Starting Eigen 2 development. The current plan is to use the last

release of tvmet (inactive for 2 years and developer unreachable) as the basis for eigen2, because it provides seemingly good expression template mechanisms, we want that, and it would take years to reinvent that wheel. We'll see. So this commit imports the last tvmet release.
2026-04-10 11:34:33 +08:00 · 2007-05-30 06:24:51 +00:00
commit 3036eeca0a
244 changed files with 95342 additions and 0 deletions
--- a/tvmet-1.7.1/tests/Makefile.am
+++ b/tvmet-1.7.1/tests/Makefile.am
@@ -0,0 +1,16 @@
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--- a/tvmet-1.7.1/tests/README
+++ b/tvmet-1.7.1/tests/README
@@ -0,0 +1,2 @@
+This directory contains files only for the developer to check new features.
+Therefore not all is working/compiling here.
--- a/tvmet-1.7.1/tests/bad_temps.cc
+++ b/tvmet-1.7.1/tests/bad_temps.cc
@@ -0,0 +1,243 @@
+/*
+ * This acts as an example on how to not introduce temporaries
+ * for evaluating expressions. The problem is related to the
+ * prod() function, where the temps are going out of scope.
+ */
+extern "C" int printf(const char*, ...);
+
+#ifndef restrict
+#define restrict  __restrict__
+#endif
+
+template<unsigned Rows, unsigned Cols> class Matrix;
+
+struct XprNull { explicit XprNull() { } };
+
+static inline
+double operator+(const double& lhs, XprNull) { return lhs; }
+
+
+struct fcnl_Assign { static inline void applyOn(double& restrict lhs, double rhs) { lhs = rhs; } };
+
+
+template<unsigned Rows, unsigned Cols,
+	 unsigned RowStride, unsigned ColStride>
+struct MetaMatrix
+{
+  enum {
+    doRows = (RowStride < Rows - 1) ? 1 : 0,
+    doCols = (ColStride < Cols - 1) ? 1 : 0
+  };
+
+  template<class Mtrx, class E, class Fcnl>
+  static inline
+  void assign2(Mtrx& mat, const E& expr, const Fcnl& fn) {
+    fn.applyOn(mat(RowStride, ColStride), expr(RowStride, ColStride));
+    MetaMatrix<Rows * doCols, Cols * doCols, RowStride * doCols, (ColStride+1) * doCols>::assign2(mat, expr, fn);
+  }
+
+  template<class Mtrx, class E, class Fcnl>
+  static inline
+  void assign(Mtrx& mat, const E& expr, const Fcnl& fn) {
+    MetaMatrix<Rows, Cols, RowStride, 0>::assign2(mat, expr, fn);
+    MetaMatrix<Rows * doRows, Cols * doRows, (RowStride+1) * doRows, 0>::assign(mat, expr, fn);
+  }
+};
+
+template<>
+struct MetaMatrix<0, 0, 0, 0>
+{
+  template<class Mtrx, class E, class Fcnl>
+  static inline void assign2(Mtrx&, const E&, const Fcnl&) { }
+
+  template<class Mtrx, class E, class Fcnl>
+  static inline void assign(Mtrx&, const E&, const Fcnl&) { }
+};
+
+
+template<unsigned Rows1, unsigned Cols1,
+	 unsigned Cols2,
+	 unsigned RowStride1, unsigned ColStride1,
+	 unsigned RowStride2, unsigned ColStride2,
+	 unsigned K>
+struct MetaGemm
+{
+  enum { doIt = (K != Cols1 - 1) };
+
+  static inline
+  double prod(const double* restrict lhs, const double* restrict rhs, unsigned i, unsigned j) {
+    return lhs[i * RowStride1 + K * ColStride1] * rhs[K * RowStride2 + j * ColStride2]
+      + MetaGemm<Rows1 * doIt, Cols1 * doIt,
+                 Cols2 * doIt, RowStride1 * doIt, ColStride1 * doIt,
+                 RowStride2 * doIt, ColStride2 * doIt, (K+1) * doIt>::prod(lhs, rhs, i, j);
+  }
+};
+
+template<>
+struct MetaGemm<0,0,0,0,0,0,0,0>
+{
+  static inline XprNull prod(const void*, const void*, unsigned, unsigned) { return XprNull(); }
+};
+
+
+template<unsigned Rows1, unsigned Cols1,
+	 unsigned Cols2,
+	 unsigned RowStride1, unsigned ColStride1,
+	 unsigned RowStride2, unsigned ColStride2>
+struct XprMMProduct
+{
+  explicit XprMMProduct(const double* restrict lhs, const double* restrict rhs) : m_lhs(lhs), m_rhs(rhs) { }
+
+  double operator()(unsigned i, unsigned j) const {
+    return MetaGemm<Rows1, Cols1,
+                    Cols2,
+                    RowStride1, ColStride1,
