/usr/include/trilinos/BelosOrthoManagerTest.hpp is in libtrilinos-belos-dev 12.10.1-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 1717 1718 1719 1720 1721 1722 1723 1724 1725 1726 1727 1728 1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 1739 1740 1741 1742 1743 1744 1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 1774 1775 1776 1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788 1789 1790 1791 1792 1793 1794 1795 1796 1797 1798 1799 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814 1815 1816 1817 1818 1819 1820 1821 1822 1823 1824 1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 1835 1836 1837 1838 1839 1840 1841 1842 1843 1844 1845 1846 1847 1848 1849 1850 1851 1852 1853 1854 1855 1856 1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 1873 1874 | //@HEADER
// ************************************************************************
//
// Belos: Block Linear Solvers Package
// Copyright 2004 Sandia Corporation
//
// Under the terms of Contract DE-AC04-94AL85000 with Sandia Corporation,
// the U.S. Government retains certain rights in this software.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
//
// 1. Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
//
// 2. Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
//
// 3. Neither the name of the Corporation nor the names of the
// contributors may be used to endorse or promote products derived from
// this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY
// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
// PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL SANDIA CORPORATION OR THE
// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
// LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
// Questions? Contact Michael A. Heroux (maherou@sandia.gov)
//
// ************************************************************************
//@HEADER
/// \file BelosOrthoManagerTest.hpp
/// \brief Tests for Belos::OrthoManager and Belos::MatOrthoManager subclasses
///
#include <BelosConfigDefs.hpp>
#include <BelosMultiVecTraits.hpp>
#include <BelosOutputManager.hpp>
#include <BelosOrthoManagerFactory.hpp>
#include <Teuchos_StandardCatchMacros.hpp>
#include <Teuchos_TimeMonitor.hpp>
#include <iostream>
#include <stdexcept>
using std::endl;
namespace Belos {
namespace Test {
/// \class OrthoManagerBenchmarker
/// \brief OrthoManager benchmark
/// \author Mark Hoemmen
///
template<class Scalar, class MV>
class OrthoManagerBenchmarker {
private:
typedef Scalar scalar_type;
typedef typename Teuchos::ScalarTraits<Scalar>::magnitudeType magnitude_type;
typedef MultiVecTraits<Scalar, MV> MVT;
typedef Teuchos::SerialDenseMatrix<int, Scalar> mat_type;
public:
/// \brief Establish baseline run time for OrthoManager benchmark
///
/// Replacing a Belos OrthoManager or MatOrthoManager's
/// projection and normalization operations with the same number
/// of vector copies establishes a rough lower bound on run
/// time, because orthogonalization generally requires that much
/// data movement. This gives us a rough sense for how long the
/// orthogonalization should take, so we can calibrate the
/// number of trials needed for accurate timings.
static void
baseline (const Teuchos::RCP<const MV>& X,
const int numCols,
const int numBlocks,
const int numTrials)
{
using Teuchos::Array;
using Teuchos::RCP;
using Teuchos::rcp;
using Teuchos::Time;
using Teuchos::TimeMonitor;
// Make some blocks to "orthogonalize." Fill with random
// data. We only need X so that we can make clones (it knows
// its data distribution).
Array<RCP<MV> > V (numBlocks);
for (int k = 0; k < numBlocks; ++k) {
V[k] = MVT::Clone (*X, numCols);
MVT::MvRandom (*V[k]);
}
// Make timers with informative labels
RCP<Time> timer = TimeMonitor::getNewCounter ("Baseline for OrthoManager benchmark");
// Baseline benchmark just copies data. It's sort of a lower
// bound proxy for the volume of data movement done by a real
// OrthoManager.
{
TimeMonitor monitor (*timer);
for (int trial = 0; trial < numTrials; ++trial) {
for (int k = 0; k < numBlocks; ++k) {
for (int j = 0; j < k; ++j)
MVT::Assign (*V[j], *V[k]);
MVT::Assign (*X, *V[k]);
}
}
}
}
/// \brief Benchmark the given orthogonalization manager
///
/// \param orthoMan [in(/out)] The orthogonalization
/// manager to benchmark
/// \param orthoManName [in] Name of the orthogonalization
/// manager (e.g., "TSQR", "ICGS", "DGKS")
/// \param normalization [in] Normalization scheme used
/// by the orthogonalization manager (only applicable
/// to the "Simple" orthogonalization)
/// \param X [in] "Prototype" multivector; not modified
/// \param numCols [in] Number of columns per block
/// \param numBlocks [in] Number of blocks
/// \param numTrials [in] Number of trials in the timing run
/// \param outMan [out] Output manager
///
/// \param resultStream [out] Output stream for printing
/// benchmark results. If displayResultsCompactly is true, it
/// will be written by all MPI rank(s), so on ranks other than
/// 0, it should be set appropriately to a "black hole stream"
/// that doesn't write anything.
///
/// \param displayResultsCompactly [in] If false, rely on
/// TimeMonitor::summarize() to print results to resultStream
/// (and ensure only MPI Rank 0 does so). If true, print
/// results in a more compact format suitable for automatic
/// parsing, using a CSV (Comma-Delimited Values) parser. In
/// "compact" mode, two lines are printed, both of which are
/// comma-delimited ASCII text. The first line begins with a
/// "comment" character #; following that are column ("field")
/// labels. The second line contains the actual data, again
/// in ASCII comma-delimited format.
static void
benchmark (const Teuchos::RCP<OrthoManager<Scalar, MV> >& orthoMan,
const std::string& orthoManName,
const std::string& normalization,
const Teuchos::RCP<const MV>& X,
const int numCols,
const int numBlocks,
const int numTrials,
const Teuchos::RCP<OutputManager<Scalar> >& outMan,
std::ostream& resultStream,
const bool displayResultsCompactly=false)
{
using Teuchos::Array;
using Teuchos::ArrayView;
using Teuchos::RCP;
using Teuchos::rcp;
using Teuchos::Time;
using Teuchos::TimeMonitor;
using std::endl;
TEUCHOS_TEST_FOR_EXCEPTION(orthoMan.is_null(), std::invalid_argument,
"orthoMan is null");
TEUCHOS_TEST_FOR_EXCEPTION(X.is_null(), std::invalid_argument,
"X is null");
TEUCHOS_TEST_FOR_EXCEPTION(numCols < 1, std::invalid_argument,
"numCols = " << numCols << " < 1");
TEUCHOS_TEST_FOR_EXCEPTION(numBlocks < 1, std::invalid_argument,
"numBlocks = " << numBlocks << " < 1");
TEUCHOS_TEST_FOR_EXCEPTION(numTrials < 1, std::invalid_argument,
"numTrials = " << numTrials << " < 1");
// Debug output stream
std::ostream& debugOut = outMan->stream(Debug);
// If you like, you can add the "baseline" as an approximate
// lower bound for orthogonalization performance. It may be
// useful as a sanity check to make sure that your
// orthogonalizations are really computing something, though
// testing accuracy can help with that too.
//
//baseline (X, numCols, numBlocks, numTrials);
// Make space to put the projection and normalization
// coefficients.
Array<RCP<mat_type> > C (numBlocks);
for (int k = 0; k < numBlocks; ++k) {
C[k] = rcp (new mat_type (numCols, numCols));
}
RCP<mat_type> B (new mat_type (numCols, numCols));
// Make some blocks to orthogonalize. Fill with random data.
// We won't be orthogonalizing X, or even modifying X. We
// only need X so that we can make clones (since X knows its
// data distribution).
Array<RCP<MV> > V (numBlocks);
for (int k = 0; k < numBlocks; ++k) {
V[k] = MVT::Clone (*X, numCols);
MVT::MvRandom (*V[k]);
}
// Make timers with informative labels. We time an additional
// first run to measure the startup costs, if any, of the
// OrthoManager instance.
RCP<Time> firstRunTimer;
{
std::ostringstream os;
os << "OrthoManager: " << orthoManName << " first run";
firstRunTimer = TimeMonitor::getNewCounter (os.str());
}
RCP<Time> timer;
{
std::ostringstream os;
os << "OrthoManager: " << orthoManName << " total over "
<< numTrials << " trials (excluding first run above)";
timer = TimeMonitor::getNewCounter (os.str());
}
// The first run lets us measure the startup costs, if any, of
// the OrthoManager instance, without these costs influencing
// the following timing runs.
{
TimeMonitor monitor (*firstRunTimer);
{
(void) orthoMan->normalize (*V[0], B);
for (int k = 1; k < numBlocks; ++k) {
// k is the number of elements in the ArrayView. We
// have to assign first to an ArrayView-of-RCP-of-MV,
// rather than to an ArrayView-of-RCP-of-const-MV, since
// the latter requires a reinterpret cast. Don't you
// love C++ type inference?
