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Double-gyre example
Define a double gyre fieldset that varies in time | def doublegyre_fieldset(times, xdim=51, ydim=51):
"""Implemented following Froyland and Padberg (2009), 10.1016/j.physd.2009.03.002"""
A = 0.25
delta = 0.25
omega = 2 * np.pi
a, b = 2, 1 # domain size
lon = np.linspace(0, a, xdim, dtype=np.float32)
lat = np.linspace(0, b, ydim, dtype=np.fl... | parcels/examples/tutorial_analyticaladvection.ipynb | OceanPARCELS/parcels | mit |
Now simulate a set of particles on this fieldset, using the AdvectionAnalytical kernel | X, Y = np.meshgrid(np.arange(0.15, 1.85, 0.1), np.arange(0.15, 0.85, 0.1))
psetAA = ParticleSet(fieldsetDG, pclass=ScipyParticle, lon=X, lat=Y)
output = psetAA.ParticleFile(name='doublegyreAA.nc', outputdt=0.1)
psetAA.execute(AdvectionAnalytical,
dt=np.inf, # needs to be set to np.inf for Analytical Ad... | parcels/examples/tutorial_analyticaladvection.ipynb | OceanPARCELS/parcels | mit |
And then show the particle trajectories in an animation | output.close()
plotTrajectoriesFile('doublegyreAA.nc', mode='movie2d_notebook') | parcels/examples/tutorial_analyticaladvection.ipynb | OceanPARCELS/parcels | mit |
Now, we can also compute these trajectories with the AdvectionRK4 kernel | psetRK4 = ParticleSet(fieldsetDG, pclass=JITParticle, lon=X, lat=Y)
psetRK4.execute(AdvectionRK4, dt=0.01, runtime=3) | parcels/examples/tutorial_analyticaladvection.ipynb | OceanPARCELS/parcels | mit |
And we can then compare the final locations of the particles from the AdvectionRK4 and AdvectionAnalytical simulations | plt.plot(psetRK4.lon, psetRK4.lat, 'r.', label='RK4')
plt.plot(psetAA.lon, psetAA.lat, 'b.', label='Analytical')
plt.legend()
plt.show() | parcels/examples/tutorial_analyticaladvection.ipynb | OceanPARCELS/parcels | mit |
The final locations are similar, but not exactly the same. Because everything else is the same, the difference has to be due to the different kernels. Which one is more correct, however, can't be determined from this analysis alone.
Bickley Jet example
Let's as a second example, do a similar analysis for a Bickley Jet,... | def bickleyjet_fieldset(times, xdim=51, ydim=51):
"""Bickley Jet Field as implemented in Hadjighasem et al 2017, 10.1063/1.4982720"""
U0 = 0.06266
L = 1770.
r0 = 6371.
k1 = 2 * 1 / r0
k2 = 2 * 2 / r0
k3 = 2 * 3 / r0
eps1 = 0.075
eps2 = 0.4
eps3 = 0.3
c3 = 0.461 * U0
c2 = ... | parcels/examples/tutorial_analyticaladvection.ipynb | OceanPARCELS/parcels | mit |
Add a zonal halo for periodic boundary conditions in the zonal direction | fieldsetBJ.add_constant('halo_west', fieldsetBJ.U.grid.lon[0])
fieldsetBJ.add_constant('halo_east', fieldsetBJ.U.grid.lon[-1])
fieldsetBJ.add_periodic_halo(zonal=True)
def ZonalBC(particle, fieldset, time):
if particle.lon < fieldset.halo_west:
particle.lon += fieldset.halo_east - fieldset.halo_west
el... | parcels/examples/tutorial_analyticaladvection.ipynb | OceanPARCELS/parcels | mit |
And simulate a set of particles on this fieldset, using the AdvectionAnalytical kernel | X, Y = np.meshgrid(np.arange(0, 19900, 100), np.arange(-100, 100, 100))
psetAA = ParticleSet(fieldsetBJ, pclass=ScipyParticle, lon=X, lat=Y, time=0)
output = psetAA.ParticleFile(name='bickleyjetAA.nc', outputdt=delta(hours=1))
psetAA.execute(AdvectionAnalytical+psetAA.Kernel(ZonalBC),
dt=np.inf,
... | parcels/examples/tutorial_analyticaladvection.ipynb | OceanPARCELS/parcels | mit |
And then show the particle trajectories in an animation | output.close()
plotTrajectoriesFile('bickleyjetAA.nc', mode='movie2d_notebook') | parcels/examples/tutorial_analyticaladvection.ipynb | OceanPARCELS/parcels | mit |
Like with the double gyre above, we can also compute these trajectories with the AdvectionRK4 kernel | psetRK4 = ParticleSet(fieldsetBJ, pclass=JITParticle, lon=X, lat=Y)
psetRK4.execute(AdvectionRK4+psetRK4.Kernel(ZonalBC),
dt=delta(minutes=5), runtime=delta(days=1)) | parcels/examples/tutorial_analyticaladvection.ipynb | OceanPARCELS/parcels | mit |
And finally, we can again compare the end locations from the AdvectionRK4 and AdvectionAnalytical simulations | plt.plot(psetRK4.lon, psetRK4.lat, 'r.', label='RK4')
plt.plot(psetAA.lon, psetAA.lat, 'b.', label='Analytical')
plt.legend()
plt.show() | parcels/examples/tutorial_analyticaladvection.ipynb | OceanPARCELS/parcels | mit |
Import required packages | import copy
from kubeflow.katib import KatibClient
from kubernetes.client import V1ObjectMeta
from kubeflow.katib import V1beta1Experiment
from kubeflow.katib import V1beta1AlgorithmSpec
from kubeflow.katib import V1beta1ObjectiveSpec
from kubeflow.katib import V1beta1FeasibleSpace
from kubeflow.katib import V1beta1Ex... | examples/v1beta1/sdk/cmaes-and-resume-policies.ipynb | kubeflow/katib | apache-2.0 |
Define your Experiment
You have to create your Experiment object before deploying it. This Experiment is similar to this example. | # Experiment name and namespace.
namespace = "kubeflow-user-example-com"
experiment_name = "cmaes-example"
metadata = V1ObjectMeta(
name=experiment_name,
namespace=namespace
)
# Algorithm specification.
algorithm_spec=V1beta1AlgorithmSpec(
algorithm_name="cmaes"
)
# Objective specification.
objective_spe... | examples/v1beta1/sdk/cmaes-and-resume-policies.ipynb | kubeflow/katib | apache-2.0 |
Define Experiments with resume policy
We will define another 2 Experiments with ResumePolicy = Never and ResumePolicy = FromVolume.
