remove dependency on scipy

kshape.py

@@ -1,22 +1,72 @@
 import math
 import numpy as np
 
-from numpy.random import randint
+from numpy.random import randint, seed
+from numpy.linalg import norm, eigh
 from numpy.linalg import norm
 from numpy.fft import fft, ifft
 
-from scipy.sparse.linalg import eigs
+
-from scipy.stats import zscore
+#from scipy.linalg import eigh
-from scipy.ndimage.interpolation import shift
+
+def zscore(a, axis=0, ddof=0):
+    a = np.asanyarray(a)
+    mns = a.mean(axis=axis)
+    sstd = a.std(axis=axis, ddof=ddof)
+    if axis and mns.ndim < a.ndim:
+        return ((a - np.expand_dims(mns, axis=axis)) /
+                np.expand_dims(sstd,axis=axis))
+    else:
+        return (a - mns) / sstd
+
+def roll_zeropad(a, shift, axis=None):
+    a = np.asanyarray(a)
+    if shift == 0: return a
+    if axis is None:
+        n = a.size
+        reshape = True
+    else:
+        n = a.shape[axis]
+        reshape = False
+    if np.abs(shift) > n:
+        res = np.zeros_like(a)
+    elif shift < 0:
+        shift += n
+        zeros = np.zeros_like(a.take(np.arange(n-shift), axis))
+        res = np.concatenate((a.take(np.arange(n-shift,n), axis), zeros), axis)
+    else:
+        zeros = np.zeros_like(a.take(np.arange(n-shift,n), axis))
+        res = np.concatenate((zeros, a.take(np.arange(n-shift), axis)), axis)
+    if reshape:
+        return res.reshape(a.shape)
+    else:
+        return res
+
+# TODO vectorized version of _ncc_c
+#def _ncc_c(x,y):
+#    """
+#    >>> _ncc_c(np.array([[1,2,3,4]]), np.array([[1,2,3,4]]))
+#    array([[ 0.13333333,  0.36666667,  0.66666667,  1.        ,  0.66666667,
+#             0.36666667,  0.13333333]])
+#    >>> _ncc_c(np.array([[1,1,1]]), np.array([[1,1,1]]))
+#    array([[ 0.33333333,  0.66666667,  1.        ,  0.66666667,  0.33333333]])
+#    >>> _ncc_c(np.array([[1,2,3]]), np.array([[-1,-1,-1]]))
+#    array([[-0.15430335, -0.46291005, -0.9258201 , -0.77151675, -0.46291005]])
+#    """
+#    x_len = x.shape[1]
+#    fft_size = 1<<(2*x_len-1).bit_length()
+#    cc = ifftn(fftn(x, (fft_size,)) * np.conj(fftn(y, (fft_size,))))
+#    cc = np.concatenate((cc[:, -(x_len-1):], cc[:, :x_len]), axis=1)
+#    return np.real(cc) / (norm(x) * norm(y))
 
 def _ncc_c(x,y):
     """
-    >>> ncc_c([1,2,3,4], [1,2,3,4])
+    >>> _ncc_c([1,2,3,4], [1,2,3,4])
     array([ 0.13333333,  0.36666667,  0.66666667,  1.        ,  0.66666667,
             0.36666667,  0.13333333])
-    >>> ncc_c([1,1,1], [1,1,1])
+    >>> _ncc_c([1,1,1], [1,1,1])
     array([ 0.33333333,  0.66666667,  1.        ,  0.66666667,  0.33333333])
-    >>> ncc_c([1,2,3], [-1,-1,-1])
+    >>> _ncc_c([1,2,3], [-1,-1,-1])
     array([-0.15430335, -0.46291005, -0.9258201 , -0.77151675, -0.46291005])
     """
     x_len = len(x)
@@ -28,25 +78,32 @@ def _ncc_c(x,y):
 
 def _sbd(x, y):
     """
-    >>> sbd([1,1,1], [1,1,1])
+    >>> _sbd([1,1,1], [1,1,1])
     (-2.2204460492503131e-16, array([1, 1, 1]))
-    >>> sbd([0,1,2], [1,2,3])
+    >>> _sbd([0,1,2], [1,2,3])
     (0.043817112532485103, array([1, 2, 3]))
-    >>> sbd([1,2,3], [0,1,2])
+    >>> _sbd([1,2,3], [0,1,2])
     (0.043817112532485103, array([0, 1, 2]))
     """
     ncc = _ncc_c(x, y)
     idx = ncc.argmax()
     dist = 1 - ncc[idx]
-    yshift = shift(y, (idx + 1) - max(len(x), len(y)))
+    yshift = roll_zeropad(y, (idx + 1) - max(len(x), len(y)))
+
     return dist, yshift
 
