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Armadillo_example
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mat_mul_cx.cpp

mat_mul_cx.cpp 16 KB
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  1. // Copyright 2015 Conrad Sanderson (http://conradsanderson.id.au)
    2. 

  2. // Copyright 2015 National ICT Australia (NICTA)
    3. 

  3. // 
    4. 

  4. // Licensed under the Apache License, Version 2.0 (the "License");
    5. 

  5. // you may not use this file except in compliance with the License.
    6. 

  6. // You may obtain a copy of the License at
    7. 

  7. // http://www.apache.org/licenses/LICENSE-2.0
    8. 

  8. // 
    9. 

  9. // Unless required by applicable law or agreed to in writing, software
    10. 

  10. // distributed under the License is distributed on an "AS IS" BASIS,
    11. 

  11. // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    12. 

  12. // See the License for the specific language governing permissions and
    13. 

  13. // limitations under the License.
    14. 

  14. // ------------------------------------------------------------------------
    15. 

  15. 

  16. 

  17. #include <armadillo>
    18. 

  18. #include "catch.hpp"
    19. 

  19. 

  20. using namespace arma;
    21. 

  21. 

  22. 

  23. TEST_CASE("mat_mul_cx_1")
    24. 

  24.   {
    25. 

  25.   mat A = 
    26. 

  26.     "\
    27. 

  27.      0.061198   0.201990   0.019678  -0.493936  -0.126745   0.051408;\
    28. 

  28.      0.437242   0.058956  -0.149362  -0.045465   0.296153   0.035437;\
    29. 

  29.     -0.492474  -0.031309   0.314156   0.419733   0.068317  -0.454499;\
    30. 

  30.      0.336352   0.411541   0.458476  -0.393139  -0.135040   0.373833;\
    31. 

  31.      0.239585  -0.428913  -0.406953  -0.291020  -0.353768   0.258704;\
    32. 

  32.     ";
    33. 

  33.   
    34. 

  34.   cx_mat C = cx_mat(A,fliplr(A));
    35. 

  35.   
    36. 

  36.   cx_mat D = cx_mat(flipud(A),-fliplr(A));
    37. 

  37.   
    38. 

  38.      double re = 2.0;
    39. 

  39.   cx_double cx = cx_double(2.0,-3.0);
    40. 

  40.   
    41. 

  41.   
    42. 

  42.   cx_mat C_times_D_t = 
    43. 

  43.     "\
    44. 

  44.     (-0.185711,0.141986) (0.320782,-0.123588) (-6.93889e-18,-0.364555) (-0.320782,-0.123588) (0.185711,0.141986);\
    45. 

  45.     (0.0354121,0.18557) (-0.214015,0.406658) (-3.46945e-18,-0.596795) (0.214015,0.406658) (-0.0354121,0.18557);\
    46. 

  46.     (-0.226682,-0.699037) (-0.0995861,-0.534099) (2.77556e-17,1.41421) (0.0995861,-0.534099) (0.226682,-0.699037);\
    47. 

  47.     (-0.366865,-0.157988) (0.711264,0.107008) (0,-0.471402) (-0.711264,0.107008) (0.366865,-0.157988);\
    48. 

  48.     (0.561849,0.870633) (-0.0814947,0.151169) (-1.38778e-17,-1.03352) (0.0814947,0.151169) (-0.561849,0.870633);\
    49. 

  49.     ";
    50. 

  50.   
    51. 

  51.   cx_mat C_t_times_D = 
    52. 

  52.     "\
    53. 

  53.     (0.148843,-0.857543) (0.406412,-0.0389706) (0.415351,0.656975) (-0.449094,0.526547) (-0.114683,-0.11312) (-0.00283814,-0.867653);\
    54. 

  54.     (0.406412,-0.0244952) (-0.375592,-0.180565) (-0.368772,-0.0694664) (0.041254,-0.478571) (0.00880269,-0.412947) (0.123148,-0.11312);\
    55. 

