SQL Server 2008, numeric library, c++, LAPACK, memory question - c++

I am trying to send a table of numbers in SQL Server 2008 like:
1att 2att 3att 4att 5att 6att 7att ... attn
--------------------------------------------
565 526 472 527 483 529 476 470 502
497 491 483 488 488 483 496 515 491
467 516 480 477 494 497 478 519 471
488 466 547 498 477 466 475 480 516
543 491 449 485 495 468 452 479 516
473 475 431 474 460 342 471 386 549
489 477 462 428 489 491 481 483 475
485 474 472 452 525 508 459 561 529
473 457 476 498 485 465 540 475 525
455 477 415 434 475 499 476 482 551
463 476 476 471 488 526 394 439 475
479 473 491 519 483 474 476 474 478
455 518 465 445 496 500 518 470 536
557 498 492 449 478 491 492 476 460
484 509 538 473 548 497 551 477 498
471 430 482 437 516 483 487 453 456
505 476 489 495 472 476 487 516 466
466 495 488 475 550 565 510 473 515
470 490 480 475 479 544 468 486 496
484 495 524 435 469 612 493 467 477
....
.... (several more rows)
....
511 471 529 553 539 501 477 474 494
via visual studio 2008 (in a c++ project) to a mathematical library LAPACK.
Is it possible to pass the table in SQL Server to LAPACK (via c++ in visual studio 2008) like a memory pointer, or store all the table in RAM, and LAPACK read memory or pointer to memory, but without writing to a file and reading it
Could you please suggest how to pass a table like this (maybe the location of table in memory, or something similar) to LAPACK?
(so I am able to do some computing with LAPACK of the table stored in SQL Server via visual studio 2008 c++ project)
----EDIT---
#MarkD, As you said in your anwer could you please give an example of computing SVD with the idea in the example, using std::vector class
?


LAPACK requires the data sent to it, to be in a FORTRAN style (Column-order) array. You won't be able to pass the data directly from SQL to LAPACK but will need to read the data into a column-ordered contiguous memory array, and pass a pointer to the first element of the array to the LAPACK routine of interest.
There are many LAPACK wrappers for C/C++ out there that make this much easier.
Edit: just saw you are looking specifically for how to pass such an array. As I mentioned, there are many wrappers out there for doing this (just do a search for C/C++ LAPACK). An easy way to create your array is to use the std::vector class. You would then read the data in, column-by-column, adding the elements to your vector- So if you wanted to column-order the array you show in your exmaple, your vector would end up looking something like:
//Column 1 Column 2 Column 3 ... last element
[565 497 467 488 ... 526 491 516 466 ... 472 483 480 547 ... ... 494]
You would then pass the LAPACK routine of interest the memory location of the first element, eg:
&myVector[0]
This is possible using std::vector, as the standard ensures that a vector uses contiguous memory storage. The LAPACK routines all also require the size/dimensions of the matrix/vectors you are passing to it (so you'll need to calculate/specify these values for the function call).
If you can post the specific LAPACK routine you want to use, I can give a more thorough example.

Related

Clojure: Sets, order and purity

Is (vec #{1 2 3}) guaranteed to always return [1 3 2] or could the order be different?
I am not so much interested in the implementation details behind this but going from unordered to ordered in general in order to keep my functions pure and easily testable.

