1-22-2016 Banded Results BCR Test



• Name: the name of the matrix (test)
• N: the dimension of the matrix (number of rows and columns)
• NNZ: number of non-zeros
• SPD: whether the matrix is specified by the user to be symmetric positive definite (values: 0 or 1)
• DB: indicate whether DB reordering is performed. Values: 0 or 1.
• K-DB: the half-bandwidth after DB reordering method (without any drop-off). If DB is specified not to be executed, then this reports the original half-bandwidth
• KnoDrp: the half-bandwidth after DB and CM reordering but before drop-off
• K: the half-bandwidth after reordering and drop-off
• FRate: fill-in rate. See NOTES below
• nuKf: non-uniform K factor. Indicates whether the K changes a lot from row to row. Values are between 0 and 1, with 0 indicating a perfectly uniform bandwidth over the entire matrix. See NOTES below
• Solves: indicates whether we managed to solve the problem or not. OK means solved fine, otherwise a reason is provided for failure
• Bstng: indicates whether we enable diagonal boosting when doing factorization. Values: 0 or 1
• SolAcc: infinity norm of the array storing the relative errors
• T-DB: time to run DB reordering for the matrix on the CPU
• T-CM: time to run CM reordering for the matrix on the CPU
• T-Drop: time to drop off off-diagonal elements to decrease bandwidth. Done on the CPU.
• T-Dtransf: data transfer from CPU to GPU
• T-Asmbl: after reordering and drop-off, copy the sparse matrix to banded matrix stored in GPU memory
• LU-M: LU method (complete, ILUT or ILUULT)
• Fill-in: the fill-in factor of ILUT (-1 indicates complete LU)
• NPrtns: the number of partitions used to solve the problem
• T-BC: time required to get off-diagonal right hand sides (Bs and Cs) from the banded matrix - done on the GPU
• T-LU: LU time
• GFlps-LU: LU GFLOPs
• T-SPK: time to solve for the spikes Vs and Ws - done on the GPU
• T-LUrdcd: time required to factorize the reduced matrices - done on the GPU
• T-PreP: the sum of all preprocessing times, see NOTES
• Kry-M: the method used in Krylov solving stage (can be BiCGStab2 (0), BiCGStab (1), or CG(2))
• nItrs: the number of Krylov-solve iterations to solve the problem
• T-Kry: time spent in the Krylov solver (on the GPU)
• Total: total time to solve the problem, sum of PreProc + T-Kry
• Pardiso: the time for the commercial tool "Pardiso" to solve the problem
• SlwD: the slowdown ratio of our solver compared to Pardiso (a value less than one means that we are faster than Pardiso. The value is shown in green if we run faster and shown in red if we run more than 5 times slower.)
• Fastest: the time when SaP runs fastest historically
• SpdUp: the speedup of this run compared to the historical fastest run (the value is shown in green if the speedup is more than 5% and shown in red if the slowdown is more than 5%)


NOTES:
1) nuKf = 1/(2KN)*[sum over i from 1 to N of (2K - K_{iLeft} - K_{iRight})], where K_{iLeft} is the row half-bandwidth to the left of the diagonal while K_{iRight} is the row half-bandwidth to the right of the diagonal.
2) FRate = the actual number of NNZ / ((2K+1)N).
3) All times reported are in miliseconds (1E-3 second)


N

K

d

NPrtns

Solves

T-LU

T-SwDef

T-MMDef

T-PreP

nItrs

T-SwInf

T-MVInf

T-Kry

T-KryPIt

T-Total

200000

10

1

1

OK

25.088

12.3314

46.8887

98.602

0.75

10.9425

30.3539

55.07

55.07

153.672

200000

10

1

1

OK

264.375

268.426

0.75

1207.38

1207.38

1475.81

200000

10

1

4

OK

18.7799

11.9865

33.5965

74.116

2.75

27.2113

77.2005

131.891

47.9604

206.007

200000

10

1

4

OK

67.1395

71.282

2.75

1161.41

422.332

1232.7

200000

10

1

8

OK

18.0611

11.8503

32.9393

72.589

2.75

26.78

76.8041

130.678

47.5193

203.267

200000

10

1

8

OK

33.9679

38.146

2.75

597.098

217.127

635.244

200000

10

1

16

OK

17.3815

11.8332

32.6547

71.611

2.75

26.5751

77.3912

131.113

47.6775

202.724

200000

10

1

16

OK

17.1303

21.287

2.75

311.909

113.421

333.196

200000

10

1

20

OK

16.6072

11.6356

32.1683

70.185

3.25

29.8339

87.5518

147.204

45.2935

217.389

200000

10

1

20

OK

13.9466

18.082

3.25

294.25

90.5385

312.332

200000

10

1

32

OK

16.6968

11.6206

32.1865

70.279

3.25

34.0877

99.9059

167.39

51.5046

237.669

200000

10

1

32

OK

9.04909

13.196

3.25

221.75

68.2308

234.946

200000

10

1

50

OK

15.9197

11.5192

31.6871

68.848

3.25

33.3428

99.1013

165.168

50.8209

234.016

200000

10

1

50

OK

6.09814

10.241

3.25

155.435

47.8262

165.676

200000

20

1

1

OK

28.6086

20.7569

41.9655

101.827

0.75

10.7679

32.3082

57.724

57.724

159.551

200000

20

1

1

OK

285.098

291.48

0.75

1268.87

1268.87

1560.35

200000

20

1

4

OK

27.0591

20.1077

41.1008

98.747

2.75

26.7571

82.952

142.946

51.9804

241.693

200000

20

1

4

OK

72.1994

78.632

2.75

1211.15

440.42

1289.79

200000

20

1

8

OK

26.3637

19.8231

40.4554

97.089

2.75

26.2927

82.9053

142.398

51.7811

239.487

200000

20

1

8

OK

36.7323

43.216

2.75

622.822

226.481

666.038

200000

20

1

16

OK

25.524

19.3862

39.7967

95.128

2.75

25.4612

82.3196

140.378

51.0465

235.506

200000

20

1

16

OK

19.9055

26.404

2.75

330.858

120.312

357.262

200000

20

1

20

OK

27.38

19.2373

41.8818

99.002

2.75

25.0236

81.9676

140.401

51.0549

239.403

200000

20

1

20

OK

16.3827

22.925

2.75

274.145

99.6891

297.07

200000

20

1

32

OK

25.2054

19.3236

39.7146

94.767

2.75

25.3445

83.336

141.311

51.3858

236.078

200000

20

1

32

OK

11.4435

17.905

2.75

183.96

66.8945

201.865

200000

20

1

50

OK

24.0538

18.8525

33.9581

87.276

2.75

24.182

81.5864

137.804

50.1105

225.08

200000

20

1

50

OK

8.52077

15.024

2.75

132.433

48.1575

147.457

200000

50

1

1

OK

58.0316

40.8997

72.3288

189.04

0.75

13.3132

32.7857

63.487

63.487

252.527

200000

50

1

1

OK

1039.28

1052.39

0.75

1457.78

1457.78

2510.17

200000

50

1

4

OK

56.1552

38.8748

71.3956

184.307

2.25

27.199

71.1206

132.623

58.9436

316.93

200000

50

1

4

OK

258.771

272.166

2.25

1118.28

497.012

1390.44

200000

50

1

8

OK

55.3574

38.1115

70.4096

181.763

2.25

26.3091

70.6815

131.18

58.3022

312.943

200000

50

1

8

OK

130.434

143.909

2.25

579.345

257.487

723.254

200000

50

1

16

OK

54.8596

37.0147

64.2935

173.964

2.25

25.257

70.6585

129.869

57.7196

303.833

200000

50

1

16

OK

77.9371

91.427

2.25

308.545

137.131

399.972

200000

50

1

20

OK

54.5303

36.822

63.7662

172.948

2.25

29.574

82.8119

151.372

67.2764

324.32

200000

50

1

20

OK

63.9104

77.492

2.25

302.514

134.451

380.006

200000

50

1

32

OK

53.9428

35.4939

61.3845

168.606

2.25

28.6152

82.3714

149.772

66.5653

318.378

200000

50

1

32

OK

46.9783

60.567

2.25

205.615

91.3844

266.182

200000

50

1

50

OK

54.2376

35.0642

61.4036

168.411

2.25

24.1597

69.6252

127.304

56.5796

295.715

200000

50

1

50

OK

36.8652

50.411

2.25

125.332

