EnvironmentSTUDIO¶

EnvironmentSTUDIO flow (es-flow for short) is a library for analysing and modeling atmospheric and marine boundary layers.

While es-flow can be used for any turbulent boundary layer analysis, its main focus is for wind and tidal site characterisation - generating the ‘best fit’ of analytical models to measured velocity data.

A key strength of es-flow is the adem. This extremely robust method allows users to:

determine detailed turbulence information from instruments like LiDAR

characterise turbulence and shear beyond tip height of even the biggest offshore wind turbines

characterise coherent structure in turbulence, crucially important for fatigue loading in wind turbines.

Atmospheric Boundary Layer PSD determined with es-flow.

Aims¶

The es-flow library provides: [1]

Parameterised profiles
- Mean Velocity (using power law, logarithmic law, MOST or Lewkowicz relations)
- Mean Veer (Using Monin-Obukhov approach)
- Reynolds Stress u'w' (using Lewkowicz relations)
- Reynolds Stress u'u', u'v', u'w', v'v', v'w', w'w' (using the adem)
- Spectra Sij (using Kaimal, von Karman)
- Spectra Sij (using adem)
- Integral turbulent intensity and lengthscale I, l
Best fit parameter sets
- To describe the above profiles analytically (given measured velocity data from an instrument).

In future, generation of artificial flow fields for simulation purposes might be considered. This would overlap with - or replace - utilities like TurbSim to produce, for example:

.wnd fields input to BEM or FVM models like Bladed, FAST and TurbineGRID
Inlet boundary conditions for DES or LES codes

Atmospheric Boundary Layer velocity profile, fitted with es-flow.

Uses¶

At Octue, es-flow is used to:

Provide a basis for developing and validating new processes, like the adem, for characterising Atmospheric Boundary Layers.

Process LiDAR and ADCP datasets from raw instrument files.

Apply windowed analyses to time series data, for flow characterisation.

Generate load cases for FAST, Bladed and our own TurbineGRID aerodynamic wind turbine analysis tools.

We’d like to hear about your use case. Please get in touch!

We use the GitHub Issue Tracker to manage bug reports and feature requests.

Analytical Models¶

Velocity Relations¶

es-flow uses a range of different velocity relations, so you can choose which is preferable. Fitting different profiles returns a metric of accuracy; but this isn’t the be-all and end-all. Always choose which formulation best represents the physics in play!

Power Law¶

Power law

Logarithmic¶

Log law

MOST¶

Most law

Lewkowicz¶

Lewkowicz 1982, modified by P&M. Include the Reynolds Stress profile

Veer Relations¶

Monin obukhov¶

Spectral Relations¶

Kaimal¶

Attached-Detached Eddy Method¶

Describe ADEM here.

Examples¶

Here, we look at example use cases for the library, and show how to achieve them in python and C++. Many of these are copied straight from the unit test cases, so you can always check there to see how everything hooks up.

Warning

To plot the figures in the examples, we use (in python) octue’s sdk, which includes plotly, or the fledgling C++ plotting library (also by this author) cpplot, either of which you’ll need to install yourself - or use your preferred plotting library (e.g. matplotlib).

Obtaining a velocity profile¶

Given a set of vertical coordinates z_i and a set of input parameters for an analytical model, how can we determine the corresponding mean velocity profile?

#include <Eigen/Dense>
#include <Eigen/Core>
#include <unsupported/Eigen/AutoDiff>

#include "relations/velocity.h"

using namespace es;

int main(const int argc, const char **argv) {

    // Basic boundary layer parameters
    double pi_coles = 0.42;
    double kappa = 0.41;
    double u_inf = 20.0;
    double shear_ratio = 23.6;
    double delta = 1000.0;

    // Get velocity at height z, where z is a simple double scalar
    double z_scalar = 1.0;
    double speed1 = lewkowicz_speed(z_scalar, pi_coles, kappa, u_inf, shear_ratio, delta);
    std::cout << "checked scalar double operation (U = " << speed1 << " m/s)" << std::endl;

    // Get velocity at a range of heights z
    double low = 1;
    double high = 100;
    int n_bins = 10;
    VectorXd z = VectorXd::LinSpaced(n_bins, low, high);
    VectorXd speed = lewkowicz_speed(z, pi_coles, kappa, u_inf, shear_ratio, delta);
    std::cout << "checked VectorXd operation: "<< speed.transpose() << std::endl;

    return 0;
}

import numpy as np
import es

def main():

    // Basic test parameters
    pi_coles = 0.42
    kappa = 0.41
    u_inf = 20.0
    shear_ratio = 23.6
    delta = 1000.0

    // Check that it works for a z value scalar
    z = 10.0
    speed = es.relations.lewkowicz_speed(z, pi_coles, kappa, u_inf, shear_ratio, delta)
    print('checked scalar operation (U = ', speed, 'm/s)')

    // Check that it works for a numpy array input (vertically spaced z)
    low = 1
    high = 100
    n_bins = 10
    z = np.linspace(low, high, n_bins)
    speed = es.relations.lewkowicz_speed(z, pi_coles, kappa, u_inf, shear_ratio, delta)
    print('checked array operation:', speed)

    return

Fitting a velocity profile¶

Imagine we have a vertical profile of velocity u(z), determined by an instrument such as a vertical LiDAR in VAD mode.

Say there are 30 data points, spaced 10m apart vertically. In reality, each data point is an ensemble of many thousands of doppler velocity readings, from a region of vertical space above and below the z coordinate, known as ‘bins’.

We wish to determine the parameter set for an analytical profile that best characterises the atmosphere at that point in time. Importantly:

We may need to fix some of the parameters, to help constrain the solver or because we know them already.
The better our first guess, the quicker the algorithm will converge, and the more likely it is to find a sensible answer.

Under the hood, es-flow uses a Levenberg-Marquadt solution to find the best fit (`Google's amazing ceres-solver library <>`_ is used for this). The gnarly details are wrapped for ease of use, and you can provide an initial guess and fix certain parameters.

#include <Eigen/Dense>
#include <Eigen/Core>
#include "fit.h"
#include "relations/velocity.h"
#include "definitions.h"

using namespace es;

int main(const int argc, const char **argv) {

    // 'True' profile parameters
    double pi_coles = 0.42;
    double kappa = KAPPA_VON_KARMAN;
    double u_inf = 20;
    double shear_ratio = 23.6;
    double delta_c = 1000;

    // Simulate measured data by taking the true profile and adding noise
    Eigen::ArrayXd z = Eigen::ArrayXd::LinSpaced(40, 1, 400);
    Eigen::ArrayXd u_original(40);
    Eigen::ArrayXd u_noisy(40);
    Eigen::ArrayXd u_fitted(40);
    u_original = lewkowicz_speed(z, pi_coles, kappa, u_inf, shear_ratio, delta_c);
    u_measured = u_original + ArrayXd::Random(40) / 4;
    std::cout << z.transpose() << std::endl <<std::endl;
    std::cout << u_measured.transpose() << std::endl <<std::endl;

    // Fit to find the value of parameters.
    // NB you can constrain different parameters, and use values other than the default,
    // see the docs for fit_lewkowicz_speed.
    Eigen::Array<double, 5, 1> fitted = fit_lewkowicz_speed(z, u_measured);
    u_fitted = lewkowicz_speed(z, fitted(0), fitted(1), fitted(2), fitted(3), fitted(4));

    // Sum of squares error, for exact and fitted. They should be similar, with fitted being lower.
    double lsq_error_noisy = pow(u_original-u_measured, 2.0).sum();
    double lsq_error_fitted = pow(u_fitted-u_measured, 2.0).sum();
    std::cout << "Sqd error (correct - noisy): " << lsq_error_noisy << std::endl;
    std::cout << "Sqd error (fitted - noisy) (should be lower): " << lsq_error_fitted << std::endl;

    return 0;
}

import numpy as np
import es

def main():

    # WARNING - THIS IS WHAT I WANT, NOT WHAT I HAVE
    # (I'm using this section to sketch a future object oriented python API out!)

    // Simulate measured data by taking a true profile and adding noise
    pi_coles = 0.42
    kappa = 0.41
    delta = 1000.0
    u_inf = 20.0
    shear_ratio = 23.6
    z = np.linspace(1, 400, 40)
    true_speed = es.relations.lewkowicz_speed(z, pi_coles, kappa, u_inf, shear_ratio, delta)
    measured_speed = true_speed + 3 * (np.random(40) - 0.5)

    // Make an initial guess and help the solver by constraining boundary layer thickness and setting the von karman constant
    initial_guess = np.array([0.5, 0.41, np.amax(measured_speed), 20, 1000)
    fix_params = numpy.array([0, 1, 0, 0, 1], dtype=bool)

    // Run the fitting process
    prof = es.LewkowiczProfile()
    prof.fit(z, measured_speed, initial_guess, fit_params)
    print(prof.params)

    return

Smearing and de-smearing¶

Say we have an instrument like a vertical profiling LiDAR, which takes measurements from a volume, rather than a point. If we capture a profile (e.g. of velocity computed by the VAD technique), each point is the average velocity in a vertical ‘bin’. However, if the shear (du/dz) changes through that bin, then the average velocity is biased… strictly speaking, the instrument applies a filter that changes the recorded velocity profile.

In order to:

compare like-for like when validating against another instrument like a met-mast,
correctly determine parameters for an analytic fit to the measurements and
post-process measured velocity data to de-filter it,

we need to be able to smear an analytically generated profile in the same way that measuring it with an instrument would.

Applying smear to a velocity profile¶

For a general timeseries signal, or an image, etc, this is done by convolution - the following python script (you can copy/paste into a jupyter notebook to see it live) shows the basics, in this case a sin(x) signal being smeared out, as if measured by an instrument whose viewport is 90 degrees wide:

import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
x = np.linspace(1, 720, 720)
sig = np.sin((x*2*3.14159/360))

# The kernel is a 'box filter'. It's like taking an average over a 'bin' of width 90 degrees on the x axis.
ker = np.ones(90)
ker = ker/sum(ker)

convolved = np.convolve(sig, ker, 'same')

fig, ax = plt.subplots(1, 1)
ax.plot(x,sig)
ax.plot(x,convolved)
ax.set_xlabel('X')
ax.set_ylabel('Amplitude')

Do you see the problem at the ends? For our use cases, we can’t ignore errors near the endpoints. Sigh.

This is solved for you by es-flow, which integrates analytical profiles over a specified vertical range, or ‘bin’. At present, we implement a top hat filter, which is pretty representative of the way in which LiDAR and SODAR units bin their measurements. Please feed back if it’d be helpful to have other (or custom) kernel shapes!

#include <Eigen/Dense>
#include <Eigen/Core>
#include <unsupported/Eigen/AutoDiff>

#include "relations/velocity.h"
#include "utilities/smear.h"

using namespace es;

int main(const int argc, const char **argv) {

    // Basic boundary layer parameters
    double pi_coles = 0.42;
    double kappa = 0.41;
    double u_inf = 20.0;
    double shear_ratio = 23.6;
    double delta = 1000.0;

    // Bin size (m in the z direction)
    double bin_size = 10;

    // Get 'correct' and 'smeared' to compare
    Eigen::ArrayXd z = Eigen::ArrayXd::LinSpaced(40, 1, 400);
    Eigen::ArrayXd speed = lewkowicz_speed(z, pi_coles, kappa, u_inf, shear_ratio, delta);
    Eigen::ArrayXd speed_smeared = lewkowicz_speed_smeared(z, bin_size, pi_coles, kappa, u_inf, shear_ratio, delta);

    std::cout << "Actual wind speed: " << speed.transpose() << std::endl;
    std::cout << "Wind speed measured with a binning instrument (es-flow): " << speed_smeared.transpose() << std::endl;

    return 0;
}

import numpy as np
import es

def main():

    # Basic boundary layer parameters
    pi_coles = 0.42
    kappa = 0.41
    u_inf = 20.0
    shear_ratio = 23.6
    delta = 1000.0

    # Bin size (m in the z direction)
    bin_size = 10

    # Get 'correct' and 'smeared' to compare
    z = np.linspace(1, 400, 40)
    speed = es.relations.lewkowicz_speed(z, pi_coles, kappa, u_inf, shear_ratio, delta)
    speed_smeared = es.relations.lewkowicz_speed_smeared(z, pi_coles, kappa, u_inf, shear_ratio, delta)

    print('Actual wind speed:', speed)
    print('Wind speed measured with a binning instrument (es-flow):', speed_smeared)

    return

De-smearing a measured profile¶

OK, so lets say we have measured profile data. We know our instrument has smeared the actual profile somewhat, and we want to correct for this.

Argh, but we can’t! De-smearing is equivalent to a deconvolution. Not only is this not guaranteed to be numerically stable, but the problem isn’t well conditioned for the case where the data points are spaced further apart from the bins… We’d need to interpolate the measured signal to a higher spatial resolution, deconvolve then interpolate back down. That’s subject to significant error, since noise/spikes/artifacts in some vertical locations pollute their neighbours.

Never fear! Once you’re fitted an analytical profile to the noisy data, es-flow makes it simple to determine a correction for the measured data.

#include <Eigen/Dense>
#include <Eigen/Core>
#include <unsupported/Eigen/AutoDiff>

#include "relations/velocity.h"
#include "utilities/smear.h"

using namespace es;

int main(const int argc, const char **argv) {

    /* First, fit an analytic profile to your data... see "Fitting a velocity profile" to get the following:
     * u_original
     * u_noisy
     * fitted_params
     * u_fitted
     */

    // Use the difference between the analytical distribution and its smeared equivalent to correct the data
    Eigen::ArrayXd u_fitted_smeared = lewkowicz_speed_smeared(z, bin_size, fitted(0), fitted(1), fitted(2), fitted(3), fitted(4));
    Eigen::ArrayXd corrector = u_fitted - u_fitted_smeared;
    Eigen::ArrayXd u_measured_corrected = u_noisy + corrector;

    std::cout << "Measured wind speed: " << u_measured.transpose() << std::endl;
    std::cout << "Postprocessed (de-smeared) measurements: " << u_measured_corrected.transpose() << std::endl;

    return 0;
}

import numpy as np
import es

def main():

    # First, fit an analytic profile to your data... see "Fitting a velocity profile" to get the following:
    # u_original
    # u_noisy
    # fitted_params
    # u_fitted

    # Use the difference between the analytical distribution and its smeared equivalent to correct the data
    u_fitted_smeared = lewkowicz_speed_smeared(z, bin_size, fitted[0], fitted[1], fitted[2], fitted[3], fitted[4])
    corrector = u_fitted - u_fitted_smeared
    u_measured_corrected = u_noisy + corrector

    print('Measured wind speed:', u_measured);
    print('Postprocessed (de-smeared) measurements:', u_measured_corrected)

    return

Getting profile derivatives¶

OK, so you fitted a profile to experimental data and have the parameter set that best represents the atmosphere at that time. But you’re a smart cookie who’s calculating other complex relations, and you also need the derivative with respect to height.