As mentioned, standard #{} sets (both PersistentArrayMap and PersistentHashMap; depending on the size) are considered unordered.
Regarding purity with respect to calling seq on a set though, the current implementation does seem to return a well-defined, consistent order; just not an easily predictable one:
(let [r (range 1000)
seqs (repeatedly 1000 #(seq (add-randomly #{} r)))]
; See how many different orders were produced
(println (count (set seqs)))
(println (first seqs)))
1
(0 893 920 558 453 584 487 637 972 519 357 716 950 275 530 929 789 389 586 410 433 765 521 451 291 443 798 779 970 249 638 299 121 734 287 65 702 70 949 218 648 812 62 74 774 475 497 580 891 164 282 769 799 273 186 430 641 529 898 370 834 233 298 188 240 110 130 982 620 311 931 882 128 399 989 377 468 259 210 229 153 621 213 670 977 343 958 887 472 7 894 59 934 473 86 756 830 613 491 154 20 224 355 592 610 806 571 466 72 454 888 463 851 770 814 859 58 964 980 205 555 552 60 835 459 175 322 510 662 27 352 493 899 416 777 694 1 631 854 69 101 24 901 547 102 788 713 385 988 135 397 773 490 752 354 884 360 998 961 55 568 797 688 763 269 676 448 527 206 966 165 715 387 652 683 85 721 862 615 681 225 865 297 39 805 274 88 217 46 682 508 149 415 239 478 878 157 345 300 743 921 4 550 204 470 646 77 106 197 405 897 726 776 940 755 902 518 232 260 823 267 119 319 534 222 603 293 95 450 329 144 504 819 818 505 723 992 176 863 471 349 512 710 192 54 92 221 141 502 871 464 801 307 935 758 290 627 517 361 264 137 356 728 976 678 327 234 856 817 104 353 15 48 945 759 242 832 969 50 956 917 557 251 394 116 585 583 75 437 516 994 930 967 687 159 848 995 709 99 540 645 749 479 890 630 916 815 281 402 669 781 740 975 429 309 458 21 388 495 952 626 875 31 113 32 811 827 407 398 136 691 847 825 139 506 396 460 483 589 581 932 174 578 855 331 363 284 208 305 955 796 708 182 256 657 514 731 619 985 485 214 193 685 804 869 836 785 635 442 561 954 656 607 241 314 782 226 235 672 420 418 262 263 304 401 673 40 129 600 729 467 445 317 294 91 810 364 987 880 515 412 553 974 341 117 665 523 172 601 108 156 358 308 908 649 531 923 223 419 365 944 181 417 979 278 56 942 33 13 867 22 618 380 257 338 500 909 993 168 833 496 947 347 501 596 872 792 90 237 826 292 109 216 191 498 829 761 375 525 367 143 742 178 640 247 328 391 990 167 707 36 41 474 187 551 996 528 971 599 376 195 889 316 668 428 303 671 794 905 368 560 565 310 366 118 522 150 886 313 384 567 238 846 962 845 196 162 393 184 219 999 461 89 100 426 604 477 844 541 351 243 131 790 963 629 873 122 933 43 231 61 654 883 598 413 29 784 800 151 369 348 575 693 44 739 258 250 674 539 301 838 424 93 6 684 951 573 408 563 850 616 866 111 997 689 28 456 374 608 737 548 538 895 411 957 134 943 64 623 465 816 334 323 189 280 198 155 295 808 248 587 285 507 227 724 476 941 911 853 494 220 842 103 697 611 170 51 25 261 768 822 201 904 590 489 778 166 447 34 252 978 775 325 594 436 828 535 813 146 741 876 228 907 306 125 276 340 148 482 622 588 17 312 606 3 520 760 720 286 279 879 536 663 12 440 332 330 382 152 544 803 642 435 342 703 783 695 973 2 948 66 484 439 236 556 373 142 359 727 371 772 444 570 757 107 532 984 23 745 719 230 625 47 526 180 786 870 537 659 158 991 350 35 849 644 881 127 927 675 383 533 910 302 564 701 566 821 787 82 76 735 492 718 771 215 97 704 277 926 751 19 335 597 938 57 609 202 68 452 200 868 11 115 946 983 339 431 462 337 698 255 503 546 9 953 857 706 632 457 427 145 5 733 624 831 244 918 824 289 112 925 730 699 712 414 839 802 860 179 344 481 732 661 245 378 913 906 658 266 324 793 680 446 524 254 404 617 283 513 572 705 959 83 634 138 346 14 455 265 449 333 650 639 569 326 746 647 45 53 559 78 924 562 542 912 664 315 914 480 132 753 900 26 766 123 203 667 392 577 807 140 321 795 441 700 268 840 16 320 133 288 381 605 163 81 120 643 79 211 38 173 126 981 421 593 636 98 422 423 614 762 582 666 554 409 574 595 124 747 171 87 169 653 679 843 160 30 400 767 896 928 696 738 809 509 736 207 874 434 690 194 511 73 486 336 96 837 937 10 660 272 499 488 903 386 270 576 717 543 271 18 395 403 469 105 185 52 545 633 114 968 253 612 628 748 209 147 655 750 852 425 864 67 296 602 318 161 651 725 372 406 438 780 711 71 939 579 877 722 42 919 80 885 986 714 677 199 841 754 791 861 591 744 960 37 183 965 892 432 379 63 212 94 362 8 686 692 764 246 190 549 922 177 915 936 820 49 858 390 84)
So yes, it seems that within a single run of a program, the order of (seq #{1 2 3}) can be relied upon, and can be considered pure. The language gives no guarantees though, and this property may not always exist, so really, I wouldn't rely on it. It's an implementation detail.
If you require a consistent ordering, it may be beneficial to have a vector along with the set to define the order. You could do something like:
(def pair [#{} []])
(defn add [p n]
(-> p
(update 0 conj n)
(update 1 conj n)))
(-> pair
(add 1)
(add 2))
=> [#{1 2} [1 2]]
Reference the set when you want to do a membership test, and the vector when you need order. Of course, this requires twice as much memory as it otherwise would though, so this may not always be practical. Additions to both sets and vectors are essentially constant however, so additions will still be quick.