ArrayView<RCP<MV> > V_0k_nonconst = V.view (0, k);
ArrayView<RCP<const MV> > V_0k =
Teuchos::av_reinterpret_cast<RCP<const MV> > (V_0k_nonconst);
(void) orthoMan->projectAndNormalize (*V[k], C, B, V_0k);
}
}
// "Test" that the trial run actually orthogonalized
// correctly. Results are printed to the OutputManager's
// Belos::Debug output stream, so depending on the
// OutputManager's chosen verbosity level, you may or may
// not see the results of the test.
//
// NOTE (mfh 22 Jan 2011) For now, these results have to be
// inspected visually. We should add a simple automatic
// test.
debugOut << "Orthogonality of V[0:" << (numBlocks-1)
<< "]:" << endl;
for (int k = 0; k < numBlocks; ++k) {
// Orthogonality of each block
debugOut << "For block V[" << k << "]:" << endl;
debugOut << " ||<V[" << k << "], V[" << k << "]> - I|| = "
<< orthoMan->orthonormError(*V[k]) << endl;
// Relative orthogonality with the previous blocks
for (int j = 0; j < k; ++j) {
debugOut << " ||< V[" << j << "], V[" << k << "] >|| = "
<< orthoMan->orthogError(*V[j], *V[k]) << endl;
}
}
}
// Run the benchmark for numTrials trials. Time all trials as
// a single run.
{
TimeMonitor monitor (*timer);
for (int trial = 0; trial < numTrials; ++trial) {
(void) orthoMan->normalize (*V[0], B);
for (int k = 1; k < numBlocks; ++k) {
ArrayView<RCP<MV> > V_0k_nonconst = V.view (0, k);
ArrayView<RCP<const MV> > V_0k =
Teuchos::av_reinterpret_cast<RCP<const MV> > (V_0k_nonconst);
(void) orthoMan->projectAndNormalize (*V[k], C, B, V_0k);
}
}
}
// Report timing results.
if (displayResultsCompactly)
{
// The "compact" format is suitable for automatic parsing,
// using a CSV (Comma-Delimited Values) parser. The first
// "comment" line may be parsed to extract column
// ("field") labels; the second line contains the actual
// data, in ASCII comma-delimited format.
using std::endl;
resultStream << "#orthoManName"
<< ",normalization"
<< ",numRows"
<< ",numCols"
<< ",numBlocks"
<< ",firstRunTimeInSeconds"
<< ",timeInSeconds"
<< ",numTrials"
<< endl;
resultStream << orthoManName
<< "," << (orthoManName=="Simple" ? normalization : "N/A")
<< "," << MVT::GetGlobalLength(*X)
<< "," << numCols
<< "," << numBlocks
<< "," << firstRunTimer->totalElapsedTime()
<< "," << timer->totalElapsedTime()
<< "," << numTrials
<< endl;
}
else {
TimeMonitor::summarize (resultStream);
}
}
};
/// \class OrthoManagerTester
/// \brief Wrapper around OrthoManager test functionality
///
template< class Scalar, class MV >
class OrthoManagerTester {
private:
typedef typename Teuchos::Array<Teuchos::RCP<MV> >::size_type size_type;
public:
typedef Scalar scalar_type;
typedef Teuchos::ScalarTraits<scalar_type> SCT;
typedef typename SCT::magnitudeType magnitude_type;
typedef Teuchos::ScalarTraits<magnitude_type> SMT;
typedef MultiVecTraits<scalar_type, MV> MVT;
typedef Teuchos::SerialDenseMatrix<int, scalar_type> mat_type;
/// \brief Run all the tests
///
/// \param OM [in/out] OrthoManager subclass instance to test
/// \param isRankRevealing [in] Whether that OrthoManager
/// subclass instance has a true rank-revealing capability.
/// If not, we do not test it on rank-deficient vectors.
/// \param S [in/out] Multivector instance
/// \param sizeX1 [in] Number of columns in X1 (a multivector
/// instance created internally for tests)
/// \param sizeX2 [in] Number of columns in X2 (a multivector
/// instance created internally for tests)
/// \param MyOM [out] Output manager for handling local output.
/// In Anasazi, this class is called BasicOutputManager. In
/// Belos, this class is called OutputManager.
///
/// \return Number of tests that failed (zero means success)
static int
runTests (const Teuchos::RCP<OrthoManager<Scalar, MV> >& OM,
const bool isRankRevealing,
const Teuchos::RCP<MV>& S,
const int sizeX1,
const int sizeX2,
const Teuchos::RCP<OutputManager<Scalar> >& MyOM)
{
using Teuchos::Array;
using Teuchos::null;
using Teuchos::RCP;
using Teuchos::rcp;
using Teuchos::rcp_dynamic_cast;
using Teuchos::tuple;
// Number of tests that have failed thus far.
int numFailed = 0;
// Relative tolerance against which all tests are performed.
const magnitude_type TOL = 1.0e-12;
// Absolute tolerance constant
//const magnitude_type ATOL = 10;
const scalar_type ZERO = SCT::zero();
const scalar_type ONE = SCT::one();
// Debug output stream
std::ostream& debugOut = MyOM->stream(Debug);
// Number of columns in the input "prototype" multivector S.
const int sizeS = MVT::GetNumberVecs (*S);
// Create multivectors X1 and X2, using the same map as multivector
// S. Then, test orthogonalizing X2 against X1. After doing so, X1
// and X2 should each be M-orthonormal, and should be mutually
// M-orthogonal.
debugOut << "Generating X1,X2 for testing... ";
RCP< MV > X1 = MVT::Clone (*S, sizeX1);
RCP< MV > X2 = MVT::Clone (*S, sizeX2);
debugOut << "done." << endl;
{
magnitude_type err;
//
// Fill X1 with random values, and test the normalization error.
//
debugOut << "Filling X1 with random values... ";
MVT::MvRandom(*X1);
debugOut << "done." << endl
<< "Calling normalize() on X1... ";
// The Anasazi and Belos OrthoManager interfaces differ.
// For example, Anasazi's normalize() method accepts either
// one or two arguments, whereas Belos' normalize() requires
// two arguments.
const int initialX1Rank = OM->normalize(*X1, Teuchos::null);
TEUCHOS_TEST_FOR_EXCEPTION(initialX1Rank != sizeX1,
std::runtime_error,
"normalize(X1) returned rank "
<< initialX1Rank << " from " << sizeX1
<< " vectors. Cannot continue.");
debugOut << "done." << endl
<< "Calling orthonormError() on X1... ";
err = OM->orthonormError(*X1);
TEUCHOS_TEST_FOR_EXCEPTION(err > TOL, std::runtime_error,
"After normalize(X1), orthonormError(X1) = "
<< err << " > TOL = " << TOL);
debugOut << "done: ||<X1,X1> - I|| = " << err << endl;
//
// Fill X2 with random values, project against X1 and normalize,
// and test the orthogonalization error.
//
debugOut << "Filling X2 with random values... ";
MVT::MvRandom(*X2);
debugOut << "done." << endl
<< "Calling projectAndNormalize(X2, C, B, tuple(X1))... "
<< std::flush;
// The projectAndNormalize() interface also differs between
// Anasazi and Belos. Anasazi's projectAndNormalize() puts
// the multivector and the array of multivectors first, and
// the (array of) SerialDenseMatrix arguments (which are
// optional) afterwards. Belos puts the (array of)
// SerialDenseMatrix arguments in the middle, and they are
// not optional.
int initialX2Rank;
{
Array<RCP<mat_type> > C (1);
RCP<mat_type> B = Teuchos::null;
initialX2Rank =
OM->projectAndNormalize (*X2, C, B, tuple<RCP<const MV> >(X1));
}
TEUCHOS_TEST_FOR_EXCEPTION(initialX2Rank != sizeX2,
std::runtime_error,
"projectAndNormalize(X2,X1) returned rank "
<< initialX2Rank << " from " << sizeX2
<< " vectors. Cannot continue.");
debugOut << "done." << endl
<< "Calling orthonormError() on X2... ";
err = OM->orthonormError (*X2);
TEUCHOS_TEST_FOR_EXCEPTION(err > TOL,
std::runtime_error,
"projectAndNormalize(X2,X1) did not meet tolerance: "
"orthonormError(X2) = " << err << " > TOL = " << TOL);
debugOut << "done: || <X2,X2> - I || = " << err << endl
<< "Calling orthogError(X2, X1)... ";
err = OM->orthogError (*X2, *X1);
TEUCHOS_TEST_FOR_EXCEPTION(err > TOL,
std::runtime_error,
"projectAndNormalize(X2,X1) did not meet tolerance: "
"orthogError(X2,X1) = " << err << " > TOL = " << TOL);
debugOut << "done: || <X2,X1> || = " << err << endl;
}
//
// If OM is an OutOfPlaceNormalizerMixin, exercise the
// out-of-place normalization routines.
