Ticket #10837: trac_10837-norms-condition-CDF-edits-v3.patch

sage/geometry/polyhedra.py

@@ -4945 +4945 @@
         sage: cube = polytopes.n_cube(3).vertices()
         sage: proj = ProjectionFuncStereographic([1.1,1.1,1.1])
         sage: ppoints = [proj(vector(x)) for x in cube]
-        sage: ppoints[0]
-        (0.0, 0.0)
+        sage: ppoints[1]
+        (-0.3182829598..., 1.18784817...)
     """
     def __init__(self, projection_point):
         """

sage/matrix/matrix2.pyx

@@ -6858 +6858 @@
         Faster routines for double precision entries from `RDF` or `CDF` are provided by
         the :class:`~sage.matrix.matrix_double_dense.Matrix_double_dense` class.  ::
         
-            sage: A = matrix(RR, 2, 3, [3*I,4,1-I,1,2,0])
+            sage: A = matrix(CC, 2, 3, [3*I,4,1-I,1,2,0])
             sage: A.norm('frob') 
             5.65685424949
             sage: A.norm(2)

sage/matrix/matrix_double_dense.pyx

@@ -579 +579 @@
                 \left(\sum_{i,j}\left\lvert{a_{i,j}}\right\rvert^2\right)^{1/2}
 
         - ``p = Infinity`` or ``p = oo``: the maximum row sum.
-        - ``p = -Infinity`` or ``p = -oo``: the minimum colum sum.
+        - ``p = -Infinity`` or ``p = -oo``: the minimum column sum.
         - ``p = 1``: the maximum column sum.
         - ``p = -1``: the minimum column sum.
         - ``p = 2``: the 2-norm, equal to the maximum singular value.
@@ -683 +683 @@
             Traceback (most recent call last):
             ...
             ValueError: condition number integer values of 'p' must be -2, -1, 1 or 2, not 632
+
+        TESTS:
+
+        Some condition numbers, first by the definition which also exercises
+        :meth:`norm`, then by this method.  ::
+
+            sage: A = matrix(CDF, [[1,2,4],[5,3,9],[7,8,6]])
+            sage: c = A.norm(2)*A.inverse().norm(2)
+            sage: d = A.condition(2)
+            sage: abs(c-d) < 1.0e-14
+            True
+            sage: c = A.norm(1)*A.inverse().norm(1)
+            sage: d = A.condition(1)
+            sage: abs(c-d) < 1.0e-14
+            True
         """
         if not self.is_square():
             raise TypeError("matrix must be square, not %s x %s" % (self.nrows(), self.ncols()))
@@ -703 +718 @@
                 p = sage.rings.integer.Integer(p)
             except:
                 raise ValueError("condition number 'p' must be +/- infinity, 'frob' or an integer, not %s" % p)
-            if not p in [-2,-1,1,2]:
+            if p not in [-2,-1,1,2]:
                 raise ValueError("condition number integer values of 'p' must be -2, -1, 1 or 2, not %s" % p)
         # may raise a LinAlgError if matrix is singular
         c = numpy.linalg.cond(self._matrix_numpy, p=p)
@@ -740 +755 @@
                 \left(\sum_{i,j}\left\lvert{a_{i,j}}\right\rvert^2\right)^{1/2}
 
         - ``p = Infinity`` or ``p = oo``: the maximum row sum.
-        - ``p = -Infinity`` or ``p = -oo``: the minimum colum sum.
+        - ``p = -Infinity`` or ``p = -oo``: the minimum column sum.
         - ``p = 1``: the maximum column sum.
         - ``p = -1``: the minimum column sum.
         - ``p = 2``: the 2-norm, equal to the maximum singular value.
@@ -809 +824 @@
             sage: abs(f-s) < 1.0e-12
             True
 
-        Return values are in `RDF`.
+        Return values are in `RDF`. ::
 
             sage: A = matrix(CDF, 2, range(4))
             sage: A.norm() in RDF

sage/modules/vector_double_dense.pyx

@@ -585 +585 @@
 
         OUTPUT:
 
-        Returned values is a double precision floating point value
-        in ``RDF`` (or an integer when ``p=0``.  The default value
+        Returned value is a double precision floating point value
+        in ``RDF`` (or an integer when ``p=0``).  The default value
         of ``p = 2`` is the "usual" Euclidean norm.  For other values:
 
         - ``p = Infinity`` or ``p = oo``: the maximum of the