MPI_Rank value is disturbed by MPI_RECV subroutine [duplicate]

This question already has an answer here:
MPI_Recv overwrites parts of memory it should not access
(1 answer)
Closed 7 years ago.
Despite having written long, heavily parallelized codes with complicated send/receives over three dimensional arrays, this simple code with a two dimensional array of integers has got me at my wits end. I combed stackoverflow for possible solutions and found one that resembled slightly with the issue I am having:
Boost.MPI: What's received isn't what was sent!
However the solutions seem to point the looping segment of code as the culprit for overwriting sections of the memory. But this one seems to act even stranger. Maybe it is a careless oversight of some simple detail on my part. The problem is with the below code:
program main
implicit none
include 'mpif.h'
integer :: i, j
integer :: counter, offset
integer :: rank, ierr, stVal
integer, dimension(10, 10) :: passMat, prntMat !! passMat CONTAINS VALUES TO BE PASSED TO prntMat
call MPI_INIT(ierr)
call MPI_COMM_RANK(MPI_COMM_WORLD, rank, ierr)
counter = 0
offset = (rank + 1)*300
do j = 1, 10
do i = 1, 10
prntMat(i, j) = 10 !! prntMat OF BOTH RANKS CONTAIN 10
passMat(i, j) = offset + counter !! passMat OF rank=0 CONTAINS 300..399 AND rank=1 CONTAINS 600..699
counter = counter + 1
end do
end do
if (rank == 1) then
call MPI_SEND(passMat(1:10, 1:10), 100, MPI_INTEGER, 0, 1, MPI_COMM_WORLD, ierr) !! SEND passMat OF rank=1 to rank=0
else
call MPI_RECV(prntMat(1:10, 1:10), 100, MPI_INTEGER, 1, 1, MPI_COMM_WORLD, stVal, ierr)
do i = 1, 10
print *, prntMat(:, i)
end do
end if
call MPI_FINALIZE(ierr)
end program main
When I compile the code with mpif90 with no flags and run it on my machine with mpirun -np 2, I get the following output with wrong values in the first four indices of the array:
0 0 400 0 604 605 606 607 608 609
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
However, when I compile it with the same compiler but with the -O3 flag on, I get the correct output:
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
This error is machine dependent. This issue turns up only on my system running Ubuntu 14.04.2, using OpenMPI 1.6.5
I tried this on other systems running RedHat and CentOS and the code ran well with and without the -O3 flag. Curiously those machines use an older version of OpenMPI - 1.4
I am guessing that the -O3 flag is performing some odd optimization that is modifying the manner in which arrays are being passed between the processes.
I also tried other versions of array allocation. The above code uses explicit shape arrays. With assumed shape and allocated arrays I am receiving equally, if not more bizarre results, with some of them seg-faulting. I tried using Valgrind to trace the origin of these seg-faults, but I still haven't gotten the hang of getting Valgrind to not give false positives when running with MPI programs.
I believe that resolving the difference in performance of the above code will help me understand the tantrums of my other codes as well.
Any help would be greatly appreciated! This code has really gotten me questioning if all the other MPI codes I wrote are sound at all.

Using the Fortran 90 interface to MPI reveals a mismatch in your call to MPI_RECV
call MPI_RECV(prntMat(1:10, 1:10), 100, MPI_INTEGER, 1, 1, MPI_COMM_WORLD, stVal, ierr)
1
Error: There is no specific subroutine for the generic ‘mpi_recv’ at (1)
This is because the status variable stVal is an integer scalar, rather than an array of MPI_STATUS_SIZE. The F77 interface (include 'mpif.h') to MPI_RECV is:
INCLUDE ’mpif.h’
MPI_RECV(BUF, COUNT, DATATYPE, SOURCE, TAG, COMM, STATUS, IERROR)
<type> BUF(*)
INTEGER COUNT, DATATYPE, SOURCE, TAG, COMM
INTEGER STATUS(MPI_STATUS_SIZE), IERROR
Changing
integer :: rank, ierr, stVal
to
integer :: rank, ierr, stVal(mpi_status_size)
produces a program that works as expected, tested with gfortran 5.1 and OpenMPI 1.8.5.
Using the F90 interface (use mpi vs include "mpif.h") lets the compiler detect the mismatched arguments at compile time rather than producing confusing runtime problems.

