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1 
2 #include "main.h"
3 
4 namespace Eigen {
5 
6   template<typename Lhs,typename Rhs>
7   const Product<Lhs,Rhs>
prod(const Lhs & lhs,const Rhs & rhs)8   prod(const Lhs& lhs, const Rhs& rhs)
9   {
10     return Product<Lhs,Rhs>(lhs,rhs);
11   }
12 
13   template<typename Lhs,typename Rhs>
14   const Product<Lhs,Rhs,LazyProduct>
lazyprod(const Lhs & lhs,const Rhs & rhs)15   lazyprod(const Lhs& lhs, const Rhs& rhs)
16   {
17     return Product<Lhs,Rhs,LazyProduct>(lhs,rhs);
18   }
19 
20   template<typename DstXprType, typename SrcXprType>
21   EIGEN_STRONG_INLINE
copy_using_evaluator(const EigenBase<DstXprType> & dst,const SrcXprType & src)22   DstXprType& copy_using_evaluator(const EigenBase<DstXprType> &dst, const SrcXprType &src)
23   {
24     call_assignment(dst.const_cast_derived(), src.derived(), internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar>());
25     return dst.const_cast_derived();
26   }
27 
28   template<typename DstXprType, template <typename> class StorageBase, typename SrcXprType>
29   EIGEN_STRONG_INLINE
copy_using_evaluator(const NoAlias<DstXprType,StorageBase> & dst,const SrcXprType & src)30   const DstXprType& copy_using_evaluator(const NoAlias<DstXprType, StorageBase>& dst, const SrcXprType &src)
31   {
32     call_assignment(dst, src.derived(), internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar>());
33     return dst.expression();
34   }
35 
36   template<typename DstXprType, typename SrcXprType>
37   EIGEN_STRONG_INLINE
copy_using_evaluator(const PlainObjectBase<DstXprType> & dst,const SrcXprType & src)38   DstXprType& copy_using_evaluator(const PlainObjectBase<DstXprType> &dst, const SrcXprType &src)
39   {
40     #ifdef EIGEN_NO_AUTOMATIC_RESIZING
41     eigen_assert((dst.size()==0 || (IsVectorAtCompileTime ? (dst.size() == src.size())
42                                                           : (dst.rows() == src.rows() && dst.cols() == src.cols())))
43                 && "Size mismatch. Automatic resizing is disabled because EIGEN_NO_AUTOMATIC_RESIZING is defined");
44   #else
45     dst.const_cast_derived().resizeLike(src.derived());
46   #endif
47 
48     call_assignment(dst.const_cast_derived(), src.derived(), internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar>());
49     return dst.const_cast_derived();
50   }
51 
52   template<typename DstXprType, typename SrcXprType>
add_assign_using_evaluator(const DstXprType & dst,const SrcXprType & src)53   void add_assign_using_evaluator(const DstXprType& dst, const SrcXprType& src)
54   {
55     typedef typename DstXprType::Scalar Scalar;
56     call_assignment(const_cast<DstXprType&>(dst), src.derived(), internal::add_assign_op<Scalar,typename SrcXprType::Scalar>());
57   }
58 
59   template<typename DstXprType, typename SrcXprType>
subtract_assign_using_evaluator(const DstXprType & dst,const SrcXprType & src)60   void subtract_assign_using_evaluator(const DstXprType& dst, const SrcXprType& src)
61   {
62     typedef typename DstXprType::Scalar Scalar;
63     call_assignment(const_cast<DstXprType&>(dst), src.derived(), internal::sub_assign_op<Scalar,typename SrcXprType::Scalar>());