Experiment with Never resume policy can't be resumed, the Suggestion resources will be deleted.
Experiment with FromVolume resume policy can be resumed, volume is attached to the Suggestio... | experiment_never_resume_name = "never-resume-cmaes"
experiment_from_volume_resume_name = "from-volume-resume-cmaes"
# Create new Experiments from the previous Experiment info.
# Define Experiment with never resume.
experiment_never_resume = copy.deepcopy(experiment)
experiment_never_resume.metadata.name = experiment_n... | examples/v1beta1/sdk/cmaes-and-resume-policies.ipynb | kubeflow/katib | apache-2.0 |
You can print the Experiment's info to verify it before submission. | print(experiment.metadata.name)
print(experiment.spec.algorithm.algorithm_name)
print("-----------------")
print(experiment_never_resume.metadata.name)
print(experiment_never_resume.spec.resume_policy)
print("-----------------")
print(experiment_from_volume_resume.metadata.name)
print(experiment_from_volume_resume.spec... | examples/v1beta1/sdk/cmaes-and-resume-policies.ipynb | kubeflow/katib | apache-2.0 |
Create your Experiment
You have to create Katib client to use the SDK. | # Create client.
kclient = KatibClient()
# Create your Experiment.
kclient.create_experiment(experiment,namespace=namespace) | examples/v1beta1/sdk/cmaes-and-resume-policies.ipynb | kubeflow/katib | apache-2.0 |
Create other Experiments. | # Create Experiment with never resume.
kclient.create_experiment(experiment_never_resume,namespace=namespace)
# Create Experiment with from volume resume.
kclient.create_experiment(experiment_from_volume_resume,namespace=namespace) | examples/v1beta1/sdk/cmaes-and-resume-policies.ipynb | kubeflow/katib | apache-2.0 |
Get your Experiment
You can get your Experiment by name and receive required data. | exp = kclient.get_experiment(name=experiment_name, namespace=namespace)
print(exp)
print("-----------------\n")
# Get the max trial count and latest status.
print(exp["spec"]["maxTrialCount"])
print(exp["status"]["conditions"][-1]) | examples/v1beta1/sdk/cmaes-and-resume-policies.ipynb | kubeflow/katib | apache-2.0 |
Get all Experiments
You can get list of the current Experiments. | # Get names from the running Experiments.
exp_list = kclient.get_experiment(namespace=namespace)
for exp in exp_list["items"]:
print(exp["metadata"]["name"]) | examples/v1beta1/sdk/cmaes-and-resume-policies.ipynb | kubeflow/katib | apache-2.0 |
List of the current Trials
You can get list of the current trials with the latest status. | # Trial list.
kclient.list_trials(name=experiment_name, namespace=namespace) | examples/v1beta1/sdk/cmaes-and-resume-policies.ipynb | kubeflow/katib | apache-2.0 |
Get the optimal HyperParameters
You can get the current optimal Trial from your Experiment. For the each metric you can see the max, min and latest value. | # Optimal HPs.
kclient.get_optimal_hyperparameters(name=experiment_name, namespace=namespace) | examples/v1beta1/sdk/cmaes-and-resume-policies.ipynb | kubeflow/katib | apache-2.0 |
Status for the Suggestion objects
You can check the Suggestion object status for more information about resume status.
For Experiment with FromVolume you should be able to check created PVC. | # Get the current Suggestion status for the never resume Experiment.
suggestion = kclient.get_suggestion(name=experiment_never_resume_name, namespace=namespace)
print(suggestion["status"]["conditions"][-1]["message"])
print("-----------------")
# Get the current Suggestion status for the from volume Experiment.
sugge... | examples/v1beta1/sdk/cmaes-and-resume-policies.ipynb | kubeflow/katib | apache-2.0 |
Delete your Experiments
You can delete your Experiments. | kclient.delete_experiment(name=experiment_name, namespace=namespace)
kclient.delete_experiment(name=experiment_never_resume_name, namespace=namespace)
kclient.delete_experiment(name=experiment_from_volume_resume_name, namespace=namespace) | examples/v1beta1/sdk/cmaes-and-resume-policies.ipynb | kubeflow/katib | apache-2.0 |
Representing Data and Engineering Features
Categorical Variables
One-Hot-Encoding (Dummy variables) | import pandas as pd
# The file has no headers naming the columns, so we pass header=None and provide the column names explicitly in "names"
data = pd.read_csv("data/adult.data", header=None, index_col=False,
names=['age', 'workclass', 'fnlwgt', 'education', 'education-num',
... | 02.2 Feature preprocessing, feature selection, interactions.ipynb | amueller/advanced_training | bsd-2-clause |
Checking string-encoded categorical data | data.gender.value_counts()
print("Original features:\n", list(data.columns), "\n")
data_dummies = pd.get_dummies(data)
print("Features after get_dummies:\n", list(data_dummies.columns))
data_dummies.head()
# Get only the columns containing features, that is all columns from 'age' to 'occupation_ Transport-moving'
# ... | 02.2 Feature preprocessing, feature selection, interactions.ipynb | amueller/advanced_training | bsd-2-clause |
Numbers can encode categoricals | # create a dataframe with an integer feature and a categorical string feature
demo_df = pd.DataFrame({'Integer Feature': [0, 1, 2, 1], 'Categorical Feature': ['socks', 'fox', 'socks', 'box']})
demo_df
pd.get_dummies(demo_df)
demo_df['Integer Feature'] = demo_df['Integer Feature'].astype(str)
pd.get_dummies(demo_df) | 02.2 Feature preprocessing, feature selection, interactions.ipynb | amueller/advanced_training | bsd-2-clause |
Binning, Discretization, Linear Models and Trees | from sklearn.linear_model import LinearRegression
