1-24-2016 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

500000

10

1

1

OK

41.2533

29.0007

57.2359

147.591

0.75

23.6291

71.2546

115.117

115.117

262.708

500000

10

1

1

OK

657.151

664.417

0.75

3001.05

3001.05

3665.47

500000

10

1

4

OK

38.9656

28.7403

56.5305

144.307

2.75

60.5618

184.127

292.73

106.447

437.037

500000

10

1

4

OK

165.155

172.65

2.75

2873.15

1044.78

3045.8

500000

10

1

10

OK

38.1268

28.8652

56.295

143.549

2.75

60.7078

186.424

295.342

107.397

438.891

500000

10

1

10

OK

67.385

74.92

2.75

1190.58

432.938

1265.5

500000

10

1

20

OK

36.7052

28.3434

55.9301

141.057

2.75

59.5681

183.436

290.449

105.618

431.506

500000

10

1

20

OK

33.9753

41.481

2.75

615.969

223.989

657.45

500000

10

1

30

OK

35.7448

28.4082

55.1436

139.347

2.75

59.5207

183.649

290.436

105.613

429.783

500000

10

1

30

OK

22.9959

30.593

2.75

428.314

155.751

458.907

500000

10

1

40

OK

35.7245

28.1781

55.0573

139.046

3.25

68.2685

211.41

333.07

102.483

472.116

500000

10

1

40

OK

17.6717

25.218

3.25

384.315

118.251

409.533

500000

10

1

50

OK

34.9162

28.3628

55.1281

138.642

3.25

68.6093

213.645

335.789

103.32

474.431

500000

10

1

50

OK

14.603

22.177

3.25

321.773

99.0071

343.95

500000

10

1

60

OK

34.5779

28.1183

54.6503

137.385

3.25

67.9899

211.344

332.444

102.29

469.829

500000

10

1

60

OK

12.3843

19.955

3.25

278.166

85.5895

298.121

500000

10

1

70

OK

34.7308

28.0284

54.6024

137.455

3.25

68.0633

211.132

332.345

102.26

469.8

500000

10

1

70

OK

10.88

18.459

3.25

248.503

76.4625

266.962

500000

10

1

80

OK

35.0775

28.2982

55.2892

138.947

3.25

77.9886

243.166

380.728

117.147

519.675

500000

10

1

80

OK

9.65757

17.198

3.25

251.203

77.2932

268.401

500000

10

1

90

OK

34.5948

27.9969

55.2488

137.911

3.25

68.1824

211.418

332.58

102.332

470.491

500000

10

1

90

OK

8.82464

16.394

3.25

206.449

63.5228

222.843

500000

10

1

100

OK

33.4607

27.8053

54.5178

135.929

3.25

76.5459

238.23

373.652

114.97

509.581

500000

10

1

100

OK

8.03974

15.623

3.25

220.632

67.8868

236.255

500000

20

1

1

OK

71.7609

48.4258

76.414

219.35

0.75

22.4828

76.8253

125.382

125.382

344.732

500000

20

1

1

OK

714.802

728.498

0.75

3158.38

3158.38

3886.88

500000

20

1

4

OK

59.7617

47.748

75.1349

205.212

2.25

57.1982

198.749

317.835

141.26

523.047

500000

20

1

4

OK

181.949

195.913

2.25

3029.12

1346.28

3225.04

500000

20

1

10

OK

61.8235

47.3689

78.5747

210.326

2.25

56.6136

198.604

316.689

140.751

527.015

500000

20

1

10

OK

72.987

87.051

2.25

1237.69

550.084

1324.74

500000

20

1

20

OK

57.4806

46.6516

74.7824

201.542

2.75

55.7821

198.15

316.323

115.027

517.865

500000

20

1

20

OK

39.727

53.739

2.75

654.823

238.117

708.562

500000

20

1

30

OK

56.5859

46.6814

74.3599

200.171

2.75

55.4188

199.039

316.351

115.037

516.522

500000

20

1

30

OK

27.4698

41.518

2.75

463.291

168.469

504.809

500000

20

1

40

OK

56.3177

46.1907

73.5878

198.669

2.75

55.2397

198.404

315.817

114.843

514.486

500000

20

1

40

OK

22.6112

36.549

2.75

361.487

131.45

398.036

500000

20

1

50

OK

61.8493

46.3201

74.3706

205.297

2.75

55.5184

200.038

318.443

115.797

523.74

500000

20

1

50

OK

20.2293

34.266

2.75

302.259

109.912

336.525

500000

20

1

60

OK

55.4466

45.6568

74.1227

197.732

2.75

54.8644

198.13

314.514

114.369

512.246

500000

20

1

60

OK

17.2374

31.232

2.75

263.536

95.8313

294.768

500000

20

1

70

OK

55.4421

45.7253

72.9221

196.632

2.75

55.0871

198.885

315.491

114.724

512.123

500000

20

1

70

OK

27.8878

41.929

2.75

238.697

86.7989

280.626

500000

20

1

80

OK

55.8364

45.7459

73.9189

198.134

2.75

55.4673

200.793

318.458

115.803

516.592

500000

20

1

80

OK

24.4709

