Installation

There are may ways to install timeseries package. Since timeseries is built using fastai2, there are also different ways to install fastai2. We will show 2 differents ways to install them and explain the motivation behin each one of them.

Method 1 : Editable Version

1A - Installing fastai2

Important :Only if you have not already installed fastai2,install fastai2 by following the steps described there.

1B - Installing `timeseries` on a local machine

Note :Installing an editable version of a package means that you will install a package from its corresponding github repository on your local machine. By doing so, you can pull the latest version whenever a new version is pushed. To install timeseries editable package, follow the instructions here below:

git clone https://github.com/ai-fast-track/timeseries.git
cd timeseries
pip install -e .

Method 2 : Non Editable version

Note :Everytime you run the !pip install git+https:// ..., you are installing the package latest version stored on github. > Important :As both fastai2 and timeseries are still under development, this is an easy way to use them in Google Colab or any other online platform. You can also use it on your local machine.

2A - Installing `fastai2` from its github repository

# Run this cell to install the latest version of fastai shared on github
!pip install git+https://github.com/fastai/fastai2.git

# Run this cell to install the latest version of fastcore shared on github
!pip install git+https://github.com/fastai/fastcore.git

2B - Installing `timeseries` from its github repository

# Run this cell to install the latest version of timeseries shared on github
!pip install git+https://github.com/ai-fast-track/timeseries.git

`Usage`

%reload_ext autoreload
%autoreload 2
%matplotlib inline

from fastai2.basics import *

from timeseries.all import *

Tutorial on timeseries package for fastai2

Example : NATOS dataset

Description

The data is generated by sensors on the hands, elbows, wrists and thumbs. The data are the x,y,z coordinates for each of the eight locations. The order of the data is as follows:

Right Arm vs Left Arm time series for the 'Not clear' Command ((#3) (see picture here above)

Channels (24)

Hand	Elbow	Hand	Elbow
0. Hand tip left, X	6. Elbow left, X	12. Wrist left, X	18. Thumb left, X
1. Hand tip left, Y	7. Elbow left, Y	13. Wrist left, X	19. Thumb left, X
2. Hand tip left, Z	8. Elbow left, Z	14. Wrist left, X	20. Thumb left, X
3. Hand tip righ, X	9. Elbow righ, X	15. Wrist righ, X	21. Thumb righ, X
4. Hand tip righ, Y	10. Elbow righ, Y	16. Wrist righ, X	22. Thumb righ, X
5. Hand tip righ, Z	11. Elbow righ, Z	17. Wrist righ, X	23. Thumb righ, X

Classes (6)

The six classes are separate actions, with the following meaning:


1: I have command	2: All clear	3: Not clear	4: Spread wings	5: Fold wings	6: Lock wings

Downloading and unzipping a time series dataset

dsname =  'NATOPS' #'NATOPS', 'LSST', 'Wine', 'Epilepsy', 'HandMovementDirection'

# url = 'http://www.timeseriesclassification.com/Downloads/NATOPS.zip'
path = unzip_data(URLs_TS.NATOPS)
path

Path('/home/farid/.fastai/data/NATOPS')

Why do I have to concatenate train and test data?

Both Train and Train dataset contains 180 samples each. We concatenate them in order to have one big dataset and then split into train and valid dataset using our own split percentage (20%, 30%, or whatever number you see fit)

fname_train = f'{dsname}_TRAIN.arff'
fname_test = f'{dsname}_TEST.arff'
fnames = [path/fname_train, path/fname_test]
fnames

[Path('/home/farid/.fastai/data/NATOPS/NATOPS_TRAIN.arff'),
 Path('/home/farid/.fastai/data/NATOPS/NATOPS_TEST.arff')]

data = TSData.from_arff(fnames)
print(data)

TSData:
 Datasets names (concatenated): ['NATOPS_TRAIN', 'NATOPS_TEST']
 Filenames:                     [Path('/home/farid/.fastai/data/NATOPS/NATOPS_TRAIN.arff'), Path('/home/farid/.fastai/data/NATOPS/NATOPS_TEST.arff')]
 Data shape: (360, 24, 51)
 Targets shape: (360,)
 Nb Samples: 360
 Nb Channels:           24
 Sequence Length: 51

items = data.get_items()

idx = 1
x1, y1 = data.x[idx],  data.y[idx]
y1

'3.0'

# You can select any channel to display buy supplying a list of channels and pass it to `chs` argument
# LEFT ARM
# show_timeseries(x1, title=y1, chs=[0,1,2,6,7,8,12,13,14,18,19,20])

# RIGHT ARM
# show_timeseries(x1, title=y1, chs=[3,4,5,9,10,11,15,16,17,21,22,23])

# ?show_timeseries(x1, title=y1, chs=range(0,24,3)) # Only the x axis coordinates

seed = 42
splits = RandomSplitter(seed=seed)(range_of(items)) #by default 80% for train split and 20% for valid split are chosen 
splits

((#288) [304,281,114,329,115,130,338,294,94,310...],
 (#72) [222,27,96,253,274,35,160,172,302,146...])

Using `Datasets` class

Creating a Datasets object

tfms = [[ItemGetter(0), ToTensorTS()], [ItemGetter(1), Categorize()]]

# Create a dataset
ds = Datasets(items, tfms, splits=splits)

ax = show_at(ds, 2, figsize=(1,1))

3.0

Creating a `Dataloaders` object

1st method : using `Datasets` object

bs = 128                            
# Normalize at batch time
tfm_norm = Normalize(scale_subtype = 'per_sample_per_channel', scale_range=(0, 1)) # per_sample , per_sample_per_channel
# tfm_norm = Standardize(scale_subtype = 'per_sample')
batch_tfms = [tfm_norm]

dls1 = ds.dataloaders(bs=bs, val_bs=bs * 2, after_batch=batch_tfms, num_workers=0, device=default_device())

dls1.show_batch(max_n=9, chs=range(0,12,3))

Using `DataBlock` class

2nd method : using `DataBlock` and `DataBlock.get_items()`

getters = [ItemGetter(0), ItemGetter(1)]  
tsdb = DataBlock(blocks=(TSBlock, CategoryBlock),
                   get_items=get_ts_items,
                   getters=getters,
                   splitter=RandomSplitter(seed=seed),
                   batch_tfms = batch_tfms)

tsdb.summary(fnames)

Setting-up type transforms pipelines
Collecting items from [Path('/home/farid/.fastai/data/NATOPS/NATOPS_TRAIN.arff'), Path('/home/farid/.fastai/data/NATOPS/NATOPS_TEST.arff')]
Found 360 items
2 datasets of sizes 288,72
Setting up Pipeline: itemgetter -> ToTensorTS
Setting up Pipeline: itemgetter -> Categorize

Building one sample
  Pipeline: itemgetter -> ToTensorTS
    starting from
      ([[-0.540579 -0.54101  -0.540603 ... -0.56305  -0.566314 -0.553712]
 [-1.539567 -1.540042 -1.538992 ... -1.532014 -1.534645 -1.536015]
 [-0.608539 -0.604609 -0.607679 ... -0.593769 -0.592854 -0.599014]
 ...
 [ 0.454542  0.449924  0.453195 ...  0.480281  0.45537   0.457275]
 [-1.411445 -1.363464 -1.390869 ... -1.468123 -1.368706 -1.386574]
 [-0.473406 -0.453322 -0.463813 ... -0.440582 -0.427211 -0.435581]], 2.0)
    applying itemgetter gives
      [[-0.540579 -0.54101  -0.540603 ... -0.56305  -0.566314 -0.553712]
 [-1.539567 -1.540042 -1.538992 ... -1.532014 -1.534645 -1.536015]
 [-0.608539 -0.604609 -0.607679 ... -0.593769 -0.592854 -0.599014]
 ...
 [ 0.454542  0.449924  0.453195 ...  0.480281  0.45537   0.457275]
 [-1.411445 -1.363464 -1.390869 ... -1.468123 -1.368706 -1.386574]
 [-0.473406 -0.453322 -0.463813 ... -0.440582 -0.427211 -0.435581]]
    applying ToTensorTS gives
      TensorTS of size 24x51
  Pipeline: itemgetter -> Categorize
    starting from
      ([[-0.540579 -0.54101  -0.540603 ... -0.56305  -0.566314 -0.553712]
 [-1.539567 -1.540042 -1.538992 ... -1.532014 -1.534645 -1.536015]
 [-0.608539 -0.604609 -0.607679 ... -0.593769 -0.592854 -0.599014]
 ...
 [ 0.454542  0.449924  0.453195 ...  0.480281  0.45537   0.457275]
 [-1.411445 -1.363464 -1.390869 ... -1.468123 -1.368706 -1.386574]
 [-0.473406 -0.453322 -0.463813 ... -0.440582 -0.427211 -0.435581]], 2.0)
    applying itemgetter gives
      2.0
    applying Categorize gives
      TensorCategory(1)

