stumpy-dev/stumpyLibrería Python escalable para el análisis de series temporales mediante matrix profiles, que permite el descubrimiento de motivos, la detección de anomalías, la segmentación semántica y la minería de patrones en streaming.
|PyPI Version| |Conda Forge Version| |PyPI Downloads| |License| |Test Status| |Code Coverage|
|RTD Status| |Binder| |JOSS| |NumFOCUS|
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.. image:: https://raw.githubusercontent.com/stumpy-dev/stumpy/main/docs/images/stumpy_logo_small.png :target: https://github.com/stumpy-dev/stumpy :alt: Logotipo de STUMPY
STUMPY es una biblioteca de Python potente y escalable que calcula eficientemente algo llamado matrix profile <https://stumpy.readthedocs.io/en/latest/Tutorial_The_Matrix_Profile.html>__, que es solo una forma académica de decir «para cada subsecuencia (verde) dentro de tu serie temporal, identifica automáticamente su vecino más cercano correspondiente (gris)»:
.. image:: https://github.com/stumpy-dev/stumpy/blob/main/docs/images/stumpy_demo.gif?raw=true :alt: GIF animado de STUMPY
Lo importante es que una vez que hayas calculado tu matrix profile (panel central de arriba), puede usarse para una variedad de tareas de minería de datos de series temporales, como:
y más ... <https://www.cs.ucr.edu/~eamonn/100_Time_Series_Data_Mining_Questions__with_Answers.pdf>__Ya seas académico, científico de datos, desarrollador de software o entusiasta de las series temporales, STUMPY es sencillo de instalar y nuestro objetivo es permitirte obtener información de tus series temporales de forma más rápida. Consulta documentación <https://stumpy.readthedocs.io/en/latest/>__ para más información.
Consulta nuestra documentación de API <https://stumpy.readthedocs.io/en/latest/api.html>__ para obtener una lista completa de las funciones disponibles y nuestros informativos tutoriales <https://stumpy.readthedocs.io/en/latest/tutorials.html>__ para ejemplos de uso más exhaustivos. A continuación, encontrarás fragmentos de código que demuestran rápidamente cómo usar STUMPY.
Uso típico (datos de series temporales unidimensionales) con STUMP <https://stumpy.readthedocs.io/en/latest/api.html#stumpy.stump>__:
.. code:: python
import stumpy
import numpy as np
if __name__ == "__main__":
your_time_series = np.random.rand(10000)
window_size = 50 # Approximately, how many data points might be found in a pattern
matrix_profile = stumpy.stump(your_time_series, m=window_size)
Uso distribuido para datos de series temporales unidimensionales con Dask Distributed mediante STUMPED <https://stumpy.readthedocs.io/en/latest/api.html#stumpy.stumped>__:
.. code:: python
import stumpy
import numpy as np
from dask.distributed import Client
if __name__ == "__main__":
with Client() as dask_client:
your_time_series = np.random.rand(10000)
window_size = 50 # Approximately, how many data points might be found in a pattern
matrix_profile = stumpy.stumped(dask_client, your_time_series, m=window_size)
Uso de GPU para datos de series temporales unidimensionales con GPU-STUMP <https://stumpy.readthedocs.io/en/latest/api.html#stumpy.gpu_stump>__:
.. code:: python
import stumpy
import numpy as np
from numba import cuda
if __name__ == "__main__":
your_time_series = np.random.rand(10000)
window_size = 50 # Approximately, how many data points might be found in a pattern
all_gpu_devices = [device.id for device in cuda.list_devices()] # Get a list of all available GPU devices
matrix_profile = stumpy.gpu_stump(your_time_series, m=window_size, device_id=all_gpu_devices)
Datos de series temporales multidimensionales con MSTUMP <https://stumpy.readthedocs.io/en/latest/api.html#stumpy.mstump>__:
.. code:: python
import stumpy
import numpy as np
if __name__ == "__main__":
your_time_series = np.random.rand(3, 1000) # Each row represents data from a different dimension while each column represents data from the same dimension
