Walking through
In this tutorial, we will see practical examples of using unsupervised machine learning methods to automate pattern discovery and get chemical insight from data generated by nonadiabatic molecular dynamics (NAMD) simulations. The NAMD data obtained within the surface hopping approximation is composed of an ensemble of trajectories that can be viewed as multivariate time series objects, where each point in time corresponds to a molecular geometry with its associated quantum properties. Thus, owing to the high dimensionality of the NAMD data, it can be cumbersome to identify the key internal coordinates of the molecule driving the excited-state dynamics by “manual” inspection of the data. This is the scenario where unsupervised learning comes to the rescue. The main idea is to use algorithms designed to find natural grouping structures within the data - clustering analysis - or find a compact data representation - dimension reduction - based on a given similarity measure between data instances.
To automate the unsupervised learning analysis in the context of nonadiabatic dynamics, we have developed a Python package called ULaMDyn, which provides a complete pipeline for analyzing NAMD trajectories data generated by the Newton-X program. This pipeline starts with collecting data from the Newton-X outputs, going through molecular representations, dimension reduction, and clustering analysis. Although ULaMDyn provides a friendly-user command-line interface to perform the whole data analysis in a single shot, in this tutorial, we will unfold the pipeline step-by-step to get a better understanding and more flexibility in the data analysis process.
Installation of required packages
Instruction: If you are running this notebook in Google colab, please restart the execution environment after the packages’ installation given by the bash commands below. This is necessary to avoid error when instantiating the classes of ulamdyn.
[1]:
%%bash
git clone https://gitlab.com/maxjr82/ulamdyn.git
Cloning into 'ulamdyn'...
[2]:
%%bash
cd ulamdyn
pip install ./
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[3]:
%%bash
pip install py3Dmol
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The NAMD dataset: fulvene
The fulvene is used in this tutorial as an example of photoactive molecule that undergoes structural transformation in a nonadiabatic dynamics simulations starting from the first excited-state. To generate the fulvene dataset, the Newton-X program was used to propagate 200 surface hopping trajectories up to 60 fs with a time step of 0.1 fs. The CAS(6,6)/6-31G* method was used to compute the quantum chemical properties for the two electronic states (S\(_0\) and S\(_1\)). For the sake of time and simplicity, only a fraction of the total number of trajectories (50 trajectories) was selected for the tutorial. The full dataset is available to download at https://doi.org/10.6084/m9.figshare.14446998.v1.
[4]:
%%bash
wget https://github.com/maxjr82/smlqc_ulamdyn/raw/main/nx_trajs_fulv.tgz
tar -zxvf nx_trajs_fulv.tgz
rm -rf nx_trajs_fulv.tgz
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5100K .......... .......... .......... .......... .......... 9% 70.5M 1s
5150K .......... .......... .......... .......... .......... 9% 56.8M 1s
5200K .......... .......... .......... .......... .......... 9% 58.9M 1s
5250K .......... .......... .......... .......... .......... 9% 57.2M 1s
5300K .......... .......... .......... .......... .......... 9% 49.2M 1s
5350K .......... .......... .......... .......... .......... 9% 56.3M 1s
5400K .......... .......... .......... .......... .......... 9% 63.3M 1s
5450K .......... .......... .......... .......... .......... 9% 115M 1s
5500K .......... .......... .......... .......... .......... 10% 182M 1s
5550K .......... .......... .......... .......... .......... 10% 217M 1s
5600K .......... .......... .......... .......... .......... 10% 248M 1s
5650K .......... .......... .......... .......... .......... 10% 62.2M 1s
5700K .......... .......... .......... .......... .......... 10% 45.5M 1s
5750K .......... .......... .......... .......... .......... 10% 54.4M 1s
5800K .......... .......... .......... .......... .......... 10% 53.1M 1s
5850K .......... .......... .......... .......... .......... 10% 46.9M 1s
5900K .......... .......... .......... .......... .......... 10% 54.3M 1s
5950K .......... .......... .......... .......... .......... 10% 47.7M 1s
6000K .......... .......... .......... .......... .......... 10% 49.1M 1s
6050K .......... .......... .......... .......... .......... 10% 164M 1s
6100K .......... .......... .......... .......... .......... 11% 162M 1s
6150K .......... .......... .......... .......... .......... 11% 185M 1s
6200K .......... .......... .......... .......... .......... 11% 211M 1s
6250K .......... .......... .......... .......... .......... 11% 247M 1s
6300K .......... .......... .......... .......... .......... 11% 71.9M 1s
6350K .......... .......... .......... .......... .......... 11% 66.2M 1s
6400K .......... .......... .......... .......... .......... 11% 53.3M 1s
6450K .......... .......... .......... .......... .......... 11% 58.8M 1s
6500K .......... .......... .......... .......... .......... 11% 49.9M 1s
6550K .......... .......... .......... .......... .......... 11% 56.1M 1s
6600K .......... .......... .......... .......... .......... 11% 48.2M 1s
6650K .......... .......... .......... .......... .......... 12% 44.6M 1s
6700K .......... .......... .......... .......... .......... 12% 43.4M 1s
6750K .......... .......... .......... .......... .......... 12% 46.1M 1s
6800K .......... .......... .......... .......... .......... 12% 178M 1s
6850K .......... .......... .......... .......... .......... 12% 234M 1s
6900K .......... .......... .......... .......... .......... 12% 255M 1s
6950K .......... .......... .......... .......... .......... 12% 197M 1s
7000K .......... .......... .......... .......... .......... 12% 55.3M 1s
7050K .......... .......... .......... .......... .......... 12% 54.3M 1s
7100K .......... .......... .......... .......... .......... 12% 37.2M 1s
7150K .......... .......... .......... .......... .......... 12% 51.8M 1s
7200K .......... .......... .......... .......... .......... 13% 48.0M 1s
7250K .......... .......... .......... .......... .......... 13% 45.2M 1s
7300K .......... .......... .......... .......... .......... 13% 60.9M 1s
7350K .......... .......... .......... .......... .......... 13% 215M 1s
7400K .......... .......... .......... .......... .......... 13% 245M 1s
7450K .......... .......... .......... .......... .......... 13% 211M 1s
7500K .......... .......... .......... .......... .......... 13% 272M 1s
7550K .......... .......... .......... .......... .......... 13% 210M 1s
7600K .......... .......... .......... .......... .......... 13% 228M 1s
7650K .......... .......... .......... .......... .......... 13% 248M 1s
7700K .......... .......... .......... .......... .......... 13% 239M 1s
7750K .......... .......... .......... .......... .......... 14% 180M 1s
7800K .......... .......... .......... .......... .......... 14% 153M 1s
7850K .......... .......... .......... .......... .......... 14% 168M 1s
7900K .......... .......... .......... .......... .......... 14% 252M 1s
7950K .......... .......... .......... .......... .......... 14% 249M 1s
8000K .......... .......... .......... .......... .......... 14% 235M 1s
8050K .......... .......... .......... .......... .......... 14% 174M 1s
8100K .......... .......... .......... .......... .......... 14% 106M 1s
8150K .......... .......... .......... .......... .......... 14% 53.8M 1s
8200K .......... .......... .......... .......... .......... 14% 48.4M 1s
8250K .......... .......... .......... .......... .......... 14% 44.8M 1s
8300K .......... .......... .......... .......... .......... 15% 55.3M 1s
8350K .......... .......... .......... .......... .......... 15% 53.9M 1s
8400K .......... .......... .......... .......... .......... 15% 49.4M 1s
8450K .......... .......... .......... .......... .......... 15% 37.3M 1s
8500K .......... .......... .......... .......... .......... 15% 44.1M 1s
8550K .......... .......... .......... .......... .......... 15% 41.7M 1s
8600K .......... .......... .......... .......... .......... 15% 45.6M 1s
8650K .......... .......... .......... .......... .......... 15% 50.8M 1s
8700K .......... .......... .......... .......... .......... 15% 53.4M 1s
8750K .......... .......... .......... .......... .......... 15% 44.0M 1s
8800K .......... .......... .......... .......... .......... 15% 49.5M 1s
8850K .......... .......... .......... .......... .......... 16% 56.3M 1s
8900K .......... .......... .......... .......... .......... 16% 50.7M 1s
8950K .......... .......... .......... .......... .......... 16% 5.86M 1s
9000K .......... .......... .......... .......... .......... 16% 42.7M 1s
9050K .......... .......... .......... .......... .......... 16% 56.6M 1s
9100K .......... .......... .......... .......... .......... 16% 54.2M 1s
9150K .......... .......... .......... .......... .......... 16% 62.8M 1s
9200K .......... .......... .......... .......... .......... 16% 227M 1s
9250K .......... .......... .......... .......... .......... 16% 216M 1s
9300K .......... .......... .......... .......... .......... 16% 52.6M 1s
9350K .......... .......... .......... .......... .......... 16% 56.0M 1s
9400K .......... .......... .......... .......... .......... 17% 55.2M 1s
9450K .......... .......... .......... .......... .......... 17% 133M 1s
9500K .......... .......... .......... .......... .......... 17% 161M 1s
9550K .......... .......... .......... .......... .......... 17% 233M 1s
9600K .......... .......... .......... .......... .......... 17% 248M 1s
9650K .......... .......... .......... .......... .......... 17% 249M 1s
9700K .......... .......... .......... .......... .......... 17% 214M 1s
9750K .......... .......... .......... .......... .......... 17% 251M 1s
9800K .......... .......... .......... .......... .......... 17% 213M 1s
9850K .......... .......... .......... .......... .......... 17% 250M 1s
9900K .......... .......... .......... .......... .......... 17% 206M 1s
9950K .......... .......... .......... .......... .......... 18% 259M 1s
10000K .......... .......... .......... .......... .......... 18% 146M 1s
10050K .......... .......... .......... .......... .......... 18% 35.8M 1s
10100K .......... .......... .......... .......... .......... 18% 51.9M 1s
10150K .......... .......... .......... .......... .......... 18% 6.22M 1s
10200K .......... .......... .......... .......... .......... 18% 55.1M 1s
10250K .......... .......... .......... .......... .......... 18% 46.1M 1s
10300K .......... .......... .......... .......... .......... 18% 48.5M 1s
10350K .......... .......... .......... .......... .......... 18% 46.3M 1s
10400K .......... .......... .......... .......... .......... 18% 53.0M 1s
10450K .......... .......... .......... .......... .......... 18% 52.6M 1s
10500K .......... .......... .......... .......... .......... 19% 53.1M 1s
10550K .......... .......... .......... .......... .......... 19% 38.1M 1s
10600K .......... .......... .......... .......... .......... 19% 49.1M 1s
10650K .......... .......... .......... .......... .......... 19% 48.7M 1s
10700K .......... .......... .......... .......... .......... 19% 55.8M 1s
10750K .......... .......... .......... .......... .......... 19% 85.3M 1s
10800K .......... .......... .......... .......... .......... 19% 228M 1s
10850K .......... .......... .......... .......... .......... 19% 249M 1s
10900K .......... .......... .......... .......... .......... 19% 206M 1s
10950K .......... .......... .......... .......... .......... 19% 201M 1s
11000K .......... .......... .......... .......... .......... 19% 220M 1s
11050K .......... .......... .......... .......... .......... 20% 225M 1s
11100K .......... .......... .......... .......... .......... 20% 214M 1s
11150K .......... .......... .......... .......... .......... 20% 237M 1s
11200K .......... .......... .......... .......... .......... 20% 259M 1s
11250K .......... .......... .......... .......... .......... 20% 7.61M 1s
11300K .......... .......... .......... .......... .......... 20% 38.0M 1s
11350K .......... .......... .......... .......... .......... 20% 54.1M 1s
11400K .......... .......... .......... .......... .......... 20% 45.5M 1s
11450K .......... .......... .......... .......... .......... 20% 45.2M 1s
11500K .......... .......... .......... .......... .......... 20% 52.9M 1s
11550K .......... .......... .......... .......... .......... 20% 54.1M 1s
11600K .......... .......... .......... .......... .......... 21% 55.2M 1s
11650K .......... .......... .......... .......... .......... 21% 49.2M 1s
11700K .......... .......... .......... .......... .......... 21% 42.9M 1s
11750K .......... .......... .......... .......... .......... 21% 55.4M 1s
11800K .......... .......... .......... .......... .......... 21% 49.8M 1s
11850K .......... .......... .......... .......... .......... 21% 55.8M 1s
11900K .......... .......... .......... .......... .......... 21% 150M 1s
11950K .......... .......... .......... .......... .......... 21% 143M 1s
12000K .......... .......... .......... .......... .......... 21% 12.4M 1s
12050K .......... .......... .......... .......... .......... 21% 52.1M 1s
12100K .......... .......... .......... .......... .......... 21% 42.0M 1s
12150K .......... .......... .......... .......... .......... 21% 54.3M 1s
12200K .......... .......... .......... .......... .......... 22% 44.1M 1s
12250K .......... .......... .......... .......... .......... 22% 151M 1s
12300K .......... .......... .......... .......... .......... 22% 255M 1s
12350K .......... .......... .......... .......... .......... 22% 257M 1s
12400K .......... .......... .......... .......... .......... 22% 202M 1s
12450K .......... .......... .......... .......... .......... 22% 239M 1s
12500K .......... .......... .......... .......... .......... 22% 219M 1s
12550K .......... .......... .......... .......... .......... 22% 246M 1s
12600K .......... .......... .......... .......... .......... 22% 206M 1s
12650K .......... .......... .......... .......... .......... 22% 251M 1s
12700K .......... .......... .......... .......... .......... 22% 78.5M 1s
12750K .......... .......... .......... .......... .......... 23% 51.6M 1s
12800K .......... .......... .......... .......... .......... 23% 50.0M 1s
12850K .......... .......... .......... .......... .......... 23% 50.6M 1s
12900K .......... .......... .......... .......... .......... 23% 51.8M 1s
12950K .......... .......... .......... .......... .......... 23% 39.3M 1s
13000K .......... .......... .......... .......... .......... 23% 45.6M 1s
13050K .......... .......... .......... .......... .......... 23% 54.9M 1s
13100K .......... .......... .......... .......... .......... 23% 42.9M 1s
13150K .......... .......... .......... .......... .......... 23% 54.7M 1s
13200K .......... .......... .......... .......... .......... 23% 56.6M 1s
13250K .......... .......... .......... .......... .......... 23% 180M 1s
13300K .......... .......... .......... .......... .......... 24% 144M 1s
13350K .......... .......... .......... .......... .......... 24% 216M 1s
13400K .......... .......... .......... .......... .......... 24% 266M 1s
13450K .......... .......... .......... .......... .......... 24% 245M 1s
13500K .......... .......... .......... .......... .......... 24% 245M 1s
13550K .......... .......... .......... .......... .......... 24% 230M 1s
13600K .......... .......... .......... .......... .......... 24% 163M 1s
13650K .......... .......... .......... .......... .......... 24% 248M 1s