Final sample: (TensorTS([[-0.5406, -0.5410, -0.5406,  ..., -0.5630, -0.5663, -0.5537],
        [-1.5396, -1.5400, -1.5390,  ..., -1.5320, -1.5346, -1.5360],
        [-0.6085, -0.6046, -0.6077,  ..., -0.5938, -0.5929, -0.5990],
        ...,
        [ 0.4545,  0.4499,  0.4532,  ...,  0.4803,  0.4554,  0.4573],
        [-1.4114, -1.3635, -1.3909,  ..., -1.4681, -1.3687, -1.3866],
        [-0.4734, -0.4533, -0.4638,  ..., -0.4406, -0.4272, -0.4356]]), TensorCategory(1))


Setting up after_item: Pipeline: ToTensor
Setting up before_batch: Pipeline: 
Setting up after_batch: Pipeline: Normalize

Building one batch
Applying item_tfms to the first sample:
  Pipeline: ToTensor
    starting from
      (TensorTS of size 24x51, TensorCategory(1))
    applying ToTensor gives
      (TensorTS of size 24x51, TensorCategory(1))

Adding the next 3 samples

No before_batch transform to apply

Collating items in a batch

Applying batch_tfms to the batch built
  Pipeline: Normalize
    starting from
      (TensorTS of size 4x24x51, TensorCategory([1, 5, 4, 5]))
    applying Normalize gives
      (TensorTS of size 4x24x51, TensorCategory([1, 5, 4, 5]))

# num_workers=0 is Microsoft Windows
dls2 = tsdb.dataloaders(fnames, num_workers=0, device=default_device())

dls2.show_batch(max_n=9, chs=range(0,12,3))

3rd method : using `DataBlock` and passing `items` object to the `DataBlock.dataloaders()`

getters = [ItemGetter(0), ItemGetter(1)] 
tsdb = DataBlock(blocks=(TSBlock, CategoryBlock),
                   getters=getters,
                   splitter=RandomSplitter(seed=seed)
                   )

dls3 = tsdb.dataloaders(data.get_items(), batch_tfms=batch_tfms, num_workers=0, device=default_device())

dls3.show_batch(max_n=9, chs=range(0,12,3))

4th method : using `TSDataLoaders` class and `TSDataLoaders.from_files()`)

dls4 = TSDataLoaders.from_files(fnames, batch_tfms=batch_tfms, num_workers=0, device=default_device())

dls4.show_batch(max_n=9, chs=range(0,12,3))

Training a Model

# Number of channels (i.e. dimensions in ARFF and TS files jargon)
c_in = get_n_channels(dls2.train) # data.n_channels
# Number of classes
c_out= dls2.c 
c_in,c_out

(24, 6)