double free or corruption (fasttop): 0x000000000063d070 *** c++ sieve program

I am writing a sieve program in c++. But for every legitimate input, the program always produces output with 4 primes founded and "2 3 5", no matter how the input varies. As I try to run the program via the console, it gives an error message saying that double free or corruption (fasttop): 0x000000000063d070 ***. Btw, I am new to c++.
And also, I am trying to format the output correctly, but the they are just flying around.
This is the desired format.
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71
73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173
179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281
283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409
419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541
547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659
661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809
811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941
947 953 967 971 977 983 991 997

Aside from your double-free being caused by calling the destructor explicitly as #PaulMcKenzie said in the comments, your problem with only outputting the first few primes is because of this line:
int n = sizeof(is_prime_);
is_prime_ is a pointer and so its size is fixed at compile time (probably 4 or 8 bytes depending on your system).
You already have limit_ as a value, you should use that to work out your n.

Verifying output to "Find the numbers between 1 and 1000 whose prime factors' sum is itself a prime" from Allain's Jumping into C++ (ch7 #3)

The question:
Design a program that finds all numbers from 1 to 1000 whose prime factors, when added
together, sum up to a prime number (for example, 12 has prime factors of 2, 2, and 3, which
sum to 7, which is prime). Implement the code for that algorithm.
I modified the problem to only sum unique factors, because I don't see why you'd count a factor twice, as in his example using 12.
My solution. Is there any good (read: automated) way to verify the output of my program?
Sample output for 1 to 1000:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
17
19
20
22
23
24
25
26
28
29
30
31
34
37
40
41
43
44
46
47
48
49
52
53
58
59
60
61
63
67
68
70
71
73
76
79
80
82
83
88
89
92
94
96
97
99
101
103
107
109
113
116
117
118
120
121
124
127
131
136
137
139
140
142
147
148
149
151
153
157
160
163
164
167
169
171
172
173
176
179
181
184
188
189
191
192
193
197
198
199
202
207
210
211
212
214
223
227
229
232
233
239
240
241
244
251
252
257
261
263
268
269
271
272
273
274
275
277
279
280
281
283
286
289
292
293
294
297
298
306
307
311
313
317
320
325
331
332
333
334
337
347
349
351
352
353
358
359
361
367
368
369
373
376
379
382
383
384
388
389
394
396
397
399
401
404
409
412
414
419
421
423
424
425
428
431
433
439
443
449
454
457
459
461
462
463
464
467
468
472
475
478
479
480
487
491
495
499
503
509
513
521
522
523
524
529
531
538
539
541
544
546
547
548
549
550
557
560
561
562
563
567
569
571
572
575
577
587
588
593
594
599
601
603
604
605
607
612
613
617
619
621
622
628
631
639
640
641
643
646
647
651
652
653
659
661
664
668
673
677
683
684
691
692
694
701
704
709
712
714
718
719
725
726
727
733
736
738
739
741
743
751
752
756
757
759
761
764
765
768
769
772
773
775
777
783
787
792
797
798
801
809
811
821
823
825
827
828
829
833
837
838
839
841
846
847
848
850
853
856
857
859
862
863
873
877
881
883
887
891
892
903
904
907
908
909
911
918
919
922
925
928
929
932
937
941
944
947
953
954
957
960
961
966
967
971
975
977
981
983
991
997
999
Update: I have solved my problem and verified the output of my program using an OEIS given series, as suggested by #MVW (shown in the source given by my new github solution). In the future, I will aim to test my programs by doing zero or more of the following (depending on the scope/importance of the problem):
google keywords for an existing solution to the problem, comparing it against my solution if I find it
unit test components for correctness as they're built and integrated, comparing these tests with known correct outputs