//
typedef Belos::OutOfPlaceNormalizerMixin<Scalar, MV> mixin_type;
RCP<mixin_type> tsqr = rcp_dynamic_cast<mixin_type>(OM);
if (! tsqr.is_null())
{
magnitude_type err;
debugOut << endl
<< "=== OutOfPlaceNormalizerMixin tests ==="
<< endl << endl;
//
// Fill X1_in with random values, and test the normalization
// error with normalizeOutOfPlace().
//
// Don't overwrite X1, else you'll mess up the tests that
// follow!
//
RCP<MV> X1_in = MVT::CloneCopy (*X1);
debugOut << "Filling X1_in with random values... ";
MVT::MvRandom(*X1_in);
debugOut << "done." << endl;
debugOut << "Filling X1_out with different random values...";
RCP<MV> X1_out = MVT::Clone(*X1_in, MVT::GetNumberVecs(*X1_in));
MVT::MvRandom(*X1_out);
debugOut << "done." << endl
<< "Calling normalizeOutOfPlace(*X1_in, *X1_out, null)... ";
const int initialX1Rank =
tsqr->normalizeOutOfPlace(*X1_in, *X1_out, Teuchos::null);
TEUCHOS_TEST_FOR_EXCEPTION(initialX1Rank != sizeX1, std::runtime_error,
"normalizeOutOfPlace(*X1_in, *X1_out, null) "
"returned rank " << initialX1Rank << " from "
<< sizeX1 << " vectors. Cannot continue.");
debugOut << "done." << endl
<< "Calling orthonormError() on X1_out... ";
err = OM->orthonormError(*X1_out);
TEUCHOS_TEST_FOR_EXCEPTION(err > TOL, std::runtime_error,
"After calling normalizeOutOfPlace(*X1_in, "
"*X1_out, null), orthonormError(X1) = "
<< err << " > TOL = " << TOL);
debugOut << "done: ||<X1_out,X1_out> - I|| = " << err << endl;
//
// Fill X2_in with random values, project against X1_out
// and normalize via projectAndNormalizeOutOfPlace(), and
// test the orthogonalization error.
//
// Don't overwrite X2, else you'll mess up the tests that
// follow!
//
RCP<MV> X2_in = MVT::CloneCopy (*X2);
debugOut << "Filling X2_in with random values... ";
MVT::MvRandom(*X2_in);
debugOut << "done." << endl
<< "Filling X2_out with different random values...";
RCP<MV> X2_out = MVT::Clone(*X2_in, MVT::GetNumberVecs(*X2_in));
MVT::MvRandom(*X2_out);
debugOut << "done." << endl
<< "Calling projectAndNormalizeOutOfPlace(X2_in, X2_out, "
<< "C, B, X1_out)...";
int initialX2Rank;
{
Array<RCP<mat_type> > C (1);
RCP<mat_type> B = Teuchos::null;
initialX2Rank =
tsqr->projectAndNormalizeOutOfPlace (*X2_in, *X2_out, C, B,
tuple<RCP<const MV> >(X1_out));
}
TEUCHOS_TEST_FOR_EXCEPTION(initialX2Rank != sizeX2,
std::runtime_error,
"projectAndNormalizeOutOfPlace(*X2_in, "
"*X2_out, C, B, tuple(X1_out)) returned rank "
<< initialX2Rank << " from " << sizeX2
<< " vectors. Cannot continue.");
debugOut << "done." << endl
<< "Calling orthonormError() on X2_out... ";
err = OM->orthonormError (*X2_out);
TEUCHOS_TEST_FOR_EXCEPTION(err > TOL, std::runtime_error,
"projectAndNormalizeOutOfPlace(*X2_in, *X2_out, "
"C, B, tuple(X1_out)) did not meet tolerance: "
"orthonormError(X2_out) = "
<< err << " > TOL = " << TOL);
debugOut << "done: || <X2_out,X2_out> - I || = " << err << endl
<< "Calling orthogError(X2_out, X1_out)... ";
err = OM->orthogError (*X2_out, *X1_out);
TEUCHOS_TEST_FOR_EXCEPTION(err > TOL, std::runtime_error,
"projectAndNormalizeOutOfPlace(*X2_in, *X2_out, "
"C, B, tuple(X1_out)) did not meet tolerance: "
"orthogError(X2_out, X1_out) = "
<< err << " > TOL = " << TOL);
debugOut << "done: || <X2_out,X1_out> || = " << err << endl;
debugOut << endl
<< "=== Done with OutOfPlaceNormalizerMixin tests ==="
<< endl << endl;
}
{
//
// Test project() on a random multivector S, by projecting S
// against various combinations of X1 and X2.
//
MVT::MvRandom(*S);
debugOut << "Testing project() by projecting a random multivector S "
"against various combinations of X1 and X2 " << endl;
const int thisNumFailed = testProject(OM,S,X1,X2,MyOM);
numFailed += thisNumFailed;
if (thisNumFailed > 0)
debugOut << " *** " << thisNumFailed
<< (thisNumFailed > 1 ? " tests" : " test")
<< " failed." << endl;
}
if (isRankRevealing)
{
// run a X1,Y2 range multivector against P_{X1,X1} P_{Y2,Y2}
// note, this is allowed under the restrictions on project(),
// because <X1,Y2> = 0
// also, <Y2,Y2> = I, but <X1,X1> != I, so biOrtho must be set to false
// it should require randomization, as
// P_{X1,X1} P_{Y2,Y2} (X1*C1 + Y2*C2) = P_{X1,X1} X1*C1 = 0
mat_type C1(sizeX1,sizeS), C2(sizeX2,sizeS);
C1.random();
C2.random();
// S := X1*C1
MVT::MvTimesMatAddMv(ONE,*X1,C1,ZERO,*S);
// S := S + X2*C2
MVT::MvTimesMatAddMv(ONE,*X2,C2,ONE,*S);
debugOut << "Testing project() by projecting [X1 X2]-range multivector "
"against P_X1 P_X2 " << endl;
const int thisNumFailed = testProject(OM,S,X1,X2,MyOM);
numFailed += thisNumFailed;
if (thisNumFailed > 0)
debugOut << " *** " << thisNumFailed
<< (thisNumFailed > 1 ? " tests" : " test")
<< " failed." << endl;
}
// This test is only distinct from the rank-1 multivector test
// (below) if S has at least 3 columns.
if (isRankRevealing && sizeS > 2)
{
MVT::MvRandom(*S);
RCP<MV> mid = MVT::Clone(*S,1);
mat_type c(sizeS,1);
MVT::MvTimesMatAddMv(ONE,*S,c,ZERO,*mid);
std::vector<int> ind(1);
ind[0] = sizeS-1;
MVT::SetBlock(*mid,ind,*S);
debugOut << "Testing normalize() on a rank-deficient multivector " << endl;
const int thisNumFailed = testNormalize(OM,S,MyOM);
numFailed += thisNumFailed;
if (thisNumFailed > 0)
debugOut << " *** " << thisNumFailed
<< (thisNumFailed > 1 ? " tests" : " test")
<< " failed." << endl;
}
// This test will only exercise rank deficiency if S has at least 2
// columns.
if (isRankRevealing && sizeS > 1)
{
// rank-1
RCP<MV> one = MVT::Clone(*S,1);
MVT::MvRandom(*one);
// put multiple of column 0 in columns 0:sizeS-1
for (int i=0; i<sizeS; i++)
{
std::vector<int> ind(1);
ind[0] = i;
RCP<MV> Si = MVT::CloneViewNonConst(*S,ind);
MVT::MvAddMv(SCT::random(),*one,ZERO,*one,*Si);
}
debugOut << "Testing normalize() on a rank-1 multivector " << endl;
const int thisNumFailed = testNormalize(OM,S,MyOM);
numFailed += thisNumFailed;
if (thisNumFailed > 0)
debugOut << " *** " << thisNumFailed
<< (thisNumFailed > 1 ? " tests" : " test")
<< " failed." << endl;
}
{
std::vector<int> ind(1);
MVT::MvRandom(*S);
debugOut << "Testing projectAndNormalize() on a random multivector " << endl;
const int thisNumFailed = testProjectAndNormalize(OM,S,X1,X2,MyOM);
numFailed += thisNumFailed;
if (thisNumFailed > 0)
debugOut << " *** " << thisNumFailed
<< (thisNumFailed > 1 ? " tests" : " test")
<< " failed." << endl;
}
if (isRankRevealing)
{
// run a X1,X2 range multivector against P_X1 P_X2
// this is allowed as <X1,X2> == 0
// it should require randomization, as
// P_X1 P_X2 (X1*C1 + X2*C2) = P_X1 X1*C1 = 0
// and
// P_X2 P_X1 (X2*C2 + X1*C1) = P_X2 X2*C2 = 0
mat_type C1(sizeX1,sizeS), C2(sizeX2,sizeS);
C1.random();
C2.random();
MVT::MvTimesMatAddMv(ONE,*X1,C1,ZERO,*S);
MVT::MvTimesMatAddMv(ONE,*X2,C2,ONE,*S);
debugOut << "Testing projectAndNormalize() by projecting [X1 X2]-range "
"multivector against P_X1 P_X2 " << endl;
const int thisNumFailed = testProjectAndNormalize(OM,S,X1,X2,MyOM);
numFailed += thisNumFailed;
if (thisNumFailed > 0)
debugOut << " *** " << thisNumFailed
<< (thisNumFailed > 1 ? " tests" : " test")
<< " failed." << endl;
}
// This test is only distinct from the rank-1 multivector test
// (below) if S has at least 3 columns.