+                    RowStride2, ColStride2, 0>::prod(m_lhs, m_rhs, i, j);
+  }
+
+private:
+  const double* restrict 			m_lhs;
+  const double* restrict 			m_rhs;
+};
+
+
+template<class E>
+struct XprMatrixTranspose
+{
+  explicit XprMatrixTranspose(const E& e) : m_expr(e) { }
+
+  double operator()(unsigned i, unsigned j) const { return m_expr(j, i); }
+
+private:
+  const E& restrict				m_expr;
+};
+
+
+template<class E, unsigned Rows, unsigned Cols>
+struct XprMatrix
+{
+  explicit XprMatrix(const E& e) : m_expr(e) { }
+
+  double operator()(unsigned i, unsigned j) const { return m_expr(i, j); }
+
+private:
+  const E& restrict				m_expr;
+};
+
+
+template<unsigned Rows, unsigned Cols,
+	 unsigned RowStride, unsigned ColStride>
+struct MatrixConstReference
+{
+  explicit MatrixConstReference(const Matrix<Rows, Cols>& rhs) : m_data(rhs.m_data) { }
+
+  double operator()(unsigned i, unsigned j) const {
+    return m_data[i * RowStride + j * ColStride];
+  }
+
+private:
+  const double* restrict 			m_data;
+};
+
+
+template<unsigned Rows, unsigned Cols>
+struct Matrix
+{
+  explicit Matrix() { m_data = new double [Rows*Cols]; }
+
+  template<class E>
+  explicit Matrix(const XprMatrix<E, Rows, Cols>& rhs) {
+    m_data = new double [Rows*Cols];
+    MetaMatrix<Rows, Cols, 0, 0>::assign(*this, rhs, fcnl_Assign());
+  }
+
+  ~Matrix() { delete [] m_data; }
+
+  double& restrict operator()(unsigned i, unsigned j) { return m_data[i * Cols + j]; }
+
+  double operator()(unsigned i, unsigned j) const { return m_data[i * Cols + j]; }
+
+  MatrixConstReference<Rows,Cols,Cols,1> const_ref() const {
+    return MatrixConstReference<Rows,Cols,Cols,1>(*this);
+  }
+
+  template <class E> Matrix& operator=(const XprMatrix<E, Rows, Cols>& rhs) {
+    MetaMatrix<Rows, Cols, 0, 0>::assign(*this, rhs, fcnl_Assign());
+    return *this;
+  }
+
+  void print() const {
+    printf("[\n");
+    for(unsigned i = 0; i != Rows; ++i) {
+      printf("\t[");
+      for(unsigned j = 0; j != Cols; ++j)
+	printf("\t%+4.2f", this->operator()(i, j));
+      printf("]\n");
+    }
+    printf("]\n");
+  }
+
+// private:
+  double* 						m_data;
+};
+
+
+template<class E1, unsigned Rows1, unsigned Cols1, unsigned Cols2>
+inline
+XprMatrix<
+  XprMMProduct<
+    Rows1, Cols1, Cols2,
+    Cols1, 1, Cols2, 1
+  >,
+  Rows1, Cols2
+>
+prod(const XprMatrix<E1, Rows1, Cols1>& lhs, const Matrix<Cols1, Cols2>& rhs) {
+  typedef XprMMProduct<
+    Rows1, Cols1, Cols2,
+    Cols1, 1, Cols2, 1
+  >							expr_type;
+  Matrix<Rows1, Cols1> 					temp_lhs(lhs);
+
+  return XprMatrix<expr_type, Rows1, Cols2>(expr_type(temp_lhs.m_data, rhs.m_data));
+}
+
+template<unsigned Rows, unsigned Cols>
+inline
+XprMatrix<
+  XprMatrixTranspose<
+    MatrixConstReference<Rows, Cols, Cols, 1>
+  >,
+  Cols, Rows
+>
+trans(const Matrix<Rows, Cols>& rhs) {
+  typedef XprMatrixTranspose<
+    MatrixConstReference<Rows, Cols, Cols, 1>
+  >							expr_type;
+  return XprMatrix<expr_type, Cols, Rows>(expr_type(rhs.const_ref()));
+}
+
+
+/**
+ * Test driver
+ */
+using namespace std;
+
+int main()
+{
+  Matrix<3,2>		B;
+  Matrix<3,3>		D;
+  Matrix<2,2>		K;
+
+  B(0,0) = -0.05;	B(0,1) =  0;
+  B(1,0) =  0;		B(1,1) =  0.05;
+  B(2,0) =  0.05;	B(2,1) = -0.05;
+
+  D(0,0) = 2000;	D(0,1) = 1000;		D(0,2) = 0;
+  D(1,0) = 1000;	D(1,1) = 2000;		D(1,2) = 0;
+  D(2,0) = 0;		D(2,1) = 0;		D(2,2) = 500;
+
+  K = prod(prod(trans(B), D), B);
+
+  printf("K = ");
+  K.print();	// wrong result, should be symetric
+}
--- a/tvmet-1.7.1/tests/bad_xpr_const_ref.cc
+++ b/tvmet-1.7.1/tests/bad_xpr_const_ref.cc
@@ -0,0 +1,164 @@
+/*
+ * $Id: bad_xpr_const_ref.cc,v 1.1 2003/10/21 19:40:38 opetzold Exp $
+ *
+ * This example shows the problem on holding references
+ * by expressions. On higher optimization levels all things
+ * are good. Without optimizations it crashs.