Central differencing? No… there’s a much more robust and accurate way. We simply use automatic differentiation:

#include <Eigen/Dense>
#include <Eigen/Core>
#include <unsupported/Eigen/AutoDiff>

#include "relations/velocity.h"

using namespace es;
using namespace Eigen;

int main(const int argc, const char **argv) {

    typedef Eigen::AutoDiffScalar<Eigen::VectorXd> ADScalar;
    ADScalar ads_z;
    ADScalar ads_speed;
    VectorXd dspeed_dz;
    dspeed_dz.setZero(n_bins);

    for (int k = 0; k < n_bins; k++) {
        ads_z.value() = z[k];
        ads_z.derivatives() = Eigen::VectorXd::Unit(1, 0);
        ads_speed = power_law_speed(ads_z, u_ref, z_ref, alpha);
        dspeed_dz[k] = ads_speed.derivatives()[0];
    }

    std::cout << "speed = ["     << speed.transpose()     << "];" << std::endl;
    std::cout << "dspeed_dz = [" << dspeed_dz.transpose() << "];" << std::endl;

    return 0;
}

# WARNING - I'm afraid no API for this has been created in python yet. TODO!
def main():
    return

Obtaining a spectral profile¶

The Atmospheric Boundary Layer has a turbulent spectrum which varies with height. At each height in a spectral profile, the amplitude of the spectrum varies with wavenumber ( frequency). There are also six terms in a turbulent spectrum S_i_j (not 9, since the tensor is symmetric, i.e. S_1_2 = S_2_1).

Warning

You’d expect a spectral profile to be a tensor with dimension nz x nf x 6. But, we don’t do that… instead we actually return 6 nz x nf arrays.

Yes, we know this is a hassle. Why? Two reasons: - It’s actually bloody annoying doing tensors with Eigen, because their tensor library is undocumented and very feature-light in terms of indexing (it’s an unsupported extension, which I firmly believe whould be part of core), so C++ users can expect some unnecessarily heavy syntax if you try. What a drag. Let’s see what happens in the next few releases.

Pybind doesn’t bind ``Eigen::Tensor``s. Sure, I could fork it and add tensors (this issue, open at the time of writing, gives some hints) but would rather be working on core features here. If a contributor wants to do the work of sorting pybind to work with ``Eigen::Tensor``s then I’ll happily update at this end.

#include <Eigen/Dense>
#include <Eigen/Core>
#include <unsupported/Eigen/AutoDiff>

#include "relations/velocity.h"

using namespace es;

int main(const int argc, const char **argv) {

    // Boundary layer parameters (full ADEM set)
    double pi_coles = 0.42;
    double kappa = 0.41;
    double u_inf = 20.0;
    double shear_ratio = 23.6;
    double delta = 1000.0;
    double beta = 0.0;
    double zeta = 0.0;
    Eigen::ArrayXd parameters = Eigen::ArrayXd(7);
    parameters << pi_coles, kappa, u_inf, shear_ratio, delta, beta, zeta;

    // Set z at which you want the spectra
    Eigen::ArrayXd z = Eigen::VectorXd::LinSpaced(40, 1, 400);

    // Set the frequency range in Hz you want
    Eigen::ArrayXd f = Eigen::VectorXd::LinSpaced(100, 0.01, 20);

    // Allocate output arrays to contain the spectral tensor
    Eigen::ArrayXXd spectrum_1_1 = Eigen::ArrayXXd(z.cols(), f.cols());
    Eigen::ArrayXXd spectrum_1_2 = Eigen::ArrayXXd(z.cols(), f.cols());
    Eigen::ArrayXXd spectrum_1_3 = Eigen::ArrayXXd(z.cols(), f.cols());
    Eigen::ArrayXXd spectrum_2_2 = Eigen::ArrayXXd(z.cols(), f.cols());
    Eigen::ArrayXXd spectrum_2_3 = Eigen::ArrayXXd(z.cols(), f.cols());
    Eigen::ArrayXXd spectrum_3_3 = Eigen::ArrayXXd(z.cols(), f.cols());

    // Calculate the spectra
    adem_spectra(
        z,
        f,
        parameters,
        spectrum_1_1,
        spectrum_1_2,
        spectrum_1_3,
        spectrum_2_2,
        spectrum_2_3,
        spectrum_3_3
        );

    // Printing to the command line sucks. Let's do something beautiful...


    return 0;
}

import numpy as np
import es

def main():

    // Basic test parameters
    pi_coles = 0.42
    kappa = 0.41
    u_inf = 20.0
    shear_ratio = 23.6
    delta = 1000.0

    // Check that it works for a z value scalar
    z = 10.0
    speed = es.relations.lewkowicz_speed(z, pi_coles, kappa, u_inf, shear_ratio, delta)
    print('checked scalar operation (U = ', speed, 'm/s)')

    // Check that it works for a numpy array input (vertically spaced z)
    low = 1
    high = 100
    n_bins = 10
    z = np.linspace(low, high, n_bins)
    speed = es.relations.lewkowicz_speed(z, pi_coles, kappa, u_inf, shear_ratio, delta)
    print('checked array operation:', speed)

    return

Fitting a turbulent spectrum to LiDAR data¶

Using the Spectral relations provided by the Attached-Detached Eddy Method relation_adem, we can fit the spectrum generated in the ADEM process to a partial spectrum obtainable from LiDAR. The spectrum obtainable from LiDAR is of course band limited, so we fit to the valid part of the LiDAR spectrum.

#include <Eigen/Dense>
#include <Eigen/Core>

#include "relations/velocity.h"
#include "relations/spectra.h"

using namespace es;

int main(const int argc, const char **argv) {

    // Create simulated 'measured' dataset (see 'Obtaining a spectral profile', above)
    // whose bandwidth goes up to 3Hz, with a noise up to 20% of magnitude applied to the 'true' spectra
    double pi_coles = 1.19;
    double kappa = 0.41;
    double u_inf = 20.0;
    double shear_ratio = 28.1;
    double delta = 1000.0;
    double beta = 1.45;
    double zeta = 2.18;
    Eigen::ArrayXd parameters = Eigen::ArrayXd(7);
    parameters << pi_coles, kappa, u_inf, shear_ratio, delta, beta, zeta;
    Eigen::ArrayXd z = Eigen::VectorXd::LinSpaced(40, 1, 500);
    true_u = lewkowicz_speed(z, pi_coles, kappa, u_inf, shear_ratio, delta_c);
    measured_u = true_u + ArrayXd::Random(40) / 4;
    Eigen::ArrayXd f_measured = Eigen::VectorXd::LinSpaced(100, 0.01, 3);
    Eigen::ArrayXd true_u(40);
    Eigen::ArrayXd measured_u(40);
    Eigen::ArrayXXd true_spectrum_1_1 = Eigen::ArrayXXd(z.cols(), f.cols());
    Eigen::ArrayXXd true_spectrum_1_2 = Eigen::ArrayXXd(z.cols(), f.cols());
    Eigen::ArrayXXd true_spectrum_1_3 = Eigen::ArrayXXd(z.cols(), f.cols());
    Eigen::ArrayXXd true_spectrum_2_2 = Eigen::ArrayXXd(z.cols(), f.cols());
    Eigen::ArrayXXd true_spectrum_2_3 = Eigen::ArrayXXd(z.cols(), f.cols());
    Eigen::ArrayXXd true_spectrum_3_3 = Eigen::ArrayXXd(z.cols(), f.cols());
    adem_spectra(
        z,
        f,
        parameters,
        true_spectrum_1_1,
        true_spectrum_1_2,
        true_spectrum_1_3,
        true_spectrum_2_2,
        true_spectrum_2_3,
        true_spectrum_3_3
    );
    Eigen::ArrayXXd measured_spectrum_1_1 = true_spectrum_1_1 * (Eigen::ArrayXXd::Random(z.cols(), f.cols()) * 0.4 + 1);
    Eigen::ArrayXXd measured_spectrum_1_2 = true_spectrum_1_2 * (Eigen::ArrayXXd::Random(z.cols(), f.cols()) * 0.4 + 1);
    Eigen::ArrayXXd measured_spectrum_1_3 = true_spectrum_1_3 * (Eigen::ArrayXXd::Random(z.cols(), f.cols()) * 0.4 + 1);
    Eigen::ArrayXXd measured_spectrum_2_2 = true_spectrum_2_2 * (Eigen::ArrayXXd::Random(z.cols(), f.cols()) * 0.4 + 1);
    Eigen::ArrayXXd measured_spectrum_2_3 = true_spectrum_2_3 * (Eigen::ArrayXXd::Random(z.cols(), f.cols()) * 0.4 + 1);
    Eigen::ArrayXXd measured_spectrum_3_3 = true_spectrum_3_3 * (Eigen::ArrayXXd::Random(z.cols(), f.cols()) * 0.4 + 1);

    // We can use the velocity to fit most of the parameters in the model, so do that first (most robust)
    // Here, we set the default fixed parameters (von karman constant and boundary layer thickness).
    Eigen::Array<double, 5, 1> fitted_params_u;
    Eigen::Array<bool, 5, 1> fixed_params_u;
    fitted_params_u << 0.5, KAPPA_VON_KARMAN, measured_u.maxCoeff();, 20, 1000;
    fixed_params_u << false, true, false, false, true;
    fit_lewkowicz_speed(z, measured_u, fixed_params_u, fitted_params_u, true);

    // We use those, plus beta=0, zeta=0 (fully equilibrium boundary layer) as an initial guess to the spectrum
    // fit - keeping the ones we've already defined fixed.
    Eigen::Array<double, 7, 1> fitted_params_s;
    Eigen::Array<bool, 7, 1> fixed_params_s;
    fitted_params_s <<
        fitted_params_u(0),
        fitted_params_u(1),
        fitted_params_u(2),
        fitted_params_u(3),
        fitted_params_u(4),
        0.0,
        0.0;
    fixed_params_s << true, true, true, true, true, false, false;
    fit_adem_spectra(
        z,
        measured_spectrum_1_1,
        measured_spectrum_1_2,
        measured_spectrum_1_3,
        measured_spectrum_2_2,
        measured_spectrum_2_3,
        measured_spectrum_3_3,
        fixed_params_u,
        fitted_params_u,
        true
    );
    std::cout << "Fitted spectral parameters:" << std::endl;
    std::cout << fitted_params.transpose() << std::endl;

}

# WARNING - I'm afraid no API for this has been created in python yet. TODO!
def main():
    return

File Formats¶

Add file format details here.

Installation¶

Third party library installation¶

Intel MKL¶

Attention

If you don’t wish to use Intel MKL, or need to build for a non-intel architecture, please contact Octue.

Download the Intel MKL library packages. Click on the icon and follow installation instructions. You’ll need the administrator password.

The tools are installed in /opt/intel/, the include directory is /opt/intel/include.

Intel TBB¶

Attention

If you don’t wish to use Intel TBB, or need to build for a non-intel architecture, please contact Octue.

TBB is installable via brew.::: brew install tbb

Download the Intel TBB library packages. Click on the icon and follow installation instructions, ensuring that the TBBROOT environment variable is set. You’ll need the administrator password.

The tools are installed in /opt/intel/, the include directory is /opt/intel/include.

Follow the Intel TBB instructions, ensuring that the TBBROOT environment variable is set.

matio¶

Building from source is possible using instructions on the matio home page, although unwieldy. The next major release of matio should bring CMake to the party, whereupon we’ll add that to the build system transparently (downloading and building it if not found).

In the meantime, you’ll most likely have success with a brew formula, although `check this issue<>`_ if you experience runtime problems with HDF5 loading the signature files. ::: brew install libmatio

Please contact Octue for Linux installation help.

Please contact Octue for Windows installation help.

ceres-solver, eigen and glog¶

Google’s ceres-solver also depends on glog and eigen, so we get three for the price of one.::: brew install homebrew/science/ceres-solver

Please contact Octue for Linux installation help.

Please contact Octue for Windows installation help.

Third party build requirements¶

Attention

These dependencies are only required if you’re building es-flow from source.

cxxopts¶

To build es-flow, cxxopts must be placed alongside es-flow. From the es-flow root directory:

cd ../thirdparty
git clone https://github.com/jarro2783/cxxopts

Then using cmake to build es-flow will find the headers correctly.

Please contact Octue for Linux installation help.

Please contact Octue for Windows installation help.

NumericalIntegration¶

To build es-flow, NumericalIntegration must be placed alongside es-flow. From the es-flow root directory:

Then using cmake to build es-flow will find the headers correctly.

Please contact Octue for Linux installation help.

Please contact Octue for Windows installation help.

Turbulence¶

es-flow is aimed at characterising shear, veer and turbulence in Atmospheric and Marine Boundary Layers. The concepts of shear and veer are well known in the wind industry, but their closely relate cousin, turbulence, is more of a mystery.

For a thorough understanding of turbulence in the ABL, a lengthy academic career is required. But, for the less patient among us, a few notes, recommended readings and resources are made available here - specific to the wind and tidal stream industries.

Coherent Structures: Notes on coherent ctructures - an explanation and exploration of this author’s pet subject, with some extremely pretty pictures.
Turbulent Effects (Wind): The “Turbulence Selector (Wind)” - a review of the many, varied ways in which turbulence can affect plant and operations in the wind industry.
Turbulent Effects (Tidal): The “Turbulence Selector (Tidal)” - the same, but for the tidal stream industry.

Coherent Structures¶

TODO

Turbulent Effects (Wind)¶

Turbulence has a wide range of effects on wind plant and operations. To help understand how turbulence impacts the industry, we put together an ‘effects selector’.

TODO - refer to the poster.

The Turbulent Effects Selector¶

The selector links: (D) design considerations, (S) turbulent scales, (E) physical effects and (N) the nature of the effect. Hover your pointer over the chart. Whichever label you hover over is linked to related issues: red items affect the item; green items are affected by it.

Turbulent effects selector (Wind).

Turbulent Effects (Tidal)¶

Turbulence has a wide range of effects on tidal stream plant and operations. The Turbulence in Marine Environments (TiME) project resulted in guidance for the tidal stream power industry, giving a comprehensive review of:

Techniques for measuring turbulence in tidal streams.
Characterisation of turbulence (including a description of several of the relations in es-flow).
Different turbulent effects that impact operations.

The Turbulent Effects Selector¶

One output of the TiME project was the “turbulent effects selector”. The selector links: (D) design considerations, (S) turbulent scales, (E) physical effects and (N) the nature of the effect. Hover your pointer over the chart. Whichever label you hover over is linked to related issues: red items affect the item; green items are affected by it.

Turbulent effects selector (Tidal).

License¶

Octue offers free academic licensing for es-flow as well as a commercial subscription. Please contact tom@octue.com for details.

Third Party Libraries¶

es-flow includes or is linked against the following third party libraries:

matio¶

A library for reading and writing MAT files.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.

Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.

THIS SOFTWARE IS PROVIDED BY CHRISTOPHER C. HULBERT ‘‘AS IS’’ AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL CHRISTOPHER C. HULBERT OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

ceres-solver¶

Ceres Solver is licensed under the New BSD license, whose terms are as follows.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
Neither the name of Google Inc., nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

This software is provided by the copyright holders and contributors “AS IS” and any express or implied warranties, including, but not limited to, the implied warranties of merchantability and fitness for a particular purpose are disclaimed. In no event shall Google Inc. be liable for any direct, indirect, incidental, special, exemplary, or consequential damages (including, but not limited to, procurement of substitute goods or services; loss of use, data, or profits; or business interruption) however caused and on any theory of liability, whether in contract, strict liability, or tort (including negligence or otherwise) arising in any way out of the use of this software, even if advised of the possibility of such damage.

Eigen¶

Eigen is licensed under the Mozilla Public License v2.

