diff --git a/.gitignore b/.gitignore index e5651dae..06c61833 100644 --- a/.gitignore +++ b/.gitignore @@ -1,3 +1,8 @@ +# Data +*.csv +*.tar +*.nc + # Prerequisites *.d @@ -39,4 +44,4 @@ build*/ .pydevproject .settings/ .idea/ -/Debug/ \ No newline at end of file +/Debug/ diff --git a/albatross/core/indexing.h b/albatross/core/indexing.h index 76ae72b7..80b17b4e 100644 --- a/albatross/core/indexing.h +++ b/albatross/core/indexing.h @@ -24,8 +24,8 @@ namespace albatross { */ template -std::vector subset(const std::vector &indices, - const std::vector &v) { +inline std::vector subset(const std::vector &indices, + const std::vector &v) { std::vector out(indices.size()); for (std::size_t i = 0; i < static_cast(indices.size()); i++) { out[i] = v[static_cast(indices[i])]; @@ -37,8 +37,8 @@ std::vector subset(const std::vector &indices, * Extract a subset of an Eigen::Vector */ template -Eigen::VectorXd subset(const std::vector &indices, - const Eigen::VectorXd &v) { +inline Eigen::VectorXd subset(const std::vector &indices, + const Eigen::VectorXd &v) { Eigen::VectorXd out(static_cast(indices.size())); for (std::size_t i = 0; i < indices.size(); i++) { out[static_cast(i)] = @@ -52,9 +52,9 @@ Eigen::VectorXd subset(const std::vector &indices, * indices. */ template -Eigen::MatrixXd subset(const std::vector &row_indices, - const std::vector &col_indices, - const Eigen::MatrixXd &v) { +inline Eigen::MatrixXd subset(const std::vector &row_indices, + const std::vector &col_indices, + const Eigen::MatrixXd &v) { Eigen::MatrixXd out(row_indices.size(), col_indices.size()); for (std::size_t i = 0; i < row_indices.size(); i++) { for (std::size_t j = 0; j < col_indices.size(); j++) { @@ -74,8 +74,8 @@ Eigen::MatrixXd subset(const std::vector &row_indices, * columns. */ template -Eigen::MatrixXd symmetric_subset(const std::vector &indices, - const Eigen::MatrixXd &v) { +inline Eigen::MatrixXd symmetric_subset(const std::vector &indices, + const Eigen::MatrixXd &v) { assert(v.rows() == v.cols()); return subset(indices, indices, v); } @@ -84,11 +84,12 @@ Eigen::MatrixXd symmetric_subset(const std::vector &indices, * Extract a subset of an Eigen::DiagonalMatrix */ template -Eigen::DiagonalMatrix +inline Eigen::DiagonalMatrix symmetric_subset(const std::vector &indices, const Eigen::DiagonalMatrix &v) { return subset(indices, v.diagonal()).asDiagonal(); } + } // namespace albatross #endif diff --git a/albatross/covariance_functions/covariance_functions.h b/albatross/covariance_functions/covariance_functions.h index 07b5b408..b33abb41 100644 --- a/albatross/covariance_functions/covariance_functions.h +++ b/albatross/covariance_functions/covariance_functions.h @@ -92,7 +92,8 @@ template struct CovarianceFunction { /* * Creates a covariance matrix given a single vector of * predictors. Element i, j of the resulting covariance - * matrix will hold + * matrix will hold the covariance between quantities + * derived from feature i and feature j. */ template Eigen::MatrixXd symmetric_covariance(const CovarianceFunction &f, diff --git a/albatross/covariance_functions/distance_metrics.h b/albatross/covariance_functions/distance_metrics.h index 30114989..ebcb9540 100644 --- a/albatross/covariance_functions/distance_metrics.h +++ b/albatross/covariance_functions/distance_metrics.h @@ -57,7 +57,16 @@ class AngularDistance : public DistanceMetric { std::string get_name() const override { return "angular_distance"; }; double operator()(const Eigen::VectorXd &x, const Eigen::VectorXd &y) const { - return acos(x.dot(y) / (x.norm() * y.norm())); + // The acos operator doesn't behave well near |1|. acos(1.), for example, + // returns NaN, so here we do some special casing, + double dot_product = x.dot(y) / (x.norm() * y.norm()); + if (dot_product > 1. - 1e-16) { + return 0.; + } else if (dot_product < -1. + 1e-16) { + return M_PI; + } else { + return acos(dot_product); + } } }; @@ -70,6 +79,26 @@ class ScalarDistance : public DistanceMetric { return fabs(x - y); } }; + +template +Eigen::MatrixXd distance_matrix(const DistanceMetrixType &distance_metric, + const std::vector &xs) { + int n = static_cast(xs.size()); + Eigen::MatrixXd D(n, n); + + int i, j; + std::size_t si, sj; + for (i = 0; i < n; i++) { + si = static_cast(i); + for (j = 0; j <= i; j++) { + sj = static_cast(j); + D(i, j) = distance_metric(xs[si], xs[sj]); + D(j, i) = D(i, j); + } + } + return D; +} + } // namespace albatross #endif diff --git a/albatross/covariance_functions/radial.h b/albatross/covariance_functions/radial.h index aeeb392e..1f4fba02 100644 --- a/albatross/covariance_functions/radial.h +++ b/albatross/covariance_functions/radial.h @@ -59,7 +59,7 @@ class SquaredExponential : public RadialCovariance { public: SquaredExponential(double length_scale = 100000., double sigma_squared_exponential = 10.) { - this->params_["length_scale"] = length_scale; + this->params_["squared_exponential_length_scale"] = length_scale; this->params_["sigma_squared_exponential"] = sigma_squared_exponential; }; @@ -78,7 +78,7 @@ class SquaredExponential : public RadialCovariance { int>::type = 0> double operator()(const X &x, const X &y) const { double distance = this->distance_metric_(x, y); - double length_scale = this->params_.at("length_scale"); + double length_scale = this->params_.at("squared_exponential_length_scale"); distance /= length_scale; double sigma = this->params_.at("sigma_squared_exponential"); return sigma * sigma * exp(-distance * distance); @@ -93,7 +93,7 @@ template class Exponential : public RadialCovariance { public: Exponential(double length_scale = 100000., double sigma_exponential = 10.) { - this->params_["length_scale"] = length_scale; + this->params_["exponential_length_scale"] = length_scale; this->params_["sigma_exponential"] = sigma_exponential; }; @@ -112,7 +112,7 @@ class Exponential : public RadialCovariance { int>::type = 0> double operator()(const X &x, const X &y) const { double distance = this->distance_metric_(x, y); - double length_scale = this->params_.at("length_scale"); + double length_scale = this->params_.at("exponential_length_scale"); distance /= length_scale; double sigma = this->params_.at("sigma_exponential"); return sigma * sigma * exp(-fabs(distance)); diff --git a/albatross/covariance_functions/scaling_function.h b/albatross/covariance_functions/scaling_function.h index 30eb5b06..168dc9d5 100644 --- a/albatross/covariance_functions/scaling_function.h +++ b/albatross/covariance_functions/scaling_function.h @@ -78,7 +78,7 @@ template class ScalingTerm : public CovarianceTerm { scaling_function_.set_params(params); } - virtual ParameterStore get_params() const { + virtual ParameterStore get_params() const override { return scaling_function_.get_params(); } diff --git a/albatross/tuning_metrics.h b/albatross/tuning_metrics.h index 7a434c19..00bdea2b 100644 --- a/albatross/tuning_metrics.h +++ b/albatross/tuning_metrics.h @@ -49,20 +49,20 @@ inline double gp_fast_loo_nll(const RegressionDataset &dataset, return negative_log_likelihood(deviations, predictions.covariance); } -inline double loo_nll(const albatross::RegressionDataset &dataset, - albatross::RegressionModel *model) { - auto loo_folds = albatross::leave_one_out(dataset); - return albatross::cross_validated_scores( - albatross::evaluation_metrics::negative_log_likelihood, loo_folds, +inline double loo_nll(const RegressionDataset &dataset, + RegressionModel *model) { + auto loo_folds = leave_one_out(dataset); + return cross_validated_scores( + evaluation_metrics::negative_log_likelihood, loo_folds, model) .sum(); } -inline double loo_rmse(const albatross::RegressionDataset &dataset, - albatross::RegressionModel *model) { - auto loo_folds = albatross::leave_one_out(dataset); - return albatross::cross_validated_scores( - albatross::evaluation_metrics::root_mean_square_error, loo_folds, +inline double loo_rmse(const RegressionDataset &dataset, + RegressionModel *model) { + auto loo_folds = leave_one_out(dataset); + return cross_validated_scores( + evaluation_metrics::root_mean_square_error, loo_folds, model) .mean(); } diff --git a/ci/run_tests.sh b/ci/run_tests.sh index 60eb3b48..dd3b04c3 100755 --- a/ci/run_tests.sh +++ b/ci/run_tests.sh @@ -5,7 +5,7 @@ cd build # Run the long integration tests in release mode so they're fast. cmake -DENABLE_AUTOLINT=ON \ -DCMAKE_BUILD_TYPE=Release -DCMAKE_C_COMPILER="$C_COMPILER" -DCMAKE_CXX_COMPILER="$CXX_COMPILER" ../ -make run_albatross_unit_tests run_inspection_example run_sinc_example run_tune_example -j4 +make run_albatross_unit_tests run_inspection_example run_sinc_example run_tune_example run_temperature_example -j4 make clang-format-all if [[ $(git --no-pager diff --name-only HEAD) ]]; then echo "######################################################" diff --git a/doc/index.rst b/doc/index.rst index f0f9b52f..4c8ba552 100644 --- a/doc/index.rst +++ b/doc/index.rst @@ -19,6 +19,17 @@ Features .. _`Gaussian Process Regression`: http://www.gaussianprocess.org/gpml/chapters/RW2.pdf +********** +Examples +********** + +- :ref:`A One dimensional example using a sinc function. <1d-example>` +- :ref:`An example spatial model for temperature estimation. ` + +.. image:: https://github.com/swift-nav/albatross/raw/akleeman/temperature-example/examples/temperature_example/mean_temperature.png + :align: center + :target: temperature-example.html + ********** Install ********** @@ -63,6 +74,7 @@ and plot the results (though this'll require a numerical python environment), :maxdepth: 1 1d-example + temperature-example ######### diff --git a/doc/temperature-example.rst b/doc/temperature-example.rst new file mode 100644 index 00000000..69a650cf --- /dev/null +++ b/doc/temperature-example.rst @@ -0,0 +1,127 @@ +################### +Temperature Example +################### + +.. _temperature-example: + +-------------- +Introduction +-------------- + +Gaussian processes are quite popular in geostatistics, though they are perhaps more commonly used in `Kriging`_. The idea is very similar to the :ref:`1D Example <1d-example>`, there is some unknown function (in our example it will be temperature as a function of location) and you have noisy observations of the function (from weather stations) which you would like to use to make estimates at new locations. + +.. _`Kriging` : https://en.wikipedia.org/wiki/Kriging + +------------------ +Temperature Data +------------------ + +For this example we'll use the `Global Summary of the Day`_ (GSOD) data to produce an estimate of the average temperature for a given day over the continental United States (CONUS). + +.. _`Global Summary of the Day` : https://data.nodc.noaa.gov/cgi-bin/iso?id=gov.noaa.ncdc:C00516 + +Here are the GSOD observation of average temperature for May 1st, 2018, + +.. image:: https://github.com/swift-nav/albatross/raw/akleeman/temperature-example/examples/temperature_example/observations.png + :align: center + +------------------ +Temperature Model +------------------ + +We're going to build our temperature model to incorporate the following priors about how temperature should be have. + +- Temperature at neighboring locations should be similar. +- There is some non-zero average temperature. +- Temperature decreases with elevation + +To accomplish this we can build a covariance function that is not dissimilar from the one used in the :ref:`1D Example <1d-example>`. +We can start with measurement noise, + +.. code-block:: c + + using Noise = IndependentNoise; + CovarianceFunction noise = {Noise(2.0)}; + +Which will include a term in our model which states that each weather station makes observations of the average temperature which are centered around the true average temperature but with a noise having standard deviation of :math:`2` degrees. + +We can then define a mean value for our field. In reality we might expect that the mean average temperature for a day would vary geographically, for this model we'll simply claim that there is some mean average temperature for all of CONUS, + +.. code-block:: c + + CovarianceFunction mean = {Constant(1.5)}; + +Then as we'd mentioned we'd like to include the concept of temperature decreasing with elevation. To do this we can +create a scaling term which scales the mean value based on the elevation. The + + +.. math:: + + \mbox{elevation_scaling}(h) = 1. + \alpha \left(H - h\right)_{+}. + +Where :math:`\left(\cdot\right)_{+}` could also be written :math:`\mbox{max}(0, \cdot)` and means it returns the +argument if positive and is otherwise :math:`0`. The resulting function will decrease at a rate of :math:`\alpha` +until :math:`h >= H` afterwhich the scaling term will flatten out to a constant value of :math:`1`. By multiplying +this term through with the mean we get a prior which will allow for higher temperatures at low elevations. + +.. code-block:: c + + // Scale the constant temperature value in a way that defaults + // to colder values for higher elevations. + using ElevationScalar = ScalingTerm; + CovarianceFunction elevation_scalar = {ElevationScalar()}; + auto elevation_scaled_mean = elevation_scalar * mean; + +Now we capture the spatial variation by saying that location near +each other in terms of great circle distance will be similar, + +.. code-block:: c + + // The angular distance is equivalent to the great circle distance + using AngularSqrExp = SquaredExponential>; + CovarianceFunction angular_sqrexp = {AngularSqrExp(9e-2, 3.5)}; + +Then add that stations at different elevations will be dissimilar, + +.. code-block:: c + + // Radial distance is the difference in lengths of the X, Y, Z + // vectors, which translates into a difference in height so + // this term means "station at different elevations will be less correlated" + using RadialExp = Exponential>; + CovarianceFunction radial_exp = {RadialExp(15000., 2.5)}; + +These can be combined to get our final covariance function, + +.. code-block:: c + + auto spatial_cov = angular_sqrexp * radial_exp; + auto covariance = elevation_scaled_mean + noise + spatial_cov; + +For the full implementation details see the `example code`_. + +.. _`example code` : https://github.com/swift-nav/albatross/blob/akleeman/temperature-example/examples/temperature_example/temperature_example.cc + +------------------- +Gridded Predictions +------------------- + +Now that we've defined the covariance function we can let ``albatross`` do the rest! + +.. code-block:: c + + auto model = gp_from_covariance(covariance); + model.fit(data); + const auto predictions = model.predict(grid_locations); + +The ``predictions`` hold information about the mean and variance of the resulting estimates. We can look at the mean of the estimates, + +.. image:: https://github.com/swift-nav/albatross/raw/akleeman/temperature-example/examples/temperature_example/mean_temperature.png + :align: center + +and perhaps more interestingly we can also get out the variance, or how confident the model is about its predictions, + +.. image:: https://github.com/swift-nav/albatross/raw/akleeman/temperature-example/examples/temperature_example/sd_temperature.png + :align: center + +Notice that the model is capable of realizing that it's estimates should be trusted less in mountainous regions! diff --git a/examples/CMakeLists.txt b/examples/CMakeLists.txt index 31a783fe..9497ad8f 100644 --- a/examples/CMakeLists.txt +++ b/examples/CMakeLists.txt @@ -71,4 +71,27 @@ add_custom_target( add_dependencies(run_inspection_example inspection_example +) + + +add_executable(temperature_example + EXCLUDE_FROM_ALL + temperature_example/temperature_example.cc +) + +add_dependencies(temperature_example + albatross +) + +target_link_libraries(temperature_example m gflags pthread nlopt) + +add_custom_target( + run_temperature_example ALL + DEPENDS ${example_HEADERS} + COMMAND temperature_example -input ${PROJECT_SOURCE_DIR}/examples/temperature_example/gsod.csv -predict ${PROJECT_SOURCE_DIR}/examples/temperature_example/prediction_locations.csv -output ./test_temperature_predictions.csv -thin 5 + COMMENT "Running temperature_example" +) + +add_dependencies(run_temperature_example + temperature_example ) \ No newline at end of file diff --git a/examples/plot_spatial_predictions.py b/examples/plot_spatial_predictions.py new file mode 100644 index 00000000..72c4ad99 --- /dev/null +++ b/examples/plot_spatial_predictions.py @@ -0,0 +1,52 @@ +import sys +import argparse +import numpy as np +import pandas as pd +import seaborn as sns +import matplotlib.pyplot as plt + +sns.set_style('darkgrid') + + +def create_parser(): + p = argparse.ArgumentParser() + p.add_argument("train") + p.add_argument("predictions") + p.add_argument("--output") + return p + + +if __name__ == "__main__": + + p = create_parser() + args = p.parse_args() + + # read in the training and prediction data + train_path = args.train + predictions_path = args.predictions + print train_path + train_data = pd.read_csv(train_path) + predictions_data = pd.read_csv(predictions_path) + std = np.sqrt(predictions_data['variance'].values) + + fig = plt.figure(figsize=(8, 8)) + n = int(np.sqrt(predictions_data.shape[0])) + truth = predictions_data['prediction'].values.reshape(n, n) + truth_isnan = np.isnan(truth).sum() + truth[truth_isnan] = 