[Scipy-svn] r4148 - in trunk/scipy/cluster: . src tests

scipy-svn@scip... scipy-svn@scip...
Thu Apr 17 21:13:29 CDT 2008


Author: damian.eads
Date: 2008-04-17 21:13:12 -0500 (Thu, 17 Apr 2008)
New Revision: 4148

Added:
   trunk/scipy/cluster/tests/pdist-minkowski-3.2-ml-iris.txt
   trunk/scipy/cluster/tests/pdist-minkowski-5.8-ml-iris.txt
   trunk/scipy/cluster/tests/test_hierarchy.py
Removed:
   trunk/scipy/cluster/tests/pdist-minkowski-0.6-ml-iris.txt
   trunk/scipy/cluster/tests/pdist-minkowski-0.6-ml.txt
   trunk/scipy/cluster/tests/pdist-minkowski-0.8-ml-iris.txt
Modified:
   trunk/scipy/cluster/hierarchy.py
   trunk/scipy/cluster/src/hierarchy.c
   trunk/scipy/cluster/tests/iris.txt
Log:
Wrote tests for about half the distance functions. Fixed Jaccard -- the C implementation was a direct copy of Hamming. It now functions as desired. Fixed check for float64 arrays in pdist so that boolean observation matrices don't generate an exception.

Modified: trunk/scipy/cluster/hierarchy.py
===================================================================
--- trunk/scipy/cluster/hierarchy.py	2008-04-17 21:15:51 UTC (rev 4147)
+++ trunk/scipy/cluster/hierarchy.py	2008-04-18 02:13:12 UTC (rev 4148)
@@ -175,7 +175,7 @@
 OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 """
 
-import _hierarchy_wrap, scipy, scipy.stats, numpy, types, math, sys
+import _hierarchy_wrap, scipy, numpy, types, math, sys, scipy.stats
 
 _cpy_non_euclid_methods = {'single': 0, 'complete': 1, 'average': 2, 'weighted': 6}
 _cpy_euclid_methods = {'centroid': 3, 'median': 4, 'ward': 5}
@@ -190,6 +190,15 @@
     def _warning(s):
         print ('[WARNING] scipy-cluster: %s' % s)
 
+def _unbiased_variance(X):
+    """
+    Computes the unbiased variance of each dimension of a collection of
+    observation vectors, represented by a matrix where the rows are the
+    observations.
+    """
+    #n = numpy.double(X.shape[1])
+    return scipy.stats.var(X, axis=0) # * n / (n - 1.0)
+
 def _copy_array_if_base_present(a):
     """
     Copies the array if its base points to a parent array.
@@ -235,7 +244,7 @@
     matrix Z. See linkage for more information on the return structure
     and algorithm.
 
-          (a condensed alias for linkage)
+      (a condensed alias for single)
     """
     return linkage(y, method='single', metric='euclidean')
 
@@ -869,7 +878,7 @@
 
       for k < n.
     """
-    return ((scipy.bitwise_and((u != v), scipy.bitwise_or(u != 0, v != 0))).sum()) / scipy.bitwise_or(u != 0, v != 0).sum()
+    return numpy.double(scipy.bitwise_and((u != v), scipy.bitwise_or(u != 0, v != 0)).sum()) / numpy.double(scipy.bitwise_or(u != 0, v != 0).sum())
 
 def kulsinski(u, v):
     """
@@ -1292,8 +1301,8 @@
     if type(X) is not _array_type:
         raise TypeError('The parameter passed must be an array.')
 
-    if X.dtype != 'double':
-        raise TypeError('X must be a float64 array')
+    if X.dtype == 'float32':
+        raise TypeError('Floating point arrays must be 64-bit.')
 
     # The C code doesn't do striding.
     [X] = _copy_arrays_if_base_present([X])
@@ -1301,7 +1310,7 @@
     s = X.shape
 
     if len(s) != 2:
-        raise ValueError('A matrix must be passed.');
+        raise ValueError('A 2-dimensional array must be passed.');
 
     m = s[0]
     n = s[1]
@@ -1310,10 +1319,27 @@
     mtype = type(metric)
     if mtype is types.FunctionType:
         k = 0
-        for i in xrange(0, m - 1):
-            for j in xrange(i+1, m):
-                dm[k] = metric(X[i, :], X[j, :])
-                k = k + 1
+        if metric == minkowski:
+            for i in xrange(0, m - 1):
+                for j in xrange(i+1, m):
+                    dm[k] = minkowski(X[i, :], X[j, :], p)
+                    k = k + 1
+        elif metric == seuclidean:
+            for i in xrange(0, m - 1):
+                for j in xrange(i+1, m):
+                    dm[k] = seuclidean(X[i, :], X[j, :], V)
+                    k = k + 1
+        elif metric == mahalanobis:
+            for i in xrange(0, m - 1):
+                for j in xrange(i+1, m):
+                    dm[k] = mahalanobis(X[i, :], X[j, :], V)
+                    k = k + 1
+        else:
+            for i in xrange(0, m - 1):
+                for j in xrange(i+1, m):
+                    dm[k] = metric(X[i, :], X[j, :])
+                    k = k + 1
+
     elif mtype is types.StringType:
         mstr = metric.lower()
 