NumericalIntegration¶

An extension library for Eigen that allows numerical integration, used under the Mozilla Public License v2.

cumtrapz¶

cumtrapz.h header file utility for numerical integration is adapted from The Biomechanical Toolkit.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.

Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.

Neither the name(s) of the copyright holders nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS “AS IS” AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

cumsum¶

cxxopts¶

An argument parser for C++11 under the MIT license.

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the “Software”), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

FindMKL¶

The Cmake system uses an implementation of FindMKL pulled from pytorch:

From PyTorch:

Copyright (c) 2016- Facebook, Inc (Adam Paszke) Copyright (c) 2014- Facebook, Inc (Soumith Chintala) Copyright (c) 2011-2014 Idiap Research Institute (Ronan Collobert) Copyright (c) 2012-2014 Deepmind Technologies (Koray Kavukcuoglu) Copyright (c) 2011-2012 NEC Laboratories America (Koray Kavukcuoglu) Copyright (c) 2011-2013 NYU (Clement Farabet) Copyright (c) 2006-2010 NEC Laboratories America (Ronan Collobert, Leon Bottou, Iain Melvin, Jason Weston) Copyright (c) 2006 Idiap Research Institute (Samy Bengio) Copyright (c) 2001-2004 Idiap Research Institute (Ronan Collobert, Samy Bengio, Johnny Mariethoz)

From Caffe2:

Caffe2 uses a copyright model similar to Caffe: each contributor holds copyright over their contributions to Caffe2. The project versioning records all such contribution and copyright details. If a contributor wants to further mark their specific copyright on a particular contribution, they should indicate their copyright solely in the commit message of the change when it is committed.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
Neither the names of Facebook, Deepmind Technologies, NYU, NEC Laboratories America and IDIAP Research Institute nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS “AS IS” AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

Version History¶

Origins¶

EnvironmentSTUDIO flow began as an internal tool at Octue, for characterising turbulence at tidal power sites. It was originated in MATLAB (then called the ‘Flow Characterisation Suite’), and grew incrementally.

Unfortunately, MATLAB is extremely unwieldy if deployed in production, requiring either (complicated and badly limited) cross compilation, expensive cloud sever licenses or build and deployment with MATLAB’s 3Gb+ runtime library (prohibitively big for practical use in cloud services).

As the move was made toward object orientation, and usage increased toward requiring a production version that could be deployed without requiring expensive MATLAB licenses, EnvironmentSTUDIO flow project was started in C++.

Gradually, capability is being ported from MATLAB (the original repo having been subsumed within this project and now being progressively deprecated).

0.1.0¶

This version bump was funded by AURA via the University of Hull. The objective of the work was to validate capabilities using measured data, and the library was refactored to allow this work to happen in collaboration with Univ. Hull and the Offshore Renewable Energy Catapult.

New Features¶

Scope of library reduced to preclude specific instrument data readers, and focus on environmental characterisation.
Library API consolidated.
ADEM functionality ported from legacy MATLAB and tested to work with C++.
Added plotting routines (using cpplot).
Documentation and build systems implemented and settled.
Google Test used to create test harness for the majority of the library.
Turbulent effects selector included into the documentation for viewing by teh Offshore Renewable Energy Catapult

Backward Incompatible API Changes¶

Entire API altered to reflect change in scope; will be much more stable going forward.

Bug Fixes & Minor Changes¶

n/a

0.0.1¶

Initial library release - development version. Highly unstable!

The work to develop this stable release and CI flow undertaken to support research funded by AURA via the University of Hull (see upcoming version 0.1.0).

New Features¶

C++ based flow library, with cmake build system
Large chunks of WIP for 0.1.0 release, included here because the work in progress was used to generate the doc builds.
Octue’s legacy es-flow MATLAB library (to be deprecated)
Outline documentation using ReadTheDocs
Autodoc build system (with automated build for releases in travis-ci)

Backward Incompatible API Changes¶

n/a (Initial release)

Bug Fixes & Minor Changes¶

n/a (Initial Release)

Bibliography¶

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S. Agarwal, N. Snavely, S. M. Seitz and R. Szeliski, Bundle Adjustment in the Large, Proceedings of the European Conference on Computer Vision, pp. 29–42, 2010.

[Bjorck]

A. Bjorck, Numerical Methods for Least Squares Problems, SIAM, 1996

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D. C. Brown, A solution to the general problem of multiple station analytical stereo triangulation, Technical Report 43, Patrick Airforce Base, Florida, 1958.

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R. H. Byrd, J. Nocedal, R. B. Schanbel, Representations of Quasi-Newton Matrices and their use in Limited Memory Methods, Mathematical Programming 63(4):129–-156, 1994.

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R.H. Byrd, R.B. Schnabel, and G.A. Shultz, Approximate solution of the trust region problem by minimization over two dimensional subspaces, Mathematical programming, 40(1):247–263, 1988.

[Chen]

Y. Chen, T. A. Davis, W. W. Hager, and S. Rajamanickam, Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate, TOMS, 35(3), 2008.

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A.R. Conn, N.I.M. Gould, and P.L. Toint, Trust region methods, Society for Industrial Mathematics, 2000.

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G.H. Golub and V. Pereyra, The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate, SIAM Journal on numerical analysis, 10(2):413–432, 1973.

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R.I. Hartley & A. Zisserman, Multiview Geometry in Computer Vision, Cambridge University Press, 2004.

[KanataniMorris]

K. Kanatani and D. D. Morris, Gauges and gauge transformations for uncertainty description of geometric structure with indeterminacy, IEEE Transactions on Information Theory 47(5):2017-2028, 2001.

[Keys]

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[KushalAgarwal]

A. Kushal and S. Agarwal, Visibility based preconditioning for bundle adjustment, In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2012.

[Kanzow]

C. Kanzow, N. Yamashita and M. Fukushima, Levenberg–Marquardt methods with strong local convergence properties for solving nonlinear equations with convex constraints, Journal of Computational and Applied Mathematics, 177(2):375–397, 2005.

[Levenberg]

K. Levenberg, A method for the solution of certain nonlinear problems in least squares, Quart. Appl. Math, 2(2):164–168, 1944.

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Na Li and Y. Saad, MIQR: A multilevel incomplete qr preconditioner for large sparse least squares problems, SIAM Journal on Matrix Analysis and Applications, 28(2):524–550, 2007.

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K. Madsen, H.B. Nielsen, and O. Tingleff, Methods for nonlinear least squares problems, 2004.

[Mandel]

J. Mandel, On block diagonal and Schur complement preconditioning, Numer. Math., 58(1):79–93, 1990.

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D.W. Marquardt, An algorithm for least squares estimation of nonlinear parameters, J. SIAM, 11(2):431–441, 1963.

[Mathew]

T.P.A. Mathew, Domain decomposition methods for the numerical solution of partial differential equations, Springer Verlag, 2008.

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S.G. Nash and A. Sofer, Assessing a search direction within a truncated newton method, Operations Research Letters, 9(4):219–221, 1990.

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J. Nocedal, Updating Quasi-Newton Matrices with Limited Storage, Mathematics of Computation, 35(151): 773–782, 1980.

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J. Nocedal & S. Wright, Numerical Optimization, Springer, 2004.

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S. S. Oren, Self-scaling Variable Metric (SSVM) Algorithms Part II: Implementation and Experiments, Management Science, 20(5), 863-874, 1974.

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C. J. F. Ridders, Accurate computation of F’(x) and F’(x) F”(x), Advances in Engineering Software 4(2), 75-76, 1978.

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A. Ruhe and P.Å. Wedin, Algorithms for separable nonlinear least squares problems, Siam Review, 22(3):318–337, 1980.

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Y. Saad, Iterative methods for sparse linear systems, SIAM, 2003.

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B. Triggs, P. F. Mclauchlan, R. I. Hartley & A. W. Fitzgibbon, Bundle Adjustment: A Modern Synthesis, Proceedings of the International Workshop on Vision Algorithms: Theory and Practice, pp. 298-372, 1999.

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Library API¶

Class Hierarchy¶

- Namespace es
  - Struct InvalidEddyTypeException
  - Struct LewkowiczSpeedResidual
  - Struct NotImplementedException
  - Struct PowerLawSpeedResidual
  - Class AdemData
  - Class BasicLidar
  - Class Bins
  - Template Class DeficitFunctor
  - Class EddySignature
  - Template Class Profile
  - Template Class Reader
  - Class VelocityProfile
  - Enum file_type_check_level
  - Enum timeseries_check_level
- Namespace utilities
  - Class CubicSplineInterpolant
  - Class LinearInterpolant
- Class spectra

File Hierarchy¶

- Directory source
  - Directory adem
    - File adem.h
    - File biot_savart.h
    - File signature.h
  - Directory io
    - File readers.h
    - File variable_readers.h
    - File variable_writers.h
  - Directory relations
    - File spectra.cpp
    - File spectra.h
    - File stress.h
    - File veer.h
    - File velocity.h
  - Directory utilities
    - File conv.h
    - File cumsum.h
    - File cumtrapz.h
    - File filter.h
    - File integration.h
    - File interp.h
    - File smear.h
    - File tensors.h
    - File trapz.h
  - File data_types.h
  - File definitions.h
  - File exceptions.h
  - File fit.h
  - File flow.h
  - File how_to.h
  - File main.cpp
  - File profile.cpp
  - File profile.h

Full API¶

Namespaces¶

Namespace cpplot¶

Namespace Eigen¶

Namespace es¶

Contents

Classes
Enums
Functions

Classes¶

Enums¶

Functions¶

Namespace std¶

Namespace utilities¶

Contents

Classes
Functions
Typedefs

Classes¶

Functions¶

Typedefs¶

Classes and Structs¶

Struct InvalidEddyTypeException¶

Defined in File exceptions.h

Inheritance Relationships¶

Base Type¶

public exception

Struct Documentation¶

struct InvalidEddyTypeException : public exception¶

Public Functions

const char *what() const¶

Public Members

std::string message = "Unknown eddy type. Eddy type string must be one of 'A', 'B1', 'B2', 'B3' or 'B4'."¶

Struct LewkowiczSpeedResidual¶

Defined in File fit.h

Struct Documentation¶

struct LewkowiczSpeedResidual¶

Cost functor for fitting lewkowicz speed profiles.

Implements operator() as required by ceres-solver. Allows some parameters to be fixed.

Internal use only (see fit_lewkowicz_speed).

Public Functions

LewkowiczSpeedResidual(double z, double u, const Array5b &fixed_params, const Array5d &initial_params)¶

Construct the cost functor.

Parameters, where supplied in input initial_params and masked in input fixed_params are in this order:

pi_coles = params[0]
kappa = params[1]
u_inf = params[2]
shear_ratio = params[3]
delta_c = params[4]

Parameters

z: Observation data point, vertical coordinate in m
u: Observation data point, horizontal speed in m/s
fixed_params: Eigen::Array<bool, 5, 1>, logical mask, true where the parameter is fixed, false where it is allowed to vary
initial_params: Eigen::Array<double, 5, 1> containing initial parameter values. These are used where fixed parameters are specified

template <typename T> bool operator()(T const *const *parameters, T *residual) const¶

Struct NotImplementedException¶

Defined in File exceptions.h

Inheritance Relationships¶

Base Type¶

public exception

Struct Documentation¶

struct NotImplementedException : public exception¶

Public Functions

const char *what() const¶

Public Members

std::string message = "Not yet implemented"¶

Struct PowerLawSpeedResidual¶

Defined in File fit.h

Struct Documentation¶

struct PowerLawSpeedResidual¶

Cost functor for fitting power law speed profiles.

Templated for automatic differentiation.

Internal use only (see fit_power_law_speed).

Public Functions

PowerLawSpeedResidual(double z, double u, double z_ref = 1.0, double u_ref = 1.0)¶

template <typename T> bool operator()(const T *const alpha, T *residual) const¶

Class AdemData¶

Defined in File adem.h

Class Documentation¶

class AdemData¶

Data container for ADEM input parameters and results.

Upcoming refactor

The AdemData class is treated as a struct, whose contents are updated by a number of functions… But, the functions operating on this should be refactored into class methods. That way, appropriate validation of the contents can be undertaken prior to application of each function.

This refactor is captured in issue #34.

Public Functions

void load(std::string file_name, bool print_var = true)¶

Load data from a *.mat file containing eddy signature data.

Parameters

file_name: File name (including relative or absolute path)
print_var: Boolean, default true. Print variables as they are read in (not advised except for debugging!)

void save(std::string filename)¶

Save eddy signature data to a *.mat file.

Parameters

filename: File name (including relative or absolute path)

Public Members

std::vector<std::string> eddy_types = {"A", "B1+B2+B3+B4"}¶: Eddy types used to create the results.

double beta¶

double delta_c¶: Atmospheric boundary layer thickness $ \delta_c $ [m].

double kappa¶: von Karman constant $ \kappa $. Typically $ \kappa = 0.41 $.

double pi_coles¶: Coles wake parameter $ \Pi $.

double shear_ratio¶: Ratio between free-stream and skin friction velocities $ S = U_{inf}/U_{\tau} $.

double u_inf¶: Free-stream velocity $ U_{inf}|_{z = \delta_c} $) [m/s].

double u_tau¶: Skin friction velocity [m/s].

double zeta¶: Scaled streamwise derivative $ \zeta $ of the Coles wake parameter $ \Pi $.

Eigen::VectorXd z¶: Vertical coordinates used in the analysis [m].

Eigen::VectorXd eta¶: Nondimensionalised vertical coordinates used in the analysis $ \eta = z/\delta_{c} $.

Eigen::VectorXd lambda_e¶: Parameterised nondimensional vertical coordinates used in the analysis.

Eigen::VectorXd u_horizontal¶: Horizontal mean velocity varying with vertical coordinate [m/s].

Eigen::ArrayXXd reynolds_stress¶: Reynolds stress profiles from all eddy types.

Eigen::ArrayXXd r13a_analytic¶: Reynolds Stress profile $R_{13A}$ determined analytically from the parameter set.

Eigen::ArrayXXd r13b_analytic¶: Reynolds Stress profile $R_{13B}$ determined analytically from the parameter set.

Eigen::ArrayXXd reynolds_stress_a¶: Reynolds Stress profiles, contributions from Type A eddies only.

Eigen::ArrayXXd reynolds_stress_b¶: Reynolds Stress profiles, contributions from Type B eddies only.

Eigen::ArrayXXd k1z¶: Wavenumbers $ k_{1}z $ for which spectra are defined at each vertical coordinate.

Eigen::Tensor<double, 3> psi¶: Turbulent Spectra $ \Psi $ (corresponding to wavenumber k1z) at each vertical coordinate.

Eigen::Tensor<double, 3> psi_a¶: Turbulent Spectra (corresponding to wavenumber k1z) at each vertical coordinate from Type A eddies only.

Eigen::Tensor<double, 3> psi_b¶: Turbulent Spectra (corresponding to wavenumber k1z) at each vertical coordinate from Type B eddies only.

Eigen::VectorXd t2wa¶: Negated convolution function $ -(T^2)\omega $ encapsulating variation of eddy strength and scale for Type A eddies.

Eigen::VectorXd t2wb¶: Negated convolution function $ -(T^2)\omega $ encapsulating variation of eddy strength and scale for Type B eddies.

Eigen::VectorXd residual_a¶: Fit residuals from the deconvolution of t2wa

Eigen::VectorXd residual_b¶: Fit residuals from the deconvolution of t2wb

Eigen::Index start_idx¶

Eigen::ArrayXXd ja_fine¶: Reynolds Stress profile $R_{13A}$ determined analytically from the parameter set, finely interpolated.