+ */
+
+extern "C" int printf(const char*, ...);
+
+#ifndef restrict
+#define restrict  __restrict__
+#endif
+
+template<unsigned Sz> class Vector;
+
+struct Fcnl_Assign {
+  static inline void apply_on(double& restrict lhs, double rhs) { lhs = rhs; }
+};
+
+struct Fcnl_Add {
+  static inline double apply_on(double lhs, double rhs) { return lhs + rhs; }
+};
+
+template<unsigned Sz, unsigned Stride=0>
+struct MetaVector
+{
+  enum {
+    doIt = (Stride < (Sz-1)) ? 1 : 0
+  };
+
+  template <class E1, class E2, class Fcnl>
+  static inline
+  void assign(E1& lhs, const E2& rhs, const Fcnl& fn) {
+    fn.apply_on(lhs(Stride), rhs(Stride));
+    MetaVector<Sz * doIt, (Stride+1) * doIt>::assign(lhs, rhs, fn);
+  }
+};
+
+template<>
+struct MetaVector<0,0>
+{
+  template <class E1, class E2, class Fcnl>
+  static inline void assign(E1&, const E2&, const Fcnl&) { }
+};
+
+
+template<class E, unsigned Sz>
+struct XprVector
+{
+  explicit XprVector(const E& e) : m_expr(e) { }
+
+  double operator()(unsigned i) const {
+    return m_expr(i);
+  }
+
+  template<class E2, class Fcnl>
+  void assign_to(E2& e, const Fcnl& fn) const {
+    MetaVector<Sz, 0>::assign(e, *this, fn);
+  }
+
+  const E						m_expr;
+};
+
+
+template<unsigned Sz, unsigned Stride=1>
+struct VectorConstReference
+{
+  explicit VectorConstReference(const Vector<Sz>& rhs) : m_data(rhs.m_data) { }
+
+  double operator()(unsigned i) const {
+    return m_data[i * Stride];
+  }
+
+  const double* restrict 				m_data;
+};
+
+
+template<unsigned Sz>
+struct Vector
+{
+  explicit Vector() { }
+
+  double& restrict operator()(unsigned i) { return m_data[i]; }
+
+  double operator()(unsigned i) const { return m_data[i]; }
+
+  typedef VectorConstReference<Sz, 1>    		ConstReference;
+
+  ConstReference const_ref() const { return ConstReference(*this); }
+
+  template<class Fcnl>
+  void assign_to(Vector& v, const Fcnl& fn) {
+    MetaVector<Sz, 0>::assign(v, *this, fn);
+  }
+
+  template<class E>
+  Vector& operator=(const XprVector<E, Sz>& rhs) {
+    rhs.assign_to(*this, Fcnl_Assign());
+    return *this;
+  }
+
+  double						m_data[Sz];
+};
+
+
+template<class BinOp, class E1, class E2>
+struct XprBinOp
+{
+  explicit XprBinOp(const E1& lhs, const E2& rhs)
+    : m_lhs(lhs), m_rhs(rhs)
+  { }
+
+  double operator()(unsigned i) const {
+    return BinOp::apply_on(m_lhs(i), m_rhs(i));
+  }
+
+  const E1& 						m_lhs;
+  const E2& 						m_rhs;
+};
+
+
+template<unsigned Sz>
+inline
+XprVector<
+  XprBinOp<
+  Fcnl_Add,
+    VectorConstReference<Sz>,
+    VectorConstReference<Sz>
+  >,
+  Sz
+>
+add (const Vector<Sz>& lhs, const Vector<Sz>& rhs) {
+  typedef XprBinOp <
+    Fcnl_Add,
+    VectorConstReference<Sz>,
+    VectorConstReference<Sz>
+  >							expr_type;
+  return XprVector<expr_type, Sz>(
+    expr_type(lhs.const_ref(), rhs.const_ref()));
+}
+
+
+int main()
+{
+
+  Vector<5>	v, v1,v2;
+
+  v1(0) = 1;
+  v1(1) = 2;
+  v1(2) = 3;
+  v1(3) = 4;
+  v1(4) = 5;
+
+  v2(0) = 1;
+  v2(1) = 2;
+  v2(2) = 3;
+  v2(3) = 4;
+  v2(4) = 5;
+
+  v = add(v1, v2);
+
+  printf("v(0) = %f\n", v(0));
+}
--- a/tvmet-1.7.1/tests/swap.cc
+++ b/tvmet-1.7.1/tests/swap.cc
@@ -0,0 +1,154 @@
+/*
+ * Test file for checking meta swap feature.
+ *
+ * Swapping using std::swap is faster than meta template implementation.