@@ -1332,14 +1358,14 @@
             elif X.dtype == 'bool':
                 _hierarchy_wrap.pdist_hamming_bool_wrap(X, dm)
             else:
-                raise TypeError('Invalid input matrix type %s for hamming.' % str(X.dtype))
+                raise TypeError('Invalid input array value type %s for hamming.' % str(X.dtype))
         elif mstr in set(['jaccard', 'jacc', 'ja', 'j']):
             if X.dtype == 'double':
-                _hierarchy_wrap.pdist_hamming_wrap(X, dm)
+                _hierarchy_wrap.pdist_jaccard_wrap(X, dm)
             elif X.dtype == 'bool':
-                _hierarchy_wrap.pdist_hamming_bool_wrap(X, dm)
+                _hierarchy_wrap.pdist_jaccard_bool_wrap(X, dm)
             else:
-                raise TypeError('Invalid input matrix type %s for jaccard.' % str(X.dtype))
+                raise TypeError('Invalid input array value type %s for jaccard.' % str(X.dtype))
         elif mstr in set(['chebyshev', 'cheby', 'cheb', 'ch']):
             _hierarchy_wrap.pdist_chebyshev_wrap(X, dm)            
         elif mstr in set(['minkowski', 'mi', 'm']):
@@ -1357,7 +1383,7 @@
                 # The C code doesn't do striding.
                 [VV] = _copy_arrays_if_base_present([V])
             else:
-                VV = scipy.stats.var(X, axis=0)
+                VV = _unbiased_variance(X)
             _hierarchy_wrap.pdist_seuclidean_wrap(X, VV, dm)
         # Need to test whether vectorized cosine works better.
         # Find out: Is there a dot subtraction operator so I can
@@ -1417,7 +1443,7 @@
             dm = pdist(X, euclidean)
         elif metric == 'test_sqeuclidean':
             if V is None:
-                V = scipy.stats.var(X, axis=0)
+                V = _unbiased_variance(X)
             dm = pdist(X, lambda u, v: seuclidean(u, v, V))
         elif metric == 'test_braycurtis':
             dm = pdist(X, braycurtis)
@@ -1431,7 +1457,7 @@
         elif metric == 'test_cityblock':
             dm = pdist(X, cityblock)
         elif metric == 'test_minkowski':
-            dm = pdist(X, minkowski)
+            dm = pdist(X, minkowski, p)
         elif metric == 'test_cosine':
             dm = pdist(X, cosine)
         elif metric == 'test_correlation':

Modified: trunk/scipy/cluster/src/hierarchy.c
===================================================================
--- trunk/scipy/cluster/src/hierarchy.c	2008-04-17 21:15:51 UTC (rev 4147)
+++ trunk/scipy/cluster/src/hierarchy.c	2008-04-18 02:13:12 UTC (rev 4148)
@@ -285,19 +285,20 @@
   int i = 0;
   double denom = 0.0, num = 0.0;
   for (i = 0; i < n; i++) {
-    num += (u[i] != v[i]) && ((u[i] != 0) || (v[i] != 0));
-    denom += (u[i] != 0) || (v[i] != 0);
+    num += (u[i] != v[i]) && ((u[i] != 0.0) || (v[i] != 0.0));
+    denom += (u[i] != 0.0) || (v[i] != 0.0);
   }
   return num / denom;
 }
 
 double jaccard_distance_bool(const char *u, const char *v, int n) {
   int i = 0;
-  double s = 0.0;
+  double s = 0.0, num = 0.0, denom = 0.0;
   for (i = 0; i < n; i++) {
-    s = s + (u[i] != v[i]);
+    num += (u[i] != v[i]) && ((u[i] != 0) || (v[i] != 0));
+    denom += (u[i] != 0) || (v[i] != 0);
   }
-  return s / (double)n;
+  return num / denom;
 }
 