Some suggestions:
You need to check the properties of your calculated numbers.
Here that means
calculating the prime factors and
calculating their sum and
testing if that sum is a prime number.
Which is what your program should do in the first place, by the way.
So one nice option for checking is comparing your output with a known solution or the output of a another program which is known to work. The tricky bit is to have such a solution or program available. And I neglect that your comparison could be plagued by errors as well :-)
If you just compare it with other implementations, e.g. programs from other folks here, it would turn out more of a voting, it would not be a proof. It would just give increased probability that your program is correct, if several independent implementations come up with the same result. Of course all implementations could err :-)
The more agree the better.
And the more diverse the implementations are, the better.
E.g. you could use different programming languages, algebraic systems or a friend with time and paper and pencil and Wikipedia. :-)
Another means is to add checks to your intermediate steps, to get more confidence in your result. Kind of building a chain of trust.
You could output the prime factors you determined and compare it with the output
of a prime factorization program which is known to work.
Then you check if your summing works.
Finally you could check if the primality test you apply to the candidate sums is working correctly by feeding it with known prime numbers and non prime numbers and so on.
That is kind of what folks do with unit testing for example. Trying to cover most parts of the code as working, hoping if the parts work, that the whole will work.
Or you could formally prove your program step by step, using Hoare Calculus for example or another formal method.
But that is tricky, and you might end up shifting program errors to errors in the proof.
And today, in the era of internet, of course, you could internet search for the solution:
Try searching for sum of prime factors is prime in the online encyclopedia of integer sequences, which should give you series A100118. :-)
It is the problem with multiplicity, but shows you what the number theory pros do, with Mathematica and program fragments to calculate the series, the argument for the case of 1 and literature. Quite impressive.

Here's the answer I get. I exclude 1 as it has no prime divisors so their sum is 0, not a prime.
Haskell> filter (isPrime . sum . map fst . primePowers) [2..1000]
[2,3,4,5,6,7,8,9,10,11,12,13,16,17,18,19,20,22,23,24,25,27,29,31,32,34,36,37,40,
41,43,44,47,48,49,50,53,54,58,59,61,64,67,68,71,72,73,79,80,81,82,83,88,89,96,97
,100,101,103,107,108,109,113,116,118,121,125,127,128,131,136,137,139,142,144,149
,151,157,160,162,163,164,165,167,169,173,176,179,181,191,192,193,197,199,200,202
,210,211,214,216,223,227,229,232,233,236,239,241,242,243,250,251,256,257,263,269
,271,272,273,274,277,281,283,284,288,289,293,298,307,311,313,317,320,324,328,331
,337,343,345,347,349,352,353,358,359,361,367,373,379,382,383,384,385,389,390,394
,397,399,400,401,404,409,419,420,421,428,431,432,433,435,439,443,449,454,457,461
,462,463,464,467,472,478,479,484,486,487,491,495,499,500,503,509,512,521,523,529
,538,541,544,547,548,557,561,562,563,568,569,570,571,576,577,578,587,593,595,596
,599,601,607,613,617,619,622,625,630,631,640,641,643,647,648,651,653,656,659,661
,665,673,677,683,691,694,701,704,709,714,715,716,719,727,729,733,739,743,751,757
,759,761,764,768,769,773,777,780,787,788,795,797,798,800,808,809,811,819,821,823
,825,827,829,838,839,840,841,853,856,857,858,859,862,863,864,877,881,883,885,887
,903,907,908,911,919,922,924,928,929,930,937,941,944,947,953,956,957,961,967,968
,971,972,977,983,991,997,1000]
Haskell> primePowers 12
[(2,2),(3,1)]
Haskell> primePowers 14
[(2,1),(7,1)]
You could hard-code this list in and test against it. I'm pretty confident these results are without error.
(read . is "of").

How to draw a (bezier) path with a fill color using GDI+?

I am making a SVG renderer for Windows using the Windows API and GDI+. SVG allows setting the 'fill' and 'stroke' style attributes on a Path. I am having some difficulty with the implementation of the 'fill' attribute.
The following path represents a spiral:
<svg:path style="fill:yellow;stroke:blue;stroke-width:2"
d="M153 334
C153 334 151 334 151 334
C151 339 153 344 156 344
C164 344 171 339 171 334
C171 322 164 314 156 314
C142 314 131 322 131 334
C131 350 142 364 156 364
C175 364 191 350 191 334
C191 311 175 294 156 294
C131 294 111 311 111 334
C111 361 131 384 156 384
C186 384 211 361 211 334
C211 300 186 274 156 274" />
The fill color is yellow, and it should fill the entire shape, this is however what I get:
My GDI+ calls look like this:
Gdiplus::GraphicsPath bezierPath;
bezierPath.AddBeziers(&gdiplusPoints[0], gdiplusPoints.size());
g.FillPath(&solidBrush, &bezierPath);
g.DrawPath(&pen, &bezierPath);
Apparently the code is correct for drawing the shape, but not for filling it. Can anyone help me in figuring out what's going wrong?

Try to set the FillMode property of your GraphicsPath to FillMode::Winding, an alternate filling method that should suits your needs.