64   }
65 
66   template<typename DstXprType, typename SrcXprType>
multiply_assign_using_evaluator(const DstXprType & dst,const SrcXprType & src)67   void multiply_assign_using_evaluator(const DstXprType& dst, const SrcXprType& src)
68   {
69     typedef typename DstXprType::Scalar Scalar;
70     call_assignment(dst.const_cast_derived(), src.derived(), internal::mul_assign_op<Scalar,typename SrcXprType::Scalar>());
71   }
72 
73   template<typename DstXprType, typename SrcXprType>
divide_assign_using_evaluator(const DstXprType & dst,const SrcXprType & src)74   void divide_assign_using_evaluator(const DstXprType& dst, const SrcXprType& src)
75   {
76     typedef typename DstXprType::Scalar Scalar;
77     call_assignment(dst.const_cast_derived(), src.derived(), internal::div_assign_op<Scalar,typename SrcXprType::Scalar>());
78   }
79 
80   template<typename DstXprType, typename SrcXprType>
swap_using_evaluator(const DstXprType & dst,const SrcXprType & src)81   void swap_using_evaluator(const DstXprType& dst, const SrcXprType& src)
82   {
83     typedef typename DstXprType::Scalar Scalar;
84     call_assignment(dst.const_cast_derived(), src.const_cast_derived(), internal::swap_assign_op<Scalar>());
85   }
86 
87   namespace internal {
88     template<typename Dst, template <typename> class StorageBase, typename Src, typename Func>
call_assignment(const NoAlias<Dst,StorageBase> & dst,const Src & src,const Func & func)89     EIGEN_DEVICE_FUNC void call_assignment(const NoAlias<Dst,StorageBase>& dst, const Src& src, const Func& func)
90     {
91       call_assignment_no_alias(dst.expression(), src, func);
92     }
93   }
94 
95 }
96 
get_cost(const XprType &)97 template<typename XprType> long get_cost(const XprType& ) { return Eigen::internal::evaluator<XprType>::CoeffReadCost; }
98 
99 using namespace std;
100 
101 #define VERIFY_IS_APPROX_EVALUATOR(DEST,EXPR) VERIFY_IS_APPROX(copy_using_evaluator(DEST,(EXPR)), (EXPR).eval());
102 #define VERIFY_IS_APPROX_EVALUATOR2(DEST,EXPR,REF) VERIFY_IS_APPROX(copy_using_evaluator(DEST,(EXPR)), (REF).eval());
103 
test_evaluators()104 void test_evaluators()
105 {
106   // Testing Matrix evaluator and Transpose
107   Vector2d v = Vector2d::Random();
108   const Vector2d v_const(v);
109   Vector2d v2;
110   RowVector2d w;
111 
112   VERIFY_IS_APPROX_EVALUATOR(v2, v);
113   VERIFY_IS_APPROX_EVALUATOR(v2, v_const);
114 
115   // Testing Transpose
116   VERIFY_IS_APPROX_EVALUATOR(w, v.transpose()); // Transpose as rvalue
117   VERIFY_IS_APPROX_EVALUATOR(w, v_const.transpose());
118 
119   copy_using_evaluator(w.transpose(), v); // Transpose as lvalue
120   VERIFY_IS_APPROX(w,v.transpose().eval());
121 
122   copy_using_evaluator(w.transpose(), v_const);
123   VERIFY_IS_APPROX(w,v_const.transpose().eval());
124 
125   // Testing Array evaluator
126   {
127     ArrayXXf a(2,3);
128     ArrayXXf b(3,2);
129     a << 1,2,3, 4,5,6;
130     const ArrayXXf a_const(a);
131 
132     VERIFY_IS_APPROX_EVALUATOR(b, a.transpose());
133 
134     VERIFY_IS_APPROX_EVALUATOR(b, a_const.transpose());
135 
136     // Testing CwiseNullaryOp evaluator
137     copy_using_evaluator(w, RowVector2d::Random());
