueError('Input for Goldstein-Price function must be within [-2, 2].')
 
-    # TODO: Write actual function here
-
-    # TODO: Change this part by returning the actual value when
-    # you compute x.
-    dummy = np.array([3,3,3]) # defined just to not break the tests
-    return dummy
+    x_ = x[:,0]
+    y_ = x[:,1]
+    j = ((1 + (x_ + y_ + 1)**2.0
+        * (19 - 14*x_ + 3*x_**2.0 - 14*y_ + 6*x_*y_ + 3*y_**2.0))
+        * (30 + (2*x_ - 3 * y_)**2.0
+        * (18 - 32*x_ + 12*x_**2.0 + 48*y_ - 36*x_*y_ + 27*y_**2.0)))
+
+    return j
 
 # TODO: Implement Booth's Function
 def booth_func(x):
@@ -231,12 +233,11 @@ def booth_func(x):
     if not np.logical_and(x >= -10, x <= 10).all():
         raise ValueError('Input for Booth function must be within [-10, 10].')
 
-    # TODO: Write actual function here
-
-    # TODO: Change this part by returning the actual value when
-    # you compute x.
-    dummy = np.array([0,0,0]) # defined just to not break the tests
-    return dummy
+    x_ = x[:,0]
+    y_ = x[:,1]
+    j = (x_ + 2 * y_ - 7)**2.0 + (2 * x_ + y_ - 5)**2.0
+
+    return j
 
 # TODO: Implement Bukin Function no. 6
 def bukin6_func(x):
@@ -273,12 +274,11 @@ def bukin6_func(x):
     if not  np.logical_and(x[:,1] >= -3, x[:,1] <= 3).all():
         raise ValueError('y-coord for Bukin N. 6 function must be within [-3, 3].')
 
-    # TODO: Write actual function here
+    x_ = x[:,0]
+    y_ = x[:,1]
+    j = 100 * np.sqrt(np.absolute(y_**2.0 - 0.01*x_**2.0)) + 0.01 * np.absolute(x_ + 10)
 
-    # TODO: Change this part by returning the actual value when
-    # you compute x.
-    dummy = np.array([0,0,0]) # defined just to not break the tests
-    return dummy
+    return j
 
 def matyas_func(x):
     """Matyas objective function
@@ -295,27 +295,19 @@ def matyas_func(x):
     -------
     numpy.ndarray 
         computed cost of size (n_particles, )
-
-    Raises
-    ------
-    IndexError
-        When the input dimensions is greater than what the function
-        allows
-    ValueError
-        When the input is out of bounds with respect to the function
-        domain
     """
+<<<<<<< HEAD
     if not x.shape[1] == 2:
         raise IndexError('Matyas function only takes two-dimensional input.')
     if not np.logical_and(x >= -10, x <= 10).all():
         raise ValueError('Input for Matyas function must be within [-10, 10].')
+=======
+    x_ = x[:,0]
+    y_ = x[:,1]
+    j = 0.26 * (x_**2.0 + y_**2.0) - 0.48 * x_ * y_
+>>>>>>> f5649c5... implemented all single-objective functions
 
-    # TODO: Write actual function here
-
-    # TODO: Change this part by returning the actual value when
-    # you compute x.
-    dummy = np.array([0,0,0]) # defined just to not break the tests
-    return dummy
+    return j
 
 def levi_func(x):
     """Levi objective function
@@ -347,12 +339,22 @@ def levi_func(x):
     if not np.logical_and(x >= -10, x <= 10).all():
         raise ValueError('Input for Levi function must be within [-10, 10].')
 
-    # TODO: Write actual function here
+    mask = np.full(x.shape, False)
+    mask[:,-1] = True
+    masked_x = np.ma.array(x, mask=mask)
+
+    w_ = 1 + (x - 1) / 4
+    masked_w_ = np.ma.array(w_, mask=mask)
+    d_ = x.shape[1] - 1
 
-    # TODO: Change this part by returning the actual value when
-    # you compute x.
-    dummy = np.array([0,0,0]) # defined just to not break the tests
-    return dummy
+    j = (np.sin(np.pi * w_[:,0])**2.0
+        + ((masked_x - 1)**2.0).sum(axis=1)
+        * (1 + 10 * np.sin(np.pi * (masked_w_).sum(axis=1) + 1)**2.0)
+        + (w_[:,d_] - 1)**2.0
+        * (1 + np.sin(2 * np.pi * w_[:,d_])**2.0 ))
+
+
+    return j
 
 def schaffer2_func(x):
     """Schaffer N.2 objective function
@@ -384,9 +386,10 @@ def schaffer2_func(x):
     if not np.logical_and(x >= -100, x <= 100).all():
         raise ValueError('Input for Schaffer function must be within [-100, 100].')
 
-    # TODO: Write actual function here
+    x_ = x[:,0]
+    y_ = x[:,1]
+    j = (0.5
+        + ((np.sin(x_**2.0 - y_**2.0)**2.0 - 0.5)
+        / ((1 + 0.001 * (x_**2.0 + y_**2.0))**2.0)))
 
-    # TODO: Change this part by returning the actual value when
-    # you compute x.
-    dummy = np.array([0,0,0]) # defined just to not break the tests
-    return dummy
+    return j