Add tests for non standard cases

tests/test_PCG.cpp

@@ -47,4 +47,63 @@ TEST_CASE("PCG", "[algebra]")
     Vector error = x - x_exact;
     REQUIRE(std::sqrt((error, error)) < 1E-10 * std::sqrt((x, x)));
   }
+
+  SECTION("singular matrix with RHS in its image")
+  {
+    SparseMatrixDescriptor<double, uint8_t> S{5};
+
+    CRSMatrix<double, uint8_t> A{S};
+
+    Vector<double> b{5};
+    b = 0;
+
+    Vector<double> x{5};
+    x = 0;
+
+    PCG{b, A, A, x, 10, 1e-12};
+    REQUIRE(std::sqrt((x, x)) == 0);
+  }
+
+  SECTION("no preconditionner non-converged")
+  {
+    SparseMatrixDescriptor S{5};
+    S(0, 0) = 2;
+    S(0, 1) = -1;
+
+    S(1, 0) = -1;
+    S(1, 1) = 2;
+    S(1, 2) = -1;
+
+    S(2, 1) = -1;
+    S(2, 2) = 2;
+    S(2, 3) = -1;
+
+    S(3, 2) = -1;
+    S(3, 3) = 2;
+    S(3, 4) = -1;
+
+    S(4, 3) = -1;
+    S(4, 4) = 2;
+
+    CRSMatrix A{S};
+
+    Vector<const double> x_exact = [] {
+      Vector<double> y{5};
+      y[0] = 1;
+      y[1] = 3;
+      y[2] = 2;
+      y[3] = 4;
+      y[4] = 5;
+      return y;
+    }();
+
+    Vector<double> b = A * x_exact;
+
+    Vector<double> x{5};
+    x = 0;
+
+    PCG{b, A, A, x, 1, 1e-12};
+    Vector error = x - x_exact;
+    REQUIRE(std::sqrt((error, error)) > 1E-10 * std::sqrt((x, x)));
+  }
 }