138     VERIFY((w.array() >= -1).all() && (w.array() <= 1).all()); // not easy to test ...
139 
140     VERIFY_IS_APPROX_EVALUATOR(w, RowVector2d::Zero());
141 
142     VERIFY_IS_APPROX_EVALUATOR(w, RowVector2d::Constant(3));
143 
144     // mix CwiseNullaryOp and transpose
145     VERIFY_IS_APPROX_EVALUATOR(w, Vector2d::Zero().transpose());
146   }
147 
148   {
149     // test product expressions
150     int s = internal::random<int>(1,100);
151     MatrixXf a(s,s), b(s,s), c(s,s), d(s,s);
152     a.setRandom();
153     b.setRandom();
154     c.setRandom();
155     d.setRandom();
156     VERIFY_IS_APPROX_EVALUATOR(d, (a + b));
157     VERIFY_IS_APPROX_EVALUATOR(d, (a + b).transpose());
158     VERIFY_IS_APPROX_EVALUATOR2(d, prod(a,b), a*b);
159     VERIFY_IS_APPROX_EVALUATOR2(d.noalias(), prod(a,b), a*b);
160     VERIFY_IS_APPROX_EVALUATOR2(d, prod(a,b) + c, a*b + c);
161     VERIFY_IS_APPROX_EVALUATOR2(d, s * prod(a,b), s * a*b);
162     VERIFY_IS_APPROX_EVALUATOR2(d, prod(a,b).transpose(), (a*b).transpose());
163     VERIFY_IS_APPROX_EVALUATOR2(d, prod(a,b) + prod(b,c), a*b + b*c);
164 
165     // check that prod works even with aliasing present
166     c = a*a;
167     copy_using_evaluator(a, prod(a,a));
168     VERIFY_IS_APPROX(a,c);
169 
170     // check compound assignment of products
171     d = c;
172     add_assign_using_evaluator(c.noalias(), prod(a,b));
173     d.noalias() += a*b;
174     VERIFY_IS_APPROX(c, d);
175 
176     d = c;
177     subtract_assign_using_evaluator(c.noalias(), prod(a,b));
178     d.noalias() -= a*b;
179     VERIFY_IS_APPROX(c, d);
180   }
181 
182   {
183     // test product with all possible sizes
184     int s = internal::random<int>(1,100);
185     Matrix<float,      1,      1> m11, res11;  m11.setRandom(1,1);
186     Matrix<float,      1,      4> m14, res14;  m14.setRandom(1,4);
187     Matrix<float,      1,Dynamic> m1X, res1X;  m1X.setRandom(1,s);
188     Matrix<float,      4,      1> m41, res41;  m41.setRandom(4,1);
189     Matrix<float,      4,      4> m44, res44;  m44.setRandom(4,4);
190     Matrix<float,      4,Dynamic> m4X, res4X;  m4X.setRandom(4,s);
191     Matrix<float,Dynamic,      1> mX1, resX1;  mX1.setRandom(s,1);
192     Matrix<float,Dynamic,      4> mX4, resX4;  mX4.setRandom(s,4);
193     Matrix<float,Dynamic,Dynamic> mXX, resXX;  mXX.setRandom(s,s);
194 
195     VERIFY_IS_APPROX_EVALUATOR2(res11, prod(m11,m11), m11*m11);
196     VERIFY_IS_APPROX_EVALUATOR2(res11, prod(m14,m41), m14*m41);
197     VERIFY_IS_APPROX_EVALUATOR2(res11, prod(m1X,mX1), m1X*mX1);
198     VERIFY_IS_APPROX_EVALUATOR2(res14, prod(m11,m14), m11*m14);
199     VERIFY_IS_APPROX_EVALUATOR2(res14, prod(m14,m44), m14*m44);
200     VERIFY_IS_APPROX_EVALUATOR2(res14, prod(m1X,mX4), m1X*mX4);
201     VERIFY_IS_APPROX_EVALUATOR2(res1X, prod(m11,m1X), m11*m1X);
202     VERIFY_IS_APPROX_EVALUATOR2(res1X, prod(m14,m4X), m14*m4X);
203     VERIFY_IS_APPROX_EVALUATOR2(res1X, prod(m1X,mXX), m1X*mXX);
204     VERIFY_IS_APPROX_EVALUATOR2(res41, prod(m41,m11), m41*m11);
205     VERIFY_IS_APPROX_EVALUATOR2(res41, prod(m44,m41), m44*m41);
206     VERIFY_IS_APPROX_EVALUATOR2(res41, prod(m4X,mX1), m4X*mX1);
207     VERIFY_IS_APPROX_EVALUATOR2(res44, prod(m41,m14), m41*m14);
208     VERIFY_IS_APPROX_EVALUATOR2(res44, prod(m44,m44), m44*m44);
209     VERIFY_IS_APPROX_EVALUATOR2(res44, prod(m4X,mX4), m4X*mX4);
210     VERIFY_IS_APPROX_EVALUATOR2(res4X, prod(m41,m1X), m41*m1X);
211     VERIFY_IS_APPROX_EVALUATOR2(res4X, prod(m44,m4X), m44*m4X);
212     VERIFY_IS_APPROX_EVALUATOR2(res4X, prod(m4X,mXX), m4X*mXX);
213     VERIFY_IS_APPROX_EVALUATOR2(resX1, prod(mX1,m11), mX1*m11);
214     VERIFY_IS_APPROX_EVALUATOR2(resX1, prod(mX4,m41), mX4*m41);
215     VERIFY_IS_APPROX_EVALUATOR2(resX1, prod(mXX,mX1), mXX*mX1);
216     VERIFY_IS_APPROX_EVALUATOR2(resX4, prod(mX1,m14), mX1*m14);
217     VERIFY_IS_APPROX_EVALUATOR2(resX4, prod(mX4,m44), mX4*m44);
218     VERIFY_IS_APPROX_EVALUATOR2(resX4, prod(mXX,mX4), mXX*mX4);
219     VERIFY_IS_APPROX_EVALUATOR2(resXX, prod(mX1,m1X), mX1*m1X);
220     VERIFY_IS_APPROX_EVALUATOR2(resXX, prod(mX4,m4X), mX4*m4X);
221     VERIFY_IS_APPROX_EVALUATOR2(resXX, prod(mXX,mXX), mXX*mXX);
222   }
223 
224   {
225     ArrayXXf a(2,3);
226     ArrayXXf b(3,2);
227     a << 1,2,3, 4,5,6;
228     const ArrayXXf a_const(a);
229 
230     // this does not work because Random is eval-before-nested:
231     // copy_using_evaluator(w, Vector2d::Random().transpose());
232 
233     // test CwiseUnaryOp
234     VERIFY_IS_APPROX_EVALUATOR(v2, 3 * v);
235     VERIFY_IS_APPROX_EVALUATOR(w, (3 * v).transpose());
236     VERIFY_IS_APPROX_EVALUATOR(b, (a + 3).transpose());
237     VERIFY_IS_APPROX_EVALUATOR(b, (2 * a_const + 3).transpose());
238 
239     // test CwiseBinaryOp
240     VERIFY_IS_APPROX_EVALUATOR(v2, v + Vector2d::Ones());
241     VERIFY_IS_APPROX_EVALUATOR(w, (v + Vector2d::Ones()).transpose().cwiseProduct(RowVector2d::Constant(3)));
242 
243     // dynamic matrices and arrays
244     MatrixXd mat1(6,6), mat2(6,6);
245     VERIFY_IS_APPROX_EVALUATOR(mat1, MatrixXd::Identity(6,6));
246     VERIFY_IS_APPROX_EVALUATOR(mat2, mat1);
247     copy_using_evaluator(mat2.transpose(), mat1);
248     VERIFY_IS_APPROX(mat2.transpose(), mat1);
249 
250     ArrayXXd arr1(6,6), arr2(6,6);
251     VERIFY_IS_APPROX_EVALUATOR(arr1, ArrayXXd::Constant(6,6, 3.0));
252     VERIFY_IS_APPROX_EVALUATOR(arr2, arr1);
253 
254     // test automatic resizing
255     mat2.resize(3,3);
256     VERIFY_IS_APPROX_EVALUATOR(mat2, mat1);
257     arr2.resize(9,9);
258     VERIFY_IS_APPROX_EVALUATOR(arr2, arr1);
259 
260     // test direct traversal
261     Matrix3f m3;
262     Array33f a3;
263     VERIFY_IS_APPROX_EVALUATOR(m3, Matrix3f::Identity());  // matrix, nullary
264     // TODO: find a way to test direct traversal with array
265     VERIFY_IS_APPROX_EVALUATOR(m3.transpose(), Matrix3f::Identity().transpose());  // transpose
266     VERIFY_IS_APPROX_EVALUATOR(m3, 2 * Matrix3f::Identity());  // unary
267     VERIFY_IS_APPROX_EVALUATOR(m3, Matrix3f::Identity() + Matrix3f::Zero());  // binary
268     VERIFY_IS_APPROX_EVALUATOR(m3.block(0,0,2,2), Matrix3f::Identity().block(1,1,2,2));  // block
269 
270     // test linear traversal
271     VERIFY_IS_APPROX_EVALUATOR(m3, Matrix3f::Zero());  // matrix, nullary
272     VERIFY_IS_APPROX_EVALUATOR(a3, Array33f::Zero());  // array
