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