if (isRankRevealing && sizeS > 2)
{
MVT::MvRandom(*S);
RCP<MV> mid = MVT::Clone(*S,1);
mat_type c(sizeS,1);
MVT::MvTimesMatAddMv(ONE,*S,c,ZERO,*mid);
std::vector<int> ind(1);
ind[0] = sizeS-1;
MVT::SetBlock(*mid,ind,*S);
debugOut << "Testing projectAndNormalize() on a rank-deficient "
"multivector " << endl;
const int thisNumFailed = testProjectAndNormalize(OM,S,X1,X2,MyOM);
numFailed += thisNumFailed;
if (thisNumFailed > 0)
debugOut << " *** " << thisNumFailed
<< (thisNumFailed > 1 ? " tests" : " test")
<< " failed." << endl;
}
// This test will only exercise rank deficiency if S has at least 2
// columns.
if (isRankRevealing && sizeS > 1)
{
// rank-1
RCP<MV> one = MVT::Clone(*S,1);
MVT::MvRandom(*one);
// Put a multiple of column 0 in columns 0:sizeS-1.
for (int i=0; i<sizeS; i++)
{
std::vector<int> ind(1);
ind[0] = i;
RCP<MV> Si = MVT::CloneViewNonConst(*S,ind);
MVT::MvAddMv(SCT::random(),*one,ZERO,*one,*Si);
}
debugOut << "Testing projectAndNormalize() on a rank-1 multivector " << endl;
bool constantStride = true;
if (! MVT::HasConstantStride(*S)) {
debugOut << "-- S does not have constant stride" << endl;
constantStride = false;
}
if (! MVT::HasConstantStride(*X1)) {
debugOut << "-- X1 does not have constant stride" << endl;
constantStride = false;
}
if (! MVT::HasConstantStride(*X2)) {
debugOut << "-- X2 does not have constant stride" << endl;
constantStride = false;
}
if (! constantStride) {
debugOut << "-- Skipping this test, since TSQR does not work on "
"multivectors with nonconstant stride" << endl;
}
else {
const int thisNumFailed = testProjectAndNormalize(OM,S,X1,X2,MyOM);
numFailed += thisNumFailed;
if (thisNumFailed > 0) {
debugOut << " *** " << thisNumFailed
<< (thisNumFailed > 1 ? " tests" : " test")
<< " failed." << endl;
}
}
}
if (numFailed != 0) {
MyOM->stream(Errors) << numFailed << " total test failures." << endl;
}
return numFailed;
}
private:
/// \fn MVDiff
///
/// Compute and return $\|X - Y\|_F$, the Frobenius (sum of
/// squares) norm of the difference between X and Y.
static magnitude_type
MVDiff (const MV& X, const MV& Y)
{
using Teuchos::RCP;
const scalar_type ONE = SCT::one();
const int numCols = MVT::GetNumberVecs(X);
TEUCHOS_TEST_FOR_EXCEPTION( (MVT::GetNumberVecs(Y) != numCols),
std::logic_error,
"MVDiff: X and Y should have the same number of columns."
" X has " << numCols << " column(s) and Y has "
<< MVT::GetNumberVecs(Y) << " columns." );
// Resid := X
RCP< MV > Resid = MVT::CloneCopy(X);
// Resid := Resid - Y
MVT::MvAddMv (-ONE, Y, ONE, *Resid, *Resid);
return frobeniusNorm (*Resid);
}
/// \fn frobeniusNorm
///
/// Compute and return the Frobenius norm of X.
static magnitude_type
frobeniusNorm (const MV& X)
{
const scalar_type ONE = SCT::one();
const int numCols = MVT::GetNumberVecs(X);
mat_type C (numCols, numCols);
// $C := X^* X$
MVT::MvTransMv (ONE, X, X, C);
magnitude_type err (0);
for (int i = 0; i < numCols; ++i)
err += SCT::magnitude (C(i,i));
return SCT::magnitude (SCT::squareroot (err));
}
static int
testProjectAndNormalize (const Teuchos::RCP< Belos::OrthoManager< Scalar, MV > > OM,
const Teuchos::RCP< const MV >& S,
const Teuchos::RCP< const MV >& X1,
const Teuchos::RCP< const MV >& X2,
const Teuchos::RCP< Belos::OutputManager< Scalar > >& MyOM)
{
return testProjectAndNormalizeNew (OM, S, X1, X2, MyOM);
}
/// Test OrthoManager::projectAndNormalize() for the specific
/// OrthoManager instance.
///
/// \return Count of errors (should be zero)
static int
testProjectAndNormalizeOld (const Teuchos::RCP< Belos::OrthoManager< Scalar, MV > >& OM,
const Teuchos::RCP< const MV >& S,
const Teuchos::RCP< const MV >& X1,
const Teuchos::RCP< const MV >& X2,
const Teuchos::RCP< Belos::OutputManager< Scalar > >& MyOM)
{
using Teuchos::Array;
using Teuchos::null;
using Teuchos::RCP;
using Teuchos::rcp;
using Teuchos::tuple;
const scalar_type ONE = SCT::one();
const magnitude_type ZERO = SCT::magnitude(SCT::zero());
// Relative tolerance against which all tests are performed.
const magnitude_type TOL = 1.0e-12;
// Absolute tolerance constant
const magnitude_type ATOL = 10;
const int sizeS = MVT::GetNumberVecs(*S);
const int sizeX1 = MVT::GetNumberVecs(*X1);
const int sizeX2 = MVT::GetNumberVecs(*X2);
int numerr = 0;
std::ostringstream sout;
//
// output tests:
// <S_out,S_out> = I
// <S_out,X1> = 0
// <S_out,X2> = 0
// S_in = S_out B + X1 C1 + X2 C2
//
// we will loop over an integer specifying the test combinations
// the bit pattern for the different tests is listed in parenthesis
//
// for the projectors, test the following combinations:
// none (00)
// P_X1 (01)
// P_X2 (10)
// P_X1 P_X2 (11)
// P_X2 P_X1 (11)
// the latter two should be tested to give the same answer
//
// for each of these, we should test with C1, C2 and B
//
// if hasM:
// with and without MX1 (1--)
// with and without MX2 (1---)
// with and without MS (1----)
//
// as hasM controls the upper level bits, we need only run test cases 0-3 if hasM==false
// otherwise, we run test cases 0-31
//
int numtests = 4;
// test ortho error before orthonormalizing
if (X1 != null) {
magnitude_type err = OM->orthogError(*S,*X1);
sout << " || <S,X1> || before : " << err << endl;
}
if (X2 != null) {
magnitude_type err = OM->orthogError(*S,*X2);
sout << " || <S,X2> || before : " << err << endl;
}
for (int t=0; t<numtests; t++) {
Array< RCP< const MV > > theX;
RCP<mat_type > B = rcp( new mat_type(sizeS,sizeS) );
Array<RCP<mat_type > > C;
if ( (t % 3) == 0 ) {
// neither <X1,Y1> nor <X2,Y2>
// C, theX and theY are already empty
}
else if ( (t % 3) == 1 ) {
// X1
theX = tuple(X1);
C = tuple( rcp(new mat_type(sizeX1,sizeS)) );
}
else if ( (t % 3) == 2 ) {
// X2
theX = tuple(X2);
C = tuple( rcp(new mat_type(sizeX2,sizeS)) );
}
else {
// X1 and X2, and the reverse.
theX = tuple(X1,X2);
C = tuple( rcp(new mat_type(sizeX1,sizeS)),
rcp(new mat_type(sizeX2,sizeS)) );
}
// We wrap up all the OrthoManager calls in a try-catch
// block, in order to check whether any of the methods throw
// an exception. For the tests we perform, every thrown
// exception is a failure.
try {
// call routine
// if (t && 3) == 3, {
// call with reversed input: X2 X1
// }
// test all outputs for correctness
// test all outputs for equivalence
// here is where the outputs go
Array<RCP<MV> > S_outs;
Array<Array<RCP<mat_type > > > C_outs;
Array<RCP<mat_type > > B_outs;
RCP<MV> Scopy;
Array<int> ret_out;
// copies of S,MS
Scopy = MVT::CloneCopy(*S);
// randomize this data, it should be overwritten
B->random();
for (size_type i=0; i<C.size(); i++) {
C[i]->random();
}
// Run test. Since S was specified by the caller and
// Scopy is a copy of S, we don't know what rank to expect
// here -- though we do require that S have rank at least
// one.