38.484

2.75

215.721

78.444

254.205

500000

20

1

90

OK

55.2932

44.8277

73.5871

196.219

2.75

55.0744

199.298

315.786

114.831

512.005

500000

20

1

90

OK

21.9194

35.882

2.75

199.474

72.536

235.356

500000

20

1

100

OK

54.094

44.9728

66.5171

188.146

2.75

54.1947

196.736

312.283

113.557

500.429

500000

20

1

100

OK

20.1537

34.169

2.75

186.394

67.7796

220.563

500000

50

1

1

OK

134.35

91.3149

155.692

421.348

0.75

25.6207

78.4129

137.734

137.734

559.082

500000

50

1

1

OK

2558.41

2588.06

0.75

3590.1

3590.1

6178.16

500000

50

1

4

OK

131.901

89.5455

154.501

416.007

1.75

44.4914

140.292

243.207

138.975

659.214

500000

50

1

4

OK

646.988

677.514

1.75

2280.28

1303.02

2957.8

500000

50

1

10

OK

129.516

88.0364

152.266

409.705

2.25

52.2193

170.333

292.396

129.954

702.101

500000

50

1

10

OK

261.756

292.419

2.25

1159.81

515.472

1452.23

500000

50

1

20

OK

134.396

86.6709

150.999

412.019

2.25

51.1964

169.598

290.454

129.091

702.473

500000

50

1

20

OK

156.327

187.124

2.25

616.064

273.806

803.188

500000

50

1

30

OK

128.635

86.5399

150.037

405.224

2.25

60.7584

201.334

343.754

152.78

748.978

500000

50

1

30

OK

105.926

136.684

2.25

513.926

228.412

650.61

500000

50

1

40

OK

127.236

85.098

141.043

393.244

2.25

50.2458

168.59

288.109

128.048

681.353

500000

50

1

40

OK

97.8489

128.646

2.25

346.974

154.211

475.62

500000

50

1

50

OK

129.423

86.1803

143.616

399.387

2.25

50.851

171.676

292.472

129.988

691.859

500000

50

1

50

OK

91.3601

122.308

2.25

294.988

131.106

417.296

500000

50

1

60

OK

128.438

85.2575

140.607

394.21

2.25

59.7619

200.489

341.253

151.668

735.463

500000

50

1

60

OK

79.7289

110.657

2.25

303.765

135.007

414.422

500000

50

1

70

OK

128.578

85.2659

139.912

393.745

2.25

50.6314

169.429

289.574

128.7

683.319

500000

50

1

70

OK

128.715

159.424

2.25

231.475

102.878

390.899

500000

50

1

80

OK

126.187

82.4422

136.609

385.127

2.25

49.426

167.008

285.676

126.967

670.803

500000

50

1

80

OK

115.727

146.535

2.25

213.107

94.7142

359.642

500000

50

1

90

OK

126.192

82.3144

135.795

384.201

2.25

49.4991

166.892

285.527

126.901

669.728

500000

50

1

90

OK

101.814

132.516

2.25

196.714

87.4284

329.23

500000

50

1

100

OK

127.607

83.0894

137.717

388.334

2.25

49.4065

168.774

287.295

127.687

675.629

500000

50

1

100

OK

91.6162

122.395

2.25

185.512

82.4498

307.907

500000

100

1

1

OK

265.339

355.602

345.673

1045.12

0.75

31.8787

92.602

177.824

177.824

1222.95

500000

100

1

1

OK

2321.41

2379.25

0.75

3663.46

3663.46

6042.71

500000

100

1

4

OK

259.631

344.885

338.8

1021.93

1.75

53.7052

163.719

310.849

177.628

1332.78

500000

100

1

4

OK

963.386

1022.08

1.75

2339.15

1336.66

3361.24

500000

100

1

10

OK

256.808

334.688

334.443

1004.48

1.75

50.5248

162.278

305.76

174.72

1310.24

500000

100

1

10

OK

550.613

609.584

1.75

994.695

568.397

1604.28

500000

100

1

20

OK

255.475

325.822

317.551

977.07

1.75

49.0795

161.048

302.783

173.019

1279.85

500000

100

1

20

OK

413.175

471.984

1.75

550.495

314.569

1022.48

500000

100

1

30

OK

257.715

280.306

316.752

933.612

2.25

60.6425

197.655

370.662

164.739

1304.27

500000

100

1

30

OK

359.808

418.836

2.25

488.044

216.908

906.88

500000

100

1

40

OK

254.579

316.875

307.845

957.829

1.75

47.8453

159.039

299.431

171.103

1257.26

500000

100

1

40

OK

335.498

394.637

1.75

325.495

185.997

720.132

500000

100

1

50

OK

256.881

316.768

309.964

962.184

1.75

47.7383

160.265

300.741

171.852

1262.92

500000

100

1

50

OK

333.551

392.63

1.75

281.787

161.021

674.417

500000

100

1

60

OK

257.17

270.295

305.043

911.3

1.75

48.3705

160

300.685

171.82

1211.98

500000

100

1