Eigen::ArrayXXd jb_fine¶: Reynolds Stress profile $R_{13B}$ determined analytically from the parameter set, finely interpolated.

Eigen::ArrayXd r13a_analytic_fine¶: Reynolds Stress profile $R_{13A}$ determined analytically from the parameter set, finely interpolated.

Eigen::ArrayXd r13b_analytic_fine¶: Reynolds Stress profile $R_{13B}$ determined analytically from the parameter set, finely interpolated.

Eigen::ArrayXd minus_t2wa_fine¶: Negated convolution function $ -(T^2)\omega $ encapsulating variation of eddy strength and scale for Type A eddies, on the grid of lambda_fine.

Eigen::ArrayXd minus_t2wb_fine¶: Negated convolution function $ -(T^2)\omega $ encapsulating variation of eddy strength and scale for Type B eddies, on the grid of lambda_fine.

Eigen::ArrayXd lambda_fine¶: Linearly, finely, spaced values of $ \lambda $ at which final.

Eigen::ArrayXd eta_fine¶: Linearly, finely, spaced values of $ \lambda $ at which final.

Class BasicLidar¶

Defined in File data_types.h

Class Documentation¶

class BasicLidar¶

Public Functions

void read(mat_t *matfp, bool print_var = true)¶

Public Members

const std::string type = "lidar_basic"¶

VectorXd t¶

VectorXd z¶

Eigen::Array<double, Eigen::Dynamic, Eigen::Dynamic> u¶

Eigen::Array<double, Eigen::Dynamic, Eigen::Dynamic> v¶

Eigen::Array<double, Eigen::Dynamic, Eigen::Dynamic> w¶

Eigen::Vector3d position¶

double half_angle¶

std::string t

std::string z

std::string u

std::string v

std::string w

std::string position

std::string half_angle

struct es::BasicLidar::[anonymous] units¶

Class Bins¶

Defined in File profile.h

Class Documentation¶

class Bins¶

Public Functions

Bins(std::vector<double> z)¶

Bins(std::vector<double> z, std::vector<double> dx, std::vector<double> dy, std::vector<double> dz)¶

Bins(std::vector<double> z, double half_angle_degrees)¶

Bins(std::vector<double> z, double half_angle_degrees, std::vector<double> dz)¶

~Bins()¶

Public Members

unsigned long n_bins¶

std::vector<double> z_ctrs¶

std::vector<double> dx¶

std::vector<double> dy¶

std::vector<double> dz¶

Template Class DeficitFunctor¶

Defined in File stress.h

Class Documentation¶

template <typename T_scalar, typename T_param> class DeficitFunctor¶

Public Functions

DeficitFunctor(const double kappa, const T_param pi_coles, const double shear_ratio, const bool lewkowicz, const bool deficit_squared = false)¶

T_scalar operator()(T_scalar eta) const¶

Class EddySignature¶

Defined in File signature.h

Class Documentation¶

class EddySignature¶

Data container for Eddy signature tensors.

Public Functions

void load(std::string file_name, bool print_var = false)¶

Load data from a *.mat file containing eddy signature data.

TODO overload with load(std::vector<std::string> file_names, bool print_var = false){} to load and average multiple signature files

Parameters

file_name: File name (including relative or absolute path)
print_var: Boolean, default true. Print variables as they are read in (not advised except for debugging!)

void save(std::string file_name)¶

Save eddy signature data to a *.mat file.

Parameters

filename: File name (including relative or absolute path)

EddySignature operator+(const EddySignature &c) const¶

Define overloaded + (plus) operator for eddy signatures.

Return

A new EddySignature() with combined signatures of the two eddy types.

Parameters

c: The EddySignature to add.

EddySignature operator*(double a) const¶

Define overloaded * (multiply) operator for eddy signatures.

Return

new EddySignature() whose signature (g, j) is element-wise multiplied by input a.

Parameters

a: The number to multiply by

EddySignature operator/(double denom) const¶

Define overloaded / (divide) operator for eddy signatures.

Return

A new EddySignature() whose signature (g, j) is element-wise divided by input denom.

Parameters

denom: A number to divide by

Eigen::ArrayXXd k1z(Eigen::ArrayXd &eta) const¶

Get k1z wavenumber array (wavenumber space for each vertical coord, e.g. 50 x 801).

Return

k1z the wavenumber-length matrix

Parameters

eta: vertical heights at which to get the k1z value, normalised (i.e. z/delta)

Eigen::ArrayXXd getJ(const Eigen::ArrayXd &locations, const bool linear = false) const¶

Interpolate the signature $J_{i,j}(\lambda)$ to new locations in lambda or eta.

To avoid warping the reconstruction, we need to do the convolution and the deconvolution with both the input and the signature on the same, equally spaced, basis. What if we want to do it on a basis different to the positions where the signature was calculated?

This function allows you to get the signature array, j, at different vertical locations

Return

[N x 6] signature array Jij interpolated to input locations

Parameters

locations: [N x 1] The lambda (or optionally eta) values at which to retrieve the signature j
linear: boolean If true, locations are on a linear basis (i.e. they are values of eta). Otherwise (default) they are on a logarithmic basis (i.e. they are values of lambda).

void computeSignature(const std::string &type, const int n_lambda = 200, const double dx = 0.002)¶

Calculate eddy intensity functions $J_{i,j}$ and $g_{i,j}$.

Eddy intensity functions $J_{i,j}(\lambda)$ are computed for type A, B1, B2, B3 or B4, which are the eddies described in Ref 1. These functions are the signatures (in terms of turbulent fluctuations) that an individual structure will contribute to Reynolds Stress in a boundary layer. They are used in the convolution integral (36) of Perry and Marusic (1995a) to determine Reynolds Stress profiles.

Eddy spectral functions $g_{i,j}(k1z,\lambda)$ are then computed from $J$. These functions are the signatures (in terms of turbulent fluctuations) that an individual structure will contribute to turbulent spectra in a boundary layer. They are used in the convolution integral (43) of Perry and Marusic (1995a) to determine Spectral Tensor profiles.

This method updates class properties j, lambda, eta, g, eddy_type, domain_spacing, domain_extents.

It works by computing induced velocity [u, v, w] of a single eddy structure on a regular grid [x,y,lambda], normalised to the eddy scale and surrounding the unit eddy, then integrating for $J$ and taking ffts for $g$.

Perry AE and Marusic I (1995a) A wall-wake model for turbulent boundary layers. Part 1. Extension of the attached eddy hypothesis J Fluid Mech vol 298 pp 361-388

Parameters

typestring: one of ‘A’, ‘B1’, ‘B2’, ‘B3’, ‘B4’
n_lambdaint: number of points logarithmically spaced in the z direction, between the outer part of the domain and a location very close to the wall. Default 200.

void applySignature(const std::string &type, const int n_lambda = 200)¶

Apply signature defaults.

Eddy intensity functions $J_{i,j}(\lambda)$ is applied for type A or B eddies, by digitisation of Figure 20 in Perry and Marusic (1995).

Note that these signatures are incomplete:

Only four terms are given (I11, I13, I22, I33, the remaining two are assumed to be zero)
Eddy spectral functions $g_{i,j}(k1z,\lambda)$ are not documented in P&M 1995, so can’t be reproduced here. Thus, signatures defined by this method cannot be used for computation of spectra (and sets arbitrary domain_spacing and domain_extents values for the x and y directions).

This method updates class properties j, lambda, eta, eddy_type, domain_spacing, domain_extents.

See Perry AE and Marusic I (1995) A wall-wake model for turbulent boundary layers. Part 1. Extension of the attached eddy hypothesis J Fluid Mech vol 298 pp 361-388

Parameters

typestring: one of ‘A’, ‘B1’, ‘B2’, ‘B3’, ‘B4’
n_lambdaint: number of points logarithmically spaced in the z direction, between the outer part of the domain and a location very close to the wall. Default 200.

Public Members

std::string eddy_type¶: Eddy type (or types, if ensembled) used to create the results.

Eigen::ArrayXd lambda¶: Mapped vertical coordinates used in the analysis.

Eigen::ArrayXd eta¶: Unmapped (cartesian space) coordinates corresponding to the points in lambda.

Eigen::Tensor<double, 3> g¶: g (6 coefficients at each vertical coord and wavenumber, e.g 50 x 801 x 6)

Eigen::Array<double, Eigen::Dynamic, 6> j¶: Eddy intensity functions $Jij(lambda)$, which is [n_lambda x 6] in size, with columns ordered as [J11 J12 J13 J22 J23 J33]. Note that the lower diagonal of the 3x3 Reynolds Stress Tensor is not included due to symmetry.

Eigen::Array3d domain_spacing¶: Spacing of the regular grid used to create the eddy intensity signatures [dx, dy, dlambda] (note for the third coordinate, points are linearly spaced in a logarithmic domain, so this is d_lambda, not d_z).

Eigen::Array<double, 3, 2> domain_extents¶: Extents of the regular grid placed over the unit eddy to create the eddy intensity signatures, in [x_min, x_max; y_min, y_max; z_min, z_max] form.

Template Class Profile¶

Defined in File profile.h

Class Documentation¶

template <class ProfileType> class Profile¶

Public Functions

Profile(const Bins &bins)¶

Profile(const Bins &bins, double x, double y, double z)¶

~Profile()¶

const std::vector<ProfileType> &getValues() const¶

void setValues(const std::vector<ProfileType> &values)¶

Public Members

template<> double position[3]¶

Bins bins¶

Template Class Reader¶

Defined in File readers.h

Class Documentation¶

template <class DataType> class Reader¶

Public Functions

Reader(const std::string &file)¶

~Reader()¶

std::string logString() const¶

DataType *read(bool print = false)¶

void checkFileType(int level)¶

void checkTimeseries(int level)¶

double getWindowDuration() const¶

void setWindowDuration(double windowDuration)¶

int getWindowSize() const¶

void setWindowSize(int windowSize)¶

void readWindow(const int index)¶

Protected Attributes

std::string file¶

mat_t *matfp¶

std::string file_type = std::string("none")¶

int windowSize¶

double windowDuration¶

DataType data¶

Class VelocityProfile¶

Defined in File profile.h

Inheritance Relationships¶

Base Type¶

public es::Profile< double > (Template Class Profile)

Class Documentation¶

class VelocityProfile : public es::Profile<double>¶

Public Functions

VelocityProfile()¶

virtual ~VelocityProfile()¶

Class spectra¶

Defined in File spectra.h

Class Documentation¶

class spectra¶

Class CubicSplineInterpolant¶

Defined in File interp.h

Class Documentation¶

class CubicSplineInterpolant¶

Public Functions

CubicSplineInterpolant(Eigen::VectorXd const &x_vec, Eigen::VectorXd const &y_vec)¶

Performs cubic interpolation (or maximum degree possible, where inputs are shorter than 4 elements)

Initialise an interpolant as follows:

Eigen::VectorXd xvals(3); Eigen::VectorXd yvals(xvals.rows());

xvals << 0, 15, 30; yvals << 0, 12, 17;

CubicSplineInterpolant s(xvals, yvals);

double operator()(double xi) const¶

Evaluate interpolant at values xi whose yi values are unknown.

Performs cubic interpolation (or maximum degree possible, where inputs are shorter than 4 elements)

Initialise and evaluate an interpolant:

// … Initialise interpolant (see constructor) … CubicSplineInterpolant s(xvals, yvals); std::cout << s(12.34) << std::endl;

Return

double interpolated value yi corresponding to location xi

Parameters

xi: double (or eigen VectorXd) of target x values for the interpolation

Eigen::VectorXd operator()(Eigen::VectorXd const &xi_vec)¶

Class LinearInterpolant¶

Defined in File interp.h

Class Documentation¶

class LinearInterpolant¶

Public Functions

LinearInterpolant(const Eigen::ArrayXd x_vec, const Eigen::ArrayXd y_vec)¶

Create a linear interpolant.

Initialise an interpolant as follows:

Eigen::ArrayXd xvals(3); Eigen::ArrayXd yvals(xvals.rows());

xvals << 0, 15, 30; yvals << 0, 12, 17;

LinearInterpolant s(xvals, yvals);

double operator()(double xi) const¶

Evaluate interpolant at values xi whose yi values are unknown.

Out of range xi values are constrained to the endpoints (i.e. nearest neighbour interpolation)

Performs linear interpolation to evaluate values yi at // … Initialise interpolant (see constructor) … LinearInterpolant s(xvals, yvals); std::cout << s(12.34) << std::endl;

Return

double interpolated value yi corresponding to location xi

Parameters

xi: double (or eigen ArrayXd) of target x values for the interpolation

Eigen::ArrayXd operator()(Eigen::ArrayXd const &xi_vec)¶

Enums¶

Enum file_type_check_level¶

Defined in File readers.h

Enum Documentation¶

enum es::file_type_check_level¶

Values:

NONE = 0¶

OAS_STANDARD = 1¶

Enum timeseries_check_level¶

Defined in File readers.h

Enum Documentation¶

enum es::timeseries_check_level¶

Values:

PRESENT = 0¶

INCREASING = 1¶

MONOTONIC = 2¶

STRICTLY_MONOTONIC = 3¶

Functions¶

Function es::adem¶

Defined in File adem.h

Function Documentation¶

AdemData es::adem(const double beta, const double delta_c, const double kappa, const double pi_coles, const double shear_ratio, const double u_inf, const double zeta, const EddySignature &signature_a, const EddySignature &signature_b, bool compute_spectra = true)¶

Compute full turbulent properties from given Attached-Detached Eddy Model parameters.

Uses the using the Lewkowicz (1982) formulation (Perry and Marusic eq.9) of the Coles wake function to determine u_h(z), spectra and Reynolds Stresses from input parameters.

Parameters

beta: The Clauser parameter, representing acceleration/decelaration of the boundary layer
delta_c: The boundary layer thickness in m
kappa: The von Karman constant, typically 0.41.
pi_coles: Coles wake parameter Pi
shear_ratio: Ratio between free stream and friction velocity S = u_inf/u_tau
u_inf: The free stream speed in m/s
zeta: Represents a scaled streamwise derivative of Pi
signature_a: EddySignature class loaded with data for type A eddies
signature_b: EddySignature class loaded with data for an ensemble of type B eddies

Template Function es::array_size¶

Defined in File variable_readers.h

Function Documentation¶

template <size_t SIZE, class T> size_t es::array_size(T (&arr)[SIZE])¶

Return the size (i.e. number of elements) in an array variable Comes from https://coderwall.com/p/nb9ngq/better-getting-array-size-in-c

Example: int arr[] = {1, 2, 3, 4, 5}; std::cout << array_size(arr) << std::endl;

Function es::checkVariableType¶

Defined in File variable_readers.h

Function Documentation¶

void es::checkVariableType(matvar_t *mat_var, int matvar_type)¶

Template Function es::coles_wake¶

Defined in File velocity.h

Function Documentation¶

template <typename T_z, typename T_param> T_z es::coles_wake(T_z const &eta, T_param const &pi_coles, const bool corrected = true)¶

Compute corner-corrected coles wake parameter W_c .