  55.     (0.415351,0.610998) (-0.368772,-0.154831) (-0.715746,-0.432138) (0.2979,-0.996616) (0.374591,-0.478571) (0.260569,0.526547);\
    56. 

  56.     (-0.449094,0.464705) (0.041254,-0.0989421) (0.2979,-0.607187) (0.00221322,-0.432138) (-0.218553,-0.0694664) (-0.202333,0.656975);\
    57. 

  57.     (-0.114683,-0.0682625) (0.00880269,-0.128059) (0.374591,-0.0989421) (-0.218553,-0.154831) (-0.38423,-0.180565) (-0.0653194,-0.0389706);\
    58. 

  58.     (-0.00283814,-0.983136) (0.123148,-0.0682625) (0.260569,0.464705) (-0.202333,0.610998) (-0.0653194,-0.0244952) (-0.348327,-0.857543);\
    59. 

  59.     ";
    60. 

  60.   
    61. 

  61.   //
    62. 

  62.   
    63. 

  63.   cx_mat re_times_C_times_D_t = 
    64. 

  64.     "\
    65. 

  65.     (-0.371422,0.283972) (0.641564,-0.247176) (-1.38778e-17,-0.72911) (-0.641564,-0.247176) (0.371422,0.283972);\
    66. 

  66.     (0.0708241,0.37114) (-0.428029,0.813317) (-6.93889e-18,-1.19359) (0.428029,0.813317) (-0.0708241,0.37114);\
    67. 

  67.     (-0.453363,-1.39807) (-0.199172,-1.0682) (5.55112e-17,2.82841) (0.199172,-1.0682) (0.453363,-1.39807);\
    68. 

  68.     (-0.733729,-0.315977) (1.42253,0.214017) (0,-0.942804) (-1.42253,0.214017) (0.733729,-0.315977);\
    69. 

  69.     (1.1237,1.74127) (-0.162989,0.302339) (-2.77556e-17,-2.06704) (0.162989,0.302339) (-1.1237,1.74127);\
    70. 

  70.     ";
    71. 

  71.   
    72. 

  72.   cx_mat re_times_C_t_times_D = 
    73. 

  73.     "\
    74. 

  74.     (0.297685,-1.71509) (0.812823,-0.0779412) (0.830702,1.31395) (-0.898189,1.05309) (-0.229366,-0.22624) (-0.00567628,-1.73531);\
    75. 

  75.     (0.812823,-0.0489904) (-0.751184,-0.36113) (-0.737545,-0.138933) (0.0825079,-0.957143) (0.0176054,-0.825894) (0.246297,-0.22624);\
    76. 

  76.     (0.830702,1.222) (-0.737545,-0.309662) (-1.43149,-0.864277) (0.595799,-1.99323) (0.749183,-0.957143) (0.521138,1.05309);\
    77. 

  77.     (-0.898189,0.92941) (0.0825079,-0.197884) (0.595799,-1.21437) (0.00442644,-0.864277) (-0.437106,-0.138933) (-0.404666,1.31395);\
    78. 

  78.     (-0.229366,-0.136525) (0.0176054,-0.256119) (0.749183,-0.197884) (-0.437106,-0.309662) (-0.768459,-0.36113) (-0.130639,-0.0779412);\
    79. 

  79.     (-0.00567628,-1.96627) (0.246297,-0.136525) (0.521138,0.92941) (-0.404666,1.222) (-0.130639,-0.0489904) (-0.696654,-1.71509);\
    80. 

  80.     ";
    81. 

  81.   
    82. 

  82.   //
    83. 

  83.   
    84. 

  84.   cx_mat C_times_re_times_D_t = 
    85. 

  85.     "\
    86. 

  86.     (-0.371422,0.283972) (0.641564,-0.247176) (-1.38778e-17,-0.72911) (-0.641564,-0.247176) (0.371422,0.283972);\
    87. 