0. + plt.pcolormesh(predictions_data['x'].values.reshape(n, n), + predictions_data['y'].values.reshape(n, n), + truth, + vmin=-1., vmax=1., + cmap='coolwarm', + label='truth') + + # Plot the mean + plt.scatter(train_data['x'], + train_data['y'], + c=train_data['target'], + cmap='coolwarm', + vmin=-1., vmax=1., + label='observations') + + plt.show() diff --git a/examples/sinc_example_utils.h b/examples/sinc_example_utils.h new file mode 100644 index 00000000..07eb58d8 --- /dev/null +++ b/examples/sinc_example_utils.h @@ -0,0 +1,175 @@ +/* + * Copyright (C) 2018 Swift Navigation Inc. + * Contact: Swift Navigation + * + * This source is subject to the license found in the file 'LICENSE' which must + * be distributed together with this source. All other rights reserved. + * + * THIS CODE AND INFORMATION IS PROVIDED "AS IS" WITHOUT WARRANTY OF ANY KIND, + * EITHER EXPRESSED OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE IMPLIED + * WARRANTIES OF MERCHANTABILITY AND/OR FITNESS FOR A PARTICULAR PURPOSE. + */ + +#ifndef ALBATROSS_SINC_EXAMPLE_UTILS_H +#define ALBATROSS_SINC_EXAMPLE_UTILS_H + +#include "csv.h" +#include +#include +#include +#include +#include + +#include "core/model.h" +#include "covariance_functions/covariance_functions.h" +#include "models/gp.h" + +#define EXAMPLE_SLOPE_VALUE sqrt(2.) +#define EXAMPLE_CONSTANT_VALUE 3.14159 + +namespace albatross { + +class SlopeTerm : public CovarianceTerm { +public: + SlopeTerm(double sigma_slope = 0.1) { + this->params_["sigma_slope"] = sigma_slope; + }; + + ~SlopeTerm(){}; + + std::string get_name() const { return "slope_term"; } + + double operator()(const double &x, const double &y) const { + double sigma_slope = this->params_.at("sigma_slope"); + return sigma_slope * sigma_slope * x * y; + } +}; +} // namespace albatross + +/* + * Randomly samples n points between low and high. + */ +std::vector random_points_on_line(const int n, const double low, + const double high) { + std::default_random_engine generator; + std::uniform_real_distribution distribution(low, high); + + std::vector xs; + for (int i = 0; i < n; i++) { + xs.push_back(distribution(generator)); + } + return xs; +}; + +/* + * Creates a grid of n points between low and high. + */ +std::vector uniform_points_on_line(const int n, const double low, + const double high) { + std::vector xs; + for (int i = 0; i < n; i++) { + double ratio = (double)i / (double)(n - 1); + xs.push_back(low + ratio * (high - low)); + } + return xs; +}; + +/* + * The noise free function we're attempting to estimate. + */ +double truth(double x) { + return x * EXAMPLE_SLOPE_VALUE + EXAMPLE_CONSTANT_VALUE + 10. * sin(x) / x; +} + +/* + * Create random noisy observations to use as train data. + */ +albatross::RegressionDataset +create_train_data(const int n, const double low, const double high, + const double measurement_noise) { + auto xs = random_points_on_line(n, low, high); + + std::default_random_engine generator; + std::normal_distribution noise_distribution(0., measurement_noise); + + Eigen::VectorXd ys(n); + + for (int i = 0; i < n; i++) { + double noise = noise_distribution(generator); + ys[i] = (truth(xs[i]) + noise); + } + + return albatross::RegressionDataset(xs, ys); +} + +albatross::RegressionDataset read_csv_input(std::string file_path) { + std::vector xs; + std::vector ys; + + io::CSVReader<2> file_in(file_path); + + file_in.read_header(io::ignore_extra_column, "x", "y"); + double x, y; + bool more_to_parse = true; + while (more_to_parse) { + more_to_parse = file_in.read_row(x, y); + if (more_to_parse) { + xs.push_back(x); + ys.push_back(y); + } + } + Eigen::Map eigen_ys(&ys[0], static_cast(ys.size())); + return albatross::RegressionDataset(xs, eigen_ys); +} + +inline bool file_exists(const std::string &name) { + std::ifstream f(name.c_str()); + return f.good(); +} + +void maybe_create_training_data(std::string input_path, const int n, + const double low, const double high, + const double meas_noise) { + /* + * Either read the input data from file, or if it doesn't exist + * generate new input data and write it to file. + */ + if (file_exists(input_path)) { + std::cout << "reading data from : " << input_path << std::endl; + } else { + std::cout << "creating training data and writing it to : " << input_path + << std::endl; + auto data = create_train_data(n, low, high, meas_noise); + std::ofstream train; + train.open(input_path); + train << "x,y" << std::endl; + for (int i = 0; i < static_cast(data.features.size()); i++) { + train << data.features[i] << ", " << data.targets.mean[i] << std::endl; + } + } +} + +void write_predictions_to_csv(const std::string output_path, + const albatross::RegressionModel &model, + const double low, const double high) { + std::ofstream output; + output.open(output_path); + + const int k = 161; + auto grid_xs = uniform_points_on_line(k, low - 2., high + 2.); + + auto predictions = model.predict(grid_xs); + + std::cout << "writing predictions to : " << output_path << std::endl; + output << "x,y,variance,truth" << std::endl; + for (int i = 0; i < k; i++) { + output << grid_xs[i]; + output << "," << predictions.mean[i]; + output << "," << predictions.covariance(i, i); + output << "," << truth(grid_xs[i]); + output << std::endl; + } + output.close(); +} + +#endif diff --git a/examples/temperature_example/gsod.csv b/examples/temperature_example/gsod.csv new file mode 100644 index 00000000..defd7ffb --- /dev/null +++ b/examples/temperature_example/gsod.csv @@ -0,0 +1,2134 @@ +STATION,LAT,LON,ELEV(M),X,Y,Z,TEMP +690150,34.3,-116.167,625.1,-2326258.41903,-4734462.88235,3574338.30297,62.7 +711680,43.733,-96.633,481.5,-533234.975136,-4585482.19146,4387036.40296,60.9 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+749171,35.135,-118.439,1219.5,-2487225.86119,-4592553.48567,3650827.16431,45.9 +749179,36.9,-121.417,72.2,-2661944.45574,-4358056.89354,3808567.69312,53.0 +749483,34.147,-83.561,290.2,592616.71005,-5251028.35058,3560115.85586,62.2 +749484,37.082,-121.597,86.3,-2669260.97207,-4339330.86721,3824709.04065,52.5 +749485,40.554,-124.133,119.2,-2723111.47729,-4017033.2049,4124995.26496,49.3 +749486,39.224,-121.003,961.0,-2548828.33828,-4241459.64407,4012220.09787,52.5 diff --git a/examples/temperature_example/make_gsod_csv.py b/examples/temperature_example/make_gsod_csv.py new file mode 100644 index 00000000..28c7d275 --- /dev/null +++ b/examples/temperature_example/make_gsod_csv.py @@ -0,0 +1,96 @@ +import sys +import gnss +import gzip +import tarfile +import argparse +import progressbar +import numpy as np +import pandas as pd +import seaborn as sns +import matplotlib.pyplot as plt + +from cStringIO import StringIO + +sns.set_style('darkgrid') + + +def create_parser(): + p = argparse.ArgumentParser() + p.add_argument("--input") + p.add_argument("--stations") + p.add_argument("--date", type=np.datetime64, default=np.datetime64('2018-05-01')) + p.add_argument("--output", default='gsod.csv') + return p + + +def read_stations(station_file): + stations = pd.read_csv(station_file) + + good = reduce(np.logical_and, [stations['LAT'].values != 0., + stations['LON'].values != 0., + stations['ELEV(M)'].values > -999., + stations['USAF'].values != '999999', + stations['END'].values >= 20180101, + stations['CTRY'].values == 'US', + stations['LAT'].values >= 25., + stations['LAT'].values <= 50., + stations['LON'].values <= -60., + stations['LON'].values >= -125., + np.logical_not(pd.isnull(stations['STATE'].values)), + np.char.find(stations['STATION NAME'].values.astype('string'), 'BUOY') == -1, + ]) + stations = stations.iloc[good] + + stations = stations[['USAF', 'WBAN', 'LAT', 'LON', 'ELEV(M)']] + ecef = gnss.ecef_from_llh([stations['LAT'].values, + stations['LON'].values, + stations['ELEV(M)'].values]) + for k, v in zip(['X', 'Y', 'Z'], ecef): + stations[k] = v + + stations.drop_duplicates(subset='USAF', inplace=True) + + return stations.set_index('USAF', drop=False) + + +def extract_date(df, date): + return df[df['YEARMODA'] == int(pd.to_datetime(date).strftime('%Y%m%d'))] + + +def get_station_from_member(member): + return member.name.split('-')[0].strip('./') + + +def add_station_info(df, stations): + merged = stations.merge(df, how='inner', left_index=True, right_on='STATION') + return merged.set_index('STATION', drop=False) + + +def iter_data(data_file, station_ids): + pbar = progressbar.ProgressBar() + with tarfile.open(data_file) as tf: + print "Extracting data for required stations" + for member in pbar(tf.getmembers()): + if get_station_from_member(member) in station_ids: + fobj = StringIO(tf.extractfile(member.name).read()) + gzf = gzip.GzipFile(fileobj=fobj) + data_string = StringIO(gzf.read()) + df = pd.read_fwf(data_string) + df = df.rename(columns={'STN---': 'STATION'}) + df['STATION'] = df['STATION'].astype('string') + yield df + + +if __name__ == "__main__": + + p = create_parser() + args = p.parse_args() + + stations = read_stations(args.stations) + observations = [extract_date(df, args.date) + for df in iter_data(args.input, stations['USAF'].values)] + obs = pd.concat(observations) + obs = add_station_info(obs, stations) + + obs = obs[['LAT', 'LON', 'ELEV(M)', 'X', 'Y', 'Z', 'TEMP']] + obs.to_csv(args.output) diff --git a/examples/temperature_example/make_prediction_locations.py b/examples/temperature_example/make_prediction_locations.py new file mode 100644 index 00000000..e8d3d242 --- /dev/null +++ b/examples/temperature_example/make_prediction_locations.py @@ -0,0 +1,64 @@ +""" +Loads elevation data and creates a CSV which can be used to +feed into temperature_example.cc in order to make predictions +at a grid over the earth surface for CONUS. +""" +import os +import sys +import gnss +import urllib2 +import argparse +import numpy as np +import pandas as pd +import xarray as xra + +from cStringIO import StringIO + +_elevation_data_url = "http://research.jisao.washington.edu/data/elevation/elev.0.5-deg.nc" + +def create_parser(): + p = argparse.ArgumentParser(__doc__) + p.add_argument("--input", default=os.path.basename(_elevation_data_url)) + p.add_argument("--output", default='prediction_locations.csv') + return p + +if __name__ == "__main__": + + p = create_parser() + args = p.parse_args() + + if not os.path.exists(args.input): + print("Downloading elevation data to: %s" % args.input) + with open(args.input, 'w') as fout: + web_data = urllib2.urlopen(_elevation_data_url) + fout.write(web_data.read()) + web_data.close() + + print("Loading elevation data from: %s" % args.input) + elev = xra.open_dataset(args.input).isel(time=0)['data'] + # Longitudes in the file are in 0, 360 but we want -180, 180 + elev['lon'] = np.mod(elev['lon'] + 180., 360.) - 180. + + # Select only CONUS + lat_inds = np.logical_and(elev['lat'] >= 25., elev['lat'] <= 50.) + lon_inds = np.logical_and(elev['lon'] >= -125., elev['lon'] <= -60.) + conus = elev.isel(lat=lat_inds, lon=lon_inds) + + # Setup the columns names to match what the c++ code expects. + locations = conus.to_dataframe().reset_index() + locations.rename(columns={'lat': 'LAT', 'lon': 'LON', 'data': 'ELEV(M)'}, + inplace=True) + locations.drop('time', axis=1, inplace=True) + ecef = gnss.ecef_from_llh([locations['LAT'].values, + locations['LON'].values, + locations['ELEV(M)'].values]) + for k, v in zip(['X', 'Y', 'Z'], ecef): + locations[k] = v + + locations['TEMP'] = np.nan + locations['STATION'] = np.arange(locations.shape[0]) + locations.set_index('STATION', inplace=True, drop=False) + locations = locations[['LAT', 'LON', 'ELEV(M)', 'X', 'Y', 'Z', 'TEMP']] + + print("Writing output to: %s" % args.output) + locations.to_csv(args.output) diff --git a/examples/temperature_example/mean_temperature.png b/examples/temperature_example/mean_temperature.png new file mode 100644 index 00000000..a0ca302e Binary files /dev/null and b/examples/temperature_example/mean_temperature.png differ diff --git a/examples/temperature_example/observations.png b/examples/temperature_example/observations.png new file mode 100644 index 00000000..9b949428 Binary files /dev/null and b/examples/temperature_example/observations.png differ diff --git a/examples/temperature_example/plot_temperature_example.py b/examples/temperature_example/plot_temperature_example.py new file mode 100644 index 00000000..b91b8470 --- /dev/null +++ b/examples/temperature_example/plot_temperature_example.py @@ -0,0 +1,156 @@ +import sys +import pyproj +import argparse +import numpy as np +import pandas as pd +import seaborn as sns +import matplotlib.pyplot as plt + +from mpl_toolkits import basemap +from mpl_toolkits.axes_grid1 import make_axes_locatable + +sns.set_style('darkgrid') + +def geographic_distance(lon0, lat0, lon1, lat1, ellps="sphere"): + """ + Computes the distance (in meters) between two points + assuming a particular earth ellipse model. + """ + geod = pyproj.Geod(ellps=ellps) + return geod.inv(lon0, lat0, lon1, lat1)[-1] + + +def bounding_box(lons, lats, pad=0.1, lon_pad=None, lat_pad=None): + + lon_diffs = lons[:, None] - lons + lat_diffs = lats[:, None] - lats + + western_most_ind = np.nonzero(np.all(lon_diffs >= 0., axis=0))[0] + western_most = np.unique(lons[western_most_ind]).item() + eastern_most_ind = np.nonzero(np.all(lon_diffs <= 0., axis=0))[0] + eastern_most = np.unique(lons[eastern_most_ind]).item() + + northern_most_ind = np.nonzero(np.all(lat_diffs <= 0., axis=0))[0] + northern_most = np.unique(lats[northern_most_ind]).item() + southern_most_ind = np.nonzero(np.all(lat_diffs >= 0., axis=0))[0] + southern_most = np.unique(lats[southern_most_ind]).item() + + # count the number of lons greater than and less than each lon + # and take the difference. The longitude (or pair of lons) that + # minimize this help us determine the median. This allows different + # definitions of longitude. + lon_rel_loc = np.abs(np.sum(lon_diffs >= 0., axis=0) - + np.sum(lon_diffs <= 0., axis=0)) + central_lons = lons[lon_rel_loc == np.min(lon_rel_loc)] + # make sure the central two aren't too far apart. + assert np.max(central_lons) - np.min(central_lons) < 90 + median_lon = np.median(central_lons) + + lat_rel_loc = np.abs(np.sum(lat_diffs >= 0., axis=0) - + np.sum(lat_diffs <= 0., axis=0)) + central_lats = lats[lat_rel_loc == np.min(lat_rel_loc)] + median_lat = np.median(central_lats) + + width = geographic_distance(western_most, median_lat, + eastern_most, median_lat) + height = geographic_distance(median_lon, northern_most, + median_lon, southern_most) + if lon_pad is None: + lon_pad = pad * np.abs(eastern_most - western_most) + if lat_pad is None: + lat_pad = pad * np.abs(northern_most - southern_most) + + return {'llcrnrlon': western_most - lon_pad, + 'urcrnrlon': eastern_most + lon_pad, + 'urcrnrlat': northern_most + lat_pad, + 'llcrnrlat': southern_most - lat_pad, + 'lon_0': median_lon, + 'lat_0': median_lat} + + +def get_basemap(lons, lats, pad=0.1, lat_pad=None, lon_pad=None, **kwdargs): + kwdargs['projection'] = kwdargs.get('projection', 'cyl') + kwdargs['resolution'] = kwdargs.get('resolution', 'i') + bm_args = bounding_box(lons, lats, pad=pad, lat_pad=lat_pad, lon_pad=lon_pad) + bm_args.update(kwdargs) + # explicitly specify axis, even if its just the gca. + bm_args['ax'] = bm_args.get('ax', None) + m = basemap.Basemap(**bm_args) + m.drawcoastlines() + m.drawcountries() + m.drawstates() + return m + + +def create_parser(): + p = argparse.ArgumentParser() + p.add_argument("train") + p.add_argument("predictions") +# p.add_argument("--output") + return p + + +if __name__ == "__main__": + + p = create_parser() + args = p.parse_args() + + # read in the training and prediction data + preds = pd.read_csv(args.predictions) + pred_lons = preds['LON'].values + pred_lats = preds['LAT'].values + + df = pd.read_csv(args.train) + lons = df['LON'].values + lats = df['LAT'].values + + norm = plt.Normalize(vmin=df['TEMP'].values.min(), vmax=df['TEMP'].values.max()) + + ncols = np.nonzero(np.diff(preds['LAT'].values) != 0)[0][0] + 1 + nrows = float(preds.shape[0]) / ncols + if not (nrows - int(nrows) == 0.): + raise ValueError("Couldn't infer data shape") + nrows = int(nrows) + + def plot_variable(variable_name, units, **kwdargs): + + fig, axes = plt.subplots(1, 1, figsize=(16, 6)) + axes = np.array(axes).reshape(-1) + + bm = get_basemap(pred_lons, pred_lats, pad=0.05, ax=axes[0]) + + # Here we plot the variable as a transparent mesh. + pred_x, pred_y = bm(pred_lons, pred_lats) + pred_values = preds[variable_name].values + land_values = basemap.maskoceans(pred_lons.reshape(nrows, ncols), + pred_lats.reshape(nrows, ncols), + pred_values.reshape(nrows, ncols), inlands=False) + pm = bm.pcolormesh(pred_x.reshape(nrows, ncols), + pred_y.reshape(nrows, ncols), + land_values.reshape(nrows, ncols), + alpha=0.7, + cmap=plt.get_cmap('coolwarm'), + linewidths=0, zorder=10000, **kwdargs) + + # Then overlay the points where we have observations. + x, y = bm(lons, lats) + sc = bm.scatter(x, y, + c='k', + edgecolor='k', + alpha=0.5, + s=10, cmap=plt.get_cmap('coolwarm'), + norm=norm, linewidths=1, zorder=10000) + + fig.tight_layout() + + divider = make_axes_locatable(axes[0]) + + cax = fig.add_axes([0.92, 0.05, 0.02, 0.7]) + + plt.colorbar(pm, ax=axes[0], cax=cax, label=units) + + + plot_variable('TEMP', "Degrees F") + plt.savefig("mean_temperature.png", norm=norm) + plot_variable('VARIANCE', "Standard Deviation (F)", vmax=3.0) + plt.savefig("sd_temperature.png") diff --git a/examples/temperature_example/prediction_locations.csv b/examples/temperature_example/prediction_locations.csv new file mode 100644 index 00000000..8ef8da98 --- /dev/null +++ b/examples/temperature_example/prediction_locations.csv @@ -0,0 +1,6501 @@ +STATION,LAT,LON,ELEV(M),X,Y,Z,TEMP 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b/examples/temperature_example/reproduce_temperature_example.sh @@ -0,0 +1,25 @@ +#!/bin/bash -x + +if [ ! -f ./gsod_2018.tar ]; then + wget ftp://ftp.ncdc.noaa.gov/pub/data/gsod/2018/gsod_2018.tar +fi + +if [ ! -f ./ish-history.csv ]; then + wget ftp://ftp.ncdc.noaa.gov/pub/data/gsod/ish-history.csv +fi + +if [ ! -f ./elev.0.5-deg.nc ]; then + wget http://research.jisao.washington.edu/data/elevation/elev.0.5-deg.nc +fi + +python make_gsod_csv.py --input ./gsod_2018.tar --stations ./isd-history.csv --output ./gsod.csv --date "2018-05-01" +python make_prediction_locations.py --input elev.0.5-deg.nc --output ./prediction_locations.csv + +cd ../../ +mkdir -p build +cd build +cmake ../ +make temperature_example + +./examples/temperature_example -input ../examples/temperature_example/gsod.csv -predict ../examples/temperature_example/prediction_locations.csv -output ./predictions.csv +python ../examples/temperature_example/plot_temperature_example.py ../examples/temperature_example/gsod.csv ./predictions.csv diff --git a/examples/temperature_example/sd_temperature.png b/examples/temperature_example/sd_temperature.png new file mode 100644 index 00000000..6db4d0fa Binary files /dev/null and b/examples/temperature_example/sd_temperature.png differ diff --git a/examples/temperature_example/temperature_example.cc b/examples/temperature_example/temperature_example.cc new file mode 100644 index 00000000..c7e16879 --- /dev/null +++ b/examples/temperature_example/temperature_example.cc @@ -0,0 +1,88 @@ +/* + * Copyright (C) 2018 Swift Navigation Inc. + * Contact: Swift Navigation + * + * This source is subject to the license found in the file 'LICENSE' which must + * be distributed together with this source. All other rights reserved. + * + * THIS CODE AND INFORMATION IS PROVIDED "AS IS" WITHOUT WARRANTY OF ANY KIND, + * EITHER EXPRESSED OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE IMPLIED + * WARRANTIES OF MERCHANTABILITY AND/OR FITNESS FOR A PARTICULAR PURPOSE. + */ + +#include "evaluate.h" +#include "gflags/gflags.h" +#include "temperature_example_utils.h" +#include "tune.h" +#include + +DEFINE_string(input, "", "path to csv containing input data."); +DEFINE_string(predict, "", "path to csv containing prediction locations."); +DEFINE_string(output, "", "path where predictions will be written in csv."); +DEFINE_string(thin, "", "path where predictions will be written in csv."); + +int main(int argc, char *argv[]) { + gflags::ParseCommandLineFlags(&argc, &argv, true); + + using namespace albatross; + + std::cout << "Reading the input data." << std::endl; + auto data = read_temperature_csv_input(FLAGS_input, std::stoi(FLAGS_thin)); + std::cout << "Using " << data.features.size() << " data points" << std::endl; + + std::cout << "Defining the model." << std::endl; + // Measurement Noise + using Noise = IndependentNoise; + CovarianceFunction noise = {Noise(2.0)}; + + // A Constant temperature value + CovarianceFunction mean = {Constant(1.5)}; + + // Scale the constant temperature value in a way that defaults + // to colder values for higher elevations. + using ElevationScalar = ScalingTerm; + CovarianceFunction elevation_scalar = {ElevationScalar()}; + auto elevation_scaled_mean = elevation_scalar * mean; + + // Radial distance is the difference in lengths of the X, Y, Z + // locations, which translates into a difference in height so + // this term means "station at different elevations will be less correlated" + using RadialExp = Exponential>; + CovarianceFunction radial_exp = {RadialExp(15000., 2.5)}; + + // The angular distance is equivalent to the great circle distance + using AngularSqrExp = SquaredExponential>; + CovarianceFunction angular_sqrexp = {AngularSqrExp(9e-2, 3.5)}; + + // We multiply the angular and elevation covariance terms. To justify this + // think of the extremes. If two stations are really far apart, regardless + // of their elevation they should be decorrelated. Similarly if two stations + // are close but are at extremely different elevations they should be + // decorrelated. + auto spatial_cov = angular_sqrexp * radial_exp; + + auto covariance = elevation_scaled_mean + noise + spatial_cov; + auto model = gp_from_covariance(covariance); + + // These parameters are that came from tuning the model to the leave + // one out negative log likelihood. + ParameterStore params = { + {"elevation_scaling_center", 3965.98}, + {"elevation_scaling_factor", 0.000810492}, + {"exponential_length_scale", 28197.6}, + {"squared_exponential_length_scale", 0.0753042}, + {"sigma_constant", 1.66872}, + {"sigma_exponential", 2.07548}, + {"sigma_independent_noise", 1.8288}, + {"sigma_squared_exponential", 3.77329}, + }; + model.set_params(params); + + std::cout << "Training the model." << std::endl; + model.fit(data); + + auto predict_features = read_temperature_csv_input(FLAGS_predict, 1).features; + std::cout << "Going to predict at " << predict_features.size() << " locations" + << std::endl; + write_predictions(FLAGS_output, predict_features, model); +} diff --git a/examples/temperature_example/temperature_example_utils.h b/examples/temperature_example/temperature_example_utils.h new file mode 100644 index 00000000..b5c8c605 --- /dev/null +++ b/examples/temperature_example/temperature_example_utils.h @@ -0,0 +1,156 @@ +/* + * Copyright (C) 2018 Swift Navigation Inc. + * Contact: Swift Navigation + * + * This source is subject to the license found in the file 'LICENSE' which must + * be distributed together with this source. All other rights reserved. + * + * THIS CODE AND INFORMATION IS PROVIDED "AS IS" WITHOUT WARRANTY OF ANY KIND, + * EITHER EXPRESSED OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE IMPLIED + * WARRANTIES OF MERCHANTABILITY AND/OR FITNESS FOR A PARTICULAR PURPOSE. + */ + +#ifndef ALBATROSS_TEMPERATURE_EXAMPLE_UTILS_H +#define ALBATROSS_TEMPERATURE_EXAMPLE_UTILS_H + +#include "csv.h" +#include +#include +#include +#include +#include + +#include "core/model.h" +#include "covariance_functions/covariance_functions.h" +#include "models/gp.h" + +namespace albatross { + +/* + * Holds the information about a single station which + * is used as the FeatureType for our Gaussian process. + */ +struct Station { + int id; + double lat; + double lon; + double height; + Eigen::Vector3d ecef; + + bool operator==(const Station &rhs) const { return (ecef == rhs.ecef); } + + template void serialize(Archive &archive) { + archive(id, lat, lon, height, ecef); + } +}; + +/* + * Provides an interface which maps the Station.ecef + * field to an arbitrary DistanceMetric defined on Eigen + * vectors. + */ +template +class StationDistance : public DistanceMetricType { +public: + StationDistance(){}; + + std::string get_name() const { + std::ostringstream oss; + oss << "station_" << DistanceMetricType::get_name(); + return oss.str(); + }; + + ~StationDistance(){}; + + double operator()(const Station &x, const Station &y) const { + return DistanceMetricType::operator()(x.ecef, y.ecef); + }; +}; + +class ElevationScalingFunction : public albatross::ScalingFunction { +public: + ElevationScalingFunction(double center = 1000., double factor = 3.5 / 300) { + this->params_["elevation_scaling_center"] = center; + this->params_["elevation_scaling_factor"] = factor; + }; + + std::string get_name() const { return "elevation_scaled"; } + + double operator()(const Station &x) const { + // This is the negative orientation rectifier function which + // allows lower elevations to have a higher variance. + double center = this->params_.at("elevation_scaling_center"); + return 1. + + this->params_.at("elevation_scaling_factor") * + fmax(0., (center - x.height)); + } +}; + +albatross::RegressionDataset +read_temperature_csv_input(std::string file_path, int thin = 5) { + std::vector features; + std::vector targets; + + io::CSVReader<8> file_in(file_path); + + file_in.read_header(io::ignore_extra_column, "STATION", "LAT", "LON", + "ELEV(M)", "X", "Y", "Z", "TEMP"); + + bool more_to_parse = true; + int count = 0; + while (more_to_parse) { + double temperature; + Station station; + more_to_parse = file_in.read_row( + station.id, station.lat, station.lon, station.height, station.ecef[0], + station.ecef[1], station.ecef[2], temperature); + if (more_to_parse && count % thin == 0) { + features.push_back(station); + targets.push_back(temperature); + } + count++; + } + Eigen::Map eigen_targets(&targets[0], + static_cast(targets.size())); + return albatross::RegressionDataset(features, eigen_targets); +} + +inline bool file_exists(const std::string &name) { + std::ifstream f(name.c_str()); + return f.good(); +} + +void write_predictions(const std::string output_path, + const std::vector features, + const albatross::RegressionModel &model) { + + std::ofstream ostream; + ostream.open(output_path); + ostream << "STATION,LAT,LON,ELEV(M),X,Y,Z,TEMP,VARIANCE" << std::endl; + + std::size_t n = features.size(); + std::size_t count = 0; + for (const auto &f : features) { + ostream << std::to_string(f.id); + ostream << ", " << std::to_string(f.lat); + ostream << ", " << std::to_string(f.lon); + ostream << ", " << std::to_string(f.height); + ostream << ", " << std::to_string(f.ecef[0]); + ostream << ", " << std::to_string(f.ecef[1]); + ostream << ", " << std::to_string(f.ecef[2]); + + std::vector one_feature = {f}; + const auto pred = model.predict(one_feature); + + ostream << ", " << std::to_string(pred.mean[0]); + ostream << ", " << std::to_string(std::sqrt(pred.covariance(0, 0))); + ostream << std::endl; + if (count % 1000 == 0) { + std::cout << count + 1 << "/" << n << std::endl; + } + count++; + } +} + +} //namespace albatross +#endif diff --git a/python/albatross_environment.yml b/python/albatross_environment.yml index a6e23ba5..202d7add 100644 --- a/python/albatross_environment.yml +++ b/python/albatross_environment.yml @@ -1,6 +1,6 @@ name: albatross dependencies: -- python=3.6 +- python=3.4 - numpy - scipy - matplotlib diff --git a/python/create_environment.sh b/python/create_environment.sh index 7094d3ca..aa9ec958 100755 --- a/python/create_environment.sh +++ b/python/create_environment.sh @@ -1,5 +1,4 @@ #!/bin/bash -conda create -n albatross python=3.6 +conda env create --file ./albatross_environment.yml source activate albatross -pip install -U -r ./requirements.txt diff --git a/tests/test_serialize.cc b/tests/test_serialize.cc index 415b7709..099baf62 100644 --- a/tests/test_serialize.cc +++ b/tests/test_serialize.cc @@ -241,7 +241,8 @@ class UnfitGaussianProcess RepresentationType create() const override { auto gp = std::make_unique("custom_name"); - gp->set_param("length_scale", log(2.)); + const auto keys = map_keys(gp->get_params()); + gp->set_param(keys[0], log(2.)); return std::move(gp); } @@ -260,7 +261,8 @@ class FitGaussianProcess auto dataset = make_toy_linear_data(); auto gp = std::make_unique("custom_name"); - gp->set_param("length_scale", log(2.)); + const auto keys = map_keys(gp->get_params()); + gp->set_param(keys[0], log(2.)); gp->fit(dataset); return std::move(gp); }