1-25-2016 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

41.3938

29.0248

57.9112

148.504

0.75

23.6549

71.2569

115.335

115.335

263.839

500000

10

1

1

OK

655.934

663.206

0.75

3013.56

3013.56

3676.77

500000

10

1

4

OK

112.759

63.1218

152.44

402.244

2.75

76.4484

231.679

700.868

254.861

1103.11

500000

10

1

4

OK

166.033

174.622

2.75

2883.9

1048.69

3058.53

500000

10

1

10

OK

147.148

48.4134

270.917

537.791

2.75

60.4409

184.536

305.538

111.105

843.329

500000

10

1

10

OK

66.8505

74.737

2.75

1183.22

430.263

1257.96

500000

10

1

20

OK

36.3916

28.3716

56.5934

141.732

2.75

59.703

183.743

291.861

106.131

433.593

500000

10

1

20

OK

34.0627

41.932

2.75

618.311

224.84

660.243

500000

10

1

30

OK

35.3862

28.3388

56.3111

140.32

2.75

59.3606

183.469

290.808

105.748

431.128

500000

10

1

30

OK

23.0696

30.973

2.75

429.873

156.317

460.846

500000

10

1

40

OK

35.3204

28.1856

56.0782

139.926

3.25

68.344

211.532

339.935

104.595

479.861

500000

10

1

40

OK

21.9163

56.359

3.25

741.023

228.007

797.382

500000

10

1

50

OK

147.54

47.8218

181.239

458.711

3.25

117.055

296.957

750.22

230.837

1208.93

500000

10

1

50

OK

14.5251

22.096

3.25

320.19

98.52

342.286

500000

10

1

60

OK

34.2911

28.1961

55.3369

137.868

3.25

68.2528

211.693

333.617

102.651

471.485

500000

10

1

60

OK

12.3335

19.93

3.25

276.959

85.2182

296.889

500000

10

1

70

OK

34.2416

28.1136

55.0436

137.504

3.25

68.3148

211.476

333.328

102.562

470.832

500000

10

1

70

OK

10.828

18.454

3.25

247.23

76.0708

265.684

500000

10

1

80

OK

34.0945

28.0395

55.6195

137.799

3.25

77.3769

239.985

377.179

116.055

514.978

500000

10

1

80

OK

9.70621

17.34

3.25

252.08

77.5631

269.42

500000

10

1

90

OK

34.4706

28.0902

60.0003

142.603

3.25

68.2725

220.006

343.791

105.782

486.394

500000

10

1

90

OK

14.0466

31.495

3.25

369.026

113.546

400.521

500000

10

1

100

OK

105.53

47.4096

92.3911

308.614

3.25

135.056

354.64

1179.06

362.787

1487.67

500000

10

1

100

OK

13.3933

30.714

3.25

4126.28

1269.63

4157

500000

20

1

1

OK

61.2113

48.4574

76.7817

209.081

0.75

22.5298

76.9551

125.921

125.921

335.002

500000

20

1

1

OK

715.452

729.099

0.75

3162.71

3162.71

3891.81

500000

20

1

4

OK

233.016

118.585

502.856

946.625

2.25

311.018

854.451

2134.53

948.681

3081.16

500000

20

1

4

OK

180.37

195.539

2.25

3001.24

1333.89

3196.78

500000

20

1

10

OK

58.1932

47.2576

75.9597

204.096

2.25

56.5451

198.463

317.635

141.171

521.731

500000

20

1

10

OK

73.1989

87.411

2.25

1239.79

551.018

1327.2

500000

20

1

20

OK

57.69

46.7283

76.1065

203.396

2.75

64.8114

275.233

722.12

262.589

925.516

500000

20

1

20

OK

45.0644

71.719

2.75

3146.29

1144.11

3218.01

500000

20

1

30

OK

63.4696

46.7189

75.4589

208.431

2.75

55.6574

199.554

318.074

115.663

526.505

500000

20

1

30

OK

27.2058

41.243

2.75

459.8

167.2

501.043

500000

20

1

40

OK

55.77

46.2221

74.1509

198.693

2.75

55.2908

198.623

316.45

115.073

515.143

500000

20

1

40

OK

22.6632

36.846

2.75

373.936

135.977

410.782

500000

20

1

50

OK

164.113

104.55

165.218

802.243

2.75

240.133

729.449

1709.18

621.52

2511.42

500000

20

1

50

OK

20.3862

34.287

2.75

303.835

110.485

338.122

500000

20

1

60

OK

54.9196

45.7741

74.482

197.609

2.75

54.8286

198.244

315.33

114.665

512.939

500000

20

1

60

OK

17.3858

31.461

2.75

264.44

96.16

295.901

500000

20

1

70

OK

