mixingtypes.cpp File Reference
#include "main.h"

Macros

#define EIGEN_SCALAR_BINARY_OP_PLUGIN    { g_called |= (!internal::is_same<LhsScalar, RhsScalar>::value); }
 
#define VERIFY_MIX_SCALAR(XPR, REF)
 

Functions

template<int SizeAtCompileType>
void mixingtypes (int size=SizeAtCompileType)
 
 EIGEN_DECLARE_TEST (mixingtypes)
 

Variables

static bool g_called
 

Macro Definition Documentation

◆ EIGEN_SCALAR_BINARY_OP_PLUGIN

#define EIGEN_SCALAR_BINARY_OP_PLUGIN    { g_called |= (!internal::is_same<LhsScalar, RhsScalar>::value); }

◆ VERIFY_MIX_SCALAR

#define VERIFY_MIX_SCALAR (   XPR,
  REF 
)
Value:
g_called = false; \
VERIFY_IS_APPROX(XPR, REF); \
VERIFY(g_called&& #XPR " not properly optimized");
static bool g_called
Definition: mixingtypes.cpp:34

Function Documentation

◆ EIGEN_DECLARE_TEST()

EIGEN_DECLARE_TEST ( mixingtypes  )
295  {
296  g_called = false; // Silence -Wunneeded-internal-declaration.
297  for (int i = 0; i < g_repeat; i++) {
298  CALL_SUBTEST_1(mixingtypes<3>());
299  CALL_SUBTEST_2(mixingtypes<4>());
300  CALL_SUBTEST_3(mixingtypes<Dynamic>(internal::random<int>(1, EIGEN_TEST_MAX_SIZE)));
301 
302  CALL_SUBTEST_4(mixingtypes<3>());
303  CALL_SUBTEST_5(mixingtypes<4>());
304  CALL_SUBTEST_6(mixingtypes<Dynamic>(internal::random<int>(1, EIGEN_TEST_MAX_SIZE)));
305  }
306 }
int i
Definition: BiCGSTAB_step_by_step.cpp:9
#define EIGEN_TEST_MAX_SIZE
Definition: boostmultiprec.cpp:16
static int g_repeat
Definition: main.h:191
#define CALL_SUBTEST_6(FUNC)
Definition: split_test_helper.h:34
#define CALL_SUBTEST_3(FUNC)
Definition: split_test_helper.h:16
#define CALL_SUBTEST_1(FUNC)
Definition: split_test_helper.h:4
#define CALL_SUBTEST_5(FUNC)
Definition: split_test_helper.h:28
#define CALL_SUBTEST_2(FUNC)
Definition: split_test_helper.h:10
#define CALL_SUBTEST_4(FUNC)
Definition: split_test_helper.h:22

References CALL_SUBTEST_1, CALL_SUBTEST_2, CALL_SUBTEST_3, CALL_SUBTEST_4, CALL_SUBTEST_5, CALL_SUBTEST_6, EIGEN_TEST_MAX_SIZE, g_called, Eigen::g_repeat, and i.

◆ mixingtypes()

