1-26-2016 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

1000000

10

1

1

OK

76.1195

56.5118

108.969

279.255

0.75

44.805

139.123

218.042

218.042

497.297

1000000

10

1

1

OK

1331.33

1344.67

0.75

6049.86

6049.86

7394.54

1000000

10

1

4

OK

93.3994

56.1804

100.132

288.081

2.75

115.649

361.08

561.601

204.219

849.682

1000000

10

1

4

OK

334.999

348.844

2.75

5809.35

2112.49

6158.2

1000000

10

1

10

OK

89.0314

55.9425

98.2281

281.634

2.75

114.879

359.988

558.397

203.053

840.031

1000000

10

1

10

OK

132.983

146.966

2.75

2356.2

856.8

2503.17

1000000

10

1

20

OK

69.3323

55.7277

97.5586

260.484

2.75

114.412

359.773

557.449

202.709

817.933

1000000

10

1

20

OK

67.8733

81.774

2.75

1222.59

444.576

1304.36

1000000

10

1

30

OK

67.8834

55.7754

97.1346

258.639

3.25

131.656

414.749

640.564

197.097

899.203

1000000

10

1

30

OK

45.7817

59.659

3.25

972.677

299.285

1032.34

1000000

10

1

40

OK

67.5397

55.5643

96.5432

257.518

2.75

114.028

359.548

556.443

202.343

813.961

1000000

10

1

40

OK

35.1936

49.272

2.75

656.657

238.784

705.929

1000000

10

1

50

OK

66.0849

55.5613

96.5378

255.952

3.25

131.37

412.99

637.877

196.27

893.829

1000000

10

1

50

OK

28.4511

42.485

3.25

623.33

191.794

665.815

1000000

10

1

60

OK

66.427

55.6388

96.9286

256.909

3.25

131.471

413.657

638.593

196.49

895.502

1000000

10

1

60

OK

24.0074

37.956

3.25

536.865

165.189

574.821

1000000

10

1

70

OK

66.0314

55.4954

96.959

256.414

3.25

148.945

468.458

722.107

222.187

978.521

1000000

10

1

70

OK

21.231

35.206

3.25

544.507

167.541

579.713

1000000

10

1

80

OK

65.8034

55.4317

96.4343

255.619

3.25

131.552

413.986

639.021

196.622

894.64

1000000

10

1

80

OK

18.8513

32.843

3.25

431.091

132.643

463.934

1000000

10

1

90

OK

80.3041

55.51

97.0329

271.289

2.75

114.244

358.849

555.163

201.877

826.452

1000000

10

1

90

OK

16.9234

30.893

2.75

343.082

124.757

373.975

1000000

10

1

100

OK

64.3642

55.2457

95.8369

253.218

3.25

148.444

467.538

720.137

221.581

973.355

1000000

10

1

100

OK

15.8121

29.863

3.25

416.207

128.064

446.07

1000000

20

1

1

OK

136.961

93.1559

132.536

404.131

0.75

41.6631

149.71

236.389

236.389

640.52

1000000

20

1

1

OK

1433.26

1458.78

0.75

6345.39

6345.39

7804.17

1000000

20

1

4

OK

111.838

92.4715

131.479

377.433

2.25

106.953

388.288

606.245

269.442

983.678

1000000

20

1

4

OK

360.094

386.194

2.25

5992.83

2663.48

6379.02

1000000

20

1

10

OK

111.228

93.0792

132.289

377.906

2.25

107.457

393.38

612.635

272.282

990.541

1000000

20

1

10

OK

145.999

171.939

2.25

2465.53

1095.79

2637.46

1000000

20

1

20

OK

117.628

91.3563

130.789

381.08

2.25

105.799

388.007

604.729

268.768

985.809

1000000

20

1

20

OK

78.5269

104.594

2.25

1291.7

574.089

1396.3

1000000

20

1

30

OK

106.496

91.8824

130.66

370.77

2.75

105.599

389.685

607.24

220.815

978.01

1000000

20

1

30

OK

53.583

79.811

2.75

902.867

328.315

982.678

1000000

20

1

40

OK

122.283

90.894

130.529

385.774

2.75

105.387

388.271

606.478

220.537

992.252

1000000

20

1

40

OK

44.4534

70.713

2.75

707.755

257.365

778.468

1000000

20

1

50

OK

119.382

90.5344

130.1

381.5

2.75

104.943

387.179

604.572

219.844

986.072

1000000

20

1

50

OK

40.3378

68.365

2.75

593.173

215.699

661.538

1000000

20

1

60

OK

104.941

90.914

129.914

367.646

2.75

105.076

389.746

606.547

220.563

974.193

1000000

20

1

60

OK

33.8537

59.974

2.75

511.494

185.998

571.468

1000000

20

1

70

OK

106.006

90.6751

129.486

367.447

2.75

105.219

389.239

606.135

220.413

973.582

1000000

20

1

70

OK

53.623

80.029

2.75

458.055

166.565

538.084

1000000

20

1

80

OK

105.716

89.942

128.926

365.757

2.75

104.749

388.905

605.449

220.163

971.206

1000000

20

1

80

OK

48.3773

74.437

2.75

415.834

151.212

490.271

1000000

20

1

90

OK

119.757

90.1141

130.677

382.079

2.75

105.716

391.063

609.286

221.559

991.365

1000000

20

1

90

OK

43.4379

69.512

2.75

383.479

139.447

452.991

1000000

20

1

100

OK

116.367

89.6543

128.602

376.066

2.75

104.438

387.017

603.469

219.443

979.535

1000000

20

1

100

OK

39.4187

65.459

2.75

357.585

130.031

423.044

1000000

50

1

1

OK

263.499

175.054

299.427

816.449

0.75

46.3236

155.324

266.199

266.199

1082.65

1000000

50

1

1

OK

5160.54

5218.41

0.75

7230.33

7230.33

12448.7

1000000

50

1

4

OK

257.363

171.225

294.933

801.51

2.25

116.458

397.166

674.719

299.875

1476.23

1000000

50

1

4

OK

1311

1371.17

2.25

5624.49

2499.77

6995.66

1000000

50

1

10

OK

253.737

169.793

292.32

794.041

2.25

96.4691

335.039

568.15

252.511

1362.19

1000000

50

1

10

OK

521.049

581.334

2.25

2309.01

1026.23

2890.35

1000000

50

1

20

OK

252.213

168.75

291.073

790.265

2.25

95.6612

334.467

566.657

251.848

1356.92

1000000

50

1

20

OK

309.639

370.117

2.25

1226.6

545.154

1596.71

1000000

50

1

30

OK

266.236

168.597

290.516

803.496

2.25

95.7339

335.344

567.438

252.195

1370.93

1000000

50

1

30

OK

212.051

272.549

2.25

875.048

388.91

1147.6

1000000

50

1

40

OK

262.99

167.087

288.785

796.802

2.25

94.801

333.564

564.834

251.037

1361.64

1000000

50

1

40

OK

192.842

253.519

2.25

694.442

308.641

947.961

1000000

50

1

50

OK

253.964

168.721

292.353

793.492

2.25

112.839

399.948

673.642

299.396

1467.13

1000000

50

1

50

OK

184.588

245.331

2.25

689.382

306.392

934.713

1000000

50

1

60

OK

251.163

166.869

287.086

783.034

2.25

112.304

395.699

667.912

296.85

1450.95

1000000

50

1

60

OK

154.892

215.356

2.25

599.404

266.402

814.76

1000000

50

1

70

OK

251.425

166.805

286.274

782.635

2.25

94.9153

334.405

565.738

251.439

1348.37

1000000

50

1

70

OK

255.249

315.894

2.25

457.466

203.318

773.36

1000000

50

1

80

OK

260.042

164.166

272.168

774.277

2.25

93.8632

331.851

562.125

249.833

1336.4

1000000

50

1

80

OK

220.754

281.152

2.25

419.389

186.395

700.541

1000000

50

1

90

OK

249.325

164.088

270.638

761.792

2.25

93.9358

332.065

561.961

249.76

1323.75

1000000

50

1

90

OK

203.194

263.754

2.25

388.305

172.58

652.059

1000000

50

1

100

OK

250.488

164.931

272.734

766.125

2.25

93.6142

333.209

562.964

250.206

1329.09

1000000

50

1

100

OK

185.516

246.069

2.25

365.589

162.484

611.658

1000000

100

1

1

OK

513.802

675.497

665.834

2010.51

0.75

54.0499

179.532

341.591

341.591

2352.1

1000000

100

1

1

OK

4654.99

4770.24

0.75

7377.36

7377.36

12147.6

1000000

100

1

4

OK

510.663

668.504

663.189

1997.63

1.75

94.1768

322.18

607.87

347.354

2605.5

1000000

100

1

4

OK

1932.93

2049.94

1.75

4718.84

2696.48

6768.78

1000000

100

1

10

OK

506.146

657.928

658.18

1977.62

1.75

90.958

320.671

602.886

344.506

2580.51

1000000

100

1

10

OK

1096.39

1213.4

1.75

1993.53

1139.16

3206.93

1000000

100

1

20

OK

504.619

648.199

652.493

1960.57

1.75

89.3778

319.224

599.618

342.639

2560.19

1000000

100

1

20

OK

812.924

930.154

1.75

1103.98

630.845

2034.13

1000000

100