 double dot_product(const double *u, const double *v, int n) {

Modified: trunk/scipy/cluster/tests/iris.txt
===================================================================
--- trunk/scipy/cluster/tests/iris.txt	2008-04-17 21:15:51 UTC (rev 4147)
+++ trunk/scipy/cluster/tests/iris.txt	2008-04-18 02:13:12 UTC (rev 4148)
@@ -1,151 +1,150 @@
-5.1,3.5,1.4,0.2
-4.9,3.0,1.4,0.2
-4.7,3.2,1.3,0.2
-4.6,3.1,1.5,0.2
-5.0,3.6,1.4,0.2
-5.4,3.9,1.7,0.4
-4.6,3.4,1.4,0.3
-5.0,3.4,1.5,0.2
-4.4,2.9,1.4,0.2
-4.9,3.1,1.5,0.1
-5.4,3.7,1.5,0.2
-4.8,3.4,1.6,0.2
-4.8,3.0,1.4,0.1
-4.3,3.0,1.1,0.1
-5.8,4.0,1.2,0.2
-5.7,4.4,1.5,0.4
-5.4,3.9,1.3,0.4
-5.1,3.5,1.4,0.3
-5.7,3.8,1.7,0.3
-5.1,3.8,1.5,0.3
-5.4,3.4,1.7,0.2
-5.1,3.7,1.5,0.4
-4.6,3.6,1.0,0.2
-5.1,3.3,1.7,0.5
-4.8,3.4,1.9,0.2
-5.0,3.0,1.6,0.2
-5.0,3.4,1.6,0.4
-5.2,3.5,1.5,0.2
-5.2,3.4,1.4,0.2
-4.7,3.2,1.6,0.2
-4.8,3.1,1.6,0.2
-5.4,3.4,1.5,0.4
-5.2,4.1,1.5,0.1
-5.5,4.2,1.4,0.2
-4.9,3.1,1.5,0.1
-5.0,3.2,1.2,0.2
-5.5,3.5,1.3,0.2
-4.9,3.1,1.5,0.1
-4.4,3.0,1.3,0.2
-5.1,3.4,1.5,0.2
-5.0,3.5,1.3,0.3
-4.5,2.3,1.3,0.3
-4.4,3.2,1.3,0.2
-5.0,3.5,1.6,0.6
-5.1,3.8,1.9,0.4
-4.8,3.0,1.4,0.3
-5.1,3.8,1.6,0.2
-4.6,3.2,1.4,0.2
-5.3,3.7,1.5,0.2
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-7.0,3.2,4.7,1.4
-6.4,3.2,4.5,1.5
-6.9,3.1,4.9,1.5
-5.5,2.3,4.0,1.3
-6.5,2.8,4.6,1.5
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-6.3,3.3,4.7,1.6
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-5.2,2.7,3.9,1.4
-5.0,2.0,3.5,1.0
-5.9,3.0,4.2,1.5
-6.0,2.2,4.0,1.0
-6.1,2.9,4.7,1.4
-5.6,2.9,3.6,1.3
-6.7,3.1,4.4,1.4
-5.6,3.0,4.5,1.5
-5.8,2.7,4.1,1.0
-6.2,2.2,4.5,1.5
-5.6,2.5,3.9,1.1
-5.9,3.2,4.8,1.8
-6.1,2.8,4.0,1.3
-6.3,2.5,4.9,1.5
-6.1,2.8,4.7,1.2
-6.4,2.9,4.3,1.3
-6.6,3.0,4.4,1.4
-6.8,2.8,4.8,1.4
-6.7,3.0,5.0,1.7
-6.0,2.9,4.5,1.5
-5.7,2.6,3.5,1.0
-5.5,2.4,3.8,1.1
-5.5,2.4,3.7,1.0
-5.8,2.7,3.9,1.2
-6.0,2.7,5.1,1.6
-5.4,3.0,4.5,1.5
-6.0,3.4,4.5,1.6
-6.7,3.1,4.7,1.5
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-5.6,3.0,4.1,1.3
-5.5,2.5,4.0,1.3
-5.5,2.6,4.4,1.2
-6.1,3.0,4.6,1.4
-5.8,2.6,4.0,1.2
-5.0,2.3,3.3,1.0
-5.6,2.7,4.2,1.3
-5.7,3.0,4.2,1.2
-5.7,2.9,4.2,1.3
-6.2,2.9,4.3,1.3
-5.1,2.5,3.0,1.1
-5.7,2.8,4.1,1.3
-6.3,3.3,6.0,2.5
-5.8,2.7,5.1,1.9
-7.1,3.0,5.9,2.1
-6.3,2.9,5.6,1.8
-6.5,3.0,5.8,2.2
-7.6,3.0,6.6,2.1
-4.9,2.5,4.5,1.7
-7.3,2.9,6.3,1.8
-6.7,2.5,5.8,1.8
-7.2,3.6,6.1,2.5
-6.5,3.2,5.1,2.0
-6.4,2.7,5.3,1.9
-6.8,3.0,5.5,2.1
-5.7,2.5,5.0,2.0
-5.8,2.8,5.1,2.4
-6.4,3.2,5.3,2.3
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Deleted: trunk/scipy/cluster/tests/pdist-minkowski-0.6-ml-iris.txt
===================================================================
--- trunk/scipy/cluster/tests/pdist-minkowski-0.6-ml-iris.txt	2008-04-17 21:15:51 UTC (rev 4147)
+++ trunk/scipy/cluster/tests/pdist-minkowski-0.6-ml-iris.txt	2008-04-18 02:13:12 UTC (rev 4148)
@@ -1 +0,0 @@
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1.8568002e+01   1.7894715e+01   1.6219054e+01   1.7763994e+01   1.8981142e+01   1.8294506e+01   1.8190541e+01   1.7081179e+01   1.7390173e+01   1.4863989e+01   1.9394676e+00   4.6383693e+00   9.8003160e-01   1.1066229e+00   1.0211725e+00   6.0103306e-01   2.2132457e+00   1.2034300e+00   1.2337044e+00   2.1096674e+00   4.7282906e+00   4.9478896e+00   4.6383693e+00   2.5152850e+00   4.5992589e+00   2.4650524e+00   2.5196315e+00   2.6058219e+00   1.5874011e+00   2.9320989e+00   1.8435146e+00   1.1359060e+00   2.4086604e+00   1.5745775e+00   1.9065209e+00   6.2402515e-01   4.6533907e-01   2.5196315e+00   3.1410377e+00   3.8599252e+00   6.0103306e-01   1.5760969e+00   2.9058572e+00   6.0103306e-01   1.0211725e+00   1.2538012e+00   2.6292664e+00   2.5602448e+00   1.0211725e+00   3.1284501e+00   4.3768242e+00   1.2337044e+00   2.4650524e+00   3.1748021e-01   2.0611757e+00   1.3720717e+00   1.4949205e+01   1.3552973e+01   1.4149173e+01   1.2746928e+01   1.5098077e+01   1.2431738e+01   1.4565741e+01   8.4189234e+00   1.4265547e+01   1.0586804e+01   1.0190228e+01   1.1845622e+01   1.3516479e+01   1.3569735e+01   1.0080743e+01   1.2587964e+01   1.1613319e+01   1.1553992e+01   1.6458101e+01   1.1661541e+01   1.3631975e+01   1.2506053e+01   1.6443605e+01   1.3518980e+01   1.3268231e+01   1.3548443e+01   1.5874084e+01   1.5647085e+01   1.3225436e+01   1.0541341e+01   1.1516902e+01   1.1044947e+01   