window_size = 50 # Approximately, how many data points might be found in a pattern
matrix_profile, matrix_profile_indices = stumpy.mstump(your_time_series, m=window_size)
Análisis distribuido de datos de series temporales multidimensionales con Dask Distributed MSTUMPED <https://stumpy.readthedocs.io/en/latest/api.html#stumpy.mstumped>__:
.. code:: python
import stumpy
import numpy as np
from dask.distributed import Client
if __name__ == "__main__":
with Client() as dask_client:
your_time_series = np.random.rand(3, 1000) # Each row represents data from a different dimension while each column represents data from the same dimension
window_size = 50 # Approximately, how many data points might be found in a pattern
matrix_profile, matrix_profile_indices = stumpy.mstumped(dask_client, your_time_series, m=window_size)
Cadenas de series temporales con Anchored Time Series Chains (ATSC) <https://stumpy.readthedocs.io/en/latest/api.html#stumpy.atsc>__:
.. code:: python
import stumpy
import numpy as np
if __name__ == "__main__":
your_time_series = np.random.rand(10000)
window_size = 50 # Approximately, how many data points might be found in a pattern
matrix_profile = stumpy.stump(your_time_series, m=window_size)
left_matrix_profile_index = matrix_profile[:, 2]
right_matrix_profile_index = matrix_profile[:, 3]
idx = 10 # Subsequence index for which to retrieve the anchored time series chain for
anchored_chain = stumpy.atsc(left_matrix_profile_index, right_matrix_profile_index, idx)
all_chain_set, longest_unanchored_chain = stumpy.allc(left_matrix_profile_index, right_matrix_profile_index)
Segmentación semántica con Fast Low-cost Unipotent Semantic Segmentation (FLUSS) <https://stumpy.readthedocs.io/en/latest/api.html#stumpy.fluss>__:
.. code:: python
import stumpy
import numpy as np
if __name__ == "__main__":
your_time_series = np.random.rand(10000)
window_size = 50 # Approximately, how many data points might be found in a pattern
matrix_profile = stumpy.stump(your_time_series, m=window_size)
subseq_len = 50
correct_arc_curve, regime_locations = stumpy.fluss(matrix_profile[:, 1],
L=subseq_len,
n_regimes=2,
excl_factor=1
)
Las versiones compatibles de Python y NumPy se determinan según la política de deprecación NEP 29 <https://numpy.org/neps/nep-0029-deprecation_policy.html>__.
NumPy <http://www.numpy.org/>__Numba <http://numba.pydata.org/>__SciPy <https://www.scipy.org/>__conda:
.. code:: bash
conda install -c conda-forge stumpy
pip:
.. code:: bash
python -m pip install stumpy
pixi:
.. code:: bash
pixi add stumpy
uv:
.. code:: bash
uv add stumpy
Para instalar stumpy desde el código fuente, consulta las instrucciones en la documentación <https://stumpy.readthedocs.io/en/latest/install.html>__.
Para comprender y apreciar completamente los algoritmos y aplicaciones subyacentes, es imprescindible que leas las original publications_. Para ver un ejemplo más detallado de cómo usar STUMPY, consulta la documentación <https://stumpy.readthedocs.io/en/latest/>__ o explora nuestros tutoriales prácticos <https://stumpy.readthedocs.io/en/latest/tutorials.html>__.
Probamos el rendimiento del cálculo del matrix profile exacto utilizando la versión del código compilada con Numba JIT sobre datos de series temporales generados aleatoriamente con varias longitudes (es decir, np.random.rand(n)) junto con diferentes recursos de hardware CPU y GPU <hardware_>_.
.. image:: https://raw.githubusercontent.com/stumpy-dev/stumpy/main/docs/images/performance.png :alt: Gráfica de rendimiento de STUMPY
Los resultados brutos se muestran en la tabla siguiente como Horas:Minutos:Segundos.Milisegundos y con un tamaño de ventana constante de m = 50. Ten en cuenta que estos tiempos de ejecución reportados incluyen el tiempo que se tarda en mover los datos desde el host a todos los dispositivos GPU. Es posible que tengas que desplazarte al lado derecho de la tabla para ver todos los tiempos de ejecución.
