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# Operation Counts for the LAPACK Routines

The parameters used in counting operations for the LAPACK routines are the matrix dimensions 3#3 and 4#4, the upper and lower bandwidths 588#588 and 589#589 for the band routines (198#198 if symmetric or triangular), and NRHS, the number of right hand sides in the solution phase. The operation counts for the LAPACK routines not listed here are not computed by a formula. In particular, the operation counts for the eigenvalue routines are problem-dependent and are computed during execution of the timing program.

Table 1: Operation counts for the Level 2 BLAS
 Level 2 BLAS multiplications additions total flops SGEMV 1,2 599#599 599#599 600#600 SSYMV 3,4 601#601 601#601 602#602 SSBMV 3,4 603#603 603#603 604#604 STRMV 3,4,5 605#605 606#606 601#601 STBMV 3,4,5 607#607 608#608 603#603 STRSV 5 605#605 606#606 601#601 STBSV 5 607#607 608#608 603#603 SGER 1 599#599 599#599 600#600 SSYR 3 605#605 605#605 609#609 SSYR2 3 609#609 601#601 610#610 1 - Plus 3#3 multiplies if 596#596 2 - Plus 3#3 multiplies if 597#597 or 53#53 3 - Plus 4#4 multiplies if 596#596 4 - Plus 4#4 multiplies if 597#597 or 53#53 5 - Less 4#4 multiplies if matrix is unit triangular

Table 2: Operation counts for the Level 3 BLAS
 Level 3 BLAS multiplications additions total flops SGEMM 611#611 611#611 612#612 SSYMM (SIDE = 'L') 613#613 613#613 614#614 SSYMM (SIDE = 'R') 615#615 615#615 616#616 SSYRK 617#617 617#617 618#618 SSYR2K 619#619 620#620 621#621 STRMM (SIDE = 'L') 622#622 623#623 624#624 STRMM (SIDE = 'R') 625#625 626#626 615#615 STRSM (SIDE = 'L') 622#622 623#623 624#624 STRSM (SIDE = 'R') 625#625 626#626 615#615

LAPACK routines:

 SGETRF multiplications: 627#627 additions: 628#628 total flops: 629#629

 SGETRI multiplications: 630#630 additions: 631#631 total flops: 632#632

 SGETRS multiplications: NRHS 633#633 additions: NRHS 634#634 total flops: NRHS 635#635

 SPOTRF multiplications: 636#636 additions: 637#637 total flops: 638#638

 SPOTRI multiplications: 639#639 additions: 640#640 total flops: 630#630

 SPOTRS multiplications: NRHS 641#641 additions: NRHS 634#634 total flops: NRHS 642#642

 SPBTRF multiplications: 643#643 additions: 644#644 total flops: 645#645

 SPBTRS multiplications: NRHS 646#646 additions: NRHS 647#647 total flops: NRHS 648#648

 SSYTRF multiplications: 649#649 additions: 637#637 total flops: 650#650

 SSYTRI multiplications: 651#651 additions: 652#652 total flops: 653#653

 SSYTRS multiplications: NRHS 641#641 additions: NRHS 634#634 total flops: NRHS 642#642

 multiplications: 655#655 additions: 656#656 total flops: 657#657

 multiplications: 659#659 additions: 660#660 total flops: 661#661

 multiplications: 662#662 additions: 663#663 total flops: 664#664

 multiplications: 665#665 additions: 666#666 total flops: 667#667

 multiplications: 668#668 additions: 669#669 total flops: 670#670

 multiplications: 671#671 additions: 672#672 total flops: 673#673

 SGEQRS multiplications: NRHS 674#674 additions: NRHS 675#675 total flops: NRHS 676#676

 multiplications: 677#677 additions: 678#678 total flops: 679#679

 multiplications: 680#680 additions: 681#681 total flops: 682#682

 STRTRI multiplications: 636#636 additions: 683#683 total flops: 651#651

 SGEHRD multiplications: 684#684 additions: 685#685 total flops: 686#686

 SSYTRD multiplications: 687#687 additions: 688#688 total flops: 689#689

 multiplications: 690#690 additions: 691#691 total flops: 692#692

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Susan Blackford 2001-08-13