diff --git a/wafo/demos.py b/wafo/demos.py index 8f73f18..f1dfbcc 100644 --- a/wafo/demos.py +++ b/wafo/demos.py @@ -1,15 +1,59 @@ -''' +""" Created on 20. jan. 2011 @author: pab -''' +""" import numpy as np from numpy import exp, meshgrid __all__ = ['peaks', 'humps', 'magic'] +def _magic_odd_order(n): + 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 + return M + + +def _magic_doubly_even_order(n): + 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]) + return M + + +def _magic_even_order(n): + 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 magic(n): - ''' + """ Return magic square for n of any orders > 2. A magic square has the property that the sum of every row and column, @@ -38,54 +82,19 @@ def magic(n): ... [30, 5, 34, 12, 14, 16], ... [ 4, 36, 29, 13, 18, 11]]) True - ''' + """ if (n < 3): raise ValueError('n must be greater than 2.') - 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 + if np.mod(n, 2) == 1: + return _magic_odd_order(n) + elif np.mod(n, 4) == 0: + return _magic_doubly_even_order(n) + return _magic_even_order(n) def peaks(x=None, y=None, n=51): - ''' + """ Return the "well" known MatLab (R) peaks function evaluated in the [-3,3] x,y range @@ -96,7 +105,7 @@ def peaks(x=None, y=None, n=51): h = plt.contourf(x,y,z) - ''' + """ if x is None: x = np.linspace(-3, 3, n) if y is None: @@ -112,7 +121,7 @@ def peaks(x=None, y=None, n=51): def humps(x=None): - ''' + """ Computes a function that has three roots, and some humps. Example @@ -122,7 +131,7 @@ def humps(x=None): >>> y = humps(x) h = plt.plot(x,y) - ''' + """ if x is None: y = np.linspace(0, 1) else: