1-23-2016 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

41.2406

29.0209

57.2848

147.677

0.75

23.6527

71.2667

115.182

115.182

262.859

500000

10

1

1

OK

657.754

664.98

0.75

3007.72

3007.72

3672.7

500000

10

1

4

OK

38.9956

28.7513

56.4732

144.283

2.75

60.5845

184.271

293.023

106.554

437.306

500000

10

1

4

OK

166.074

173.546

2.75

2879.53

1047.1

3053.08

500000

10

1

10

OK

37.9233

28.5685

56.2125

142.922

2.75

60.0967

183.861

291.723

106.081

434.645

500000

10

1

10

OK

67.3668

74.909

2.75

1191.2

433.164

1266.11

500000

10

1

20

OK

36.7334

28.3573

55.5952

140.798

2.75

59.6015

183.546

290.715

105.715

431.513

500000

10

1

20

OK

34.0005

41.525

2.75

616.974

224.354

658.499

500000

10

1

30

OK

35.8523

28.3271

55.1363

139.389

2.75

59.2838

183.283

289.675

105.336

429.064

500000

10

1

30

OK

23.0223

30.581

2.75

428.489

155.814

459.07

500000

10

1

40

OK

43.0104

28.2228

56.0465

147.703

3.25

68.5117

211.968

334.729

102.994

482.432

500000

10

1

40

OK

17.6667

25.205

3.25

384.803

118.401

410.008

500000

10

1

50

OK

34.5407

28.0673

54.8235

137.529

3.25

67.8756

210.585

331.554

102.017

469.083

500000

10

1

50

OK

14.4571

22.027

3.25

318.607

98.0329

340.634

500000

10

1

60

OK

34.6837

28.1215

55.0105

137.955

3.25

68.0182

211.423

332.496

102.306

470.451

500000

10

1

60

OK

12.2444

19.828

3.25

275.808

84.864

295.636

500000

10

1

70

OK

34.9224

28.4076

54.946

138.565

3.25

68.9474

214.412

336.957

103.679

475.522

500000

10

1

70

OK

10.7929

18.353

3.25

246.136

75.7342

264.489

500000

10

1

80

OK

34.7328

27.9986

55.2999

138.26

3.25

77.4228

240.228

377.148

116.046

515.408

500000

10

1

80

OK

9.68045

17.242

3.25

251.498

77.384

268.74

500000

10

1

90

OK

34.7049

27.9829

55.2116

138.116

3.25

68.1981

211.502

332.761

102.388

470.877

500000

10

1

90

OK

8.72288

16.303

3.25

204.469

62.9135

220.772

500000

10

1

100

OK

33.8001

28.1181

54.9881

137.19

3.25

77.4237

241.846

378.672

116.514

515.862

500000

10

1

100

OK

8.05264

15.62

3.25

214.432

65.9791

230.052

500000

20

1

1

OK

62.6205

48.9945

77.038

211.351

0.75

22.7264

77.9299

126.89

126.89

338.241

500000

20

1

1

OK

714.521

728.273

0.75

3161.72

3161.72

3890

500000

20

1

4

OK

60.1347

48.3093

75.9913

207.062

2.25

57.8273

201.608

321.827

143.034

528.889

500000

20

1

4

OK

180.492

194.456

2.25

2995.66

1331.41

3190.12

500000

20

1

10

OK

58.5183

47.2624

74.762

203.169

2.25

56.5303

198.456

316.536

140.683

519.705

500000

20

1

10

OK

73.1355

87.129

2.25

1238.24

550.33

1325.37

500000

20

1

20

OK

57.5657

46.711

74.8178

201.701

2.75

56.0076

198.557

317.183

115.339

518.884

500000

20

1

20

OK

39.7033

53.657

2.75

654.151

237.873

707.808

500000

20

1

30

OK

63.3125

46.6527

74.9002

207.605

2.75

55.5541

199.304

317.516

115.46

525.121

500000

20

1

30

OK

27.1911

41.216

2.75

459.196

166.98

500.412

500000

20

1

40

OK

56.958

46.8585

74.4508

201.023

2.75

55.9329

201.422

319.826

116.3

520.849

500000

20

1

40

OK

22.6376

36.726

2.75

361.89

131.596

398.616

500000

20

1

50

OK

55.2224

45.7956

73.0097

196.589

2.75

54.8208

197.081

313.485

113.995

510.074

500000

20

1

50

OK

20.5822

34.685

2.75

305.033

110.921

339.718

500000

20

1

60

OK

55.4555

45.7239

74.2169

197.991

2.75

55.0913

198.527

315.842

114.852

513.833

500000

20

1

60

OK

17.3348

31.386

2.75

266.022

96.7353

297.408

500000

20

1