//
// Note that Anasazi and Belos differ, among other places,
// in the order of arguments to projectAndNormalize().
int ret = OM->projectAndNormalize(*Scopy,C,B,theX);
sout << "projectAndNormalize() returned rank " << ret << endl;
if (ret == 0) {
sout << " *** Error: returned rank is zero, cannot continue tests" << endl;
numerr++;
break;
}
ret_out.push_back(ret);
// projectAndNormalize() is only required to return a
// basis of rank "ret"
// this is what we will test:
// the first "ret" columns in Scopy
// the first "ret" rows in B
// save just the parts that we want
// we allocate S and MS for each test, so we can save these as views
// however, save copies of the C and B
if (ret < sizeS) {
std::vector<int> ind(ret);
for (int i=0; i<ret; i++) {
ind[i] = i;
}
S_outs.push_back( MVT::CloneViewNonConst(*Scopy,ind) );
B_outs.push_back( rcp( new mat_type(Teuchos::Copy,*B,ret,sizeS) ) );
}
else {
S_outs.push_back( Scopy );
B_outs.push_back( rcp( new mat_type(*B) ) );
}
C_outs.push_back( Array<RCP<mat_type > >(0) );
if (C.size() > 0) {
C_outs.back().push_back( rcp( new mat_type(*C[0]) ) );
}
if (C.size() > 1) {
C_outs.back().push_back( rcp( new mat_type(*C[1]) ) );
}
// do we run the reversed input?
if ( (t % 3) == 3 ) {
// copies of S,MS
Scopy = MVT::CloneCopy(*S);
// Fill the B and C[i] matrices with random data. The
// data will be overwritten by projectAndNormalize().
// Filling these matrices here is only to catch some
// bugs in projectAndNormalize().
B->random();
for (size_type i=0; i<C.size(); i++) {
C[i]->random();
}
// flip the inputs
theX = tuple( theX[1], theX[0] );
// Run test.
// Note that Anasazi and Belos differ, among other places,
// in the order of arguments to projectAndNormalize().
ret = OM->projectAndNormalize(*Scopy,C,B,theX);
sout << "projectAndNormalize() returned rank " << ret << endl;
if (ret == 0) {
sout << " *** Error: returned rank is zero, cannot continue tests" << endl;
numerr++;
break;
}
ret_out.push_back(ret);
// projectAndNormalize() is only required to return a
// basis of rank "ret"
// this is what we will test:
// the first "ret" columns in Scopy
// the first "ret" rows in B
// save just the parts that we want
// we allocate S and MS for each test, so we can save these as views
// however, save copies of the C and B
if (ret < sizeS) {
std::vector<int> ind(ret);
for (int i=0; i<ret; i++) {
ind[i] = i;
}
S_outs.push_back( MVT::CloneViewNonConst(*Scopy,ind) );
B_outs.push_back( rcp( new mat_type(Teuchos::Copy,*B,ret,sizeS) ) );
}
else {
S_outs.push_back( Scopy );
B_outs.push_back( rcp( new mat_type(*B) ) );
}
C_outs.push_back( Array<RCP<mat_type > >() );
// reverse the Cs to compensate for the reverse projectors
C_outs.back().push_back( rcp( new mat_type(*C[1]) ) );
C_outs.back().push_back( rcp( new mat_type(*C[0]) ) );
// flip the inputs back
theX = tuple( theX[1], theX[0] );
}
// test all outputs for correctness
for (size_type o=0; o<S_outs.size(); o++) {
// S^T M S == I
{
magnitude_type err = OM->orthonormError(*S_outs[o]);
if (err > TOL) {
sout << endl
<< " *** Test (number " << (t+1) << " of " << numtests
<< " total tests) failed: Tolerance exceeded! Error = "
<< err << " > TOL = " << TOL << "."
<< endl << endl;
numerr++;
}
sout << " || <S,S> - I || after : " << err << endl;
}
// S_in = X1*C1 + C2*C2 + S_out*B
{
RCP<MV> tmp = MVT::Clone(*S,sizeS);
MVT::MvTimesMatAddMv(ONE,*S_outs[o],*B_outs[o],ZERO,*tmp);
if (C_outs[o].size() > 0) {
MVT::MvTimesMatAddMv(ONE,*X1,*C_outs[o][0],ONE,*tmp);
if (C_outs[o].size() > 1) {
MVT::MvTimesMatAddMv(ONE,*X2,*C_outs[o][1],ONE,*tmp);
}
}
magnitude_type err = MVDiff(*tmp,*S);
if (err > ATOL*TOL) {
sout << endl
<< " *** Test (number " << (t+1) << " of " << numtests
<< " total tests) failed: Tolerance exceeded! Error = "
<< err << " > ATOL*TOL = " << (ATOL*TOL) << "."
<< endl << endl;
numerr++;
}
sout << " " << t << "|| S_in - X1*C1 - X2*C2 - S_out*B || : " << err << endl;
}
// <X1,S> == 0
if (theX.size() > 0 && theX[0] != null) {
magnitude_type err = OM->orthogError(*theX[0],*S_outs[o]);
if (err > TOL) {
sout << endl
<< " *** Test (number " << (t+1) << " of " << numtests
<< " total tests) failed: Tolerance exceeded! Error = "
<< err << " > TOL = " << TOL << "."
<< endl << endl;
numerr++;
}
sout << " " << t << "|| <X[0],S> || after : " << err << endl;
}
// <X2,S> == 0
if (theX.size() > 1 && theX[1] != null) {
magnitude_type err = OM->orthogError(*theX[1],*S_outs[o]);
if (err > TOL) {
sout << endl
<< " *** Test (number " << (t+1) << " of " << numtests
<< " total tests) failed: Tolerance exceeded! Error = "
<< err << " > TOL = " << TOL << "."
<< endl << endl;
numerr++;
}
sout << " " << t << "|| <X[1],S> || after : " << err << endl;
}
}
}
catch (Belos::OrthoError& e) {
sout << " *** Error: OrthoManager threw exception: " << e.what() << endl;
numerr++;
}
} // test for
// NOTE (mfh 05 Nov 2010) Since Belos::MsgType is an enum,
// doing bitwise logical computations on Belos::MsgType values
// (such as "Debug | Errors") and passing the result into
// MyOM->stream() confuses the compiler. As a result, we have
// to do some type casts to make it work.
const int msgType = (numerr > 0) ?
(static_cast<int>(Debug) | static_cast<int>(Errors)) :
static_cast<int>(Debug);
// We report debug-level messages always. We also report
// errors if at least one test failed.
MyOM->stream(static_cast< MsgType >(msgType)) << sout.str() << endl;
return numerr;
}
/// Test OrthoManager::normalize() for the specific OrthoManager
/// instance.
///
/// \return Count of errors (should be zero)
static int
testNormalize (const Teuchos::RCP< Belos::OrthoManager< Scalar, MV > >& OM,
const Teuchos::RCP< const MV >& S,
const Teuchos::RCP< Belos::OutputManager< Scalar > >& MyOM)
{
using Teuchos::Array;
using Teuchos::RCP;
using Teuchos::rcp;
using Teuchos::tuple;
const scalar_type ONE = SCT::one();
std::ostringstream sout;
// Total number of failed tests in this call of this routine.
int numerr = 0;
// Relative tolerance against which all tests are performed.
// We are measuring things in the Frobenius norm $\| \cdot \|_F$.
// The following bounds hold for all $m \times n$ matrices $A$:
// \[
// \|A\|_2 \leq \|A\|_F \leq \sqrt{r} \|A\|_2,
// \]
// where $r$ is the (column) rank of $A$. We bound this above
// by the number of columns in $A$.
//
// An accurate normalization in the Euclidean norm of a matrix
// $A$ with at least as many rows m as columns n, should
// produce orthogonality $\|Q^* Q - I\|_2$ less than a factor
// of machine precision times a low-order polynomial in m and
// n, and residual $\|A - Q B\|_2$ (where $A = Q B$ is the
// computed normalization) less than that bound times the norm
// of $A$.
