def _simulate_sincos(D1, D2, D3, N, num_inducing, plot_sim=False):
_np.random.seed(<NUM_LIT>)<EOL>x = _np.linspace(<NUM_LIT:0>, <NUM_LIT:4> * _np.pi, N)[:, None]<EOL>s1 = _np.vectorize(lambda x: _np.sin(x))<EOL>s2 = _np.vectorize(lambda x: _np.cos(x))<EOL>s3 = _np.vectorize(lambda x:-_np.exp(-_np.cos(<NUM_LIT:2> * x)))<EOL>sS = _np.vectorize(lambda x: _np.cos(x))<EOL>s1 = s1(x)<EOL>s2 = s2(x)<EOL>s3 = s3(x)<EOL>sS = sS(x)<EOL>s1 -= s1.mean(); s1 /= s1.std(<NUM_LIT:0>)<EOL>s2 -= s2.mean(); s2 /= s2.std(<NUM_LIT:0>)<EOL>s3 -= s3.mean(); s3 /= s3.std(<NUM_LIT:0>)<EOL>sS -= sS.mean(); sS /= sS.std(<NUM_LIT:0>)<EOL>Y1, Y2, Y3, S1, S2, S3 = _generate_high_dimensional_output(D1, D2, D3, s1, s2, s3, sS)<EOL>slist = [sS, s1, s2, s3]<EOL>slist_names = ["<STR_LIT>", "<STR_LIT>", "<STR_LIT>", "<STR_LIT>"]<EOL>Ylist = [Y1, Y2, Y3]<EOL>if plot_sim:<EOL><INDENT>from matplotlib import pyplot as plt<EOL>import matplotlib.cm as cm<EOL>import itertools<EOL>fig = plt.figure("<STR_LIT>", figsize=(<NUM_LIT:8>, <NUM_LIT:6>))<EOL>fig.clf()<EOL>ax = fig.add_subplot(<NUM_LIT:2>, <NUM_LIT:1>, <NUM_LIT:1>)<EOL>labls = slist_names<EOL>for S, lab in zip(slist, labls):<EOL><INDENT>ax.plot(S, label=lab)<EOL><DEDENT>ax.legend()<EOL>for i, Y in enumerate(Ylist):<EOL><INDENT>ax = fig.add_subplot(<NUM_LIT:2>, len(Ylist), len(Ylist) + <NUM_LIT:1> + i)<EOL>ax.imshow(Y, aspect='<STR_LIT>', cmap=cm.gray)  <EOL>ax.set_title("<STR_LIT>".format(i + <NUM_LIT:1>))<EOL><DEDENT>plt.draw()<EOL>plt.tight_layout()<EOL><DEDENT>return slist, [S1, S2, S3], Ylist<EOL>
Simulate some data drawn from sine and cosine for use in demos of MRD