13700K .......... .......... .......... .......... .......... 24% 238M 1s
13750K .......... .......... .......... .......... .......... 24% 202M 1s
13800K .......... .......... .......... .......... .......... 24% 220M 1s
13850K .......... .......... .......... .......... .......... 25% 257M 1s
13900K .......... .......... .......... .......... .......... 25% 232M 1s
13950K .......... .......... .......... .......... .......... 25% 100M 1s
14000K .......... .......... .......... .......... .......... 25% 50.1M 1s
14050K .......... .......... .......... .......... .......... 25% 40.9M 1s
14100K .......... .......... .......... .......... .......... 25% 43.3M 1s
14150K .......... .......... .......... .......... .......... 25% 55.0M 1s
14200K .......... .......... .......... .......... .......... 25% 42.2M 1s
14250K .......... .......... .......... .......... .......... 25% 43.5M 1s
14300K .......... .......... .......... .......... .......... 25% 45.2M 1s
14350K .......... .......... .......... .......... .......... 25% 50.7M 1s
14400K .......... .......... .......... .......... .......... 26% 46.8M 1s
14450K .......... .......... .......... .......... .......... 26% 40.6M 1s
14500K .......... .......... .......... .......... .......... 26% 46.6M 1s
14550K .......... .......... .......... .......... .......... 26% 49.7M 1s
14600K .......... .......... .......... .......... .......... 26% 44.6M 1s
14650K .......... .......... .......... .......... .......... 26% 54.1M 1s
14700K .......... .......... .......... .......... .......... 26% 47.4M 1s
14750K .......... .......... .......... .......... .......... 26% 54.2M 1s
14800K .......... .......... .......... .......... .......... 26% 40.3M 1s
14850K .......... .......... .......... .......... .......... 26% 53.6M 1s
14900K .......... .......... .......... .......... .......... 26% 43.1M 1s
14950K .......... .......... .......... .......... .......... 27% 51.9M 1s
15000K .......... .......... .......... .......... .......... 27% 95.0M 1s
15050K .......... .......... .......... .......... .......... 27% 207M 1s
15100K .......... .......... .......... .......... .......... 27% 244M 1s
15150K .......... .......... .......... .......... .......... 27% 226M 1s
15200K .......... .......... .......... .......... .......... 27% 235M 1s
15250K .......... .......... .......... .......... .......... 27% 227M 1s
15300K .......... .......... .......... .......... .......... 27% 207M 1s
15350K .......... .......... .......... .......... .......... 27% 251M 1s
15400K .......... .......... .......... .......... .......... 27% 199M 1s
15450K .......... .......... .......... .......... .......... 27% 268M 1s
15500K .......... .......... .......... .......... .......... 28% 215M 1s
15550K .......... .......... .......... .......... .......... 28% 266M 1s
15600K .......... .......... .......... .......... .......... 28% 243M 1s
15650K .......... .......... .......... .......... .......... 28% 230M 1s
15700K .......... .......... .......... .......... .......... 28% 251M 1s
15750K .......... .......... .......... .......... .......... 28% 126M 1s
15800K .......... .......... .......... .......... .......... 28% 172M 1s
15850K .......... .......... .......... .......... .......... 28% 218M 1s
15900K .......... .......... .......... .......... .......... 28% 251M 1s
15950K .......... .......... .......... .......... .......... 28% 212M 1s
16000K .......... .......... .......... .......... .......... 28% 242M 1s
16050K .......... .......... .......... .......... .......... 29% 71.3M 1s
16100K .......... .......... .......... .......... .......... 29% 50.1M 1s
16150K .......... .......... .......... .......... .......... 29% 43.4M 1s
16200K .......... .......... .......... .......... .......... 29% 53.0M 1s
16250K .......... .......... .......... .......... .......... 29% 41.1M 1s
16300K .......... .......... .......... .......... .......... 29% 52.3M 1s
16350K .......... .......... .......... .......... .......... 29% 57.0M 1s
16400K .......... .......... .......... .......... .......... 29% 63.1M 1s
16450K .......... .......... .......... .......... .......... 29% 55.2M 1s
16500K .......... .......... .......... .......... .......... 29% 14.1M 1s
16550K .......... .......... .......... .......... .......... 29% 48.5M 1s
16600K .......... .......... .......... .......... .......... 30% 44.2M 1s
16650K .......... .......... .......... .......... .......... 30% 45.3M 1s
16700K .......... .......... .......... .......... .......... 30% 49.9M 1s
16750K .......... .......... .......... .......... .......... 30% 52.4M 1s
16800K .......... .......... .......... .......... .......... 30% 45.4M 1s
16850K .......... .......... .......... .......... .......... 30% 53.1M 1s
16900K .......... .......... .......... .......... .......... 30% 45.3M 1s
16950K .......... .......... .......... .......... .......... 30% 53.5M 1s
17000K .......... .......... .......... .......... .......... 30% 36.9M 1s
17050K .......... .......... .......... .......... .......... 30% 52.8M 1s
17100K .......... .......... .......... .......... .......... 30% 55.5M 1s
17150K .......... .......... .......... .......... .......... 31% 48.7M 1s
17200K .......... .......... .......... .......... .......... 31% 54.1M 1s
17250K .......... .......... .......... .......... .......... 31% 54.3M 1s
17300K .......... .......... .......... .......... .......... 31% 144M 1s
17350K .......... .......... .......... .......... .......... 31% 130M 1s
17400K .......... .......... .......... .......... .......... 31% 208M 1s
17450K .......... .......... .......... .......... .......... 31% 246M 1s
17500K .......... .......... .......... .......... .......... 31% 220M 1s
17550K .......... .......... .......... .......... .......... 31% 263M 1s
17600K .......... .......... .......... .......... .......... 31% 185M 1s
17650K .......... .......... .......... .......... .......... 31% 241M 1s
17700K .......... .......... .......... .......... .......... 32% 251M 1s
17750K .......... .......... .......... .......... .......... 32% 177M 1s
17800K .......... .......... .......... .......... .......... 32% 198M 1s
17850K .......... .......... .......... .......... .......... 32% 229M 1s
17900K .......... .......... .......... .......... .......... 32% 180M 1s
17950K .......... .......... .......... .......... .......... 32% 214M 1s
18000K .......... .......... .......... .......... .......... 32% 240M 1s
18050K .......... .......... .......... .......... .......... 32% 201M 1s
18100K .......... .......... .......... .......... .......... 32% 255M 1s
18150K .......... .......... .......... .......... .......... 32% 149M 1s
18200K .......... .......... .......... .......... .......... 32% 53.5M 1s
18250K .......... .......... .......... .......... .......... 32% 46.8M 1s
18300K .......... .......... .......... .......... .......... 33% 54.8M 1s
18350K .......... .......... .......... .......... .......... 33% 39.7M 1s
18400K .......... .......... .......... .......... .......... 33% 37.6M 1s
18450K .......... .......... .......... .......... .......... 33% 40.7M 1s
18500K .......... .......... .......... .......... .......... 33% 51.7M 1s
18550K .......... .......... .......... .......... .......... 33% 45.5M 1s
18600K .......... .......... .......... .......... .......... 33% 53.4M 1s
18650K .......... .......... .......... .......... .......... 33% 51.9M 1s
18700K .......... .......... .......... .......... .......... 33% 44.0M 1s
18750K .......... .......... .......... .......... .......... 33% 46.0M 1s
18800K .......... .......... .......... .......... .......... 33% 46.1M 1s
18850K .......... .......... .......... .......... .......... 34% 49.0M 1s
18900K .......... .......... .......... .......... .......... 34% 48.8M 1s
18950K .......... .......... .......... .......... .......... 34% 52.1M 1s
19000K .......... .......... .......... .......... .......... 34% 50.4M 1s
19050K .......... .......... .......... .......... .......... 34% 38.6M 1s
19100K .......... .......... .......... .......... .......... 34% 48.8M 1s
19150K .......... .......... .......... .......... .......... 34% 45.5M 1s
19200K .......... .......... .......... .......... .......... 34% 48.1M 1s
19250K .......... .......... .......... .......... .......... 34% 61.2M 1s
19300K .......... .......... .......... .......... .......... 34% 45.7M 1s
19350K .......... .......... .......... .......... .......... 34% 53.1M 1s
19400K .......... .......... .......... .......... .......... 35% 136M 1s
19450K .......... .......... .......... .......... .......... 35% 233M 1s
19500K .......... .......... .......... .......... .......... 35% 237M 1s
19550K .......... .......... .......... .......... .......... 35% 172M 1s
19600K .......... .......... .......... .......... .......... 35% 143M 1s
19650K .......... .......... .......... .......... .......... 35% 230M 1s
19700K .......... .......... .......... .......... .......... 35% 229M 1s
19750K .......... .......... .......... .......... .......... 35% 223M 1s
19800K .......... .......... .......... .......... .......... 35% 219M 1s
19850K .......... .......... .......... .......... .......... 35% 182M 1s
19900K .......... .......... .......... .......... .......... 35% 212M 1s
19950K .......... .......... .......... .......... .......... 36% 200M 1s
20000K .......... .......... .......... .......... .......... 36% 229M 1s
20050K .......... .......... .......... .......... .......... 36% 232M 1s
20100K .......... .......... .......... .......... .......... 36% 198M 1s
20150K .......... .......... .......... .......... .......... 36% 207M 1s
20200K .......... .......... .......... .......... .......... 36% 261M 1s
20250K .......... .......... .......... .......... .......... 36% 165M 1s
20300K .......... .......... .......... .......... .......... 36% 138M 1s
20350K .......... .......... .......... .......... .......... 36% 190M 1s
20400K .......... .......... .......... .......... .......... 36% 78.9M 1s
20450K .......... .......... .......... .......... .......... 36% 45.5M 1s
20500K .......... .......... .......... .......... .......... 37% 50.4M 1s
20550K .......... .......... .......... .......... .......... 37% 45.6M 1s
20600K .......... .......... .......... .......... .......... 37% 48.0M 1s
20650K .......... .......... .......... .......... .......... 37% 6.44M 1s
20700K .......... .......... .......... .......... .......... 37% 51.9M 1s
20750K .......... .......... .......... .......... .......... 37% 52.9M 1s
20800K .......... .......... .......... .......... .......... 37% 54.9M 1s
20850K .......... .......... .......... .......... .......... 37% 45.2M 1s
20900K .......... .......... .......... .......... .......... 37% 53.9M 1s
20950K .......... .......... .......... .......... .......... 37% 53.6M 1s
21000K .......... .......... .......... .......... .......... 37% 55.4M 1s
21050K .......... .......... .......... .......... .......... 38% 45.0M 1s
21100K .......... .......... .......... .......... .......... 38% 43.6M 1s
21150K .......... .......... .......... .......... .......... 38% 42.3M 1s
21200K .......... .......... .......... .......... .......... 38% 48.5M 1s
21250K .......... .......... .......... .......... .......... 38% 45.0M 1s
21300K .......... .......... .......... .......... .......... 38% 51.1M 1s
21350K .......... .......... .......... .......... .......... 38% 52.3M 1s
21400K .......... .......... .......... .......... .......... 38% 42.7M 1s
21450K .......... .......... .......... .......... .......... 38% 42.7M 1s
21500K .......... .......... .......... .......... .......... 38% 102M 1s
21550K .......... .......... .......... .......... .......... 38% 215M 1s
21600K .......... .......... .......... .......... .......... 39% 179M 1s
21650K .......... .......... .......... .......... .......... 39% 208M 1s
21700K .......... .......... .......... .......... .......... 39% 248M 1s
21750K .......... .......... .......... .......... .......... 39% 245M 1s
21800K .......... .......... .......... .......... .......... 39% 229M 1s
21850K .......... .......... .......... .......... .......... 39% 215M 1s
21900K .......... .......... .......... .......... .......... 39% 241M 1s
21950K .......... .......... .......... .......... .......... 39% 243M 1s
22000K .......... .......... .......... .......... .......... 39% 209M 1s
22050K .......... .......... .......... .......... .......... 39% 234M 1s
22100K .......... .......... .......... .......... .......... 39% 276M 1s
22150K .......... .......... .......... .......... .......... 40% 256M 1s
22200K .......... .......... .......... .......... .......... 40% 254M 1s
22250K .......... .......... .......... .......... .......... 40% 178M 1s
22300K .......... .......... .......... .......... .......... 40% 266M 1s
22350K .......... .......... .......... .......... .......... 40% 261M 1s
22400K .......... .......... .......... .......... .......... 40% 250M 1s
22450K .......... .......... .......... .......... .......... 40% 224M 1s
22500K .......... .......... .......... .......... .......... 40% 86.4M 1s
22550K .......... .......... .......... .......... .......... 40% 49.6M 1s
22600K .......... .......... .......... .......... .......... 40% 46.4M 1s
22650K .......... .......... .......... .......... .......... 40% 53.7M 1s
22700K .......... .......... .......... .......... .......... 41% 42.9M 1s
22750K .......... .......... .......... .......... .......... 41% 52.3M 1s
22800K .......... .......... .......... .......... .......... 41% 44.9M 1s
22850K .......... .......... .......... .......... .......... 41% 42.3M 1s
22900K .......... .......... .......... .......... .......... 41% 43.4M 1s
22950K .......... .......... .......... .......... .......... 41% 46.7M 1s
23000K .......... .......... .......... .......... .......... 41% 53.4M 1s
23050K .......... .......... .......... .......... .......... 41% 50.0M 1s
23100K .......... .......... .......... .......... .......... 41% 46.1M 1s
23150K .......... .......... .......... .......... .......... 41% 53.4M 1s
23200K .......... .......... .......... .......... .......... 41% 42.8M 1s
23250K .......... .......... .......... .......... .......... 42% 37.1M 1s
23300K .......... .......... .......... .......... .......... 42% 11.5M 1s
23350K .......... .......... .......... .......... .......... 42% 54.8M 1s
23400K .......... .......... .......... .......... .......... 42% 48.0M 1s
23450K .......... .......... .......... .......... .......... 42% 49.4M 1s
23500K .......... .......... .......... .......... .......... 42% 41.6M 1s
23550K .......... .......... .......... .......... .......... 42% 50.9M 1s
23600K .......... .......... .......... .......... .......... 42% 35.4M 1s
23650K .......... .......... .......... .......... .......... 42% 50.7M 1s
23700K .......... .......... .......... .......... .......... 42% 46.8M 1s
23750K .......... .......... .......... .......... .......... 42% 101M 1s
23800K .......... .......... .......... .......... .......... 43% 222M 1s
23850K .......... .......... .......... .......... .......... 43% 273M 1s
23900K .......... .......... .......... .......... .......... 43% 232M 1s
23950K .......... .......... .......... .......... .......... 43% 54.3M 1s
24000K .......... .......... .......... .......... .......... 43% 51.1M 1s
24050K .......... .......... .......... .......... .......... 43% 43.1M 1s
24100K .......... .......... .......... .......... .......... 43% 42.6M 1s
24150K .......... .......... .......... .......... .......... 43% 143M 1s
24200K .......... .......... .......... .......... .......... 43% 240M 1s
24250K .......... .......... .......... .......... .......... 43% 228M 1s