273     VERIFY_IS_APPROX_EVALUATOR(m3.transpose(), Matrix3f::Zero().transpose());  // transpose
274     VERIFY_IS_APPROX_EVALUATOR(m3, 2 * Matrix3f::Zero());  // unary
275     VERIFY_IS_APPROX_EVALUATOR(m3, Matrix3f::Zero() + m3);  // binary
276 
277     // test inner vectorization
278     Matrix4f m4, m4src = Matrix4f::Random();
279     Array44f a4, a4src = Matrix4f::Random();
280     VERIFY_IS_APPROX_EVALUATOR(m4, m4src);  // matrix
281     VERIFY_IS_APPROX_EVALUATOR(a4, a4src);  // array
282     VERIFY_IS_APPROX_EVALUATOR(m4.transpose(), m4src.transpose());  // transpose
283     // TODO: find out why Matrix4f::Zero() does not allow inner vectorization
284     VERIFY_IS_APPROX_EVALUATOR(m4, 2 * m4src);  // unary
285     VERIFY_IS_APPROX_EVALUATOR(m4, m4src + m4src);  // binary
286 
287     // test linear vectorization
288     MatrixXf mX(6,6), mXsrc = MatrixXf::Random(6,6);
289     ArrayXXf aX(6,6), aXsrc = ArrayXXf::Random(6,6);
290     VERIFY_IS_APPROX_EVALUATOR(mX, mXsrc);  // matrix
291     VERIFY_IS_APPROX_EVALUATOR(aX, aXsrc);  // array
292     VERIFY_IS_APPROX_EVALUATOR(mX.transpose(), mXsrc.transpose());  // transpose
293     VERIFY_IS_APPROX_EVALUATOR(mX, MatrixXf::Zero(6,6));  // nullary
294     VERIFY_IS_APPROX_EVALUATOR(mX, 2 * mXsrc);  // unary
295     VERIFY_IS_APPROX_EVALUATOR(mX, mXsrc + mXsrc);  // binary
296 
297     // test blocks and slice vectorization
298     VERIFY_IS_APPROX_EVALUATOR(m4, (mXsrc.block<4,4>(1,0)));
299     VERIFY_IS_APPROX_EVALUATOR(aX, ArrayXXf::Constant(10, 10, 3.0).block(2, 3, 6, 6));
300 
301     Matrix4f m4ref = m4;
302     copy_using_evaluator(m4.block(1, 1, 2, 3), m3.bottomRows(2));
303     m4ref.block(1, 1, 2, 3) = m3.bottomRows(2);
304     VERIFY_IS_APPROX(m4, m4ref);
305 
306     mX.setIdentity(20,20);
307     MatrixXf mXref = MatrixXf::Identity(20,20);
308     mXsrc = MatrixXf::Random(9,12);
309     copy_using_evaluator(mX.block(4, 4, 9, 12), mXsrc);
310     mXref.block(4, 4, 9, 12) = mXsrc;
311     VERIFY_IS_APPROX(mX, mXref);
312 
313     // test Map
314     const float raw[3] = {1,2,3};
315     float buffer[3] = {0,0,0};
316     Vector3f v3;
317     Array3f a3f;
318     VERIFY_IS_APPROX_EVALUATOR(v3, Map<const Vector3f>(raw));
319     VERIFY_IS_APPROX_EVALUATOR(a3f, Map<const Array3f>(raw));
320     Vector3f::Map(buffer) = 2*v3;
321     VERIFY(buffer[0] == 2);
322     VERIFY(buffer[1] == 4);
323     VERIFY(buffer[2] == 6);
324 
325     // test CwiseUnaryView
326     mat1.setRandom();
327     mat2.setIdentity();
328     MatrixXcd matXcd(6,6), matXcd_ref(6,6);
329     copy_using_evaluator(matXcd.real(), mat1);
330     copy_using_evaluator(matXcd.imag(), mat2);
331     matXcd_ref.real() = mat1;
332     matXcd_ref.imag() = mat2;
333     VERIFY_IS_APPROX(matXcd, matXcd_ref);
334 
335     // test Select
336     VERIFY_IS_APPROX_EVALUATOR(aX, (aXsrc > 0).select(aXsrc, -aXsrc));
337 
338     // test Replicate
339     mXsrc = MatrixXf::Random(6, 6);
340     VectorXf vX = VectorXf::Random(6);
341     mX.resize(6, 6);
342     VERIFY_IS_APPROX_EVALUATOR(mX, mXsrc.colwise() + vX);
343     matXcd.resize(12, 12);
344     VERIFY_IS_APPROX_EVALUATOR(matXcd, matXcd_ref.replicate(2,2));
345     VERIFY_IS_APPROX_EVALUATOR(matXcd, (matXcd_ref.replicate<2,2>()));