+----------+-------------------+--------------+-------------+-------------+-------------+-------------+-------------+-------------+----------------+----------------+
| i | n = 2\ :sup:i | GPU-STOMP | STUMP.2 | STUMP.16 | STUMPED.128 | STUMPED.256 | GPU-STUMP.1 | GPU-STUMP.2 | GPU-STUMP.DGX1 | GPU-STUMP.DGX2 |
+==========+===================+==============+=============+=============+=============+=============+=============+=============+================+================+
| 6 | 64 | 00:00:10.00 | 00:00:00.00 | 00:00:00.00 | 00:00:05.77 | 00:00:06.08 | 00:00:00.03 | 00:00:01.63 | NaN | NaN |
+----------+-------------------+--------------+-------------+-------------+-------------+-------------+-------------+-------------+----------------+----------------+
| 7 | 128 | 00:00:10.00 | 00:00:00.00 | 00:00:00.00 | 00:00:05.93 | 00:00:07.29 | 00:00:00.04 | 00:00:01.66 | NaN | NaN |
+----------+-------------------+--------------+-------------+-------------+-------------+-------------+-------------+-------------+----------------+----------------+
| 8 | 256 | 00:00:10.00 | 00:00:00.00 | 00:00:00.01 | 00:00:05.95 | 00:00:07.59 | 00:00:00.08 | 00:00:01.69 | 00:00:06.68 | 00:00:25.68 |
+----------+-------------------+--------------+-------------+-------------+-------------+-------------+-------------+-------------+----------------+----------------+
| 9 | 512 | 00:00:10.00 | 00:00:00.00 | 00:00:00.02 | 00:00:05.97 | 00:00:07.47 | 00:00:00.13 | 00:00:01.66 | 00:00:06.59 | 00:00:27.66 |
+----------+-------------------+--------------+-------------+-------------+-------------+-------------+-------------+-------------+----------------+----------------+
| 10 | 1024 | 00:00:10.00 | 00:00:00.02 | 00:00:00.04 | 00:00:05.69 | 00:00:07.64 | 00:00:00.24 | 00:00:01.72 | 00:00:06.70 | 00:00:30.49 |
+----------+-------------------+--------------+-------------+-------------+-------------+-------------+-------------+-------------+----------------+----------------+
| 11 | 2048 | NaN | 00:00:00.05 | 00:00:00.09 | 00:00:05.60 | 00:00:07.83 | 00:00:00.53 | 00:00:01.88 | 00:00:06.87 | 00:00:31.09 |
+----------+-------------------+--------------+-------------+-------------+-------------+-------------+-------------+-------------+----------------+----------------+
| 12 | 4096 | NaN | 00:00:00.22 | 00:00:00.19 | 00:00:06.26 | 00:00:07.90 | 00:00:01.04 | 00:00:02.19 | 00:00:06.91 | 00:00:33.93 |
+----------+-------------------+--------------+-------------+-------------+-------------+-------------+-------------+-------------+----------------+----------------+
| 13 | 8192 | NaN | 00:00:00.50 | 00:00:00.41 | 00:00:06.29 | 00:00:07.73 | 00:00:01.97 | 00:00:02.49 | 00:00:06.61 | 00:00:33.81 |
+----------+-------------------+--------------+-------------+-------------+-------------+-------------+-------------+-------------+----------------+----------------+
| 14 | 16384 | NaN | 00:00:01.79 | 00:00:00.99 | 00:00:06.24 | 00:00:08.18 | 00:00:03.69 | 00:00:03.29 | 00:00:07.36 | 00:00:35.23 |
+----------+-------------------+--------------+-------------+-------------+-------------+-------------+-------------+-------------+----------------+----------------+
| 15 | 32768 | NaN | 00:00:06.17 | 00:00:02.39 | 00:00:06.48 | 00:00:08.29 | 00:00:07.45 | 00:00:04.93 | 00:00:07.02 | 00:00:36.09 |
+----------+-------------------+--------------+-------------+-------------+-------------+-------------+-------------+-------------+----------------+----------------+
| 16 | 65536 | NaN | 00:00:22.94 | 00:00:06.42 | 00:00:07.33 | 00:00:09.01 | 00:00:14.89 | 00:00:08.12 | 00:00:08.10 | 00:00:36.54 |
+----------+-------------------+--------------+-------------+-------------+-------------+-------------+-------------+-------------+----------------+----------------+
| 17 | 131072 | 00:00:10.00 | 00:01:29.27 | 00:00:19.52 | 00:00:09.75 | 00:00:10.53 | 00:00:29.97 | 00:00:15.42 | 00:00:09.45 | 00:00:37.33 |
