Merge pull request #94 from fplll/stats

Generate more statistics

src/fpylll/algorithms/bkz.py

@@ -15,7 +15,7 @@
 from fpylll import Enumeration
 from fpylll import EnumerationError
 from fpylll.util import adjust_radius_to_gh_bound
-from fpylll.algorithms.bkz_stats import BKZTreeTracer, dummy_tracer
+from fpylll.tools.bkz_stats import BKZTreeTracer, dummy_tracer
 
 
 class BKZReduction:

src/fpylll/algorithms/bkz2.py

@@ -3,7 +3,7 @@
 from random import randint
 from fpylll import BKZ, Enumeration, EnumerationError
 from fpylll.algorithms.bkz import BKZReduction as BKZBase
-from fpylll.algorithms.bkz_stats import dummy_tracer
+from fpylll.tools.bkz_stats import dummy_tracer
 from fpylll.util import gaussian_heuristic
 
 

src/fpylll/algorithms/pbkz.py

@@ -13,7 +13,7 @@
 from fpylll import BKZ, Enumeration, EnumerationError
 from fpylll.algorithms.bkz import BKZReduction as BKZ1
 from fpylll.algorithms.bkz2 import BKZReduction as BKZ2
-from fpylll.algorithms.bkz_stats import BKZTreeTracer, dummy_tracer
+from fpylll.tools.bkz_stats import BKZTreeTracer, dummy_tracer
 from fpylll.util import adjust_radius_to_gh_bound
 
 

src/fpylll/algorithms/bkz_stats.py → src/fpylll/tools/bkz_stats.py

@@ -12,6 +12,7 @@
 import copy
 from collections import OrderedDict
 from math import log
+from fpylll.tools.quality import basis_quality
 
 
 def pretty_dict(d, keyword_width=None, round_bound=9999):
@@ -730,8 +731,12 @@ def exit(self, **kwds):
                     pass
 
         if label[0] == "tour":
-            node.data["r_0"] = Statistic(self.instance.M.get_r(0, 0), repr="min")
-            node.data["/"] = Statistic(self.instance.M.get_current_slope(0, self.instance.A.nrows), repr="min")
+            data = basis_quality(self.instance.M)
+            for k, v in data.items():
+                if k == "/":
+                    node.data[k] = Statistic(v, repr="max")
+                else:
+                    node.data[k] = Statistic(v, repr="min")
 
         if self.verbosity and label[0] == "tour":
             report = OrderedDict()
@@ -746,14 +751,14 @@ def exit(self, **kwds):
                 report["svp"] = node.find("enumeration", True)["cputime"]
             except KeyError:
                 pass
+            report["#enum"] = node.sum("#enum")
             report["lll"] = node.sum("cputime", label="lll")
             try:
                 report["pruner"] = node.find("pruner", True)["cputime"]
             except KeyError:
                 pass
             report["r_0"] = node["r_0"]
             report["/"] = node["/"]
-            report["#enum"] = node.sum("#enum")
 
             print(pretty_dict(report))
 

src/fpylll/tools/quality.py

@@ -0,0 +1,65 @@
+# -*- coding: utf-8 -*-
+"""
+
+"""
+
+from math import log, exp
+from collections import OrderedDict
+from fpylll.util import gaussian_heuristic
+
+
+def basis_quality(M):
+    r"""
+    Return a dictionary with various expressions of quality of the basis corresponding to ``M``.
+
+    Let `|b_i^*|` be the norm of the `i`-th Gram-Schmidt vector.  Let `Λ` be the lattice spanned by
+    the basis of dimension `d`.
+
+        - ``r_0`` - `|b_0|^2`
+
+        - ``\`` - the slope of `\log(|b_i^*|)`
+
+        - ``rhf`` - the root-Hermite factor `|b_0|/\Vol(Λ)^{1/d}` also written as `\delta_0`
+
+        - ``hv/hv`` - the dth-root of the fraction of the first and second half-volumes, i.e. the
+          dth-root of `∏_{i=0}^{d/2-1} |b_i|/∏_{i=d/2}^{d-1} |b_i|`.  If `d` is odd, the length
+          `|b_{d//2}|` is ignored.
+
+        - ``r_0/gh`` - `|b_0|/GH` where `GH = Γ(d/2+1)^{1/d}/π^{1/2} ⋅ \Vol(Λ)^{1/d}` is the Gaussian
+          Heuristic for the shortest vector.
+
+    :param M: A MatGSO object.
+
+    :example:
+
+        >>> from fpylll import IntegerMatrix, GSO, LLL, set_random_seed
+        >>> set_random_seed(1337)
+        >>> A = IntegerMatrix.random(100, "qary", bits=30, k=50)
+        >>> _ = LLL.reduction(A)
+        >>> M = GSO.Mat(A); _ = M.update_gso()
+
+        >>> from fpylll.tools.quality import basis_quality
+        >>> from fpylll.tools.bkz_stats import pretty_dict
+        >>> str(pretty_dict(basis_quality(M)))
+        '{"r_0":   2^34.0,  "r_0/gh": 9.389811,  "rhf": 1.020530,  "/": -0.08550,  "hv/hv": 2.940943}'
+
+    """
+
+    d = M.d
+
+    ret = OrderedDict()
+
+    r = [M.get_r(i, i) for i in range(d)]
+
+    log_volume = sum(log(r_)/2 for r_ in r)
+
+    lhs = sum(log(r_)/2 for r_ in r[:d//2])
+    rhs = sum(log(r_)/2 for r_ in r[d//2 + (d%2):])
+
+    ret["r_0"] = r[0]
+    ret["r_0/gh"] = r[0]/gaussian_heuristic(r)
+    ret["rhf"] = exp((log(r[0])/2.0 - log_volume/d)/d)
+    ret['/']   = M.get_current_slope(0, d)
+    ret["hv/hv"] = exp((lhs - rhs)/d)
+
+    return ret

tests/test_bkz_python.py

@@ -10,7 +10,7 @@
 from fpylll.algorithms.simple_dbkz import DBKZReduction as SimpleDualBKZ
 from fpylll.algorithms.bkz import BKZReduction as BKZ
 from fpylll.algorithms.bkz2 import BKZReduction as BKZ2
-from fpylll.algorithms.bkz_stats import BKZTreeTracer
+from fpylll.tools.bkz_stats import BKZTreeTracer
 
 from fpylll import BKZ as fplll_bkz
 from fpylll.util import set_random_seed