1

30

OK

513.44

630.458

662.294

1962.76

1.75

90.8941

325.049

608.542

347.738

2571.3

1000000

100

1

30

OK

718.882

836.138

1.75

803.421

459.098

1639.56

1000000

100

1

40

OK

503.164

638.436

621.379

1918.48

1.75

88.2148

316.948

595.553

340.316

2514.04

1000000

100

1

40

OK

681.768

798.939

1.75

653.65

373.514

1452.59

1000000

100

1

50

OK

522.844

644.137

631.53

1954.36

1.75

89.0702

322.211

603.163

344.665

2557.52

1000000

100

1

50

OK

665.688

783.443

1.75

570.374

325.928

1353.82

1000000

100

1

60

OK

519.254

547.966

620.541

1843.69

1.75

89.2721

318.87

599.206

342.403

2442.9

1000000

100

1

60

OK

640.862

757.782

1.75

505.998

289.142

1263.78

1000000

100

1

70

OK

518.972

504.043

616.343

1795.79

1.75

89.418

317.579

598.113

341.779

2393.9

1000000

100

1

70

OK

630.999

748.298

1.75

466.274

266.442

1214.57

1000000

100

1

80

OK

506.881

630.616

610.991

1903.75

1.75

87.7978

316.75

594.984

339.991

2498.73

1000000

100

1

80

OK

617.146

734.432

1.75

436.014

249.151

1170.45

1000000

100

1

90

OK

512.718

601.913

604.121

1873.74

1.75

87.6409

313.764

592.861

338.778

2466.6

1000000

100

1

90

OK

617.156

734.526

1.75

412.644

235.797

1147.17

1000000

100

1

100

OK

516.226

623.462

607.801

1902.24

1.75

86.5902

315.553

592.649

338.657

2494.89

1000000

100

1

100

OK

615.469

732.795

1.75

396.099

226.342

1128.89

1000000

200

1

1

OK

1537.6

1860.52

1816.41

5672.85

0.75

96.9913

261.931

552.825

552.825

6225.68

1000000

200

1

1

OK

5907.87

6137.88

0.75

7617.96

7617.96

13755.8

1000000

200

1

4

OK

1514.39

1832.05

1806.59

5611.14

1.75

168.359

468.299

983.176

561.815

6594.31

1000000

200

1

4

OK

2929.56

3160.79

1.75

4915.34

2808.77

8076.13

1000000

200

1

10

OK

1510.17

1794.58

1766.95

5530.05

1.75

162.338

465.033

971.084

554.905

6501.14

1000000

200

1

10

OK

2068

2300.25

1.75

2181.67

1246.67

4481.92

1000000

200

1

20

OK

1509.06

1764.48

1703.15

5434.7

1.75

159.229

460.252

965.696

551.826

6400.4

1000000

200

1

20

OK

1827.94

2060.92

1.75

1302.55

744.313

3363.47

1000000

200

1

30

OK

1547.54

1394.82

1732.22

5139.15

1.75

162.069

463.001

971.744

555.282

6110.89

1000000

200

1

30

OK

1753.17

1984.3

1.75

988.789

565.022

2973.09

1000000

200

1

40

OK

1516.89

1724.67

1651.03

5349.53

1.75

157.775

450.879

953.732

544.99

6303.27

1000000

200

1

40

OK

1662.61

1894.35

1.75

849.002

485.144

2743.35

1000000

200

1

50

OK

1538.01

1740.5

1682.55

5417.77

1.75

158.239

459.447

962.652

550.087

6380.43

1000000

200

1

50

OK

1638.31

1870.18

1.75

767.177

438.387

2637.36

1000000

200

1

60

OK

1560.83

1347.06

1666.12

5038.24

1.75

159.32

452.817

958.188

547.536

5996.43

1000000

200

1

60

OK

1663.88

1895.72

1.75

705.325

403.043

2601.04

1000000

200

1

70

OK

1567.48

1194.09

1640.25

4867.03

1.75

159.69

450.259

953.782

545.018

5820.81

1000000

200

1

70

OK

1655.11

1886.9

1.75

662.363

378.493

2549.27

1000000

200

1

80

OK

1543.72

1072.67

1608.27

4687.37

1.75

158.04

441.314

944.565

539.751

5631.94

1000000

200

1

80

OK

1630.16

1862.05

1.75

637.347

364.198

2499.4

1000000

200

1

90

OK

1545.15

957.138

1575.45

4540.01

1.75

157.976

439.492

946.425

540.814

5486.43

1000000

200

1

90

OK

1633.32

1865.29

1.75

615.366

351.638

2480.66

1000000

200

1

100

OK

1526.49

1647.14

1578.9

5206.78

1.75

153.866

442.429

941.578

538.045

6148.36

1000000

200

1

100

OK

1593.17

1825.47

1.75

606.918

346.81

2432.39