+----------+-------------------+--------------+-------------+-------------+-------------+-------------+-------------+-------------+----------------+----------------+
| 18 | 262144 | 00:00:18.00 | 00:05:56.50 | 00:01:08.44 | 00:00:33.38 | 00:00:24.07 | 00:00:59.62 | 00:00:27.41 | 00:00:13.18 | 00:00:39.30 |
+----------+-------------------+--------------+-------------+-------------+-------------+-------------+-------------+-------------+----------------+----------------+
| 19 | 524288 | 00:00:46.00 | 00:25:34.58 | 00:03:56.82 | 00:01:35.27 | 00:03:43.66 | 00:01:56.67 | 00:00:54.05 | 00:00:19.65 | 00:00:41.45 |
+----------+-------------------+--------------+-------------+-------------+-------------+-------------+-------------+-------------+----------------+----------------+
| 20 | 1048576 | 00:02:30.00 | 01:51:13.43 | 00:19:54.75 | 00:04:37.15 | 00:03:01.16 | 00:05:06.48 | 00:02:24.73 | 00:00:32.95 | 00:00:46.14 |
+----------+-------------------+--------------+-------------+-------------+-------------+-------------+-------------+-------------+----------------+----------------+
| 21 | 2097152 | 00:09:15.00 | 09:25:47.64 | 03:05:07.64 | 00:13:36.51 | 00:08:47.47 | 00:20:27.94 | 00:09:41.43 | 00:01:06.51 | 00:01:02.67 |
+----------+-------------------+--------------+-------------+-------------+-------------+-------------+-------------+-------------+----------------+----------------+
| 22 | 4194304 | NaN | 36:12:23.74 | 10:37:51.21 | 00:55:44.43 | 00:32:06.70 | 01:21:12.33 | 00:38:30.86 | 00:04:03.26 | 00:02:23.47 |
+----------+-------------------+--------------+-------------+-------------+-------------+-------------+-------------+-------------+----------------+----------------+
| 23 | 8388608 | NaN | 143:16:09.94| 38:42:51.42 | 03:33:30.53 | 02:00:49.37 | 05:11:44.45 | 02:33:14.60 | 00:15:46.26 | 00:08:03.76 |
+----------+-------------------+--------------+-------------+-------------+-------------+-------------+-------------+-------------+----------------+----------------+
| 24 | 16777216 | NaN | NaN | NaN | 14:39:11.99 | 07:13:47.12 | 20:43:03.80 | 09:48:43.42 | 01:00:24.06 | 00:29:07.84 |
+----------+-------------------+--------------+-------------+-------------+-------------+-------------+-------------+-------------+----------------+----------------+
| NaN | 17729800 | 09:16:12.00 | NaN | NaN | 15:31:31.75 | 07:18:42.54 | 23:09:22.43 | 10:54:08.64 | 01:07:35.39 | 00:32:51.55 |
+----------+-------------------+--------------+-------------+-------------+-------------+-------------+-------------+-------------+----------------+----------------+
| 25 | 33554432 | NaN | NaN | NaN | 56:03:46.81 | 26:27:41.29 | 83:29:21.06 | 39:17:43.82 | 03:59:32.79 | 01:54:56.52 |
+----------+-------------------+--------------+-------------+-------------+-------------+-------------+-------------+-------------+----------------+----------------+
| 26 | 67108864 | NaN | NaN | NaN | 211:17:37.60| 106:40:17.17| 328:58:04.68| 157:18:30.50| 15:42:15.94 | 07:18:52.91 |
+----------+-------------------+--------------+-------------+-------------+-------------+-------------+-------------+-------------+----------------+----------------+
| NaN | 100000000 | 291:07:12.00 | NaN | NaN | NaN | 234:51:35.39| NaN | NaN | 35:03:44.61 | 16:22:40.81 |
+----------+-------------------+--------------+-------------+-------------+-------------+-------------+-------------+-------------+----------------+----------------+
| 27 | 134217728 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | 64:41:55.09 | 29:13:48.12 |
+----------+-------------------+--------------+-------------+-------------+-------------+-------------+-------------+-------------+----------------+----------------+
^^^^^^^^^^^^^^^^^^ Recursos de Hardware ^^^^^^^^^^^^^^^^^^
.. _hardware:
GPU-STOMP: Estos resultados se reproducen del artículo original Matrix Profile II <https://ieeexplore.ieee.org/abstract/document/7837898>__ - NVIDIA Tesla K80 (contiene 2 GPU) y sirve como referencia de rendimiento para comparar.
