Generalized magic

pywafo/src/wafo/demos.py

@@ -10,20 +10,70 @@ __all__ = ['peaks', 'humps', 'magic']
 
 def magic(n):
     '''
-    Return magic square  for n of odd orders.
+    Return magic square  for n of any orders > 2.
     
     A magic square has the property that the sum of every row and column, 
     as well as both diagonals, is the same number.
     
-    
+    Examples
+    --------
+    >>> magic(3)
+    array([[8, 1, 6],
+           [3, 5, 7],
+           [4, 9, 2]])
+           
+    >>> magic(4)
+    array([[16,  2,  3, 13],
+           [ 5, 11, 10,  8],
+           [ 9,  7,  6, 12],
+           [ 4, 14, 15,  1]])
+           
+    >>> magic(6)
+    array([[35,  1,  6, 26, 19, 24],
+           [ 3, 32,  7, 21, 23, 25],
+           [31,  9,  2, 22, 27, 20],
+           [ 8, 28, 33, 17, 10, 15],
+           [30,  5, 34, 12, 14, 16],
+           [ 4, 36, 29, 13, 18, 11]])
     '''
-    if np.mod(n,1)==1: # odd order
+    if np.mod(n,2)==1: # odd order
         ix = np.arange(n) + 1
         J, I = np.meshgrid(ix, ix)
         A = np.mod(I + J - (n + 3) / 2, n)
         B = np.mod(I + 2 * J - 2, n)
         M = n * A + B + 1
+    elif np.mod(n,4)==0: # doubly even order
+        M = np.arange(1,n*n+1).reshape(n,n)
+        ix = np.mod(np.arange(n) + 1,4)//2 
+        J, I = np.meshgrid(ix, ix)
+        iz = np.flatnonzero(I==J)
+        M.put(iz, n*n+1-M.flat[iz])
+    else: # singly even order
+        p = n//2
+        M0 = magic(p)
         
+        M = np.hstack((np.vstack((M0, M0+3*p*p)),np.vstack((M0+2*p*p, M0+p*p))))
+        
+        if n>2:
+            k = (n-2)//4
+            Jvec = np.hstack((np.arange(k), np.arange(n-k+1, n)))
+            for i in range(p):
+                for j in Jvec:
+                    temp = M[i][j]
+                    M[i][j]=M[i+p][j]
+                    M[i+p][j] = temp
+                
+            i=k 
+            j=0
+            temp = M[i][j]; 
+            M[i][j] = M[i+p][j]
+            M[i+p][j] = temp;
+
+            j=i;
+            temp=M[i+p][j]; 
+            M[i+p][j]=M[i][j]; 
+            M[i][j]=temp;
+
     return M
 
 def peaks(x=None, y=None, n=51):
@@ -35,7 +85,8 @@ def peaks(x=None, y=None, n=51):
     -------
     >>> import matplotlib.pyplot as plt
     >>> x,y,z = peaks()
-    >>> h = plt.contourf(x,y,z)
+    
+    h = plt.contourf(x,y,z)
     
     '''
     if x is None:
@@ -60,7 +111,8 @@ def humps(x=None):
     >>> import matplotlib.pyplot as plt
     >>> x = np.linspace(0,1)
     >>> y = humps(x)
-    >>> h = plt.plot(x,y)
+    
+    h = plt.plot(x,y)
     '''
     if x is None:
         y = np.linspace(0, 1)
@@ -69,5 +121,9 @@ def humps(x=None):
 
     return 1.0 / ((y - 0.3) ** 2 + 0.01) + 1.0 / ((y - 0.9) ** 2 + 0.04) + 2 * y - 5.2
 
+def test_docstrings():
+    import doctest
+    doctest.testmod()
+    
 if __name__ == '__main__':
-    pass
+    test_docstrings()