infinity: Implement cone_bound_find_lambda

infinity/library/src/infinity-nd.c

@@ -22,6 +22,7 @@
 #include <multirow/util.h>
 
 #include <infinity/infinity-nd.h>
+#include <multirow/linalg.h>
 
 static long lp_count = 0;
 static double lp_time = 0;
@@ -41,6 +42,41 @@ static double sfree_mip_time = 0;
 static long scale_ahull_lp_count = 0;
 static double scale_ahull_lp_time = 0;
 
+static int cone_bound_find_lambda(const struct RayList *rays,
+                                  const double *f,
+                                  const double *x,
+                                  double *lambda)
+{
+    int rval = 0;
+    double *A = 0;
+    double *b = 0;
+    int dim = rays->dim;
+    int nrays = rays->nrays;
+
+    A = (double*) malloc(nrays * dim * sizeof(double));
+    b = (double*) malloc(dim * sizeof(double));
+    abort_if(!A, "could not allocate A");
+    abort_if(!b, "could not allocate b");
+
+    for (int i = 0; i < dim; i++)
+    {
+        b[i] = x[i] - f[i];
+        for (int j = 0; j < nrays; j++)
+            A[i * nrays + j] = rays->values[j * dim + i];
+    }
+
+    rval = LINALG_solve(nrays, dim, A, b, lambda);
+    abort_if(rval, "LINALG_solve failed");
+
+    for (int i = 0; i < dim; i++)
+        abort_iff(lambda[0] < 0, "lambda[i] is negative (%lf)", i, lambda[i]);
+
+CLEANUP:
+    if(A) free(A);
+    if(b) free(b);
+    return rval;
+}
+
 static int create_sfree_mip(int nrows,
                             int nrays,
                             const double *f,

infinity/library/tests/infinity-nd-test.cpp

@@ -27,6 +27,7 @@ extern "C" {
 #include "../src/infinity-nd.c"
 }
 
+const double E = 1e-6;
 
 TEST(InfinityNDTest, find_violated_cone_test)
 {
@@ -164,11 +165,11 @@ TEST(InfinityNDTest, cone_bound_test_1)
 
     rval = cone_bound(2, 6, f, rays, rx1, x, beta, &epsilon);
     abort_if(rval, "cone_bound failed");
-    EXPECT_NEAR(0.5, epsilon, 1e-6);
+    EXPECT_NEAR(0.5, epsilon, E);
 
     rval = cone_bound(2, 6, f, rays, rx2, x, beta, &epsilon);
     abort_if(rval, "cone_bound failed");
-    EXPECT_NEAR(1.0, epsilon, 1e-6);
+    EXPECT_NEAR(1.0, epsilon, E);
 
     CLEANUP:
     if(rval) FAIL();
@@ -197,7 +198,7 @@ TEST(InfinityNDTest, cone_bound_test_2)
 
     rval = cone_bound(2, 2, f, rays, rx, x1, beta1, &epsilon);
     abort_if(rval, "cone_bound failed");
-    EXPECT_NEAR(1.0, epsilon, 1e-6);
+    EXPECT_NEAR(1.0, epsilon, E);
 
     rval = cone_bound(2, 2, f, rays, rx, x1, beta2, &epsilon);
     abort_if(rval, "cone_bound failed");
@@ -205,7 +206,7 @@ TEST(InfinityNDTest, cone_bound_test_2)
 
     rval = cone_bound(2, 2, f, rays, rx, x2, beta2, &epsilon);
     abort_if(rval, "cone_bound failed");
-    EXPECT_NEAR(1.0, epsilon, 1e-6);
+    EXPECT_NEAR(1.0, epsilon, E);
 
     rval = cone_bound(2, 2, f, rays, rx, x2, beta3, &epsilon);
     abort_if(rval, "cone_bound failed");
@@ -239,7 +240,7 @@ TEST(InfinityNDTest, bound_test_1)
 