+ */
+
+#include <iostream>
+#include <algorithm>				// min, max
+
+#include <tvmet/Matrix.h>
+#include <tvmet/Vector.h>
+
+
+using namespace tvmet;
+using namespace std;
+
+NS_TVMET_BEGIN
+
+template<size_t Sz, size_t Idx=0>
+class MetaSwap // later, should be MetaVector
+{
+private:
+  enum {
+    doIt = (Idx < (Sz-1)) ? 1 : 0		/**< recursive counter */
+  };
+
+public:
+  template<class E1, class E2>
+  static inline
+  void
+  swap(E1& e1, E2& e2) {
+    // XXX BUG: const problem?, we have to use the operator() for Vectors
+    fcnl_Swap<typename E1::value_type, typename E2::value_type>::applyOn(e1(Idx), e2(Idx));
+    MetaSwap<Sz * doIt, (Idx+1) * doIt>::swap(e1, e2);
+  }
+};
+
+template<>
+class MetaSwap<0, 0>
+{
+public:
+  template<class E1, class E2> static inline void swap(E1&, E2&) { }
+};
+
+
+/**
+ * \fun swap
+ * \brief swaps to vector expressions XprVector<E, Sz>
+ */
+template<class E1, class E2, size_t Sz>
+inline
+void swap(XprVector<E1, Sz> e1, XprVector<E2, Sz> e2) {
+  MetaSwap<Sz>::swap(e1, e2);
+}
+
+/**
+ * \fun swap
+ * \brief swaps to vector
+ */
+template<class T1, class T2, size_t Sz>
+inline
+void swap(Vector<T1, Sz>& lhs, Vector<T2, Sz>& rhs) {
+  swap(lhs.asXpr(), rhs.asXpr());
+}
+
+
+/**
+ * \fun swap2
+ * \brief swaps to vector expressions XprVector<E, Sz>
+ */
+template<class E1, class E2, size_t Sz>
+inline
+void swap2(XprVector<E1, Sz> e1, XprVector<E2, Sz> e2) {
+  // loops are faster than meta templates
+  for(size_t i = 0; i < Sz; ++i)
+    std::swap(e1[i], e2[i]);
+}
+
+/**
+ * \fun swap2
+ * \brief swaps to vector
+ */
+template<class T1, class T2, size_t Sz>
+inline
+void swap2(Vector<T1, Sz>& lhs, Vector<T2, Sz>& rhs) {
+  // loops are faster than meta templates
+  for(size_t i = 0; i < Sz; ++i)
+    std::swap(lhs[i], rhs[i]);
+}
+
+
+NS_TVMET_END
+
+
+
+
+template<class V1, class V2>
+void test_meta_swap(V1& v1, V2& v2) {
+  tvmet::swap(v1, v2);
+}
+
+template<class V1, class V2>
+void test_loop_swap(V1& v1, V2& v2) {
+  tvmet::swap2(v1, v2);
+}
+
+
+
+template<class M1, class M2>
+void test_meta_mswap(M1& m1, M2& m2) {
+  tvmet::swap2(row(m1, 0), row(m2, 0));
+  tvmet::swap2(col(m1, 0), col(m2, 0));
+}
+
+
+#define LOOPS	1000000
+
+int main() {
+  typedef Matrix<double, 4, 4>				matrix_type;
+  typedef Vector<double, 4>				vector_type;
+
+  //----------------------------------------------------------------
+  vector_type v1(1);
+  vector_type v2(4);
+
+  cout << "\nSwap Vectors\n\n";
+  cout << v1 << endl;
+  cout << v2 << endl;
+  for(size_t i = 0; i < LOOPS; ++i)
+    test_meta_swap(v1, v2);
+  cout << v1 << endl;
+  cout << v2 << endl;
+  for(size_t i = 0; i < LOOPS; ++i)
+    test_loop_swap(v1, v2);
+  cout << v1 << endl;
+  cout << v2 << endl;
+
+  //----------------------------------------------------------------
+  matrix_type m1, m2;
+  vector_type rv;
+
+  m1 = 1,2,3,4,
+       5,6,7,8,
+       9,10,11,12,
+       13,14,15,16;
+  m2 = transpose(m1);
+
+  cout << "\nSwap Matrix\n\n";
+  cout << m1 << endl;
+  cout << m2 << endl;
+  test_meta_mswap(m1, m2);
+  cout << m1 << endl;
+  cout << m2 << endl;
+}
--- a/tvmet-1.7.1/tests/t.cc
+++ b/tvmet-1.7.1/tests/t.cc
@@ -0,0 +1,414 @@
+#include <iostream>
+#include <tvmet/Vector.h>
+#include <tvmet/Matrix.h>
+
+using std::cout;
+using std::endl;
+
+struct separator {
+  std::ostream& print_on(std::ostream& os) const {
+    for(std::size_t i = 0; i < 63; ++i) os << "-";
+    return os;
+  }
+};
+
+std::ostream& operator<<(std::ostream& os, const separator& s) {
+  return s.print_on(os);
+}
+
+template<class T1, class T2 = T1>
+class TestBase
+{
+public:
+  typedef T1					value_type;