24300K .......... .......... .......... .......... .......... 43% 70.8M 1s
24350K .......... .......... .......... .......... .......... 43% 58.1M 1s
24400K .......... .......... .......... .......... .......... 44% 52.2M 1s
24450K .......... .......... .......... .......... .......... 44% 46.7M 1s
24500K .......... .......... .......... .......... .......... 44% 52.5M 1s
24550K .......... .......... .......... .......... .......... 44% 212M 1s
24600K .......... .......... .......... .......... .......... 44% 245M 1s
24650K .......... .......... .......... .......... .......... 44% 252M 1s
24700K .......... .......... .......... .......... .......... 44% 186M 1s
24750K .......... .......... .......... .......... .......... 44% 246M 1s
24800K .......... .......... .......... .......... .......... 44% 235M 1s
24850K .......... .......... .......... .......... .......... 44% 275M 1s
24900K .......... .......... .......... .......... .......... 44% 48.6M 1s
24950K .......... .......... .......... .......... .......... 45% 40.3M 1s
25000K .......... .......... .......... .......... .......... 45% 52.0M 1s
25050K .......... .......... .......... .......... .......... 45% 53.9M 1s
25100K .......... .......... .......... .......... .......... 45% 42.4M 1s
25150K .......... .......... .......... .......... .......... 45% 50.1M 1s
25200K .......... .......... .......... .......... .......... 45% 53.5M 1s
25250K .......... .......... .......... .......... .......... 45% 36.7M 1s
25300K .......... .......... .......... .......... .......... 45% 48.4M 1s
25350K .......... .......... .......... .......... .......... 45% 53.3M 1s
25400K .......... .......... .......... .......... .......... 45% 89.6M 1s
25450K .......... .......... .......... .......... .......... 45% 219M 1s
25500K .......... .......... .......... .......... .......... 46% 95.5M 1s
25550K .......... .......... .......... .......... .......... 46% 54.4M 1s
25600K .......... .......... .......... .......... .......... 46% 57.0M 1s
25650K .......... .......... .......... .......... .......... 46% 195M 1s
25700K .......... .......... .......... .......... .......... 46% 246M 1s
25750K .......... .......... .......... .......... .......... 46% 259M 1s
25800K .......... .......... .......... .......... .......... 46% 236M 1s
25850K .......... .......... .......... .......... .......... 46% 57.9M 1s
25900K .......... .......... .......... .......... .......... 46% 39.5M 1s
25950K .......... .......... .......... .......... .......... 46% 39.5M 1s
26000K .......... .......... .......... .......... .......... 46% 53.4M 1s
26050K .......... .......... .......... .......... .......... 47% 52.9M 1s
26100K .......... .......... .......... .......... .......... 47% 131M 1s
26150K .......... .......... .......... .......... .......... 47% 229M 1s
26200K .......... .......... .......... .......... .......... 47% 253M 1s
26250K .......... .......... .......... .......... .......... 47% 118M 1s
26300K .......... .......... .......... .......... .......... 47% 207M 1s
26350K .......... .......... .......... .......... .......... 47% 260M 1s
26400K .......... .......... .......... .......... .......... 47% 259M 1s
26450K .......... .......... .......... .......... .......... 47% 69.2M 1s
26500K .......... .......... .......... .......... .......... 47% 48.2M 1s
26550K .......... .......... .......... .......... .......... 47% 48.9M 1s
26600K .......... .......... .......... .......... .......... 48% 44.8M 1s
26650K .......... .......... .......... .......... .......... 48% 46.3M 1s
26700K .......... .......... .......... .......... .......... 48% 53.9M 1s
26750K .......... .......... .......... .......... .......... 48% 44.3M 1s
26800K .......... .......... .......... .......... .......... 48% 40.9M 1s
26850K .......... .......... .......... .......... .......... 48% 47.3M 1s
26900K .......... .......... .......... .......... .......... 48% 44.2M 1s
26950K .......... .......... .......... .......... .......... 48% 171M 1s
27000K .......... .......... .......... .......... .......... 48% 210M 1s
27050K .......... .......... .......... .......... .......... 48% 249M 0s
27100K .......... .......... .......... .......... .......... 48% 143M 0s
27150K .......... .......... .......... .......... .......... 49% 171M 0s
27200K .......... .......... .......... .......... .......... 49% 233M 0s
27250K .......... .......... .......... .......... .......... 49% 270M 0s
27300K .......... .......... .......... .......... .......... 49% 242M 0s
27350K .......... .......... .......... .......... .......... 49% 248M 0s
27400K .......... .......... .......... .......... .......... 49% 208M 0s
27450K .......... .......... .......... .......... .......... 49% 247M 0s
27500K .......... .......... .......... .......... .......... 49% 255M 0s
27550K .......... .......... .......... .......... .......... 49% 97.3M 0s
27600K .......... .......... .......... .......... .......... 49% 46.1M 0s
27650K .......... .......... .......... .......... .......... 49% 52.5M 0s
27700K .......... .......... .......... .......... .......... 50% 53.3M 0s
27750K .......... .......... .......... .......... .......... 50% 43.0M 0s
27800K .......... .......... .......... .......... .......... 50% 46.7M 0s
27850K .......... .......... .......... .......... .......... 50% 47.3M 0s
27900K .......... .......... .......... .......... .......... 50% 55.7M 0s
27950K .......... .......... .......... .......... .......... 50% 56.6M 0s
28000K .......... .......... .......... .......... .......... 50% 36.0M 0s
28050K .......... .......... .......... .......... .......... 50% 51.1M 0s
28100K .......... .......... .......... .......... .......... 50% 49.2M 0s
28150K .......... .......... .......... .......... .......... 50% 50.3M 0s
28200K .......... .......... .......... .......... .......... 50% 44.6M 0s
28250K .......... .......... .......... .......... .......... 51% 52.3M 0s
28300K .......... .......... .......... .......... .......... 51% 55.0M 0s
28350K .......... .......... .......... .......... .......... 51% 65.9M 0s
28400K .......... .......... .......... .......... .......... 51% 213M 0s
28450K .......... .......... .......... .......... .......... 51% 253M 0s
28500K .......... .......... .......... .......... .......... 51% 259M 0s
28550K .......... .......... .......... .......... .......... 51% 253M 0s
28600K .......... .......... .......... .......... .......... 51% 36.0M 0s
28650K .......... .......... .......... .......... .......... 51% 43.9M 0s
28700K .......... .......... .......... .......... .......... 51% 49.1M 0s
28750K .......... .......... .......... .......... .......... 51% 52.0M 0s
28800K .......... .......... .......... .......... .......... 52% 53.7M 0s
28850K .......... .......... .......... .......... .......... 52% 86.0M 0s
28900K .......... .......... .......... .......... .......... 52% 85.0M 0s
28950K .......... .......... .......... .......... .......... 52% 59.8M 0s
29000K .......... .......... .......... .......... .......... 52% 227M 0s
29050K .......... .......... .......... .......... .......... 52% 163M 0s
29100K .......... .......... .......... .......... .......... 52% 66.9M 0s
29150K .......... .......... .......... .......... .......... 52% 48.0M 0s
29200K .......... .......... .......... .......... .......... 52% 54.4M 0s
29250K .......... .......... .......... .......... .......... 52% 54.5M 0s
29300K .......... .......... .......... .......... .......... 52% 47.4M 0s
29350K .......... .......... .......... .......... .......... 53% 115M 0s
29400K .......... .......... .......... .......... .......... 53% 273M 0s
29450K .......... .......... .......... .......... .......... 53% 239M 0s
29500K .......... .......... .......... .......... .......... 53% 230M 0s
29550K .......... .......... .......... .......... .......... 53% 257M 0s
29600K .......... .......... .......... .......... .......... 53% 251M 0s
29650K .......... .......... .......... .......... .......... 53% 249M 0s
29700K .......... .......... .......... .......... .......... 53% 50.1M 0s
29750K .......... .......... .......... .......... .......... 53% 39.5M 0s
29800K .......... .......... .......... .......... .......... 53% 45.8M 0s
29850K .......... .......... .......... .......... .......... 53% 56.0M 0s
29900K .......... .......... .......... .......... .......... 53% 49.0M 0s
29950K .......... .......... .......... .......... .......... 54% 52.5M 0s
30000K .......... .......... .......... .......... .......... 54% 55.0M 0s
30050K .......... .......... .......... .......... .......... 54% 54.7M 0s
30100K .......... .......... .......... .......... .......... 54% 84.6M 0s
30150K .......... .......... .......... .......... .......... 54% 225M 0s
30200K .......... .......... .......... .......... .......... 54% 224M 0s
30250K .......... .......... .......... .......... .......... 54% 222M 0s
30300K .......... .......... .......... .......... .......... 54% 129M 0s
30350K .......... .......... .......... .......... .......... 54% 145M 0s
30400K .......... .......... .......... .......... .......... 54% 265M 0s
30450K .......... .......... .......... .......... .......... 54% 55.9M 0s
30500K .......... .......... .......... .......... .......... 55% 47.9M 0s
30550K .......... .......... .......... .......... .......... 55% 54.4M 0s
30600K .......... .......... .......... .......... .......... 55% 53.8M 0s
30650K .......... .......... .......... .......... .......... 55% 54.1M 0s
30700K .......... .......... .......... .......... .......... 55% 48.4M 0s
30750K .......... .......... .......... .......... .......... 55% 57.0M 0s
30800K .......... .......... .......... .......... .......... 55% 37.5M 0s
30850K .......... .......... .......... .......... .......... 55% 47.7M 0s
30900K .......... .......... .......... .......... .......... 55% 43.0M 0s
30950K .......... .......... .......... .......... .......... 55% 57.2M 0s
31000K .......... .......... .......... .......... .......... 55% 243M 0s
31050K .......... .......... .......... .......... .......... 56% 221M 0s
31100K .......... .......... .......... .......... .......... 56% 220M 0s
31150K .......... .......... .......... .......... .......... 56% 196M 0s
31200K .......... .......... .......... .......... .......... 56% 205M 0s
31250K .......... .......... .......... .......... .......... 56% 133M 0s
31300K .......... .......... .......... .......... .......... 56% 50.7M 0s
31350K .......... .......... .......... .......... .......... 56% 53.2M 0s
31400K .......... .......... .......... .......... .......... 56% 38.6M 0s
31450K .......... .......... .......... .......... .......... 56% 51.4M 0s
31500K .......... .......... .......... .......... .......... 56% 54.8M 0s
31550K .......... .......... .......... .......... .......... 56% 51.5M 0s
31600K .......... .......... .......... .......... .......... 57% 75.8M 0s
31650K .......... .......... .......... .......... .......... 57% 109M 0s
31700K .......... .......... .......... .......... .......... 57% 185M 0s
31750K .......... .......... .......... .......... .......... 57% 257M 0s
31800K .......... .......... .......... .......... .......... 57% 265M 0s
31850K .......... .......... .......... .......... .......... 57% 68.1M 0s
31900K .......... .......... .......... .......... .......... 57% 54.3M 0s
31950K .......... .......... .......... .......... .......... 57% 48.2M 0s
32000K .......... .......... .......... .......... .......... 57% 56.2M 0s
32050K .......... .......... .......... .......... .......... 57% 47.6M 0s
32100K .......... .......... .......... .......... .......... 57% 55.6M 0s
32150K .......... .......... .......... .......... .......... 58% 49.4M 0s
32200K .......... .......... .......... .......... .......... 58% 83.2M 0s
32250K .......... .......... .......... .......... .......... 58% 69.1M 0s
32300K .......... .......... .......... .......... .......... 58% 54.3M 0s
32350K .......... .......... .......... .......... .......... 58% 159M 0s
32400K .......... .......... .......... .......... .......... 58% 242M 0s
32450K .......... .......... .......... .......... .......... 58% 42.7M 0s
32500K .......... .......... .......... .......... .......... 58% 55.7M 0s
32550K .......... .......... .......... .......... .......... 58% 58.8M 0s
32600K .......... .......... .......... .......... .......... 58% 231M 0s
32650K .......... .......... .......... .......... .......... 58% 208M 0s
32700K .......... .......... .......... .......... .......... 59% 241M 0s
32750K .......... .......... .......... .......... .......... 59% 251M 0s
32800K .......... .......... .......... .......... .......... 59% 260M 0s
32850K .......... .......... .......... .......... .......... 59% 219M 0s
32900K .......... .......... .......... .......... .......... 59% 253M 0s
32950K .......... .......... .......... .......... .......... 59% 245M 0s
33000K .......... .......... .......... .......... .......... 59% 182M 0s
33050K .......... .......... .......... .......... .......... 59% 73.0M 0s
33100K .......... .......... .......... .......... .......... 59% 54.1M 0s
33150K .......... .......... .......... .......... .......... 59% 57.1M 0s
33200K .......... .......... .......... .......... .......... 59% 56.3M 0s
33250K .......... .......... .......... .......... .......... 60% 40.8M 0s
33300K .......... .......... .......... .......... .......... 60% 48.3M 0s
33350K .......... .......... .......... .......... .......... 60% 53.9M 0s
33400K .......... .......... .......... .......... .......... 60% 50.1M 0s
33450K .......... .......... .......... .......... .......... 60% 37.4M 0s
33500K .......... .......... .......... .......... .......... 60% 46.5M 0s
33550K .......... .......... .......... .......... .......... 60% 52.8M 0s
33600K .......... .......... .......... .......... .......... 60% 41.5M 0s
33650K .......... .......... .......... .......... .......... 60% 54.4M 0s
33700K .......... .......... .......... .......... .......... 60% 165M 0s
33750K .......... .......... .......... .......... .......... 60% 240M 0s
33800K .......... .......... .......... .......... .......... 61% 209M 0s
33850K .......... .......... .......... .......... .......... 61% 234M 0s
33900K .......... .......... .......... .......... .......... 61% 244M 0s
33950K .......... .......... .......... .......... .......... 61% 199M 0s
34000K .......... .......... .......... .......... .......... 61% 229M 0s
34050K .......... .......... .......... .......... .......... 61% 253M 0s
34100K .......... .......... .......... .......... .......... 61% 245M 0s
34150K .......... .......... .......... .......... .......... 61% 208M 0s
34200K .......... .......... .......... .......... .......... 61% 252M 0s
34250K .......... .......... .......... .......... .......... 61% 177M 0s
34300K .......... .......... .......... .......... .......... 61% 196M 0s
34350K .......... .......... .......... .......... .......... 62% 219M 0s
34400K .......... .......... .......... .......... .......... 62% 232M 0s
34450K .......... .......... .......... .......... .......... 62% 229M 0s
34500K .......... .......... .......... .......... .......... 62% 222M 0s
34550K .......... .......... .......... .......... .......... 62% 204M 0s
34600K .......... .......... .......... .......... .......... 62% 251M 0s
34650K .......... .......... .......... .......... .......... 62% 236M 0s
34700K .......... .......... .......... .......... .......... 62% 70.1M 0s
34750K .......... .......... .......... .......... .......... 62% 41.0M 0s
34800K .......... .......... .......... .......... .......... 62% 53.7M 0s
34850K .......... .......... .......... .......... .......... 62% 51.9M 0s
