Trac #18763: COIN backend should support basis status and tableau dat…

…a functions

This is for COIN backend support in #18733 and #18688.

Should add
(1) `getBasisStatus`, `setBasisStatus`,
(2) `getBInvARow`, `getBInvACol`, `getBasics`,
to src/sage/numerical/backends/coin_backend.{pxd,pyx}

Possible that one needs to add other functions as well, such as
`enableSimplexInterface`...

Reference to the relevant Clp header file:
https://projects.coin-or.org/Osi/browser/trunk/Osi/src/OsiClp/OsiClpSolv
erInterface.hpp?rev=1472

URL: http://trac.sagemath.org/18763
Reported by: mkoeppe
Ticket author(s): Yuan Zhou
Reviewer(s): Vincent Delecroix

src/sage/numerical/backends/coin_backend.pxd

@@ -118,6 +118,17 @@ cdef extern from "coin/OsiSolverInterface.hpp":
         # miscellaneous
         double getInfinity()
 
+        # info about basis status
+        void getBasisStatus(int * cstat, int * rstat)
+        int setBasisStatus(int * cstat, int * rstat)
+
+        # Enable Simplex
+        void enableSimplexInterface(bool doingPrimal)
+
+        # Get tableau
+        void getBInvARow(int row, double* z, double * slack)
+        void getBInvACol(int col, double* vec)
+
 cdef extern from "coin/CbcModel.hpp":
      cdef cppclass CbcModel:
          # default constructor
@@ -174,3 +185,7 @@ cdef class CoinBackend(GenericBackend):
     cdef str prob_name
 
     cpdef CoinBackend copy(self)
+    cpdef get_basis_status(self)
+    cpdef int set_basis_status(self, list cstat, list rstat) except -1
+    cpdef get_binva_row(self, int i)
+    cpdef get_binva_col(self, int j)