There are two alternative functional forms for the wake parameter. Perry and Marusic (1995) used the Lewkowicz (1982) wake function, where the second ( 1/… ) term is artificially applied to ensure that the velocity defect function has zero gradient at z= :

\[ W_c[\eta, \Pi] & = & 2 \eta^2 \left( 3 - 2\eta \right) - \frac{1}{\Pi}\eta^2 \left( 1 - \eta \right) \left( 1 - 2\eta \right) \]

Note: Jones, Marusic and Perry 2001 refer to this correction as the ‘corner’ function and use an alternative correction (recommended by Prof. Coles) to the pure wall flow (instead of the wake) which is not a function of Pi, allowing reversion to the original (Coles 1956) wake parameter W :

\[ W[\eta, \Pi] & = & 2 \eta^2 \left( 3 - 2\eta \right) \]

This function implements the former by default!

This function is templated so that it can be called with active scalars (allows use of autodiff), doubles/floats, Eigen::Arrays (directly) or Eigen::VectorXds (the latter via template specialisation) of z values.

Parameters

eta: Nondimensional height values
pi_coles: The coles wake parameter Pi
corrected: Boolean flag, default true. If true, return Lewkowicz (1982) corrected wake function. If false, return the original uncorrected wake parameter.

Template Function es::deficit¶

Defined in File velocity.h

Function Documentation¶

template <typename T_eta, typename T_param> T_eta es::deficit(T_eta const &eta, const double kappa, T_param const &pi_coles, const double shear_ratio, const bool lewkowicz = false)¶

Get the velocity deficit integrand $ f $ used in computation of $ R_{13} $.

TODO move into velocity.h, reuse in lewkowicz_speed and jones_speed functions;. In their original derivation of the ADEM, Perry and Marusic 1995 eqn. 2 use the velocity distribution of Lewkowicz 1982 as a basis to determine the shear stress profile. This led to an integrand for the mean velocity deficit profile:

\[\begin{split} f & = & \frac{U_{1} - \overline{U}}{U_{\tau}} \\ & = & - \frac{1}{\kappa} \ln \left( \eta \right) + \frac{\Pi}{\kappa} W_c[1, \Pi] - \frac{\Pi}{\kappa} W_c[\eta, \Pi], \\ W_c[\eta, \Pi] & = & 2 \eta^2 \left( 3 - 2\eta \right) - \frac{1}{\Pi}\eta^2 \left( 1 - \eta \right) \left( 1 - 2\eta \right) \end{split}\]

Jones, Marusic and Perry (2001) eqn 1.9 uses an alternative formulation, thereby removing the non-physical dependency of the wake factor on . This leads to the velocity deficit function:

\[\begin{split} f & = & \frac{U_{1} - \overline{U}}{U_{\tau}} \\ & = & - \frac{1}{\kappa} \ln \left( \eta \right) + \frac{1}{3\kappa} \left(\eta^{3} - 1 \right) + 2 \frac{\Pi}{\kappa} \left( 1 - 3\eta^{2} + 2\eta^{3} \right) \end{split}\]

This function is templated so that it can be called with active scalars (allows use of autodiff), doubles/floats, Eigen::Arrays (directly) or Eigen::VectorXds (the latter via template specialisation) of z values.

Return

Parameters

eta: Nondimensional height values
kappa: von Karman constant
pi_coles: The coles wake parameter Pi
shear_ratio: Shear ratio S
lewkowicz: Boolean flag, default false. If true, use Lewkowicz (1982) velocity deficit funciton. If false, use Jones et at (2001).

Function es::fit_lewkowicz_speed(const Eigen::ArrayXd&, const Eigen::ArrayXd&, const Array5b&, const Array5d&, bool)¶

Defined in File fit.h

Function Documentation¶

Array5d es::fit_lewkowicz_speed(const Eigen::ArrayXd &z, const Eigen::ArrayXd &u, const Array5b &fixed_params, const Array5d &initial_params, bool print_report = true)

Determine best fit of Lewkowicz relation to input speed profile.

Robustly fits Lewkowicz speed relation $ u = f(z, \Pi, \kappa, U_{inf}, S, \delta_{c}) $ to input data $ u, z $.

An initial guess is required, and parameters can be fixed to help constrain the fitting process. See also fit_lewkowicz_speed(const Eigen::ArrayXd &z, const Eigen::ArrayXd &u, bool print_report = true) for providing a set of default values and fixed parameters.

Parameters are as follows:

pi_coles = params[0]
kappa = params[1]
u_inf = params[2]
shear_ratio = params[3]
delta_c = params[4]

The fitting process uses a Levenberg-Marquadt solver (provided by ceres-solver) with Automatic differentiation (for improved numeric stability and convergence over numerical differentiation approaches), and a Cauchy Loss function of parameter 0.5 (for robustness agains outlying data entries).

Return

Array5d containing fitted values [pi_coles, kappa, u_inf, shear_ratio, delta_c]

Parameters

z: Vertical locations in m (or normalised, if z_ref = 1.0)
u: Observed speeds at corresponding vertical locations, in m/s
fixed_params: Eigen::Array<bool, 5, 1>, logical mask, true where the parameter is fixed, false where it is allowed to vary
initial_params: Eigen::Array<double, 5, 1> containing initial parameter values. These are used where fixed parameters are specified
print_report: bool, default true. If true, the solver prints iterations summary and full final convergence and solution report (for debugging and validation purposes).

Function es::fit_lewkowicz_speed(const Eigen::ArrayXd&, const Eigen::ArrayXd&, bool)¶

Defined in File fit.h

Function Documentation¶

Array5d es::fit_lewkowicz_speed(const Eigen::ArrayXd &z, const Eigen::ArrayXd &u, bool print_report = true)

Determine best fit of Lewkowicz relation to input speed profile.

Robustly fits Lewkowicz speed relation $ u = f(z, \Pi, \kappa, U_{inf}, S, \delta_{c}) $ to input data $ u, z $, using ‘sensible’ initial guesses (for Atmospheric Boundary Layer in Northern European conditions) and fixed parameters to constrain the fitting process:

- von Karman constant \form#3 is fixed according to the value in definitions.h.
- Boundary layer thickness \form#24 is fixed to a default value of ``1000 m``.

Return

Array5d containing fitted values [pi_coles, kappa, u_inf, shear_ratio, delta_c]

Parameters

z: Vertical locations in m (or normalised, if z_ref = 1.0)
u: Observed speeds at corresponding vertical locations, in m/s
print_report: bool, default true. If true, the solver prints iterations summary and full final convergence and solution report (for debugging and validation purposes).

Function es::fit_power_law_speed¶

Defined in File fit.h

Function Documentation¶

double es::fit_power_law_speed(const Eigen::ArrayXd &z, const Eigen::ArrayXd &u, const double z_ref = 1.0, const double u_ref = 1.0)¶

Determine best fit of power law to input speed profile.

Return

Parameters

z: Vertical locations in m (or normalised, if z_ref = 1.0)
u:
z_ref: Optional reference height (default 1.0) by which the input z is normalised
u_ref: Optional reference velocity (default 1.0) by which the input u is normalised

Function es::get_mean_speed¶

Defined in File adem.h

Function Documentation¶

void es::get_mean_speed(AdemData &data)¶

Get the mean speed profile and update the data structure with it.

Parameters

data:

Function es::get_reynolds_stresses¶

Defined in File adem.h

Function Documentation¶

void es::get_reynolds_stresses(AdemData &data, const EddySignature &signature_a, const EddySignature &signature_b)¶

Get the Reynolds Stress distributions from T2w and J distributions.

The ouptut Reynolds Stress matrix is of size output_dim_size = input_dim_size - kernel_dim_size + 1 (requires: input_dim_size >= kernel_dim_size). Legacy MATLAB equivalent is:

[R, RA, RB] = getReynoldsStresses(T2wA, T2wB, JA, JB);

Parameters

data:

Function es::get_spectra¶

Defined in File adem.h

Function Documentation¶

void es::get_spectra(AdemData &data, const EddySignature &signature_a, const EddySignature &signature_b)¶

Get the premultiplied power spectra.

Computes tensors $ \Psi_{a} $ (psi_a) and $ \Psi_{b} $ (psi_b) from the scale functions and the eddy signatures, and adds them to the AdemData object.

The output spectral tensors have dimension [nz x nk x 6], where nz should agree with the number of elements in the t2w scale functions, and nk represents the number of wavenumbers for which the spectrum is computed.

Parameters

data: AdemData object, which must have properties t2wa, `t2wb’ and u_tau defined already.
signature_a: Signature object for Type A eddies
signature_b: Signature object for Type B eddies

Function es::get_t2w¶

Defined in File adem.h

Function Documentation¶

void es::get_t2w(AdemData &data, const EddySignature &signature_a, const EddySignature &signature_b)¶

Get the T^2w distributions from the eddy signatures by deconvolution.

These distributions are used for calculation of Spectra and Stress terms.

Updates t2wa, t2wb, lambda_fine, residual_a and residual_b in the input data structure.

Parameters

data:
signature_a:
signature_b:

Function es::getVariable¶

Defined in File variable_readers.h

Function Documentation¶

matvar_t *es::getVariable(mat_t *matfp, const std::string var_name, bool print_var = true, int max_rank = 2)¶

Get pointer to a variable and check validity. Optionally print variable and check rank.

Return

Parameters

matfp:
var_name:
print_var:
max_rank: The maximum rank of the variable. Default 2 as everything is an array in MATLAB.

Template Function es::lewkowicz_speed¶

Defined in File velocity.h

Function Documentation¶

template <typename T_z, typename T_param> T_z es::lewkowicz_speed(T_z const &z, T_param const &pi_coles, T_param const &kappa, T_param const &u_inf, T_param const &shear_ratio, T_param const &delta_c)¶

Compute Lewkowicz (1982) velocity profile.

TODO refactor to base it on velocity deficit, keep code DRY TODO Refactor to find usages as VectorXd and change them to array uses; remove the VectorXd template specialization

Used by Perry and Marusic 1995 (from eqs 2 and 7).

Templated so that it can be called with active scalars (allows use of autodiff), doubles/floats, Eigen::Arrays (directly) or Eigen::VectorXds (via template specialisation) of z values.

Parameters

z: height in m (or Nondimensional heights (eta = z/delta_c) where delta_c = 1.0)
pi_coles: The coles wake parameter Pi
kappa: von Karman constant
u_inf: Speed of flow at z = delta (m/s)
shear_ratio: Shear / skin friction velocity ratio (shear_ratio = u_inf / u_tau)
delta_c: Boundary layer thickness in m, used to normalise z. Defaults to 1.0.

Template Function es::marusic_jones_speed¶

Defined in File velocity.h

Function Documentation¶

template <typename T_z, typename T_pi_j> T_z es::marusic_jones_speed(T_z const &z, T_pi_j const pi_j, const double kappa, const double z_0, const double delta, const double u_inf, const double u_tau)¶

Compute speed profile according to Marusic and Jones’ relations.

TODO refactor to base it on velocity deficit, keep code DRY

Templated so that it can be called with active scalars (allows use of autodiff), doubles/floats, Eigen::Arrays (directly) or Eigen::VectorXds (via template specialisation) of z values.

Speed is computed as:

\[\begin{split} \frac{\overline{U}}{U_{\tau}} & = & \frac{1}{\kappa} \ln \left( \frac{z+z_0}{k_s} \right) + Br + \frac{\Pi_j}{\kappa} W_c[\eta, \Pi_j] \\ W_c[\eta, \Pi_j] & = & 2 \eta^2 \left( 3 - 2\eta \right) - \frac{1}{3\Pi_j}\eta^3 \\ \eta & = & \frac{z+z_0}{\delta + z_0} \end{split}\]

which reduces to the defecit relation:

\[ U_{D}^{*} = \frac{U_\infty-\overline{U}}{U_{\tau}} = -\frac{1}{\kappa} \ln \left( \eta \right) + \frac{1}{3\kappa} \left(\eta^3 - 1 \right) + 2 \frac{\Pi_j}{\kappa} \left(1 - 3\eta^2 + 2\eta^3 \right) \]

Parameters

z: Height(s) in m at which you want to get speed.
pi_j: Jones’ modification of the Coles wake factor. Double or AutoDiffScalar type accepted.
kappa: von Karman constant
z_0: Roughness length - represents distance of hypothetical smooth wall from actual rough wall z0 = 0.25k_s (m)
delta: Boundary layer thickness (m)
u_inf: Speed of flow at z = delta (m/s)
u_tau: Shear / skin friction velocity (governed by ratio parameter S = u_inf / u_tau)

Template Function es::most_law_speed¶

Defined in File velocity.h

Function Documentation¶

template <typename T> T es::most_law_speed(T const &z, const double kappa, const double d, const double z0, const double L)¶

Compute speed profile according to the MOST law.

Templated so that it can be called with active scalars (allows use of autodiff), doubles/floats, Eigen::Arrays (directly) or Eigen::VectorXds (via template specialisation) of z values.

MOST law speed is computed as:

TODO

Parameters

z: Height value(s) at which you want to get speed (m)
kappa: von Karman constant
d: Zero plane offset distance (e.g. for forest canopies) (m)
z0: Roughness length (m)
L: Monin-Obukhov length (m)

Function es::NaiveBiotSavart¶

Defined in File biot_savart.h

Function Documentation¶

Matrix3Xd es::NaiveBiotSavart(Matrix3Xd startNodes, Matrix3Xd endNodes, Matrix3Xd locations, VectorXd gamma, VectorXd effective_core_radius_squared)¶

O(N^2) ‘Naive’ application of the biot savart law to determine the action of many vortex lines on many control points.

Outputs:

Parameters

startNodes: [3 x n] Start nodes of vortex lines in x, y, z coords
endNodes: [3 x n] End nodes of vortex lines in x, y, z coords
locations: [3 x p] Locations in x, y, z coords at which induction is required
gamma: [n x 1] Circulation of each vortex line
rcEffSqd: [n x 1] Square of the effective vortex core radius for each vortex line

induction[3 x p] double Induction in u, v, w directions of the input vortex lines at the input control points

Function es::operator<<(std::ostream&, AdemData const&)¶

Defined in File adem.h

Function Documentation¶

std::ostream &es::operator<<(std::ostream &os, AdemData const &data)

Print information about the AdemData attributes to ostream using the << operator.

Return

os The same ostream, with the data representation added to the stream

Parameters

os: The ostream to print to
data: The AdemDataclass instance

Template Function es::operator<<(::std::ostream&, const Reader<DataType>&)¶

Defined in File readers.h

Function Documentation¶

Warning

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- std::ostream &es::operator<<(std::ostream&, AdemData const&)
- std::ostream &es::operator<<(std::ostream&, const Bins&)
- template <class DataType>
  std::ostream &es::operator<<(std::ostream&, const Reader<DataType>&)
- template <class ProfileType>
  std::ostream &es::operator<<(std::ostream&, const Profile<ProfileType>&)

Function es::operator<<(::std::ostream&, const Bins&)¶

Defined in File profile.cpp

Function Documentation¶

Warning

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- std::ostream &es::operator<<(std::ostream&, AdemData const&)
- std::ostream &es::operator<<(std::ostream&, const Bins&)
- template <class DataType>
  std::ostream &es::operator<<(std::ostream&, const Reader<DataType>&)
- template <class ProfileType>
  std::ostream &es::operator<<(std::ostream&, const Profile<ProfileType>&)

Template Function es::operator<<(::std::ostream&, const Profile<ProfileType>&)¶

Defined in File profile.h

Function Documentation¶

Warning

doxygenfunction: Unable to resolve multiple matches for function “es::operator<<” with arguments (::std::ostream&, const Profile<ProfileType>&) in doxygen xml output for project “My Project” from directory: ./doxyoutput/xml. Potential matches:

- std::ostream &es::operator<<(std::ostream&, AdemData const&)
- std::ostream &es::operator<<(std::ostream&, const Bins&)
- template <class DataType>
  std::ostream &es::operator<<(std::ostream&, const Reader<DataType>&)
- template <class ProfileType>
  std::ostream &es::operator<<(std::ostream&, const Profile<ProfileType>&)

Template Function es::power_law_speed¶

Defined in File velocity.h

Function Documentation¶

template <typename T, typename Talf> T es::power_law_speed(T const &z, const double u_ref, const double z_ref, Talf const &alpha)¶

Compute speed profile according to the power law.