1.1741421e+01   1.5513515e+01   1.1061726e+01   1.3973799e+01   1.3378578e+01   1.5621176e+01   1.0435315e+01   1.2113655e+01   1.2232650e+01   1.2786907e+01   1.2302913e+01   9.0487423e+00   1.2042373e+01   1.0608917e+01   1.1428733e+01   1.2816251e+01   8.4950667e+00   1.1713794e+01   1.9098910e+01   1.5729118e+01   1.9190544e+01   1.6688193e+01   1.7848999e+01   2.1558564e+01   1.1950217e+01   2.0277352e+01   1.9931833e+01   2.3108353e+01   1.6113637e+01   1.7673275e+01   1.7782121e+01   1.6305410e+01   1.6430438e+01   1.6943162e+01   1.6335430e+01   2.5515941e+01   2.5266906e+01   1.6896031e+01   1.8862638e+01   1.4583109e+01   2.3041560e+01   1.6424987e+01   1.8599072e+01   1.8813252e+01   1.5528301e+01   1.4311193e+01   1.8241083e+01   1.7914146e+01   2.1001149e+01   2.4839535e+01   1.8486325e+01   1.5545880e+01   1.6531118e+01   2.1386990e+01   1.8707574e+01   1.4845159e+01   1.3885107e+01   1.6522806e+01   1.7123369e+01   1.6445405e+01   1.5729118e+01   1.8990048e+01   1.9566845e+01   1.7476427e+01   1.7692813e+01   1.6295164e+01   1.7843270e+01   1.4155799e+01   2.9891849e+00   1.3720717e+00   4.6533907e-01   2.0611757e+00   1.7799212e+00   1.1359060e+00   1.2480503e+00   1.6856955e+00   3.9500734e+00   2.7441434e+00   4.0481603e+00   2.4086604e+00   6.2402515e-01   2.9784994e+00   1.2337044e+00   1.8435146e+00   1.2337044e+00   1.2699208e+00   2.4404310e+00   1.7965249e+00   1.2020661e+00   1.2480503e+00   8.1287374e-01   6.3496042e-01   1.8435146e+00   1.7965249e+00   2.1654045e+00   2.0600534e+00   1.7432492e+00   1.7799212e+00   9.3067814e-01   1.2845725e+00   1.7799212e+00   2.4768885e+00   8.1287374e-01   6.2402515e-01   4.1027239e+00   2.1079600e+00   1.3720717e+00   2.3563262e+00   1.6856955e+00   1.0211725e+00   1.2699208e+00   9.8003160e-01   3.0000000e-01   1.5885580e+01   1.4342699e+01   1.6726423e+01   1.3015952e+01   1.6263978e+01   1.3245927e+01   1.4264810e+01   8.8961475e+00   1.5615144e+01   1.0794471e+01   9.0966241e+00   1.3187697e+01   1.4004123e+01   1.4760482e+01   1.0964233e+01   1.5028936e+01   1.2788364e+01   1.2278631e+01   1.7040550e+01   1.2113655e+01   1.4259081e+01   1.3500058e+01   1.7242856e+01   1.4525171e+01   1.4542971e+01   1.5162979e+01   1.7122087e+01   1.7361002e+01   1.4374434e+01   1.1119462e+01   1.1837173e+01   1.1363242e+01   1.2476580e+01   1.6390006e+01   1.2062629e+01   1.2612885e+01   1.5869143e+01   1.6278714e+01   1.1572443e+01   1.2500793e+01   1.2690654e+01   1.4232228e+01   1.2949021e+01   8.1258010e+00   1.2669797e+01   1.1806409e+01   1.2394540e+01   1.4021062e+01   8.3567683e+00   1.2519379e+01   1.8737933e+01   1.6522234e+01   2.1105670e+01   1.8025065e+01   1.9590654e+01   2.3628381e+01   1.2525860e+01   2.1925476e+01   2.0880164e+01   1.8637340e+01   1.6970100e+01   1.8723742e+01   1.9593859e+01   1.6856171e+01   1.7380354e+01   1.7787417e+01   1.8023258e+01   2.2240849e+01   2.6577362e+01   1.7401998e+01   1.9849461e+01   1.5378705e+01   2.4600487e+01   1.7426407e+01   1.8345685e+01   1.9845368e+01   1.6621080e+01   1.5814189e+01   1.9448698e+01   1.9796449e+01   2.2472697e+01   2.1628673e+01   1.9700284e+01   1.6662369e+01   1.7345859e+01   2.3471116e+01   1.7250384e+01   1.7350188e+01   1.5337280e+01   1.9246402e+01   1.9840267e+01   1.9170162e+01   1.6522234e+01   1.9956596e+01   1.9308243e+01   1.9261198e+01   1.8513258e+01   1.7987051e+01   1.6388067e+01   1.5572449e+01   3.9243446e+00   3.1702938e+00   5.7837411e+00   4.3044426e+00   1.2480503e+00   3.2484124e+00   5.0617707e+00   7.0185681e+00   2.8352192e+00   2.0228388e+00   4.0000000e-01   2.6621660e+00   9.8003160e-01   1.6872569e+00   1.0683811e+00   1.4448053e+00   4.7544555e+00   1.9065209e+00   3.6016092e+00   3.5752200e+00   1.9394676e+00   2.4674089e+00   2.9320989e+00   3.8537088e+00   3.8423451e+00   1.0683811e+00   2.2524858e+00   2.1958558e+00   4.3044426e+00   4.3768242e+00   2.6292664e+00   4.3044426e+00   5.8857526e+00   2.9320989e+00   3.1284501e+00   6.5652439e+00   5.4475242e+00   2.6292664e+00   1.2034300e+00   4.3366937e+00   1.6872569e+00   4.7544555e+00   1.7382670e+00   3.6635621e+00   1.4944658e+01   1.3285812e+01   1.5700236e+01   1.0777549e+01   1.4966823e+01   1.1538395e+01   1.3297809e+01   1.0066697e+01   1.4370445e+01   1.0508179e+01   1.0958178e+01   