     rval = bound(2, 6, f, rays, x, beta1, &epsilon, tx);
     abort_if(rval, "bound failed");
-    EXPECT_NEAR(epsilon, 0.5, 1e-6);
+    EXPECT_NEAR(epsilon, 0.5, E);
     EXPECT_TRUE(tx[0]);
     EXPECT_FALSE(tx[1]);
     EXPECT_FALSE(tx[2]);
@@ -249,7 +250,7 @@ TEST(InfinityNDTest, bound_test_1)
 
     rval = bound(2, 6, f, rays, x, beta2, &epsilon, tx);
     abort_if(rval, "bound failed");
-    EXPECT_NEAR(epsilon, 1.0, 1e-6);
+    EXPECT_NEAR(epsilon, 1.0, E);
     EXPECT_TRUE(tx[0]);
     EXPECT_FALSE(tx[1]);
     EXPECT_FALSE(tx[2]);
@@ -308,11 +309,11 @@ TEST(InfinityNDTest, psi_test)
 
     rval = INFINITY_psi(2, q1, 1.0, &lp, &value);
     abort_if(rval, "GREDDY_ND_psi failed");
-    EXPECT_NEAR(value, 2.0, 1e-6);
+    EXPECT_NEAR(value, 2.0, E);
 
     rval = INFINITY_psi(2, q2, 2.0, &lp, &value);
     abort_if(rval, "GREDDY_ND_psi failed");
-    EXPECT_NEAR(value, 8.0, 1e-6);
+    EXPECT_NEAR(value, 8.0, E);
 
 CLEANUP:
     LP_free(&lp);
@@ -360,11 +361,11 @@ TEST(InfinityNDTest, psi_test_2)
 
     rval = INFINITY_psi(3, q1, 1.0, &lp, &value);
     abort_if(rval, "GREDDY_ND_psi failed");
-    EXPECT_NEAR(value, 1.0, 1e-6);
+    EXPECT_NEAR(value, 1.0, E);
 
     rval = INFINITY_psi(3, q2, 1.0, &lp, &value);
     abort_if(rval, "GREDDY_ND_psi failed");
-    EXPECT_NEAR(value, 2.0, 1e-6);
+    EXPECT_NEAR(value, 2.0, E);
 
 CLEANUP:
     if(rval) FAIL();
@@ -411,7 +412,7 @@ TEST(InfinityNDTest, psi_test_3)
 
     rval = INFINITY_psi(lfree.nrows, q, 1.0, &lp, &value);
     abort_if(rval, "GREDDY_ND_psi failed");
-    EXPECT_NEAR(value, 1.0, 1e-6);
+    EXPECT_NEAR(value, 1.0, E);
 
 CLEANUP:
     if(rval) FAIL();
@@ -445,12 +446,12 @@ TEST(DISABLED_InfinityNDTest, generate_cut_test_1)
     rval = INFINITY_ND_generate_lfree(&model, &lfree);
     abort_if(rval, "INFINITY_ND_generate_lfree failed");
 
-    EXPECT_NEAR(lfree.beta[0], 0.5, 1e-6);
-    EXPECT_NEAR(lfree.beta[1], 0.5, 1e-6);
-    EXPECT_NEAR(lfree.beta[2], 0.5, 1e-6);
-    EXPECT_NEAR(lfree.beta[3], 0.5, 1e-6);
-    EXPECT_NEAR(lfree.beta[4], 1.0, 1e-6);
-    EXPECT_NEAR(lfree.beta[5], 1.0, 1e-6);
+    EXPECT_NEAR(lfree.beta[0], 0.5, E);
+    EXPECT_NEAR(lfree.beta[1], 0.5, E);
+    EXPECT_NEAR(lfree.beta[2], 0.5, E);
+    EXPECT_NEAR(lfree.beta[3], 0.5, E);
+    EXPECT_NEAR(lfree.beta[4], 1.0, E);
+    EXPECT_NEAR(lfree.beta[5], 1.0, E);
 