Templated so that it can be called with active scalars (allows use of autodiff), doubles/floats, Eigen::Arrays (directly) or Eigen::VectorXds (via template specialisation) of z values (to obtain shear profile u/dz) and/or alpha values (to obtain variational jacobean for fitting parameter alpha).

Power law speed is computed as:

\[ \frac{\overline{U}}{\overline{U}_{ref}} = \left(\frac{z}{z_{ref}}\right)^{\alpha} \]

Parameters

z: Height(s) in m at which you want to get speed.
u_ref: Reference speed in m/s
z_ref: Reference height in m
alpha: Power law exponent. Must be of same type as input z (allows autodifferentiation).

Function es::readArray32d¶

Defined in File variable_readers.h

Function Documentation¶

Array32d es::readArray32d(mat_t *matfp, const std::string var_name, bool print_var)¶

Function es::readArray3d¶

Defined in File variable_readers.h

Function Documentation¶

Array3d es::readArray3d(mat_t *matfp, const std::string var_name, bool print_var)¶

Function es::readArrayXd¶

Defined in File variable_readers.h

Function Documentation¶

ArrayXd es::readArrayXd(mat_t *matfp, const std::string var_name, bool print_var)¶

Function es::readArrayXXd¶

Defined in File variable_readers.h

Function Documentation¶

ArrayXXd es::readArrayXXd(mat_t *matfp, const std::string var_name, bool print_var)¶

Function es::readDouble¶

Defined in File variable_readers.h

Function Documentation¶

double es::readDouble(mat_t *matfp, const std::string var_name, bool print_var)¶

Function es::readString¶

Defined in File variable_readers.h

Function Documentation¶

std::string es::readString(mat_t *matfp, const std::string var_name, bool print_var)¶

Function es::readTensor3d¶

Defined in File variable_readers.h

Function Documentation¶

Tensor<double, 3> es::readTensor3d(mat_t *matfp, const std::string var_name, bool print_var)¶

Function es::readVector3d¶

Defined in File variable_readers.h

Function Documentation¶

Vector3d es::readVector3d(mat_t *matfp, const std::string var_name, bool print_var)¶

Function es::readVectorXd¶

Defined in File variable_readers.h

Function Documentation¶

VectorXd es::readVectorXd(mat_t *matfp, const std::string var_name, bool print_var)¶

Function es::reynolds_stress_13¶

Defined in File stress.h

Function Documentation¶

void es::reynolds_stress_13(Eigen::ArrayXd &r13_a, Eigen::ArrayXd &r13_b, const double beta, const Eigen::ArrayXd &eta, const double kappa, const double pi_coles, const double shear_ratio, const double zeta)¶

Compute Horizontal-Vertical Reynolds Stress R13 profile.

Gets Reynolds Stress profiles due to Type A and B eddies.

Can use either the Lewkowicz formulation for velocity deficit (per Perry and Marusic 1995) or

TODO - presently, the integrations here are sensitive to the chosen eta distribution. Refactor according to issue #38

TODO - Determine whether it will be an advantage to template this function so that it can be called with active scalars (allows use of autodiff), doubles/floats, Eigen::Arrays (directly) or Eigen::VectorXds (via template specialisation) of eta values.

References

[1] Perry AE and Marusic I (1995) A wall-wake model for turbulent boundary layers. Part 1. Extension of the attached eddy hypothesis J Fluid Mech vol 298 pp 361-388

Future Improvements

[1] Optional different mean profile formulations including account for the free surface

[2] Support directional variation with height; i.e. compatible with mean profile formulations using U(y)

[3] Added formulation for contribution of smaller Type C eddies

[4] For the given wall formulation, can f be calculated more efficiently? See schlichting and gersten p. 593

Parameters

beta: Clauser parameter $ \Beta $, representing acceleration/decelaration of the boundary layer
eta: Nondimensional vertical coordinates at which you want to get stress $ R_{13} $. Values must ascend but not necessarily be monotonic.
kappa: von Karman constant.
pi_coles: Coles wake parameter $ \Pi $
shear_ratio: Ratio between free-stream and skin friction velocities $ S = U_{inf}/U_{\tau} $
zeta: Scaled streamwise derivative $ \zeta $ of the Coles wake parameter $ \Pi $

Template Function es::veer_lhs¶

Defined in File veer.h

Function Documentation¶

template <typename T> T es::veer_lhs(T const &ui, const double ui_g, const double phi)¶

Computes the left hand side of the veer relations given u(z) or v(z).

Templated so that it can be called with active scalars (allows use of autodiff), doubles/floats, Eigen::Arrays (directly) or Eigen::VectorXds (via template specialisation) of u values.

The veer relations are:

\[\begin{split} 2 |\mathbf{\Omega}| sin(\phi) (\overline{v}_g - \overline{v}) & = & \frac{\partial}{\partial z} \bigg( \nu\frac{\partial\overline{u}}{\partial z} - \overline{u'w'}\bigg) \\ 2 |\mathbf{\Omega}| sin(\phi) (\overline{u}_g - \overline{u}) & = & \frac{\partial}{\partial z} \bigg(\nu\frac{\partial\overline{v}}{\partial z} - \overline{v'w'}\bigg) \end{split}\]

Parameters

ui: Mean velocity component at a given height (m/s)
ui_g: Mean geostrophic velocity component outside the atmospheric boundary layer (m/s)
phi: Latitude (degrees)

Template Function es::veer_rhs¶

Defined in File veer.h

Function Documentation¶

template <typename T> T es::veer_rhs(T &ui, T &uiu3_bar, const double nu)¶

Computes the right hand side of the veer relations given u(z) or v(z).

See veer_lhs() for the full relation.

Templated so that it can be called with active scalars (allows use of autodiff), doubles/floats, Eigen::Arrays (directly) or Eigen::VectorXds (via template specialisation) of u values.

Parameters

ui: Mean velocity component at a given height (m/s){
uiu3_bar: Mean cross term of unsteady velocity components $ \overline{u_i'u_3'}} $ (m^2/s^2)
nu: Kinematic viscosity of the fluid (m^2/s)

Function es::writeArray32d¶

Defined in File variable_writers.h

Function Documentation¶

void es::writeArray32d(mat_t *mat_fp, const std::string &var_name, const Eigen::Array<double, 3, 2> &var)¶

Function es::writeArray3d¶

Defined in File variable_writers.h

Function Documentation¶

void es::writeArray3d(mat_t *mat_fp, const std::string &var_name, const Eigen::Array3d &var)¶

Function es::writeArrayXd¶

Defined in File variable_writers.h

Function Documentation¶

void es::writeArrayXd(mat_t *mat_fp, const std::string &var_name, const Eigen::ArrayXd &var)¶

Function es::writeArrayXXd¶

Defined in File variable_writers.h

Function Documentation¶

void es::writeArrayXXd(mat_t *mat_fp, const std::string &var_name, const Eigen::ArrayXXd &var)¶

Function es::writeDouble¶

Defined in File variable_writers.h

Function Documentation¶

void es::writeDouble(mat_t *mat_fp, const std::string &var_name, const double var)¶

Function es::writeString¶

Defined in File variable_writers.h

Function Documentation¶

void es::writeString(mat_t *mat_fp, const std::string &var_name, std::string &var)¶

Function es::writeTensor3d¶

Defined in File variable_writers.h

Function Documentation¶

void es::writeTensor3d(mat_t *mat_fp, const std::string &var_name, const Tensor<double, 3> &var)¶

Function main¶

Defined in File main.cpp

Function Documentation¶

Warning

doxygenfunction: Cannot find function “main” in doxygen xml output for project “My Project” from directory: ./doxyoutput/xml

Template Function utilities::array_to_tensor¶

Defined in File tensors.h

Function Documentation¶

template <typename Scalar, typename... Dims> auto utilities::array_to_tensor(const ArrayType<Scalar> &matrix, Dims... dims)¶

convert Eigen Tensor<> to an Array<>

int main () {
    Eigen::Tensor<double,4> my_rank4 (2,2,2,2);
    my_rank4.setRandom();

    Eigen::ArrayXd         myarray =  Tensor_to_Array(my_rank4, 4,4);
    Eigen::Tensor<double,3> my_rank3 =  Array_to_Tensor(mymatrix, 2,2,4);

    std::cout << my_rank3 << std::endl;

    return 0;
}

Return

Function utilities::conv¶

Defined in File conv.h

Function Documentation¶

Eigen::VectorXd utilities::conv(const Eigen::VectorXd &input, const Eigen::VectorXd &kernel)¶

Convolve an input vector with a kernel, returning an output of the same length as the input.

Uses zero-padded fft based output

Parameters

out:
input:
kernel:

Function utilities::convolution_matrix¶

Defined in File conv.h

Function Documentation¶

Eigen::MatrixXd utilities::convolution_matrix(const Eigen::VectorXd &k, const Eigen::Index n)¶

Determines the convolution matrix C for impulse response (kernel) vector k.

convolution_matrix(k, n) * x is equivalent to conv(k, x)

C is a toeplitz matrix where the upper diagonal is entirely zero, the lower diagonal is zero for cases where

TODO sparse alternative. Large signals produce epically big, mostly empty, matrices.

Example:

Eigen::VectorXd k(5)
Eigen::VectorXd x(7)
k << 1, 2, 3, 2, 1;
x << 1, 2, 1, 2, 1, 2, 1;
Eigen::MatrixXd c = convolution_matrix(k, 7);
std::cout << "Convolved result c * x: " << c * x << std::endl

Parameters

k: Column vector input
n: Desired dimension of the output matrix. i.e. if convolving with vector x of length 8, n should be 8.
c: Convolution matrix

Template Function utilities::cumsum¶

Defined in File cumsum.h

Function Documentation¶

template <typename DerivedX, typename DerivedY>
EIGEN_STRONG_INLINE void utilities::cumsum(Eigen::PlainObjectBase< DerivedY > & y, const Eigen::MatrixBase< DerivedX > & x, const int dim = 1)

Template Function utilities::cumulative_integrate¶

Defined in File integration.h

Function Documentation¶

template <typename T_functor> Eigen::ArrayXd utilities::cumulative_integrate(const Eigen::ArrayXd &x, const T_functor &functor, const int max_subintervals = 200)¶

Cumulative numerical integration of a functor in 1D, using gauss-Kronrod61 integration.

Operates in the first dimension (colwise). Applied by reference or returns by value.

Return

The cumulative integration of f with respect to x, over the domain in input x

Template Parameters

T_functor: Type of the functor class instance supplied to the integrator

Parameters

x: The domain of x over which to do a cumulative integration. Output values of the cumulative integral are given at these x locations.
functor: The integrand functor. This functor must, given a scalar value of x, return a scalar of the same type containing the value of the integrand function at the input point.
max_subintervals: The maximum number of subintervals allowed in the subdivision process of quadrature functions, for each segment in x. This corresponds to the amount of memory allocated for said functions.

Template Function utilities::deconv¶

Defined in File filter.h

Function Documentation¶

template <typename DerivedIn, typename DerivedOut> void utilities::deconv(Eigen::ArrayBase<DerivedOut> &z, const Eigen::ArrayBase<DerivedIn> &b, const Eigen::ArrayBase<DerivedIn> &a)¶

One-dimensional deconvolution.

z = deconv(b, a) deconvolves vector a out of column b, returning a column vector

Function utilities::diagonal_loading_deconv¶

Defined in File conv.h

Function Documentation¶

Eigen::VectorXd utilities::diagonal_loading_deconv(const Eigen::VectorXd &input, const Eigen::VectorXd &kernel, const double alpha = 0.1)¶

stably solve Fredholm Integral of the first kind by deconvolution with diagonal loading

Useful site: http://eeweb.poly.edu/iselesni/lecture_notes/least_squares/LeastSquares_SPdemos/deconvolution/html/deconv_demo.html

Return

deconvolved signal, same length as input signal.

Parameters

input: Input signal
kernel: Kernel (impulse response) to deconvolve out of the input signal
alpha: Stabilisation parameter alpha. Default 0.1.

Template Function utilities::fft_next_good_size¶

Defined in File conv.h

Function Documentation¶

template <typename T> T utilities::fft_next_good_size(const T n)¶

Find the next good size for an fft, to pad with minimal number of zeros.

Return

M Length to pad the signal to, for optimal FFT performance

Parameters

N: Length of a signal

Template Function utilities::filter(Eigen::ArrayBase<DerivedOut>&, const Eigen::ArrayBase<DerivedIn>&, const Eigen::ArrayBase<DerivedIn>&, const Eigen::ArrayBase<DerivedIn>&)¶

Defined in File filter.h

Function Documentation¶

template <typename DerivedOut, typename DerivedIn> void utilities::filter(Eigen::ArrayBase<DerivedOut> &y, const Eigen::ArrayBase<DerivedIn> &b, const Eigen::ArrayBase<DerivedIn> &a, const Eigen::ArrayBase<DerivedIn> &x)

One-dimensional digital filter.

Filters the input 1d array (or std::vector<>) x with the filter described by coefficient arrays b and a.

See https://en.wikipedia.org/wiki/Digital_filter

If a(0) is not equal to 1, the filter coefficients are normalised by a(0).

a(0)*y(n-1) = b(0)*x(n-1) + b(1)*x(n-2) + … + b(nb)*x(n-nb-1) - a(1)*y(n-2) - … - a(na)*y(n-na-1)

Template Function utilities::filter(std::vector<T>&, const std::vector<T>&, const std::vector<T>&, const std::vector<T>&)¶

Defined in File filter.h

Function Documentation¶

template <typename T> void utilities::filter(std::vector<T> &y, const std::vector<T> &b, const std::vector<T> &a, const std::vector<T> &x)

Function utilities::lowpass_fft_deconv¶

Defined in File conv.h

Function Documentation¶

Eigen::VectorXd utilities::lowpass_fft_deconv(const Eigen::VectorXd &input, const Eigen::VectorXd &kernel, const std::string &flag, double stab = 0.01)¶

stably solve Fredholm Integral of the first kind by fft based deconvolution with a gaussian low pass filter

Return

Parameters

input:
kernel:
stab: Stabilisation parameter as a proportion of the max magnitude of the kernel. Fixes the lowpass total cutoff point. For example, default 0.01 creates a low pass gaussian filter, between 0 and the point where the FFT of the kernel reaches 1% of its max (usually DC) magnitude. Set <= 0 to circumvent low pass filtering.
flag:

Template Function utilities::matrix_to_tensor¶

Defined in File tensors.h

Function Documentation¶

template <typename Scalar, typename... Dims> auto utilities::matrix_to_tensor(const MatrixType<Scalar> &matrix, Dims... dims)¶

convert Eigen Matrix<> to a Tensor

int main () {
    Eigen::Tensor<double,4> my_rank4 (2,2,2,2);
    my_rank4.setRandom();

    Eigen::MatrixXd         mymatrix =  Tensor_to_Matrix(my_rank4, 4,4);
    Eigen::Tensor<double,3> my_rank3 =  Matrix_to_Tensor(mymatrix, 2,2,4);

    std::cout << my_rank3 << std::endl;

    return 0;
}

Return

Template Function utilities::tensor_dims¶

Defined in File tensors.h

Function Documentation¶

template <typename T> std::string utilities::tensor_dims(T &tensor)¶

Return a string representation of tensor dimensions.