  87.     (0.0708241,0.37114) (-0.428029,0.813317) (-6.93889e-18,-1.19359) (0.428029,0.813317) (-0.0708241,0.37114);\
    88. 

  88.     (-0.453363,-1.39807) (-0.199172,-1.0682) (5.55112e-17,2.82841) (0.199172,-1.0682) (0.453363,-1.39807);\
    89. 

  89.     (-0.733729,-0.315977) (1.42253,0.214017) (0,-0.942804) (-1.42253,0.214017) (0.733729,-0.315977);\
    90. 

  90.     (1.1237,1.74127) (-0.162989,0.302339) (-2.77556e-17,-2.06704) (0.162989,0.302339) (-1.1237,1.74127);\
    91. 

  91.     ";
    92. 

  92.   
    93. 

  93.   cx_mat C_t_times_re_times_D = 
    94. 

  94.     "\
    95. 

  95.     (0.297685,-1.71509) (0.812823,-0.0779412) (0.830702,1.31395) (-0.898189,1.05309) (-0.229366,-0.22624) (-0.00567628,-1.73531);\
    96. 

  96.     (0.812823,-0.0489904) (-0.751184,-0.36113) (-0.737545,-0.138933) (0.0825079,-0.957143) (0.0176054,-0.825894) (0.246297,-0.22624);\
    97. 

  97.     (0.830702,1.222) (-0.737545,-0.309662) (-1.43149,-0.864277) (0.595799,-1.99323) (0.749183,-0.957143) (0.521138,1.05309);\
    98. 

  98.     (-0.898189,0.92941) (0.0825079,-0.197884) (0.595799,-1.21437) (0.00442644,-0.864277) (-0.437106,-0.138933) (-0.404666,1.31395);\
    99. 

  99.     (-0.229366,-0.136525) (0.0176054,-0.256119) (0.749183,-0.197884) (-0.437106,-0.309662) (-0.768459,-0.36113) (-0.130639,-0.0779412);\
    100. 

  100.     (-0.00567628,-1.96627) (0.246297,-0.136525) (0.521138,0.92941) (-0.404666,1.222) (-0.130639,-0.0489904) (-0.696654,-1.71509);\
    101. 

  101.     ";
    102. 

  102.   
    103. 

  103.   //
    104. 

  104.   
    105. 

  105.   cx_mat re_times_C_times_re_times_D_t = 
    106. 

  106.     "\
    107. 

  107.     (-0.742845,0.567944) (1.28313,-0.494352) (-2.77556e-17,-1.45822) (-1.28313,-0.494352) (0.742845,0.567944);\
    108. 

  108.     (0.141648,0.742279) (-0.856058,1.62663) (-1.38778e-17,-2.38718) (0.856058,1.62663) (-0.141648,0.742279);\
    109. 

  109.     (-0.906726,-2.79615) (-0.398345,-2.13639) (1.11022e-16,5.65683) (0.398345,-2.13639) (0.906726,-2.79615);\
    110. 

  110.     (-1.46746,-0.631953) (2.84506,0.428033) (0,-1.88561) (-2.84506,0.428033) (1.46746,-0.631953);\
    111. 

  111.     (2.2474,3.48253) (-0.325979,0.604678) (-5.55112e-17,-4.13407) (0.325979,0.604678) (-2.2474,3.48253);\
    112. 

  112.     ";
    113. 

  113.   
    114. 

  114.   cx_mat re_times_C_t_times_re_times_D = 
    115. 

  115.     "\
    116. 

  116.     (0.59537,-3.43017) (1.62565,-0.155882) (1.6614,2.6279) (-1.79638,2.10619) (-0.458732,-0.452481) (-0.0113526,-3.47061);\
    117. 

  117.     (1.62565,-0.0979807) (-1.50237,-0.722259) (-1.47509,-0.277865) (0.165016,-1.91429) (0.0352108,-1.65179) (0.492593,-0.452481);\
    118. 