+
+#@profile
 def _extract_shape(idx, x, j, cur_center):
     """
-    >>> extract_shape(np.array([0,1,2]), np.array([[1,2,3], [4,5,6]]), 1, np.array([0,3,4]))
+    >>> _extract_shape(np.array([0,1,2]), np.array([[1,2,3], [4,5,6]]), 1, np.array([0,3,4]))
-    array([ -1.00000000e+00,  -3.06658683e-19,   1.00000000e+00])
+    array([-1.,  0.,  1.])
-    >>> extract_shape(np.array([0,1,2]), np.array([[-1,2,3], [4,-5,6]]), 1, np.array([0,3,4]))
+    >>> _extract_shape(np.array([0,1,2]), np.array([[-1,2,3], [4,-5,6]]), 1, np.array([0,3,4]))
     array([-0.96836405,  1.02888681, -0.06052275])
+    >>> _extract_shape(np.array([1,0,1,0]), np.array([[1,2,3,4], [0,1,2,3], [-1,1,-1,1], [1,2,2,3]]), 0, np.array([0,0,0,0]))
+    array([-1.2089303 , -0.19618238,  0.19618238,  1.2089303 ])
+    >>> _extract_shape(np.array([0,0,1,0]), np.array([[1,2,3,4],[0,1,2,3],[-1,1,-1,1],[1,2,2,3]]), 0, np.array([-1.2089303,-0.19618238,0.19618238,1.2089303]))
+    array([-1.19623139, -0.26273649,  0.26273649,  1.19623139])
     """
     _a = []
     for i in range(len(idx)):
@@ -69,39 +126,40 @@ def _extract_shape(idx, x, j, cur_center):
     p = np.eye(columns) - p
 
     m = np.dot(np.dot(p, s), p)
-    _, vec = eigs(m, 1)
+    _, vec = eigh(m)
-    centroid = np.real(vec[:,0])
+    centroid = vec[:,-1]
     finddistance1 = math.sqrt(((a[0] - centroid) ** 2).sum())
     finddistance2 = math.sqrt(((a[0] + centroid) ** 2).sum())
 
     if finddistance1 >= finddistance2:
         centroid *= -1
-    return zscore(centroid, ddof=1)
 
+    return zscore(centroid, ddof=1)
 
 def _kshape(x, k):
     """
-    >>> kshape(np.array([[1,2,3,4], [0,1,2,3], [-1,1,-1,1], [1,2,2,3]]), 2)
+    >>> from numpy.random import seed; seed(0)
-    (array([0, 0, 1, 0]), array([[-1.19623139, -0.26273649,  0.26273649,  1.19623139],
+    >>> _kshape(np.array([[1,2,3,4], [0,1,2,3], [-1,1,-1,1], [1,2,2,3]]), 2)
+    (array([0, 0, 1, 0]), array([[-1.2244258 , -0.35015476,  0.52411628,  1.05046429],
            [-0.8660254 ,  0.8660254 , -0.8660254 ,  0.8660254 ]]))
     """
     m = x.shape[0]
     idx = randint(0, k, size=m)
     centroids = np.zeros((k,x.shape[1]))
-
     distances = np.empty((m, k))
+
     for _ in range(100):
         old_idx = idx
         for j in range(k):
-            res = _extract_shape(idx, x, j, centroids[j])
+            centroids[j] = _extract_shape(idx, x, j, centroids[j])
-            centroids[j] = res
 
         for i in range(m):
-            for j in range(k):
+             for j in range(k):
-                distances[i,j] = 1 - max(_ncc_c(x[i], centroids[j]))
+                 distances[i,j] = 1 - max(_ncc_c(x[i], centroids[j]))
         idx = distances.argmin(1)
-        if norm(old_idx - idx) == 0:
+        if np.array_equal(old_idx, idx):
             break
+
     return idx, centroids
 
 def kshape(x, k):