toms641_test(): Fortran77 version Test toms641(). 1 inputs ****** matrix a of coefficients 1) 22 10 2 3 7 2) 14 7 10 0 8 3) -1 13 -1 -11 3 4) -3 -2 13 -2 4 5) 9 8 1 -2 4 6) 9 1 -7 5 -1 7) 2 -6 6 5 1 8) 4 5 0 -2 2 Matrix B of right hand sides: 1) 12 1 2) 7 0 3) -14 0 4) -1 0 5) 1 0 6) 8 0 7) 8 0 8) -1 0 MINPRM= 2 MAXPRM= 3 TR= 1 outputs ******* ier = 1 nocoef = 2 the matrix a of coefficients has rank r = 3. the row space of a is spanned by the linear independent rows 1, 2, 3, the column space of a is spanned by the linear independent columns 1, 2, 3, ============================================================================================ each of the integers given below is in fixed-radix form. from left to right, the numbers are coef(1),coef(2),...,coef(l), and the value of the integer is coef(1)*base**(l-1)+coef(2)*base**(l-2)+...+coef(l) with base = 10000. ============================================================================================ the null space of a is spanned by the subsequent linear independent integer vectors vector no. 1 -1357 2124 413 2596 0 vector no. 2 -413 -708 -1003 0 2596 For each right hand side of the system the solution or least squares solution with minimum euclidean norm was computed. right-hand side no. 1 the system is consistent. numerators of the elements of the solution 1 2263 4240 -8552 -4480 1941 5040 1 3099 80 368 6400 right-hand side no. 2 the system is inconsistent. numerators of the elements of the solution 405 432 88 4736 -40 -3968 145 7664 72 9600 common denominator for all solutions 1 9169 2800 1 inputs ****** matrix a of coefficients 1) 492087 -709497 187957 -259731 -900605 -245025 214306 -949049 729469 744219 -397833 -2970 606256 697417 359680 2) -350227 -361288 -216539 164600 -837399 101957 -260009 -20655 337077 -74434 23128 -633695 -152083 567074 -283167 3) 282479 -478604 -1102418 109328 381875 -418832 692579 109496 -369762 -543023 745290 -149995 -638732 25778 580502 4) 91341 -401532 -147343 266670 -310153 538117 171466 437626 -14578 -847067 -415763 -241116 554064 -315262 -270857 5) 99897 -657650 -632981 -160398 241297 387996 307451 219860 -233916 -821091 142918 -363595 -56018 89552 378 6) -301068 -70933 374333 507914 -394894 18595 38960 177457 -375014 -241288 -1313456 -405068 1014990 -470652 -219886 7) -615366 562702 684876 494229 80686 -276158 -695252 -131317 -133348 575095 274542 472610 -164129 387111 -398100 8) 508703 561881 1860 267772 848669 159042 214123 -8012 -83117 324641 671975 370555 -733148 412712 572533 9) 720241 -134916 308234 -257128 -744452 -67798 355054 -1269458 573099 968986 153335 -169652 902516 545830 359061 10) -157890 -4483 130424 90998 -366923 481801 69782 299287 -383766 -352561 204854 -308907 -42515 -175646 -603725 11) 233409 -13077 -291423 481490 1147212 422390 583629 -204427 -472674 -582579 466999 23633 -60490 640406 427714 12) 918902 46783 691388 -644399 218594 1022455 658106 -30196 -136038 277270 172579 425328 649680 -627671 645470 13) 311750 20737 -237472 601304 -239831 -396442 651570 -596281 125793 295719 741647 53769 -244240 661274 577991 14) 191554 234091 268379 50158 -250918 -129758 -159052 -264225 488413 759604 753499 495538 -694572 616066 209756 15) 182191 10115 -32461 375880 -59164 23958 -113900 -19560 108217 -221548 207284 242288 524976 -115334 -153142 16) -122348 -151131 -155484 483042 14284 309464 275043 -61430 -210491 -584856 2568 -362870 41415 470732 -339069 17) 717504 -149106 505757 -202633 309393 336444 -83013 -1039658 416580 656707 -458682 141851 1121306 757765 260048 18) 362375 -384187 -859582 -303658 