 CLEANUP:
     if(rval) FAIL();
@@ -485,12 +486,12 @@ TEST(InfinityNDTest, generate_cut_test_2)
     rval = INFINITY_ND_generate_lfree(&model, &lfree);
     abort_if(rval, "INFINITY_ND_generate_lfree failed");
 
-    EXPECT_NEAR(lfree.beta[0], 0.75, 1e-6);
-    EXPECT_NEAR(lfree.beta[1], 2.25, 1e-6);
-    EXPECT_NEAR(lfree.beta[2], 0.75, 1e-6);
-    EXPECT_NEAR(lfree.beta[3], 2.25, 1e-6);
-    EXPECT_NEAR(lfree.beta[4], 0.75, 1e-6);
-    EXPECT_NEAR(lfree.beta[5], 2.25, 1e-6);
+    EXPECT_NEAR(lfree.beta[0], 0.75, E);
+    EXPECT_NEAR(lfree.beta[1], 2.25, E);
+    EXPECT_NEAR(lfree.beta[2], 0.75, E);
+    EXPECT_NEAR(lfree.beta[3], 2.25, E);
+    EXPECT_NEAR(lfree.beta[4], 0.75, E);
+    EXPECT_NEAR(lfree.beta[5], 2.25, E);
 
 CLEANUP:
     CG_free_model(&model);
@@ -534,3 +535,68 @@ TEST(InfinityNDTest, scale_to_ahull_test)
 CLEANUP:
     if(rval) FAIL();
 }
+
+TEST(InfinityNDTest, cone_bound_find_lambda_test)
+{
+    int rval = 0;
+
+    double f[] = { 1/2.0, 1/3.0 };
+    double x[] = { 3.0, 3.0 };
+    double ray_values[] = {
+            1.0, 2.0,
+            3.0, 2.0,
+    };
+
+    struct RayList rays = {.values = ray_values, .nrays = 2, .dim = 2};
+    double lambda[2];
+
+    rval = cone_bound_find_lambda(&rays, f, x, lambda);
+    abort_if(rval, "cone_bound_find_lambda failed");
+
+    EXPECT_NEAR(lambda[0], 3/4.0, E);
+    EXPECT_NEAR(lambda[1], 7/12.0, E);
+
+ CLEANUP:
+    if(rval) FAIL();
+}
+
+TEST(InfinityNDTest, cone_bound_find_lambda_test_2)
+{
+    int rval = 0;
+
+    double f[] = { 1/2.0, 1/3.0, 5/6.0 };
+    double x[] = { 3.0, 3.0, 6.0 };
+    double ray_values[] = {
+            1.0, 2.0, 3.0,
+            3.0, 2.0, 5.0,
+    };
+
+    struct RayList rays = {.values = ray_values, .nrays = 2, .dim = 3};
+    double lambda[2];
+
+    rval = cone_bound_find_lambda(&rays, f, x, lambda);
+    abort_if(rval, "cone_bound_find_lambda failed");
+
+    EXPECT_NEAR(lambda[0], 3/4.0, E);
+    EXPECT_NEAR(lambda[1], 7/12.0, E);
+
+CLEANUP:
+    if(rval) FAIL();
+}
+
+TEST(InfinityNDTest, cone_bound_find_lambda_test_3)
+{
+    int rval = 0;
+    double f[] = { 1/2.0, 1/2.0 };
+    double x[] = { 3.0, 3.0 };
+    double ray_values[] = {
+             0.0, -1.0,
+            -1.0,  0.0,
+    };
+
+    struct RayList rays = {.values = ray_values, .nrays = 2, .dim = 2};
+    double lambda[2];
+
+    rval = cone_bound_find_lambda(&rays, f, x, lambda);
+    EXPECT_NE(rval, 0);
+}

multirow/include/multirow/linalg.h

@@ -33,8 +33,8 @@ double LINALG_dot(int n, double *x, double *y);
 double LINALG_norm(int n, double *x);
 
