[mlpack-git] master: add correlation coeff sdp test from wiki (6ad2c10)

[gitdub at big.cc.gt.atl.ga.us]

Repository : https://github.com/mlpack/mlpack

On branch  : master
Link       : https://github.com/mlpack/mlpack/compare/904762495c039e345beba14c1142fd719b3bd50e...f94823c800ad6f7266995c700b1b630d5ffdcf40

>---------------------------------------------------------------

commit 6ad2c1014d21e533ff8d906a42aaa719cb2eab1d
Author: Stephen Tu <tu.stephenl at gmail.com>
Date:   Fri Jan 16 13:50:48 2015 -0800

    add correlation coeff sdp test from wiki


>---------------------------------------------------------------

6ad2c1014d21e533ff8d906a42aaa719cb2eab1d
 src/mlpack/tests/sdp_primal_dual_test.cpp | 109 ++++++++++++++++++++++++++++++
 1 file changed, 109 insertions(+)

diff --git a/src/mlpack/tests/sdp_primal_dual_test.cpp b/src/mlpack/tests/sdp_primal_dual_test.cpp
index 4f22a7d..2d1b013 100644
--- a/src/mlpack/tests/sdp_primal_dual_test.cpp
+++ b/src/mlpack/tests/sdp_primal_dual_test.cpp
@@ -391,6 +391,115 @@ BOOST_AUTO_TEST_CASE(LogChebychevApproxSdp)
   BOOST_REQUIRE(stat1.first);
 }
 
+/**
+ * Example 1 on the SDP wiki
+ *
+ *   min   x_13
+ *   s.t.
+ *         -0.2 <= x_12 <= -0.1
+ *          0.4 <= x_23 <=  0.5
+ *          x_11 = x_22 = x_33 = 1
+ *          X >= 0
+ *
+ */
+BOOST_AUTO_TEST_CASE(CorrelationCoeffToySdp)
+{
+  // The semi-definite constraint looks like:
+  //
+  // [ 1  x_12  x_13  0  0  0  0 ]
+  // [     1    x_23  0  0  0  0 ]
+  // [            1   0  0  0  0 ]
+  // [               s1  0  0  0 ]  >= 0
+  // [                  s2  0  0 ]
+  // [                     s3  0 ]
+  // [                        s4 ]
+
+
+  // x_11 == 0
+  arma::sp_mat A0(7, 7); A0.zeros();
+  A0(0, 0) = 1.;
+
+  // x_22 == 0
+  arma::sp_mat A1(7, 7); A1.zeros();
+  A1(1, 1) = 1.;
+
+  // x_33 == 0
+  arma::sp_mat A2(7, 7); A2.zeros();
+  A2(2, 2) = 1.;
+
+  // x_12 <= -0.1  <==>  x_12 + s1 == -0.1, s1 >= 0
+  arma::sp_mat A3(7, 7); A3.zeros();
+  A3(1, 0) = A3(0, 1) = 1.; A3(3, 3) = 2.;
+
+  // -0.2 <= x_12  <==>  x_12 - s2 == -0.2, s2 >= 0
+  arma::sp_mat A4(7, 7); A4.zeros();
+  A4(1, 0) = A4(0, 1) = 1.; A4(4, 4) = -2.;
+
+  // x_23 <= 0.5  <==>  x_23 + s3 == 0.5, s3 >= 0
+  arma::sp_mat A5(7, 7); A5.zeros();
+  A5(2, 1) = A5(1, 2) = 1.; A5(5, 5) = 2.;
+
+  // 0.4 <= x_23  <==>  x_23 - s4 == 0.4, s4 >= 0
+  arma::sp_mat A6(7, 7); A6.zeros();
+  A6(2, 1) = A6(1, 2) = 1.; A6(6, 6) = -2.;
+
+  std::vector<arma::sp_mat> ais({A0, A1, A2, A3, A4, A5, A6});
+
+  SDP sdp(7, 7 + 4 + 4 + 4 + 3 + 2 + 1, 0);
+
+  for (size_t j = 0; j < 3; j++)
+  {
+    // x_j4 == x_j5 == x_j6 == x_j7 == 0
+    for (size_t i = 0; i < 4; i++)
+    {
+      arma::sp_mat A(7, 7); A.zeros();
+      A(i + 3, j) = A(j, i + 3) = 1;
+      ais.emplace_back(A);
+    }
+  }
+
+  // x_45 == x_46 == x_47 == 0
+  for (size_t i = 0; i < 3; i++)
+  {
+    arma::sp_mat A(7, 7); A.zeros();
+    A(i + 4, 3) = A(3, i + 4) = 1;
+    ais.emplace_back(A);
+  }
+
+  // x_56 == x_57 == 0
+  for (size_t i = 0; i < 2; i++)
+  {
+    arma::sp_mat A(7, 7); A.zeros();
+    A(i + 5, 4) = A(4, i + 5) = 1;
+    ais.emplace_back(A);
+  }
+
+  // x_67 == 0
+  arma::sp_mat A(7, 7); A.zeros();
+  A(6, 5) = A(5, 6) = 1;
+  ais.emplace_back(A);
+
+  std::swap(sdp.SparseA(), ais);
+
+  sdp.SparseB().zeros();
+
+  sdp.SparseB()[0] = sdp.SparseB()[1] = sdp.SparseB()[2] = 1.;
+
+  sdp.SparseB()[3] = -0.2; sdp.SparseB()[4] = -0.4;
+
+  sdp.SparseB()[5] = 1.; sdp.SparseB()[6] = 0.8;
+
+  sdp.SparseC().zeros();
+  sdp.SparseC()(0, 2) = sdp.SparseC()(2, 0) = 1.;
+
+  PrimalDualSolver solver(sdp);
+  arma::mat X, Z;
+  arma::vec ysparse, ydense;
+  const auto p = solver.Optimize(X, ysparse, ydense, Z);
+  BOOST_REQUIRE(p.first);
+  BOOST_REQUIRE_CLOSE(p.second, 2 * (-0.978), 1e-3);
+}
+
 ///**
 // * Maximum variance unfolding (MVU) SDP to learn the unrolled gram matrix. For
 // * the SDP formulation, see: