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

0.08

1

OK

102.595

113.047

118.82

375.126

0.75

47.0034

151.69

234.137

234.137

609.263

1000000

10

0.08

1

OK

1516.16

1531.36

1.75

10590.9

6051.94

12122.3

1000000

10

0.06

1

OK

79.6255

111.805

116.986

348.299

0.75

46.5002

149.447

231.104

231.104

579.403

1000000

10

0.06

1

OK

1515.49

1530.66

0.75

5882.56

5882.56

7413.22

1000000

10

0.04

1

OK

102.379

112.008

119.317

374.309

1.75

83.9119

269.499

414.911

237.092

789.22

1000000

10

0.04

1

OK

1516.4

1531.56

1.75

10578.3

6044.72

12109.8

1000000

10

0.02

1

OK

79.5599

111.805

117.716

348.972

0.75

46.475

149.435

230.888

230.888

579.86

1000000

10

0.02

1

OK

1515.92

1531.11

3.75

19986.8

5329.82

21517.9

1000000

10

0.01

1

OK

79.5302

111.817

117.432

348.789

0.75

46.48

149.454

230.991

230.991

579.78

1000000

10

0.01

1

OK

1515.07

1530.24

0.75

5878.99

5878.99

7409.23

1000000

10

0.08

4

OK

96.5557

111.523

108.064

356.535

30.25

1150.8

3722.43

5669.31

187.415

6025.84

1000000

10

0.08

4

OK

382.276

398.02

32.25

68270.6

2116.92

68668.6

1000000

10

0.06

4

OK

97.0061

112.771

109.428

359.897

32.25

1222.16

3964.74

6042.26

187.357

6402.16

1000000

10

0.06

4

OK

381.269

397.016

34.75

73434.1

2113.21

73831.1

1000000

10

0.04

4

OK

96.1345

111.57

108.198

356.379

35.25

1314.99

4258.64

6488.55

184.072

6844.93

1000000

10

0.04

4

OK

382.566

398.449

30.25

65157.3

2153.96

65555.7

1000000

10

0.02

4

OK

76.2765

111.794

107.108

335.223

33.75

1261.94

4082.3

6221.34

184.336

6556.56

1000000

10

0.02

4

OK

381.301

397.068

32.75

69281.4

2115.46

69678.5

1000000

10

0.01

4

OK

96.4651

111.559

108.091

356.516

34.25

1297.25

4200.42

6398.69

186.823

6755.21

1000000

10

0.01

4

OK

381.669

397.342

33.25

71339.8

2145.56

71737.1

1000000

10

0.08

10

NConv

93.2533

111.227

106.736

351.839

50.25

1863.06

6038.29

9193.84

182.962

9545.68

1000000

10

0.08

10

NConv

153.857

169.684

50.25

43164.1

858.987

43333.8

1000000

10

0.06

10

NConv

74.3448

111.252

106.826

332.433

50.25

1861.05

6039.24

9194.48

182.975

9526.91

1000000

10

0.06

10

NConv

153.833

169.661

50.25

43157.2

858.849

43326.8

1000000

10

0.04

10

NConv

93.1788

111.228

108.164

353.495

50.25

1865.52

6045.64

9215.42

183.391

9568.92

1000000

10

0.04

10

NConv

153.769

169.655

50.25

43141.1

858.53

43310.8

1000000

10

0.02

10

NConv

93.9354

111.492

107.856

353.815

50.25

1868.44

6048.55

9222.12

183.525

9575.93

1000000

10

0.02

10

NConv

154.118

169.964

50.25

43166.4

859.033

43336.4

1000000

10

0.01

10

NConv

93.7096

111.444

107.631

353.325

50.25

1861.76

6040.22

9195.28

182.991

9548.6

1000000

10

0.01

10

NConv

154.175

169.999

50.25

43173.2

859.168

43343.2

1000000

10

0.08

20

NConv

90.7993

112.215

108.475

352.389

50.25

1877.81

6131.68

9329.89

185.669

9682.28

1000000

10

0.08

20

NConv

78.9152

94.772

50.25

22285.8

443.499

22380.6

1000000

10

0.06

20

NConv

90.4883

110.993

107.015

348.985

50.25

1853.21

6033.94

9175.12

182.589

9524.11

1000000

10

0.06

20

NConv

78.9205

94.786

50.25

22282.2

443.426

22376.9

1000000

10

0.04

20

NConv

72.4432

110.993

105.867

329.332

50.25

1853.47

6033.6

9177.44

182.636

9506.78

1000000

10

0.04

20

NConv

78.9645

94.855

50.25

22309.7

443.975

22404.6

1000000

10

0.02

20

NConv

72.9033

111.005

106.248

330.101

50.25

1853.86

6035.2

9176.12

182.609

9506.23

1000000

10

0.02

20

NConv

78.9123

94.738

50.25

22282.4

443.431

22377.2

1000000

10

0.01

20

NConv

90.1387

111.042

107.451

349.188

50.25

1859.22

6042.35

9203.67

183.158

9552.86

1000000

10

0.01

20

NConv

78.9097

94.792

50.25

22279.4

443.37

22374.2

1000000

10

0.08

30

NConv

87.415

111.264

107.251

346.367

50.25

1853.56

6041.46

9189.04

182.867

9535.41

1000000

10

0.08

30

NConv

53.4929

69.449

50.25

15362.6

305.724

15432.1

1000000

10

0.06

30

NConv

87.0682

111.525

106.995

346.117

50.25

1852.93

6038.66

9182.64

182.739

9528.76

1000000

10

0.06

30

NConv

53.5034

69.394

50.25

15365.5

305.78

15434.9

1000000

10

0.04

30

NConv

71.0778

111.235

106.171

328.353

50.25

1849.33

6035.1

9168.04

182.449

9496.4

1000000

10

0.04

30

NConv

53.4638

69.293

50.25

15328.7

305.048

15397.9

1000000

10

0.02

30

NConv

71.1349

111.273

105.442

327.748

50.25

1849.39

6036.32

9168.52

182.458

9496.27

1000000

10

0.02

30

NConv

53.4558

69.296

50.25

15327.6

305.027

15396.9

1000000

10

0.01

30

NConv

87.4164

111.242

107.555

346.739

50.25

1853.7

6041.38

9192.91

182.943

9539.65

1000000

10

0.01

30

NConv

53.4354

69.335

50.25

15357.8

305.628

15427.2

1000000

10

0.08

40

NConv

71.0277

110.729

105.228

326.899

50.25

1848.45

6033.03

9164.96

182.387

9491.86

1000000

10

0.08

40

NConv

42.1599

59.354

50.25

11998.1

238.768

12057.4

1000000

10

0.06

40

NConv

70.7341

110.732

105.112

326.49

50.25

1847.63

6032.16

9163.97

182.368

9490.46

1000000

10

0.06

40

NConv

41.4666

57.311

50.25

11865.6

236.131

11922.9

1000000

10

0.04

40

NConv

87.0251

110.975

106.378

344.921

50.25

1851.29

6036.29

9173.55

182.558

9518.47

1000000

10

0.04

40

NConv

41.4821

57.357

50.25

11879.3

236.405

11936.7

1000000

10

0.02

40

NConv

79.2841

110.918

106.486

336.789

50.25

1854.56

6042.72

9193.69

182.959

9530.48

1000000

10

0.02

40

NConv

41.462

57.325

50.25

11872.5

236.269

11929.8

1000000

10

0.01

40

NConv

71.3671

110.972

105.723

328.054

50.25

1850.69

6035.9

9169.71

182.482

9497.76

1000000

10

0.01

40

NConv

41.4954

57.393

50.25

11874.4

236.306

11931.8

1000000

10

0.08

50

NConv

69.6309

110.623

105.384

325.638

50.25

1842.19

6021.42

9143.68

181.964

9469.31

1000000

10

0.08

50

NConv

34.3165

50.139

50.25

9783.85

194.703

9833.99

1000000

10

0.06

50

NConv

69.29

110.613

105.711

325.48

50.25

1842.42

6021.62

9141.86

181.928

9467.34

1000000

10

0.06

50

NConv

34.3156

50.194

50.25

9794.16

194.909

9844.36

1000000

10

0.04

50

NConv

83.6919

110.617

106.136

340.957

50.25

1846.33

6027.85

9163.16

182.351

9504.12

1000000

10

0.04

50

NConv

34.3561

50.24

50.25

9766.19

194.352

9816.43

1000000

10

0.02

50

NConv

69.4578

110.86

105.284

325.52

50.25

1844.63

6025.19

9153.43

182.158

9478.95

1000000

10

0.02

50

NConv

34.3181

50.414

50.25

9780.67

194.64

9831.09

1000000

10

0.01

50

NConv

84.6783

111.805

106.789

343.91

50.25

1863.48

6112.48

9269.09

184.459

9613

1000000

10

0.01

50

NConv

34.2787

50.17

50.25

9768.92

194.406

9819.09

1000000

10

0.08

60

NConv

84.2057

111.094

106.491

342.18

50.25

1849.77

6041.2

9180.56

182.698

9522.74

1000000

10

0.08

60

NConv

29.0557

44.95

50.25

8381.74

166.801

8426.69

1000000

10

0.06

60

NConv

77.2823

111

105.925

334.193

50.25

1848.12

6037.81

9173.21

182.552

9507.41

1000000

10

0.06

60

NConv

29.0432

44.941

50.25

8381.02

166.786

8425.96

1000000

10

0.04

60

NConv

83.6634

110.966

105.849

340.766

50.25

1844.07

6032.06

9154.79

182.185

9495.56

1000000

10

0.04

60

NConv

29.049

44.911

50.25

8375.42

166.675

8420.33

1000000

10

0.02

60

NConv

69.39

110.978

105.805

326.083

50.25

1844.13

6032.23

9158.12

182.251

9484.2

1000000

10

0.02

60

NConv

29.0298

45.132

50.25

8368.61

166.54

8413.75

1000000

10

0.01

60

NConv

69.3739

110.976

105.707

325.821

50.25

1843.74

6031.77

9153.47

182.159

9479.29

1000000

10

0.01

60

NConv

29.0409

44.933

50.25

8369.38

166.555

8414.32

1000000

10

0.08

70

NConv

77.0601

110.633

106.016

333.912

50.25

1848.52

6036.05

9173.8

182.563

9507.71

1000000

10

0.08

70

NConv

25.8728

41.809

50.25

7460.54

148.469

7502.35

1000000

10

0.06

70

NConv

69.7275

110.628

105.307

325.75

50.25

1844.52

6030.47

9153.09

182.151

9478.84

1000000

10

0.06

70

NConv

26.0107

41.909

50.25

7457.74

148.413

7499.65

1000000

10

0.04

70

NConv

69.6566

110.633

105.688

325.989

50.25

1845.01

6030.95

9156.01

182.209

9482

1000000

10

0.04

70

NConv

25.9123

41.833

50.25

7462.22

148.502

7504.05

1000000

10

0.02

70

NConv

84.7013

110.615

105.82

341.677

50.25

1844.94

6030.88

9154.09

182.171

9495.77

1000000

10

0.02

70

NConv

25.8776

41.796

50.25

7451.92

148.297

7493.71

1000000

10

0.01

70

NConv

84.1085

110.638

105.814

341.053

50.25

1844.7

6030.69

9153.14

182.152

9494.19

1000000

10

0.01

70

NConv

25.8923

41.75

50.25

7451.56

148.29

7493.31

1000000

10

0.08

80

NConv

69.6005

110.332

105.086

325.156

50.25

1843.47

6034.29

9156.33

182.215

9481.48

1000000

10

0.08

80

NConv

23.3782

39.242

50.25

6700.94

133.352

6740.19

1000000

10

0.06

80

NConv

84.4445

110.372

106.263

341.753

50.25

1847.25

6040.21

9178.01

182.647

9519.76

1000000

10

0.06

80

NConv

23.3879

39.217

50.25

6700.5

133.343

6739.72

1000000

10

0.04

80

NConv

69.0591

110.333

104.608

324.083

50.25

1843.84

6034.8

9159.21

182.273

9483.29

1000000

10

0.04

80

NConv

23.6668

39.597

50.25

6763.66

134.6

6803.25

1000000

10

0.02

80

NConv

83.9029

110.343

105.827

340.727

50.25

1843.5

6034.7

9157.15

182.232

9497.87

1000000

10

0.02

80

NConv

23.4129

39.322

50.25

6702.97

133.392

6742.29

1000000

10

0.01

80

NConv

83.99

110.495

105.637

341.067

50.25

1844.8

6036.92

9160.07

182.29

9501.14

1000000

10

0.01

80

NConv

23.4381

39.303

50.25

6718.89

133.709

6758.19

1000000

10

0.08

90

NConv

69.1372

110.8

105.49

325.46

50.25

1848.49

6037.9

9170.83

182.504

9496.29

1000000

10

0.08

90

NConv

21.1158

37.021

50.25

6115.08

121.693

6152.1

1000000

10

0.06

90

NConv

83.9648

110.932

106.47

341.904

50.25

1849.43

6038.99

9167.82

182.444

9509.73

1000000

10

0.06

90

NConv

21.4346

37.335

50.25

6122.4

121.839

6159.73

1000000

10

0.04

90

NConv

83.7081

110.799

106.583

341.745

50.25

1852.47

6043.64

9190.49

182.895

9532.23

1000000

10

0.04

90

NConv

21.1267

37.015

50.25

6120.07

121.793

6157.09

1000000

10

0.02

90

NConv

70.1987

111.988

106.856

329.372

50.25

1868.23

6127.47

9289.98

184.875

9619.35

1000000

10

0.02

90

NConv

21.1062

37.019

50.25

6109.8

121.588

6146.82

1000000

10

0.01

90

NConv

69.2995

110.805

105.793

325.933

50.25

1848.01

6037.08

9166.59

182.42

9492.52

1000000

10

0.01

90

NConv

21.1564

37.048

50.25

6129.6

121.982

6166.65

1000000

10

0.08

100

NConv

67.2945

110.218

103.805

321.164

50.25

1837.54

6017.79

9127.9

181.65

9449.07

1000000

10

0.08

100

NConv

20.0491

35.977

50.25

5715.75

113.746

5751.72

1000000

10

0.06

100

NConv

67.567

110.193

104.034

321.684

50.25

1837.09

6017.09

9127.42

181.64

9449.1

1000000

10

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NConv

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NConv

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NConv

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NConv

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NConv

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0.08

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NConv

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NConv

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NConv

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NConv

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NConv

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NConv

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NConv

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NConv

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NConv

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0.08

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NConv

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NConv

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NConv

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NConv

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NConv

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NConv

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0.02

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NConv

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0.02

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NConv

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0.01

30

NConv

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0.01

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NConv

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0.08

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NConv

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10088.8

200.771

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0.08

40

NConv

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12545.7

249.665

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0.06

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NConv

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6623.33

10095.4

200.903

10612.3

1000000

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0.06

40

NConv

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50.25