54.9882

45.7116

73.423

196.634

2.75

55.0428

198.949

315.969

114.898

512.603

500000

20

1

70

OK

27.5055

41.547

2.75

237.122

86.2262

278.669

500000

20

1

80

OK

55.5001

45.3068

73.7802

197.334

2.75

54.7623

206.356

325.261

118.277

522.595

500000

20

1

80

OK

29.3606

56.196

2.75

365.012

132.732

421.208

500000

20

1

90

OK

61.7231

46.368

76.2711

266.345

2.75

55.0469

199.395

316.77

115.189

583.115

500000

20

1

90

OK

22.1968

36.157

2.75

200.028

72.7375

236.185

500000

20

1

100

OK

53.5966

44.9834

66.9388

187.957

2.75

54.1285

196.717

312.602

113.673

500.559

500000

20

1

100

OK

20.2383

34.136

2.75

187.154

68.056

221.29

500000

50

1

1

OK

134.365

91.6809

161.057

427.066

0.75

25.7227

78.4161

139.799

139.799

566.865

500000

50

1

1

OK

2574.7

2670.14

0.75

3669.21

3669.21

6339.35

500000

50

1

4

OK

132.781

89.5003

157.657

420.363

1.75

44.6063

140.722

245.053

140.03

665.416

500000

50

1

4

OK

646.546

677.011

1.75

2279.09

1302.33

2956.1

500000

50

1

10

OK

149.377

90.432

196.189

690.709

2.25

52.3785

170.663

294.356

130.825

985.065

500000

50

1

10

OK

261.867

292.643

2.25

1158.19

514.752

1450.83

500000

50

1

20

OK

128.188

86.6183

151.707

406.313

2.25

51.2338

173.925

296.737

131.883

703.05

500000

50

1

20

OK

167.021

259.052

2.25

794.659

353.182

1053.71

500000

50

1

30

OK

129.482

86.4925

152.598

408.852

2.25

60.7734

201.457

344.582

153.148

753.434

500000

50

1

30

OK

105.771

136.464

2.25

514.597

228.71

651.061

500000

50

1

40

OK

127.26

85.4323

146.279

398.824

2.25

50.2871

168.511

300.699

133.644

699.523

500000

50

1

40

OK

95.9399

126.909

2.25

349.133

155.17

476.042

500000

50

1

50

OK

127.559

85.3473

142.157

395.317

2.25

50.2098

169.468

289.552

128.69

684.869

500000

50

1

50

OK

92.3667

123.455

2.25

293.833

130.592

417.288

500000

50

1

60

OK

297.73

161.898

376.241

1018.19

2.25

177.027

671.651

1500.38

666.833

2518.57

500000

50

1

60

OK

77.7467

109.077

2.25

302.715

134.54

411.792

500000

50

1

70

OK

127.902

85.0709

140.122

392.928

2.25

50.571

169.231

289.566

128.696

682.494

500000

50

1

70

OK

123.318

154.354

2.25

243.357

108.159

397.711

500000

50

1

80

OK

126.646

82.5392

138.593

388.586

2.25

49.5318

167.371

287.394

127.731

675.98

500000

50

1

80

OK

113.381

144.073

2.25

212.683

94.5258

356.756

500000

50

1

90

OK

125.809

82.262

136.358

384.196

2.25

49.4868

166.866

285.771

127.009

669.967

500000

50

1

90

OK

99.684

189.691

2.25

392.112

174.272

581.803

500000

50

1

100

OK

127.773

83.1222

139.721

390.625

2.25

49.3845

168.759

288.462

128.205

679.087

500000

50

1

100

OK

92.7822

123.612

2.25

186.671

82.9649

310.283

500000

100

1

1

OK

529.216

488.784

733.046

1890.3

0.75

31.8238

91.7164

177.99

177.99

2068.29

500000

100

1

1

OK

2336.24

2393.96

0.75

3777.37

3777.37

6171.33

500000

100

1

4

OK

259.518

344.869

339.307

1022.18

1.75

53.8545

163.747

311.538

178.022

1333.72

500000

100

1

4

OK

1084.75

1144.08

1.75

2447.36

1398.49

3591.43

500000

100

1

10

OK

260.211

334.162

335.356

1007.72

1.75

50.7413

162.34

306.297

175.027

1314.02

500000

100

1

10

OK

1265.55

1352.48

1.75

1156.78

661.018

2509.26

500000

100

1

20

OK

258.952

325.606

318.346

981.059

1.75

49.1312

161.199

303.554

173.459

1284.61

500000

100

1

20

OK

409.116

569.426

1.75

551.912

315.378

1121.34

500000

100

1

30

OK

257.373

280.314

316.957

933.21

