if EIGEN_NICE_RANDOM is defined, the random functions will return numbers with

few bits left of the comma and for floating-point types will never return zero.
This replaces the custom functions in test/main.h, so one does not anymore need
to think about that when writing tests.

Eigen/src/Core/MathFunctions.h

@@ -89,7 +89,14 @@ inline float ei_pow(float x, float y)  { return std::pow(x, y); }
 
 template<> inline float ei_random(float a, float b)
 {
+#ifdef EIGEN_NICE_RANDOM
+  int i;
+  do { i = ei_random<int>(256*int(a),256*int(b));
+  } while(i==0);
+  return i/256.f;
+#else
   return a + (b-a) * std::rand() / RAND_MAX;
+#endif
 }
 template<> inline float ei_random()
 {
@@ -123,7 +130,14 @@ inline double ei_pow(double x, double y)  { return std::pow(x, y); }
 
 template<> inline double ei_random(double a, double b)
 {
+#ifdef EIGEN_NICE_RANDOM
+  int i;
+  do { i= ei_random<int>(256*int(a),256*int(b));
+  } while(i==0);
+  return i/256.;
+#else
   return a + (b-a) * std::rand() / RAND_MAX;
+#endif
 }
 template<> inline double ei_random()
 {

test/adjoint.cpp

@@ -41,19 +41,19 @@ template<typename MatrixType> void adjoint(const MatrixType& m)
   if (ei_is_same_type<RealScalar,float>::ret)
     largerEps = 1e-3f;
 
-  MatrixType m1 = test_random_matrix<MatrixType>(rows, cols),
+  MatrixType m1 = MatrixType::Random(rows, cols),
-             m2 = test_random_matrix<MatrixType>(rows, cols),
+             m2 = MatrixType::Random(rows, cols),
              m3(rows, cols),
              mzero = MatrixType::Zero(rows, cols),
              identity = SquareMatrixType::Identity(rows, rows),
-             square = test_random_matrix<SquareMatrixType>(rows, rows);
+             square = SquareMatrixType::Random(rows, rows);
-  VectorType v1 = test_random_matrix<VectorType>(rows),
+  VectorType v1 = VectorType::Random(rows),
-             v2 = test_random_matrix<VectorType>(rows),
+             v2 = VectorType::Random(rows),
-             v3 = test_random_matrix<VectorType>(rows),
+             v3 = VectorType::Random(rows),
              vzero = VectorType::Zero(rows);
 
-  Scalar s1 = test_random<Scalar>(),
+  Scalar s1 = ei_random<Scalar>(),
-         s2 = test_random<Scalar>();
+         s2 = ei_random<Scalar>();
 
   // check basic compatibility of adjoint, transpose, conjugate
   VERIFY_IS_APPROX(m1.transpose().conjugate().adjoint(),    m1);

test/array.cpp

@@ -38,12 +38,12 @@ template<typename MatrixType> void scalarAdd(const MatrixType& m)
   int rows = m.rows();
   int cols = m.cols();
 
-  MatrixType m1 = test_random_matrix<MatrixType>(rows, cols),
+  MatrixType m1 = MatrixType::Random(rows, cols),
-             m2 = test_random_matrix<MatrixType>(rows, cols),
+             m2 = MatrixType::Random(rows, cols),
              m3(rows, cols);
 
-  Scalar  s1 = test_random<Scalar>(),
+  Scalar  s1 = ei_random<Scalar>(),
-          s2 = test_random<Scalar>();
+          s2 = ei_random<Scalar>();
 
   VERIFY_IS_APPROX(m1.cwise() + s1, s1 + m1.cwise());
   VERIFY_IS_APPROX(m1.cwise() + s1, MatrixType::Constant(rows,cols,s1) + m1);

test/basicstuff.cpp

@@ -34,18 +34,18 @@ template<typename MatrixType> void basicStuff(const MatrixType& m)
 