  118.     (1.6614,2.44399) (-1.47509,-0.619323) (-2.86299,-1.72855) (1.1916,-3.98646) (1.49837,-1.91429) (1.04228,2.10619);\
    119. 

  119.     (-1.79638,1.85882) (0.165016,-0.395768) (1.1916,-2.42875) (0.00885288,-1.72855) (-0.874212,-0.277865) (-0.809332,2.6279);\
    120. 

  120.     (-0.458732,-0.27305) (0.0352108,-0.512237) (1.49837,-0.395768) (-0.874212,-0.619323) (-1.53692,-0.722259) (-0.261278,-0.155882);\
    121. 

  121.     (-0.0113526,-3.93254) (0.492593,-0.27305) (1.04228,1.85882) (-0.809332,2.44399) (-0.261278,-0.0979807) (-1.39331,-3.43017);\
    122. 

  122.     ";
    123. 

  123.   
    124. 

  124.   //
    125. 

  125.   
    126. 

  126.   cx_mat cx_times_C_times_D_t = 
    127. 

  127.     "\
    128. 

  128.     (0.0545359,0.841106) (0.2708,-1.20952) (-1.09366,-0.72911) (-1.01233,0.71517) (0.797381,-0.273161);\
    129. 

  129.     (0.627534,0.264904) (0.791946,1.45536) (-1.79039,-1.19359) (1.648,0.171273) (0.485885,0.477376);\
    130. 

  130.     (-2.55047,-0.718029) (-1.80147,-0.769439) (4.24262,2.82841) (-1.40312,-1.36696) (-1.64375,-2.07812);\
    131. 

  131.     (-1.20769,0.784617) (1.74355,-1.91978) (-1.41421,-0.942804) (-1.1015,2.34781) (0.259764,-1.41657);\
    132. 

  132.     (3.7356,0.0557187) (0.290519,0.546823) (-3.10056,-2.06704) (0.616498,0.0578546) (1.4882,3.42681);\
    133. 

  133.     ";
    134. 

  134.   
    135. 

  135.   cx_mat cx_times_C_t_times_D = 
    136. 

  136.     "\
    137. 

  137.     (-2.27494,-2.16161) (0.695911,-1.29718) (2.80163,0.0678966) (0.681454,2.40038) (-0.568727,0.117809) (-2.60864,-1.72679);\
    138. 

  138.     (0.739338,-1.26823) (-1.29288,0.765647) (-0.945944,0.967385) (-1.35321,-1.0809) (-1.22124,-0.852303) (-0.0930641,-0.595685);\
    139. 

  139.     (2.6637,-0.0240567) (-1.20204,0.796656) (-2.72791,1.28296) (-2.39405,-2.88693) (-0.686531,-2.08092) (2.10078,0.271388);\
    140. 

  140.     (0.495926,2.27669) (-0.214318,-0.321646) (-1.22576,-2.10807) (-1.29199,-0.870917) (-0.645505,0.516726) (1.56626,1.92095);\
    141. 

  141.     (-0.434154,0.207524) (-0.366573,-0.282527) (0.452357,-1.32166) (-0.901598,0.345997) (-1.31015,0.791559) (-0.247551,0.118017);\
    142. 

  142.     (-2.95508,-1.95776) (0.0415092,-0.50597) (1.91525,0.147703) (1.42833,1.82899) (-0.204124,0.146968) (-3.26928,-0.670106);\
    143. 

  143.     ";
    144. 

  144.   
    145. 

  145.   //
    146. 

  146.   
    147. 

  147.   cx_mat C_times_cx_times_D_t = 
    148. 

  148.     "\
    149. 

  149.     (0.0545359,0.841106) (0.2708,-1.20952) (-1.09366,-0.72911) (-1.01233,0.71517) (0.797381,-0.273161);\
    150. 

