Notes on fastai Book Ch. 14

ai
fastai
notes
pytorch
Chapter 14 covers building a ResNet from scratch.
Author

Christian Mills

Published

March 29, 2022

This post is part of the following series: 
#hide
# !pip install -Uqq fastbook
import fastbook
fastbook.setup_book()
#hide
from fastbook import *
import inspect
def print_source(obj):
    for line in inspect.getsource(obj).split("\n"):
        print(line)

ResNets

Going Back to Imagenette

def get_data(url, presize, resize):
    path = untar_data(url)
    print(path)
    return DataBlock(
        blocks=(ImageBlock, CategoryBlock), get_items=get_image_files, 
        splitter=GrandparentSplitter(valid_name='val'),
        get_y=parent_label, item_tfms=Resize(presize),
        batch_tfms=[*aug_transforms(min_scale=0.5, size=resize),
                    Normalize.from_stats(*imagenet_stats)],
    ).dataloaders(path, bs=128)
URLs.IMAGENETTE_160
'https://s3.amazonaws.com/fast-ai-imageclas/imagenette2-160.tgz'
dls = get_data(URLs.IMAGENETTE_160, 160, 128)
dls.show_batch(max_n=4)

Average Pooling

  • take the average of activations across a convolutional grid
  • an alternative to the approach of using stride-2 layers to downscale input dimensions to the a single output vector
  • used in fully convolutional networks to allow the model to be used on image sizes other than what the model was trained on

Note: A fully convolutional network is a good choice when the objects you want to classify don’t have a single correct orientation or size (e.g. most natural photos) * It would not be a good choice for applications like MNIST where their is a fixed correct orientation for each character

# Take the mean over the x and y axes
# Will always convert a grid of activations into a single activation per image
def avg_pool(x): return x.mean((2,3))
def block(ni, nf): return ConvLayer(ni, nf, stride=2)
def get_model():
    return nn.Sequential(
        block(3, 16),
        block(16, 32),
        block(32, 64),
        block(64, 128),
        block(128, 256),
        nn.AdaptiveAvgPool2d(1),
        Flatten(),
        nn.Linear(256, dls.c))
ConvLayer
fastai.layers.ConvLayer
print_source(ConvLayer)
class ConvLayer(nn.Sequential):
    "Create a sequence of convolutional (`ni` to `nf`), ReLU (if `use_activ`) and `norm_type` layers."
    @delegates(nn.Conv2d)
    def __init__(self, ni, nf, ks=3, stride=1, padding=None, bias=None, ndim=2, norm_type=NormType.Batch, bn_1st=True,
                 act_cls=defaults.activation, transpose=False, init='auto', xtra=None, bias_std=0.01, **kwargs):
        if padding is None: padding = ((ks-1)//2 if not transpose else 0)
        bn = norm_type in (NormType.Batch, NormType.BatchZero)
        inn = norm_type in (NormType.Instance, NormType.InstanceZero)
        if bias is None: bias = not (bn or inn)
        conv_func = _conv_func(ndim, transpose=transpose)
        conv = conv_func(ni, nf, kernel_size=ks, bias=bias, stride=stride, padding=padding, **kwargs)
        act = None if act_cls is None else act_cls()
        init_linear(conv, act, init=init, bias_std=bias_std)
        if   norm_type==NormType.Weight:   conv = weight_norm(conv)
        elif norm_type==NormType.Spectral: conv = spectral_norm(conv)
        layers = [conv]
        act_bn = []
        if act is not None: act_bn.append(act)
        if bn: act_bn.append(BatchNorm(nf, norm_type=norm_type, ndim=ndim))
        if inn: act_bn.append(InstanceNorm(nf, norm_type=norm_type, ndim=ndim))
        if bn_1st: act_bn.reverse()
        layers += act_bn
        if xtra: layers.append(xtra)
        super().__init__(*layers)

Adaptive Average Pooling

  • averages a grid of activations into whatever sized destination you require
nn.AdaptiveAvgPool2d
torch.nn.modules.pooling.AdaptiveAvgPool2d
  • input: \((N, C, H_{in}, W_{in})\) or \((C, H_{in}, W_{in})\)
  • output: \((N, C, S_{0}, S_{1})\) or \((C, S_{0}, S_{1})\), where \(S=output_size\)
print_source(nn.AdaptiveAvgPool2d)
class AdaptiveAvgPool2d(_AdaptiveAvgPoolNd):
    r"""Applies a 2D adaptive average pooling over an input signal composed of several input planes.