346 
347     // test partial reductions
348     VectorXd vec1(6);
349     VERIFY_IS_APPROX_EVALUATOR(vec1, mat1.rowwise().sum());
350     VERIFY_IS_APPROX_EVALUATOR(vec1, mat1.colwise().sum().transpose());
351 
352     // test MatrixWrapper and ArrayWrapper
353     mat1.setRandom(6,6);
354     arr1.setRandom(6,6);
355     VERIFY_IS_APPROX_EVALUATOR(mat2, arr1.matrix());
356     VERIFY_IS_APPROX_EVALUATOR(arr2, mat1.array());
357     VERIFY_IS_APPROX_EVALUATOR(mat2, (arr1 + 2).matrix());
358     VERIFY_IS_APPROX_EVALUATOR(arr2, mat1.array() + 2);
359     mat2.array() = arr1 * arr1;
360     VERIFY_IS_APPROX(mat2, (arr1 * arr1).matrix());
361     arr2.matrix() = MatrixXd::Identity(6,6);
362     VERIFY_IS_APPROX(arr2, MatrixXd::Identity(6,6).array());
363 
364     // test Reverse
365     VERIFY_IS_APPROX_EVALUATOR(arr2, arr1.reverse());
366     VERIFY_IS_APPROX_EVALUATOR(arr2, arr1.colwise().reverse());
367     VERIFY_IS_APPROX_EVALUATOR(arr2, arr1.rowwise().reverse());
368     arr2.reverse() = arr1;
369     VERIFY_IS_APPROX(arr2, arr1.reverse());
370     mat2.array() = mat1.array().reverse();
371     VERIFY_IS_APPROX(mat2.array(), mat1.array().reverse());
372 
373     // test Diagonal
374     VERIFY_IS_APPROX_EVALUATOR(vec1, mat1.diagonal());
375     vec1.resize(5);
376     VERIFY_IS_APPROX_EVALUATOR(vec1, mat1.diagonal(1));
377     VERIFY_IS_APPROX_EVALUATOR(vec1, mat1.diagonal<-1>());
378     vec1.setRandom();
379 
380     mat2 = mat1;
381     copy_using_evaluator(mat1.diagonal(1), vec1);
382     mat2.diagonal(1) = vec1;
383     VERIFY_IS_APPROX(mat1, mat2);
384 
385     copy_using_evaluator(mat1.diagonal<-1>(), mat1.diagonal(1));
386     mat2.diagonal<-1>() = mat2.diagonal(1);
387     VERIFY_IS_APPROX(mat1, mat2);
388   }
389 
390   {
391     // test swapping
392     MatrixXd mat1, mat2, mat1ref, mat2ref;
393     mat1ref = mat1 = MatrixXd::Random(6, 6);
394     mat2ref = mat2 = 2 * mat1 + MatrixXd::Identity(6, 6);
395     swap_using_evaluator(mat1, mat2);
396     mat1ref.swap(mat2ref);
397     VERIFY_IS_APPROX(mat1, mat1ref);
398     VERIFY_IS_APPROX(mat2, mat2ref);
399 
400     swap_using_evaluator(mat1.block(0, 0, 3, 3), mat2.block(3, 3, 3, 3));
401     mat1ref.block(0, 0, 3, 3).swap(mat2ref.block(3, 3, 3, 3));
402     VERIFY_IS_APPROX(mat1, mat1ref);
403     VERIFY_IS_APPROX(mat2, mat2ref);
404 
405     swap_using_evaluator(mat1.row(2), mat2.col(3).transpose());
406     mat1.row(2).swap(mat2.col(3).transpose());
407     VERIFY_IS_APPROX(mat1, mat1ref);
408     VERIFY_IS_APPROX(mat2, mat2ref);
409   }
410 
411   {
412     // test compound assignment
413     const Matrix4d mat_const = Matrix4d::Random();
414     Matrix4d mat, mat_ref;
415     mat = mat_ref = Matrix4d::Identity();
416     add_assign_using_evaluator(mat, mat_const);
417     mat_ref += mat_const;
418     VERIFY_IS_APPROX(mat, mat_ref);
419 
420     subtract_assign_using_evaluator(mat.row(1), 2*mat.row(2));
421     mat_ref.row(1) -= 2*mat_ref.row(2);
422     VERIFY_IS_APPROX(mat, mat_ref);
423 
424     const ArrayXXf arr_const = ArrayXXf::Random(5,3);
425     ArrayXXf arr, arr_ref;
426     arr = arr_ref = ArrayXXf::Constant(5, 3, 0.5);
427     multiply_assign_using_evaluator(arr, arr_const);