12672.8

252.194

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1000000

20

0.04

40

NConv

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189.779

155.087

515.69

50.25

1686.61

6614.24

10067.2

200.342

10582.9

1000000

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0.04

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NConv

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12543.8

249.628

12629

1000000

20

0.02

40

NConv

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156.555

505.338

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1706.9

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10198.5

202.955

10703.8

1000000

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0.02

40

NConv

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12542.8

249.608

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0.01

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NConv

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10069.3

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0.01

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NConv

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0.08

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NConv

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NConv

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NConv

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0.06

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NConv

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0.04

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NConv

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10039.9

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0.04

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NConv

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10436

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0.02

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NConv

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0.02

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NConv

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0.01

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NConv

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NConv

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0.08

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NConv

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10073.2

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0.08

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NConv

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0.06

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NConv

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10057.1

200.141

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0.06

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NConv

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0.04

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NConv

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10053.6

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NConv

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0.02

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NConv

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10059.9

200.198

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0.02

60

NConv

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0.01

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NConv

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10053.7

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0.01

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NConv

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0.08

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NConv

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10047.8

199.956

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0.08

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NConv

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0.06

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NConv

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10048

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NConv

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0.04

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NConv

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NConv

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NConv

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NConv

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NConv

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NConv

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0.08

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NConv

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10086.3

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0.08

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NConv

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0.06

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NConv

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NConv

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0.04

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NConv

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NConv

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NConv

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NConv

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NConv

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NConv

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NConv

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NConv

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NConv

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0.01

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NConv

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0.08

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0.08

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0.06

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0.04

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OK

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NConv

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NConv

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NConv

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NConv

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1950.32

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10

NConv

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0.08

20

NConv

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20

NConv

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20

NConv

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20