    The output is of size H x W, for any input size.
    The number of output features is equal to the number of input planes.

    Args:
        output_size: the target output size of the image of the form H x W.
                     Can be a tuple (H, W) or a single H for a square image H x H.
                     H and W can be either a ``int``, or ``None`` which means the size will
                     be the same as that of the input.

    Shape:
        - Input: :math:`(N, C, H_{in}, W_{in})` or :math:`(C, H_{in}, W_{in})`.
        - Output: :math:`(N, C, S_{0}, S_{1})` or :math:`(C, S_{0}, S_{1})`, where
          :math:`S=\text{output\_size}`.

    Examples:
        >>> # target output size of 5x7
        >>> m = nn.AdaptiveAvgPool2d((5,7))
        >>> input = torch.randn(1, 64, 8, 9)
        >>> output = m(input)
        >>> # target output size of 7x7 (square)
        >>> m = nn.AdaptiveAvgPool2d(7)
        >>> input = torch.randn(1, 64, 10, 9)
        >>> output = m(input)
        >>> # target output size of 10x7
        >>> m = nn.AdaptiveAvgPool2d((None, 7))
        >>> input = torch.randn(1, 64, 10, 9)
        >>> output = m(input)

    """

    output_size: _size_2_opt_t

    def forward(self, input: Tensor) -> Tensor:
        return F.adaptive_avg_pool2d(input, self.output_size)
def get_learner(m):
    return Learner(dls, m, loss_func=nn.CrossEntropyLoss(), metrics=accuracy
                  ).to_fp16()

learn = get_learner(get_model())
learn.model
Sequential(
  (0): ConvLayer(
    (0): Conv2d(3, 16, kernel_size=(3, 3), stride=(2, 2), padding=(1, 1), bias=False)
    (1): BatchNorm2d(16, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
    (2): ReLU()
  )
  (1): ConvLayer(
    (0): Conv2d(16, 32, kernel_size=(3, 3), stride=(2, 2), padding=(1, 1), bias=False)
    (1): BatchNorm2d(32, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
    (2): ReLU()
  )
  (2): ConvLayer(
    (0): Conv2d(32, 64, kernel_size=(3, 3), stride=(2, 2), padding=(1, 1), bias=False)
    (1): BatchNorm2d(64, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
    (2): ReLU()
  )
  (3): ConvLayer(
    (0): Conv2d(64, 128, kernel_size=(3, 3), stride=(2, 2), padding=(1, 1), bias=False)
    (1): BatchNorm2d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
    (2): ReLU()
  )
  (4): ConvLayer(
    (0): Conv2d(128, 256, kernel_size=(3, 3), stride=(2, 2), padding=(1, 1), bias=False)
    (1): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
    (2): ReLU()
  )
  (5): AdaptiveAvgPool2d(output_size=1)
  (6): Flatten(full=False)
  (7): Linear(in_features=256, out_features=10, bias=True)
)
learn.lr_find()
SuggestedLRs(valley=0.0008317637839354575)

learn.fit_one_cycle(5, 3e-3)
epoch train_loss valid_loss accuracy time
0 1.885349 2.287517 0.341401 00:03
1 1.525377 2.245459 0.395159 00:03
2 1.290083 1.217583 0.609172 00:03
3 1.145256 1.164249 0.631338 00:03
4 1.045142 1.064749 0.668025 00:03

Note: We won’t necessarily get better results simply by adding more layers.

learn = get_learner(
    nn.Sequential(
        block(3, 16),
        block(16, 32),
        block(32, 64),
        block(64, 128),
        block(128, 256),
        block(256, 512),
        block(512, 1024),
        nn.AdaptiveAvgPool2d(1),
        Flatten(),
        nn.Linear(1024, dls.c)))
learn.lr_find()
SuggestedLRs(valley=0.0002754228771664202)

learn.fit_one_cycle(10, 0.03)
epoch train_loss valid_loss accuracy time
0 1.826138 3.406225 0.314395 00:03
1 1.752539 3.521486 0.296051 00:03
2 1.531295 2.125122 0.382420 00:03
3 1.322462 1.528130 0.530955 00:04
4 1.180348 1.409803 0.559236 00:03
5 1.112325 1.155497 0.638217 00:03
6 0.977593 0.918580 0.706242 00:03
7 0.870830 1.019607 0.680000 00:03
8 0.780924 0.779768 0.750573 00:03
9 0.706074 0.767961 0.759490 00:03

Note: Needed to train for more epochs to achieve the same accuracy.