template<int SizeAtCompileType>
void mixingtypes ( int  size = SizeAtCompileType)
48  {
49  typedef std::complex<float> CF;
50  typedef std::complex<double> CD;
53  typedef Matrix<std::complex<float>, SizeAtCompileType, SizeAtCompileType> Mat_cf;
54  typedef Matrix<std::complex<double>, SizeAtCompileType, SizeAtCompileType> Mat_cd;
57  typedef Matrix<std::complex<float>, SizeAtCompileType, 1> Vec_cf;
58  typedef Matrix<std::complex<double>, SizeAtCompileType, 1> Vec_cd;
59 
60  Mat_f mf = Mat_f::Random(size, size);
61  Mat_d md = mf.template cast<double>();
62  // Mat_d rd = md;
63  Mat_cf mcf = Mat_cf::Random(size, size);
64  Mat_cd mcd = mcf.template cast<complex<double> >();
65  Mat_cd rcd = mcd;
66  Vec_f vf = Vec_f::Random(size, 1);
67  Vec_d vd = vf.template cast<double>();
68  Vec_cf vcf = Vec_cf::Random(size, 1);
69  Vec_cd vcd = vcf.template cast<complex<double> >();
70  float sf = internal::random<float>();
71  double sd = internal::random<double>();
72  complex<float> scf = internal::random<complex<float> >();
73  complex<double> scd = internal::random<complex<double> >();
74 
75  mf + mf;
76 
79 
80  while (std::abs(sf) < epsf) sf = internal::random<float>();
81  while (std::abs(sd) < epsd) sd = internal::random<double>();
82  while (std::abs(scf) < epsf) scf = internal::random<CF>();
83  while (std::abs(scd) < epsd) scd = internal::random<CD>();
84 
85  // check scalar products
86  VERIFY_MIX_SCALAR(vcf * sf, vcf * complex<float>(sf));
87  VERIFY_MIX_SCALAR(sd * vcd, complex<double>(sd) * vcd);
88  VERIFY_MIX_SCALAR(vf * scf, vf.template cast<complex<float> >() * scf);
89  VERIFY_MIX_SCALAR(scd * vd, scd * vd.template cast<complex<double> >());
90 
91  VERIFY_MIX_SCALAR(vcf * 2, vcf * complex<float>(2));
92  VERIFY_MIX_SCALAR(vcf * 2.1, vcf * complex<float>(2.1));
93  VERIFY_MIX_SCALAR(2 * vcf, vcf * complex<float>(2));
94  VERIFY_MIX_SCALAR(2.1 * vcf, vcf * complex<float>(2.1));
95 
96  // check scalar quotients
97  VERIFY_MIX_SCALAR(vcf / sf, vcf / complex<float>(sf));
98  VERIFY_MIX_SCALAR(vf / scf, vf.template cast<complex<float> >() / scf);
99  VERIFY_MIX_SCALAR(vf.array() / scf, vf.template cast<complex<float> >().array() / scf);
100  VERIFY_MIX_SCALAR(scd / vd.array(), scd / vd.template cast<complex<double> >().array());
101 
102  // check scalar increment
103  VERIFY_MIX_SCALAR(vcf.array() + sf, vcf.array() + complex<float>(sf));
104  VERIFY_MIX_SCALAR(sd + vcd.array(), complex<double>(sd) + vcd.array());
105  VERIFY_MIX_SCALAR(vf.array() + scf, vf.template cast<complex<float> >().array() + scf);
106  VERIFY_MIX_SCALAR(scd + vd.array(), scd + vd.template cast<complex<double> >().array());
107 
108  // check scalar subtractions
109  VERIFY_MIX_SCALAR(vcf.array() - sf, vcf.array() - complex<float>(sf));
110  VERIFY_MIX_SCALAR(sd - vcd.array(), complex<double>(sd) - vcd.array());
111  VERIFY_MIX_SCALAR(vf.array() - scf, vf.template cast<complex<float> >().array() - scf);
112  VERIFY_MIX_SCALAR(scd - vd.array(), scd - vd.template cast<complex<double> >().array());
113 
114  // check scalar powers
115  // NOTE: scalar exponents use a unary op.
116  VERIFY_IS_APPROX(pow(vcf.array(), sf), Eigen::pow(vcf.array(), complex<float>(sf)));
117  VERIFY_IS_APPROX(vcf.array().pow(sf), Eigen::pow(vcf.array(), complex<float>(sf)));
118  VERIFY_MIX_SCALAR(pow(sd, vcd.array()), Eigen::pow(complex<double>(sd), vcd.array()));