1.1770874e+01   1.2243948e+01   1.3377582e+01   9.2099134e+00   1.3943877e+01   1.1077285e+01   1.0586804e+01   1.5424179e+01   1.0149607e+01   1.3012133e+01   1.2053876e+01   1.5762118e+01   1.3066477e+01   1.3247734e+01   1.3987735e+01   1.5879523e+01   1.6246477e+01   1.2952973e+01   9.3143156e+00   9.6410330e+00   9.1658052e+00   1.0813285e+01   1.4870325e+01   9.4670761e+00   1.1663634e+01   1.4801876e+01   1.4708005e+01   9.8667010e+00   1.0340823e+01   1.0550351e+01   1.2909712e+01   1.1241066e+01   9.9314085e+00   1.0794471e+01   1.0213635e+01   1.0748161e+01   1.2665879e+01   8.7999548e+00   1.0821191e+01   1.7842778e+01   1.4874653e+01   2.0110592e+01   1.6750478e+01   1.8466434e+01   2.2716973e+01   1.4178033e+01   2.0878528e+01   1.9534887e+01   1.9274137e+01   1.5989379e+01   1.7385461e+01   1.8535852e+01   1.5022060e+01   1.5786192e+01   1.6794631e+01   1.6873441e+01   1.9531053e+01   2.5478890e+01   1.5691453e+01   1.8992682e+01   1.3539520e+01   2.3572128e+01   1.6048147e+01   1.7548276e+01   1.9010270e+01   1.5253349e+01   1.4519345e+01   1.8169708e+01   1.8771066e+01   2.1391056e+01   1.8942346e+01   1.8425433e+01   1.5310675e+01   1.5811284e+01   2.2577570e+01   1.6503004e+01   1.6243921e+01   1.3992343e+01   1.8280982e+01   1.8850628e+01   1.8208718e+01   1.4874653e+01   1.9082206e+01   1.8533380e+01   1.8185706e+01   1.7058389e+01   1.6846714e+01   1.5590842e+01   1.4165590e+01   1.1359060e+00   1.5319850e+00   2.1958558e+00   2.8198290e+00   1.0211725e+00   1.6257475e+00   2.9891849e+00   4.5546238e+00   4.7945480e+00   3.2728146e+00   8.5602218e-01   3.5027891e+00   1.9394676e+00   2.2149867e+00   2.2986581e+00   1.3720717e+00   2.6076804e+00   1.5319850e+00   2.6292664e+00   1.3720717e+00   1.9428691e+00   9.7877528e-01   1.4773595e+00   1.9617216e+00   1.7044794e+00   3.6519699e+00   3.3475964e+00   2.1958558e+00   2.1654045e+00   2.4032464e+00   2.1958558e+00   1.8793802e+00   1.2845725e+00   1.1359060e+00   2.1010911e+00   1.4773595e+00   2.4086604e+00   3.5753219e+00   9.3067814e-01   2.8352192e+00   4.6533907e-01   2.6519650e+00   1.1359060e+00   1.5495174e+01   1.4091742e+01   1.6467395e+01   1.3524603e+01   1.6268059e+01   1.3499808e+01   1.3865506e+01   9.1026803e+00   1.5532634e+01   1.1525561e+01   1.0798526e+01   1.3271597e+01   1.4236036e+01   1.4820377e+01   1.1215273e+01   1.4807567e+01   1.3020865e+01   1.2470879e+01   1.7285766e+01   1.2476580e+01   1.4186968e+01   1.3590107e+01   1.7396241e+01   1.4606164e+01   1.4507565e+01   1.5035837e+01   1.7052793e+01   1.7231674e+01   1.4477344e+01   1.1377718e+01   1.2285397e+01   1.1789546e+01   1.2698076e+01   1.6589897e+01   1.2443071e+01   1.1661923e+01   1.5652212e+01   1.6451663e+01   1.1778144e+01   1.2961981e+01   1.3119092e+01   1.4236480e+01   1.3202276e+01   9.7168810e+00   1.3010921e+01   1.1946808e+01   1.2600802e+01   1.4038979e+01   9.2493015e+00   1.2767629e+01   1.8344693e+01   1.6832510e+01   2.0915584e+01   1.8059318e+01   1.9533030e+01   2.3352678e+01   1.2813825e+01   2.1745287e+01   2.0966670e+01   2.1436371e+01   1.6712435e+01   1.8824194e+01   1.9463631e+01   1.7288747e+01   1.7684657e+01   1.7565447e+01   1.7944140e+01   2.4039820e+01   2.6493846e+01   1.7720395e+01   1.9504506e+01   1.5765238e+01   2.4421905e+01   1.7545011e+01   1.7839035e+01   1.9420400e+01   1.6729751e+01   1.5850778e+01   1.9522918e+01   1.9560676e+01   2.2334398e+01   2.3371852e+01   1.9780264e+01   1.6718154e+01   1.7526334e+01   2.3194192e+01   1.6117648e+01   1.7218049e+01   1.5408911e+01   1.9015475e+01   1.9661695e+01   1.8949808e+01   1.6832510e+01   1.9630268e+01   1.8810081e+01   1.9162699e+01   1.8702086e+01   1.7920616e+01   1.5303222e+01   1.5684795e+01   2.2968911e+00   9.8003160e-01   1.1066229e+00   4.6533907e-01   1.8793802e+00   3.7572369e+00   3.4336612e+00   3.6878258e+00   3.1702938e+00   1.0079368e+00   3.2181600e+00   1.1359060e+00   9.3067814e-01   1.2034300e+00   2.2289625e+00   1.6872569e+00   9.3067814e-01   7.3049739e-01   4.6533907e-01   4.6533907e-01   4.6533907e-01   1.2034300e+00   1.2034300e+00   9.3067814e-01   1.8347096e+00   2.6281695e+00   9.8003160e-01   7.8728875e-01   1.5319850e+00   9.8003160e-01   2.4068601e+00   1.0000000e-01   8.1287374e-01   4.1553586e+00   1.9600632e+00   1.1359060e+00   