Building a Modern CNN: ResNet

Skip Connections

  • skip connections make the network easier to train with SGD

    • x + conv2(conv1(x))

  • Identity Mapping: returning the input without changing it at all

  • residual: prediction minus target

  • The authors of the ResNet paper noticed that a network with more layers performed worse than a network with fewer layers, all other factors being equal

    • this was true on both the training and validation sets

  • Key Insight:

    • start with a model with fewer layers that is trained well, and add more layers to it that do nothing at all the result should be a larger network that does exactly the same thing as the smaller network, proving there are always deep networks that should be at least as good as a more shallow network
    • however, SGD was not finding these

  • Using skip connections also helps smooth the loss function, which makes training easier

Note: Use zero for the initial value of gamma in batch normalization * allows training at higher learning rates * recall: \(y*gamma + beta\)

class ResBlock(Module):
    def __init__(self, ni, nf):
        self.convs = nn.Sequential(
            ConvLayer(ni,nf),
            ConvLayer(nf,nf, norm_type=NormType.BatchZero))
        
    def forward(self, x): return x + self.convs(x)

Note: The above implementation requires the stride to be 1 and ni==nf in order for x + self.convs(x) to work. * Need to change the shape of x to match the result of self.convs(x) * Can use an average pooling layer with a stride of 2 to change the shape * Can use a 1x1 convolution to change the number of channels

def _conv_block(ni,nf,stride):
    return nn.Sequential(
        ConvLayer(ni, nf, stride=stride),
        ConvLayer(nf, nf, act_cls=None, norm_type=NormType.BatchZero))
class ResBlock(Module):
    def __init__(self, ni, nf, stride=1):
        self.convs = _conv_block(ni,nf,stride)
        self.idconv = noop if ni==nf else ConvLayer(ni, nf, 1, act_cls=None)
        self.pool = noop if stride==1 else nn.AvgPool2d(2, ceil_mode=True)