119  VERIFY_IS_APPROX(Eigen::pow(vf.array(), scf), Eigen::pow(vf.template cast<complex<float> >().array(), scf));
120  VERIFY_IS_APPROX(vf.array().pow(scf), Eigen::pow(vf.template cast<complex<float> >().array(), scf));
121  VERIFY_MIX_SCALAR(Eigen::pow(scd, vd.array()), Eigen::pow(scd, vd.template cast<complex<double> >().array()));
122 
123  // check dot product
124  vf.dot(vf);
125  VERIFY_IS_APPROX(vcf.dot(vf), vcf.dot(vf.template cast<complex<float> >()));
126 
127  // check diagonal product
128  VERIFY_IS_APPROX(vf.asDiagonal() * mcf, vf.template cast<complex<float> >().asDiagonal() * mcf);
129  VERIFY_IS_APPROX(vcd.asDiagonal() * md, vcd.asDiagonal() * md.template cast<complex<double> >());
130  VERIFY_IS_APPROX(mcf * vf.asDiagonal(), mcf * vf.template cast<complex<float> >().asDiagonal());
131  VERIFY_IS_APPROX(md * vcd.asDiagonal(), md.template cast<complex<double> >() * vcd.asDiagonal());
132 
133  // check inner product
134  VERIFY_IS_APPROX((vf.transpose() * vcf).value(), (vf.template cast<complex<float> >().transpose() * vcf).value());
135 
136  // check outer product
137  VERIFY_IS_APPROX((vf * vcf.transpose()).eval(), (vf.template cast<complex<float> >() * vcf.transpose()).eval());
138 
139  // coeff wise product
140 
141  VERIFY_IS_APPROX((vf * vcf.transpose()).eval(), (vf.template cast<complex<float> >() * vcf.transpose()).eval());
142 
143  Mat_cd mcd2 = mcd;
144  VERIFY_IS_APPROX(mcd.array() *= md.array(), mcd2.array() *= md.array().template cast<std::complex<double> >());
145 
146  // check matrix-matrix products
147  VERIFY_IS_APPROX(sd * md * mcd, (sd * md).template cast<CD>().eval() * mcd);
148  VERIFY_IS_APPROX(sd * mcd * md, sd * mcd * md.template cast<CD>());
149  VERIFY_IS_APPROX(scd * md * mcd, scd * md.template cast<CD>().eval() * mcd);
150  VERIFY_IS_APPROX(scd * mcd * md, scd * mcd * md.template cast<CD>());
151 
152  VERIFY_IS_APPROX(sf * mf * mcf, sf * mf.template cast<CF>() * mcf);
153  VERIFY_IS_APPROX(sf * mcf * mf, sf * mcf * mf.template cast<CF>());
154  VERIFY_IS_APPROX(scf * mf * mcf, scf * mf.template cast<CF>() * mcf);
155  VERIFY_IS_APPROX(scf * mcf * mf, scf * mcf * mf.template cast<CF>());
156 
157  VERIFY_IS_APPROX(sd * md.adjoint() * mcd, (sd * md).template cast<CD>().eval().adjoint() * mcd);
158  VERIFY_IS_APPROX(sd * mcd.adjoint() * md, sd * mcd.adjoint() * md.template cast<CD>());
159  VERIFY_IS_APPROX(sd * md.adjoint() * mcd.adjoint(), (sd * md).template cast<CD>().eval().adjoint() * mcd.adjoint());
160  VERIFY_IS_APPROX(sd * mcd.adjoint() * md.adjoint(), sd * mcd.adjoint() * md.template cast<CD>().adjoint());
161  VERIFY_IS_APPROX(sd * md * mcd.adjoint(), (sd * md).template cast<CD>().eval() * mcd.adjoint());
162  VERIFY_IS_APPROX(sd * mcd * md.adjoint(), sd * mcd * md.template cast<CD>().adjoint());
163 
164  VERIFY_IS_APPROX(sf * mf.adjoint() * mcf, (sf * mf).template cast<CF>().eval().adjoint() * mcf);
165  VERIFY_IS_APPROX(sf * mcf.adjoint() * mf, sf * mcf.adjoint() * mf.template cast<CF>());
166  VERIFY_IS_APPROX(sf * mf.adjoint() * mcf.adjoint(), (sf * mf).template cast<CF>().eval().adjoint() * mcf.adjoint());
167  VERIFY_IS_APPROX(sf * mcf.adjoint() * mf.adjoint(), sf * mcf.adjoint() * mf.template cast<CF>().adjoint());
168  VERIFY_IS_APPROX(sf * mf * mcf.adjoint(), (sf * mf).template cast<CF>().eval() * mcf.adjoint());