60

OK

320.994

380.127

1.75

251.735

143.849

631.862

500000

100

1

70

OK

260.475

250.761

304.898

895.269

2.25

59.9094

196.534

368.772

163.899

1264.04

500000

100

1

70

OK

321.522

380.623

2.25

283.572

126.032

664.195

500000

100

1

80

OK

257.435

225.896

298.426

860.901

1.75

47.1751

156.949

296.706

169.546

1157.61

500000

100

1

80

OK

311.457

370.463

1.75

216.996

123.998

587.459

500000

100

1

90

OK

254.448

200.589

290.733

824.637

2.25

57.405

188.841

358.087

159.15

1182.72

500000

100

1

90

OK

307.926

369.132

2.25

250.755

111.447

619.887

500000

100

1

100

OK

291.766

317.1

368.732

1348.59

1.75

61.2326

209.591

448.886

256.506

1797.47

500000

100

1

100

OK

309.652

368.556

1.75

279.362

159.635

647.918

500000

200

1

1

OK

1080.93

989.177

1010.99

3479.22

0.75

70.4605

167.737

445.289

445.289

3924.51

500000

200

1

1

OK

3911.57

4026.74

0.75

3837

3837

7863.74

500000

200

1

4

OK

887.373

1050.12

1177.14

3428.6

1.75

95.8877

236.652

497.862

284.493

3926.46

500000

200

1

4

OK

1885.98

2027.92

1.75

2900.88

1657.65

4928.8

500000

200

1

10

OK

971.017

1046.54

1252.08

3507.48

1.75

90.2098

233.87

508.778

290.73

4016.26

500000

200

1

10

OK

1304.29

1420.52

1.75

1110.3

634.459

2530.82

500000

200

1

20

OK

775.021

3466.81

4505.77

8974.46

1.75

87.3179

228.088

480.203

274.402

9454.66

500000

200

1

20

OK

903.403

1019.64

1.75

684.205

390.974

1703.85

500000

200

1

30

OK

852.232

874.957

1473.05

3432.96

1.75

88.1696

229.305

482.688

275.822

3915.65

500000

200

1

30

OK

882.951

1000.26

1.75

490.812

280.464

1491.07

500000

200

1

40

OK

919.761

762.951

1287.95

3212.86

1.75

91.8643

229.953

587.958

335.976

3800.82

500000

200

1

40

OK

847.028

963.387

1.75

419.158

239.519

1382.55

500000

200

1

50

OK

784.677

962.623

997.014

2971.92

1.75

84.043

223.929

473.021

270.298

3444.94

500000

200

1

50

OK

1257.12

1374.41

1.75

497.735

284.42

1872.15

500000

200

1

60

OK

823.484

506.434

792.012

4680.27

1.75

86.5928

221.527

472.208

269.833

5152.48

500000

200

1

60

OK

2813.52

3324.04

1.75

347.18

198.389

3671.22

500000

200

1

70

OK

1322.19

939.343

1557.04

4125.1

1.75

87.7741

220.792

475.896

271.941

4600.99

500000

200

1

70

OK

832.175

948.799

1.75

333.532

190.59

1282.33

500000

200

1

80

OK

774.794

502.098

731.22

2239.75

1.75

87.0914

209.526

466.621

266.641

2706.37

500000

200

1

80

OK

819.766

936.181

1.75

312.457

178.547

1248.64

500000

200

1

90

OK

782.429

526.005

719.274

2266.64

1.75

84.2143

209.462

458.92

262.24

2725.56

500000

200

1

90

OK

815.178

931.717

1.75

300.63

171.789

1232.35

500000

200

1

100

OK

775.335

772.681

724.487

2497.44

1.75

81.3308

212.835

457.459

261.405

2954.9

500000

200

1

100

OK

793.669

910.232

1.75

293.083

167.476

1203.32

500000

500

1

1

OoM (in setup stage)

500000

500

1

1

OoM (in setup stage)

500000

500

1

4

OoM (in setup stage)

500000

500

1

4

OoM (in setup stage)

500000

500

1

10

OoM (in setup stage)

500000

500

1

10

OoM (in setup stage)

500000

500

1

20

OoM (in setup stage)

500000

500

1

20

OoM (in setup stage)

500000

500

1

30

OoM (in setup stage)

500000

500

1

30

OoM (in setup stage)

500000

500

1

40

OoM (in setup stage)

500000

500

1

40

OoM (in setup stage)

500000

500

1

50

OoM (in setup stage)

500000

500

1

50

OoM (in setup stage)

500000

500

1

60

OoM (in setup stage)

500000

500

1

60

OoM (in setup stage)

500000

500

1

70

OoM (in setup stage)

500000

500

1

70

OoM (in setup stage)

500000

500

1

80

OoM (in setup stage)

500000

500

1

80

OoM (in setup stage)

500000

500

1

90

OoM (in setup stage)

500000

500

1

90

OoM (in setup stage)

500000

500

1

100

OoM (in setup stage)

500000

500

1

100

OoM (in setup stage)