+  typedef T2					value_type2;
+
+  typedef tvmet::Vector<value_type, 3>		vector_type;
+  typedef tvmet::Matrix<value_type, 3, 3>	matrix_type;
+  typedef tvmet::Vector<value_type2, 3>		vector_type2;
+  typedef tvmet::Matrix<value_type2, 3, 3>	matrix_type2;
+
+private:
+  vector_type					v0;
+  matrix_type					M0;
+
+protected:
+  vector_type					v1, v2, v3;
+  matrix_type					M1, M2, M3;
+
+protected:
+  TestBase()
+  {
+    v0 = 1,2,3;
+    M0 = 1,4,7,2,5,8,3,6,9;
+    reset();
+  }
+
+  ~TestBase() { }
+
+  void reset()
+  {
+    v1 = v0; v2 = v0; v3 = v0;
+    M1 = M0; M2 = M0; M3 = M0;
+  }
+
+public:
+  void show_v1(const std::string& op) {
+    cout << separator() << endl
+	 << op << " = "
+	 << v1 << endl
+	 << separator() << endl;
+  }
+
+  void show_v2(const std::string& op) {
+    cout << separator() << endl
+	 << op << " = "
+	 << v2 << endl
+	 << separator() << endl;
+  }
+
+  void show_v3(const std::string& op) {
+    cout << separator() << endl
+	 << op << " = "
+	 << v3 << endl
+	 << separator() << endl;
+  }
+
+  void show_v() {
+    cout << separator() << endl;
+    cout << "v1 = " << v1 << endl
+	 << "v2 = " << v2 << endl
+	 << "v3 = " << v3 << endl;
+    cout << separator() << endl;
+  }
+
+  void show_M1(const std::string& op) {
+    cout << separator() << endl
+	 << op << " = "
+	 << M1 << endl
+	 << separator() << endl;
+  }
+
+  void show_M2(const std::string& op) {
+    cout << separator() << endl
+	 << op << " = "
+	 << M2 << endl
+	 << separator() << endl;
+  }
+
+  void show_M3(const std::string& op) {
+    cout << separator() << endl
+	 << op << " = "
+	 << M3 << endl
+	 << separator() << endl;
+  }
+
+  void show_M() {
+    cout << separator() << endl;
+    cout << "M1 = " << M1 << endl
+	 << "M2 = " << M2 << endl
+	 << "M3 = " << M3 << endl;
+    cout << separator() << endl;
+  }
+};
+
+
+
+
+/*
+ * Vector
+ */
+class TestV : public TestBase<double>
+{
+public:
+  TestV() { }
+
+public:
+  void case1()  {
+    reset();
+
+    v1 = v2 + v2 + v3;
+
+    show_v1("v2 + v2 + v3");
+  }
+  void case2()  {
+    reset();
+
+    v1 = sin( (v2 + v2) * v2 );
+
+    show_v1("sin( (v2 + v2) * v2 )");
+  }
+  void case3()  {
+    reset();
+
+    v1 = (v2 + v2) * (v2 + v2);
+
+    show_v1("(v2 + v2) * (v2 + v2)");
+  }
+  void case4()  {
+    reset();
+
+    v1 = (v2 + v2) * (v2 + v2) / 4;
+
+    show_v1("(v2 + v2) * (v2 + v2) / 4");
+  }
+  void case5()  {
+    reset();
+
+  }
+};
+
+/*
+ * Matrix
+ */
+class TestM : public TestBase<double>
+{
+public:
+  TestM() { }
+
+public:
+  void case1()  {
+    reset();
+
+    M1 = M2 + M3;
+
+    show_M1("M2 + M3");
+  }
+  void case2()  {
+    reset();
+
+    M1 = M2 + M2 + M2 + M2;
+
+    show_M1("M2 + M2 + M2 + M2");
+  }
+  void case3()  {
+    reset();
+
+    /*
+      XXX: missing feature element_wise XprMatrix * Xprmatrix
+
+      M1 = ( M2 + M2 ) * ( M2 + M2 );
+
+      M1 = tvmet::element_wise::product( M2 + M2, M2 + M2 );
+
+      show_M1("empty");
+    */
+  }
+  void case4()  {
+    reset();
+
+    M1 = sin(M2 + M2);			// UFUNC(XprMatrix)
+
+    show_M1("sin(M2 + M2)");
+  }
+  void case5()  {
+    reset();
+
+    M1 = trans(M2);			// = XprMatrix
+
+    show_M1("trans(M2)");
+  }
+  void case6()  {
+    reset();
+
+    M1 = trans(M2) + M2; 		// XprMatrix + Matrix
+
+    show_M1("trans(M2) + M2");
+  }
+  void case7()  {
+    reset();
+
+    M1 = M2 + trans(M2); 		// Matrix + XprMatrix
+
+    show_M1("M2 + trans(M2)");
+  }
+  void case8()  {
+    reset();
+
+    /*
+     * WRONG results, should be:
+     *   120  264  408
+     *   144  324  504
+     *   168  384  600
+     * there seems to be a side effect!!