169  VERIFY_IS_APPROX(sf * mcf * mf.adjoint(), sf * mcf * mf.template cast<CF>().adjoint());
170 
171  VERIFY_IS_APPROX(sf * mf * vcf, (sf * mf).template cast<CF>().eval() * vcf);
172  VERIFY_IS_APPROX(scf * mf * vcf, (scf * mf.template cast<CF>()).eval() * vcf);
173  VERIFY_IS_APPROX(sf * mcf * vf, sf * mcf * vf.template cast<CF>());
174  VERIFY_IS_APPROX(scf * mcf * vf, scf * mcf * vf.template cast<CF>());
175 
176  VERIFY_IS_APPROX(sf * vcf.adjoint() * mf, sf * vcf.adjoint() * mf.template cast<CF>().eval());
177  VERIFY_IS_APPROX(scf * vcf.adjoint() * mf, scf * vcf.adjoint() * mf.template cast<CF>().eval());
178  VERIFY_IS_APPROX(sf * vf.adjoint() * mcf, sf * vf.adjoint().template cast<CF>().eval() * mcf);
179  VERIFY_IS_APPROX(scf * vf.adjoint() * mcf, scf * vf.adjoint().template cast<CF>().eval() * mcf);
180 
181  VERIFY_IS_APPROX(sd * md * vcd, (sd * md).template cast<CD>().eval() * vcd);
182  VERIFY_IS_APPROX(scd * md * vcd, (scd * md.template cast<CD>()).eval() * vcd);
183  VERIFY_IS_APPROX(sd * mcd * vd, sd * mcd * vd.template cast<CD>().eval());
184  VERIFY_IS_APPROX(scd * mcd * vd, scd * mcd * vd.template cast<CD>().eval());
185 
186  VERIFY_IS_APPROX(sd * vcd.adjoint() * md, sd * vcd.adjoint() * md.template cast<CD>().eval());
187  VERIFY_IS_APPROX(scd * vcd.adjoint() * md, scd * vcd.adjoint() * md.template cast<CD>().eval());
188  VERIFY_IS_APPROX(sd * vd.adjoint() * mcd, sd * vd.adjoint().template cast<CD>().eval() * mcd);
189  VERIFY_IS_APPROX(scd * vd.adjoint() * mcd, scd * vd.adjoint().template cast<CD>().eval() * mcd);
190 
191  VERIFY_IS_APPROX(sd * vcd.adjoint() * md.template triangularView<Upper>(),
192  sd * vcd.adjoint() * md.template cast<CD>().eval().template triangularView<Upper>());
193  VERIFY_IS_APPROX(scd * vcd.adjoint() * md.template triangularView<Lower>(),
194  scd * vcd.adjoint() * md.template cast<CD>().eval().template triangularView<Lower>());
195  VERIFY_IS_APPROX(sd * vcd.adjoint() * md.transpose().template triangularView<Upper>(),
196  sd * vcd.adjoint() * md.transpose().template cast<CD>().eval().template triangularView<Upper>());
197  VERIFY_IS_APPROX(scd * vcd.adjoint() * md.transpose().template triangularView<Lower>(),
198  scd * vcd.adjoint() * md.transpose().template cast<CD>().eval().template triangularView<Lower>());
199  VERIFY_IS_APPROX(sd * vd.adjoint() * mcd.template triangularView<Lower>(),
200  sd * vd.adjoint().template cast<CD>().eval() * mcd.template triangularView<Lower>());
201  VERIFY_IS_APPROX(scd * vd.adjoint() * mcd.template triangularView<Upper>(),
202  scd * vd.adjoint().template cast<CD>().eval() * mcd.template triangularView<Upper>());
203  VERIFY_IS_APPROX(sd * vd.adjoint() * mcd.transpose().template triangularView<Lower>(),
204  sd * vd.adjoint().template cast<CD>().eval() * mcd.transpose().template triangularView<Lower>());
205  VERIFY_IS_APPROX(scd * vd.adjoint() * mcd.transpose().template triangularView<Upper>(),
206  scd * vd.adjoint().template cast<CD>().eval() * mcd.transpose().template triangularView<Upper>());
207 
208  // Not supported yet: trmm
209  // VERIFY_IS_APPROX(sd*mcd*md.template triangularView<Lower>(), sd*mcd*md.template cast<CD>().eval().template
210  // triangularView<Lower>()); VERIFY_IS_APPROX(scd*mcd*md.template triangularView<Upper>(), scd*mcd*md.template