Return

string The output string like “[2 x 3 x 4]” for a rank 3 tensor

Parameters

tensor: An Eigen::Tensor

Template Function utilities::tensor_to_array¶

Defined in File tensors.h

Function Documentation¶

template <typename Scalar, int rank, typename sizeType> auto utilities::tensor_to_array(const Eigen::Tensor<Scalar, rank> &tensor, const sizeType rows, const sizeType cols)¶

Convert Eigen Tensor<> to an Array<>

int main () {
    Eigen::Tensor<double,4> my_rank4 (2,2,2,2);
    my_rank4.setRandom();

    Eigen::ArrayXd         myarray =  Tensor_to_Array(my_rank4, 4,4);
    Eigen::Tensor<double,3> my_rank3 =  Array_to_Tensor(mymatrix, 2,2,4);

    std::cout << my_rank3 << std::endl;

    return 0;
}

Return

Template Function utilities::tensor_to_matrix¶

Defined in File tensors.h

Function Documentation¶

template <typename Scalar, int rank, typename sizeType> auto utilities::tensor_to_matrix(const Eigen::Tensor<Scalar, rank> &tensor, const sizeType rows, const sizeType cols)¶

convert Eigen Tensor to a Matrix

int main () {
    Eigen::Tensor<double,4> my_rank4 (2,2,2,2);
    my_rank4.setRandom();

    Eigen::MatrixXd         mymatrix =  Tensor_to_Matrix(my_rank4, 4,4);
    Eigen::Tensor<double,3> my_rank3 =  Matrix_to_Tensor(mymatrix, 2,2,4);

    std::cout << my_rank3 << std::endl;

    return 0;
}

Return

Template Function utilities::trapz(Eigen::ArrayBase<OtherDerived> const&, const Eigen::ArrayBase<Derived>&, Eigen::Index)¶

Defined in File trapz.h

Function Documentation¶

Warning

doxygenfunction: Unable to resolve multiple matches for function “utilities::trapz” with arguments (Eigen::ArrayBase<OtherDerived> const&, const Eigen::ArrayBase<Derived>&, Eigen::Index) in doxygen xml output for project “My Project” from directory: ./doxyoutput/xml. Potential matches:

- template <typename Derived, typename OtherDerived>
  EIGEN_STRONG_INLINE void utilities::trapz(Eigen::ArrayBase< OtherDerived > const &, const Eigen::ArrayBase< Derived > &, Eigen::Index)
- template <typename Derived>
  EIGEN_STRONG_INLINE Eigen::Array<typename Eigen::ArrayBase<Derived>::Scalar, Eigen::ArrayBase<Derived>::RowsAtCompileTime, Eigen::ArrayBase<Derived>::ColsAtCompileTime> utilities::trapz(const Eigen::ArrayBase< Derived > &, Eigen::Index)
- template <typename DerivedX, typename DerivedY, typename DerivedOut>
  EIGEN_STRONG_INLINE Eigen::Array<typename Eigen::ArrayBase<DerivedOut>::Scalar, Eigen::ArrayBase<DerivedOut>::RowsAtCompileTime, Eigen::ArrayBase<DerivedOut>::ColsAtCompileTime> utilities::trapz(const Eigen::ArrayBase< DerivedX > &, const Eigen::ArrayBase< DerivedY > &)
- template <typename DerivedX, typename DerivedY, typename DerivedOut>
  EIGEN_STRONG_INLINE void utilities::trapz(Eigen::ArrayBase< DerivedOut > const &, const Eigen::ArrayBase< DerivedX > &, const Eigen::ArrayBase< DerivedY > &)

Template Function utilities::trapz(const Eigen::ArrayBase<Derived>&, Eigen::Index)¶

Defined in File trapz.h

Function Documentation¶

Warning

doxygenfunction: Unable to resolve multiple matches for function “utilities::trapz” with arguments (const Eigen::ArrayBase<Derived>&, Eigen::Index) in doxygen xml output for project “My Project” from directory: ./doxyoutput/xml. Potential matches:

- template <typename Derived, typename OtherDerived>
  EIGEN_STRONG_INLINE void utilities::trapz(Eigen::ArrayBase< OtherDerived > const &, const Eigen::ArrayBase< Derived > &, Eigen::Index)
- template <typename Derived>
  EIGEN_STRONG_INLINE Eigen::Array<typename Eigen::ArrayBase<Derived>::Scalar, Eigen::ArrayBase<Derived>::RowsAtCompileTime, Eigen::ArrayBase<Derived>::ColsAtCompileTime> utilities::trapz(const Eigen::ArrayBase< Derived > &, Eigen::Index)
- template <typename DerivedX, typename DerivedY, typename DerivedOut>
  EIGEN_STRONG_INLINE Eigen::Array<typename Eigen::ArrayBase<DerivedOut>::Scalar, Eigen::ArrayBase<DerivedOut>::RowsAtCompileTime, Eigen::ArrayBase<DerivedOut>::ColsAtCompileTime> utilities::trapz(const Eigen::ArrayBase< DerivedX > &, const Eigen::ArrayBase< DerivedY > &)
- template <typename DerivedX, typename DerivedY, typename DerivedOut>
  EIGEN_STRONG_INLINE void utilities::trapz(Eigen::ArrayBase< DerivedOut > const &, const Eigen::ArrayBase< DerivedX > &, const Eigen::ArrayBase< DerivedY > &)

Template Function utilities::trapz(Eigen::ArrayBase<DerivedOut> const&, const Eigen::ArrayBase<DerivedX>&, const Eigen::ArrayBase<DerivedY>&)¶

Defined in File trapz.h

Function Documentation¶

Warning

doxygenfunction: Unable to resolve multiple matches for function “utilities::trapz” with arguments (Eigen::ArrayBase<DerivedOut> const&, const Eigen::ArrayBase<DerivedX>&, const Eigen::ArrayBase<DerivedY>&) in doxygen xml output for project “My Project” from directory: ./doxyoutput/xml. Potential matches:

- template <typename Derived, typename OtherDerived>
  EIGEN_STRONG_INLINE void utilities::trapz(Eigen::ArrayBase< OtherDerived > const &, const Eigen::ArrayBase< Derived > &, Eigen::Index)
- template <typename Derived>
  EIGEN_STRONG_INLINE Eigen::Array<typename Eigen::ArrayBase<Derived>::Scalar, Eigen::ArrayBase<Derived>::RowsAtCompileTime, Eigen::ArrayBase<Derived>::ColsAtCompileTime> utilities::trapz(const Eigen::ArrayBase< Derived > &, Eigen::Index)
- template <typename DerivedX, typename DerivedY, typename DerivedOut>
  EIGEN_STRONG_INLINE Eigen::Array<typename Eigen::ArrayBase<DerivedOut>::Scalar, Eigen::ArrayBase<DerivedOut>::RowsAtCompileTime, Eigen::ArrayBase<DerivedOut>::ColsAtCompileTime> utilities::trapz(const Eigen::ArrayBase< DerivedX > &, const Eigen::ArrayBase< DerivedY > &)
- template <typename DerivedX, typename DerivedY, typename DerivedOut>
  EIGEN_STRONG_INLINE void utilities::trapz(Eigen::ArrayBase< DerivedOut > const &, const Eigen::ArrayBase< DerivedX > &, const Eigen::ArrayBase< DerivedY > &)

Template Function utilities::trapz(const Eigen::ArrayBase<DerivedX>&, const Eigen::ArrayBase<DerivedY>&)¶

Defined in File trapz.h

Function Documentation¶

Warning

doxygenfunction: Unable to resolve multiple matches for function “utilities::trapz” with arguments (const Eigen::ArrayBase<DerivedX>&, const Eigen::ArrayBase<DerivedY>&) in doxygen xml output for project “My Project” from directory: ./doxyoutput/xml. Potential matches:

- template <typename Derived, typename OtherDerived>
  EIGEN_STRONG_INLINE void utilities::trapz(Eigen::ArrayBase< OtherDerived > const &, const Eigen::ArrayBase< Derived > &, Eigen::Index)
- template <typename Derived>
  EIGEN_STRONG_INLINE Eigen::Array<typename Eigen::ArrayBase<Derived>::Scalar, Eigen::ArrayBase<Derived>::RowsAtCompileTime, Eigen::ArrayBase<Derived>::ColsAtCompileTime> utilities::trapz(const Eigen::ArrayBase< Derived > &, Eigen::Index)
- template <typename DerivedX, typename DerivedY, typename DerivedOut>
  EIGEN_STRONG_INLINE Eigen::Array<typename Eigen::ArrayBase<DerivedOut>::Scalar, Eigen::ArrayBase<DerivedOut>::RowsAtCompileTime, Eigen::ArrayBase<DerivedOut>::ColsAtCompileTime> utilities::trapz(const Eigen::ArrayBase< DerivedX > &, const Eigen::ArrayBase< DerivedY > &)
- template <typename DerivedX, typename DerivedY, typename DerivedOut>
  EIGEN_STRONG_INLINE void utilities::trapz(Eigen::ArrayBase< DerivedOut > const &, const Eigen::ArrayBase< DerivedX > &, const Eigen::ArrayBase< DerivedY > &)

Defines¶

Define acosd¶

Defined in File definitions.h

Define Documentation¶

acosd(x)¶

Define asind¶

Defined in File definitions.h

Define Documentation¶

asind(x)¶

Define cosd¶

Defined in File definitions.h

Define Documentation¶

cosd(x)¶

Define fourpi¶

Defined in File biot_savart.h

Define Documentation¶

fourpi¶

Define invfourpi¶

Defined in File biot_savart.h

Define Documentation¶

invfourpi¶

Define KAPPA_VON_KARMAN¶

Defined in File definitions.h

Define Documentation¶

KAPPA_VON_KARMAN¶

Define OMEGA_WORLD¶

Defined in File definitions.h

Define Documentation¶

OMEGA_WORLD¶

Define pi¶

Defined in File biot_savart.h

Define Documentation¶

pi¶

Define sind¶

Defined in File definitions.h

Define Documentation¶

sind(x)¶

Define tand¶

Defined in File definitions.h

Define Documentation¶

tand(x)¶

Typedefs¶

Typedef Array32d¶

Defined in File variable_readers.h

Typedef Documentation¶

typedef Eigen::Array<double, 3, 2> Array32d¶

Typedef Array32d¶

Defined in File variable_writers.h

Typedef Documentation¶

typedef Eigen::Array<double, 3, 2> Array32d

Typedef Array33d¶

Defined in File signature.h

Typedef Documentation¶

typedef Eigen::Array<double, 3, 3> Array33d¶

Typedef Array53d¶

Defined in File signature.h

Typedef Documentation¶

typedef Eigen::Array<double, 5, 3> Array53d¶

Typedef Array5b¶

Defined in File fit.h

Typedef Documentation¶

typedef Eigen::Array<bool, 5, 1> Array5b¶

Typedef Array5d¶

Defined in File fit.h

Typedef Documentation¶

typedef Eigen::Array<double, 5, 1> Array5d¶

Typedef utilities::ArrayType¶

Defined in File tensors.h

Typedef Documentation¶

using utilities::ArrayType = typedef Eigen::Array<T,Eigen::Dynamic, Eigen::Dynamic>

Typedef utilities::MatrixType¶

Defined in File tensors.h

Typedef Documentation¶

using utilities::MatrixType = typedef Eigen::Matrix<T,Eigen::Dynamic, Eigen::Dynamic>

Directories¶

Directory source¶

Directory path: source

Subdirectories¶

Files¶

Directory adem¶

↰ Parent directory (source)

Directory path: source/adem

Files¶

Directory io¶

↰ Parent directory (source)

Directory path: source/io

Files¶

Directory relations¶

↰ Parent directory (source)

Directory path: source/relations

Files¶

Directory utilities¶

↰ Parent directory (source)

Directory path: source/utilities

Files¶

File adem.h¶

↰ Parent directory (source/adem)

Contents

Definition (source/adem/adem.h)
Includes
Namespaces
Classes
Functions

Definition (source/adem/adem.h)¶

Program Listing for File adem.h¶

↰ Return to documentation for file (source/adem/adem.h)

/*
 * adem.h Implementation of the Attached-Detached Eddy Method
 *
 * Author:              Tom Clark  (thclark @ github)
 *
 * Copyright (c) 2019 Octue Ltd. All Rights Reserved.
 *
 */

#ifndef SOURCE_ADEM_H_
#define SOURCE_ADEM_H_

#include <vector>
#include <iostream>
#include <boost/algorithm/string/classification.hpp> // Include boost::for is_any_of
#include <boost/algorithm/string/split.hpp> // Include for boost::split
#include <Eigen/Dense>
#include <Eigen/Core>
#include <stdexcept>
#include <unsupported/Eigen/CXX11/Tensor>
#include <unsupported/Eigen/FFT>
#include <unsupported/Eigen/Splines>

#include "cpplot.h"

#include "adem/signature.h"
#include "profile.h"
#include "io/variable_readers.h"
#include "relations/stress.h"
#include "relations/velocity.h"
#include "utilities/conv.h"
#include "utilities/interp.h"
#include "utilities/filter.h"
#include "utilities/tensors.h"


using namespace utilities;
using namespace cpplot;


namespace es {


class AdemData {
public:

    std::vector<std::string> eddy_types = {"A", "B1+B2+B3+B4"};

    double beta;

    double delta_c;

    double kappa;

    double pi_coles;

    double shear_ratio;

    double u_inf;

    double u_tau;

    double zeta;

    Eigen::VectorXd z;

    Eigen::VectorXd eta;

    Eigen::VectorXd lambda_e;

    Eigen::VectorXd u_horizontal;

    Eigen::ArrayXXd reynolds_stress;

    Eigen::ArrayXXd r13a_analytic;

    Eigen::ArrayXXd r13b_analytic;

    Eigen::ArrayXXd reynolds_stress_a;

    Eigen::ArrayXXd reynolds_stress_b;

    Eigen::ArrayXXd k1z;

    Eigen::Tensor<double, 3> psi;

    Eigen::Tensor<double, 3> psi_a;

    Eigen::Tensor<double, 3> psi_b;

    Eigen::VectorXd t2wa;

    Eigen::VectorXd t2wb;

    Eigen::VectorXd residual_a;

    Eigen::VectorXd residual_b;

    Eigen::Index start_idx;

    // TODO consider whether we can tidy these variables up

    Eigen::ArrayXXd ja_fine;

    Eigen::ArrayXXd jb_fine;

    Eigen::ArrayXd r13a_analytic_fine;

    Eigen::ArrayXd r13b_analytic_fine;

    Eigen::ArrayXd minus_t2wa_fine;

    Eigen::ArrayXd minus_t2wb_fine;