2.6292664e+00   1.8793802e+00   1.1359060e+00   1.3720717e+00   9.5244063e-01   3.1748021e-01   1.4725295e+01   1.3225436e+01   1.5656797e+01   1.2312490e+01   1.5375897e+01   1.2426806e+01   1.2977234e+01   8.2564023e+00   1.4698049e+01   1.0056743e+01   8.5114308e+00   1.2270388e+01   1.3295967e+01   1.3866426e+01   1.0144011e+01   1.3993710e+01   1.1889800e+01   1.1506808e+01   1.6288193e+01   1.1390093e+01   1.3151101e+01   1.2661442e+01   1.6434971e+01   1.3679267e+01   1.3644731e+01   1.4197215e+01   1.6219928e+01   1.6354615e+01   1.3485437e+01   1.0385431e+01   1.1137020e+01   1.0671434e+01   1.1693932e+01   1.5546262e+01   1.1185277e+01   1.0746831e+01   1.4817906e+01   1.5519994e+01   1.0700300e+01   1.1770874e+01   1.1943377e+01   1.3295840e+01   1.2184996e+01   7.5241539e+00   1.1890723e+01   1.0929683e+01   1.1550501e+01   1.3136108e+01   7.7031654e+00   1.1708978e+01   1.7322409e+01   1.5675730e+01   2.0033331e+01   1.7073335e+01   1.8548675e+01   2.2516592e+01   1.1808104e+01   2.0906475e+01   2.0024980e+01   2.0545041e+01   1.5786590e+01   1.7837112e+01   1.8546631e+01   1.6057790e+01   1.6479067e+01   1.6584809e+01   1.7011024e+01   2.3202565e+01   2.5620295e+01   1.6654830e+01   1.8599072e+01   1.4517204e+01   2.3591291e+01   1.6557208e+01   1.6937692e+01   1.8599942e+01   1.5729748e+01   1.4843306e+01   1.8514877e+01   1.8750034e+01   2.1491080e+01   2.2575579e+01   1.8761579e+01   1.5776405e+01   1.6522744e+01   2.2354833e+01   1.5145712e+01   1.6276024e+01   1.4376347e+01   1.8124039e+01   1.8707574e+01   1.8043717e+01   1.5675730e+01   1.8706756e+01   1.7870457e+01   1.8215532e+01   1.7683922e+01   1.6970100e+01   1.4324535e+01   1.4611615e+01   2.0600534e+00   3.5147734e+00   2.2289625e+00   1.1359060e+00   1.4295913e+00   5.1171773e+00   6.5123974e+00   5.0171180e+00   2.6500939e+00   5.7155780e+00   3.8590103e+00   3.5685848e+00   4.0481603e+00   2.5781299e+00   4.1703514e+00   2.9059510e+00   1.6856955e+00   3.6016092e+00   2.8179114e+00   2.0413535e+00   1.6529143e+00   1.6257475e+00   3.9834057e+00   4.5825506e+00   3.8044623e+00   2.0600534e+00   2.1941208e+00   3.2976039e+00   2.0600534e+00   3.1748021e-01   2.4650524e+00   3.1074178e+00   1.9428691e+00   6.0103306e-01   4.3917116e+00   5.5180183e+00   1.1359060e+00   3.5173564e+00   7.8728875e-01   3.3475964e+00   1.5745775e+00   1.6735385e+01   1.5325525e+01   1.6644523e+01   1.2851853e+01   1.4580767e+01   1.2048822e+01   1.6200007e+01   8.7080563e+00   1.3062815e+01   1.0519416e+01   1.0546398e+01   1.2502190e+01   1.3572927e+01   1.2436165e+01   9.1699403e+00   1.5001274e+01   1.2305869e+01   1.1343580e+01   1.6479039e+01   1.1655248e+01   1.5461651e+01   1.2080147e+01   1.6303403e+01   1.3061676e+01   1.2124274e+01   1.4159539e+01   1.5317018e+01   1.6271430e+01   1.2119901e+01   1.0466619e+01   1.1584112e+01   1.1114311e+01   1.1535386e+01   1.5222552e+01   1.1784536e+01   1.5511934e+01   1.5840873e+01   1.5596877e+01   1.1109071e+01   1.2124653e+01   1.2164102e+01   1.3427787e+01   1.2190349e+01   9.3206148e+00   1.1859330e+01   1.1266995e+01   1.0435158e+01   1.1707330e+01   8.6485997e+00   1.1349750e+01   2.0887950e+01   1.5466570e+01   1.9819004e+01   1.5414117e+01   1.8509842e+01   2.2173824e+01   1.2192287e+01   1.8803540e+01   1.9722318e+01   2.4654236e+01   1.7984552e+01   1.7314585e+01   1.8420681e+01   1.6248623e+01   1.5970653e+01   1.8856897e+01   1.6978513e+01   2.6979555e+01   2.4853709e+01   1.6931298e+01   2.0803484e+01   1.4184923e+01   2.2297391e+01   1.6094959e+01   2.0334019e+01   2.0725222e+01   1.5030679e+01   1.4974508e+01   1.7671813e+01   1.8520744e+01   2.0309716e+01   2.6281171e+01   1.7913977e+01   1.5031048e+01   1.6323139e+01   2.2002227e+01   2.0365488e+01   1.7418024e+01   1.4555341e+01   1.9159766e+01   1.9809353e+01   1.9083663e+01   1.5466570e+01   2.0940700e+01   2.1336409e+01   1.8124514e+01   1.7546255e+01   1.6943162e+01   1.9486620e+01   1.4839072e+01   2.2968911e+00   1.4295913e+00   6.2402515e-01   2.1079600e+00   4.9611467e+00   4.6998864e+00   4.3044426e+00   2.1654045e+00   4.4328796e+00   2.1181110e+00   2.6076804e+00   2.1941208e+00   3.3251194e+00   2.4674089e+00   2.1096674e+00   1.0079368e+00   1.9081610e+00   1.5760969e+00   1.9081610e+00   1.2337044e+00   6.2402515e-01   2.2597668e+00   