Some doctests modifs to mitigate numerical noise.

sagemath · Oct 28, 2014 · 9c30abb · 9c30abb
1 parent cad29f8
commit 9c30abb
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Showing 5 changed files with 14 additions and 14 deletions.
diff --git a/src/sage/matrix/matrix2.pyx b/src/sage/matrix/matrix2.pyx
@@ -4939,9 +4939,9 @@ cdef class Matrix(matrix1.Matrix):
 
             sage: em = A.change_ring(RDF).eigenmatrix_left()
             sage: eigenvalues = em[0]; eigenvalues.dense_matrix().zero_at(2e-15)
-            [ 13.348469228349...                0.0                 0.0]
-            [                0.0 -1.348469228349...                 0.0]
-            [                0.0                0.0                 0.0]
+            [13.348469228349...                0.0                 0.0]
+            [               0.0 -1.348469228349...                 0.0]
+            [               0.0                0.0                 0.0]
             sage: eigenvectors = em[1]; eigenvectors # not tested
             [ 0.440242867...  0.567868371...  0.695493875...]
             [ 0.897878732...  0.278434036... -0.341010658...]
@@ -5598,9 +5598,9 @@ cdef class Matrix(matrix1.Matrix):
             sage: A = matrix(QQ, 3, 3, range(9))
             sage: em = A.change_ring(RDF).eigenmatrix_left()
             sage: evalues = em[0]; evalues.dense_matrix().zero_at(2e-15)
-            [ 13.348469228349...                0.0                 0.0]
-            [                0.0 -1.348469228349...                 0.0]
-            [                0.0                0.0                 0.0]
+            [13.348469228349...                0.0                 0.0]
+            [               0.0 -1.348469228349...                 0.0]
+            [               0.0                0.0                 0.0]
             sage: evectors = em[1];
             sage: for i in range(3):
             ....:     scale = evectors[i,0].sign()

diff --git a/src/sage/rings/complex_double.pyx b/src/sage/rings/complex_double.pyx
@@ -1629,8 +1629,8 @@ cdef class ComplexDoubleElement(FieldElement):
             sage: a = CDF(1,1); b = CDF(2,3)
             sage: c = a^b; c # indirect doctest
             -0.163450932107355 + 0.09600498360894891*I
-            sage: c^(1/b)
-            1.0000000000000002 + 1.0*I
+            sage: c^(1/b) # rel tol 2e-16
+            1.0 + 1.0*I
 
         We compute the cube root of `-1` then cube it and observe a
         rounding error::

diff --git a/src/sage/rings/polynomial/polynomial_element.pyx b/src/sage/rings/polynomial/polynomial_element.pyx
@@ -5357,8 +5357,8 @@ cdef class Polynomial(CommutativeAlgebraElement):
             [(-1.0911236359717227 - 0.6299605249474374*I, 1), (3.885780586188048e-16 + 1.2599210498948734*I, 1), (1.0911236359717211 - 0.6299605249474363*I, 1)]
             sage: f.roots(multiplicities=False)  # abs tol 1e-14
             [-1.0911236359717227 - 0.6299605249474374*I, 3.885780586188048e-16 + 1.2599210498948734*I, 1.0911236359717211 - 0.6299605249474363*I]
-            sage: [f(z) for z in f.roots(multiplicities=False)]  # abs tol 1e-12
-            [1.3704315460216776e-15 + 3.3306690738754696e-15*I, 5.287107591627866e-16 + 1.9984014443252818e-15*I, 2.0616104309811867e-16 + 1.7763568394002505e-15*I]
+            sage: [abs(f(z)) for z in f.roots(multiplicities=False)]  # abs tol 1e-14
+            [6.586578339425543e-15, 9.252438285348772e-16, 9.984360324875084e-16]
             sage: f = i*x^3 + 2; f
             I*x^3 + 2.0
             sage: f.roots()  # abs tol 1e-14
@@ -5610,9 +5610,9 @@ cdef class Polynomial(CommutativeAlgebraElement):
 
             sage: R.<u> = QQ[]
             sage: g = -27*u^14 - 32*u^9
-            sage: g.roots(CDF, multiplicities=False)  # abs tol 1e-15
+            sage: g.roots(CDF, multiplicities=False)  # abs tol 2e-15
             [-1.0345637159435719, 0.0, -0.3196977699902601 - 0.9839285635706636*I, -0.3196977699902601 + 0.9839285635706636*I, 0.8369796279620465 - 0.6081012947885318*I, 0.8369796279620465 + 0.6081012947885318*I]
-            sage: g.roots(CDF)  # abs tol 1e-15
+            sage: g.roots(CDF)  # abs tol 2e-15
             [(-1.0345637159435719, 1), (0.0, 9), (-0.3196977699902601 - 0.9839285635706636*I, 1), (-0.3196977699902601 + 0.9839285635706636*I, 1), (0.8369796279620465 - 0.6081012947885318*I, 1), (0.8369796279620465 + 0.6081012947885318*I, 1)]
 
         This shows that the issue at :trac:`2418` is fixed::

diff --git a/src/sage/rings/polynomial/real_roots.pyx b/src/sage/rings/polynomial/real_roots.pyx
@@ -1573,7 +1573,7 @@ cdef class interval_bernstein_polynomial_float(interval_bernstein_polynomial):
             sage: bp2
             <IBP: (-0.369375, -0.45125, -0.3275, 0.14500000000000002, 0.99) + [-0.1 .. 0.01] over [1/2 .. 1]>
             sage: bp1, bp2, ok = bp.de_casteljau(ctx, 2/3)
-            sage: bp1
+            sage: bp1 # rel tol 2e-16
             <IBP: (0.5, 0.30000000000000004, -0.2555555555555555, -0.5444444444444444, -0.32172839506172846) + [-0.1 .. 0.01] over [0 .. 2/3]>
             sage: bp2  # rel tol 3e-15
             <IBP: (-0.32172839506172846, -0.21037037037037046, 0.028888888888888797, 0.4266666666666666, 0.99) + [-0.1 .. 0.01] over [2/3 .. 1]>

diff --git a/src/sage/stats/hmm/chmm.pyx b/src/sage/stats/hmm/chmm.pyx
@@ -1337,7 +1337,7 @@ cdef class GaussianMixtureHiddenMarkovModel(GaussianHiddenMarkovModel):
             (2.18905068682..., 15)
             sage: m.log_likelihood(v)
             2.18905068682...
-            sage: m  # rel tol 3e-14
+            sage: m  # rel tol 6e-14
             Gaussian Mixture Hidden Markov Model with 2 States
             Transition matrix:
             [   0.8746363339773399   0.12536366602266016]