Creating a model

model = inception_time(c_in, c_out).to(device=default_device())
model

Sequential(
  (0): SequentialEx(
    (layers): ModuleList(
      (0): InceptionModule(
        (convs): ModuleList(
          (0): Conv1d(24, 32, kernel_size=(39,), stride=(1,), padding=(19,), bias=False)
          (1): Conv1d(24, 32, kernel_size=(19,), stride=(1,), padding=(9,), bias=False)
          (2): Conv1d(24, 32, kernel_size=(9,), stride=(1,), padding=(4,), bias=False)
        )
        (maxpool_bottleneck): Sequential(
          (0): MaxPool1d(kernel_size=3, stride=1, padding=1, dilation=1, ceil_mode=False)
          (1): Conv1d(24, 32, kernel_size=(1,), stride=(1,), bias=False)
        )
        (bn_relu): Sequential(
          (0): BatchNorm1d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
          (1): ReLU()
        )
      )
    )
  )
  (1): SequentialEx(
    (layers): ModuleList(
      (0): InceptionModule(
        (bottleneck): Conv1d(128, 32, kernel_size=(1,), stride=(1,))
        (convs): ModuleList(
          (0): Conv1d(32, 32, kernel_size=(39,), stride=(1,), padding=(19,), bias=False)
          (1): Conv1d(32, 32, kernel_size=(19,), stride=(1,), padding=(9,), bias=False)
          (2): Conv1d(32, 32, kernel_size=(9,), stride=(1,), padding=(4,), bias=False)
        )
        (maxpool_bottleneck): Sequential(
          (0): MaxPool1d(kernel_size=3, stride=1, padding=1, dilation=1, ceil_mode=False)
          (1): Conv1d(128, 32, kernel_size=(1,), stride=(1,), bias=False)
        )
        (bn_relu): Sequential(
          (0): BatchNorm1d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
          (1): ReLU()
        )
      )
    )
  )
  (2): SequentialEx(
    (layers): ModuleList(
      (0): InceptionModule(
        (bottleneck): Conv1d(128, 32, kernel_size=(1,), stride=(1,))
        (convs): ModuleList(
          (0): Conv1d(32, 32, kernel_size=(39,), stride=(1,), padding=(19,), bias=False)
          (1): Conv1d(32, 32, kernel_size=(19,), stride=(1,), padding=(9,), bias=False)
          (2): Conv1d(32, 32, kernel_size=(9,), stride=(1,), padding=(4,), bias=False)
        )
        (maxpool_bottleneck): Sequential(
          (0): MaxPool1d(kernel_size=3, stride=1, padding=1, dilation=1, ceil_mode=False)
          (1): Conv1d(128, 32, kernel_size=(1,), stride=(1,), bias=False)
        )
        (bn_relu): Sequential(
          (0): BatchNorm1d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
          (1): ReLU()
        )
      )
      (1): Shortcut(
        (act_fn): ReLU(inplace=True)
        (conv): Conv1d(128, 128, kernel_size=(1,), stride=(1,), bias=False)
        (bn): BatchNorm1d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
      )
    )
  )
  (3): SequentialEx(
    (layers): ModuleList(
      (0): InceptionModule(
        (bottleneck): Conv1d(128, 32, kernel_size=(1,), stride=(1,))
        (convs): ModuleList(
          (0): Conv1d(32, 32, kernel_size=(39,), stride=(1,), padding=(19,), bias=False)
          (1): Conv1d(32, 32, kernel_size=(19,), stride=(1,), padding=(9,), bias=False)
          (2): Conv1d(32, 32, kernel_size=(9,), stride=(1,), padding=(4,), bias=False)
        )
        (maxpool_bottleneck): Sequential(
          (0): MaxPool1d(kernel_size=3, stride=1, padding=1, dilation=1, ceil_mode=False)
          (1): Conv1d(128, 32, kernel_size=(1,), stride=(1,), bias=False)
        )
        (bn_relu): Sequential(
          (0): BatchNorm1d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
          (1): ReLU()
        )
      )
    )
  )
  (4): SequentialEx(
    (layers): ModuleList(
      (0): InceptionModule(
        (bottleneck): Conv1d(128, 32, kernel_size=(1,), stride=(1,))
        (convs): ModuleList(
          (0): Conv1d(32, 32, kernel_size=(39,), stride=(1,), padding=(19,), bias=False)
          (1): Conv1d(32, 32, kernel_size=(19,), stride=(1,), padding=(9,), bias=False)
          (2): Conv1d(32, 32, kernel_size=(9,), stride=(1,), padding=(4,), bias=False)
        )
        (maxpool_bottleneck): Sequential(
          (0): MaxPool1d(kernel_size=3, stride=1, padding=1, dilation=1, ceil_mode=False)
          (1): Conv1d(128, 32, kernel_size=(1,), stride=(1,), bias=False)
        )
        (bn_relu): Sequential(
          (0): BatchNorm1d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
          (1): ReLU()
        )
      )
    )
  )
  (5): SequentialEx(
    (layers): ModuleList(
      (0): InceptionModule(
        (bottleneck): Conv1d(128, 32, kernel_size=(1,), stride=(1,))
        (convs): ModuleList(
          (0): Conv1d(32, 32, kernel_size=(39,), stride=(1,), padding=(19,), bias=False)
          (1): Conv1d(32, 32, kernel_size=(19,), stride=(1,), padding=(9,), bias=False)
          (2): Conv1d(32, 32, kernel_size=(9,), stride=(1,), padding=(4,), bias=False)
        )
        (maxpool_bottleneck): Sequential(
          (0): MaxPool1d(kernel_size=3, stride=1, padding=1, dilation=1, ceil_mode=False)
          (1): Conv1d(128, 32, kernel_size=(1,), stride=(1,), bias=False)
        )
        (bn_relu): Sequential(
          (0): BatchNorm1d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
          (1): ReLU()
        )
      )
      (1): Shortcut(
        (act_fn): ReLU(inplace=True)
        (conv): Conv1d(128, 128, kernel_size=(1,), stride=(1,), bias=False)
        (bn): BatchNorm1d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
      )
    )
  )
  (6): AdaptiveConcatPool1d(
    (ap): AdaptiveAvgPool1d(output_size=1)
    (mp): AdaptiveMaxPool1d(output_size=1)
  )
  (7): Flatten(full=False)
  (8): Linear(in_features=256, out_features=6, bias=True)
)