    def forward(self, x):
        return F.relu(self.convs(x) + self.idconv(self.pool(x)))
noop
<function fastai.imports.noop(x=None, *args, **kwargs)>
print_source(noop)
def noop (x=None, *args, **kwargs):
    "Do nothing"
    return x
def block(ni,nf): return ResBlock(ni, nf, stride=2)
learn = get_learner(get_model())
learn.model
Sequential(
  (0): ResBlock(
    (convs): Sequential(
      (0): ConvLayer(
        (0): Conv2d(3, 16, kernel_size=(3, 3), stride=(2, 2), padding=(1, 1), bias=False)
        (1): BatchNorm2d(16, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
        (2): ReLU()
      )
      (1): ConvLayer(
        (0): Conv2d(16, 16, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)
        (1): BatchNorm2d(16, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
      )
    )
    (idconv): ConvLayer(
      (0): Conv2d(3, 16, kernel_size=(1, 1), stride=(1, 1), bias=False)
      (1): BatchNorm2d(16, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
    )
    (pool): AvgPool2d(kernel_size=2, stride=2, padding=0)
  )
  (1): ResBlock(
    (convs): Sequential(
      (0): ConvLayer(
        (0): Conv2d(16, 32, kernel_size=(3, 3), stride=(2, 2), padding=(1, 1), bias=False)
        (1): BatchNorm2d(32, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
        (2): ReLU()
      )
      (1): ConvLayer(
        (0): Conv2d(32, 32, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)
        (1): BatchNorm2d(32, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
      )
    )
    (idconv): ConvLayer(
      (0): Conv2d(16, 32, kernel_size=(1, 1), stride=(1, 1), bias=False)
      (1): BatchNorm2d(32, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
    )
    (pool): AvgPool2d(kernel_size=2, stride=2, padding=0)
  )
  (2): ResBlock(
    (convs): Sequential(
      (0): ConvLayer(
        (0): Conv2d(32, 64, kernel_size=(3, 3), stride=(2, 2), padding=(1, 1), bias=False)
        (1): BatchNorm2d(64, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
        (2): ReLU()
      )
      (1): ConvLayer(
        (0): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)
        (1): BatchNorm2d(64, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
      )
    )
    (idconv): ConvLayer(
      (0): Conv2d(32, 64, kernel_size=(1, 1), stride=(1, 1), bias=False)
      (1): BatchNorm2d(64, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
    )
    (pool): AvgPool2d(kernel_size=2, stride=2, padding=0)
  )
  (3): ResBlock(
    (convs): Sequential(
      (0): ConvLayer(
        (0): Conv2d(64, 128, kernel_size=(3, 3), stride=(2, 2), padding=(1, 1), bias=False)
        (1): BatchNorm2d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
        (2): ReLU()
      )
      (1): ConvLayer(
        (0): Conv2d(128, 128, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)
        (1): BatchNorm2d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
      )
    )
    (idconv): ConvLayer(
      (0): Conv2d(64, 128, kernel_size=(1, 1), stride=(1, 1), bias=False)
      (1): BatchNorm2d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
    )
    (pool): AvgPool2d(kernel_size=2, stride=2, padding=0)
  )
  (4): ResBlock(
    (convs): Sequential(
      (0): ConvLayer(
        (0): Conv2d(128, 256, kernel_size=(3, 3), stride=(2, 2), padding=(1, 1), bias=False)
        (1): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
        (2): ReLU()
      )
      (1): ConvLayer(
        (0): Conv2d(256, 256, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)
        (1): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
      )
    )
    (idconv): ConvLayer(
      (0): Conv2d(128, 256, kernel_size=(1, 1), stride=(1, 1), bias=False)
      (1): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
    )
    (pool): AvgPool2d(kernel_size=2, stride=2, padding=0)
  )
  (5): AdaptiveAvgPool2d(output_size=1)
  (6): Flatten(full=False)
  (7): Linear(in_features=256, out_features=10, bias=True)
)
learn.fit_one_cycle(5, 3e-3)
epoch train_loss valid_loss accuracy time
0 1.975520 1.854834 0.346242 00:04
1 1.658158 1.478215 0.517197 00:04
2 1.377669 1.307936 0.585478 00:04
3 1.162053 1.106804 0.642548 00:04
4 1.027879 1.009977 0.674140 00:04 
# Try training with a model that is twice as deep
def block(ni, nf):
    return nn.Sequential(ResBlock(ni, nf, stride=2), ResBlock(nf, nf))
learn = get_learner(get_model())
learn.fit_one_cycle(5, 3e-3)
epoch train_loss valid_loss accuracy time
0 1.940119 1.815366 0.372484 00:05
1 1.602748 1.461486 0.526879 00:05
2 1.296337 1.346131 0.571210 00:05
3 1.052998 0.996216 0.678471 00:05
4 0.926301 0.901209 0.713121 00:05

A State-of-the-Art ResNet

Top-5 Accuracy

  • a metric testing how often the label we want is in the top-5 predictions of our model
  • used in ImageNet competition because many of the images contained multiple objects, or objects that could be easily confused or were mislabeled

Stem

  • the first few layers of a CNN
  • the stem has a different structure than the main body of the CNN
  • the vast majority of computation in a deep convolutional network occurs in the early layers
    • we should keep the early layers as fast and simple as possible
  • the vast majority of parameters are in the last layers
  • a ResNet block takes more computation than a plain convolutional block
def _resnet_stem(*sizes):
    return [
        ConvLayer(sizes[i], sizes[i+1], 3, stride = 2 if i==0 else 1)
            for i in range(len(sizes)-1)
    ] + [nn.MaxPool2d(kernel_size=3, stride=2, padding=1)]
_resnet_stem(3,32,32,64)
[ConvLayer(
   (0): Conv2d(3, 32, kernel_size=(3, 3), stride=(2, 2), padding=(1, 1), bias=False)
   (1): BatchNorm2d(32, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
   (2): ReLU()
 ),
 ConvLayer(
   (0): Conv2d(32, 32, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)
   (1): BatchNorm2d(32, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
   (2): ReLU()
 ),
 ConvLayer(
   (0): Conv2d(32, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)
   (1): BatchNorm2d(64, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)
   (2): ReLU()
 ),
 MaxPool2d(kernel_size=3, stride=2, padding=1, dilation=1, ceil_mode=False)]
class ResNet(nn.Sequential):
    def __init__(self, n_out, layers, expansion=1):
        stem = _resnet_stem(3,32,32,64)
        self.block_szs = [64, 64, 128, 256, 512]
        for i in range(1,5): self.block_szs[i] *= expansion
        blocks = [self._make_layer(*o) for o in enumerate(layers)]
        super().__init__(*stem, *blocks,
                         nn.AdaptiveAvgPool2d(1), Flatten(),
                         nn.Linear(self.block_szs[-1], n_out))
    