//
// Since we are measuring both of these quantitites in the
// Frobenius norm instead, we should scale this bound by
// $\sqrt{n}$.
const int numRows = MVT::GetGlobalLength(*S);
const int numCols = MVT::GetNumberVecs(*S);
const int sizeS = MVT::GetNumberVecs(*S);
// A good heuristic is to scale the bound by the square root
// of the number of floating-point operations. One could
// perhaps support this theoretically, since we are using
// uniform random test problems.
const magnitude_type fudgeFactor =
SMT::squareroot(magnitude_type(numRows) *
magnitude_type(numCols) *
magnitude_type(numCols));
const magnitude_type TOL = SMT::eps() * fudgeFactor *
SMT::squareroot(magnitude_type(numCols));
// Absolute tolerance scaling: the Frobenius norm of the test
// matrix S. TOL*ATOL is the absolute tolerance for the
// residual $\|A - Q*B\|_F$.
const magnitude_type ATOL = frobeniusNorm (*S);
sout << "The test matrix S has Frobenius norm " << ATOL
<< ", and the relative error tolerance is TOL = "
<< TOL << "." << endl;
const int numtests = 1;
for (int t = 0; t < numtests; ++t) {
try {
// call routine
// test all outputs for correctness
// S_copy gets a copy of S; we normalize in place, so we
// need a copy to check whether the normalization
// succeeded.
RCP< MV > S_copy = MVT::CloneCopy (*S);
// Matrix of coefficients from the normalization.
RCP< mat_type > B (new mat_type (sizeS, sizeS));
// The contents of B will be overwritten, but fill with
// random data just to make sure that the normalization
// operated on all the elements of B on which it should
// operate.
B->random();
const int reportedRank = OM->normalize (*S_copy, B);
sout << "normalize() returned rank " << reportedRank << endl;
if (reportedRank == 0) {
sout << " *** Error: Cannot continue, since normalize() "
"reports that S has rank 0" << endl;
numerr++;
break;
}
//
// We don't know in this routine whether the input
// multivector S has full rank; it is only required to
// have nonzero rank. Thus, we extract the first
// reportedRank columns of S_copy and the first
// reportedRank rows of B, and perform tests on them.
//
// Construct S_view, a view of the first reportedRank
// columns of S_copy.
std::vector<int> indices (reportedRank);
for (int j = 0; j < reportedRank; ++j)
indices[j] = j;
RCP< MV > S_view = MVT::CloneViewNonConst (*S_copy, indices);
// Construct B_top, a copy of the first reportedRank rows
// of B.
//
// NOTE: We create this as a copy and not a view, because
// otherwise it would not be safe with respect to RCPs.
// This is because mat_type uses raw pointers
// inside, so that a view would become invalid when B
// would fall out of scope.
RCP< mat_type > B_top (new mat_type (Teuchos::Copy, *B, reportedRank, sizeS));
// Check ||<S_view,S_view> - I||
{
const magnitude_type err = OM->orthonormError(*S_view);
if (err > TOL) {
sout << " *** Error: Tolerance exceeded: err = "
<< err << " > TOL = " << TOL << endl;
numerr++;
}
sout << " || <S,S> - I || after : " << err << endl;
}
// Check the residual ||Residual|| = ||S_view * B_top -
// S_orig||, where S_orig is a view of the first
// reportedRank columns of S.
{
// Residual is allocated with reportedRank columns. It
// will contain the result of testing the residual error
// of the normalization (i.e., $\|S - S_in*B\|$). It
// should have the dimensions of S. Its initial value
// is a copy of the first reportedRank columns of S.
RCP< MV > Residual = MVT::CloneCopy (*S);
// Residual := Residual - S_view * B_view
MVT::MvTimesMatAddMv (-ONE, *S_view, *B_top, ONE, *Residual);
// Compute ||Residual||
const magnitude_type err = frobeniusNorm (*Residual);
if (err > ATOL*TOL) {
sout << " *** Error: Tolerance exceeded: err = "
<< err << " > ATOL*TOL = " << (ATOL*TOL) << endl;
numerr++;
}
sout << " " << t << "|| S - Q*B || : " << err << endl;
}
}
catch (Belos::OrthoError& e) {
sout << " *** Error: the OrthoManager's normalize() method "
"threw an exception: " << e.what() << endl;
numerr++;
}
} // test for
const MsgType type = (numerr == 0) ? Debug : static_cast<MsgType> (static_cast<int>(Errors) | static_cast<int>(Debug));
MyOM->stream(type) << sout.str();
MyOM->stream(type) << endl;
return numerr;
}
/// Test OrthoManager::projectAndNormalize() for the specific
/// OrthoManager instance.
///
/// \return Count of errors (should be zero)
static int
testProjectAndNormalizeNew (const Teuchos::RCP< Belos::OrthoManager< Scalar, MV > > OM,
const Teuchos::RCP< const MV >& S,
const Teuchos::RCP< const MV >& X1,
const Teuchos::RCP< const MV >& X2,
const Teuchos::RCP< Belos::OutputManager< Scalar > >& MyOM)
{
using Teuchos::Array;
using Teuchos::null;
using Teuchos::RCP;
using Teuchos::rcp;
using Teuchos::tuple;
// We collect all the output in this string wrapper, and print
// it at the end.
std::ostringstream sout;
// Total number of failed tests in this call of this routine.
int numerr = 0;
const int numRows = MVT::GetGlobalLength(*S);
const int numCols = MVT::GetNumberVecs(*S);
const int sizeS = MVT::GetNumberVecs(*S);
// Relative tolerance against which all tests are performed.
// We are measuring things in the Frobenius norm $\| \cdot \|_F$.
// The following bounds hold for all $m \times n$ matrices $A$:
// \[
// \|A\|_2 \leq \|A\|_F \leq \sqrt{r} \|A\|_2,
// \]
// where $r$ is the (column) rank of $A$. We bound this above
// by the number of columns in $A$.
//
// Since we are measuring both of these quantitites in the
// Frobenius norm instead, we scale all error tests by
// $\sqrt{n}$.
//
// A good heuristic is to scale the bound by the square root
// of the number of floating-point operations. One could
// perhaps support this theoretically, since we are using
// uniform random test problems.
const magnitude_type fudgeFactor =
SMT::squareroot(magnitude_type(numRows) *
magnitude_type(numCols) *
magnitude_type(numCols));
const magnitude_type TOL = SMT::eps() * fudgeFactor *
SMT::squareroot(magnitude_type(numCols));
// Absolute tolerance scaling: the Frobenius norm of the test
// matrix S. TOL*ATOL is the absolute tolerance for the
// residual $\|A - Q*B\|_F$.
const magnitude_type ATOL = frobeniusNorm (*S);
sout << "-- The test matrix S has Frobenius norm " << ATOL
<< ", and the relative error tolerance is TOL = "
<< TOL << "." << endl;
// Q will contain the result of projectAndNormalize() on S.
RCP< MV > Q = MVT::CloneCopy(*S);
// We use this for collecting the residual error components
RCP< MV > Residual = MVT::CloneCopy(*S);
// Number of elements in the X array of blocks against which
// to project S.
const int num_X = 2;
Array< RCP< const MV > > X (num_X);
X[0] = MVT::CloneCopy(*X1);
X[1] = MVT::CloneCopy(*X2);
// Coefficients for the normalization
RCP< mat_type > B (new mat_type (sizeS, sizeS));
// Array of coefficients matrices from the projection.
// For our first test, we allocate each of these matrices
// with the proper dimensions.
Array< RCP< mat_type > > C (num_X);
for (int k = 0; k < num_X; ++k)
{
C[k] = rcp (new mat_type (MVT::GetNumberVecs(*X[k]), sizeS));
C[k]->random(); // will be overwritten
}
try {
// Q*B := (I - X X^*) S
const int reportedRank = OM->projectAndNormalize (*Q, C, B, X);
// Pick out the first reportedRank columns of Q.
std::vector<int> indices (reportedRank);
for (int j = 0; j < reportedRank; ++j)
indices[j] = j;
RCP< const MV > Q_left = MVT::CloneView (*Q, indices);
// Test whether the first reportedRank columns of Q are
// orthogonal.
{
const magnitude_type orthoError = OM->orthonormError (*Q_left);
sout << "-- ||Q(1:" << reportedRank << ")^* Q(1:" << reportedRank
<< ") - I||_F = " << orthoError << endl;
if (orthoError > TOL)
{
sout << " *** Error: ||Q(1:" << reportedRank << ")^* Q(1:"
<< reportedRank << ") - I||_F = " << orthoError
<< " > TOL = " << TOL << "." << endl;
numerr++;
}
}
// Compute the residual: if successful, S = Q*B +
// X (X^* S =: C) in exact arithmetic. So, the residual is
// S - Q*B - X1 C1 - X2 C2.