from sklearn.tree import DecisionTreeRegressor
X, y = mglearn.datasets.make_wave(n_samples=100)
plt.plot(X[:, 0], y, 'o')
line = np.linspace(-3, 3, 1000)[:-1].reshape(-1, 1)
reg = LinearRegression().fit(X, y)
plt.plot(line, reg.predict(line), label="linear regression"... | 02.2 Feature preprocessing, feature selection, interactions.ipynb | amueller/advanced_training | bsd-2-clause |
Interactions and Polynomials | X_combined = np.hstack([X, X_binned])
print(X_combined.shape)
plt.plot(X[:, 0], y, 'o')
reg = LinearRegression().fit(X_combined, y)
line_combined = np.hstack([line, line_binned])
plt.plot(line, reg.predict(line_combined), label='linear regression combined')
for bin in bins:
plt.plot([bin, bin], [-3, 3], ':', c=... | 02.2 Feature preprocessing, feature selection, interactions.ipynb | amueller/advanced_training | bsd-2-clause |
Univariate Non-linear transformations | rnd = np.random.RandomState(0)
X_org = rnd.normal(size=(1000, 3))
w = rnd.normal(size=3)
X = np.random.poisson(10 * np.exp(X_org))
y = np.dot(X_org, w)
np.bincount(X[:, 0])
bins = np.bincount(X[:, 0])
plt.bar(range(len(bins)), bins, color='w')
plt.ylabel("number of appearances")
plt.xlabel("value")
from sklearn.lin... | 02.2 Feature preprocessing, feature selection, interactions.ipynb | amueller/advanced_training | bsd-2-clause |
Automatic Feature Selection
Univariate statistics | from sklearn.datasets import load_breast_cancer
from sklearn.feature_selection import SelectPercentile
from sklearn.model_selection import train_test_split
cancer = load_breast_cancer()
# get deterministic random numbers
rng = np.random.RandomState(42)
noise = rng.normal(size=(len(cancer.data), 50))
# add noise featu... | 02.2 Feature preprocessing, feature selection, interactions.ipynb | amueller/advanced_training | bsd-2-clause |
Model-based Feature Selection | from sklearn.feature_selection import SelectFromModel
from sklearn.ensemble import RandomForestClassifier
select = SelectFromModel(RandomForestClassifier(n_estimators=100, random_state=42), threshold="median")
select.fit(X_train, y_train)
X_train_l1 = select.transform(X_train)
print(X_train.shape)
print(X_train_l1.sha... | 02.2 Feature preprocessing, feature selection, interactions.ipynb | amueller/advanced_training | bsd-2-clause |
Recursive Feature Elimination | from sklearn.feature_selection import RFE
select = RFE(RandomForestClassifier(n_estimators=100, random_state=42), n_features_to_select=40)
#select = RFE(LogisticRegression(penalty="l1"), n_features_to_select=40)
select.fit(X_train, y_train)
# visualize the selected features:
mask = select.get_support()
plt.matshow(mas... | 02.2 Feature preprocessing, feature selection, interactions.ipynb | amueller/advanced_training | bsd-2-clause |
Sequential Feature Selection | from mlxtend.feature_selection import SequentialFeatureSelector
sfs = SequentialFeatureSelector(LogisticRegression(), k_features=40,
forward=True, scoring='accuracy',cv=5)
sfs = sfs.fit(X_train, y_train)
mask = np.zeros(80, dtype='bool')
mask[np.array(sfs.k_feature_idx_)] = True
plt.... | 02.2 Feature preprocessing, feature selection, interactions.ipynb | amueller/advanced_training | bsd-2-clause |
Exercises
Choose either the Boston housing dataset or the adult dataset from above. Compare a linear model with interaction features against one without interaction features.
Use feature selection to determine which interaction features were most important. | data = pd.read_csv("data/adult.data", header=None, index_col=False,
names=['age', 'workclass', 'fnlwgt', 'education', 'education-num',
'marital-status', 'occupation', 'relationship', 'race', 'gender',
'capital-gain', 'capital-loss', 'hours-per-week... | 02.2 Feature preprocessing, feature selection, interactions.ipynb | amueller/advanced_training | bsd-2-clause |
Ahora vamos a ver una serie de modelos basados en árboles de decisión. Los árboles de decisión son modelos muy intuitivos. Codifican una serie de decisiones del tipo "SI" "ENTONCES", de forma similar a cómo las personas tomamos decisiones. Sin embargo, qué pregunta hacer y cómo proceder a cada respuesta es lo que apren... | from figures import make_dataset
x, y = make_dataset()
X = x.reshape(-1, 1)
plt.figure()
plt.xlabel('Característica X')
plt.ylabel('Objetivo y')
plt.scatter(X, y);
from sklearn.tree import DecisionTreeRegressor
reg = DecisionTreeRegressor(max_depth=5)
reg.fit(X, y)
X_fit = np.linspace(-3, 3, 1000).reshape((-1, 1))
... | notebooks-spanish/18-arboles_y_bosques.ipynb | pagutierrez/tutorial-sklearn | cc0-1.0 |
Un único árbol de decisión nos permite estimar la señal de una forma no paraḿetrica, pero está claro que tiene algunos problemas. En algunas regiones, el modelo muestra un alto sesgo e infra-aprende los datos (observa las regiones planas, donde no predecimos correctamente los datos), mientras que en otras el modelo mue... | from sklearn.datasets import make_blobs
from sklearn.model_selection import train_test_split
from sklearn.tree import DecisionTreeClassifier
from figures import plot_2d_separator
X, y = make_blobs(centers=[[0, 0], [1, 1]], random_state=61526, n_samples=100)
X_train, X_test, y_train, y_test = train_test_split(X, y, ra... | notebooks-spanish/18-arboles_y_bosques.ipynb | pagutierrez/tutorial-sklearn | cc0-1.0 |
Hay varios parámetros que controla la complejidad de un árbol, pero uno que es bastante fácil de entender es la máxima profundidad. Esto limita hasta que nivel se puede afinar particionando el espacio, o, lo que es lo mismo, cuantas reglas del tipo "Si-Entonces" podemos preguntar antes de decidir la clase de un patrón.... | # %matplotlib inline