  150.     (0.627534,0.264904) (0.791946,1.45536) (-1.79039,-1.19359) (1.648,0.171273) (0.485885,0.477376);\
    151. 

  151.     (-2.55047,-0.718029) (-1.80147,-0.769439) (4.24262,2.82841) (-1.40312,-1.36696) (-1.64375,-2.07812);\
    152. 

  152.     (-1.20769,0.784617) (1.74355,-1.91978) (-1.41421,-0.942804) (-1.1015,2.34781) (0.259764,-1.41657);\
    153. 

  153.     (3.7356,0.0557187) (0.290519,0.546823) (-3.10056,-2.06704) (0.616498,0.0578546) (1.4882,3.42681);\
    154. 

  154.     ";
    155. 

  155.   
    156. 

  156.   cx_mat C_t_times_cx_times_D = 
    157. 

  157.     "\
    158. 

  158.     (-2.27494,-2.16161) (0.695911,-1.29718) (2.80163,0.0678966) (0.681454,2.40038) (-0.568727,0.117809) (-2.60864,-1.72679);\
    159. 

  159.     (0.739338,-1.26823) (-1.29288,0.765647) (-0.945944,0.967385) (-1.35321,-1.0809) (-1.22124,-0.852303) (-0.0930641,-0.595685);\
    160. 

  160.     (2.6637,-0.0240567) (-1.20204,0.796656) (-2.72791,1.28296) (-2.39405,-2.88693) (-0.686531,-2.08092) (2.10078,0.271388);\
    161. 

  161.     (0.495926,2.27669) (-0.214318,-0.321646) (-1.22576,-2.10807) (-1.29199,-0.870917) (-0.645505,0.516726) (1.56626,1.92095);\
    162. 

  162.     (-0.434154,0.207524) (-0.366573,-0.282527) (0.452357,-1.32166) (-0.901598,0.345997) (-1.31015,0.791559) (-0.247551,0.118017);\
    163. 

  163.     (-2.95508,-1.95776) (0.0415092,-0.50597) (1.91525,0.147703) (1.42833,1.82899) (-0.204124,0.146968) (-3.26928,-0.670106);\
    164. 

  164.     ";
    165. 

  165.   
    166. 

  166.   //
    167. 

  167.   
    168. 

  168.   cx_mat cx_times_C_times_cx_times_D_t = 
    169. 

  169.     "\
    170. 

  170.     (2.63239,1.5186) (-3.08696,-3.23144) (-4.37466,1.82277) (0.120855,4.46732) (0.775277,-2.93847);\
    171. 

  171.     (2.04978,-1.35279) (5.94997,0.534883) (-7.16154,2.98398) (3.80983,-4.60147) (2.4039,-0.502904);\
    172. 

  172.     (-7.25503,6.21536) (-5.91125,3.86553) (16.9705,-7.07103) (-6.90711,1.47546) (-9.52185,0.775005);\
    173. 

  173.     (-0.0615364,5.19232) (-2.27222,-9.07021) (-5.65682,2.35701) (4.84042,8.00013) (-3.73018,-3.61243);\
    174. 

  174.     (7.63835,-11.0954) (2.22151,0.22209) (-12.4022,5.16759) (1.40656,-1.73378) (13.2568,2.38902);\
    175. 

  175.     ";
    176. 

  176.   
    177. 

  177.   cx_mat cx_times_C_t_times_cx_times_D = 
    178. 

  178.     "\
    179. 

  179.     (-11.0347,2.5016) (-2.49971,-4.68209) (5.80694,-8.26908) (8.56404,2.7564) (-0.784027,1.9418) (-10.3976,4.37232);\
    180. 

  180.     (-2.326,-4.75446) (-0.288817,5.40993) (1.01027,4.7726) (-5.94913,1.89781) (-4.99938,1.9591) (-1.97318,-0.912178);\
    181. 