   // this test relies a lot on Random.h, and there's not much more that we can do
   // to test it, hence I consider that we will have tested Random.h
-  MatrixType m1 = test_random_matrix<MatrixType>(rows, cols),
+  MatrixType m1 = MatrixType::Random(rows, cols),
-             m2 = test_random_matrix<MatrixType>(rows, cols),
+             m2 = MatrixType::Random(rows, cols),
              m3(rows, cols),
              mzero = MatrixType::Zero(rows, cols),
              identity = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
                               ::Identity(rows, rows),
-             square = test_random_matrix<Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> >(rows, rows);
+             square = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>::Random(rows, rows);
-  VectorType v1 = test_random_matrix<VectorType>(rows),
+  VectorType v1 = VectorType::Random(rows),
-             v2 = test_random_matrix<VectorType>(rows),
+             v2 = VectorType::Random(rows),
              vzero = VectorType::Zero(rows);
 
-  Scalar x = test_random<Scalar>();
+  Scalar x = ei_random<Scalar>();
 
   int r = ei_random<int>(0, rows-1),
       c = ei_random<int>(0, cols-1);

test/cholesky.cpp

@@ -43,12 +43,12 @@ template<typename MatrixType> void cholesky(const MatrixType& m)
   typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
   typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
 
-  MatrixType a0 = test_random_matrix<MatrixType>(rows,cols);
+  MatrixType a0 = MatrixType::Random(rows,cols);
-  VectorType vecB = test_random_matrix<VectorType>(rows);
+  VectorType vecB = VectorType::Random(rows);
-  MatrixType matB = test_random_matrix<MatrixType>(rows,cols);
+  MatrixType matB = MatrixType::Random(rows,cols);
   SquareMatrixType symm =  a0 * a0.adjoint();
   // let's make sure the matrix is not singular or near singular
-  MatrixType a1 = test_random_matrix<MatrixType>(rows,cols);
+  MatrixType a1 = MatrixType::Random(rows,cols);
   symm += a1 * a1.adjoint();
 
   #ifdef HAS_GSL

test/cwiseop.cpp

@@ -43,16 +43,16 @@ template<typename MatrixType> void cwiseops(const MatrixType& m)
   int rows = m.rows();
   int cols = m.cols();
 
-  MatrixType m1 = test_random_matrix<MatrixType>(rows, cols),
+  MatrixType m1 = MatrixType::Random(rows, cols),
-             m2 = test_random_matrix<MatrixType>(rows, cols),
+             m2 = MatrixType::Random(rows, cols),
              m3(rows, cols),
              mzero = MatrixType::Zero(rows, cols),
              mones = MatrixType::Ones(rows, cols),
              identity = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
                               ::Identity(rows, rows),
-             square = test_random_matrix<Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> >(rows, rows);
+             square = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>::Random(rows, rows);
-  VectorType v1 = test_random_matrix<VectorType>(rows),
+  VectorType v1 = VectorType::Random(rows),
-             v2 = test_random_matrix<VectorType>(rows),
+             v2 = VectorType::Random(rows),
              vzero = VectorType::Zero(rows);
 
   int r = ei_random<int>(0, rows-1),

test/eigensolver.cpp

@@ -45,12 +45,12 @@ template<typename MatrixType> void eigensolver(const MatrixType& m)
 
   RealScalar largerEps = 10*test_precision<RealScalar>();
 
-  MatrixType a = test_random_matrix<MatrixType>(rows,cols);
+  MatrixType a = MatrixType::Random(rows,cols);
-  MatrixType a1 = test_random_matrix<MatrixType>(rows,cols);
+  MatrixType a1 = MatrixType::Random(rows,cols);
   MatrixType symmA =  a.adjoint() * a + a1.adjoint() * a1;
 
-  MatrixType b = test_random_matrix<MatrixType>(rows,cols);
+  MatrixType b = MatrixType::Random(rows,cols);
-  MatrixType b1 = test_random_matrix<MatrixType>(rows,cols);
+  MatrixType b1 = MatrixType::Random(rows,cols);
   MatrixType symmB = b.adjoint() * b + b1.adjoint() * b1;
 
