Defer Imports for Top-Level Import Time

autokoopman/observable/reweighted.py

@@ -1,151 +1,166 @@
 from autokoopman.observable import SymbolicObservable, KoopmanObservable
 import math
 import numpy as np
-import sympy as sp
-from scipy.stats import cauchy, laplace
-from scipy.optimize import nnls
 
 
 def make_gaussian_kernel(sigma=1.0):
-  """the baseline"""
-  def kernel(x, xp):
-    return np.exp(-np.linalg.norm(x-xp)**2.0 / (2.0*sigma**2.0))
-  return kernel
+    """the baseline"""
+
+    def kernel(x, xp):
+        return np.exp(-np.linalg.norm(x - xp) ** 2.0 / (2.0 * sigma**2.0))
+
+    return kernel
 
 
 def rff_reweighted_map(n, X, Y, wx, wy, sigma=1.0):
-  """build a RFF explicit feature map"""
-  assert len(X) == len(Y)
-  R = n
-  D = X.shape[1]
-  N = len(X)
-  W    = np.random.normal(loc=0, scale=(1.0/np.sqrt(sigma)), size=(R, D))
-  b    = np.random.uniform(-np.pi, np.pi, size = R)
-
-  # get ground truth kernel for training
-  kernel = make_gaussian_kernel(sigma)
-
-  # solve NNLS problem
-  M = np.zeros((N, R))
-  bo = np.zeros((N,))
-  for jdx, (xi, yi, wxi, wyi) in enumerate(zip(X, Y, wx, wy)):
-    wi = np.sum(wxi) * np.sum(wyi)
-    k = wi * kernel(xi, yi)
-    if np.isclose(np.abs(wi), 0.0):
-      continue
-    bo[jdx] = k
-    for idx, (omegai, bi) in enumerate(zip(W, b)):
-      M[jdx, idx] = wi * np.cos(np.dot(omegai, xi) + bi) * np.cos(np.dot(omegai, yi) + bi)
-
-  a, _ = nnls(M, bo, maxiter=1000)
-
-  # get new values
-  new_idxs = (np.abs(a) > 3E-5)
-  W = W[new_idxs]
-  b = b[new_idxs]
-  a = a[new_idxs]
-
-  return a, W, b
+    """build a RFF explicit feature map"""
+    from scipy.optimize import nnls
+
+    assert len(X) == len(Y)
+    R = n
+    D = X.shape[1]
+    N = len(X)
+    W = np.random.normal(loc=0, scale=(1.0 / np.sqrt(sigma)), size=(R, D))
+    b = np.random.uniform(-np.pi, np.pi, size=R)
+
+    # get ground truth kernel for training
+    kernel = make_gaussian_kernel(sigma)
+
+    # solve NNLS problem
+    M = np.zeros((N, R))
+    bo = np.zeros((N,))
+    for jdx, (xi, yi, wxi, wyi) in enumerate(zip(X, Y, wx, wy)):
+        wi = np.sum(wxi) * np.sum(wyi)
+        k = wi * kernel(xi, yi)
+        if np.isclose(np.abs(wi), 0.0):
+            continue
+        bo[jdx] = k
+        for idx, (omegai, bi) in enumerate(zip(W, b)):
+            M[jdx, idx] = (
+                wi * np.cos(np.dot(omegai, xi) + bi) * np.cos(np.dot(omegai, yi) + bi)
+            )
+
+    a, _ = nnls(M, bo, maxiter=1000)
+
+    # get new values
+    new_idxs = np.abs(a) > 3e-5
+    W = W[new_idxs]
+    b = b[new_idxs]
+    a = a[new_idxs]
+
+    return a, W, b
 
 
 def subsampled_dense_grid(d, D, gamma, deg=8):
-  """sparse grid gaussian quadrature"""
-  points, weights = np.polynomial.hermite.hermgauss(deg)
-  points *= 2 * math.sqrt(gamma)
-  weights /= math.sqrt(math.pi)
-  # Now @weights must sum to 1.0, as the kernel value at 0 is 1.0
-  subsampled_points = np.random.choice(points, size=(D, d), replace=True, p=weights)
-  subsampled_weights = np.ones(D) / math.sqrt(D)
-  return subsampled_points, subsampled_weights
+    """sparse grid gaussian quadrature"""
+    points, weights = np.polynomial.hermite.hermgauss(deg)
+    points *= 2 * math.sqrt(gamma)
+    weights /= math.sqrt(math.pi)
+    # Now @weights must sum to 1.0, as the kernel value at 0 is 1.0
+    subsampled_points = np.random.choice(points, size=(D, d), replace=True, p=weights)
+    subsampled_weights = np.ones(D) / math.sqrt(D)
+    return subsampled_points, subsampled_weights
 