  181.     (5.25522,-8.0392) (-0.0141081,5.19942) (-1.60693,10.7496) (-13.4489,1.40828) (-7.61581,-2.10224) (5.01572,-5.75956);\
    182. 

  182.     (7.82193,3.06561) (-1.39358,-0.000336933) (-8.77574,-0.538863) (-5.19673,2.13413) (0.259168,2.96997) (8.89536,-0.856878);\
    183. 

  183.     (-0.245734,1.71751) (-1.58073,0.534664) (-3.06026,-4.00039) (-0.765206,3.39679) (-0.24563,5.51358) (-0.14105,0.978686);\
    184. 

  184.     (-11.7834,4.94974) (-1.43489,-1.13647) (4.27362,-5.45035) (8.34364,-0.626995) (0.0326548,0.906309) (-8.54888,8.46764);\
    185. 

  185.     ";
    186. 

  186.   
    187. 

  187.   
    188. 

  188.   
    189. 

  189.   REQUIRE( accu(abs( C*D.t() - C_times_D_t )) == Approx(0.0).epsilon(0.00005) );
    190. 

  190.   REQUIRE( accu(abs( C.t()*D - C_t_times_D )) == Approx(0.0).epsilon(0.00005) );
    191. 

  191.   
    192. 

  192.   //
    193. 

  193.   
    194. 

  194.   REQUIRE( accu(abs( re*C*D.t() - re_times_C_times_D_t )) == Approx(0.0).epsilon(0.00005) );
    195. 

  195.   REQUIRE( accu(abs( re*C.t()*D - re_times_C_t_times_D )) == Approx(0.0).epsilon(0.00005) );
    196. 

  196.   
    197. 

  197.   REQUIRE( accu(abs( C*re*D.t() - C_times_re_times_D_t )) == Approx(0.0).epsilon(0.00005) );
    198. 

  198.   REQUIRE( accu(abs( C.t()*re*D - C_t_times_re_times_D )) == Approx(0.0).epsilon(0.00005) );
    199. 

  199.   
    200. 

  200.   REQUIRE( accu(abs( re*C*re*D.t() - re_times_C_times_re_times_D_t )) == Approx(0.0).epsilon(0.00010) );
    201. 

  201.   REQUIRE( accu(abs( re*C.t()*re*D - re_times_C_t_times_re_times_D )) == Approx(0.0).epsilon(0.00010) );
    202. 

  202.   
    203. 

  203.   //
    204. 

  204.   
    205. 

  205.   REQUIRE( accu(abs( (re*C)*D.t() - re_times_C_times_D_t )) == Approx(0.0).epsilon(0.00005) );
    206. 

  206.   REQUIRE( accu(abs( (re*C.t())*D - re_times_C_t_times_D )) == Approx(0.0).epsilon(0.00005) );
    207. 

  207.   
    208. 

  208.   REQUIRE( accu(abs( C*(re*D.t()) - C_times_re_times_D_t )) == Approx(0.0).epsilon(0.00005) );
    209. 

  209.   REQUIRE( accu(abs( C.t()*(re*D) - C_t_times_re_times_D )) == Approx(0.0).epsilon(0.00005) );
    210. 

  210.   
    211. 

  211.   REQUIRE( accu(abs( (re*C)*(re*D.t()) - re_times_C_times_re_times_D_t )) == Approx(0.0).epsilon(0.00010) );
    212. 

  212.   REQUIRE( accu(abs( (re*C.t())*(re*D) - re_times_C_t_times_re_times_D )) == Approx(0.0).epsilon(0.00010) );
    213. 

  213. 

  214. 

  215.   REQUIRE( accu(abs( C*D.t().eval() - C_times_D_t )) == Approx(0.0).epsilon(0.00005) );
    216. 

  216.   REQUIRE( accu(abs( C.t().eval()*D - C_t_times_D )) == Approx(0.0).epsilon(0.00005) );
    217. 

  217.   
    218. 