 /**
- * Given an invertible n-by-n matrix A and an n-dimensional vector b, this
- * function set x to A^(-1) b. Returns zero if the operation is successful and
- * non-zero otherwise.
+ * Given a full rank m-by-n matrix A and an m-dimensional vector b, this
+ * function finds x such that Ax = b. Returns zero if the operation is
+ * successful and non-zero otherwise.
  */
-int LINALG_solve(int n, double *A, double *b, double *x);
+int LINALG_solve(int n, int m, double *A, double *b, double *x);

multirow/include/multirow/util.h

@@ -78,6 +78,7 @@ void time_printf(const char *fmt,
 #define UNUSED(x) (void)(x)
 
 #define min(x,y) ((x) < (y) ? (x) : (y))
+#define max(x,y) ((x) > (y) ? (x) : (y))
 #define sign(x) ((x) > 0 ? 1 : ((x) < 0 ? -1 : 0))
 #define swap(x, y, T) do { T SWAP = x; x = y; y = SWAP; } while (0)
 

multirow/src/linalg.c

@@ -17,8 +17,9 @@
  * with this program. If not, see <http://www.gnu.org/licenses/>.
  */
 
-#include<cblas.h>
-#include<lapacke.h>
+#include <math.h>
+#include <cblas.h>
+#include <lapacke.h>
 #include <multirow/util.h>
 
 void LINALG_scale(int n, double *x, double alpha)
@@ -36,16 +37,14 @@ double LINALG_norm(int n, double *x)
     return cblas_dasum(n, x, 1);
 }
 
-int LINALG_solve(int n, double *A, double *b, double *x)
+int LINALG_solve(int n, int m, double *A, double *b, double *x)
 {
     int rval = 0;
-    int ignored[n];
-    double A_copy[n * n];
+    double A_copy[n * m];
+    memcpy(x, b, m * sizeof(double));
+    memcpy(A_copy, A, n * m * sizeof(double));
 
-    memcpy(x, b, n * sizeof(double));
-    memcpy(A_copy, A, n * n * sizeof(double));
-
-    rval = LAPACKE_dgesv(LAPACK_ROW_MAJOR, n, 1, A_copy, n, ignored, x, 1);
+    LAPACKE_dgels(LAPACK_ROW_MAJOR, 'N', m, n, 1, A_copy, n, x, 1);
     abort_if(rval, "LAPACKE_dgesv failed");
 
 CLEANUP:

multirow/tests/linalg-test.cpp

@@ -62,7 +62,7 @@ TEST(LinAlgTest, solve_test)
     double b[] = { 1.0, 3.0, 5.0 };
     double x[] = { 0.0, 0.0, 0.0 };
 
-    rval = LINALG_solve(3, A, b, x);
+    rval = LINALG_solve(3, 3, A, b, x);
     abort_if(rval, "LINALG_solve failed");
 
     // Should compute x correctly
@@ -81,3 +81,27 @@ TEST(LinAlgTest, solve_test)
 CLEANUP:
     if(rval) FAIL();
 }
+
+TEST(LinAlgTest, solve_test_2)
+{
+    int rval = 0;
+
+    double A[] = {
+            1.0, 3.0,
+            0.0, 0.0,
+            2.0, 2.0,
+            3.0, 5.0,
+    };
+    double b[] = { 5/2.0, 0.0, 8/3.0, 31/6.0 };
+    double x[2];
+
+    rval = LINALG_solve(2, 4, A, b, x);
+    abort_if(rval, "LINALG_solve failed");
+
+    // Should compute x correctly
+    EXPECT_NEAR(x[0], 3/4.0, E);
+    EXPECT_NEAR(x[1], 7/12.0, E);
+
+CLEANUP:
+    if(rval) FAIL();
+}