1.9341935e+00   3.9995803e+00   0.0000000e+00   1.4295913e+00   3.0306837e+00   0.0000000e+00   2.0600534e+00   1.2034300e+00   2.1654045e+00   3.7587604e+00   2.0600534e+00   2.5152850e+00   3.8655529e+00   1.2337044e+00   2.3988602e+00   1.4295913e+00   2.1079600e+00   1.2337044e+00   1.4580767e+01   1.3110450e+01   1.3769493e+01   1.2080662e+01   1.4652619e+01   1.1855256e+01   1.4084933e+01   6.8368930e+00   1.3862137e+01   9.7626002e+00   9.1098636e+00   1.1324953e+01   1.3043780e+01   1.3076995e+01   9.5164235e+00   1.2209314e+01   1.1000223e+01   1.1057973e+01   1.5939828e+01   1.1082459e+01   1.3061676e+01   1.2037718e+01   1.5946233e+01   1.3045457e+01   1.2845810e+01   1.3144641e+01   1.5471938e+01   1.5211277e+01   1.2706937e+01   1.0032797e+01   1.0897113e+01   1.0447505e+01   1.1219362e+01   1.4953058e+01   1.0365843e+01   1.3436549e+01   1.2982765e+01   1.5151439e+01   9.8630031e+00   1.1461051e+01   1.1586793e+01   1.2305869e+01   1.1770874e+01   8.0202304e+00   1.1435749e+01   1.0077215e+01   1.0871601e+01   1.2363878e+01   7.6582738e+00   1.1151062e+01   1.8513828e+01   1.5087681e+01   1.8747043e+01   1.6167006e+01   1.7329665e+01   2.1147509e+01   1.0058318e+01   1.9864074e+01   1.9444558e+01   2.2623523e+01   1.5624756e+01   1.7153417e+01   1.7314471e+01   1.5612720e+01   1.5754520e+01   1.6412718e+01   1.5854906e+01   2.5080378e+01   2.4827937e+01   1.6323534e+01   1.8387986e+01   1.3880508e+01   2.2634459e+01   1.5907135e+01   1.8108339e+01   1.8401564e+01   1.5001832e+01   1.3780256e+01   1.7703852e+01   1.7524152e+01   2.0586191e+01   2.4438069e+01   1.7941377e+01   1.5059656e+01   1.5997452e+01   2.0976491e+01   1.8131337e+01   1.4366177e+01   1.3336993e+01   1.6081745e+01   1.6635606e+01   1.5996286e+01   1.5087681e+01   1.8500417e+01   1.9048067e+01   1.6988752e+01   1.7153241e+01   1.5804067e+01   1.7260689e+01   1.3576723e+01   1.9065209e+00   3.2967448e+00   5.2174040e+00   2.0720948e+00   2.3592959e+00   1.2480503e+00   1.6872569e+00   1.6872569e+00   9.8003160e-01   7.8728875e-01   7.8728875e-01   2.6281695e+00   2.9891849e+00   2.6602921e+00   2.2705666e+00   2.4086604e+00   6.3496042e-01   1.2034300e+00   2.4650524e+00   2.4768885e+00   7.8728875e-01   1.3720717e+00   1.2845725e+00   2.2968911e+00   2.4749599e+00   1.0211725e+00   2.2968911e+00   3.6878258e+00   9.5244063e-01   2.1654045e+00   5.5437705e+00   3.2826324e+00   2.6292664e+00   2.4086604e+00   3.2967448e+00   9.8003160e-01   2.6281695e+00   1.0000000e-01   1.7632210e+00   1.5163271e+01   1.3485437e+01   1.5938663e+01   1.1223752e+01   1.5307072e+01   1.1888002e+01   1.3417623e+01   1.0621763e+01   1.4721277e+01   1.0878046e+01   1.1557923e+01   1.2049819e+01   1.2810900e+01   1.3692367e+01   9.5599586e+00   1.4214780e+01   1.1334163e+01   1.1045811e+01   1.5877667e+01   1.0614099e+01   1.3151272e+01   1.2437761e+01   1.6155637e+01   1.3448523e+01   1.3603183e+01   1.4294079e+01   1.6238014e+01   1.6486610e+01   1.3254830e+01   9.8072539e+00   1.0116001e+01   9.6682093e+00   1.1229914e+01   1.5191671e+01   9.7084199e+00   1.1718608e+01   1.5044070e+01   1.5187558e+01   1.0167937e+01   1.0753799e+01   1.0951892e+01   1.3196318e+01   1.1675337e+01   1.0495743e+01   1.1170011e+01   1.0535701e+01   1.1080677e+01   1.3015050e+01   9.3159181e+00   1.1183015e+01   1.7816203e+01   1.5153324e+01   2.0279449e+01   1.6986262e+01   1.8622128e+01   2.2871385e+01   1.4542009e+01   2.1111626e+01   1.9872954e+01   1.8834769e+01   1.6101675e+01   1.7673568e+01   1.8713651e+01   1.5331404e+01   1.5996810e+01   1.6869307e+01   1.7081981e+01   2.0388736e+01   2.5728398e+01   1.6123532e+01   1.9055612e+01   1.3783359e+01   2.3805685e+01   1.6357474e+01   1.7570255e+01   1.9123174e+01   1.5538562e+01   1.4739293e+01   1.8402604e+01   1.9010270e+01   2.1647657e+01   1.9821456e+01   1.8648709e+01   1.5630845e+01   1.6179526e+01   2.2724588e+01   1.6421085e+01   1.6412194e+01   1.4213520e+01   1.8422806e+01   1.8955742e+01   1.8341956e+01   1.5153324e+01   1.9138262e+01   1.8516581e+01   1.8353326e+01   1.7396241e+01   1.7040989e+01   1.5526685e+01   1.4375002e+01   1.3720717e+00   3.5753219e+00   4.0456776e+00   4.8240043e+00   3.8981003e+00   1.6872569e+00   3.2230929e+00   2.1096674e+00   9.7877528e-01   2.1958558e+00   1.9600632e+00   