34900K .......... .......... .......... .......... .......... 63% 44.8M 0s
34950K .......... .......... .......... .......... .......... 63% 37.1M 0s
35000K .......... .......... .......... .......... .......... 63% 50.0M 0s
35050K .......... .......... .......... .......... .......... 63% 55.1M 0s
35100K .......... .......... .......... .......... .......... 63% 55.4M 0s
35150K .......... .......... .......... .......... .......... 63% 37.7M 0s
35200K .......... .......... .......... .......... .......... 63% 52.9M 0s
35250K .......... .......... .......... .......... .......... 63% 52.3M 0s
35300K .......... .......... .......... .......... .......... 63% 48.1M 0s
35350K .......... .......... .......... .......... .......... 63% 45.3M 0s
35400K .......... .......... .......... .......... .......... 63% 54.2M 0s
35450K .......... .......... .......... .......... .......... 64% 13.6M 0s
35500K .......... .......... .......... .......... .......... 64% 41.8M 0s
35550K .......... .......... .......... .......... .......... 64% 46.7M 0s
35600K .......... .......... .......... .......... .......... 64% 45.4M 0s
35650K .......... .......... .......... .......... .......... 64% 53.2M 0s
35700K .......... .......... .......... .......... .......... 64% 55.9M 0s
35750K .......... .......... .......... .......... .......... 64% 56.6M 0s
35800K .......... .......... .......... .......... .......... 64% 7.08M 0s
35850K .......... .......... .......... .......... .......... 64% 240M 0s
35900K .......... .......... .......... .......... .......... 64% 247M 0s
35950K .......... .......... .......... .......... .......... 64% 258M 0s
36000K .......... .......... .......... .......... .......... 64% 178M 0s
36050K .......... .......... .......... .......... .......... 65% 243M 0s
36100K .......... .......... .......... .......... .......... 65% 233M 0s
36150K .......... .......... .......... .......... .......... 65% 259M 0s
36200K .......... .......... .......... .......... .......... 65% 232M 0s
36250K .......... .......... .......... .......... .......... 65% 210M 0s
36300K .......... .......... .......... .......... .......... 65% 266M 0s
36350K .......... .......... .......... .......... .......... 65% 150M 0s
36400K .......... .......... .......... .......... .......... 65% 82.8M 0s
36450K .......... .......... .......... .......... .......... 65% 46.5M 0s
36500K .......... .......... .......... .......... .......... 65% 53.7M 0s
36550K .......... .......... .......... .......... .......... 65% 54.3M 0s
36600K .......... .......... .......... .......... .......... 66% 56.7M 0s
36650K .......... .......... .......... .......... .......... 66% 47.3M 0s
36700K .......... .......... .......... .......... .......... 66% 45.6M 0s
36750K .......... .......... .......... .......... .......... 66% 51.5M 0s
36800K .......... .......... .......... .......... .......... 66% 7.32M 0s
36850K .......... .......... .......... .......... .......... 66% 42.5M 0s
36900K .......... .......... .......... .......... .......... 66% 43.7M 0s
36950K .......... .......... .......... .......... .......... 66% 53.2M 0s
37000K .......... .......... .......... .......... .......... 66% 48.5M 0s
37050K .......... .......... .......... .......... .......... 66% 47.0M 0s
37100K .......... .......... .......... .......... .......... 66% 56.4M 0s
37150K .......... .......... .......... .......... .......... 67% 56.7M 0s
37200K .......... .......... .......... .......... .......... 67% 89.5M 0s
37250K .......... .......... .......... .......... .......... 67% 225M 0s
37300K .......... .......... .......... .......... .......... 67% 187M 0s
37350K .......... .......... .......... .......... .......... 67% 235M 0s
37400K .......... .......... .......... .......... .......... 67% 242M 0s
37450K .......... .......... .......... .......... .......... 67% 201M 0s
37500K .......... .......... .......... .......... .......... 67% 251M 0s
37550K .......... .......... .......... .......... .......... 67% 191M 0s
37600K .......... .......... .......... .......... .......... 67% 230M 0s
37650K .......... .......... .......... .......... .......... 67% 196M 0s
37700K .......... .......... .......... .......... .......... 68% 241M 0s
37750K .......... .......... .......... .......... .......... 68% 245M 0s
37800K .......... .......... .......... .......... .......... 68% 263M 0s
37850K .......... .......... .......... .......... .......... 68% 6.05M 0s
37900K .......... .......... .......... .......... .......... 68% 56.5M 0s
37950K .......... .......... .......... .......... .......... 68% 45.3M 0s
38000K .......... .......... .......... .......... .......... 68% 57.1M 0s
38050K .......... .......... .......... .......... .......... 68% 44.0M 0s
38100K .......... .......... .......... .......... .......... 68% 44.1M 0s
38150K .......... .......... .......... .......... .......... 68% 47.3M 0s
38200K .......... .......... .......... .......... .......... 68% 50.3M 0s
38250K .......... .......... .......... .......... .......... 69% 45.4M 0s
38300K .......... .......... .......... .......... .......... 69% 51.0M 0s
38350K .......... .......... .......... .......... .......... 69% 56.8M 0s
38400K .......... .......... .......... .......... .......... 69% 46.9M 0s
38450K .......... .......... .......... .......... .......... 69% 45.7M 0s
38500K .......... .......... .......... .......... .......... 69% 59.9M 0s
38550K .......... .......... .......... .......... .......... 69% 48.1M 0s
38600K .......... .......... .......... .......... .......... 69% 49.8M 0s
38650K .......... .......... .......... .......... .......... 69% 26.1M 0s
38700K .......... .......... .......... .......... .......... 69% 262M 0s
38750K .......... .......... .......... .......... .......... 69% 11.1M 0s
38800K .......... .......... .......... .......... .......... 70% 26.0M 0s
38850K .......... .......... .......... .......... .......... 70% 38.2M 0s
38900K .......... .......... .......... .......... .......... 70% 56.5M 0s
38950K .......... .......... .......... .......... .......... 70% 225M 0s
39000K .......... .......... .......... .......... .......... 70% 265M 0s
39050K .......... .......... .......... .......... .......... 70% 236M 0s
39100K .......... .......... .......... .......... .......... 70% 61.3M 0s
39150K .......... .......... .......... .......... .......... 70% 11.8M 0s
39200K .......... .......... .......... .......... .......... 70% 52.2M 0s
39250K .......... .......... .......... .......... .......... 70% 56.2M 0s
39300K .......... .......... .......... .......... .......... 70% 230M 0s
39350K .......... .......... .......... .......... .......... 71% 204M 0s
39400K .......... .......... .......... .......... .......... 71% 214M 0s
39450K .......... .......... .......... .......... .......... 71% 254M 0s
39500K .......... .......... .......... .......... .......... 71% 249M 0s
39550K .......... .......... .......... .......... .......... 71% 180M 0s
39600K .......... .......... .......... .......... .......... 71% 215M 0s
39650K .......... .......... .......... .......... .......... 71% 235M 0s
39700K .......... .......... .......... .......... .......... 71% 262M 0s
39750K .......... .......... .......... .......... .......... 71% 244M 0s
39800K .......... .......... .......... .......... .......... 71% 19.4M 0s
39850K .......... .......... .......... .......... .......... 71% 53.0M 0s
39900K .......... .......... .......... .......... .......... 72% 53.4M 0s
39950K .......... .......... .......... .......... .......... 72% 48.6M 0s
40000K .......... .......... .......... .......... .......... 72% 42.2M 0s
40050K .......... .......... .......... .......... .......... 72% 14.1M 0s
40100K .......... .......... .......... .......... .......... 72% 52.5M 0s
40150K .......... .......... .......... .......... .......... 72% 43.3M 0s
40200K .......... .......... .......... .......... .......... 72% 51.5M 0s
40250K .......... .......... .......... .......... .......... 72% 52.2M 0s
40300K .......... .......... .......... .......... .......... 72% 36.0M 0s
40350K .......... .......... .......... .......... .......... 72% 18.9M 0s
40400K .......... .......... .......... .......... .......... 72% 51.9M 0s
40450K .......... .......... .......... .......... .......... 73% 45.6M 0s
40500K .......... .......... .......... .......... .......... 73% 13.6M 0s
40550K .......... .......... .......... .......... .......... 73% 207M 0s
40600K .......... .......... .......... .......... .......... 73% 244M 0s
40650K .......... .......... .......... .......... .......... 73% 242M 0s
40700K .......... .......... .......... .......... .......... 73% 229M 0s
40750K .......... .......... .......... .......... .......... 73% 207M 0s
40800K .......... .......... .......... .......... .......... 73% 215M 0s
40850K .......... .......... .......... .......... .......... 73% 236M 0s
40900K .......... .......... .......... .......... .......... 73% 204M 0s
40950K .......... .......... .......... .......... .......... 73% 250M 0s
41000K .......... .......... .......... .......... .......... 74% 248M 0s
41050K .......... .......... .......... .......... .......... 74% 206M 0s
41100K .......... .......... .......... .......... .......... 74% 280M 0s
41150K .......... .......... .......... .......... .......... 74% 255M 0s
41200K .......... .......... .......... .......... .......... 74% 249M 0s
41250K .......... .......... .......... .......... .......... 74% 216M 0s
41300K .......... .......... .......... .......... .......... 74% 244M 0s
41350K .......... .......... .......... .......... .......... 74% 168M 0s
41400K .......... .......... .......... .......... .......... 74% 177M 0s
41450K .......... .......... .......... .......... .......... 74% 160M 0s
41500K .......... .......... .......... .......... .......... 74% 249M 0s
41550K .......... .......... .......... .......... .......... 75% 241M 0s
41600K .......... .......... .......... .......... .......... 75% 53.4M 0s
41650K .......... .......... .......... .......... .......... 75% 48.4M 0s
41700K .......... .......... .......... .......... .......... 75% 54.4M 0s
41750K .......... .......... .......... .......... .......... 75% 53.8M 0s
41800K .......... .......... .......... .......... .......... 75% 40.2M 0s
41850K .......... .......... .......... .......... .......... 75% 44.5M 0s
41900K .......... .......... .......... .......... .......... 75% 40.0M 0s
41950K .......... .......... .......... .......... .......... 75% 53.4M 0s
42000K .......... .......... .......... .......... .......... 75% 52.3M 0s
42050K .......... .......... .......... .......... .......... 75% 45.1M 0s
42100K .......... .......... .......... .......... .......... 75% 52.8M 0s
42150K .......... .......... .......... .......... .......... 76% 42.1M 0s
42200K .......... .......... .......... .......... .......... 76% 50.3M 0s
42250K .......... .......... .......... .......... .......... 76% 37.7M 0s
42300K .......... .......... .......... .......... .......... 76% 50.3M 0s
42350K .......... .......... .......... .......... .......... 76% 50.8M 0s
42400K .......... .......... .......... .......... .......... 76% 54.7M 0s
42450K .......... .......... .......... .......... .......... 76% 49.5M 0s
42500K .......... .......... .......... .......... .......... 76% 56.7M 0s
42550K .......... .......... .......... .......... .......... 76% 46.1M 0s
42600K .......... .......... .......... .......... .......... 76% 52.7M 0s
42650K .......... .......... .......... .......... .......... 76% 41.8M 0s
42700K .......... .......... .......... .......... .......... 77% 52.2M 0s
42750K .......... .......... .......... .......... .......... 77% 115M 0s
42800K .......... .......... .......... .......... .......... 77% 252M 0s
42850K .......... .......... .......... .......... .......... 77% 203M 0s
42900K .......... .......... .......... .......... .......... 77% 255M 0s
42950K .......... .......... .......... .......... .......... 77% 255M 0s
43000K .......... .......... .......... .......... .......... 77% 261M 0s
43050K .......... .......... .......... .......... .......... 77% 214M 0s
43100K .......... .......... .......... .......... .......... 77% 222M 0s
43150K .......... .......... .......... .......... .......... 77% 257M 0s
43200K .......... .......... .......... .......... .......... 77% 266M 0s
43250K .......... .......... .......... .......... .......... 78% 208M 0s
43300K .......... .......... .......... .......... .......... 78% 232M 0s
43350K .......... .......... .......... .......... .......... 78% 194M 0s
43400K .......... .......... .......... .......... .......... 78% 235M 0s
43450K .......... .......... .......... .......... .......... 78% 210M 0s
43500K .......... .......... .......... .......... .......... 78% 152M 0s
43550K .......... .......... .......... .......... .......... 78% 223M 0s
43600K .......... .......... .......... .......... .......... 78% 226M 0s
43650K .......... .......... .......... .......... .......... 78% 249M 0s
43700K .......... .......... .......... .......... .......... 78% 248M 0s
43750K .......... .......... .......... .......... .......... 78% 93.2M 0s
43800K .......... .......... .......... .......... .......... 79% 55.4M 0s
43850K .......... .......... .......... .......... .......... 79% 39.3M 0s
43900K .......... .......... .......... .......... .......... 79% 53.0M 0s
43950K .......... .......... .......... .......... .......... 79% 46.8M 0s
44000K .......... .......... .......... .......... .......... 79% 54.0M 0s
44050K .......... .......... .......... .......... .......... 79% 39.4M 0s
44100K .......... .......... .......... .......... .......... 79% 50.0M 0s
44150K .......... .......... .......... .......... .......... 79% 51.4M 0s
44200K .......... .......... .......... .......... .......... 79% 38.2M 0s
44250K .......... .......... .......... .......... .......... 79% 51.9M 0s
44300K .......... .......... .......... .......... .......... 79% 53.1M 0s
44350K .......... .......... .......... .......... .......... 80% 53.2M 0s
44400K .......... .......... .......... .......... .......... 80% 37.7M 0s
44450K .......... .......... .......... .......... .......... 80% 54.7M 0s
44500K .......... .......... .......... .......... .......... 80% 53.7M 0s
44550K .......... .......... .......... .......... .......... 80% 43.8M 0s
44600K .......... .......... .......... .......... .......... 80% 47.1M 0s
44650K .......... .......... .......... .......... .......... 80% 54.3M 0s
44700K .......... .......... .......... .......... .......... 80% 53.6M 0s
44750K .......... .......... .......... .......... .......... 80% 50.9M 0s
44800K .......... .......... .......... .......... .......... 80% 39.0M 0s
44850K .......... .......... .......... .......... .......... 80% 56.3M 0s
44900K .......... .......... .......... .......... .......... 81% 47.7M 0s
44950K .......... .......... .......... .......... .......... 81% 3.84M 0s
45000K .......... .......... .......... .......... .......... 81% 236M 0s
45050K .......... .......... .......... .......... .......... 81% 246M 0s
45100K .......... .......... .......... .......... .......... 81% 176M 0s
45150K .......... .......... .......... .......... .......... 81% 247M 0s
45200K .......... .......... .......... .......... .......... 81% 210M 0s
45250K .......... .......... .......... .......... .......... 81% 265M 0s
45300K .......... .......... .......... .......... .......... 81% 248M 0s
45350K .......... .......... .......... .......... .......... 81% 195M 0s
45400K .......... .......... .......... .......... .......... 81% 238M 0s
45450K .......... .......... .......... .......... .......... 82% 237M 0s
45500K .......... .......... .......... .......... .......... 82% 254M 0s
45550K .......... .......... .......... .......... .......... 82% 9.49M 0s
45600K .......... .......... .......... .......... .......... 82% 46.4M 0s
45650K .......... .......... .......... .......... .......... 82% 41.2M 0s
45700K .......... .......... .......... .......... .......... 82% 53.9M 0s
45750K .......... .......... .......... .......... .......... 82% 44.6M 0s
45800K .......... .......... .......... .......... .......... 82% 54.8M 0s
45850K .......... .......... .......... .......... .......... 82% 55.5M 0s
45900K .......... .......... .......... .......... .......... 82% 41.7M 0s
45950K .......... .......... .......... .......... .......... 82% 34.2M 0s
46000K .......... .......... .......... .......... .......... 83% 44.0M 0s
46050K .......... .......... .......... .......... .......... 83% 50.8M 0s
46100K .......... .......... .......... .......... .......... 83% 55.6M 0s
46150K .......... .......... .......... .......... .......... 83% 46.4M 0s
46200K .......... .......... .......... .......... .......... 83% 57.2M 0s
46250K .......... .......... .......... .......... .......... 83% 54.9M 0s
46300K .......... .......... .......... .......... .......... 83% 8.43M 0s
46350K .......... .......... .......... .......... .......... 83% 50.2M 0s
46400K .......... .......... .......... .......... .......... 83% 56.0M 0s
46450K .......... .......... .......... .......... .......... 83% 6.13M 0s
46500K .......... .......... .......... .......... .......... 83% 215M 0s
46550K .......... .......... .......... .......... .......... 84% 179M 0s
46600K .......... .......... .......... .......... .......... 84% 229M 0s
46650K .......... .......... .......... .......... .......... 84% 257M 0s
46700K .......... .......... .......... .......... .......... 84% 235M 0s
46750K .......... .......... .......... .......... .......... 84% 199M 0s
46800K .......... .......... .......... .......... .......... 84% 252M 0s
46850K .......... .......... .......... .......... .......... 84% 223M 0s
46900K .......... .......... .......... .......... .......... 84% 253M 0s
46950K .......... .......... .......... .......... .......... 84% 57.4M 0s
47000K .......... .......... .......... .......... .......... 84% 48.1M 0s
47050K .......... .......... .......... .......... .......... 84% 50.6M 0s
47100K .......... .......... .......... .......... .......... 85% 52.6M 0s
47150K .......... .......... .......... .......... .......... 85% 43.9M 0s
47200K .......... .......... .......... .......... .......... 85% 47.9M 0s
47250K .......... .......... .......... .......... .......... 85% 44.8M 0s
47300K .......... .......... .......... .......... .......... 85% 53.4M 0s
47350K .......... .......... .......... .......... .......... 85% 41.4M 0s
47400K .......... .......... .......... .......... .......... 85% 38.7M 0s
47450K .......... .......... .......... .......... .......... 85% 53.4M 0s
47500K .......... .......... .......... .......... .......... 85% 6.68M 0s
47550K .......... .......... .......... .......... .......... 85% 195M 0s
47600K .......... .......... .......... .......... .......... 85% 283M 0s
47650K .......... .......... .......... .......... .......... 86% 219M 0s
47700K .......... .......... .......... .......... .......... 86% 253M 0s
47750K .......... .......... .......... .......... .......... 86% 266M 0s
47800K .......... .......... .......... .......... .......... 86% 237M 0s
47850K .......... .......... .......... .......... .......... 86% 226M 0s
47900K .......... .......... .......... .......... .......... 86% 218M 0s
47950K .......... .......... .......... .......... .......... 86% 241M 0s
48000K .......... .......... .......... .......... .......... 86% 254M 0s
48050K .......... .......... .......... .......... .......... 86% 174M 0s
48100K .......... .......... .......... .......... .......... 86% 221M 0s
48150K .......... .......... .......... .......... .......... 86% 61.4M 0s
48200K .......... .......... .......... .......... .......... 86% 51.7M 0s
48250K .......... .......... .......... .......... .......... 87% 46.1M 0s
48300K .......... .......... .......... .......... .......... 87% 47.5M 0s
48350K .......... .......... .......... .......... .......... 87% 51.0M 0s
48400K .......... .......... .......... .......... .......... 87% 39.2M 0s
48450K .......... .......... .......... .......... .......... 87% 37.7M 0s
48500K .......... .......... .......... .......... .......... 87% 48.0M 0s
48550K .......... .......... .......... .......... .......... 87% 50.8M 0s
48600K .......... .......... .......... .......... .......... 87% 23.6M 0s
48650K .......... .......... .......... .......... .......... 87% 46.6M 0s
48700K .......... .......... .......... .......... .......... 87% 17.8M 0s
48750K .......... .......... .......... .......... .......... 87% 47.2M 0s
48800K .......... .......... .......... .......... .......... 88% 53.3M 0s
48850K .......... .......... .......... .......... .......... 88% 23.4M 0s
48900K .......... .......... .......... .......... .......... 88% 53.6M 0s
48950K .......... .......... .......... .......... .......... 88% 30.8M 0s
49000K .......... .......... .......... .......... .......... 88% 187M 0s
49050K .......... .......... .......... .......... .......... 88% 199M 0s
49100K .......... .......... .......... .......... .......... 88% 251M 0s
49150K .......... .......... .......... .......... .......... 88% 247M 0s
49200K .......... .......... .......... .......... .......... 88% 232M 0s
49250K .......... .......... .......... .......... .......... 88% 160M 0s
49300K .......... .......... .......... .......... .......... 88% 240M 0s
49350K .......... .......... .......... .......... .......... 89% 245M 0s
49400K .......... .......... .......... .......... .......... 89% 228M 0s
49450K .......... .......... .......... .......... .......... 89% 212M 0s
49500K .......... .......... .......... .......... .......... 89% 218M 0s
49550K .......... .......... .......... .......... .......... 89% 220M 0s
49600K .......... .......... .......... .......... .......... 89% 229M 0s
49650K .......... .......... .......... .......... .......... 89% 203M 0s
49700K .......... .......... .......... .......... .......... 89% 217M 0s
49750K .......... .......... .......... .......... .......... 89% 229M 0s
49800K .......... .......... .......... .......... .......... 89% 81.6M 0s
49850K .......... .......... .......... .......... .......... 89% 44.1M 0s
49900K .......... .......... .......... .......... .......... 90% 48.7M 0s
49950K .......... .......... .......... .......... .......... 90% 46.4M 0s
50000K .......... .......... .......... .......... .......... 90% 45.9M 0s
50050K .......... .......... .......... .......... .......... 90% 39.2M 0s
50100K .......... .......... .......... .......... .......... 90% 46.9M 0s
50150K .......... .......... .......... .......... .......... 90% 57.9M 0s
50200K .......... .......... .......... .......... .......... 90% 27.8M 0s
50250K .......... .......... .......... .......... .......... 90% 45.8M 0s
50300K .......... .......... .......... .......... .......... 90% 15.6M 0s
50350K .......... .......... .......... .......... .......... 90% 51.5M 0s
50400K .......... .......... .......... .......... .......... 90% 15.5M 0s
50450K .......... .......... .......... .......... .......... 91% 49.6M 0s
50500K .......... .......... .......... .......... .......... 91% 52.5M 0s
50550K .......... .......... .......... .......... .......... 91% 33.4M 0s
50600K .......... .......... .......... .......... .......... 91% 46.9M 0s
50650K .......... .......... .......... .......... .......... 91% 51.9M 0s
50700K .......... .......... .......... .......... .......... 91% 48.5M 0s
50750K .......... .......... .......... .......... .......... 91% 51.8M 0s
50800K .......... .......... .......... .......... .......... 91% 53.4M 0s
50850K .......... .......... .......... .......... .......... 91% 51.3M 0s
50900K .......... .......... .......... .......... .......... 91% 45.9M 0s
50950K .......... .......... .......... .......... .......... 91% 51.3M 0s
51000K .......... .......... .......... .......... .......... 92% 52.3M 0s
51050K .......... .......... .......... .......... .......... 92% 135M 0s
51100K .......... .......... .......... .......... .......... 92% 209M 0s
51150K .......... .......... .......... .......... .......... 92% 175M 0s
51200K .......... .......... .......... .......... .......... 92% 236M 0s
51250K .......... .......... .......... .......... .......... 92% 253M 0s
51300K .......... .......... .......... .......... .......... 92% 267M 0s
51350K .......... .......... .......... .......... .......... 92% 194M 0s
51400K .......... .......... .......... .......... .......... 92% 223M 0s
51450K .......... .......... .......... .......... .......... 92% 233M 0s
51500K .......... .......... .......... .......... .......... 92% 250M 0s
51550K .......... .......... .......... .......... .......... 93% 241M 0s
51600K .......... .......... .......... .......... .......... 93% 76.1M 0s
51650K .......... .......... .......... .......... .......... 93% 54.1M 0s
51700K .......... .......... .......... .......... .......... 93% 256M 0s
51750K .......... .......... .......... .......... .......... 93% 198M 0s
51800K .......... .......... .......... .......... .......... 93% 33.5M 0s
51850K .......... .......... .......... .......... .......... 93% 68.9M 0s
51900K .......... .......... .......... .......... .......... 93% 51.6M 0s
51950K .......... .......... .......... .......... .......... 93% 46.3M 0s
52000K .......... .......... .......... .......... .......... 93% 47.4M 0s
52050K .......... .......... .......... .......... .......... 93% 51.1M 0s
52100K .......... .......... .......... .......... .......... 94% 45.4M 0s
52150K .......... .......... .......... .......... .......... 94% 52.2M 0s
52200K .......... .......... .......... .......... .......... 94% 51.8M 0s
52250K .......... .......... .......... .......... .......... 94% 54.2M 0s
52300K .......... .......... .......... .......... .......... 94% 44.6M 0s
52350K .......... .......... .......... .......... .......... 94% 55.8M 0s
52400K .......... .......... .......... .......... .......... 94% 53.0M 0s
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52500K .......... .......... .......... .......... .......... 94% 45.5M 0s
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52600K .......... .......... .......... .......... .......... 94% 52.9M 0s
52650K .......... .......... .......... .......... .......... 95% 4.17M 0s
52700K .......... .......... .......... .......... .......... 95% 48.0M 0s
52750K .......... .......... .......... .......... .......... 95% 135M 0s
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52850K .......... .......... .......... .......... .......... 95% 222M 0s
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53000K .......... .......... .......... .......... .......... 95% 259M 0s
53050K .......... .......... .......... .......... .......... 95% 239M 0s
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53150K .......... .......... .......... .......... .......... 95% 242M 0s
53200K .......... .......... .......... .......... .......... 96% 236M 0s
53250K .......... .......... .......... .......... .......... 96% 212M 0s
53300K .......... .......... .......... .......... .......... 96% 248M 0s
53350K .......... .......... .......... .......... .......... 96% 221M 0s
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53450K .......... .......... .......... .......... .......... 96% 205M 0s
53500K .......... .......... .......... .......... .......... 96% 243M 0s
53550K .......... .......... .......... .......... .......... 96% 227M 0s
53600K .......... .......... .......... .......... .......... 96% 248M 0s
53650K .......... .......... .......... .......... .......... 96% 227M 0s
53700K .......... .......... .......... .......... .......... 96% 237M 0s
53750K .......... .......... .......... .......... .......... 96% 240M 0s
53800K .......... .......... .......... .......... .......... 97% 74.6M 0s
53850K .......... .......... .......... .......... .......... 97% 47.5M 0s
53900K .......... .......... .......... .......... .......... 97% 55.3M 0s
53950K .......... .......... .......... .......... .......... 97% 73.2M 0s
54000K .......... .......... .......... .......... .......... 97% 149M 0s
54050K .......... .......... .......... .......... .......... 97% 48.5M 0s
54100K .......... .......... .......... .......... .......... 97% 55.5M 0s
54150K .......... .......... .......... .......... .......... 97% 56.7M 0s
54200K .......... .......... .......... .......... .......... 97% 43.2M 0s
54250K .......... .......... .......... .......... .......... 97% 48.9M 0s
54300K .......... .......... .......... .......... .......... 97% 53.1M 0s
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54400K .......... .......... .......... .......... .......... 98% 46.1M 0s
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54600K .......... .......... .......... .......... .......... 98% 47.7M 0s
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54750K .......... .......... .......... .......... .......... 98% 7.65M 0s
54800K .......... .......... .......... .......... .......... 98% 43.5M 0s
54850K .......... .......... .......... .......... .......... 98% 57.5M 0s
54900K .......... .......... .......... .......... .......... 99% 63.5M 0s
54950K .......... .......... .......... .......... .......... 99% 49.1M 0s
55000K .......... .......... .......... .......... .......... 99% 51.6M 0s
55050K .......... .......... .......... .......... .......... 99% 76.3M 0s
55100K .......... .......... .......... .......... .......... 99% 249M 0s
55150K .......... .......... .......... .......... .......... 99% 264M 0s
55200K .......... .......... .......... .......... .......... 99% 72.7M 0s
55250K .......... .......... .......... .......... .......... 99% 57.4M 0s
55300K .......... .......... .......... .......... .......... 99% 58.0M 0s
55350K .......... .......... .......... .......... .......... 99% 81.8M 0s
55400K .......... .......... .......... .......... .......... 99% 106M 0s
55450K .......... .... 100% 74.7M=1.0s
2024-11-12 18:24:47 (56.9 MB/s) - ‘nx_trajs_fulv.tgz’ saved [56795768/56795768]
After downloading and unpacking the NAMD data, we need to move to the working directory that contains the 50 TRAJ folders with the simulation results. ULaMDyn will automatically recognize the available trajectories to extract all the information required to perform the analysis.
[5]:
import os
TUTORIAL_DIR = "nx_trajs_fulv"
os.chdir(TUTORIAL_DIR)
os.listdir('./')
[5]:
['TRAJ5',
'TRAJ42',
'geom.xyz',
'TRAJ27',
'TRAJ41',
'TRAJ13',
'TRAJ20',
'TRAJ38',
'TRAJ10',
'TRAJ45',
'TRAJ16',
'TRAJ50',
'TRAJ24',
'TRAJ32',
'TRAJ14',
'TRAJ36',
'TRAJ9',
'TRAJ4',
'TRAJ22',
'TRAJ49',
'TRAJ7',
'TRAJ2',
'TRAJ34',
'TRAJ33',
'TRAJ18',
'TRAJ26',
'TRAJ6',
'TRAJ19',
'TRAJ25',
'TRAJ48',
'TRAJ12',
'TRAJ15',
'TRAJ37',
'TRAJ28',
'TRAJ29',
'TRAJ47',
'TRAJ11',
'TRAJ23',
'TRAJ30',
'TRAJ3',
'TRAJ17',
'TRAJ40',
'TRAJ31',
'TRAJ1',
'TRAJ35',
'TRAJ8',
'TRAJ43',
'TRAJ21',
'TRAJ44',
'TRAJ46',
'TRAJ39']
ULaMDyn via command-line interface
The command-line interface (CLI) of ULaMDyn provides an alias to a set of predefined wrapper functions to assist through the complete process of performing unsupervised learning analysis on NAMD data. Alternatively, one can also use the CLI to easily extract the relevant computed quantities available in the multiple trajectories and export the collected information as structured datasets in csv format. To check for the options available in the CLI, one can run the help function in a shell terminal.