    def _make_layer(self, idx, n_layers):
        stride = 1 if idx==0 else 2
        ch_in,ch_out = self.block_szs[idx:idx+2]
        return nn.Sequential(*[
            ResBlock(ch_in if i==0 else ch_out, ch_out, stride if i==0 else 1)
            for i in range(n_layers)
        ])
rn = ResNet(dls.c, [2,2,2,2])
learn = get_learner(rn)
learn.fit_one_cycle(5, 3e-3)
epoch train_loss valid_loss accuracy time
0 1.676334 3.144195 0.332229 00:05
1 1.330461 1.301046 0.601274 00:05
2 1.081648 1.654932 0.530701 00:05
3 0.883710 0.889572 0.725096 00:06
4 0.752461 0.770025 0.751592 00:05

Note: The optimized stem kept training time just as fast as before despite the model having more channels.

Bottleneck Layers

  • instead of stacking two convolutions with a kernel size of 3, bottleneck layers use three convolutions
    • two \(1x1\) (at the beginning and the end) and one \(3x3\)
  • \(1x1\) convolutions are much faster so the block executes faster than the earlier type of ResNet block above
    • allows us to use more convolutional filters
def _conv_block(ni,nf,stride):
    return nn.Sequential(
        ConvLayer(ni, nf//4, 1),
        ConvLayer(nf//4, nf//4, stride=stride), 
        ConvLayer(nf//4, nf, 1, act_cls=None, norm_type=NormType.BatchZero))
# Use bigger images
dls = get_data(URLs.IMAGENETTE_320, presize=320, resize=224)
/home/innom-dt/.fastai/data/imagenette2-320
rn = ResNet(dls.c, [3,4,6,3], 4)

Note: Deeper networks like this take more epochs to show improvements in accuracy.

learn = get_learner(rn)
learn.lr_find()
SuggestedLRs(valley=2.2908675418875646e-06)

learn.fit_one_cycle(20, 3e-3)
epoch train_loss valid_loss accuracy time
0 1.631725 1.667390 0.491720 00:26
1 1.396282 1.772770 0.492739 00:26
2 1.244810 1.644604 0.520764 00:26
3 1.147434 2.000461 0.433121 00:26
4 1.061841 1.668560 0.537580 00:26
5 0.971388 1.221623 0.634395 00:26
6 0.875570 1.315725 0.606369 00:26
7 0.773697 1.347997 0.625987 00:26
8 0.693710 1.044750 0.662166 00:26
9 0.642479 0.847296 0.715669 00:26
10 0.597677 0.815032 0.728662 00:26
11 0.554460 1.310289 0.632357 00:26
12 0.504132 0.645502 0.797707 00:26
13 0.444430 0.553372 0.839490 00:26
14 0.404554 0.524731 0.840510 00:26
15 0.363680 0.430417 0.869299 00:26
16 0.326445 0.468357 0.858854 00:26
17 0.291472 0.398314 0.882038 00:26
18 0.273819 0.441020 0.865987 00:26
19 0.266643 0.429735 0.868280 00:26 
# Try training for much longer with MixUp
rn = ResNet(dls.c, [3,4,6,3], 4)
learn = Learner(dls, rn, loss_func=CrossEntropyLossFlat(), metrics=accuracy, cbs=MixUp).to_fp16()
learn.cbs
(#5) [TrainEvalCallback,Recorder,ProgressCallback,MixUp,MixedPrecision]
learn.lr_find()
SuggestedLRs(valley=0.002511886414140463)