211  // cast<CD>().eval().template triangularView<Upper>()); VERIFY_IS_APPROX(sd*md*mcd.template triangularView<Lower>(),
212  // sd*md.template cast<CD>().eval()*mcd.template triangularView<Lower>()); VERIFY_IS_APPROX(scd*md*mcd.template
213  // triangularView<Upper>(), scd*md.template cast<CD>().eval()*mcd.template triangularView<Upper>());
214 
215  // Not supported yet: symv
216  // VERIFY_IS_APPROX(sd*vcd.adjoint()*md.template selfadjointView<Upper>(), sd*vcd.adjoint()*md.template
217  // cast<CD>().eval().template selfadjointView<Upper>()); VERIFY_IS_APPROX(scd*vcd.adjoint()*md.template
218  // selfadjointView<Lower>(), scd*vcd.adjoint()*md.template cast<CD>().eval().template selfadjointView<Lower>());
219  // VERIFY_IS_APPROX(sd*vd.adjoint()*mcd.template selfadjointView<Lower>(), sd*vd.adjoint().template
220  // cast<CD>().eval()*mcd.template selfadjointView<Lower>()); VERIFY_IS_APPROX(scd*vd.adjoint()*mcd.template
221  // selfadjointView<Upper>(), scd*vd.adjoint().template cast<CD>().eval()*mcd.template selfadjointView<Upper>());
222 
223  // Not supported yet: symm
224  // VERIFY_IS_APPROX(sd*vcd.adjoint()*md.template selfadjointView<Upper>(), sd*vcd.adjoint()*md.template
225  // cast<CD>().eval().template selfadjointView<Upper>()); VERIFY_IS_APPROX(scd*vcd.adjoint()*md.template
226  // selfadjointView<Upper>(), scd*vcd.adjoint()*md.template cast<CD>().eval().template selfadjointView<Upper>());
227  // VERIFY_IS_APPROX(sd*vd.adjoint()*mcd.template selfadjointView<Upper>(), sd*vd.adjoint().template
228  // cast<CD>().eval()*mcd.template selfadjointView<Upper>()); VERIFY_IS_APPROX(scd*vd.adjoint()*mcd.template
229  // selfadjointView<Upper>(), scd*vd.adjoint().template cast<CD>().eval()*mcd.template selfadjointView<Upper>());
230 
231  rcd.setZero();
232  VERIFY_IS_APPROX(Mat_cd(rcd.template triangularView<Upper>() = sd * mcd * md),
233  Mat_cd((sd * mcd * md.template cast<CD>().eval()).template triangularView<Upper>()));
234  VERIFY_IS_APPROX(Mat_cd(rcd.template triangularView<Upper>() = sd * md * mcd),
235  Mat_cd((sd * md.template cast<CD>().eval() * mcd).template triangularView<Upper>()));
236  VERIFY_IS_APPROX(Mat_cd(rcd.template triangularView<Upper>() = scd * mcd * md),
237  Mat_cd((scd * mcd * md.template cast<CD>().eval()).template triangularView<Upper>()));
238  VERIFY_IS_APPROX(Mat_cd(rcd.template triangularView<Upper>() = scd * md * mcd),
239  Mat_cd((scd * md.template cast<CD>().eval() * mcd).template triangularView<Upper>()));
240 
241  VERIFY_IS_APPROX(md.array() * mcd.array(), md.template cast<CD>().eval().array() * mcd.array());
242  VERIFY_IS_APPROX(mcd.array() * md.array(), mcd.array() * md.template cast<CD>().eval().array());
243 
244  VERIFY_IS_APPROX(md.array() + mcd.array(), md.template cast<CD>().eval().array() + mcd.array());
245  VERIFY_IS_APPROX(mcd.array() + md.array(), mcd.array() + md.template cast<CD>().eval().array());
246 
247  VERIFY_IS_APPROX(md.array() - mcd.array(), md.template cast<CD>().eval().array() - mcd.array());
248  VERIFY_IS_APPROX(mcd.array() - md.array(), mcd.array() - md.template cast<CD>().eval().array());
249 
250  if (mcd.array().abs().minCoeff() > epsd) {
251  VERIFY_IS_APPROX(md.array() / mcd.array(), md.template cast<CD>().eval().array() / mcd.array());
252  }
253  if (md.array().abs().minCoeff() > epsd) {