   SelfAdjointEigenSolver<MatrixType> eiSymm(symmA);

test/geometry.cpp

@@ -49,10 +49,10 @@ template<typename Scalar> void geometry(void)
   typedef Translation<Scalar,3> Translation3;
 
   Quaternion q1, q2;
-  Vector3 v0 = test_random_matrix<Vector3>(),
+  Vector3 v0 = Vector3::Random(),
-    v1 = test_random_matrix<Vector3>(),
+    v1 = Vector3::Random(),
-    v2 = test_random_matrix<Vector3>();
+    v2 = Vector3::Random();
-  Vector2 u0 = test_random_matrix<Vector2>();
+  Vector2 u0 = Vector2::Random();
   Matrix3 matrot1;
 
   Scalar a = ei_random<Scalar>(-M_PI, M_PI);
@@ -134,7 +134,7 @@ template<typename Scalar> void geometry(void)
   t1.setIdentity();
   t1.linear() = q1.toRotationMatrix();
 
-  v0 << 50, 2, 1;//= test_random_matrix<Vector3>().cwiseProduct(Vector3(10,2,0.5));
+  v0 << 50, 2, 1;//= ei_random_matrix<Vector3>().cwiseProduct(Vector3(10,2,0.5));
   t0.scale(v0);
   t1.prescale(v0);
 
@@ -169,8 +169,8 @@ template<typename Scalar> void geometry(void)
 
   // 2D transformation
   Transform2 t20, t21;
-  Vector2 v20 = test_random_matrix<Vector2>();
+  Vector2 v20 = Vector2::Random();
-  Vector2 v21 = test_random_matrix<Vector2>();
+  Vector2 v21 = Vector2::Random();
   for (int k=0; k<2; ++k)
     if (ei_abs(v21[k])<1e-3) v21[k] = 1e-3;
   t21.setIdentity();

test/inverse.cpp

@@ -38,7 +38,7 @@ template<typename MatrixType> void inverse(const MatrixType& m)
   typedef typename NumTraits<Scalar>::Real RealScalar;
   typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType;
 
-  MatrixType m1 = test_random_matrix<MatrixType>(rows, cols),
+  MatrixType m1 = MatrixType::Random(rows, cols),
              m2(rows, cols),
              mzero = MatrixType::Zero(rows, cols),
              identity = MatrixType::Identity(rows, rows);
@@ -46,7 +46,7 @@ template<typename MatrixType> void inverse(const MatrixType& m)
   if (ei_is_same_type<RealScalar,float>::ret)
   {
     // let's build a more stable to inverse matrix
-    MatrixType a = test_random_matrix<MatrixType>(rows,cols);
+    MatrixType a = MatrixType::Random(rows,cols);
     m1 += m1 * m1.adjoint() + a * a.adjoint();
   }
 

test/linearstructure.cpp

@@ -38,13 +38,13 @@ template<typename MatrixType> void linearStructure(const MatrixType& m)
 
   // this test relies a lot on Random.h, and there's not much more that we can do
   // to test it, hence I consider that we will have tested Random.h
-  MatrixType m1 = test_random_matrix<MatrixType>(rows, cols),
+  MatrixType m1 = MatrixType::Random(rows, cols),
-             m2 = test_random_matrix<MatrixType>(rows, cols),
+             m2 = MatrixType::Random(rows, cols),
              m3(rows, cols),
              mzero = MatrixType::Zero(rows, cols);
 
-  Scalar s1 = test_random<Scalar>();
+  Scalar s1 = ei_random<Scalar>();
-  while (ei_abs(s1)<1e-3) s1 = test_random<Scalar>();
+  while (ei_abs(s1)<1e-3) s1 = ei_random<Scalar>();
 
   int r = ei_random<int>(0, rows-1),
       c = ei_random<int>(0, cols-1);

test/lu.cpp

@@ -56,7 +56,7 @@ template<typename MatrixType> void lu_non_invertible()
   int rank = ei_random<int>(1, std::min(rows, cols)-1);
 
