mjo/cone/symmetric_pd.py: drop inverse_symmetric_pd().

This function is now available in SageMath:

  sage: A = matrix.identity(QQ,2)
  sage: A.inverse_positive_definite()
  [1 0]
  [0 1]

diff --git a/mjo/cone/symmetric_pd.py b/mjo/cone/symmetric_pd.py
index e68496455c27258df8eb6591c300e8427d302d48..5dcacfb8ea82b658a0c6d9bb46aed9a3034e2512 100644 (file)
--- a/mjo/cone/symmetric_pd.py
+++ b/mjo/cone/symmetric_pd.py
@@ -142,60 +142,3 @@ def random_symmetric_pd(V):
     # condition ensures that we don't get the zero matrix in a
     # nontrivial space.
     return random_symmetric_psd(V, rank=V.dimension())
-
-
-def inverse_symmetric_pd(M):
-    r"""
-    Compute the inverse of a symmetric positive-definite matrix.
-
-    The symmetric positive-definite matrix ``M`` has a Cholesky
-    factorization, which can be used to invert ``M`` in a fast,
-    numerically-stable way.
-
-    INPUT:
-
-    - ``M`` -- The matrix to invert.
-
-    OUTPUT:
-
-    The inverse of ``M``. The Cholesky factorization uses roots, so the
-    returned matrix will have as its base ring the algebraic closure of
-    the base ring of ``M``.
-
-    SETUP::
-
-        sage: from mjo.cone.symmetric_pd import inverse_symmetric_pd
-
-    EXAMPLES:
-
-    If we start with a rational matrix, its inverse will be over a field
-    extension of that rationals that is necessarily contained in
-    ``QQbar`` (which contails ALL roots)::
-
-        sage: M = matrix(QQ, [[3,1],[1,5]])
-        sage: M_inv = inverse_symmetric_pd(M)
-        sage: M_inv.base_ring().is_subring(QQbar)
-        True
-
-    TESTS:
-
-    This "inverse" should actually act like an inverse::
-
-        sage: set_random_seed()
-        sage: n = ZZ.random_element(5)
-        sage: V = VectorSpace(QQ,n)
-        sage: from mjo.cone.symmetric_pd import random_symmetric_pd
-        sage: M = random_symmetric_pd(V)
-        sage: M_inv = inverse_symmetric_pd(M)
-        sage: I = identity_matrix(QQ,n)
-        sage: M_inv * M == I
-        True
-        sage: M * M_inv == I
-        True
-
-    """
-    # M = L * L.transpose()
-    # The default "echelonize" inverse() method works just fine for
-    # triangular matrices.
-    L_inverse = M.cholesky().inverse()
-    return L_inverse.transpose()*L_inverse