431743 -382511 356992 -194016 320219 -461458 215142 83803 -386386 194762 186723 19) 55446 248625 52618 861254 623512 -1335000 92472 -1319502 288512 777378 -270360 590661 103096 1306164 424516 20) 932120 -325993 -623721 -188670 -244095 -382160 713474 -413942 79136 101336 751155 111598 187597 -285886 484845 21) -350125 -19109 463457 -396770 198772 549338 -193343 896664 -276366 -737453 -572295 472391 290185 -1123052 -564571 22) -40551 174553 216024 567650 183856 32852 -638864 43472 229986 119611 -529480 88563 -66670 665740 -399425 23) 10999 98144 -279193 -52699 -136987 47828 47830 779035 -147852 -390133 -14656 -76321 -166227 -929415 75384 24) -318425 -66824 -225986 127704 268559 439151 310059 918952 -719924 -881586 723391 131856 -587941 -623020 -104359 25) -544900 -219563 677676 64239 -702188 232508 -809728 230537 113145 51123 -876125 -21356 562646 -32725 -879899 26) 149767 73148 610233 -274640 465932 -170888 -74268 -896286 330500 996330 134231 643900 103819 816604 620203 27) -92822 228283 -69496 -307181 191211 19716 175565 318160 -646743 125889 -212430 -522264 -302790 -526335 144904 28) -581144 -122653 -225720 -290154 403635 -580239 -592118 -6537 -66192 301738 -118623 -33003 -683797 404314 2233 29) -1112 -107494 -576317 -519415 -102546 180727 480081 360092 -27089 -390767 -74095 -719809 -326443 -509519 421942 30) -105312 -260725 -306438 366643 -56987 -619982 -27366 -483587 94019 288139 -326606 -292645 -185832 835981 169046 Matrix B of right hand sides: 1) 187 499 -239 2) -444 255 243 3) -585 422 -604 4) 348 475 579 5) 333 -560 -327 6) -331 -607 141 7) -201 -296 571 8) -219 -301 226 9) -521 -110 -202 10) -365 -479 314 11) 603 -485 -100 12) 488 239 376 13) -67 291 253 14) 105 -211 251 15) -33 163 80 16) 538 -22 -315 17) 497 -377 -70 18) 84 -423 467 19) 27 592 -7 20) -517 166 287 21) -23 -384 -553 22) 156 -403 610 23) -2 -172 468 24) 96 405 -540 25) -184 -360 -134 26) 616 412 -57 27) -256 -380 -277 28) -592 -61 -532 29) 368 618 550 30) -431 -85 286 MINPRM= 22 MAXPRM= 42 TR= 4 outputs ******* ier = 1 nocoef = 42 the matrix a of coefficients has rank r = 12. the row space of a is spanned by the linear independent rows 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, the column space of a is spanned by the linear independent columns 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ============================================================================================ each of the integers given below is in fixed-radix form. from left to right, the numbers are coef(1),coef(2),...,coef(l), and the value of the integer is coef(1)*base**(l-1)+coef(2)*base**(l-2)+...+coef(l) with base = 10000. ============================================================================================ the null space of a is spanned by the subsequent linear independent integer vectors vector no. 1 -190 -7474 -1059 -7409 -4585 -3232 -5525 -9058 -9851 -9916 -5726 -2943 -3311 -4345 -4344 -6155 -9988 -316 188 8313 6470 7189 6437 2285 4637 7260 3488 1598 6160 4473 3743 4106 1728 9414 2784 8740 -568 -8639 -4035 -4209 -2284 -3290 -9485 -4005 -6756 -5873 -3207 -5211 -9116 -9982 -8685 -1581 -2790 -1064 2521 1130 1344 7124 7493 380 236 6626 8199 7311 2956 5732 6347 2712 5887 684 6260 -188 -5792 -5340 -5844 -9312 -4792 -4257 -7023 -6861 -3398 -8849 -1516 -8010 -7758 -9016 -3527 -2100 -2480 378 8224 4140 564 9648 3038 9023 5609 3459 6915 9952 8546 9856 9409 7935 7909 719 276 8571 7842 4572 224 1476 3292 804 6531 1879 858 4052 3490 9580 7222 8016 327 7284 -187 -8733 -4176 -2079 -7363 -1811 -9193 -6361 -306 -2439 -6377 -5238 -3959 -3986 -5421 -1043 -4183 -2952 -188 -2767 -1984 -4231 -2762 -7800 -7801 -6739 -6909 -1559 -2075 -5968 -9131 -6142 -1761 -2462 -7278 -6968 190 7474 1059 7409 4585 3232 5525 9058 9851 9916 5726 2943 3311 4345 4344 6155 9988 316 -188 -9322 -922 -7727 -5287 -1282 -6789 -7355 -138 -8878 -5084 -9656 -36 -4645 -813 -9769 -1058 -7244 378 4190 6331 8413 4248 7050 415 5230 6856 7796 4254 7816 4684 7254 1595 6489 7623 6260 1 1092 8972 5916 7348 8969 3672 1041 3158 78 8169 7008 9223 5927 9935 3903 1012 3544 0 0 vector no. 2 126 556 5067 2356 2374 6519 11 8331 3409 9865 5647 8286 6317 3635 6294 3534 2313 0 -124 -387 -6026 -1598 -5376 -6574 -6971 -6438 -395 -4267 -7157 -4634 -456 -2857 -4593 -6437 -6835 -9920 375 5449 9448 3083 7026 5629 4083 2532 7311 319 4906 111 5332 6895 2672 1377 1818 8896 -9076 -68 -4840 -9649 -974 -9368 -851 -9856 -5519 -320 -6643 -6637 -4850 -1765 -3193 -4464 -6536 124 2404 4930 2674 3076 4569 1275 6627 3696 8827 5006 4999 3042 3935 2763 7147 3383 6928 -250 -6994 -7805 -7182 -850 -7076 -9895 -5337 -3709 -7812 -6352 -4016 -4531 -9726 -5398 -2100 -8792 -944 -2016 -8904 -1075 -7699 -7994 -4304 -189 -3301 -4559 -7849 -365 -2586 -1077 -8170 -709 -6547 -7008 125 2488 9450 8053 1575 4541 2795 7574 204 1626 4251 6825 5972 9324 3614 695 6122 1968 124 387 6026 1598 5376 6574 6971 6438 395 4267 7157 4634 456 2857 4593 6437 6835 9920 -126 -556 -5067 -2356 -2374 -6519 -11 -8331 -3409 -9865 -5647 -8286 -6317 -3635 -6294 -3534 -2313 0 124 8455 1642 5901 6175 8552 4187 7195 3601 2506 8553 6095 800 7168 7273 9276 3026 7952 -249 -6910 -3285 -1803 -2351 -7104 -8375 -4390 -7202 -5013 -7107 -2190 -1601 -4337 -4547 -8552 -6053 -5904 0 1 1092 8972 5916 7348 8969 3672 1041 3158 78 8169 7008 9223 5927 9935 3903 1012 3544 0 vector no. 3 -123 -8370 -7122 -522 -7676 -8580 -2667 -6248 -7093 -9707 -9308 -4268 -7870 -1779 -6423 -5728 -288 -2912 124 387 6026 1598 5376 6574 6971 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8172 3154 2481 4677 746 4028 8816 0 0 1 1092 8972 5916 7348 8969 3672 1041 3158 78 8169 7008 9223 5927 9935 3903 1012 3544 For each right hand side of the system was computed. right-hand side no. 1 the system is inconsistent. numerators of the elements of the solution 193 3356 2224 5453 4123 2411 1429 5088 8395 8565 7283 4245 367 7423 7107 5067 6129 3382 1892 5818 4454 3938 7239 1755 5134 5055 3727 8189 3177 5701 4519 2801 1720 2193 1926 226 9930 3850 420 227 2378 7395 7225 3763 3043 3935 4863 3143 2136 989 9130 6493 2101 8214 8731 1346 2477 2961 3858 655 6686 223 7140 7754 9382 647 8851 479 5961 8879 444 9998 6127 5572 1005 4916 6980 1032 609 5079 5125 8905 3916 8311 1630 8074 6155 5718 1419 5698 8287 9760 7962 9271 194 4599 5547 4408 -325 -6361 -4222 -1490 -1420 -1316 -7053 -4687 -7495 -4427 -2984 -9966 -798 -7624 -8688 -6974 -8673 -4503 -8129 -3889 -7224 -5306 -6578 -6293 -1428 -3420 -6189 -977 -1647 -9611 -9607 -6447 -9328 -9893 -9422 -6447 -8020 -6931 -9529 -9560 -3501 -3390 -920 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-2719 -516 -3913 -6461 -4708 -1489 -3400 -3110 -9659 -2844 -1250 -1175 -2265 -9017 -2013 -9979 -976 -7433 -5099 -1882 -7433 -1812 -4961 -6203 -820 -9937 -8530 -3269 -8293 -6102 -3928 -6698 -4424 -2014 -5293 1243 4168 1356 2463 1567 4995 7902 2495 1288 5089 5407 5669 2006 3502 6276 1712 8720 6137 8288 5241 3203 9986 1786 6617 7461 4701 4154 4300 9844 2650 3396 9082 2537 1712 4358 3105 7193 4736 9046 6052 4154 3841 5202 3708 7051 4201 5516 5602 1201 0 0 0 right-hand side no. 2 the system is inconsistent. numerators of the elements of the solution -1807 -4713 -2402 -3862 -2153 -631 -1696 -1440 -4160 -79 -9571 -6744 -6307 -9340 -5927 -407 -8898 -8534 -4760 -7830 -9195 -1584 -9848 -5793 -2486 -1755 -3415 -9502 -6442 -1445 -7080 -4830 -5539 -5509 -9105 -991 -2638 -6418 -5249 -3874 -1922 -1999 -9136 -2891 -3056 -1914 -1276 -1191 -410 -2029 -703 -6010 -4301 -1937 -3699 -7262 -8815 -7854 -9897 -8951 -2408 -4487 -2836 -1104 -9723 -552 -321 -4158 -7378 -8776 -691 -4325 -4101 -3617 -9226 -8809 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1654 1968 5697 3514 3872 6155 5921 5131 5525 5912 52 9287 9555 8478 2581 9161 6766 3958 5435 9839 3061 1682 200 3181 7441 218 1900 5441 3305 5537 7923 3137 8643 9833 2614 5096 323 8500 7049 -1939 -5984 -4882 -2997 -1930 -5606 -3184 -2927 -1386 -5933 -8450 -5708 -5034 -5884 -8685 -7135 -7114 -5984 -9049 -7044 -9602 -5559 -2517 -8634 -2362 -8510 -6725 -9036 -5098 -265 -8943 -9478 -975 -5276 -2932 -7231 -9548 -6382 -8789 -5273 -3390 -6210 -6860 -9400 -2220 -1239 -7892 -8187 -3170 -690 -4595 -9442 -2776 -2223 -906 -8800 -2729 -8289 -590 -7894 -7052 -6784 -1705 -1266 -4501 -5557 -8697 -6480 -9514 -8428 -1582 -615 -6027 -3135 -682 -577 -7354 -1374 -9635 -1273 -7443 -3268 -732 -7702 -6570 -607 -1557 -6263 -8274 -4348 -5206 -8369 -7886 -5415 -3877 -6274 -5147 -560 0 0 0 right-hand side no. 3 the system is inconsistent. numerators of the elements of the solution -788 -4278 -6937 -2266 -680 -1590 -5533 -6115 -6534 -4931 -2706 -4853 -9750 -7843 -5989 -881 -1085 -2922 -7036 -3853 -3375 -9003 -9261 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-818 -5896 -8904 -1535 -8492 -1530 -3012 -7065 -8640 -510 -1265 -8811 -605 -4750 -9038 -1770 -702 -4229 -2947 -1747 -830 -5000 -2952 0 0 0 common denominator for all solutions -225 -669 -3961 -8474 -172 -1676 -8282 -9619 -1154 -9971 -5833 -807 -2266 -6633 -1628 -2903 -8220 -5210 -8355 -6692 -6835 -6979 -7880 -2240 -9474 -9669 -8420 -3667 -9232 -7229 -1985 -719 -8520 -695 -2579 -1039 -8748 -312 -7695 -1952 -8303 -6150 -7754 -5185 -6576 -2588 -226 -7653 -3885 1 inputs ****** matrix a of coefficients 1) 100006 100005 100004 100003 100002 100001 2) 100005 100005 100004 100003 100002 100001 3) 100004 100004 100004 100003 100002 100001 4) 100003 100003 100003 100003 100002 100001 5) 100002 100002 100002 100002 100001 100000 6) 100001 100001 100001 100001 100000 99999 7) 100000 100000 100000 100000 99999 99998 Matrix B of right hand sides: 1) 1 1 2) 1 2 3) 1 3 4) 1 4 5) 1 5 6) 1 6 7) 1 7 MINPRM= 8 MAXPRM= 15 TR= 3 outputs ******* ier = 0 nocoef = 2 the matrix a of coefficients has rank r = 5. the row space of a is spanned by the linear independent rows 1, 2, 3, 4, 5, the column space of a is spanned by the linear independent columns 1, 2, 3, 4, 5, ============================================================================================ each of the integers given below is in fixed-radix form. from left to right, the numbers are coef(1),coef(2),...,coef(l), and the value of the integer is coef(1)*base**(l-1)+coef(2)*base**(l-2)+...+coef(l) with base = 10000. ============================================================================================ the null space of a is spanned by the subsequent linear independent integer vectors vector no. 1 0 0 0 1 -2 1 For each right hand side of the system was computed. right-hand side no. 1 the system is consistent. numerators of the elements of the solution 0 0 0 -20 20 0 right-hand side no. 2 the system is consistent. numerators of the elements of the solution 20 0 0 -200 -140 200 140 0 common denominator for all solutions -20 toms641_test(): Normal end of execution.