2.25

60.7622

197.542

370.902

164.845

1304.11

500000

100

1

30

OK

362.689

531.739

2.25

489.324

217.477

1021.06

500000

100

1

40

OK

253.714

316.276

308.057

956.149

1.75

47.8561

158.665

299.361

171.063

1255.51

500000

100

1

40

OK

336.509

395.655

1.75

326.485

186.563

722.14

500000

100

1

50

OK

260.678

316.502

310.274

965.45

1.75

48.1202

168.771

313.498

179.142

1278.95

500000

100

1

50

OK

330.159

389.374

1.75

283.475

161.986

672.849

500000

100

1

60

OK

256.704

270.087

305.682

910.907

1.75

48.5387

159.889

301.202

172.115

1212.11

500000

100

1

60

OK

321.297

380.133

1.75

252.887

144.507

633.02

500000

100

1

70

OK

257.831

254.06

310.682

901.221

2.25

59.7684

194.145

369.947

164.421

1271.17

500000

100

1

70

OK

317.369

376.38

2.25

284.086

126.26

660.466

500000

100

1

80

OK

254.428

223.598

295.73

852.426

1.75

46.9747

155.05

295.153

168.659

1147.58

500000

100

1

80

OK

311.618

370.748

1.75

217.74

124.423

588.488

500000

100

1

90

OK

254.33

200.672

291.575

825.299

2.25

57.6886

188.858

359.19

159.64

1184.49

500000

100

1

90

OK

307.69

366.582

2.25

250.147

111.176

616.729

500000

100

1

100

OK

257.002

314.43

296.069

945.678

1.75

46.5106

157.556

300.902

171.944

1246.58

500000

100

1

100

OK

307.99

366.626

1.75

197.056

112.603

563.682

500000

200

1

1

OK

769.627

967.164

910.877

2877.06

0.75

56.5047

132.778

281.948

281.948

3159.01

500000

200

1

1

OK

2961.8

3076.68

0.75

3777.95

3777.95

6854.63

500000

200

1

4

OK

767.802

947.498

901.672

2849.69

1.75

95.9457

236.179

496.998

283.999

3346.69

500000

200

1

4

OK

1473.71

1589.43

1.75

2450.54

1400.31

4039.98

500000

200

1

10

OK

766.44

901.838

861.032

2758.31

1.75

89.7653

232.943

486.079

277.759

3244.39

500000

200

1

10

OK

1053.56

1169.38

1.75

1109.75

634.142

2279.13

500000

200

1

20

OK

760.907

873.701

833.723

2696.76

1.75

87.2282

227.86

478.722

273.555

3175.48

500000

200

1

20

OK

918.209

1035.24

1.75

642.061

366.892

1677.3

500000

200

1

30

OK

783.625

686.879

842.337

2544.79

1.75

88.0188

228.996

480.583

274.619

3025.38

500000

200

1

30

OK

877.854

994.179

1.75

488.502

279.144

1482.68

500000

200

1

40

OK

779.253

550.806

812.541

2374.58

1.75

86.2563

223.152

473.166

270.381

2847.75

500000

200

1

40

OK

845.644

961.653

1.75

415.702

237.544

1377.36

500000

200

1

50

OK

770.118

838.308

797.622

2632.73

1.75

83.9244

223.705

472.058

269.747

3104.79

500000

200

1

50

OK

819.469

935.487

1.75

376.902

215.373

1312.39

500000

200

1

60

OK

794.095

506.187

791.914

2328.44

1.75

86.7124

221.652

471.84

269.623

2800.28

500000

200

1

60

OK

831.298

947.003

1.75

344.681

196.961

1291.68

500000

200

1

70

OK

793.21

515.135

766.341

2314.92

1.75

97.9003

219.859

485.393

277.367

2800.31

500000

200

1

70

OK

829.463

945.376

1.75

322.997

184.57

1268.37

500000

200

1

80

OK

774.664

502.81

741.721

2249.82

1.75

82.7996

209.539

481.268

275.01

2731.09

500000

200

1

80

OK

819.718

936.026

1.75

311.574

178.042

1247.6

500000

200

1

90

OK

782.72

525.917

751.015

2298.7

1.75

84.9334

210.033

462.693

264.396

2761.39

500000

200

1

90

OK

814.255

929.989

1.75

303.058

173.176

1233.05

500000

200

1

100

OK

795.479

787.317

724.989

2532.74

1.75

81.7096

213.579

464.025

265.157

2996.76

500000

200

1

100

OK

795.262

912.072

1.75

293.912

167.95

1205.98

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)