   MatrixType m1(rows, cols), m2(cols, cols2), m3(rows, cols2), k(1,1);
-  m1 = test_random_matrix<MatrixType>(rows,cols);
+  m1 = MatrixType::Random(rows,cols);
   if(rows <= cols)
     for(int i = rank; i < rows; i++) m1.row(i).setZero();
   else
@@ -72,12 +72,12 @@ template<typename MatrixType> void lu_non_invertible()
   VERIFY((m1 * lu.kernel()).isMuchSmallerThan(m1));
   lu.computeKernel(&k);
   VERIFY((m1 * k).isMuchSmallerThan(m1));
-  m2 = test_random_matrix<MatrixType>(cols,cols2);
+  m2 = MatrixType::Random(cols,cols2);
   m3 = m1*m2;
-  m2 = test_random_matrix<MatrixType>(cols,cols2);
+  m2 = MatrixType::Random(cols,cols2);
   lu.solve(m3, &m2);
   VERIFY_IS_APPROX(m3, m1*m2);
-  m3 = test_random_matrix<MatrixType>(rows,cols2);
+  m3 = MatrixType::Random(rows,cols2);
   VERIFY(!lu.solve(m3, &m2));
 }
 
@@ -90,12 +90,12 @@ template<typename MatrixType> void lu_invertible()
   int size = ei_random<int>(10,200);
 
   MatrixType m1(size, size), m2(size, size), m3(size, size);
-  m1 = test_random_matrix<MatrixType>(size,size);
+  m1 = MatrixType::Random(size,size);
 
   if (ei_is_same_type<RealScalar,float>::ret)
   {
     // let's build a matrix more stable to inverse
-    MatrixType a = test_random_matrix<MatrixType>(size,size*2);
+    MatrixType a = MatrixType::Random(size,size*2);
     m1 += a * a.adjoint();
   }
 
@@ -105,11 +105,11 @@ template<typename MatrixType> void lu_invertible()
   VERIFY(lu.isInjective());
   VERIFY(lu.isSurjective());
   VERIFY(lu.isInvertible());
-  m3 = test_random_matrix<MatrixType>(size,size);
+  m3 = MatrixType::Random(size,size);
   lu.solve(m3, &m2);
   VERIFY_IS_APPROX(m3, m1*m2);
   VERIFY_IS_APPROX(m2, lu.inverse()*m3);
-  m3 = test_random_matrix<MatrixType>(size,size);
+  m3 = MatrixType::Random(size,size);
   VERIFY(lu.solve(m3, &m2));
 }
 

test/main.h

@@ -135,6 +135,7 @@ namespace Eigen
 
 
 #define EIGEN_INTERNAL_DEBUGGING
+#define EIGEN_NICE_RANDOM
 #include <Eigen/Core>
 
 namespace Eigen {
@@ -221,26 +222,6 @@ inline bool test_ei_isMuchSmallerThan(const MatrixBase<Derived>& m,
   return m.isMuchSmallerThan(s, test_precision<typename ei_traits<Derived>::Scalar>());
 }
 
-template<typename T> T test_random();
-
-template<> int test_random() { return ei_random<int>(-100,100); }
-template<> float test_random() { return float(ei_random<int>(-1000,1000)) / 256.f; }
-template<> double test_random() { return double(ei_random<int>(-1000,1000)) / 256.; }
-template<> std::complex<float> test_random()
-{ return std::complex<float>(test_random<float>(),test_random<float>()); }
-template<> std::complex<double> test_random()
-{ return std::complex<double>(test_random<double>(),test_random<double>()); }
-
-template<typename MatrixType>
-MatrixType test_random_matrix(int rows = MatrixType::RowsAtCompileTime, int cols = MatrixType::ColsAtCompileTime)
-{
-  MatrixType res(rows, cols);
-  for (int j=0; j<cols; ++j)
-    for (int i=0; i<rows; ++i)
-      res.coeffRef(i,j) = test_random<typename MatrixType::Scalar>();
-  return res;
-}
-
 } // end namespace Eigen
 