1.9081610e+00   3.0000000e-01   9.3067814e-01   6.3496042e-01   1.1359060e+00   9.3067814e-01   4.6533907e-01   3.0000000e-01   1.6856955e+00   2.8810032e+00   3.3425881e+00   1.4295913e+00   1.6257475e+00   2.0628679e+00   1.4295913e+00   2.2801540e+00   6.0103306e-01   1.6872569e+00   3.9531919e+00   1.8435146e+00   1.3720717e+00   2.9891849e+00   1.3720717e+00   1.1066229e+00   1.2480503e+00   1.7448317e+00   1.0211725e+00   1.4976806e+01   1.3522416e+01   1.5928049e+01   1.2796972e+01   1.5680723e+01   1.2851945e+01   1.3290140e+01   8.0712326e+00   1.4985709e+01   1.0709970e+01   9.8656983e+00   1.2633631e+01   1.3643417e+01   1.4219923e+01   1.0541341e+01   1.4260102e+01   1.2340665e+01   1.1881396e+01   1.6641737e+01   1.1816770e+01   1.3539520e+01   1.2983768e+01   1.6783417e+01   1.4030863e+01   1.3940115e+01   1.4475808e+01   1.6502369e+01   1.6652959e+01   1.3849158e+01   1.0751191e+01   1.1596210e+01   1.1119462e+01   1.2064736e+01   1.5945124e+01   1.1715670e+01   1.1079239e+01   1.5098077e+01   1.5848156e+01   1.1122550e+01   1.2246817e+01   1.2433306e+01   1.3641155e+01   1.2565128e+01   8.8080682e+00   1.2333832e+01   1.1326250e+01   1.1955835e+01   1.3455472e+01   8.4044206e+00   1.2113655e+01   1.7699108e+01   1.6125088e+01   2.0334019e+01   1.7441240e+01   1.8902895e+01   2.2802717e+01   1.1634456e+01   2.1201880e+01   2.0364638e+01   2.0843425e+01   1.6106091e+01   1.8190541e+01   1.8859715e+01   1.6540481e+01   1.6937421e+01   1.6928155e+01   1.7348045e+01   2.3486710e+01   2.5918777e+01   1.7062596e+01   1.8905970e+01   1.5014650e+01   2.3877323e+01   1.6906681e+01   1.7253783e+01   1.8885161e+01   1.6085913e+01   1.5211055e+01   1.8879373e+01   1.9032847e+01   2.1778721e+01   2.2839614e+01   1.9127999e+01   1.6123532e+01   1.6920457e+01   2.2625611e+01   1.5496514e+01   1.6620546e+01   1.4756657e+01   1.8422262e+01   1.9034611e+01   1.8335254e+01   1.6125088e+01   1.9028012e+01   1.8193362e+01   1.8531313e+01   1.8044957e+01   1.7301002e+01   1.4679679e+01   1.5023003e+01   1.2538012e+00   5.0171180e+00   5.8948198e+00   4.3366937e+00   2.0228388e+00   5.1700126e+00   3.1541992e+00   3.3078726e+00   3.2538196e+00   3.0306837e+00   3.2648893e+00   1.9394676e+00   1.0211725e+00   2.7232965e+00   2.5152850e+00   1.7632210e+00   1.4773595e+00   8.1287374e-01   3.3078726e+00   2.8818172e+00   3.6487468e+00   6.2402515e-01   1.7382670e+00   3.0944563e+00   6.2402515e-01   1.1359060e+00   2.1096674e+00   2.3563262e+00   2.9784994e+00   1.8793802e+00   3.3918985e+00   4.6223377e+00   2.0000000e-01   3.1541992e+00   1.0211725e+00   3.0944563e+00   1.2034300e+00   1.5623172e+01   1.4144710e+01   1.5388959e+01   1.2285620e+01   1.4565741e+01   1.1844494e+01   1.5028771e+01   7.6716480e+00   1.3654500e+01   9.9370695e+00   9.5813407e+00   1.0662773e+01   1.3202276e+01   1.2904025e+01   9.4425804e+00   1.3775505e+01   1.0375005e+01   1.1103359e+01   1.6079200e+01   1.1226807e+01   1.4128453e+01   1.1998446e+01   1.6006895e+01   1.2987160e+01   1.2662535e+01   1.2386330e+01   1.5362768e+01   1.4387982e+01   1.2548905e+01   1.0143725e+01   1.1082459e+01   1.0632980e+01   1.1270701e+01   1.4958017e+01   9.7925804e+00   1.4327393e+01   1.4579315e+01   1.5266793e+01   9.2739892e+00   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6.1982358e+00   2.5398417e+00   3.4917521e+00   1.1453386e+01   1.2139224e+01   3.8258056e+00   5.0748344e+00   5.1984987e+00   1.0130826e+01   3.1053060e+00   4.8796304e+00   5.0291590e+00   2.9891849e+00   2.9891849e+00   4.2186872e+00   5.1614633e+00   7.9913456e+00   1.0678375e+01   4.4322192e+00   2.1079600e+00   4.7026362e+00   9.0582525e+00   5.0094739e+00   2.5094325e+00   2.9891849e+00   4.8711511e+00   5.3468360e+00   4.6717100e+00   5.2639976e+00   5.1562598e+00   5.7369312e+00   4.7544555e+00   3.9941117e+00   3.4410701e+00   4.8372469e+00   3.8981003e+00   7.7551774e+00   2.0720948e+00   4.7876069e+00   2.5381307e+00   1.1408443e+01   2.4994860e+00   6.9603606e+00   1.1868819e+01   3.3311669e+00   7.9761706e+00   2.8823731e+00   6.5993914e+00   1.5319850e+00   3.1715064e+00   6.8420260e+00   4.0750538e+00   8.0053041e+00   3.1430403e+00   5.1700126e+00   1.9048813e+00   3.7966977e+00   3.6016092e+00   2.2986581e+00   1.4295913e+00   1.4773595e+00   2.9058572e+00   8.687