from figures import plot_tree_interactive
plot_tree_interactive() | notebooks-spanish/18-arboles_y_bosques.ipynb | pagutierrez/tutorial-sklearn | cc0-1.0 |
Los árboles de decisión son rápidos de entrenar, fáciles de entender y suele llevar a modelos interpretables. Sin embargo, un solo árbol de decisión a veces tiende al sobre-aprendizaje. Jugando con el gráfico anterior, puedes ver como el modelo empieza a sobre-entrenar antes incluso de que consiga una buena separación ... | from figures import plot_forest_interactive
plot_forest_interactive() | notebooks-spanish/18-arboles_y_bosques.ipynb | pagutierrez/tutorial-sklearn | cc0-1.0 |
Elegir el estimador óptimo usando validación cruzada | from sklearn.model_selection import GridSearchCV
from sklearn.datasets import load_digits
from sklearn.ensemble import RandomForestClassifier
digits = load_digits()
X, y = digits.data, digits.target
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)
rf = RandomForestClassifier(n_estimators=20... | notebooks-spanish/18-arboles_y_bosques.ipynb | pagutierrez/tutorial-sklearn | cc0-1.0 |
Gradient Boosting
Otro método útil tipo ensemble es el Boosting. En lugar de utilizar digamos 200 estimadores en paralelo, construimos uno por uno los 200 estimadores, de forma que cada uno refina los resultados del anterior. La idea es que aplicando un conjunto de modelos muy simples, se obtiene al final un modelo fin... | from sklearn.ensemble import GradientBoostingRegressor
clf = GradientBoostingRegressor(n_estimators=100, max_depth=5, learning_rate=.2)
clf.fit(X_train, y_train)
print(clf.score(X_train, y_train))
print(clf.score(X_test, y_test)) | notebooks-spanish/18-arboles_y_bosques.ipynb | pagutierrez/tutorial-sklearn | cc0-1.0 |
<div class="alert alert-success">
<b>Ejercicio: Validación cruzada para Gradient Boosting</b>:
<ul>
<li>
Utiliza una búsqueda *grid* para optimizar los parámetros `learning_rate` y `max_depth` de un *Gradient Boosted
Decision tree* para el dataset de los dígitos manuscritos.
</li>
</ul>
<... | from sklearn.datasets import load_digits
from sklearn.ensemble import GradientBoostingClassifier
digits = load_digits()
X_digits, y_digits = digits.data, digits.target
# divide el dataset y aplica búsqueda grid | notebooks-spanish/18-arboles_y_bosques.ipynb | pagutierrez/tutorial-sklearn | cc0-1.0 |
Importancia de las características
Las clases RandomForest y GradientBoosting tienen un atributo feature_importances_ una vez que han sido entrenados. Este atributo es muy importante e interesante. Básicamente, cuantifica la contribución de cada característica al rendimiento del árbol. | X, y = X_digits[y_digits < 2], y_digits[y_digits < 2]
rf = RandomForestClassifier(n_estimators=300, n_jobs=1)
rf.fit(X, y)
print(rf.feature_importances_) # un valor por característica
plt.figure()
plt.imshow(rf.feature_importances_.reshape(8, 8), cmap=plt.cm.viridis, interpolation='nearest') | notebooks-spanish/18-arboles_y_bosques.ipynb | pagutierrez/tutorial-sklearn | cc0-1.0 |
Nonlinear regression with fixed basis functions
Given a set of basis functions $\phi_h(x)$, we represent our function class as $y_{pred}(x;\mathbf{w}) = \sum_h w_h \phi_h(x)$, and want to learn a vector $\mathbf{w}{opt}$ of weights such that $y{pred}(x;\mathbf{w}{opt}) \approx y{true}(x)$ | n_basis_fxns=15
basis_points=np.linspace(xmin,xmax,n_basis_fxns)
basis_fxns = np.empty(n_basis_fxns,dtype=object)
class RBF():
def __init__(self,center,r=1.0):
self.c=center
self.r=r
def __call__(self,x):
return np.exp(-(np.sum((x-self.c)**2) / (2*self.r**2)))
class StepFxn():
def... | notebooks/Gaussian Process tinker.ipynb | maxentile/msm-learn | mit |
Adaptive basis functions
$$y(\mathbf{x}; \mathbf{w}) = \sum_h w_h^{(2)} \text{tanh}\left(
\sum_i w_{hi}^{(1)}x_i + w_{h0}^{(1)}
\right) + w_0^{(2)}$$ | import gptools
# reproducing Figure 1 from: http://mlg.eng.cam.ac.uk/pub/pdf/Ras04.pdf
import numpy as np
import numpy.random as npr
from numpy.linalg import cholesky
from numpy.matlib import repmat
xs = np.linspace(-5,5,1000)
ns = len(xs)
keps=1e-9
m = lambda x: 0.25*x**2
def K_mat(xs_1,xs_2):
diff_mat = repmat... | notebooks/Gaussian Process tinker.ipynb | maxentile/msm-learn | mit |
Sparse Tensor Representation & Conversion
Q1. Convert tensor x into a SparseTensor. | x = tf.constant([[1, 0, 0, 0],
[0, 0, 2, 0],
[0, 0, 0, 0]], dtype=tf.int32)
sp = ...
print(sp.eval()) | programming/Python/tensorflow/exercises/Sparse_Tensors.ipynb | diegocavalca/Studies | cc0-1.0 |
Q2. Investigate the dtype, indices, dense_shape and values of the SparseTensor sp in Q1. | print("dtype:", ...)
print("indices:", ...)
print("dense_shape:", ...)
print("values:", ...) | programming/Python/tensorflow/exercises/Sparse_Tensors.ipynb | diegocavalca/Studies | cc0-1.0 |
Q3. Let's write a custom function that converts a SparseTensor to Tensor. Complete it. | def dense_to_sparse(tensor):
indices = tf.where(tf.not_equal(tensor, 0))
return tf.SparseTensor(indices=indices,
values=..., # for zero-based index
dense_shape=tf.to_int64(tf.shape(tensor)))
# Test
print(dense_to_sparse(x).eval()) | programming/Python/tensorflow/exercises/Sparse_Tensors.ipynb | diegocavalca/Studies | cc0-1.0 |
Q4. Convert the SparseTensor sp to a Tensor using tf.sparse_to_dense. | output = ...
print(output.eval())
print("Check if this is identical with x:\n", x.eval()) | programming/Python/tensorflow/exercises/Sparse_Tensors.ipynb | diegocavalca/Studies | cc0-1.0 |
Q5. Convert the SparseTensor sp to a Tensor using tf.sparse_tensor_to_dense. | output = ...