+     */
+
+    M1 = prod((M2 + M2), (M2 + M2)); 	// XprMatrix * XprMatrix
+
+    show_M1("prod((M2 + M2), (M2 + M2))");
+  }
+  void case9()  {
+    reset();
+
+    M1 = (M2 + M2) * (M2 + M2); 	// XprMatrix * XprMatrix
+
+    show_M1("(M2 + M2) * (M2 + M2)");
+  }
+  void case10()  {
+    reset();
+
+  }
+};
+
+/*
+ * Matrix-Vector
+ */
+class TestMV : public TestBase<double>
+{
+public:
+  TestMV() { }
+
+public:
+  void case1()  {
+    reset();
+
+    v1 = M1 * v2;
+
+    show_v1("M1 * v2");
+  }
+  void case2()  {
+    reset();
+
+    v1 = (M1 * v2) + v2;
+
+    show_v1("(M1 * v2) + v2");
+  }
+  void case3()  {
+    reset();
+
+    v1 = (M1 * v2) + (M1 * v2);
+
+    show_v1("(M1 * v2) + (M1 * v2)");
+  }
+  void case4()  {
+    reset();
+
+    v1 = (M1 * v2) * (M1 * v2); 	// element wise: XprVector * XprVector
+
+    show_v1("element_wise: (M1 * v2) * (M1 * v2)");
+  }
+  void case5()  {
+    reset();
+
+    using namespace tvmet::element_wise;
+    v1 = (M1 * v2) / (M1 * v2); 	// element_wise: XprVector / XprVector
+
+    show_v1("element_wise: (M1 * v2) / (M1 * v2)");
+  }
+  void case6()  {
+    reset();
+
+    v1 = prod(M1, v2);
+
+    show_v1("trans_prod(M1, v2)");
+  }
+  void case7()  {
+    reset();
+
+    v1 = prod(M1, v2) + v2;// XprVector + Vector
+
+    show_v1("prod(M1, v2) + v2");
+  }
+  void case8()  {
+    reset();
+
+    using namespace tvmet::element_wise;
+    v1 += prod(M1, v2) / v2;// element_wise: XprVector + Vector
+
+    show_v1("v1 += prod(M1, v2) / v2");
+  }
+  void case9()  {
+    reset();
+
+    v1 = prod(M1, v2) + prod(M1, v2);// element wise: XprVector * XprVector
+
+    show_v1("prod(M1, v2) + prod(M1, v2)");
+  }
+  void case10()  {
+    reset();
+
+    using namespace tvmet::element_wise;
+    v1 = prod(M1, v2) / prod(M1, v2);// element_wise: XprVector / XprVector
+
+    all_elements( v1 == 1 );
+
+    show_v1("prod(M1, v2) / prod(M1, v2)");
+  }
+  void case11()  {
+    reset();
+
+    v1 = M1 * (v1+v1);
+
+    show_v1("M1 * (v1+v1)");
+  }
+  void case12()  {
+    reset();
+
+    v1 = M1 * prod(M1, v2);
+
+    show_v1("M1 * prod(M1, v2)");
+  }
+};
+
+
+
+
+
+/*
+ * Main
+ */
+int main()
+{
+  tvmet::Matrix<double, 3,3> MM;
+  MM = 1,2,3,4,5,6,7,8,9;
+  tvmet::Matrix<double, 3,3> MM2( MM );
+
+  TestV						v;
+  TestM						M;
+  TestMV					Mv;
+
+  v.show_v();
+  M.show_M();
+
+  cout << "*****************************************************************" << endl;
+
+#if 1
+  v.case1();
+  v.case2();
+  v.case3();
+  v.case4();
+  v.case5();
+
+  cout << "*****************************************************************" << endl;
+#endif
+
+#if 1
+  M.case1();
+  M.case2();
+  M.case3();
+  M.case4();
+  M.case5();
+  M.case6();
+  M.case7();
+  M.case8();
+  M.case9();
+  M.case10();
+
+  cout << "*****************************************************************" << endl;
+#endif
+
+#if 1
+  Mv.case1();
+  Mv.case2();
+  Mv.case3();
+  Mv.case4();
+  Mv.case5();
+#endif
+  Mv.case6();
+  Mv.case7();
+  Mv.case8();
+  Mv.case9();
+  Mv.case10();
+  Mv.case11();
+  Mv.case12();
+}
--- a/tvmet-1.7.1/tests/tvmet.cc
+++ b/tvmet-1.7.1/tests/tvmet.cc
@@ -0,0 +1,312 @@
+/*
+ * $Id: tvmet.cc,v 1.3 2003/10/21 19:37:06 opetzold Exp $
+ *
+ * This file shows the basic principle used by tvmet. Therefore
+ * you will not find promotion etc. here.