 
 def dense_grid(d, D, gamma, deg=8):
-  """dense grid gaussian quadrature"""
-  points, weights = np.polynomial.hermite.hermgauss(deg)
-  points *= 2 * math.sqrt(gamma)
-  weights /= math.sqrt(math.pi)
-  points = np.atleast_2d(points).T
-  return points, weights
+    """dense grid gaussian quadrature"""
+    points, weights = np.polynomial.hermite.hermgauss(deg)
+    points *= 2 * math.sqrt(gamma)
+    weights /= math.sqrt(math.pi)
+    points = np.atleast_2d(points).T
+    return points, weights
 
 
 def sparse_grid_map(n, d, sigma=1.0):
-  """sparse GQ explicit map"""
-  d, D = d, n
-  gamma = 1/(2*sigma*sigma)
-  points, weights = subsampled_dense_grid(d, D, gamma=gamma)
-  def inner(x):
-    prod = x @ points.T
-    return np.hstack((weights * np.cos(prod), weights * np.sin(prod)))
-  return inner
+    """sparse GQ explicit map"""
+    d, D = d, n
+    gamma = 1 / (2 * sigma * sigma)
+    points, weights = subsampled_dense_grid(d, D, gamma=gamma)
+
+    def inner(x):
+        prod = x @ points.T
+        return np.hstack((weights * np.cos(prod), weights * np.sin(prod)))
+
+    return inner
 
 
 def dense_grid_map(n, d, sigma=1.0):
-  """dense GQ explicit map"""
-  d, D = d, n
-  gamma = 1/(2*sigma*sigma)
-  points, weights = dense_grid(d, D, gamma=gamma)
-  def inner(x):
-    prod = x @ points.T
-    return np.hstack((weights * np.cos(prod), weights * np.sin(prod)))
-  return inner
+    """dense GQ explicit map"""
+    d, D = d, n
+    gamma = 1 / (2 * sigma * sigma)
+    points, weights = dense_grid(d, D, gamma=gamma)
+
+    def inner(x):
+        prod = x @ points.T
+        return np.hstack((weights * np.cos(prod), weights * np.sin(prod)))
+
+    return inner
 
 
 def quad_reweighted_map(n, X, Y, wx, wy, sigma=1.0):
-  """build a RFF explicit feature map"""
-  assert len(X) == len(Y)
-  R = int(n / 2.0)
-  D = X.shape[1]
-  N = len(X)
-  W, a = subsampled_dense_grid(D, R, gamma=1/(2*sigma*sigma))
-  #W    = np.random.normal(loc=0, scale=(1.0/np.sqrt(sigma)), size=(R, D))
-  b    = np.random.uniform(-np.pi, np.pi, size = R)
-  #print(X.shape, W.shape)
-  #b = np.arccos(-np.sqrt(np.cos(2*X.T.dot(W)) + 1)/np.sqrt(2.0))
-  #print(b)
-
-  # get ground truth kernel for training
-  kernel = make_gaussian_kernel(sigma)
-
-  # solve NNLS problem
-  M = np.zeros((N, R))
-  bo = np.zeros((N,))
-  for jdx, (xi, yi, wxi, wyi) in enumerate(zip(X, Y, wx, wy)):
-      k = kernel(xi, yi)
-      bo[jdx] = k
-      for idx, (omegai, ai, bi) in enumerate(zip(W, a, b)):
-        M[jdx, idx] = np.cos(np.dot(omegai, xi - yi)) 
-
-  a, _ = nnls(M, bo, maxiter=1000)
-
-  # get new values
-  new_idxs = (np.abs(a) > 1E-7)
-  W = W[new_idxs]
-  b = b[new_idxs]
-  a = a[new_idxs]
-
-  return a, W, b
+    """build a RFF explicit feature map"""
+    from scipy.optimize import nnls
+
+    assert len(X) == len(Y)
+    R = int(n / 2.0)
+    D = X.shape[1]
+    N = len(X)
+    W, a = subsampled_dense_grid(D, R, gamma=1 / (2 * sigma * sigma))
+    # W    = np.random.normal(loc=0, scale=(1.0/np.sqrt(sigma)), size=(R, D))
+    b = np.random.uniform(-np.pi, np.pi, size=R)
+    # print(X.shape, W.shape)
+    # b = np.arccos(-np.sqrt(np.cos(2*X.T.dot(W)) + 1)/np.sqrt(2.0))
+    # print(b)
+
+    # get ground truth kernel for training
+    kernel = make_gaussian_kernel(sigma)
+
+    # solve NNLS problem
+    M = np.zeros((N, R))
+    bo = np.zeros((N,))
+    for jdx, (xi, yi, wxi, wyi) in enumerate(zip(X, Y, wx, wy)):
+        k = kernel(xi, yi)
+        bo[jdx] = k
+        for idx, (omegai, ai, bi) in enumerate(zip(W, a, b)):
+            M[jdx, idx] = np.cos(np.dot(omegai, xi - yi))
+
+    a, _ = nnls(M, bo, maxiter=1000)
+
+    # get new values
+    new_idxs = np.abs(a) > 1e-7
+    W = W[new_idxs]
+    b = b[new_idxs]
+    a = a[new_idxs]
+
+    return a, W, b
 