254  VERIFY_IS_APPROX(mcd.array() / md.array(), mcd.array() / md.template cast<CD>().eval().array());
255  }
256 
257  if (md.array().abs().minCoeff() > epsd || mcd.array().abs().minCoeff() > epsd) {
258  VERIFY_IS_APPROX(md.array().pow(mcd.array()), md.template cast<CD>().eval().array().pow(mcd.array()));
259  VERIFY_IS_APPROX(mcd.array().pow(md.array()), mcd.array().pow(md.template cast<CD>().eval().array()));
260 
261  VERIFY_IS_APPROX(pow(md.array(), mcd.array()), md.template cast<CD>().eval().array().pow(mcd.array()));
262  VERIFY_IS_APPROX(pow(mcd.array(), md.array()), mcd.array().pow(md.template cast<CD>().eval().array()));
263  }
264 
265  rcd = mcd;
266  VERIFY_IS_APPROX(rcd = md, md.template cast<CD>().eval());
267  rcd = mcd;
268  VERIFY_IS_APPROX(rcd += md, mcd + md.template cast<CD>().eval());
269  rcd = mcd;
270  VERIFY_IS_APPROX(rcd -= md, mcd - md.template cast<CD>().eval());
271  rcd = mcd;
272  VERIFY_IS_APPROX(rcd.array() *= md.array(), mcd.array() * md.template cast<CD>().eval().array());
273  rcd = mcd;
274  if (md.array().abs().minCoeff() > epsd) {
275  VERIFY_IS_APPROX(rcd.array() /= md.array(), mcd.array() / md.template cast<CD>().eval().array());
276  }
277 
278  rcd = mcd;
279  VERIFY_IS_APPROX(rcd.noalias() += md + mcd * md,
280  mcd + (md.template cast<CD>().eval()) + mcd * (md.template cast<CD>().eval()));
281 
282  VERIFY_IS_APPROX(rcd.noalias() = md * md, ((md * md).eval().template cast<CD>()));
283  rcd = mcd;
284  VERIFY_IS_APPROX(rcd.noalias() += md * md, mcd + ((md * md).eval().template cast<CD>()));
285  rcd = mcd;
286  VERIFY_IS_APPROX(rcd.noalias() -= md * md, mcd - ((md * md).eval().template cast<CD>()));
287 
288  VERIFY_IS_APPROX(rcd.noalias() = mcd + md * md, mcd + ((md * md).eval().template cast<CD>()));
289  rcd = mcd;
290  VERIFY_IS_APPROX(rcd.noalias() += mcd + md * md, mcd + mcd + ((md * md).eval().template cast<CD>()));
291  rcd = mcd;
292  VERIFY_IS_APPROX(rcd.noalias() -= mcd + md * md, -((md * md).eval().template cast<CD>()));
293 }
AnnoyingScalar abs(const AnnoyingScalar &x)
Definition: AnnoyingScalar.h:135
AnnoyingScalar sqrt(const AnnoyingScalar &x)
Definition: AnnoyingScalar.h:134
#define EIGEN_EMPTY
Definition: Macros.h:1081
Matrix2f mf
Definition: MatrixBase_cast.cpp:2
Matrix2d md
Definition: MatrixBase_cast.cpp:1
Scalar Scalar int size
Definition: benchVecAdd.cpp:17
EIGEN_DEVICE_FUNC const GlobalUnaryPowReturnType< Derived, ScalarExponent > pow(const Eigen::ArrayBase< Derived > &x, const ScalarExponent &exponent)
Definition: GlobalFunctions.h:137
The matrix class, also used for vectors and row-vectors.
Definition: Eigen/Eigen/src/Core/Matrix.h:186
#define min(a, b)
Definition: datatypes.h:22
#define VERIFY_IS_APPROX(a, b)
Definition: integer_types.cpp:13
#define VERIFY_MIX_SCALAR(XPR, REF)
Definition: mixingtypes.cpp:42
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC bfloat16 pow(const bfloat16 &a, const bfloat16 &b)
Definition: BFloat16.h:625
EIGEN_DEVICE_FUNC NewType cast(const OldType &x)
Definition: MathFunctions.h:362
internal::nested_eval< T, 1 >::type eval(const T &xpr)
Definition: sparse_permutations.cpp:47

References abs(), Eigen::internal::cast(), EIGEN_EMPTY, eval(), md, mf, min, Eigen::bfloat16_impl::pow(), size, sqrt(), VERIFY_IS_APPROX, and VERIFY_MIX_SCALAR.

Variable Documentation

◆ g_called

bool g_called
static

Referenced by EIGEN_DECLARE_TEST().