STUMP.2: stumpy.stump <https://stumpy.readthedocs.io/en/latest/api.html#stumpy.stump>__ ejecutado con 2 CPUs en total - procesadores 2x Intel(R) Xeon(R) CPU E5-2650 v4 @ 2.20GHz paralelizados con Numba en un solo servidor sin Dask.
STUMP.16: stumpy.stump <https://stumpy.readthedocs.io/en/latest/api.html#stumpy.stump>__ ejecutado con 16 CPUs en total - procesadores 16x Intel(R) Xeon(R) CPU E5-2650 v4 @ 2.20GHz paralelizados con Numba en un solo servidor sin Dask.STUMPED.128: stumpy.stumped <https://stumpy.readthedocs.io/en/latest/api.html#stumpy.stumped>__ ejecutado con 128 CPU en total - 8x procesadores Intel(R) Xeon(R) CPU E5-2650 v4 @ 2.20GHz por 16 servidores, paralelizado con Numba y distribuido con Dask Distributed.
STUMPED.256: stumpy.stumped <https://stumpy.readthedocs.io/en/latest/api.html#stumpy.stumped>__ ejecutado con 256 CPU en total - 8x procesadores Intel(R) Xeon(R) CPU E5-2650 v4 @ 2.20GHz por 32 servidores, paralelizado con Numba y distribuido con Dask Distributed.
GPU-STUMP.1: stumpy.gpu_stump <https://stumpy.readthedocs.io/en/latest/api.html#stumpy.gpu_stump>__ ejecutado con 1x GPU NVIDIA GeForce GTX 1080 Ti, 512 hilos por bloque, límite de potencia de 200W, compilado a CUDA con Numba y paralelizado con Python multiprocessing
GPU-STUMP.2: stumpy.gpu_stump <https://stumpy.readthedocs.io/en/latest/api.html#stumpy.gpu_stump>__ ejecutado con 2x GPU NVIDIA GeForce GTX 1080 Ti, 512 hilos por bloque, límite de potencia de 200W, compilado a CUDA con Numba y paralelizado con Python multiprocessing
GPU-STUMP.DGX1: stumpy.gpu_stump <https://stumpy.readthedocs.io/en/latest/api.html#stumpy.gpu_stump>__ ejecutado con 8x NVIDIA Tesla V100, 512 hilos por bloque, compilado a CUDA con Numba y paralelizado con Python multiprocessing
GPU-STUMP.DGX2: stumpy.gpu_stump <https://stumpy.readthedocs.io/en/latest/api.html#stumpy.gpu_stump>__ ejecutado con 16x NVIDIA Tesla V100, 512 hilos por bloque, compilado a CUDA con Numba y paralelizado con Python multiprocessing
Las pruebas están escritas en el directorio tests y se procesan con PyTest <https://docs.pytest.org/en/latest/>__; requieren coverage.py para el análisis de cobertura de código. Las pruebas se pueden ejecutar con:
.. code:: bash
./test.sh
STUMPY es compatible con Python 3.10+ <https://python3statement.org/>__ y, debido al uso de nombres/identificadores de variables unicode, no es compatible con Python 2.x. Dadas las pequeñas dependencias, STUMPY puede funcionar en versiones anteriores de Python, pero esto está fuera del alcance de nuestro soporte y recomendamos encarecidamente que actualice a la versión más reciente de Python.
Primero, por favor revisa las discusiones <https://github.com/stumpy-dev/stumpy/discussions>__ y los issues <https://github.com/stumpy-dev/stumpy/issues?utf8=%E2%9C%93&q=>__ en Github para ver si tu pregunta ya ha sido respondida allí. Si no hay una solución disponible allí, no dudes en abrir una nueva discusión o issue y los autores intentarán responder en un plazo razonable.
¡Damos la bienvenida a contribuciones <https://github.com/stumpy-dev/stumpy/blob/main/CONTRIBUTING.md>__ en cualquier forma! La ayuda con la documentación, especialmente ampliando los tutoriales, siempre es bienvenida. Para contribuir, por favor haz un fork del proyecto <https://github.com/stumpy-dev/stumpy/fork>__, haz tus cambios y envía un pull request. Haremos todo lo posible para resolver cualquier problema contigo e incorporar tu código a la rama principal.