print(output.eval())
print("Check if this is identical with x:\n", x.eval()) | programming/Python/tensorflow/exercises/Sparse_Tensors.ipynb | diegocavalca/Studies | cc0-1.0 |
Streamfunction and velocity potential from zonal and meridional wind component
windspharm is a Python library developed by
Andrew Dawson which provides an pythonic interface to the pyspharm module, which is basically a bindings to the [spherepack] Fortran library
Installation
1) Download and unpack pyspharm
2) Downlo... | from windspharm.standard import VectorWind
from windspharm.tools import prep_data, recover_data, order_latdim | notebooks/spharm.ipynb | nicolasfauchereau/metocean | unlicense |
usual imports | import os, sys
import pandas as pd
import numpy as np
from numpy import ma
from matplotlib import pyplot as plt
from mpl_toolkits.basemap import Basemap as bm
dpath = os.path.join(os.environ.get('HOME'), 'data/NCEP1') | notebooks/spharm.ipynb | nicolasfauchereau/metocean | unlicense |
defines a function to plot a 2D field map | def plot_field(X, lat, lon, vmin, vmax, step, cmap=plt.get_cmap('jet'), ax=False, title=False, grid=False):
if not ax:
f, ax = plt.subplots(figsize=(10, (X.shape[0] / float(X.shape[1])) * 10))
m.ax = ax
im = m.contourf(lons, lats, X, np.arange(vmin, vmax+step, step), latlon=True, cmap=cmap, extend=... | notebooks/spharm.ipynb | nicolasfauchereau/metocean | unlicense |
load the wind data using xray | import xray; print(xray.__version__)
dset_u = xray.open_dataset(os.path.join(dpath,'uwnd.2014.nc'))
dset_v = xray.open_dataset(os.path.join(dpath,'vwnd.2014.nc'))
dset_u = dset_u.sel(level=200)
dset_v = dset_v.sel(level=200)
dset_u = dset_u.mean('time')
dset_v = dset_v.mean('time')
lats = dset_u['lat'].values
lo... | notebooks/spharm.ipynb | nicolasfauchereau/metocean | unlicense |
Sparse Tensor Representation & Conversion
Q1. Convert tensor x into a SparseTensor. | x = tf.constant([[1, 0, 0, 0],
[0, 0, 2, 0],
[0, 0, 0, 0]], dtype=tf.int32)
sp = tf.SparseTensor(indices=[[0, 0], [1, 2]], values=[1, 2], dense_shape=[3, 4])
print(sp.eval()) | programming/Python/tensorflow/exercises/Sparse_Tensors-Solutions.ipynb | diegocavalca/Studies | cc0-1.0 |
Q2. Investigate the dtype, indices, dense_shape and values of the SparseTensor sp in Q1. | print("dtype:", sp.dtype)
print("indices:", sp.indices.eval())
print("dense_shape:", sp.dense_shape.eval())
print("values:", sp.values.eval()) | programming/Python/tensorflow/exercises/Sparse_Tensors-Solutions.ipynb | diegocavalca/Studies | cc0-1.0 |
Q3. Let's write a custom function that converts a SparseTensor to Tensor. Complete it. | def dense_to_sparse(tensor):
indices = tf.where(tf.not_equal(tensor, 0))
return tf.SparseTensor(indices=indices,
values=tf.gather_nd(tensor, indices) - 1, # for zero-based index
dense_shape=tf.to_int64(tf.shape(tensor)))
# Test
print(dense_to_sparse(x).eva... | programming/Python/tensorflow/exercises/Sparse_Tensors-Solutions.ipynb | diegocavalca/Studies | cc0-1.0 |
Q4. Convert the SparseTensor sp to a Tensor using tf.sparse_to_dense. | output = tf.sparse_to_dense(sparse_indices=[[0, 0], [1, 2]], sparse_values=[1, 2], output_shape=[3, 4])
print(output.eval())
print("Check if this is identical with x:\n", x.eval()) | programming/Python/tensorflow/exercises/Sparse_Tensors-Solutions.ipynb | diegocavalca/Studies | cc0-1.0 |
Q5. Convert the SparseTensor sp to a Tensor using tf.sparse_tensor_to_dense. | output = tf.sparse_tensor_to_dense(s)
print(output.eval())
print("Check if this is identical with x:\n", x.eval()) | programming/Python/tensorflow/exercises/Sparse_Tensors-Solutions.ipynb | diegocavalca/Studies | cc0-1.0 |
5 Link Analysis
5.1 PageRank
5.1.1 Eearly Search Engines and Term Spam
inverted index:
a data structure that makes it easy to find all the palces where that a term given occurs.
term spam:
techniques for fooling search engines.
To combat term spam, Google introduced two innovations:
PageRank was used to simulate... | plt.imshow(plt.imread('./res/fig_5_1.png'))
plt.imshow(plt.imread('./res/eg_5_1.png')) | Mining_of_Massive_Datasets/Link_Analysis/note.ipynb | facaiy/book_notes | cc0-1.0 |
PageRank $v$ simulate random surfers:
start at a random page of all $n$.
$v_i^0 = \frac{1}{n} \quad i = 1, 2, \dotsc, n$.
randomly choose next page linked.
$v^{k+1} = M v^{k}$
give us the distribution of the surfer after $k+1$ stpes. | # eg. 5.1
matrix_5_1 = np.array([
[0, 1/3, 1/3, 1/3],
[1/2, 0, 0, 1/2],
[1, 0, 0, 0],
[0, 1/2, 1/2, 0]
]).T
matrix_5_1
n = matrix_5_1.shape[1]
v = np.ones((n,1)) / n
v
def dist_after_surfing(M, v=None, steps=1):
if v is None:
n... | Mining_of_Massive_Datasets/Link_Analysis/note.ipynb | facaiy/book_notes | cc0-1.0 |
Markov processes:
It is known that the distribution of the surfer approaches a limiting distribution $v$ that satisfies $v = Mv$, provided two conditions are met:
The graph is trongly connnected.
namely, it is possible to get from any node to any other node.