[6]:
! run-ulamdyn --help
usage: run-ulamdyn [-h] [--save_dataset] [--save_xyz] [--use_au] [--create_stats] [--bootstrap]
{ring_analysis,dim_reduction,clustering,sampling,nma} ...
options:
-h, --help show this help message and exit
--save_dataset Select data set to build from the MD outputs and save as csv file.
Options: all, properties, gradients, nacs, velocities, vibspec.
--save_xyz Write the requested data from all trajectories into XYZ file(s). The argument should be given as a comma separated list of strings,
starting with geoms or grads and followed by optional subargs (example: "hops" or "hops,S21" or a query in the form "TRAJ==10").
--use_au If selected, the XYZ Cartesian coordinates or gradients will be written in atomic units (useful for MLatom training).
--create_stats Generate a data set with basic statistics (mean, median, and std) for all the trajectories.
Options: all, ekin, vibspec.
--bootstrap Compute the basic statistics and confidence intervals for the properties data set using the bootstrap approach.
Options: n_repeats, and/or n_samples, and/or ci_level.
Analysis:
{ring_analysis,dim_reduction,clustering,sampling,nma}
ring_analysis Cremer-Pople analysis for a cyclic substructure.
dim_reduction Dimensionality reduction analysis in molecular configuration space.
clustering Perform cluster analysis in geometry or trajectory space.
sampling Sample new molecular geometries using Gaussian Mixture model.
nma Perform Normal Mode analysis to describe the molecular motion.
Unsupervised analysis pipeline
As shown in the CLI example above, ULaMDyn performed the complete clustering analysis in an automated way, starting from the data collection, then converting geometries into a descriptor, and finally running the clustering algorithm on the geometries’ space. In addition, the program performed several statistical analysis by groupping the data according the cluster labels provided by the clustering algorithm. In the next, we will unfold this pipeline process to see how ULaMDyn can be used to perform this analysis step-by-step in a Python framework.
[12]:
import numpy as np
import pandas as pd
import ulamdyn as umd
# Packages for visualization
import py3Dmol
import seaborn as sns
import matplotlib as mpl
import matplotlib.pyplot as plt
[13]:
# Plot settings
%matplotlib inline
mpl.rcParams['figure.figsize'] = [7.8,5.9]
mpl.rcParams['axes.labelsize'] = 15
mpl.rcParams['xtick.labelsize'] = 13
mpl.rcParams['ytick.labelsize'] = 13
mpl.rcParams['legend.fontsize'] = 15
# plt.style.use('seaborn-white')
sns.set(color_codes=True)
legend_settings = {'loc':'upper center', 'ncol':3, 'frameon':True, 'facecolor':'white',
'framealpha':0.8, 'bbox_to_anchor':(0.5, 1.11)}
[14]:
def view_molecule(xyz_geom, style):
for k in style.keys():
assert k in ('line', 'stick', 'sphere', 'carton')
molview = py3Dmol.view(width=350,height=350)
molview.addModel(xyz_geom,'xyz')
molview.setStyle(style)
molview.setBackgroundColor('0xeeeeee')
molview.zoomTo()
return molview
Read and inspect data
The first step in the pipeline for analyzing the nonadiabatic MD data is to collect the relevant quantities (e.g., molecular geometries, potential energy for each electronic state, kinetic energy, energy-gradients, oscillator strength, etc.) computed by the MD program for each trajectory. In the case of Newton-X CS, this information is typically outputted in unstructured text files that you can find in each TRAJXX/RESULTS folder. Thus, ULaMDyn provides built-in classes to collect all these
data and stores them in a Python object for easy manipulation. In the next, we will see how these data collection classes can be used in a Python environment.
Collect molecular geometries from NAMD trajectories
[15]:
geoms_loader = umd.GetCoords()
geoms_loader.read_all_trajs()
[16]:
print(geoms_loader)
------------------------------------------------
Current status of the GetCoords class variables:
------------------------------------------------
• dataset -> None
• eq_xyz, array of shape -> (12, 3)
• labels -> ['C', 'C', 'C', 'C', 'C', 'C', 'H', 'H', 'H', 'H', 'H', 'H']
• rmsd, array of shape -> (30028,)
• traj_time, array of shape -> (30028, 2)
• trajectories -> {'TRAJ1': 60.0, 'TRAJ2': 60.0, 'TRAJ3': 57.8, 'TRAJ4': 60.0, 'TRAJ5': 60.0, 'TRAJ6': 60.0, 'TRAJ7': 60.0, 'TRAJ8': 60.0, 'TRAJ9': 60.0, 'TRAJ10': 60.0, 'TRAJ11': 60.0, 'TRAJ12': 60.0, 'TRAJ13': 60.0, 'TRAJ14': 60.0, 'TRAJ15': 60.0, 'TRAJ16': 60.0, 'TRAJ17': 60.0, 'TRAJ18': 60.0, 'TRAJ19': 60.0, 'TRAJ20': 60.0, 'TRAJ21': 60.0, 'TRAJ22': 60.0, 'TRAJ23': 60.0, 'TRAJ24': 60.0, 'TRAJ25': 60.0, 'TRAJ26': 60.0, 'TRAJ27': 60.0, 'TRAJ28': 60.0, 'TRAJ29': 60.0, 'TRAJ30': 60.0, 'TRAJ31': 60.0, 'TRAJ32': 60.0, 'TRAJ33': 60.0, 'TRAJ34': 60.0, 'TRAJ35': 60.0, 'TRAJ36': 60.0, 'TRAJ37': 60.0, 'TRAJ38': 60.0, 'TRAJ39': 60.0, 'TRAJ40': 60.0, 'TRAJ41': 60.0, 'TRAJ42': 60.0, 'TRAJ43': 60.0, 'TRAJ44': 60.0, 'TRAJ45': 60.0, 'TRAJ46': 60.0, 'TRAJ47': 60.0, 'TRAJ48': 60.0, 'TRAJ49': 60.0, 'TRAJ50': 60.0}
• xyz, array of shape -> (30028, 12, 3)
Once all molecular geometries have been collected and loaded into the class variable, one can easily access any particular geometry of the dataset in the XYZ format by specifying the TRAJ and time indices. Then, the selected geometry can be visualized in the Jupyter notebook by using py3Dmol.
[17]:
# Select geometry either from trajectory and time indices
# or by the geometry number in the loaded dataset.
geometry = geoms_loader[9,10.0]
print(geometry)
12
TRAJ = 9 | time = 10.0
C -1.04108537 0.39497082 0.03064102
C -1.25596310 -1.24557193 -0.05131952
C -0.07134525 -1.66552592 -0.03300498
C 1.00918101 -0.58196867 0.05089400
C 0.24810232 0.50942902 0.06853013
C 0.91058271 1.95719001 0.08733781
H -1.85932628 1.01074471 -0.06895255
H -2.07245770 -1.80836479 -0.03161288
H 0.09471855 -2.74239259 0.03521695
H 1.98639311 -0.73316306 -0.13853527
H 0.09293532 2.73814602 0.01169130
H 1.95826467 2.16650638 0.03911399
[18]:
s = {'stick': {'radius': .15}, 'sphere': {'scale': 0.20}}
view_molecule(geometry, s)
3Dmol.js failed to load for some reason. Please check your browser console for error messages.
[18]:
<py3Dmol.view at 0x7fa37ca8b1c0>
If a reference geometry named geom.xyz is available in the working directory, the read_all_trajs() method will compute, by default, the RMSD between each current geometry read from the trajectories and a given reference geometry. In our example, the reference geometry is the ground-state one (S\(_0\) minimum). For some unsupervised learning algorithms implemented in ULaMDyn, it is also possible to use the RMSD as a distance metric to compare pair of geometries.
[19]:
rmsd_vals = geoms_loader.rmsd
hist = plt.hist(rmsd_vals, bins=50, alpha=0.8)
plt.xlabel(r"RMSD $\AA$")
plt.ylabel("Frequency")
plt.show()
Build dataset with chemical properties
The quantum mechanical quantities such as potential energies and oscillator strength are collected from the Newton-X outputs using the GetProperties class. In the case of fulvene dynamics, we have available the potential energy of the ground and first excited-state, the oscillator strength corresponding to the transition between these two states, and also the MCSCF coefficients of the CAS wave function. In addition, there is also a function to collect the state’s population computed by
Newton-X. In the next cells, we will see examples of how to extract these data.
[20]:
properties_loader = umd.GetProperties()
[21]:
df_props = properties_loader.energies()
Reading energies from TRAJ1...
Reading energies from TRAJ2...
Reading energies from TRAJ3...
Reading energies from TRAJ4...
Reading energies from TRAJ5...
Reading energies from TRAJ6...
Reading energies from TRAJ7...
Reading energies from TRAJ8...
Reading energies from TRAJ9...
Reading energies from TRAJ10...
Reading energies from TRAJ11...
Reading energies from TRAJ12...
Reading energies from TRAJ13...
Reading energies from TRAJ14...
Reading energies from TRAJ15...
Reading energies from TRAJ16...
Reading energies from TRAJ17...
Reading energies from TRAJ18...
Reading energies from TRAJ19...
Reading energies from TRAJ20...
Reading energies from TRAJ21...
Reading energies from TRAJ22...
Reading energies from TRAJ23...
Reading energies from TRAJ24...
Reading energies from TRAJ25...
Reading energies from TRAJ26...
Reading energies from TRAJ27...
Reading energies from TRAJ28...
Reading energies from TRAJ29...
Reading energies from TRAJ30...
Reading energies from TRAJ31...
Reading energies from TRAJ32...
Reading energies from TRAJ33...
Reading energies from TRAJ34...
Reading energies from TRAJ35...
Reading energies from TRAJ36...
Reading energies from TRAJ37...
Reading energies from TRAJ38...
Reading energies from TRAJ39...
Reading energies from TRAJ40...
Reading energies from TRAJ41...
Reading energies from TRAJ42...
Reading energies from TRAJ43...
Reading energies from TRAJ44...
Reading energies from TRAJ45...
Reading energies from TRAJ46...
Reading energies from TRAJ47...
Reading energies from TRAJ48...
Reading energies from TRAJ49...
Reading energies from TRAJ50...
-----------------------------------------------------
The properties dataset is empty.
Updating class variable with the current loaded data.
-----------------------------------------------------
[22]:
df_props
[22]:
| TRAJ | time | State | Total_Energy | Hops_S12 | Hops_S21 | DE21 | S1 | |
|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 0.0 | 2 | -6271.713990 | 0 | 0 | 3.852182 | -6276.740507 |
| 1 | 1 | 0.1 | 2 | -6271.714018 | 0 | 0 | 3.839637 | -6276.777841 |
| 2 | 1 | 0.2 | 2 | -6271.714045 | 0 | 0 | 3.825025 | -6276.812753 |
| 3 | 1 | 0.3 | 2 | -6271.714072 | 0 | 0 | 3.808371 | -6276.844754 |
| 4 | 1 | 0.4 | 2 | -6271.714099 | 0 | 0 | 3.789650 | -6276.873408 |
| ... | ... | ... | ... | ... | ... | ... | ... | ... |
| 30023 | 50 | 59.6 | 1 | -6271.038141 | 0 | 0 | 2.957308 | -6273.467928 |
| 30024 | 50 | 59.7 | 1 | -6271.038141 | 0 | 0 | 2.948355 | -6273.450758 |
| 30025 | 50 | 59.8 | 1 | -6271.038114 | 0 | 0 | 2.938260 | -6273.432499 |
| 30026 | 50 | 59.9 | 1 | -6271.038086 | 0 | 0 | 2.927103 | -6273.413642 |
| 30027 | 50 | 60.0 | 1 | -6271.038032 | 0 | 0 | 2.914885 | -6273.394811 |
30028 rows × 8 columns
Note that, for consistency, the datasets generated by ULaMDyn will contain two primary indices, corresponding to the columns TRAJ and time, which allow to identify each data point in the whole set of NAMD trajectories available.
[23]:
_ = properties_loader.populations()
Reading populations from TRAJ1...
Reading populations from TRAJ2...
Reading populations from TRAJ3...
Reading populations from TRAJ4...
Reading populations from TRAJ5...
Reading populations from TRAJ6...
Reading populations from TRAJ7...
Reading populations from TRAJ8...
Reading populations from TRAJ9...
Reading populations from TRAJ10...
Reading populations from TRAJ11...
Reading populations from TRAJ12...
Reading populations from TRAJ13...
Reading populations from TRAJ14...
Reading populations from TRAJ15...
Reading populations from TRAJ16...
Reading populations from TRAJ17...
Reading populations from TRAJ18...
Reading populations from TRAJ19...
Reading populations from TRAJ20...
Reading populations from TRAJ21...
Reading populations from TRAJ22...
Reading populations from TRAJ23...
Reading populations from TRAJ24...
Reading populations from TRAJ25...
Reading populations from TRAJ26...
Reading populations from TRAJ27...
Reading populations from TRAJ28...
Reading populations from TRAJ29...
Reading populations from TRAJ30...
Reading populations from TRAJ31...
Reading populations from TRAJ32...
Reading populations from TRAJ33...
Reading populations from TRAJ34...
Reading populations from TRAJ35...
Reading populations from TRAJ36...
Reading populations from TRAJ37...
Reading populations from TRAJ38...
Reading populations from TRAJ39...
Reading populations from TRAJ40...
Reading populations from TRAJ41...
Reading populations from TRAJ42...
Reading populations from TRAJ43...
Reading populations from TRAJ44...
Reading populations from TRAJ45...
Reading populations from TRAJ46...
Reading populations from TRAJ47...
Reading populations from TRAJ48...
Reading populations from TRAJ49...
Reading populations from TRAJ50...