55.7031

175.743

200000

100

1

1

OK

109.664

153.596

144.421

440.434

0.75

17.6247

38.004

79.107

79.107

519.541

200000

100

1

1

OK

927.766

951.901

0.75

1466.48

1466.48

2418.38

200000

100

1

4

OK

107.18

144.534

141.36

425.681

1.75

28.5886

67.1049

135.492

77.424

561.173

200000

100

1

4

OK

383.326

408.002

1.75

939.106

536.632

1347.11

200000

100

1

8

OK

106.154

139.923

132.492

411.214

1.75

27.0692

66.4126

133.224

76.128

544.438

200000

100

1

8

OK

251.023

275.555

1.75

495.756

283.289

771.311

200000

100

1

16

OK

106.104

135.651

129.833

404.23

1.75

25.7355

65.9435

131.062

74.8926

535.292

200000

100

1

16

OK

172.977

197.455

1.75

268.375

153.357

465.83

200000

100

1

20

OK

105.765

134.076

129.213

401.619

1.75

25.4207

65.7362

130.652

74.6583

532.271

200000

100

1

20

OK

162.157

186.61

1.75

224.502

128.287

411.112

200000

100

1

32

OK

104.579

94.4664

122.618

354.388

1.75

24.2721

63.4183

126.838

72.4789

481.226

200000

100

1

32

OK

141.519

165.991

1.75

156.965

89.6943

322.956

200000

100

1

50

OK

106.412

124.964

122.233

386.117

2.25

29.3667

78.1663

154.515

68.6733

540.632

200000

100

1

50

OK

131.096

155.598

2.25

141.505

62.8911

297.103

200000

200

1

1

OK

314.34

416.674

369.193

1193.6

0.75

28.0181

54.5302

120.327

120.327

1313.93

200000

200

1

1

OK

1182.19

1229.49

0.75

1511.6

1511.6

2741.09

200000

200

1

4

OK

313.845

387.794

349.752

1144.98

1.75

44.2941

95.6976

205.524

117.442

1350.51

200000

200

1

4

OK

594.658

642.037

1.75

987.553

564.316

1629.59

200000

200

1

8

OK

309.088

371.53

338.326

1111.79

1.75

41.2807

93.194

199.84

114.194

1311.63

200000

200

1

8

OK

438.866

486.179

1.75

526.077

300.615

1012.26

200000

200

1

16

OK

319.516

234.63

333.708

982.314

1.75

39.5494

91.934

196.616

112.352

1178.93

200000

200

1

16

OK

379.261

426.53

1.75

302.587

172.907

729.117

200000

200

1

20

OK

311.423

351.973

322.9

1078.76

1.75

38.4231

91.1591

194.592

111.195

1273.35

200000

200

1

20

OK

359.341

406.924

1.75

257.388

147.079

664.312

200000

200

1

32

OK

312.777

209.44

295.868

911.859

1.75

36.0308

84.9115

185.576

106.043

1097.43

200000

200

1

32

OK

345.901

393.16

1.75

191.007

109.147

584.167

200000

200

1

50

OK

317.24

315.117

289.364

1012.58

1.75

38.4842

84.5901

187.935

107.391

1200.51

200000

200

1

50

OK

323.949

371.649

1.75

160.116

91.4949

531.765

200000

500

1

1

OK

1688.74

1533.85

1859.93

5397.64

0.75

66.1944

111.861

259.763

259.763

5657.41

200000

500

1

1

OK

2662.37

2782.33

0.75

1755.75

1755.75

4538.07

200000

500

1

4

OK

1688.86

1427.74

1754.42

5183.6

1.75

104.355

193.767

443.026

253.158

5626.63

200000

500

1

4

OK

1840.59

1960.98

1.75

1154.56

659.75

3115.54

200000

500

1

8

OK

1695.46

1339.75

1658.34

5003.71

1.75

97.1954

186.423

428.259

244.719

5431.97

200000

500

1

8

OK

1672.5

1793.02

1.75

657.834

375.905

2450.85

200000

500

1

16

OK

1720.92

1230.4

1512.53

4769.41

1.75

90.3388

175.223

410.174

234.385

5179.58

200000

500

1

16

OK

1562.83

1683.47

1.75

424.559

242.605

2108.03

200000

500

1

20

OK

1727.25

1183.25

1467.69

4682.31

1.75

90.5318

170.922

405.937

231.964

5088.24

200000

500

1

20

OK

1567.45

1687.83

1.75

373.372

213.355

2061.2

200000

500

1

32

NConv

1779.02

976.484

1364.42

4438.23

1000.25

41309.9

72058.2

176233

176.189

180671

200000

500

1

32

OK

1520.33

1640.99

1.75

305.574

174.614

1946.56

200000

500

1

50

OK

1814.08

959.012

1169.05

4231.7

1.75

82.4546

146.307

372.51

212.863

4604.21

200000

500

1

50

OK

1491.97

1612.23

1.75

266.754

152.431

1878.99