+ */
+
+extern "C" int printf(const char*, ...);
+
+#ifndef restrict
+#define restrict  __restrict__
+#endif
+
+template<unsigned Rows, unsigned Cols> class Matrix;
+
+struct XprNull { explicit XprNull() { } };
+
+static inline
+double operator+(const double& lhs, XprNull) { return lhs; }
+
+
+struct Fcnl_Assign { static inline void apply_on(double& restrict lhs, double rhs) { lhs = rhs; } };
+
+
+template<unsigned Rows, unsigned Cols,
+	 unsigned RowStride, unsigned ColStride>
+struct MetaMatrix
+{
+  enum {
+    doRows = (RowStride < Rows - 1) ? 1 : 0,
+    doCols = (ColStride < Cols - 1) ? 1 : 0
+  };
+
+  template<class E1, class E2, class Fcnl>
+  static inline
+  void assign2(E1& lhs, const E2& rhs, const Fcnl& fn) {
+    fn.apply_on( lhs(RowStride, ColStride), rhs(RowStride, ColStride) );
+    MetaMatrix<Rows * doCols, Cols * doCols, RowStride * doCols, (ColStride+1) * doCols>::assign2(lhs, rhs, fn);
+  }
+
+  template<class E1, class E2, class Fcnl>
+  static inline
+  void assign(E1& lhs, const E2& rhs, const Fcnl& fn) {
+    MetaMatrix<Rows, Cols, RowStride, 0>::assign2(lhs, rhs, fn);
+    MetaMatrix<Rows * doRows, Cols * doRows, (RowStride+1) * doRows, 0>::assign(lhs, rhs, fn);
+  }
+};
+
+template<>
+struct MetaMatrix<0, 0, 0, 0>
+{
+  template<class E1, class E2, class Fcnl>
+  static inline void assign2(E1&, const E2&, const Fcnl&) { }
+
+  template<class E1, class E2, class Fcnl>
+  static inline void assign(E1&, const E2&, const Fcnl&) { }
+};
+
+
+template<unsigned Rows1, unsigned Cols1,
+	 unsigned Cols2,
+	 unsigned RowStride1, unsigned ColStride1,
+	 unsigned RowStride2, unsigned ColStride2,
+	 unsigned K>
+struct MetaGemm
+{
+  enum { doIt = (K != Cols1 - 1) };
+
+  template<class E1, class E2>
+  static inline
+  double prod(const E1& lhs, const E2& rhs, unsigned i, unsigned j) {
+    return lhs(i, K) * rhs(K, j)
+      + MetaGemm<Rows1 * doIt, Cols1 * doIt,
+      Cols2 * doIt, RowStride1 * doIt, ColStride1 * doIt,
+      RowStride2 * doIt, ColStride2 * doIt, (K+1) * doIt>::prod(lhs, rhs, i, j);
+  }
+};
+
+template<>
+struct MetaGemm<0,0,0,0,0,0,0,0>
+{
+  template<class E1, class E2>
+  static inline XprNull prod(const E1&, const E2&, unsigned, unsigned) { return XprNull(); }
+};
+
+
+template<class E1, class E2,
+         unsigned Rows1, unsigned Cols1,
+	 unsigned Cols2,
+	 unsigned RowStride1, unsigned ColStride1,
+	 unsigned RowStride2, unsigned ColStride2>
+struct XprMMProduct
+{
+  explicit XprMMProduct(const E1& lhs, const E2& rhs) : m_lhs(lhs), m_rhs(rhs) { }
+
+  double operator()(unsigned i, unsigned j) const {
+    return MetaGemm<
+      Rows1, Cols1,
+      Cols2,
+      RowStride1, ColStride1,
+      RowStride2, ColStride2, 0>::prod(m_lhs, m_rhs, i, j);
+  }
+
+//   void assign_to(Matrix<Rows1, Cols2>& rhs) const {
+//     MetaMatrix<Rows1, Cols2, 0, 0>::assign(rhs, *this, Fcnl_Assign());
+//   }
+
+private:
+  const E1					m_lhs;
+  const E2		 			m_rhs;
+};
+
+
+template<class E>
+struct XprMatrixTranspose
+{
+  explicit XprMatrixTranspose(const E& e) : m_expr(e) { }
+
+  double operator()(unsigned i, unsigned j) const { return m_expr(j, i); }
+
+//   template<unsigned Rows, unsigned Cols>
+//   void assign_to(Matrix<Rows, Cols>& rhs) const {
+//     MetaMatrix<Rows, Cols, 0, 0>::assign(rhs, *this, Fcnl_Assign());
+//   }
+
+private:
+  const E					m_expr;
+};
+
+
+template<class E, unsigned Rows, unsigned Cols>
+struct XprMatrix
+{
+  explicit XprMatrix(const E& e) : m_expr(e) { }
+
+  double operator()(unsigned i, unsigned j) const { return m_expr(i, j); }
+
+  void assign_to(Matrix<Rows, Cols>& rhs) const {
+    MetaMatrix<Rows, Cols, 0, 0>::assign(rhs, *this, Fcnl_Assign());
+  }
+
+private:
+  const E					m_expr;
+};
+
+
+template<unsigned Rows, unsigned Cols,
+	 unsigned RowStride, unsigned ColStride>
+struct MatrixConstReference
+{
+  explicit MatrixConstReference(const Matrix<Rows, Cols>& rhs) : m_data(rhs.m_data) { }
+