[24]:
df_props = properties_loader.dataset
df_props
[24]:
| TRAJ | time | State | Total_Energy | Hops_S12 | Hops_S21 | DE21 | S1 | Pop1 | Pop2 | |
|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 0.0 | 2 | -6271.713990 | 0 | 0 | 3.852182 | -6276.740507 | 0.000000 | 1.000000e+00 |
| 1 | 1 | 0.1 | 2 | -6271.714018 | 0 | 0 | 3.839637 | -6276.777841 | 0.000001 | 9.999989e-01 |
| 2 | 1 | 0.2 | 2 | -6271.714045 | 0 | 0 | 3.825025 | -6276.812753 | 0.000004 | 9.999964e-01 |
| 3 | 1 | 0.3 | 2 | -6271.714072 | 0 | 0 | 3.808371 | -6276.844754 | 0.000006 | 9.999936e-01 |
| 4 | 1 | 0.4 | 2 | -6271.714099 | 0 | 0 | 3.789650 | -6276.873408 | 0.000008 | 9.999916e-01 |
| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
| 30023 | 50 | 59.6 | 1 | -6271.038141 | 0 | 0 | 2.957308 | -6273.467928 | 1.000000 | 2.321440e-07 |
| 30024 | 50 | 59.7 | 1 | -6271.038141 | 0 | 0 | 2.948355 | -6273.450758 | 1.000000 | 1.469556e-07 |
| 30025 | 50 | 59.8 | 1 | -6271.038114 | 0 | 0 | 2.938260 | -6273.432499 | 1.000000 | 1.115193e-07 |
| 30026 | 50 | 59.9 | 1 | -6271.038086 | 0 | 0 | 2.927103 | -6273.413642 | 1.000000 | 1.251270e-07 |
| 30027 | 50 | 60.0 | 1 | -6271.038032 | 0 | 0 | 2.914885 | -6273.394811 | 1.000000 | 1.869723e-07 |
30028 rows × 10 columns
[25]:
egap = df_props['DE21'].values
hist = plt.hist(egap, bins=50, alpha=0.8)
plt.xlabel(r"S$_0$-S$_1$ energy gap (eV)")
plt.ylabel("Frequency")
plt.show()
Geometry-based descriptors
[26]:
geoms_loader.xyz
[26]:
array([[[-1.17011027, 0.32892165, -0.04880431],
[-1.33595893, -1.10235717, 0.08826031],
[ 0.07813233, -1.68450973, 0.08371418],
...,
[ 2.08413222, -0.56710914, 0.04163883],
[ 0.36090265, 2.80427644, 0.15999523],
[ 1.87742744, 2.07998925, 0.06344612]],
[[-1.17009904, 0.32722287, -0.04883062],
[-1.3352209 , -1.10354471, 0.08816412],
[ 0.07797813, -1.68578747, 0.08389662],
...,
[ 2.0835327 , -0.56644704, 0.04307052],
[ 0.35768954, 2.80912331, 0.16216635],
[ 1.87931688, 2.07674128, 0.0627888 ]],
[[-1.17003061, 0.32551303, -0.04884248],
[-1.33436844, -1.10473665, 0.08806767],
[ 0.0778281 , -1.68704068, 0.08407352],
...,
[ 2.0828739 , -0.56582214, 0.04446104],
[ 0.35444625, 2.81379853, 0.16432876],
[ 1.8812048 , 2.07338819, 0.06213557]],
...,
[[-1.15575277, 0.18820841, 0.20108705],
[-1.19114507, -0.98830266, 0.03428959],
[ 0.07003643, -1.6413994 , -0.17449003],
...,
[ 1.87553781, -0.58559218, -0.01304511],
[ 0.47200174, 2.45773948, -0.74605658],
[ 1.53693159, 2.20295005, 0.69547681]],
[[-1.15756582, 0.18921336, 0.19808514],
[-1.19267827, -0.98859216, 0.03336453],
[ 0.06850806, -1.64310416, -0.17447832],
...,
[ 1.87462959, -0.58360654, -0.01118773],
[ 0.47887559, 2.45507978, -0.74051501],
[ 1.53718073, 2.2080186 , 0.68991625]],
[[-1.15933222, 0.19034722, 0.19506302],
[-1.19420535, -0.9889576 , 0.03241057],
[ 0.06697331, -1.64478863, -0.17445305],
...,
[ 1.87422078, -0.58169668, -0.00930462],
[ 0.48561041, 2.45264341, -0.73498533],
[ 1.5375595 , 2.21302762, 0.68429186]]])
In ULaMDyn, there are two classes of symmetry-aware descriptors (translational and rotational invariant) based on molecular geometries: the pairwise atom-atom distances (R2 family of descriptors) and the Z-Matrix representation. Each one of these descriptors is handled by Python classes that take a GetCoords() object as input to access the NAMD molecular geometries and convert them into the specified descriptor type. As you will see in the example below, the R2 descriptor class
contains the function build_descriptor(), which returns a Pandas data frame object with the descriptor calculated for all geometries of each NAMD trajectory. Other variants of the R2 descriptor supported by this function include:
inv-R2 -> inverse of the R2 matrix
delta-R2 -> difference in the R2 descriptor of each MD frame and a reference geometry
RE -> inverse R2 of each MD frame normalized by the R2 vector of a reference geometry
[27]:
atom_dist = umd.R2(geoms_loader)
df_r2 = atom_dist.build_descriptor(variant='R2')
df_r2.head()
[27]:
| TRAJ | time | r12 | r13 | r23 | r14 | r24 | r34 | r15 | r25 | ... | r212 | r312 | r412 | r512 | r612 | r712 | r812 | r912 | r1012 | r1112 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 0.0 | 1.447360 | 2.372673 | 1.529240 | 2.392659 | 2.373981 | 1.365330 | 1.395893 | 2.297261 | ... | 4.522587 | 4.172448 | 2.914349 | 2.236683 | 1.091192 | 4.006476 | 5.540837 | 5.098959 | 2.655246 | 1.683378 |
| 1 | 1 | 0.1 | 1.446765 | 2.372240 | 1.528449 | 2.392770 | 2.374176 | 1.366707 | 1.397138 | 2.297722 | ... | 4.521959 | 4.171557 | 2.911907 | 2.235791 | 1.090342 | 4.008308 | 5.543325 | 5.095413 | 2.651139 | 1.691629 |
| 2 | 1 | 0.2 | 1.446155 | 2.371748 | 1.527545 | 2.392830 | 2.374330 | 1.368172 | 1.398351 | 2.298104 | ... | 4.521179 | 4.170548 | 2.909249 | 2.234833 | 1.089398 | 4.010258 | 5.545897 | 5.091789 | 2.646963 | 1.699895 |
| 3 | 1 | 0.3 | 1.445535 | 2.371200 | 1.526529 | 2.392841 | 2.374441 | 1.369723 | 1.399532 | 2.298409 | ... | 4.520252 | 4.169425 | 2.906380 | 2.233810 | 1.088363 | 4.012306 | 5.548541 | 5.088094 | 2.642723 | 1.708158 |
| 4 | 1 | 0.4 | 1.444908 | 2.370599 | 1.525402 | 2.392807 | 2.374513 | 1.371358 | 1.400684 | 2.298639 | ... | 4.519182 | 4.168190 | 2.903305 | 2.232728 | 1.087243 | 4.014435 | 5.551243 | 5.084338 | 2.638424 | 1.716401 |
5 rows × 68 columns
[28]:
idx_all_hops = df_props.query("Hops_S21 == 1").index.tolist() + df_props.query("Hops_S12 == 1").index.tolist()
idx_no_hops = df_props.query("Hops_S21 == 0 and Hops_S12 == 0").index.tolist()
h1 = plt.hist(df_r2.iloc[idx_all_hops]['r56'], bins=20, color='red', alpha=0.5, label='Hops')
h2 = plt.hist(df_r2.iloc[idx_no_hops]['r56'].sample(len(idx_all_hops)), bins=20, color='blue',
alpha=0.5, label='No hops')
plt.xlabel(r"C5-C6 bond distance ($\AA$)")
plt.ylabel("Frequency")
plt.legend()
plt.show()
[29]:
for traj in df_r2['TRAJ'].unique():
t = df_r2.query(f"TRAJ == {traj}")['time'].values
c5_c6_dist = df_r2.query(f"TRAJ == {traj}")['r56'].values
plt.plot(t, c5_c6_dist, c='k', lw=0.3, alpha=0.5)
plt.scatter(df_r2.iloc[idx_all_hops]['time'], df_r2.iloc[idx_all_hops]['r56'],
color='red', s=1.5)
plt.xlabel("Time (fs)")
plt.ylabel(r"C5-C6 bond distance ($\AA$)")
plt.xlim(0,60)
plt.tight_layout()
plt.show()
Dimensionality reduction
In unsupervised learning analysis, dimensionality reduction is a key concept that refers to the process of reducing the number of features or variables in a dataset. The main goal is to find a low-dimensional representation of the data while still capturing the most important information contained in the data, thereby reducing the complexity of the analysis. This is important because as the number of features or variables increases, the difficulty of visualizing and analyzing the data also increases. By compressing the data in a meaningful way, it becomes easier to identify patterns, relationships, and clusters within the data. There are various techniques used in dimension reduction, including principal component analysis (PCA), isometric feature mapping (Isomap), and t-distributed stochastic neighbor embedding (t-SNE), each of which has its own strengths and weaknesses. These algorithms can be used either as a data exploration tool for visual inspection of the data structure via scatter plots or as a preprocessing step to provide effectively compact input data for supervised learning methods.
[30]:
dimred = umd.DimensionReduction(data=df_r2, dt=0.5, scaler='standard')
Scaling data with standard method
Isomap
In the example below, we will use the Isomap algorithm, which is a manifold learning technique used as a non-linear feature reduction method that aims at preserving the geodesic distances between data points in the low-dimensional space. The main assumption behind Isomap is that the data, even though it may be recorded in a very high dimensional space, inherently leaves in a low dimensional structure which can be encoded in terms of a manifold. In a nutshell, the Isomap algorithm works as follows:
Given some abstract data points \(X_1,...,X_n\) and a distance function \(d(x_i,x_j)\);
Build a \(k\)-nearest neighbor graph (using fixed radius or KNN algorithm) where the edges are weighted by the distances. These are local distances;
In the \(k\)NN graph, compute the shortest path distances between all pair of data points and store them in a matrix D. They correspond to the geodesic distances;
Then apply the classical multidimensional scaling (MDS) method using the distance matrix D as input to find the low-dimensional space embedding that preserves the geodesic distances.
[31]:
df_isomap = dimred.isomap(n_components=2)
***********************************
* Starting the Isomap analysis: *
***********************************
The following set of parameters will be used:
n_neighbors = 30
radius = None
n_components = 2
eigen_solver = auto
tol = 0
max_iter = None
path_method = auto
neighbors_algorithm = auto
n_jobs = -1
metric = cosine
p = 2
metric_params = None
[32]:
idx = df_isomap.index.tolist()
colors = df_props['DE21'].iloc[idx].values
plt.scatter(df_isomap['X1'], df_isomap['X2'], c=colors, cmap='jet', s=3.0, alpha=0.5)
plt.xlabel('X1')
plt.ylabel('X2')
plt.title('Isomap @ R2 descriptor')
cbar = plt.colorbar(pad=0.01)
cbar.set_label(r"S$_0$-S$_1$ energy gap (eV)")
plt.tight_layout()
plt.show()
Note that, in the two-dimensional representation of the R2 descriptor generated by Isomap, the molecular geometries characterized by a large energy gap (red dots) appear separated from those corresponding to a small energy gap (blue dots). This qualitative picture indicates that the geometries near the crossing seams should have distinguished features compared to the other geometries.
[33]:
sns.regplot(x=df_isomap['X1'], y=df_r2.iloc[idx]['r56'], scatter_kws={'s': 3.0},
line_kws={'color':'red'})
plt.ylabel(r"C5-C6 bond distance ($\AA$)")
plt.show()
In nonlinear dimensionality reduction, finding the relationship between the embedded dimensions and the original features to determine which one is contributing the most to the clustering patterns is usually complicated. One alternative to get an intuition about those relationships is to plot each geometrical feature of the molecules against the embedded dimensions.
Gradient-based descriptors
Because the type of analysis we are doing here is essentially a postprocessing step on the NAMD simulation data, we do not need to be restricted to looking only at the molecular geometries. In principle, any quantum chemical information available in the simulations can be used as a descriptor for unsupervised learning analysis. For example, the energy-gradient matrices of each potential energy surface carry valuable information on how fast the geometries can change during the dynamics. Hence, we will use here the difference between the energy-gradient matrices of the S\(_1\) and S\(_0\) states as an example of descriptor.
[34]:
grads_loader = umd.GetGradients()
grads_loader.build_dataframe()
Reading gradients from TRAJ1...
Reading gradients from TRAJ2...
Reading gradients from TRAJ3...
Reading gradients from TRAJ4...
Reading gradients from TRAJ5...
Reading gradients from TRAJ6...
Reading gradients from TRAJ7...
Reading gradients from TRAJ8...
Reading gradients from TRAJ9...
Reading gradients from TRAJ10...
Reading gradients from TRAJ11...
Reading gradients from TRAJ12...
Reading gradients from TRAJ13...
Reading gradients from TRAJ14...
Reading gradients from TRAJ15...
Reading gradients from TRAJ16...
Reading gradients from TRAJ17...
Reading gradients from TRAJ18...
Reading gradients from TRAJ19...
Reading gradients from TRAJ20...
Reading gradients from TRAJ21...
Reading gradients from TRAJ22...
Reading gradients from TRAJ23...
Reading gradients from TRAJ24...
Reading gradients from TRAJ25...
Reading gradients from TRAJ26...
Reading gradients from TRAJ27...
Reading gradients from TRAJ28...
Reading gradients from TRAJ29...
Reading gradients from TRAJ30...
Reading gradients from TRAJ31...
Reading gradients from TRAJ32...
Reading gradients from TRAJ33...
Reading gradients from TRAJ34...
Reading gradients from TRAJ35...
Reading gradients from TRAJ36...
Reading gradients from TRAJ37...
Reading gradients from TRAJ38...
Reading gradients from TRAJ39...
Reading gradients from TRAJ40...
Reading gradients from TRAJ41...
Reading gradients from TRAJ42...
Reading gradients from TRAJ43...
Reading gradients from TRAJ44...
Reading gradients from TRAJ45...
Reading gradients from TRAJ46...
Reading gradients from TRAJ47...
Reading gradients from TRAJ48...
Reading gradients from TRAJ49...
Reading gradients from TRAJ50...