There are no dead ends.
eigenvalue and eigenv... | # eg 5.2
v_ = dist_after_surfing(matrix_5_1, v, 10)
v_
v_ = dist_after_surfing(matrix_5_1, v, 50)
v_
v_ = dist_after_surfing(matrix_5_1, v, 75)
v_ | Mining_of_Massive_Datasets/Link_Analysis/note.ipynb | facaiy/book_notes | cc0-1.0 |
5.1.3 Structure of the Web
Some structures in reality violate the assumptions needed for the Markov-process iteration to converge to a limit. | plt.figure(figsize = (10,10))
plt.imshow(plt.imread('./res/fig_5_2.png')) | Mining_of_Massive_Datasets/Link_Analysis/note.ipynb | facaiy/book_notes | cc0-1.0 |
Two problems we need to avoid by modifing PageRank:
the dead end.
spider traps.
the groups of pages that all have outlinks but they never link to any other pages.
5.1.4 Avoiding Dead Ends
Dead Ends $\to$ $M$ is no longer stochastic, since some of the columns will sum to 0 rather than 1.
If we compute $M^iv$... | # eg 5.3
plt.imshow(plt.imread('./res/fig_5_3.png'))
M = np.array([
[0, 1/3, 1/3, 1/3],
[1/2, 0, 0, 1/2],
[0, 0, 0, 0],
[0, 1/2, 1/2, 0]
]).T
M
dist_after_surfing(M, v, 50) | Mining_of_Massive_Datasets/Link_Analysis/note.ipynb | facaiy/book_notes | cc0-1.0 |
Two Solutions
1. Drop the dead end
recursive deletion of dead ends, and solve the remaining graph $G'$.
then we restore $G$ from $G'$, recursivly.
$$ e = \sum \frac{v_p}{k_p} $$
where $e \in (G - G')$, $p \in G'$ and is the predecessor of $e$, $k$ is the number of successors of $p$ in $G$. | # eg 5.4
plt.imshow(plt.imread('./res/fig_5_4.png'))
M_G = np.array([
[0, 1/3, 1/3, 1/3, 0],
[1/2, 0, 0, 1/2, 0],
[0, 0, 0, 0, 1],
[0, 1/2, 1/2, 0, 0],
[0, 0, 0, 0, 0]
]).T
M_G
from sklearn.preprocessing import normalize
index = [0, 1, 3]
M = M_G.take(index, axis=0).take(... | Mining_of_Massive_Datasets/Link_Analysis/note.ipynb | facaiy/book_notes | cc0-1.0 |
2. modify the process of moving
"taxation"
5.1.5 Spider Traps and Taxation
spider traps:
a set of nodes with no dead ends but no arcs out.
they cause the PageRank calculation to place all the weights within the spider traps. | plt.imshow(plt.imread('./res/fig_5_6.png'))
M = np.array([
[0, 1/3, 1/3, 1/3],
[1/2, 0, 0, 1/2],
[0, 0, 1, 0],
[0, 1/2, 1/2, 0]
]).T
M
np.round(dist_after_surfing(M, steps=50), 3) | Mining_of_Massive_Datasets/Link_Analysis/note.ipynb | facaiy/book_notes | cc0-1.0 |
Solution:
allow each random surfer a small probability of teleporting to a random page.
$$v = \beta M v + (1 - \beta) \frac{e}{n}$$
where $n$ is the number of nodes in $G$, and $e$ is a vector of all 1's. | def dist_using_taxation(M, v=None, beta=1, steps=1):
n = M.shape[1]
if v is None:
v = np.ones((n,1)) / n
e = np.ones(v.shape)
for __ in xrange(steps):
v = beta * M.dot(v) + (1-beta) * e / n
return v
dist_using_taxation(M, beta=0.8, steps=30) | Mining_of_Massive_Datasets/Link_Analysis/note.ipynb | facaiy/book_notes | cc0-1.0 |
Although C gets more than half of the PageRank for itself, the effect has been limited.
Note that for a random surfer, there are three path to move:
follow a link.
teleport to a random page. $\gets$ taxation
goes nowhere. $\gets$ dead ends
Since there will always be some fraction of a surfer operating on the We... | matrix_5_1
import string
df_M = pd.DataFrame(matrix_5_1, index=list(string.uppercase[0:4]), columns=list(string.uppercase[0:4]))
df_M
def compact_representation_of_sparse_matrix(df):
"""It is introduced in Example 5.7"""
degree = df.apply(np.count_nonzero, axis=0)
dest = df.apply(np.nonzero, a... | Mining_of_Massive_Datasets/Link_Analysis/note.ipynb | facaiy/book_notes | cc0-1.0 |
5.2.2 PageRank Iteration Using MapReduce
estimate: $$v' = \beta M v + (1 - \beta) \frac{e}{n}$$
if $v$ is much too large to fit in main memory, we could use the method of triping:
break $M $into stripes and break $v$ into corresponding horizontal stripes.
5.2.3 Use of Combiners to Consolidate the Result Vector
There ... | plt.imshow(plt.imread('./res/fig_5_12.png')) | Mining_of_Massive_Datasets/Link_Analysis/note.ipynb | facaiy/book_notes | cc0-1.0 |
Each task gets $M_{ij}$ and $v_j$.
Thus, $v$ is transmitted over the network $k$ times, but $M$ is sent only once.
The advantage of this approach is:
We can keep both the $v_j$ and $v'i$ in main memory as we process $M{ij}$.
5.2.4 Representing Blocks of the Transition Matrix
for each columns of $M_{ij}$, we need l... | plt.figure(figsize=(10,10))
plt.imshow(plt.imread('./res/fig_5_14.png'))
#todo | Mining_of_Massive_Datasets/Link_Analysis/note.ipynb | facaiy/book_notes | cc0-1.0 |
5.2.5 Other Efficient Approaches to PageRank Iteration
We can assign all the blocks of one row of blocks to a single Map task,
namely, use blocks $M_{i1}$ through $M_{ik}$ and all of $v$ to compute $v'i$.