+  double operator()(unsigned i, unsigned j) const {
+    return m_data[i * RowStride + j * ColStride];
+  }
+
+private:
+  const double* restrict 			m_data;
+};
+
+
+template<unsigned Rows, unsigned Cols>
+struct Matrix
+{
+  explicit Matrix() { m_data = new double [Rows*Cols]; }
+
+  template<class E>
+  explicit Matrix(const XprMatrix<E, Rows, Cols>& rhs) {
+    m_data = new double [Rows*Cols];
+    MetaMatrix<Rows, Cols, 0, 0>::assign(*this, rhs, Fcnl_Assign());
+  }
+
+  ~Matrix() { delete [] m_data; }
+
+  double& restrict operator()(unsigned i, unsigned j) { return m_data[i * Cols + j]; }
+
+  double operator()(unsigned i, unsigned j) const { return m_data[i * Cols + j]; }
+
+  MatrixConstReference<Rows,Cols,Cols,1> const_ref() const {
+    return MatrixConstReference<Rows,Cols,Cols,1>(*this);
+  }
+
+  Matrix& operator=(const Matrix<Rows, Cols>& rhs) {
+    rhs.assign_to(*this);
+    return *this;
+  }
+
+  void assign_to(Matrix<Rows, Cols>& rhs) const {
+    MetaMatrix<Rows, Cols, 0, 0>::assign(rhs, *this, Fcnl_Assign());
+  }
+
+  template <class E>
+  Matrix& operator=(const XprMatrix<E, Rows, Cols>& rhs) {
+    rhs.assign_to(*this);
+    return *this;
+  }
+
+  template <class E>
+  void assign_to(XprMatrix<E, Rows, Cols>& rhs) const {
+    MetaMatrix<Rows, Cols, 0, 0>::assign(rhs, *this, Fcnl_Assign());
+  }
+
+  void print() const {
+    printf("[\n");
+    for(unsigned i = 0; i != Rows; ++i) {
+      printf("\t[");
+      for(unsigned j = 0; j != Cols; ++j)
+	printf("\t%+4.2f", this->operator()(i, j));
+      printf("]\n");
+    }
+    printf("]\n");
+  }
+
+  double* 						m_data;
+};
+
+
+template<unsigned Rows1, unsigned Cols1,
+	 unsigned Cols2>
+inline
+XprMatrix<
+  XprMMProduct<
+    MatrixConstReference<Rows1, Cols1, Cols1, 1>,
+    MatrixConstReference<Cols1, Cols2, Cols2, 1>,
+    Rows1, Cols1,	// M1(Rows1, Cols1)
+    Cols2, 		// M2(Cols1, Cols2)
+    Cols1, 1, 		// Stride M1
+    Cols2, 1		// Stride M2
+  >,
+  Rows1, Cols2		// return Dim
+>
+prod(const Matrix<Rows1, Cols1>& lhs, const Matrix<Cols1, Cols2>& rhs) {
+  typedef XprMMProduct<
+    MatrixConstReference<Rows1, Cols1, Cols1, 1>,
+    MatrixConstReference<Cols1, Cols2, Cols2, 1>,
+    Rows1, Cols1,
+    Cols2,
+    Cols1, 1,
+    Cols2, 1
+  >							expr_type;
+  return XprMatrix<expr_type, Rows1, Cols2>(
+    expr_type(lhs.const_ref(), rhs.const_ref()));
+}
+
+template<class E1, unsigned Rows1, unsigned Cols1, unsigned Cols2>
+inline
+XprMatrix<
+  XprMMProduct<
+    XprMatrix<E1, Rows1, Cols1>,
+    MatrixConstReference<Cols1, Cols2, Cols2, 1>,
+    Rows1, Cols1, Cols2,
+    Cols1, 1, Cols2, 1
+  >,
+  Rows1, Cols2
+  >
+prod(const XprMatrix<E1, Rows1, Cols1>& lhs, const Matrix<Cols1, Cols2>& rhs) {
+  typedef XprMMProduct<
+    XprMatrix<E1, Rows1, Cols1>,
+    MatrixConstReference<Cols1, Cols2, Cols2, 1>,
+    Rows1, Cols1, Cols2,
+    Cols1, 1, Cols2, 1
+  >							expr_type;
+  return XprMatrix<expr_type, Rows1, Cols2>(expr_type(lhs, rhs.const_ref()));
+}
+
+
+template<unsigned Rows, unsigned Cols>
+inline
+XprMatrix<
+  XprMatrixTranspose<
+    MatrixConstReference<Rows, Cols, Cols, 1>
+  >,
+  Cols, Rows
+>
+trans(const Matrix<Rows, Cols>& rhs) {
+  typedef XprMatrixTranspose<
+    MatrixConstReference<Rows, Cols, Cols, 1>
+  >							expr_type;
+  return XprMatrix<expr_type, Cols, Rows>(expr_type(rhs.const_ref()));
+}
+
+
+/**
+ * Test driver
+ */
+int main()
+{
+  Matrix<3,2>		B;
+  Matrix<3,3>		D;
+
+  B(0,0) = -0.05;	B(0,1) =  0;
+  B(1,0) =  0;		B(1,1) =  0.05;
+  B(2,0) =  0.05;	B(2,1) = -0.05;
+
+  D(0,0) = 2000;	D(0,1) = 1000;		D(0,2) = 0;
+  D(1,0) = 1000;	D(1,1) = 2000;		D(1,2) = 0;
+  D(2,0) = 0;		D(2,1) = 0;		D(2,2) = 500;
+
+  printf("B = ");
+  B.print();
+  printf("D = ");
+  D.print();
+  printf("\n***********************************************\n");
+
+  Matrix<2,2>		K;
+
+  K = prod(prod(trans(B), D), B);
+
+  printf("Check: (equal prod(prod(trans(B), D), B)\n");
+  printf(" K = ");
+  K.print();
+}