[35]:
df_gdiff = grads_loader.datasets['S2'] - grads_loader.datasets['S1']
df_gdiff.insert(0, "TRAJ", df_props['TRAJ'].values)
df_gdiff.insert(1, "time", df_props['time'].values)
df_gdiff.head()
[35]:
| TRAJ | time | Gx1 | Gy1 | Gz1 | Gx2 | Gy2 | Gz2 | Gx3 | Gy3 | ... | Gz9 | Gx10 | Gy10 | Gz10 | Gx11 | Gy11 | Gz11 | Gx12 | Gy12 | Gz12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 0.0 | -3.995985 | -3.634359 | 0.102500 | -2.309150 | 5.699686 | -0.523269 | 6.311249 | 2.122976 | ... | 0.190308 | 0.013113 | -0.002946 | -0.123871 | -0.098520 | 0.096437 | -0.291259 | 0.130365 | -0.017000 | -0.137181 |
| 1 | 1 | 0.1 | -3.992956 | -3.643739 | 0.104824 | -2.320324 | 5.701558 | -0.522106 | 6.310457 | 2.122704 | ... | 0.192587 | 0.013431 | -0.003409 | -0.125089 | -0.096668 | 0.095532 | -0.292995 | 0.129690 | -0.016902 | -0.137010 |
| 2 | 1 | 0.2 | -3.989125 | -3.652717 | 0.107128 | -2.332208 | 5.703425 | -0.520901 | 6.310272 | 2.122282 | ... | 0.194784 | 0.013719 | -0.003893 | -0.126216 | -0.094840 | 0.094581 | -0.294662 | 0.128976 | -0.016846 | -0.136834 |
| 3 | 1 | 0.3 | -3.984472 | -3.661639 | 0.109390 | -2.344914 | 5.705446 | -0.519626 | 6.310493 | 2.121660 | ... | 0.196892 | 0.013971 | -0.004412 | -0.127229 | -0.093038 | 0.093588 | -0.296275 | 0.128224 | -0.016830 | -0.136662 |
| 4 | 1 | 0.4 | -3.979005 | -3.670339 | 0.111612 | -2.358433 | 5.707595 | -0.518279 | 6.311152 | 2.120817 | ... | 0.198907 | 0.014177 | -0.004962 | -0.128123 | -0.091271 | 0.092560 | -0.297834 | 0.127439 | -0.016851 | -0.136492 |
5 rows × 38 columns
[36]:
dimred = umd.DimensionReduction(data=df_gdiff, dt=0.5, scaler='standard')
df_isomap = dimred.isomap(n_components=2, metric='euclidean')
Scaling data with standard method
***********************************
* Starting the Isomap analysis: *
***********************************
The following set of parameters will be used:
n_neighbors = 30
radius = None
n_components = 2
eigen_solver = auto
tol = 0
max_iter = None
path_method = auto
neighbors_algorithm = auto
n_jobs = -1
metric = euclidean
p = 2
metric_params = None
[37]:
idx = df_isomap.index.tolist()
colors = df_props['DE21'].iloc[idx].values
plt.scatter(df_isomap['X1'], df_isomap['X2'], c=colors, cmap='jet', s=3.0, alpha=0.5)
plt.xlabel('X1')
plt.ylabel('X2')
plt.title('Isomap @ Gradients difference', fontsize=15)
cbar = plt.colorbar(pad=0.01)
cbar.set_label(r"S$_0$-S$_1$ energy gap (eV)")
plt.tight_layout()
plt.show()
Although the Isomap diagram derived from the gradient difference descriptors looks different from the one obtained with the R2 descriptor (geometry-based), one can observe that geometries with small and large energy gaps between the S\(_0\) and S\(_1\) states still appear as distinct groups in the plot.
Clustering analysis
Clustering is a subfield of unsupervised data analysis where the learning task consists of finding commonalities in a set of objects so that objects sharing a high similarity with respect to a given metric fall into the same group (called a cluster). In contrast, dissimilar objects are assigned to distinct groups. In principle, it is not required to perform dimensionality reduction prior to clustering analysis since the similarity metric used to compare pairs of data points can be computed in the original high-dimensional space of the data. However, datasets with a very large number of features may lead to the curse of dimensionality problem, which tends to degrade the performance of clustering algorithms. So, in this case, it might be recommended to reduce the dimension of the data before applying a clustering method.
There are many different algorithms to perform clustering analysis that differ essentially in the understanding of what constitutes a cluster and how to find them. The algorithms available in ULaMDyn for clustering analysis are:
K-Means clustering
Hierarchical agglomerative clustering
Spectral clustering (equivalent to kernel K-Means)
Primary goal: split the NAMD dataset into smaller subgroups of similar molecular geometries to facilitate the identification of the key active internal coordinates related to the photochemical process.
[38]:
zmt = umd.ZMatrix(geoms_loader)
df_dzmt = zmt.build_descriptor(delta=True, apply_to_delta='sigmoid')
[39]:
clustering = umd.ClusterGeoms(data=df_dzmt, dt=0.5, scaler='standard')
df_kmeans = clustering.kmeans(n_clusters=3)
Scaling data with standard method
***********************************************
* Starting the K-Means clustering analysis: *
***********************************************
The following set of parameters will be used:
n_clusters = 3
init = k-means++
max_iter = 1000
tol = 1e-06
n_init = 100
verbose = 0
random_state = 51
copy_x = True
algorithm = lloyd
____________________________________
Number of geometries per cluster:
cluster 0 ---> 2686
cluster 1 ---> 2820
cluster 2 ---> 539
____________________________________
[40]:
df_cluster = pd.merge(df_props, df_kmeans, left_index=True, right_index=True)
df_cluster
[40]:
| TRAJ | time | State | Total_Energy | Hops_S12 | Hops_S21 | DE21 | S1 | Pop1 | Pop2 | kmeans_labels | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 0.0 | 2 | -6271.713990 | 0 | 0 | 3.852182 | -6276.740507 | 0.000000 | 1.000000e+00 | 0 |
| 5 | 1 | 0.5 | 2 | -6271.714099 | 0 | 0 | 3.768888 | -6276.898361 | 0.000009 | 9.999911e-01 | 0 |
| 10 | 1 | 1.0 | 2 | -6271.714099 | 0 | 0 | 3.635252 | -6276.962906 | 0.000002 | 9.999979e-01 | 0 |
| 15 | 1 | 1.5 | 2 | -6271.714018 | 0 | 0 | 3.454052 | -6276.932075 | 0.000007 | 9.999926e-01 | 0 |
| 20 | 1 | 2.0 | 2 | -6271.713936 | 0 | 0 | 3.229667 | -6276.831883 | 0.000010 | 9.999897e-01 | 1 |
| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
| 30007 | 50 | 58.0 | 1 | -6271.037923 | 0 | 0 | 2.911538 | -6273.560474 | 0.999990 | 9.805550e-06 | 2 |
| 30012 | 50 | 58.5 | 1 | -6271.038005 | 0 | 0 | 2.967648 | -6273.555467 | 0.999995 | 4.746033e-06 | 2 |
| 30017 | 50 | 59.0 | 1 | -6271.038086 | 0 | 0 | 2.984437 | -6273.537100 | 0.999998 | 1.821589e-06 | 2 |
| 30022 | 50 | 59.5 | 1 | -6271.038141 | 0 | 0 | 2.965036 | -6273.483657 | 1.000000 | 3.676896e-07 | 2 |
| 30027 | 50 | 60.0 | 1 | -6271.038032 | 0 | 0 | 2.914885 | -6273.394811 | 1.000000 | 1.869723e-07 | 2 |
6045 rows × 11 columns
[41]:
select_cols = ['time', 'DE21', 'Hops_S21', 'Hops_S12']
df_cluster.groupby(by=['kmeans_labels']).mean()[select_cols].reset_index()
[41]:
| kmeans_labels | time | DE21 | Hops_S21 | Hops_S12 | |
|---|---|---|---|---|---|
| 0 | 0 | 37.146128 | 4.502345 | 0.000000 | 0.000000 |
| 1 | 1 | 20.710106 | 1.548206 | 0.003191 | 0.001418 |
| 2 | 2 | 42.723562 | 1.339882 | 0.003711 | 0.000000 |
[42]:
sns.displot(data=df_cluster, x="DE21", hue="kmeans_labels", palette="Set1")
plt.xlabel(r"S$_0$-S$_1$ energy gap (eV)")
plt.show()
Once the cluster labels have been determined, we can use the Isomap low-dimensional representation to visualize how the data points are distributed in clusters. This is helpful to check the effectiveness of the clustering algorithm in identifying groups of similar data points.
[43]:
dimred = umd.DimensionReduction(data=df_dzmt, dt=0.5, scaler='standard')
df_isomap = dimred.isomap(n_components=2, metric='euclidean')
df_isomap = pd.merge(df_isomap, df_kmeans, left_index=True, right_index=True)
Scaling data with standard method
***********************************
* Starting the Isomap analysis: *
***********************************
The following set of parameters will be used:
n_neighbors = 30
radius = None
n_components = 2
eigen_solver = auto
tol = 0
max_iter = None
path_method = auto
neighbors_algorithm = auto
n_jobs = -1
metric = euclidean
p = 2
metric_params = None
[44]:
sns.scatterplot(data=df_isomap, x='X1', y='X2', hue='kmeans_labels', alpha=0.8)
plt.xlabel('X1')
plt.ylabel('X2')
plt.title('Isomap @ Delta Z-Matrix', fontsize=15)
plt.show()
[45]:
zmat = umd.ZMatrix(geoms_loader)
df_zmt = zmat.build_descriptor()
df_zmt = pd.merge(df_zmt, df_kmeans, left_index=True, right_index=True)
df_zmt.head()
[45]:
| TRAJ | time | r21 | r32 | r43 | r54 | r65 | r71 | r82 | r93 | ... | d4321 | d5432 | d6543 | d7123 | d8213 | d9321 | d10432 | d11654 | d12654 | kmeans_labels | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 0.0 | 1.447360 | 1.529240 | 1.365330 | 1.524298 | 1.338307 | 0.995543 | 1.019582 | 1.051487 | ... | -3.223870 | 9.300478 | 172.316382 | 171.230514 | -173.922934 | -159.814224 | 161.757855 | -173.820349 | -9.632035 | 0 |
| 5 | 1 | 0.5 | 1.444278 | 1.524166 | 1.373076 | 1.518747 | 1.344414 | 1.036955 | 1.037297 | 1.044822 | ... | -3.311373 | 9.160352 | 171.932151 | 171.209759 | -174.687412 | -159.289842 | 160.991317 | -173.240792 | -8.931099 | 0 |
| 10 | 1 | 1.0 | 1.441208 | 1.516387 | 1.382832 | 1.510701 | 1.354165 | 1.083254 | 1.059178 | 1.041370 | ... | -3.366445 | 8.966530 | 171.570774 | 171.218018 | -175.432781 | -158.825301 | 160.398034 | -172.673497 | -8.168832 | 0 |
| 15 | 1 | 1.5 | 1.438597 | 1.506085 | 1.394343 | 1.500289 | 1.367334 | 1.129308 | 1.082647 | 1.041649 | ... | -3.390897 | 8.722355 | 171.230920 | 171.252786 | -176.144431 | -158.428343 | 159.985230 | -172.103087 | -7.361343 | 0 |
| 20 | 1 | 2.0 | 1.436835 | 1.493481 | 1.407330 | 1.487681 | 1.383574 | 1.171135 | 1.105279 | 1.045731 | ... | -3.386561 | 8.431232 | 170.910728 | 171.311978 | -176.812617 | -158.107017 | 159.757299 | -171.516341 | -6.525217 | 1 |
5 rows × 33 columns
[46]:
sns.displot(data=df_zmt, x="r65", hue="kmeans_labels", palette="Set1")
plt.xlabel(r"C5-C6 bond distance ($\AA$)")
plt.show()
[47]:
cluster_labels = list(df_zmt['kmeans_labels'].unique())
colors = ['blue', 'gold', 'red']
idx_hops = df_cluster[(df_cluster['Hops_S21'] == 1) | (df_cluster['Hops_S12'] == 1)].index.tolist()
for l,c in zip(cluster_labels, colors):
zmt = df_zmt[df_zmt['kmeans_labels'] == l].abs()
plt.scatter(zmt['r65'], zmt['d12654'], s=8, c=c, alpha=0.4,
label='cluster ' + str(l))
df_zmt_hops = df_zmt.abs().loc[idx_hops]
zmt = df_zmt_hops[df_zmt_hops['kmeans_labels'] == l]
if zmt.shape[0] != 0:
plt.scatter(zmt['r65'], zmt['d12654'], s=150, alpha=0.8, marker='*',
edgecolors='k', c=c)
plt.ylabel('H$_11$-C$_6$-C$_5$-C$_4$ angle ($^\circ$)', labelpad=10)
plt.xlabel('C$_5$-C$_6$ bond length ($\AA$)', labelpad=10)
plt.legend(**legend_settings)
plt.show()
[48]:
traj, time = df_cluster.query("kmeans_labels == 1").sample(1)[['TRAJ', 'time']].values.flatten()
print(f" Geometry for TRAJ{int(traj)} | time = {time} fs")
s = {'stick': {'radius': .15}, 'sphere': {'scale': 0.20}}
view_molecule(geoms_loader[traj, time], s)
Geometry for TRAJ14 | time = 52.5 fs
3Dmol.js failed to load for some reason. Please check your browser console for error messages.
[48]:
<py3Dmol.view at 0x7fa37bf6ff70>
Smooth Overlap of Atomic Positions (SOAP)
To describe the local atomic environments , we have created the Smooth Overlap of Atomic Positions (SOAP) descriptors. The SOAP descriptors is generated using a radial cutoff distance (\(r_{cut}\)) of 14 Å, which defines the spatial extent within which atomic environments are considered. The angular component is expanded using spherical harmonics up to a maximum angular momentum quantum number (\(l_{max}\)) of 6. The radial part of the atomic densities is expanded using a polynomial basis with a maximum radial quantum number (\(n_{max}\)) of 8. To obtain the final SOAP descriptor, we have computed the average SOAP representation for each atomic environment by averaging the overlap of atomic densities across the system, using the outer product of the spherical harmonics and the polynomial basis functions. The total length of the feature vector is 952.
[ ]:
atom_dist = umd.SOAPDescriptor(geoms_loader, r_cut=14, l_max=6, n_max=8,
average='outer', rbf='polynomial',
atoms=geoms_loader.labels)
df_soap = atom_dist.create_features()
df_soap.head()
| TRAJ | time | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | ... | 942 | 943 | 944 | 945 | 946 | 947 | 948 | 949 | 950 | 951 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 0.0 | 0.002793 | -0.010802 | 0.018978 | -0.013030 | -0.025305 | 0.061499 | 0.098811 | 0.306872 | ... | 0.046198 | -0.066262 | -0.132263 | -0.064191 | 0.396419 | 0.483721 | 0.197328 | 0.672379 | 0.291917 | 0.130280 |
| 1 | 1 | 0.1 | 0.002779 | -0.010755 | 0.018913 | -0.012997 | -0.025230 | 0.061327 | 0.098435 | 0.304577 | ... | 0.046212 | -0.066083 | -0.132067 | -0.064109 | 0.397873 | 0.485025 | 0.197780 | 0.673476 | 0.292275 | 0.130390 |
| 2 | 1 | 0.2 | 0.002764 | -0.010705 | 0.018845 | -0.012968 | -0.025141 | 0.061152 | 0.098045 | 0.302281 | ... | 0.046232 | -0.065904 | -0.131873 | -0.064028 | 0.399336 | 0.486341 | 0.198236 | 0.674589 | 0.292639 | 0.130502 |
| 3 | 1 | 0.3 | 0.002749 | -0.010653 | 0.018775 | -0.012945 | -0.025038 | 0.060975 | 0.097643 | 0.299991 | ... | 0.046255 | -0.065724 | -0.131681 | -0.063949 | 0.400806 | 0.487663 | 0.198697 | 0.675711 | 0.293010 | 0.130620 |
| 4 | 1 | 0.4 | 0.002732 | -0.010599 | 0.018703 | -0.012925 | -0.024923 | 0.060796 | 0.097230 | 0.297713 | ... | 0.046283 | -0.065544 | -0.131492 | -0.063870 | 0.402274 | 0.488990 | 0.199155 | 0.676847 | 0.293381 | 0.130735 |
5 rows × 954 columns