NConv

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26009.2

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NConv

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NConv

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20

NConv

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NConv

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NConv

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NConv

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NConv

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NConv

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NConv

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NConv

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NConv

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NConv

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NConv

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30

NConv

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18336.1

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0.08

40

NConv

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1911.07

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221.99

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40

NConv

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14587.1

290.29

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NConv

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1000000

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0.06

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NConv

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14573.9

290.029

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0.04

40

NConv

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1911.25

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222.042

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0.04

40

NConv

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14576.8

290.085

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0.02

40

NConv

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221.763

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0.02

40

NConv

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14584.9

290.247

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0.01

40

NConv

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221.57

12124.8

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0.01

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NConv

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14577.5

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0.08

50

NConv

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0.08

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NConv

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12263.1

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0.06

50

NConv

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12150.9

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NConv

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0.04

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NConv

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222.14

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NConv

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12252.3

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NConv

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NConv

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12282.8

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0.01

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NConv

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1911.7

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0.01

50

NConv

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12371

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NConv

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NConv

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NConv

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NConv

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NConv

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NConv

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10713

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NConv

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NConv

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NConv

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NConv

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NConv

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NConv

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0.06

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NConv

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NConv

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0.04

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NConv

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NConv

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NConv

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NConv

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NConv

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NConv

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NConv

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NConv

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NConv

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NConv

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0.04

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NConv

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NConv

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NConv

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NConv

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NConv

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NConv

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NConv

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0.04

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NConv

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NConv

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NConv

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NConv

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100

NConv

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100

NConv

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100

NConv

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0.06

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0.06

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0.04

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OK

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0.04

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NConv

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