learn.fit_one_cycle(100, 1e-3)
epoch train_loss valid_loss accuracy time
0 2.357731 2.383324 0.130191 00:27
1 2.336724 2.336634 0.139108 00:27
2 2.307106 2.287395 0.160764 00:26
3 2.270103 2.233956 0.206369 00:27
4 2.230594 2.175580 0.248408 00:27
5 2.186367 2.114939 0.285605 00:26
6 2.138676 2.052963 0.314904 00:26
7 2.093770 1.997618 0.340892 00:26
8 2.050327 1.941644 0.362038 00:26
9 2.008452 1.897457 0.381146 00:26
10 1.976088 1.857476 0.393376 00:26
11 1.942721 1.811248 0.414013 00:26
12 1.913029 1.795007 0.415796 00:26
13 1.887761 1.753944 0.427771 00:26
14 1.867352 1.726478 0.446369 00:26
15 1.850482 1.703274 0.458089 00:26
16 1.820035 1.656702 0.478471 00:26
17 1.804909 1.627078 0.489172 00:26
18 1.777827 1.597916 0.509045 00:26
19 1.754695 1.580777 0.500637 00:26
20 1.730523 1.532980 0.521274 00:26
21 1.719565 1.506606 0.532229 00:26
22 1.699022 1.465760 0.549045 00:26
23 1.671000 1.451764 0.551083 00:26
24 1.642783 1.409297 0.568408 00:26
25 1.624837 1.379675 0.586752 00:26
26 1.601221 1.365560 0.586752 00:26
27 1.586046 1.327966 0.597452 00:26
28 1.569099 1.349460 0.584713 00:26
29 1.547596 1.318505 0.599236 00:27
30 1.545876 1.287586 0.611465 00:26
31 1.516503 1.269668 0.616815 00:26
32 1.510151 1.259776 0.620892 00:26
33 1.499429 1.274317 0.611720 00:26
34 1.492611 1.246700 0.622675 00:26
35 1.470544 1.241083 0.624204 00:27
36 1.453925 1.201963 0.639236 00:27
37 1.450406 1.166396 0.649172 00:27
38 1.444372 1.220421 0.629045 00:26
39 1.447028 1.173165 0.648153 00:26
40 1.425553 1.183527 0.636433 00:26
41 1.415466 1.161390 0.647643 00:26
42 1.405419 1.155593 0.648662 00:26
43 1.411261 1.179044 0.636688 00:26
44 1.404317 1.118105 0.665733 00:26
45 1.392309 1.119027 0.663949 00:26
46 1.382899 1.081154 0.674395 00:26
47 1.374947 1.107488 0.661911 00:26
48 1.364989 1.132930 0.655287 00:26
49 1.371344 1.078784 0.674904 00:27
50 1.365992 1.086367 0.673885 00:26
51 1.355748 1.102273 0.663185 00:26
52 1.346135 1.069236 0.672357 00:26
53 1.342680 1.059305 0.681019 00:26
54 1.342354 1.056270 0.683057 00:26
55 1.348057 1.054993 0.680000 00:26
56 1.327710 1.040115 0.682293 00:26
57 1.331265 1.082385 0.669299 00:26
58 1.328200 1.027992 0.686879 00:26
59 1.328389 1.039981 0.681529 00:26
60 1.319880 1.033769 0.682293 00:27
61 1.323757 1.039335 0.681783 00:27
62 1.308027 1.014351 0.690191 00:27
63 1.317649 1.047797 0.677197 00:27
64 1.291757 1.013592 0.690955 00:27
65 1.303231 1.045248 0.680255 00:26
66 1.296039 1.027358 0.684331 00:26
67 1.298419 1.015950 0.692994 00:27
68 1.295830 1.029434 0.684841 00:26
69 1.301385 1.021460 0.687898 00:26
70 1.297332 1.003877 0.695032 00:26
71 1.304215 1.015531 0.689936 00:26
72 1.301384 0.997708 0.696051 00:26
73 1.299483 0.999720 0.696561 00:26
74 1.279976 0.983441 0.702420 00:26
75 1.283374 0.998377 0.694522 00:26
76 1.297397 0.997266 0.693248 00:26
77 1.292927 0.989717 0.697580 00:27

References

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