5.2.6 Exercise
ex 5.2.1
the fraction of 1's should be less than $\frac{log_2 n}{n}$.
ex 5.2.2
略
ex 5.2.3
略
ex 5... | plt.imshow(plt.imread('./res/fig_5_15.png'))
beta = 0.8
M = matrix_5_1
S = ['B', 'D']
e_s = pd.Series(np.zeros(4), index=list(string.uppercase[0:4]))
for s in S:
e_s[s] = 1
e_s
M
print('v = \n{} v \n+ \n{}'.format(beta*M, (1-beta)*e_s/np.sum(e_s))) | Mining_of_Massive_Datasets/Link_Analysis/note.ipynb | facaiy/book_notes | cc0-1.0 |
5.3.3 Using Topic-Sensitive PageRank
Integrate topic-sensitive PageRank into a search engine
Select topics
Pick a teleport set for each topic, and compute the topic-sensitive PageRank vector.
Find a way of determining the topic of a particular search query.
Use the corresponding topic-sensitive PageRank to resp... | plt.figure(figsize=(10,10))
plt.imshow(plt.imread('./res/fig_5_16.png')) | Mining_of_Massive_Datasets/Link_Analysis/note.ipynb | facaiy/book_notes | cc0-1.0 |
Links from Accessible Pages: comments contained spam link in blog or news sites.
5.4.2 Analysis of a Spam Farm
Given: $n$ pages in total, $m$ support pages, $y$ is the PageRank of target page $t$.
then:
the PageRank of each support page:
$$\frac{\beta y}{m} + \frac{1 - \beta}{n}$$
support $x$ is the contribute of al... | beta = 0.85
x_coe = 1 / (1 - beta**2)
c = beta / (1+beta)
print('y = {} x + {} m/n'.format(x_coe, c)) | Mining_of_Massive_Datasets/Link_Analysis/note.ipynb | facaiy/book_notes | cc0-1.0 |
Then to run the LdaModel on it | model = SklLdaModel(num_topics=2, id2word=dictionary, iterations=20, random_state=1)
model.fit(corpus)
model.transform(corpus) | docs/notebooks/sklearn_wrapper.ipynb | ELind77/gensim | lgpl-2.1 |
Integration with Sklearn
To provide a better example of how it can be used with Sklearn, Let's use CountVectorizer method of sklearn. For this example we will use 20 Newsgroups data set. We will only use the categories rec.sport.baseball and sci.crypt and use it to generate topics. | import numpy as np
from gensim import matutils
from gensim.models.ldamodel import LdaModel
from sklearn.datasets import fetch_20newsgroups
from sklearn.feature_extraction.text import CountVectorizer
from gensim.sklearn_integration.sklearn_wrapper_gensim_ldamodel import SklLdaModel
rand = np.random.mtrand.RandomState(1... | docs/notebooks/sklearn_wrapper.ipynb | ELind77/gensim | lgpl-2.1 |
Next, we just need to fit X and id2word to our Lda wrapper. | obj = SklLdaModel(id2word=id2word, num_topics=5, iterations=20)
lda = obj.fit(X) | docs/notebooks/sklearn_wrapper.ipynb | ELind77/gensim | lgpl-2.1 |
Example for Using Grid Search | from sklearn.model_selection import GridSearchCV
from gensim.models.coherencemodel import CoherenceModel
def scorer(estimator, X, y=None):
goodcm = CoherenceModel(model=estimator.gensim_model, texts= texts, dictionary=estimator.gensim_model.id2word, coherence='c_v')
return goodcm.get_coherence()
obj = SklLdaM... | docs/notebooks/sklearn_wrapper.ipynb | ELind77/gensim | lgpl-2.1 |
Example of Using Pipeline | from sklearn.pipeline import Pipeline
from sklearn import linear_model
def print_features_pipe(clf, vocab, n=10):
''' Better printing for sorted list '''
coef = clf.named_steps['classifier'].coef_[0]
print coef
print 'Positive features: %s' % (' '.join(['%s:%.2f' % (vocab[j], coef[j]) for j in np.argso... | docs/notebooks/sklearn_wrapper.ipynb | ELind77/gensim | lgpl-2.1 |
LSI Model
To use LsiModel begin with importing LsiModel wrapper | from gensim.sklearn_integration import SklLsiModel | docs/notebooks/sklearn_wrapper.ipynb | ELind77/gensim | lgpl-2.1 |
Example of Using Pipeline | model = SklLsiModel(num_topics=15, id2word=id2word)
clf = linear_model.LogisticRegression(penalty='l2', C=0.1) # l2 penalty used
pipe = Pipeline((('features', model,), ('classifier', clf)))
pipe.fit(corpus, data.target)
print_features_pipe(pipe, id2word.values())
print(pipe.score(corpus, data.target)) | docs/notebooks/sklearn_wrapper.ipynb | ELind77/gensim | lgpl-2.1 |
Random Projections Model
To use RpModel begin with importing RpModel wrapper | from gensim.sklearn_integration import SklRpModel | docs/notebooks/sklearn_wrapper.ipynb | ELind77/gensim | lgpl-2.1 |
Example of Using Pipeline | model = SklRpModel(num_topics=2)
np.random.mtrand.RandomState(1) # set seed for getting same result
clf = linear_model.LogisticRegression(penalty='l2', C=0.1) # l2 penalty used
pipe = Pipeline((('features', model,), ('classifier', clf)))
pipe.fit(corpus, data.target)
print_features_pipe(pipe, id2word.values())
print(... | docs/notebooks/sklearn_wrapper.ipynb | ELind77/gensim | lgpl-2.1 |
LDASeq Model
To use LdaSeqModel begin with importing LdaSeqModel wrapper | from gensim.sklearn_integration import SklLdaSeqModel | docs/notebooks/sklearn_wrapper.ipynb | ELind77/gensim | lgpl-2.1 |
Example of Using Pipeline | test_data = data.data[0:2]
test_target = data.target[0:2]
id2word = Dictionary(map(lambda x: x.split(), test_data))
corpus = [id2word.doc2bow(i.split()) for i in test_data]
model = SklLdaSeqModel(id2word=id2word, num_topics=2, time_slice=[1, 1, 1], initialize='gensim')
clf = linear_model.LogisticRegression(penalty='l2... | docs/notebooks/sklearn_wrapper.ipynb | ELind77/gensim | lgpl-2.1 |
Setup MPSLib
Setup MPSlib, and select to compute entropy using for example | # Initialize MPSlib using the mps_snesim_tree algorthm, and a simulation grid of size [80,70,1]
#O = mps.mpslib(method='mps_genesim', simulation_grid_size=[80,70,1], n_max_cpdf_count=30, verbose_level=-1)
O = mps.mpslib(method='mps_snesim_tree', simulation_grid_size=[80,70,1], verbose_level=-1)
O.delete_local_files()
O... | scikit-mps/examples/ex_mpslib_entropy.ipynb | ergosimulation/mpslib | lgpl-3.0 |
Plot entropy | fig = plt.figure(figsize=(18, 6))
plt.subplot(1,2,1)
plt.hist(O.SI)