//
// Residual := S
MVT::MvAddMv (SCT::one(), *S, SCT::zero(), *Residual, *Residual);
{
// Pick out the first reportedRank rows of B. Make a deep
// copy, since mat_type is not safe with respect
// to RCP-based memory management (it uses raw pointers
// inside).
RCP< const mat_type > B_top (new mat_type (Teuchos::Copy, *B, reportedRank, B->numCols()));
// Residual := Residual - Q(:, 1:reportedRank) * B(1:reportedRank, :)
MVT::MvTimesMatAddMv (-SCT::one(), *Q_left, *B_top, SCT::one(), *Residual);
}
// Residual := Residual - X[k]*C[k]
for (int k = 0; k < num_X; ++k)
MVT::MvTimesMatAddMv (-SCT::one(), *X[k], *C[k], SCT::one(), *Residual);
const magnitude_type residErr = frobeniusNorm (*Residual);
sout << "-- ||S - Q(:, 1:" << reportedRank << ")*B(1:"
<< reportedRank << ", :) - X1*C1 - X2*C2||_F = "
<< residErr << endl;
if (residErr > ATOL * TOL)
{
sout << " *** Error: ||S - Q(:, 1:" << reportedRank
<< ")*B(1:" << reportedRank << ", :) "
<< "- X1*C1 - X2*C2||_F = " << residErr
<< " > ATOL*TOL = " << (ATOL*TOL) << "." << endl;
numerr++;
}
// Verify that Q(1:reportedRank) is orthogonal to X[k], for
// all k. This test only makes sense if reportedRank > 0.
if (reportedRank == 0)
{
sout << "-- Reported rank of Q is zero: skipping Q, X[k] "
"orthogonality test." << endl;
}
else
{
for (int k = 0; k < num_X; ++k)
{
// Q should be orthogonal to X[k], for all k.
const magnitude_type projErr = OM->orthogError(*X[k], *Q_left);
sout << "-- ||<Q(1:" << reportedRank << "), X[" << k
<< "]>||_F = " << projErr << endl;
if (projErr > ATOL*TOL)
{
sout << " *** Error: ||<Q(1:" << reportedRank << "), X["
<< k << "]>||_F = " << projErr << " > ATOL*TOL = "
<< (ATOL*TOL) << "." << endl;
numerr++;
}
}
}
} catch (Belos::OrthoError& e) {
sout << " *** Error: The OrthoManager subclass instance threw "
"an exception: " << e.what() << endl;
numerr++;
}
// Print out the collected diagnostic messages, which possibly
// include error messages.
const MsgType type = (numerr == 0) ? Debug : static_cast<MsgType> (static_cast<int>(Errors) | static_cast<int>(Debug));
MyOM->stream(type) << sout.str();
MyOM->stream(type) << endl;
return numerr;
}
/// Test OrthoManager::project() for the specific OrthoManager instance.
///
/// \return Count of errors (should be zero)
static int
testProjectNew (const Teuchos::RCP< Belos::OrthoManager< Scalar, MV > > OM,
const Teuchos::RCP< const MV >& S,
const Teuchos::RCP< const MV >& X1,
const Teuchos::RCP< const MV >& X2,
const Teuchos::RCP< Belos::OutputManager< Scalar > >& MyOM)
{
using Teuchos::Array;
using Teuchos::null;
using Teuchos::RCP;
using Teuchos::rcp;
using Teuchos::tuple;
// We collect all the output in this string wrapper, and print
// it at the end.
std::ostringstream sout;
// Total number of failed tests in this call of this routine.
int numerr = 0;
const int numRows = MVT::GetGlobalLength(*S);
const int numCols = MVT::GetNumberVecs(*S);
const int sizeS = MVT::GetNumberVecs(*S);
// Relative tolerance against which all tests are performed.
// We are measuring things in the Frobenius norm $\| \cdot \|_F$.
// The following bounds hold for all $m \times n$ matrices $A$:
// \[
// \|A\|_2 \leq \|A\|_F \leq \sqrt{r} \|A\|_2,
// \]
// where $r$ is the (column) rank of $A$. We bound this above
// by the number of columns in $A$.
//
// Since we are measuring both of these quantitites in the
// Frobenius norm instead, we scale all error tests by
// $\sqrt{n}$.
//
// A good heuristic is to scale the bound by the square root
// of the number of floating-point operations. One could
// perhaps support this theoretically, since we are using
// uniform random test problems.
const magnitude_type fudgeFactor =
SMT::squareroot(magnitude_type(numRows) *
magnitude_type(numCols) *
magnitude_type(numCols));
const magnitude_type TOL = SMT::eps() * fudgeFactor *
SMT::squareroot(magnitude_type(numCols));
// Absolute tolerance scaling: the Frobenius norm of the test
// matrix S. TOL*ATOL is the absolute tolerance for the
// residual $\|A - Q*B\|_F$.
const magnitude_type ATOL = frobeniusNorm (*S);
sout << "The test matrix S has Frobenius norm " << ATOL
<< ", and the relative error tolerance is TOL = "
<< TOL << "." << endl;
// Make some copies of S, X1, and X2. The OrthoManager's
// project() method shouldn't modify X1 or X2, but this is a a
// test and we don't know that it doesn't!
RCP< MV > S_copy = MVT::CloneCopy(*S);
RCP< MV > Residual = MVT::CloneCopy(*S);
const int num_X = 2;
Array< RCP< const MV > > X (num_X);
X[0] = MVT::CloneCopy(*X1);
X[1] = MVT::CloneCopy(*X2);
// Array of coefficients matrices from the projection.
// For our first test, we allocate each of these matrices
// with the proper dimensions.
Array< RCP< mat_type > > C (num_X);
for (int k = 0; k < num_X; ++k)
{
C[k] = rcp (new mat_type (MVT::GetNumberVecs(*X[k]), sizeS));
C[k]->random(); // will be overwritten
}
try {
// Compute the projection: S_copy := (I - X X^*) S
OM->project(*S_copy, C, X);
// Compute the residual: if successful, S = S_copy + X (X^*
// S =: C) in exact arithmetic. So, the residual is
// S - S_copy - X1 C1 - X2 C2.
//
// Residual := S - S_copy
MVT::MvAddMv (SCT::one(), *S, -SCT::one(), *S_copy, *Residual);
// Residual := Residual - X[k]*C[k]
for (int k = 0; k < num_X; ++k)
MVT::MvTimesMatAddMv (-SCT::one(), *X[k], *C[k], SCT::one(), *Residual);
magnitude_type residErr = frobeniusNorm (*Residual);
sout << " ||S - S_copy - X1*C1 - X2*C2||_F = " << residErr;
if (residErr > ATOL * TOL)
{
sout << " *** Error: ||S - S_copy - X1*C1 - X2*C2||_F = " << residErr
<< " > ATOL*TOL = " << (ATOL*TOL) << ".";
numerr++;
}
for (int k = 0; k < num_X; ++k)
{
// S_copy should be orthogonal to X[k] now.
const magnitude_type projErr = OM->orthogError(*X[k], *S_copy);
if (projErr > TOL)
{
sout << " *** Error: S is not orthogonal to X[" << k
<< "] by a factor of " << projErr << " > TOL = "
<< TOL << ".";
numerr++;
}
}
} catch (Belos::OrthoError& e) {
sout << " *** Error: The OrthoManager subclass instance threw "
"an exception: " << e.what() << endl;
numerr++;
}
// Print out the collected diagnostic messages, which possibly
// include error messages.
const MsgType type = (numerr == 0) ? Debug : static_cast<MsgType> (static_cast<int>(Errors) | static_cast<int>(Debug));
MyOM->stream(type) << sout.str();
MyOM->stream(type) << endl;
return numerr;
}
static int
testProject (const Teuchos::RCP< Belos::OrthoManager< Scalar, MV > > OM,
const Teuchos::RCP< const MV >& S,
const Teuchos::RCP< const MV >& X1,
const Teuchos::RCP< const MV >& X2,
const Teuchos::RCP< Belos::OutputManager< Scalar > >& MyOM)
{
return testProjectNew (OM, S, X1, X2, MyOM);
}
/// Test OrthoManager::project() for the specific OrthoManager instance.