Creating a Learner object

# opt_func = partial(Adam, lr=3e-3, wd=0.01)
#Or use Ranger
def opt_func(p, lr=slice(3e-3)): return Lookahead(RAdam(p, lr=lr, mom=0.95, wd=0.01))

#Learner    
loss_func = LabelSmoothingCrossEntropy() 
learn = Learner(dls2, model, opt_func=opt_func, loss_func=loss_func, metrics=accuracy)

print(learn.summary())

Sequential (Input shape: ['64 x 24 x 51'])
================================================================
Layer (type)         Output Shape         Param #    Trainable 
================================================================
Conv1d               64 x 32 x 51         29,952     True      
________________________________________________________________
Conv1d               64 x 32 x 51         14,592     True      
________________________________________________________________
Conv1d               64 x 32 x 51         6,912      True      
________________________________________________________________
MaxPool1d            64 x 24 x 51         0          False     
________________________________________________________________
Conv1d               64 x 32 x 51         768        True      
________________________________________________________________
BatchNorm1d          64 x 128 x 51        256        True      
________________________________________________________________
ReLU                 64 x 128 x 51        0          False     
________________________________________________________________
Conv1d               64 x 32 x 51         4,128      True      
________________________________________________________________
Conv1d               64 x 32 x 51         39,936     True      
________________________________________________________________
Conv1d               64 x 32 x 51         19,456     True      
________________________________________________________________
Conv1d               64 x 32 x 51         9,216      True      
________________________________________________________________
MaxPool1d            64 x 128 x 51        0          False     
________________________________________________________________
Conv1d               64 x 32 x 51         4,096      True      
________________________________________________________________
BatchNorm1d          64 x 128 x 51        256        True      
________________________________________________________________
ReLU                 64 x 128 x 51        0          False     
________________________________________________________________
Conv1d               64 x 32 x 51         4,128      True      
________________________________________________________________
Conv1d               64 x 32 x 51         39,936     True      
________________________________________________________________
Conv1d               64 x 32 x 51         19,456     True      
________________________________________________________________
Conv1d               64 x 32 x 51         9,216      True      
________________________________________________________________
MaxPool1d            64 x 128 x 51        0          False     
________________________________________________________________
Conv1d               64 x 32 x 51         4,096      True      
________________________________________________________________
BatchNorm1d          64 x 128 x 51        256        True      
________________________________________________________________
ReLU                 64 x 128 x 51        0          False     
________________________________________________________________
ReLU                 64 x 128 x 51        0          False     
________________________________________________________________
Conv1d               64 x 128 x 51        16,384     True      
________________________________________________________________
BatchNorm1d          64 x 128 x 51        256        True      
________________________________________________________________
Conv1d               64 x 32 x 51         4,128      True      
________________________________________________________________
Conv1d               64 x 32 x 51         39,936     True      
________________________________________________________________
Conv1d               64 x 32 x 51         19,456     True      
________________________________________________________________
Conv1d               64 x 32 x 51         9,216      True      
________________________________________________________________
MaxPool1d            64 x 128 x 51        0          False     
________________________________________________________________
Conv1d               64 x 32 x 51         4,096      True      
________________________________________________________________
BatchNorm1d          64 x 128 x 51        256        True      
________________________________________________________________
ReLU                 64 x 128 x 51        0          False     
________________________________________________________________
Conv1d               64 x 32 x 51         4,128      True      
________________________________________________________________
Conv1d               64 x 32 x 51         39,936     True      
________________________________________________________________
Conv1d               64 x 32 x 51         19,456     True      
________________________________________________________________
Conv1d               64 x 32 x 51         9,216      True      
________________________________________________________________
MaxPool1d            64 x 128 x 51        0          False     
________________________________________________________________
Conv1d               64 x 32 x 51         4,096      True      
________________________________________________________________
BatchNorm1d          64 x 128 x 51        256        True      
________________________________________________________________
ReLU                 64 x 128 x 51        0          False     
________________________________________________________________
Conv1d               64 x 32 x 51         4,128      True      
________________________________________________________________
Conv1d               64 x 32 x 51         39,936     True      
________________________________________________________________
Conv1d               64 x 32 x 51         19,456     True      
________________________________________________________________
Conv1d               64 x 32 x 51         9,216      True      
________________________________________________________________
MaxPool1d            64 x 128 x 51        0          False     
________________________________________________________________
Conv1d               64 x 32 x 51         4,096      True      
________________________________________________________________
BatchNorm1d          64 x 128 x 51        256        True      
________________________________________________________________
ReLU                 64 x 128 x 51        0          False     
________________________________________________________________
ReLU                 64 x 128 x 51        0          False     
________________________________________________________________
Conv1d               64 x 128 x 51        16,384     True      
________________________________________________________________
BatchNorm1d          64 x 128 x 51        256        True      
________________________________________________________________
AdaptiveAvgPool1d    64 x 128 x 1         0          False     
________________________________________________________________
AdaptiveMaxPool1d    64 x 128 x 1         0          False     
________________________________________________________________
Flatten              64 x 256             0          False     
________________________________________________________________
Linear               64 x 6               1,542      True      
________________________________________________________________