428     arr_ref *= arr_const;
429     VERIFY_IS_APPROX(arr, arr_ref);
430 
431     divide_assign_using_evaluator(arr.row(1), arr.row(2) + 1);
432     arr_ref.row(1) /= (arr_ref.row(2) + 1);
433     VERIFY_IS_APPROX(arr, arr_ref);
434   }
435 
436   {
437     // test triangular shapes
438     MatrixXd A = MatrixXd::Random(6,6), B(6,6), C(6,6), D(6,6);
439     A.setRandom();B.setRandom();
440     VERIFY_IS_APPROX_EVALUATOR2(B, A.triangularView<Upper>(), MatrixXd(A.triangularView<Upper>()));
441 
442     A.setRandom();B.setRandom();
443     VERIFY_IS_APPROX_EVALUATOR2(B, A.triangularView<UnitLower>(), MatrixXd(A.triangularView<UnitLower>()));
444 
445     A.setRandom();B.setRandom();
446     VERIFY_IS_APPROX_EVALUATOR2(B, A.triangularView<UnitUpper>(), MatrixXd(A.triangularView<UnitUpper>()));
447 
448     A.setRandom();B.setRandom();
449     C = B; C.triangularView<Upper>() = A;
450     copy_using_evaluator(B.triangularView<Upper>(), A);
451     VERIFY(B.isApprox(C) && "copy_using_evaluator(B.triangularView<Upper>(), A)");
452 
453     A.setRandom();B.setRandom();
454     C = B; C.triangularView<Lower>() = A.triangularView<Lower>();
455     copy_using_evaluator(B.triangularView<Lower>(), A.triangularView<Lower>());
456     VERIFY(B.isApprox(C) && "copy_using_evaluator(B.triangularView<Lower>(), A.triangularView<Lower>())");
457 
458 
459     A.setRandom();B.setRandom();
460     C = B; C.triangularView<Lower>() = A.triangularView<Upper>().transpose();
461     copy_using_evaluator(B.triangularView<Lower>(), A.triangularView<Upper>().transpose());
462     VERIFY(B.isApprox(C) && "copy_using_evaluator(B.triangularView<Lower>(), A.triangularView<Lower>().transpose())");
463 
464 
465     A.setRandom();B.setRandom(); C = B; D = A;
466     C.triangularView<Upper>().swap(D.triangularView<Upper>());
467     swap_using_evaluator(B.triangularView<Upper>(), A.triangularView<Upper>());
468     VERIFY(B.isApprox(C) && "swap_using_evaluator(B.triangularView<Upper>(), A.triangularView<Upper>())");
469 
470 
471     VERIFY_IS_APPROX_EVALUATOR2(B, prod(A.triangularView<Upper>(),A), MatrixXd(A.triangularView<Upper>()*A));
472 
473     VERIFY_IS_APPROX_EVALUATOR2(B, prod(A.selfadjointView<Upper>(),A), MatrixXd(A.selfadjointView<Upper>()*A));
474   }
475 
476   {
477     // test diagonal shapes
478     VectorXd d = VectorXd::Random(6);
479     MatrixXd A = MatrixXd::Random(6,6), B(6,6);
480     A.setRandom();B.setRandom();
481 
482     VERIFY_IS_APPROX_EVALUATOR2(B, lazyprod(d.asDiagonal(),A), MatrixXd(d.asDiagonal()*A));
483     VERIFY_IS_APPROX_EVALUATOR2(B, lazyprod(A,d.asDiagonal()), MatrixXd(A*d.asDiagonal()));
484   }
485 
486   {
487     // test CoeffReadCost
488     Matrix4d a, b;
489     VERIFY_IS_EQUAL( get_cost(a), 1 );
490     VERIFY_IS_EQUAL( get_cost(a+b), 3);
491     VERIFY_IS_EQUAL( get_cost(2*a+b), 4);
492     VERIFY_IS_EQUAL( get_cost(a*b), 1);
493     VERIFY_IS_EQUAL( get_cost(a.lazyProduct(b)), 15);
494     VERIFY_IS_EQUAL( get_cost(a*(a*b)), 1);
495     VERIFY_IS_EQUAL( get_cost(a.lazyProduct(a*b)), 15);
496     VERIFY_IS_EQUAL( get_cost(a*(a+b)), 1);
497     VERIFY_IS_EQUAL( get_cost(a.lazyProduct(a+b)), 15);
498   }
499 }
500