plt.plot(np.array([1, 1])*O.H,[-5,5],'k:')
plt.xlabel('SelfInformation')
plt.title('Entropy = %3.1f' % (O.H))
plt.subplot(1,2,2)
plt.plot(O.SI,'.', label='SI')
plt.plot(np.cumsum(O.SI)/(np.arange(1,1+len(O.SI))),'-',label='H')
plt.legend()
plt.grid(... | scikit-mps/examples/ex_mpslib_entropy.ipynb | ergosimulation/mpslib | lgpl-3.0 |
Entropy as a function of number of conditional data | TI, TI_filename = mps.trainingimages.strebelle(di=4, coarse3d=1)
n_cond_arr = np.array([1,2,4,6,8,12,16,24,32,64])
H=np.zeros(n_cond_arr.size) # entropy
t=np.zeros(n_cond_arr.size) # simulation time
i=0
SI=[]
for n_cond in n_cond_arr:
O = mps.mpslib(method='mps_snesim_tree', simulation_grid_... | scikit-mps/examples/ex_mpslib_entropy.ipynb | ergosimulation/mpslib | lgpl-3.0 |
Now I will create an object that knows how to deal with Martian times and illuminations. | inca = kmaspice.MarsSpicer() | notebooks/blog_post.ipynb | michaelaye/planet4 | isc |
I saved some predefined places and their locations into the code, so that I don't need to remember the coordinates all the time. So let's justify the variable name by actually setting it on top of Inca City: | inca.goto('inca') | notebooks/blog_post.ipynb | michaelaye/planet4 | isc |
By default, when I don't provide a time, the time is set to the current time. In the UTC timezone, that is: | inca.time.isoformat() | notebooks/blog_post.ipynb | michaelaye/planet4 | isc |
To double-check how close we are to spring time in the southern hemisphere on Mars, I need to look at a value called L_s, which is the solar longitude.
This value measures the time of the seasons on Mars as its angular position during its trip around the sun which southern spring being at Ls = 180. | round(inca.l_s, 1) | notebooks/blog_post.ipynb | michaelaye/planet4 | isc |
So, we are pretty close to spring then. But do we already have sunlight in Inca? We should remember that we are in polar areas, where we have darkness for half a year, just like on Earth. Let's have a look what is the local time in Inca: | inca.local_soltime | notebooks/blog_post.ipynb | michaelaye/planet4 | isc |
Right, that's still in the night, so that most likely means that the sun is below the horizon, right? | round(inca.illum_angles.dsolar,1) | notebooks/blog_post.ipynb | michaelaye/planet4 | isc |
Solar angles are measured from the local normal direction, with the sun directly over head being defined as 0. Which means the horizon is at 90 degrees. Hence, this value of 96 means the sun is below the horizon. But it is local night, so we would expect that!
Now comes the magic, let's just advance the time by a coupl... | inca.advance_time_by(7*3600)
round(inca.illum_angles.dsolar) | notebooks/blog_post.ipynb | michaelaye/planet4 | isc |
Oh yes! This is just 2 degrees above the horizon, the sun is lurking over it just a tiny bit. But all you humans that work so much in helping us know what this means, right? Where there is sun, there is energy. And this energy can be used to sublime CO2 gas and create the wonderful fans we are studying.
Let's make this... | inca.advance_time_by(-7*3600) | notebooks/blog_post.ipynb | michaelaye/planet4 | isc |
Now, I will create a loop with 100 elements, and check and write down the time each 10 minutes (= 600 seconds). I save the stuff in 2 new arrays to have it easier to plot things over time. | times = []
angles = []
for i in range(100):
inca.advance_time_by(600)
times.append(inca.local_soltime[3])
angles.append(inca.illum_angles.dsolar) | notebooks/blog_post.ipynb | michaelaye/planet4 | isc |
I'm now importing the pandas library, an amazing toolbox to deal with time-series data. Especially, the plots automatically get nicely formatted time-axes. | import pandas as pd
data = pd.Series(angles, index=times) | notebooks/blog_post.ipynb | michaelaye/planet4 | isc |
I need to switch this notebook to show plots inside this notebook and not outside as an extra window, which is my default: | %pylab inline
data.plot() | notebooks/blog_post.ipynb | michaelaye/planet4 | isc |
Here we see how the sun's angle is developing over time. As expected we see a minimum (i.e. highest sun over horizon) right around noon.
Do you hear the CO2 ice crackling?? ;)
I find it amazing to know that in a couple of hours some of our beloved fans are being created!
Next I wondered how long we already have the su... | times = []
angles = []
for i in range(2000):
inca.advance_time_by(-600)
times.append(inca.time)
angles.append(inca.illum_angles.dsolar)
pd.Series(angles,index=times).plot() | notebooks/blog_post.ipynb | michaelaye/planet4 | isc |
Part B
Print out a famous quote! In the code below, fill out the string variables to contain the name of a famous person, and a quote that they said. | famous_person = ""
their_quote = ""
### BEGIN SOLUTION
### END SOLUTION
print("{}, at age {}, said:\n\n\"{}\"".format(famous_person, favorite_number, their_quote))
assert len(famous_person) > 0
assert len(their_quote) > 0 | assignments/A1/A1_Q1.ipynb | eds-uga/csci1360e-su17 | mit |
Part C
You're working late on a homework assignment and have copied a few lines from a Wikipedia article. In your tired stupor, your copy/paste skills leave something to be desired. Rather than try to force your mouse hand to stop shaking, you figure it's easier to write a small Python program to strip out errant white... | line1 = 'Python supports multiple programming paradigms, including object-oriented, imperative\n'
line2 = ' and functional programming or procedural styles. It features a dynamic type\n'
line3 = ' system and automatic memory management and has a large and comprehensive standard library.\n '
### BEGIN SOLUTION
### EN... | assignments/A1/A1_Q1.ipynb | eds-uga/csci1360e-su17 | mit |
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