///
/// \return Count of errors (should be zero)
static int
testProjectOld (const Teuchos::RCP< Belos::OrthoManager< Scalar, MV > > OM,
const Teuchos::RCP< const MV >& S,
const Teuchos::RCP< const MV >& X1,
const Teuchos::RCP< const MV >& X2,
const Teuchos::RCP< Belos::OutputManager< Scalar > >& MyOM)
{
using Teuchos::Array;
using Teuchos::null;
using Teuchos::RCP;
using Teuchos::rcp;
using Teuchos::tuple;
const scalar_type ONE = SCT::one();
// We collect all the output in this string wrapper, and print
// it at the end.
std::ostringstream sout;
// Total number of failed tests in this call of this routine.
int numerr = 0;
const int numRows = MVT::GetGlobalLength(*S);
const int numCols = MVT::GetNumberVecs(*S);
const int sizeS = MVT::GetNumberVecs(*S);
const int sizeX1 = MVT::GetNumberVecs(*X1);
const int sizeX2 = MVT::GetNumberVecs(*X2);
// Relative tolerance against which all tests are performed.
// We are measuring things in the Frobenius norm $\| \cdot \|_F$.
// The following bounds hold for all $m \times n$ matrices $A$:
// \[
// \|A\|_2 \leq \|A\|_F \leq \sqrt{r} \|A\|_2,
// \]
// where $r$ is the (column) rank of $A$. We bound this above
// by the number of columns in $A$.
//
// Since we are measuring both of these quantitites in the
// Frobenius norm instead, we scale all error tests by
// $\sqrt{n}$.
//
// A good heuristic is to scale the bound by the square root
// of the number of floating-point operations. One could
// perhaps support this theoretically, since we are using
// uniform random test problems.
const magnitude_type fudgeFactor =
SMT::squareroot(magnitude_type(numRows) *
magnitude_type(numCols) *
magnitude_type(numCols));
const magnitude_type TOL = SMT::eps() * fudgeFactor *
SMT::squareroot(magnitude_type(numCols));
// Absolute tolerance scaling: the Frobenius norm of the test
// matrix S. TOL*ATOL is the absolute tolerance for the
// residual $\|A - Q*B\|_F$.
const magnitude_type ATOL = frobeniusNorm (*S);
sout << "The test matrix S has Frobenius norm " << ATOL
<< ", and the relative error tolerance is TOL = "
<< TOL << "." << endl;
//
// Output tests:
// <S_out,X1> = 0
// <S_out,X2> = 0
// S_in = S_out + X1 C1 + X2 C2
//
// We will loop over an integer specifying the test combinations.
// The bit pattern for the different tests is listed in parentheses.
//
// For the projectors, test the following combinations:
// none (00)
// P_X1 (01)
// P_X2 (10)
// P_X1 P_X2 (11)
// P_X2 P_X1 (11)
// The latter two should be tested to give the same result.
//
// For each of these, we should test with C1 and C2:
//
// if hasM:
// with and without MX1 (1--)
// with and without MX2 (1---)
// with and without MS (1----)
//
// As hasM controls the upper level bits, we need only run test
// cases 0-3 if hasM==false. Otherwise, we run test cases 0-31.
//
int numtests = 8;
// test ortho error before orthonormalizing
if (X1 != null) {
magnitude_type err = OM->orthogError(*S,*X1);
sout << " || <S,X1> || before : " << err << endl;
}
if (X2 != null) {
magnitude_type err = OM->orthogError(*S,*X2);
sout << " || <S,X2> || before : " << err << endl;
}
for (int t = 0; t < numtests; ++t)
{
Array< RCP< const MV > > theX;
Array< RCP< mat_type > > C;
if ( (t % 3) == 0 ) {
// neither X1 nor X2
// C and theX are already empty
}
else if ( (t % 3) == 1 ) {
// X1
theX = tuple(X1);
C = tuple( rcp(new mat_type(sizeX1,sizeS)) );
}
else if ( (t % 3) == 2 ) {
// X2
theX = tuple(X2);
C = tuple( rcp(new mat_type(sizeX2,sizeS)) );
}
else {
// X1 and X2, and the reverse.
theX = tuple(X1,X2);
C = tuple( rcp(new mat_type(sizeX1,sizeS)),
rcp(new mat_type(sizeX2,sizeS)) );
}
try {
// call routine
// if (t && 3) == 3, {
// call with reversed input: X2 X1
// }
// test all outputs for correctness
// test all outputs for equivalence
// here is where the outputs go
Array< RCP< MV > > S_outs;
Array< Array< RCP< mat_type > > > C_outs;
RCP< MV > Scopy;
// copies of S,MS
Scopy = MVT::CloneCopy(*S);
// randomize this data, it should be overwritten
for (size_type i = 0; i < C.size(); ++i) {
C[i]->random();
}
// Run test.
// Note that Anasazi and Belos differ, among other places,
// in the order of arguments to project().
OM->project(*Scopy,C,theX);
// we allocate S and MS for each test, so we can save these as views
// however, save copies of the C
S_outs.push_back( Scopy );
C_outs.push_back( Array< RCP< mat_type > >(0) );
if (C.size() > 0) {
C_outs.back().push_back( rcp( new mat_type(*C[0]) ) );
}
if (C.size() > 1) {
C_outs.back().push_back( rcp( new mat_type(*C[1]) ) );
}
// do we run the reversed input?
if ( (t % 3) == 3 ) {
// copies of S,MS
Scopy = MVT::CloneCopy(*S);
// randomize this data, it should be overwritten
for (size_type i = 0; i < C.size(); ++i) {
C[i]->random();
}
// flip the inputs
theX = tuple( theX[1], theX[0] );
// Run test.
// Note that Anasazi and Belos differ, among other places,
// in the order of arguments to project().
OM->project(*Scopy,C,theX);
// we allocate S and MS for each test, so we can save these as views
// however, save copies of the C
S_outs.push_back( Scopy );
// we are in a special case: P_X1 and P_X2, so we know we applied
// two projectors, and therefore have two C[i]
C_outs.push_back( Array<RCP<mat_type > >() );
// reverse the Cs to compensate for the reverse projectors
C_outs.back().push_back( rcp( new mat_type(*C[1]) ) );
C_outs.back().push_back( rcp( new mat_type(*C[0]) ) );
// flip the inputs back
theX = tuple( theX[1], theX[0] );
}
// test all outputs for correctness
for (size_type o = 0; o < S_outs.size(); ++o) {
// S_in = X1*C1 + C2*C2 + S_out
{
RCP<MV> tmp = MVT::CloneCopy(*S_outs[o]);
if (C_outs[o].size() > 0) {
MVT::MvTimesMatAddMv(ONE,*X1,*C_outs[o][0],ONE,*tmp);
if (C_outs[o].size() > 1) {
MVT::MvTimesMatAddMv(ONE,*X2,*C_outs[o][1],ONE,*tmp);
}
}
magnitude_type err = MVDiff(*tmp,*S);
if (err > ATOL*TOL) {
sout << " vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv tolerance exceeded! test failed!" << endl;
numerr++;
}
sout << " " << t << "|| S_in - X1*C1 - X2*C2 - S_out || : " << err << endl;
}
// <X1,S> == 0
if (theX.size() > 0 && theX[0] != null) {
magnitude_type err = OM->orthogError(*theX[0],*S_outs[o]);
if (err > TOL) {
sout << " vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv tolerance exceeded! test failed!" << endl;
numerr++;
}
sout << " " << t << "|| <X[0],S> || after : " << err << endl;
}
// <X2,S> == 0
if (theX.size() > 1 && theX[1] != null) {
magnitude_type err = OM->orthogError(*theX[1],*S_outs[o]);
if (err > TOL) {
sout << " vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv tolerance exceeded! test failed!" << endl;
numerr++;
}
sout << " " << t << "|| <X[1],S> || after : " << err << endl;
}
}
// test all outputs for equivalence
// check all combinations:
// output 0 == output 1
// output 0 == output 2
// output 1 == output 2
for (size_type o1=0; o1<S_outs.size(); o1++) {
for (size_type o2=o1+1; o2<S_outs.size(); o2++) {
// don't need to check MS_outs because we check
// S_outs and MS_outs = M*S_outs
// don't need to check C_outs either
//
// check that S_outs[o1] == S_outs[o2]
magnitude_type err = MVDiff(*S_outs[o1],*S_outs[o2]);
if (err > TOL) {
sout << " vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv tolerance exceeded! test failed!" << endl;
numerr++;
}
}
}
}
catch (Belos::OrthoError& e) {
sout << " ------------------------------------------- project() threw exception" << endl;
sout << " Error: " << e.what() << endl;
numerr++;
}
} // test for
MsgType type = Debug;
if (numerr>0) type = Errors;
MyOM->stream(type) << sout.str();
MyOM->stream(type) << endl;
return numerr;
}
};
} // namespace Test
} // namespace Belos
|