70

OK

55.4862

45.7545

73.013

196.878

2.75

55.3129

199.306

316.454

115.074

513.332

500000

20

1

70

OK

27.4669

41.499

2.75

236.884

86.1396

278.383

500000

20

1

80

OK

55.4204

45.228

73.1164

196.367

2.75

54.8693

198.027

314.507

114.366

510.874

500000

20

1

80

OK

24.834

38.879

2.75

215.837

78.4862

254.716

500000

20

1

90

OK

55.2756

44.8048

73.5644

196.212

2.75

55.0658

199.31

316.061

114.931

512.273

500000

20

1

90

OK

22.0881

36.168

2.75

199.544

72.5615

235.712

500000

20

1

100

OK

53.9565

45.0037

66.5048

188.07

2.75

54.188

196.717

312.162

113.513

500.232

500000

20

1

100

OK

20.018

34.005

2.75

186.214

67.7142

220.219

500000

50

1

1

OK

134.26

91.3778

155.88

421.551

0.75

25.6514

78.4206

137.912

137.912

559.463

500000

50

1

1

OK

2563.54

2593.04

0.75

3593.19

3593.19

6186.24

500000

50

1

4

OK

131.905

89.4862

154.867

416.293

1.75

44.4725

140.296

243.393

139.082

659.686

500000

50

1

4

OK

656.845

687.441

1.75

2307.84

1318.77

2995.28

500000

50

1

10

OK

129.461

88.009

152.17

409.538

2.25

52.162

170.354

292.299

129.911

701.837

500000

50

1

10

OK

261.649

292.356

2.25

1158.34

514.818

1450.7

500000

50

1

20

OK

134.502

86.6694

151.001

412.177

2.25

51.2015

169.616

290.464

129.095

702.641

500000

50

1

20

OK

156.326

187.034

2.25

616.162

273.85

803.196

500000

50

1

30

OK

128.718

86.5218

149.935

405.149

2.25

60.735

201.304

343.348

152.599

748.497

500000

50

1

30

OK

105.71

136.503

2.25

513.493

228.219

649.996

500000

50

1

40

OK

127.547

85.2571

141.17

393.875

2.25

50.338

168.823

288.696

128.309

682.571

500000

50

1

40

OK

96.8904

127.608

2.25

347.692

154.53

475.3

500000

50

1

50

OK

127.928

85.3165

141.51

394.602

2.25

50.2631

169.395

288.971

128.432

683.573

500000

50

1

50

OK

92.1973

122.894

2.25

293.173

130.299

416.067

500000

50

1

60

OK

128.296

85.1646

140.71

394.303

2.25

59.7883

200.306

341.181

151.636

735.484

500000

50

1

60

OK

77.8876

108.634

2.25

301.46

133.982

410.094

500000

50

1

70

OK

128.453

85.1927

139.758

393.329

2.25

50.5802

169.251

289.143

128.508

682.472

500000

50

1

70

OK

128.791

159.415

2.25

231.083

102.704

390.498

500000

50

1

80

OK

126.355

82.5546

136.696

385.486

2.25

49.7727

167.743

291.741

129.663

677.227

500000

50

1

80

OK

110.625

141.287

2.25

211.834

94.1484

353.121

500000

50

1

90

OK

129.981

82.5144

142.183

394.622

2.25

49.7996

167.321

289.417

128.63

684.039

500000

50

1

90

OK

101.395

132.207

2.25

196.525

87.3444

328.732

500000

50

1

100

OK

127.42

82.8757

137.625

387.757

2.25

49.2868

168.56

286.795

127.464

674.552

500000

50

1

100

OK

92.4496

123.184

2.25

185.262

82.3387

308.446

500000

100

1

1

OK

262.664

352.328

341.576

1035.11

0.75

31.5924

91.5809

176.308

176.308

1211.42

500000

100

1

1

OK

2319.32

2377.34

0.75

3662.79

3662.79

6040.13

500000

100

1

4

OK

259.689

344.838

338.951

1022.22

1.75

53.7389

163.745

310.694

177.539

1332.91

500000

100

1

4

OK

957.652

1016.37

1.75

2337.29

1335.59

3353.66

500000

100

1

10

OK

256.794

333.913

334.392

1003.6

1.75

50.5129

162.257

305.653

174.659

1309.25

500000

100

1

10

OK

551.078

609.93

1.75

997.089

569.765

1607.02

500000

100

1

20

OK

258.365

328.824

321.806

987.671

1.75

49.5045

162.918

305.326

174.472

1293

500000

100

1

20

OK

405.102

463.992

1.75

550.567

314.61

1014.56

500000

100

1

30

OK

261.074

284.003

320.795

944.863

