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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


  
    


next up previous contents
Next: Caveats Up: Operation Counts for the Previous: Operation Counts for the   Contents
Susan Blackford 2001-08-13