Si has utilizado este código en una publicación científica y deseas citarlo, por favor utiliza el artículo del Journal of Open Source Software <http://joss.theoj.org/papers/10.21105/joss.01504>__.
S.M. Law, (2019). *STUMPY: A Powerful and Scalable Python Library for Time Series Data Mining*. Journal of Open Source Software, 4(39), 1504.
.. code:: bibtex
@article{law2019stumpy,
author = {Law, Sean M.},
title = {{STUMPY: A Powerful and Scalable Python Library for Time Series Data Mining}},
journal = {{The Journal of Open Source Software}},
volume = {4},
number = {39},
pages = {1504},
year = {2019}
}
.. _publications:
Yeh, Chin-Chia Michael, et al. (2016) Matrix Profile I: All Pairs Similarity Joins for Time Series: A Unifying View that Includes Motifs, Discords, and Shapelets. ICDM:1317-1322. Enlace <https://ieeexplore.ieee.org/abstract/document/7837992>__
Zhu, Yan, et al. (2016) Matrix Profile II: Exploiting a Novel Algorithm and GPUs to Break the One Hundred Million Barrier for Time Series Motifs and Joins. ICDM:739-748. Enlace <https://ieeexplore.ieee.org/abstract/document/7837898>__
Yeh, Chin-Chia Michael, et al. (2017) Matrix Profile VI: Meaningful Multidimensional Motif Discovery. ICDM:565-574. Enlace <https://ieeexplore.ieee.org/abstract/document/8215529>__
Zhu, Yan, et al. (2017) Matrix Profile VII: Time Series Chains: A New Primitive for Time Series Data Mining. ICDM:695-704. Enlace <https://ieeexplore.ieee.org/abstract/document/8215542>__
Gharghabi, Shaghayegh, et al. (2017) Matrix Profile VIII: Domain Agnostic Online Semantic Segmentation at Superhuman Performance Levels. ICDM:117-126. Enlace <https://ieeexplore.ieee.org/abstract/document/8215484>__
Zhu, Yan, et al. (2017) Exploiting a Novel Algorithm and GPUs to Break the Ten Quadrillion Pairwise Comparisons Barrier for Time Series Motifs and Joins. KAIS:203-236. Enlace <https://link.springer.com/article/10.1007%2Fs10115-017-1138-x>__
Zhu, Yan, et al. (2018) Matrix Profile XI: SCRIMP++: Time Series Motif Discovery at Interactive Speeds. ICDM:837-846. Enlace <https://ieeexplore.ieee.org/abstract/document/8594908>__
Yeh, Chin-Chia Michael, et al. (2018) Time Series Joins, Motifs, Discords and Shapelets: a Unifying View that Exploits the Matrix Profile. Data Min Knowl Disc:83-123. Enlace <https://link.springer.com/article/10.1007/s10618-017-0519-9>__
Gharghabi, Shaghayegh, et al. (2018) "Matrix Profile XII: MPdist: A Novel Time Series Distance Measure to Allow Data Mining in More Challenging Scenarios." ICDM:965-970. Enlace <https://ieeexplore.ieee.org/abstract/document/8594928>__
Zimmerman, Zachary, et al. (2019) Matrix Profile XIV: Scaling Time Series Motif Discovery with GPUs to Break a Quintillion Pairwise Comparisons a Day and Beyond. SoCC '19:74-86. Enlace <https://dl.acm.org/doi/10.1145/3357223.3362721>__
Akbarinia, Reza, and Betrand Cloez. (2019) Efficient Matrix Profile Computation Using Different Distance Functions. arXiv:1901.05708. Enlace <https://arxiv.org/abs/1901.05708>__
Kamgar, Kaveh, et al. (2019) Matrix Profile XV: Exploiting Time Series Consensus Motifs to Find Structure in Time Series Sets. ICDM:1156-1161. Enlace <https://ieeexplore.ieee.org/abstract/document/8970797>__
| STUMPY | Copyright 2019 TD Ameritrade. Publicado bajo los términos de la licencia BSD de 3 cláusulas. | STUMPY es una marca comercial de TD Ameritrade IP Company, Inc. Todos los derechos reservados.