2.25

61.2484

200.305

373.925

166.189

1318.79

500000

100

1

30

OK

359.227

418.078

2.25

487.221

216.543

905.299

500000

100

1

40

OK

254.517

316.856

307.727

957.24

1.75

47.8246

159.009

299.556

171.175

1256.8

500000

100

1

40

OK

335.563

394.644

1.75

325.314

185.894

719.958

500000

100

1

50

OK

261.344

316.949

310.191

966.838

1.75

47.7176

160.162

300.361

171.635

1267.2

500000

100

1

50

OK

329.793

388.793

1.75

281.787

161.021

670.58

500000

100

1

60

OK

257.296

270.25

305.218

911.291

1.75

48.3805

160.032

301.233

172.133

1212.52

500000

100

1

60

OK

324.893

383.982

1.75

253.584

144.905

637.566

500000

100

1

70

OK

257.496

248.08

301.264

885.829

2.25

59.3803

194.15

365.706

162.536

1251.53

500000

100

1

70

OK

317.039

376.028

2.25

281.61

125.16

657.638

500000

100

1

80

OK

254.967

224.014

295.053

852.866

1.75

46.8131

155.296

294.302

168.173

1147.17

500000

100

1

80

OK

311.442

370.56

1.75

216.749

123.857

587.309

500000

100

1

90

OK

254.582

200.588

290.541

824.552

2.25

57.4207

188.895

358.144

159.175

1182.7

500000

100

1

90

OK

307.563

366.477

2.25

248.978

110.657

615.455

500000

100

1

100

OK

264.242

306.474

299.194

948.284

1.75

46.6861

159.756

299.333

171.047

1247.62

500000

100

1

100

OK

308.072

366.991

1.75

196.61

112.349

563.601

500000

200

1

1

OK

770.291

968.131

911.016

2879.76

0.75

56.4619

132.85

281.804

281.804

3161.57

500000

200

1

1

OK

2957.61

3073.14

0.75

3781.98

3781.98

6855.12

500000

200

1

4

OK

768.011

941.957

901.049

2839.94

1.75

96.0023

236.743

497.143

284.082

3337.09

500000

200

1

4

OK

1489.28

1606.09

1.75

2467.2

1409.83

4073.29

500000

200

1

10

OK

763.064

902.63

860.642

2756.38

1.75

89.6588

233.097

487.259

278.434

3243.64

500000

200

1

10

OK

1038.02

1154.08

1.75

1083.56

619.175

2237.64

500000

200

1

20

OK

761.241

873.348

834.16

2697.24

1.75

87.143

227.964

478.12

273.211

3175.36

500000

200

1

20

OK

914.124

1031.26

1.75

644.149

368.085

1675.41

500000

200

1

30

OK

783.697

686.501

842.668

2545.41

1.75

87.9082

229.235

481.149

274.942

3026.55

500000

200

1

30

OK

878.223

994.767

1.75

488.584

279.191

1483.35

500000

200

1

40

OK

779.784

551.046

811.908

2375.32

1.75

86.2376

223.287

473.343

270.482

2848.67

500000

200

1

40

OK

845.281

961.578

1.75

417.07

238.326

1378.65

500000

200

1

50

OK

770.686

838.842

798.015

2635.37

1.75

83.8569

223.858

471.294

269.311

3106.67

500000

200

1

50

OK

819.92

936.612

1.75

376.752

215.287

1313.36

500000

200

1

60

OK

796.05

506.396

791.781

2330.57

1.75

86.7116

221.914

472.106

269.775

2802.67

500000

200

1

60

OK

831.037

947.144

1.75

344.008

196.576

1291.15

500000

200

1

70

OK

794.774

515.581

766.299

2316.4

1.75

86.7971

219.504

471.887

269.65

2788.28

500000

200

1

70

OK

829.221

945.541

1.75

323.745

184.997

1269.29

500000

200

1

80

OK

774.407

502.474

730.772

2238.45

1.75

82.174

209.347

455.42

260.24

2693.87

500000

200

1

80

OK

819.319

936.062

1.75

310.979

177.702

1247.04

500000

200

1

90

OK

782.325

525.792

719.026

2266.79

1.75

84.2041

209.523

457.367

261.353

2724.16

500000

200

1

90

OK

814.889

931.516

1.75

298.772

170.727

1230.29

500000

200

1

100

OK

773.216

772.81

724.336

2496.22

1.75

81.2224

212.797

457.473

261.413

2953.7

500000

200

1

100

OK

794.311

911.12

1.75

292.956

167.403

1204.08

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)