  218.   //
    219. 

  219.   
    220. 

  220.   REQUIRE( accu(abs( re*C*D.t().eval() - re_times_C_times_D_t )) == Approx(0.0).epsilon(0.00005) );
    221. 

  221.   REQUIRE( accu(abs( re*C.t().eval()*D - re_times_C_t_times_D )) == Approx(0.0).epsilon(0.00005) );
    222. 

  222.   
    223. 

  223.   REQUIRE( accu(abs( C*re*D.t().eval() - C_times_re_times_D_t )) == Approx(0.0).epsilon(0.00005) );
    224. 

  224.   REQUIRE( accu(abs( C.t().eval()*re*D - C_t_times_re_times_D )) == Approx(0.0).epsilon(0.00005) );
    225. 

  225.   
    226. 

  226.   REQUIRE( accu(abs( re*C*re*D.t().eval() - re_times_C_times_re_times_D_t )) == Approx(0.0).epsilon(0.00010) );
    227. 

  227.   REQUIRE( accu(abs( re*C.t().eval()*re*D - re_times_C_t_times_re_times_D )) == Approx(0.0).epsilon(0.00010) );
    228. 

  228.   
    229. 

  229.   //
    230. 

  230.   
    231. 

  231.   REQUIRE( accu(abs( (re*C)*(D.t().eval()) - re_times_C_times_D_t )) == Approx(0.0).epsilon(0.00005) );
    232. 

  232.   REQUIRE( accu(abs( (re*C.t()).eval()*D - re_times_C_t_times_D )) == Approx(0.0).epsilon(0.00005) );
    233. 

  233.   
    234. 

  234.   REQUIRE( accu(abs( C*(re*D.t()).eval() - C_times_re_times_D_t )) == Approx(0.0).epsilon(0.00005) );
    235. 

  235.   REQUIRE( accu(abs( C.t().eval()*(re*D) - C_t_times_re_times_D )) == Approx(0.0).epsilon(0.00005) );
    236. 

  236.   
    237. 

  237.   REQUIRE( accu(abs( (re*C)*(re*D.t()).eval() - re_times_C_times_re_times_D_t )) == Approx(0.0).epsilon(0.00010) );
    238. 

  238.   REQUIRE( accu(abs( (re*C.t()).eval()*(re*D) - re_times_C_t_times_re_times_D )) == Approx(0.0).epsilon(0.00010) );
    239. 

  239. 

  240. 

  241.   //
    242. 

  242.   
    243. 

  243.   REQUIRE( accu(abs( cx*C*D.t() - cx_times_C_times_D_t )) == Approx(0.0).epsilon(0.00010) );
    244. 

  244.   REQUIRE( accu(abs( cx*C.t()*D - cx_times_C_t_times_D )) == Approx(0.0).epsilon(0.00010) );
    245. 

  245.   
    246. 

  246.   REQUIRE( accu(abs( C*cx*D.t() - C_times_cx_times_D_t )) == Approx(0.0).epsilon(0.00010) );
    247. 

  247.   REQUIRE( accu(abs( C.t()*cx*D - C_t_times_cx_times_D )) == Approx(0.0).epsilon(0.00010) );
    248. 

  248.   
    249. 

  249.   REQUIRE( accu(abs( cx*C*cx*D.t() - cx_times_C_times_cx_times_D_t )) == Approx(0.0).epsilon(0.00030) );
    250. 

  250.   REQUIRE( accu(abs( cx*C.t()*cx*D - cx_times_C_t_times_cx_times_D )) == Approx(0.0).epsilon(0.00030) );
    251. 

  251.   
    252. 

  252.   //
    253. 

  253.   
    254. 