 

test/sum.cpp

@@ -31,7 +31,7 @@ template<typename MatrixType> void matrixSum(const MatrixType& m)
   int rows = m.rows();
   int cols = m.cols();
 
-  MatrixType m1 = test_random_matrix<MatrixType>(rows, cols);
+  MatrixType m1 = MatrixType::Random(rows, cols);
 
   VERIFY_IS_MUCH_SMALLER_THAN(MatrixType::Zero(rows, cols).sum(), Scalar(1));
   VERIFY_IS_APPROX(MatrixType::Ones(rows, cols).sum(), Scalar(rows*cols));
@@ -45,7 +45,7 @@ template<typename VectorType> void vectorSum(const VectorType& w)
   typedef typename VectorType::Scalar Scalar;
   int size = w.size();
 
-  VectorType v = test_random_matrix<VectorType>(size);
+  VectorType v = VectorType::Random(size);
   for(int i = 1; i < size; i++)
   {
     Scalar s = Scalar(0);

test/svd.cpp

@@ -35,9 +35,9 @@ template<typename MatrixType> void svd(const MatrixType& m)
 
   typedef typename MatrixType::Scalar Scalar;
   typedef typename NumTraits<Scalar>::Real RealScalar;
-  MatrixType a = test_random_matrix<MatrixType>(rows,cols);
+  MatrixType a = MatrixType::Random(rows,cols);
   Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> b =
-    test_random_matrix<Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> >(rows,1);
+    Matrix<Scalar, MatrixType::RowsAtCompileTime, 1>::Random(rows,1);
   Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> x(cols,1), x2(cols,1);
 
   RealScalar largerEps = test_precision<RealScalar>();
@@ -56,7 +56,7 @@ template<typename MatrixType> void svd(const MatrixType& m)
   {
     if (ei_is_same_type<RealScalar,float>::ret)
     {
-      MatrixType a1 = test_random_matrix<MatrixType>(rows,cols);
+      MatrixType a1 = MatrixType::Random(rows,cols);
       a += a * a.adjoint() + a1 * a1.adjoint();
     }
     SVD<MatrixType> svd(a);

test/triangular.cpp

@@ -35,8 +35,8 @@ template<typename MatrixType> void triangular(const MatrixType& m)
   int rows = m.rows();
   int cols = m.cols();
 
-  MatrixType m1 = test_random_matrix<MatrixType>(rows, cols),
+  MatrixType m1 = MatrixType::Random(rows, cols),
-             m2 = test_random_matrix<MatrixType>(rows, cols),
+             m2 = MatrixType::Random(rows, cols),
              m3(rows, cols),
              m4(rows, cols),
              r1(rows, cols),
@@ -47,8 +47,8 @@ template<typename MatrixType> void triangular(const MatrixType& m)
                               ::Identity(rows, rows),
              square = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
                               ::Random(rows, rows);
-  VectorType v1 = test_random_matrix<VectorType>(rows),
+  VectorType v1 = VectorType::Random(rows),
-             v2 = test_random_matrix<VectorType>(rows),
+             v2 = VectorType::Random(rows),
              vzero = VectorType::Zero(rows);
 
   MatrixType m1up = m1.template part<Eigen::Upper>();
@@ -81,9 +81,9 @@ template<typename MatrixType> void triangular(const MatrixType& m)
   m1.template part<Eigen::Lower>() = (m2.transpose() * m2).lazy();
   VERIFY_IS_APPROX(m3.template part<Eigen::Lower>(), m1);
 
-  m1 = test_random_matrix<MatrixType>(rows, cols);
+  m1 = MatrixType::Random(rows, cols);
   for (int i=0; i<rows; ++i)
-    while (ei_abs2(m1(i,i))<1e-3) m1(i,i) = test_random<Scalar>();
+    while (ei_abs2(m1(i,i))<1e-3) m1(i,i) = ei_random<Scalar>();
 
   Transpose<MatrixType> trm4(m4);
   // test back and forward subsitution