 
 class ReweightedRFFObservable(SymbolicObservable):
-    def __init__(self, dimension, num_features, gamma, X, Y, wx, wy, feat_type='rff'):
+    def __init__(self, dimension, num_features, gamma, X, Y, wx, wy, feat_type="rff"):
+        import sympy as sp
+
         self.dimension, self.num_features = dimension, num_features
         n = num_features
-        if feat_type == 'quad':
-          self.a, self.W, self.b = quad_reweighted_map(n, X, Y, wx, wy, np.sqrt(1/(2*gamma)))
-        elif feat_type == 'rff':
-          self.a, self.W, self.b = rff_reweighted_map(n, X, Y, wx, wy, np.sqrt(1/(2*gamma)))
+        if feat_type == "quad":
+            self.a, self.W, self.b = quad_reweighted_map(
+                n, X, Y, wx, wy, np.sqrt(1 / (2 * gamma))
+            )
+        elif feat_type == "rff":
+            self.a, self.W, self.b = rff_reweighted_map(
+                n, X, Y, wx, wy, np.sqrt(1 / (2 * gamma))
+            )
         else:
-          raise ValueError('feat_type must be quad or rff')
-        
+            raise ValueError("feat_type must be quad or rff")
+
         # make sympy variables for each of the state dimensions
-        self.variables = [f'x{i}' for i in range(self.dimension)]
+        self.variables = [f"x{i}" for i in range(self.dimension)]
         self._observables = sp.symbols(self.variables)
         X = sp.Matrix(self._observables)
-        
+
         # build observables sympy expressions from self.weights from self.weights, x.T @ points
         self.expressions = []
         for ai, wi, bi in zip(self.a, self.W, self.b):
             self.expressions.append(np.sqrt(ai) * sp.cos(X.dot(wi)))
             self.expressions.append(np.sqrt(ai) * sp.sin(X.dot(wi)))
 
-        super(ReweightedRFFObservable, self).__init__(self.variables, self.expressions) 
+        super(ReweightedRFFObservable, self).__init__(self.variables, self.expressions)

autokoopman/observable/rff.py

@@ -1,11 +1,12 @@
 import numpy as np
-from scipy.stats import cauchy, laplace
 
 from .observables import KoopmanObservable
 
 
 class RFFObservable(KoopmanObservable):
     def __init__(self, dimension, num_features, gamma, metric="rbf"):
+        from scipy.stats import cauchy, laplace
+
         super(RFFObservable, self).__init__()
         self.gamma = gamma
         self.dimension = dimension
@@ -49,4 +50,4 @@ def obs_grad(self, X: np.ndarray) -> np.ndarray:
     def compute_kernel(self, X: np.ndarray) -> np.ndarray:
         Z = self.transform(X)
         K = Z.dot(Z.T)
-        return K
+        return K