  254.   REQUIRE( accu(abs( (cx*C)*D.t() - cx_times_C_times_D_t )) == Approx(0.0).epsilon(0.00010) );
    255. 

  255.   REQUIRE( accu(abs( (cx*C.t())*D - cx_times_C_t_times_D )) == Approx(0.0).epsilon(0.00010) );
    256. 

  256.   
    257. 

  257.   REQUIRE( accu(abs( C*(cx*D.t()) - C_times_cx_times_D_t )) == Approx(0.0).epsilon(0.00010) );
    258. 

  258.   REQUIRE( accu(abs( C.t()*(cx*D) - C_t_times_cx_times_D )) == Approx(0.0).epsilon(0.00010) );
    259. 

  259.   
    260. 

  260.   REQUIRE( accu(abs( (cx*C)*(cx*D.t()) - cx_times_C_times_cx_times_D_t )) == Approx(0.0).epsilon(0.00030) );
    261. 

  261.   REQUIRE( accu(abs( (cx*C.t())*(cx*D) - cx_times_C_t_times_cx_times_D )) == Approx(0.0).epsilon(0.00030) );
    262. 

  262. 

  263. 

  264.   REQUIRE( accu(abs( C*D.t().eval() - C_times_D_t )) == Approx(0.0).epsilon(0.00005) );
    265. 

  265.   REQUIRE( accu(abs( C.t().eval()*D - C_t_times_D )) == Approx(0.0).epsilon(0.00005) );
    266. 

  266.   
    267. 

  267.   //
    268. 

  268.   
    269. 

  269.   REQUIRE( accu(abs( cx*C*D.t().eval() - cx_times_C_times_D_t )) == Approx(0.0).epsilon(0.00010) );
    270. 

  270.   REQUIRE( accu(abs( cx*C.t().eval()*D - cx_times_C_t_times_D )) == Approx(0.0).epsilon(0.00010) );
    271. 

  271.   
    272. 

  272.   REQUIRE( accu(abs( C*cx*D.t().eval() - C_times_cx_times_D_t )) == Approx(0.0).epsilon(0.00010) );
    273. 

  273.   REQUIRE( accu(abs( C.t().eval()*cx*D - C_t_times_cx_times_D )) == Approx(0.0).epsilon(0.00010) );
    274. 

  274.   
    275. 

  275.   REQUIRE( accu(abs( cx*C*cx*D.t().eval() - cx_times_C_times_cx_times_D_t )) == Approx(0.0).epsilon(0.00030) );
    276. 

  276.   REQUIRE( accu(abs( cx*C.t().eval()*cx*D - cx_times_C_t_times_cx_times_D )) == Approx(0.0).epsilon(0.00030) );
    277. 

  277.   
    278. 

  278.   //
    279. 

  279.   
    280. 

  280.   REQUIRE( accu(abs( (cx*C)*(D.t().eval()) - cx_times_C_times_D_t )) == Approx(0.0).epsilon(0.00010) );
    281. 

  281.   REQUIRE( accu(abs( (cx*C.t()).eval()*D   - cx_times_C_t_times_D )) == Approx(0.0).epsilon(0.00010) );
    282. 

  282.   
    283. 

  283.   REQUIRE( accu(abs( C*(cx*D.t()).eval() - C_times_cx_times_D_t )) == Approx(0.0).epsilon(0.00010) );
    284. 

  284.   REQUIRE( accu(abs( C.t().eval()*(cx*D) - C_t_times_cx_times_D )) == Approx(0.0).epsilon(0.00010) );
    285. 

  285.   
    286. 

  286.   REQUIRE( accu(abs( (cx*C)*(cx*D.t()).eval() - cx_times_C_times_cx_times_D_t )) == Approx(0.0).epsilon(0.00030) );
    287. 

  287.   REQUIRE( accu(abs( (cx*C.t()).eval()*(cx*D) - cx_times_C_t_times_cx_times_D )) == Approx(0.0).epsilon(0.00030) );
    288. 

  288.   }
    289. 

  289. 

  290. 

  291.