Total params: 472,742
Total trainable params: 472,742
Total non-trainable params: 0

Optimizer used: <function opt_func at 0x7ff7286aa598>
Loss function: LabelSmoothingCrossEntropy()

Callbacks:
  - TrainEvalCallback
  - Recorder
  - ProgressCallback

LR find

lr_min, lr_steep = learn.lr_find()
lr_min, lr_steep

(0.03630780577659607, 0.0003981071640737355)

Train

#lr_max=1e-3
epochs=30; lr_max=lr_steep;  pct_start=.7; moms=(0.95,0.85,0.95); wd=1e-2
learn.fit_one_cycle(epochs, lr_max=lr_max, pct_start=pct_start,  moms=moms, wd=wd)
# learn.fit_one_cycle(epochs=20, lr_max=lr_steep)

Ploting the loss function

learn.recorder.plot_loss()

Showing the results

learn.show_results(max_n=9, chs=range(0,12,3))

Showing the confusion matrix

interp = ClassificationInterpretation.from_learner(learn)
interp.plot_confusion_matrix()

Credit

timeseries for fastai2 was inspired by Ignacio's Oguiza timeseriesAI (https://github.com/timeseriesAI/timeseriesAI.git).> Inception Time model definition is a modified version of [Ignacio Oguiza] (https://github.com/timeseriesAI/timeseriesAI/blob/master/torchtimeseries/models/InceptionTime.py) and [Thomas Capelle] (https://github.com/tcapelle/TimeSeries_fastai/blob/master/inception.py) implementaions

epoch	train_loss	valid_loss	accuracy	time
0	2.834904	1.795923	0.152778	00:02
1	2.842472	1.798778	0.152778	00:01
2	2.811872	1.802382	0.152778	00:02
3	2.776238	1.806626	0.152778	00:02
4	2.728971	1.811036	0.152778	00:01
5	2.668968	1.815441	0.194444	00:02
6	2.605878	1.815416	0.222222	00:02
7	2.509938	1.808677	0.236111	00:02
8	2.395904	1.782158	0.250000	00:02
9	2.286265	1.583869	0.361111	00:02
10	2.162855	1.421896	0.458333	00:02
11	2.033385	1.281669	0.486111	00:02
12	1.913663	0.952594	0.777778	00:02
13	1.793140	0.873441	0.791667	00:02
14	1.680594	0.827057	0.819444	00:02
15	1.580222	0.728311	0.833333	00:02
16	1.486642	0.712666	0.847222	00:02
17	1.400012	0.711462	0.833333	00:02
18	1.324036	0.714839	0.819444	00:01
19	1.254413	0.697279	0.847222	00:01
20	1.189490	0.691324	0.861111	00:02
21	1.130941	0.692367	0.847222	00:02
22	1.077336	0.691770	0.847222	00:02
23	1.027858	0.683175	0.875000	00:02
24	0.982550	0.675254	0.875000	00:01
25	0.940221	0.667658	0.888889	00:02
26	0.902526	0.663029	0.875000	00:02
27	0.867685	0.666622	0.861111	00:02
28	0.836503	0.660849	0.861111	00:01
29	0.808390	0.658917	0.861111	00:02