    Eigen::ArrayXd lambda_fine;

    Eigen::ArrayXd eta_fine;

    void load(std::string file_name, bool print_var = true) {
        std::cout << "Reading adem data from file " << file_name << std::endl;

        // Open the MAT file for reading
        mat_t *matfp = Mat_Open(file_name.c_str(), MAT_ACC_RDONLY);
        if (matfp == NULL) {
            std::string msg = "Error reading MAT file: ";
            throw std::invalid_argument(msg + file_name);
        }

        // Use the variable readers to assist
        k1z                 = readArrayXXd(matfp, "k1z", print_var);
        beta                = readDouble(matfp, "beta", print_var);
        delta_c             = readDouble(matfp, "delta_c", print_var);
        kappa               = readDouble(matfp, "kappa", print_var);
        pi_coles            = readDouble(matfp, "pi_coles", print_var);
        shear_ratio         = readDouble(matfp, "shear_ratio", print_var);
        u_inf               = readDouble(matfp, "u_inf", print_var);
        u_tau               = readDouble(matfp, "u_tau", print_var);
        zeta                = readDouble(matfp, "zeta", print_var);
        z                   = readVectorXd(matfp, "z", print_var);
        eta                 = readVectorXd(matfp, "eta", print_var);
        lambda_e            = readVectorXd(matfp, "lambda_e", print_var);
        u_horizontal        = readVectorXd(matfp, "u_horizontal", print_var);
        reynolds_stress     = readArrayXXd(matfp, "reynolds_stress", print_var);
        reynolds_stress_a   = readArrayXXd(matfp, "reynolds_stress_a", print_var);
        reynolds_stress_b   = readArrayXXd(matfp, "reynolds_stress_b", print_var);
        k1z                 = readArrayXXd(matfp, "k1z", print_var);
        psi                 = readTensor3d(matfp, "psi", print_var);
        psi_a               = readTensor3d(matfp, "psi_a", print_var);
        psi_b               = readTensor3d(matfp, "psi_b", print_var);
        t2wa                = readVectorXd(matfp, "t2wa", print_var);
        t2wb                = readVectorXd(matfp, "t2wb", print_var);
        residual_a          = readVectorXd(matfp, "residual_a", print_var);
        residual_b          = readVectorXd(matfp, "residual_b", print_var);

        // Special handling to split the string of types into a vector of strings
        std::string typestr = readString(matfp, "eddy_types", print_var);
        boost::split(eddy_types, typestr, boost::is_any_of(", "), boost::token_compress_on);

        // Close the file
        Mat_Close(matfp);
        std::cout << "Finished reading adem data" << std::endl;
    }

    void save(std::string filename) {
        std::cout << "Writing signature data..." << std::endl;
        throw std::invalid_argument("Error writing mat file - function not implemented");
    }

};


std::ostream &operator<<(std::ostream &os, AdemData const &data) {
    os << "AdemData() with fields:" << std::endl;
    os << "    eddy_types:        ";
    for (std::vector<std::string>::const_iterator i = data.eddy_types.begin(); i != data.eddy_types.end(); ++i) {
        os << *i << ", ";
    }
    os << std::endl;
    os << "    beta:              " << data.beta << std::endl
       << "    delta_c:           " << data.delta_c << std::endl
       << "    kappa:             " << data.kappa << std::endl
       << "    pi_coles:          " << data.pi_coles << std::endl
       << "    shear_ratio:       " << data.shear_ratio << std::endl
       << "    u_inf:             " << data.u_inf << std::endl
       << "    u_tau:             " << data.u_tau << std::endl
       << "    zeta:              " << data.zeta << std::endl
       << "    z:                 [" << data.z.size() << " x 1]" << std::endl
       << "    eta:               [" << data.eta.size() << " x 1]" << std::endl
       << "    lambda_e:          [" << data.lambda_e.size() << " x 1]" << std::endl
       << "    u_horizontal:      [" << data.u_horizontal.size() << " x 1]" << std::endl
       << "    reynolds_stress:   [" << data.reynolds_stress.rows() << " x " << data.reynolds_stress.cols() << "]" << std::endl
       << "    reynolds_stress_a: [" << data.reynolds_stress_a.rows() << " x " << data.reynolds_stress_a.cols() << "]" << std::endl
       << "    reynolds_stress_b: [" << data.reynolds_stress_b.rows() << " x " << data.reynolds_stress_b.cols() << "]" << std::endl
       << "    k1z:               [" << data.k1z.rows() << " x " << data.k1z.cols() << "]" << std::endl
       << "    psi:               [" << tensor_dims(data.psi) << "]" << std::endl
       << "    psi_a:             [" << tensor_dims(data.psi_a) << "]" << std::endl
       << "    psi_b:             [" << tensor_dims(data.psi_b) << "]" << std::endl
       << "    t2wa:              [" << data.t2wa.size() << " x 1]" << std::endl
       << "    t2wb:              [" << data.t2wb.size() << " x 1]" << std::endl
       << "    residual_a:        [" << data.residual_a.size() << " x 1]" << std::endl
       << "    residual_b:        [" << data.residual_b.size() << " x 1]" << std::endl;
    return os;
}


void get_t2w(AdemData& data, const EddySignature& signature_a, const EddySignature& signature_b) {

    /* On the largest eddy scales:
     * lambda_e is the scale of a given eddy, which contributes to the stresses and spectra in the boundary layer.
     *
     * As far as the signatures are concerned, lambda is mapped for a domain spanning the actual eddy.
     * For a signature, values lambda < 0 are valid; since an eddy exerts an influence a short distance above itself
     * (eddies accelerate flow above them, and decelerate flow below).
     *
     * As far as the deconvolution is concerned, lambda is mapped over the whole boundary layer.
     * For a boundary layer profile, values < 0 are not meaningful: R_ij and S_ij must definitively be 0 outside
     * the boundary layer.
     *
     * Since values of lambda < 0 are theoretically valid for an eddy signature, the signatures as produced by
     * EddySignature().computeSignatures() extend out beyond lambda_e (to z/delta = 1.5, in our implementation).
     * Having an eddy whose scale is of the same size as the boundary layer would therefore create an influence outside
     * the boundary layer, breaking all assumptions about boundary layers ever.
     *
     * For us to maintain the fundamental boundary layer top condition that U = U_inf and u' = 0 for all z/delta >= 1,
     * we assume that eddies can have no influence above their own scale (following Perry & Marusic 1995 pp. 371-2).
     *
     * Clipping the signatures like this is the equivalent of setting the eddy signatures to zero where lambda < 0.
     *
     */
    data.start_idx = 0;
    for (Eigen::Index i=0; i<signature_a.lambda.rows(); i++) {
        if (signature_a.lambda(i) >= 0) {
            data.start_idx = i;
            break;
        }
    }
    Eigen::Index n_lambda_signature = signature_a.lambda.rows() - data.start_idx;
    Eigen::ArrayXd lambda_signature = signature_a.lambda.bottomRows(n_lambda_signature);

    /* On the smallest eddy scales:
     *
     * So the smallest scale we want to go to is lambda_1, which can be defined by the physics of the problem (i.e. the
     * cutoff beyond which viscosity takes over). This scale is defined by the Karman number K_tau.
     *  P&M 1995 again give us an approximate relation: lambda_1 ~= 100 nu/u_tau.
     *
     * As far as this function goes, we take lambda_1 as the smallest scale in the eddy signature array, which assumes
     * that signatures were computed on an appropriate grid.
     *
     */
    double d_lambda_fine = signature_a.domain_spacing(2);
    double lambda_min = lambda_signature(0);
    double lambda_max = lambda_signature(n_lambda_signature-1);
    Eigen::Index n_lambda_fine = round((lambda_max - lambda_min)/d_lambda_fine);

    Eigen::ArrayXd lambda_fine = Eigen::ArrayXd::LinSpaced(n_lambda_fine, lambda_min, lambda_max);

    // Hard limit on lambda max
    double mymax = log(1.0/0.01);
    Eigen::Index up_to = 0;
    for (Eigen::Index i=0; i<lambda_fine.rows(); i++) {
        if (lambda_fine(i) >= mymax) {
            up_to = i;
            break;
        }
    }
    lambda_fine = lambda_fine.topRows(up_to);

    Eigen::ArrayXd eta_fine = lambda_fine.exp().inverse();

    /* On the signatures:
     *
     * To avoid warping the reconstruction, we need to do the convolution and the deconvolution with
     * both the input and the signature on the same, linearly spaced, basis.
     *
     * To do this, we interpolate to a fine distribution and store the fine values.
     *
     */
    Eigen::ArrayXXd ja_fine = signature_a.getJ(lambda_fine);
    Eigen::ArrayXXd jb_fine = signature_b.getJ(lambda_fine);
    Eigen::ArrayXd j13a_fine = ja_fine.col(2);
    Eigen::ArrayXd j13b_fine = jb_fine.col(2);

    // Get an ascending version of eta, containing the point eta=0, for use in determining analytic R13 distributions
    Eigen::ArrayXd bounded_eta = Eigen::ArrayXd(eta_fine.rows()+2);
    bounded_eta.setZero();
    bounded_eta.middleRows(1, eta_fine.rows()) = eta_fine.reverse();
    bounded_eta.bottomRows(1) = 1.0;

    // Get Reynolds Stresses, trim the zero point, reverse back so the ordering is consistent with lambda coordinates
    Eigen::ArrayXd r13a_fine;
    Eigen::ArrayXd r13b_fine;
    reynolds_stress_13(r13a_fine, r13b_fine, data.beta, bounded_eta, data.kappa, data.pi_coles, data.shear_ratio, data.zeta);
    r13a_fine = r13a_fine.middleRows(1, eta_fine.rows());
    r13b_fine = r13b_fine.middleRows(1, eta_fine.rows());
    r13a_fine.reverseInPlace();
    r13b_fine.reverseInPlace();

    // Produce visual check that eta is ascending exponentially
    ScatterPlot pc = ScatterPlot();
    pc.x = Eigen::ArrayXd::LinSpaced(bounded_eta.rows(), 1, bounded_eta.rows());
    pc.y = bounded_eta;
    Layout layc = Layout("Check that eta ascends exponentially");
    layc.xTitle("Row number");
    layc.yTitle("$\\eta$");
    Figure figc = Figure();
    figc.add(pc);
    figc.setLayout(layc);
    figc.write("check_that_eta_ascends_exponentially.json");

    // Produce a visual check that lambda is ascending linearly
    ScatterPlot pc1 = ScatterPlot();
    pc1.x = Eigen::ArrayXd::LinSpaced(lambda_fine.rows(), 1, lambda_fine.rows());
    pc1.y = lambda_fine;
    Layout layc1 = Layout("Check that lambda ascends linearly");
    layc1.xTitle("Row number");
    layc1.yTitle("$\\lambda$");
    Figure figc1 = Figure();
    figc1.add(pc1);
    figc1.setLayout(layc1);
    figc1.write("check_that_lambda_ascends.json");

    // Double check J13 and interpolations
    ScatterPlot pja = ScatterPlot();
    pja.x = lambda_signature;
    pja.y = signature_a.j.bottomRows(n_lambda_signature).col(2);
    pja.name = "Type A (signature)";
    ScatterPlot pjaf = ScatterPlot();
    pjaf.x = lambda_fine;
    pjaf.y = j13a_fine;
    pjaf.name = "Type A (fine)";
    ScatterPlot pjb = ScatterPlot();
    pjb.x = lambda_signature;
    pjb.y = signature_b.j.bottomRows(n_lambda_signature).col(2);
    pjb.name = "Type B (signature)";
    ScatterPlot pjbf = ScatterPlot();
    pjbf.x = lambda_fine;
    pjbf.y = j13b_fine;
    pjbf.name = "Type B (fine)";
    Layout layj = Layout();
    layj.xTitle("$\\lambda$");
    layj.yTitle("$J_{13}$");
    Figure figj = Figure();
    figj.add(pja);
    figj.add(pjaf);
    figj.add(pjb);
    figj.add(pjbf);
    figj.setLayout(layj);
    figj.write("check_j13.json");

    // Deconvolve out the A and B structure contributions to the Reynolds Stresses
    // NOTE: it's actually -1*T^2w in this variable
    Eigen::ArrayXd minus_t2wa_fine;
    Eigen::ArrayXd minus_t2wb_fine;
//    double stability = 0.005;
//    minus_t2wa_fine = utilities::lowpass_fft_deconv(r13a_fine, j13a_fine, "Type_A", stability);
//    minus_t2wb_fine = utilities::lowpass_fft_deconv(r13b_fine, j13b_fine, "Type_B", stability);

    double alpha = 0.1;
    minus_t2wa_fine = utilities::diagonal_loading_deconv(r13a_fine, j13a_fine, alpha);
    minus_t2wb_fine = utilities::diagonal_loading_deconv(r13b_fine, j13b_fine, alpha);

    // Test the roundtripping convolution without any of the remapping
    Eigen::ArrayXd r13a_fine_recon = conv(minus_t2wa_fine.matrix(), j13a_fine.matrix()).matrix();
    Eigen::ArrayXd r13b_fine_recon = conv(minus_t2wb_fine.matrix(), j13b_fine.matrix()).matrix();

    // Show Reynolds Stresses behaving as part of validation
    ScatterPlot pa = ScatterPlot();
    pa.x = lambda_fine;
    pa.y = -1.0*r13a_fine;
    pa.name = "Type A (input)";

    ScatterPlot pb = ScatterPlot();
    pb.x = lambda_fine;
    pb.y = -1.0*r13b_fine;
    pb.name = "Type B (input)";

    ScatterPlot par = ScatterPlot();
    par.x = lambda_fine;
    par.y = -1.0*r13a_fine_recon;
    par.name = "Type A (reconstructed)";

    ScatterPlot pbr = ScatterPlot();
    pbr.x = lambda_fine;
    pbr.y = -1.0*r13b_fine_recon;
    pbr.name = "Type B (reconstructed)";

    Layout lay = Layout();
    lay.xTitle("$\\lambda$");
    lay.yTitle("$-\\overline{u_1u_3}/U_\\tau^2$");

    Figure fig = Figure();
    fig.add(pa);
    fig.add(pb);
    fig.add(par);
    fig.add(pbr);
    fig.setLayout(lay);
    fig.write("check_r13_fine_reconstruction.json");

    // Create a plot to show the t2w terms
    Figure figt = Figure();
    ScatterPlot pt = ScatterPlot();
    pt.x = lambda_fine;
    pt.y = minus_t2wa_fine;
    pt.name = "$-T_{A}^2(\\lambda - \\lambda_E)\\omega_{A}(\\lambda-\\lambda_E)$";
    figt.add(pt);
    ScatterPlot pt2 = ScatterPlot();
    pt2.x = lambda_fine;
    pt2.y = minus_t2wb_fine;
    pt2.name = "$-T_{B}^2(\\lambda - \\lambda_E)\\omega_{B}(\\lambda-\\lambda_E)$";
    figt.add(pt2);
    Layout layt = Layout();
    layt.xTitle("$\\lambda - \\lambda_E$");
    figt.setLayout(layt);
    figt.write("check_t2w.json");
    std::cout << "Wrote figure check_t2w" << std::endl;


    // Extend by padding out to the same length as lambda_e.
    // The T^2w distributions converge to a constant at high lambda (close to the wall) so padding with the last value
    // in the vector is physically valid. This will result in the Reynolds Stresses and Spectra, which are obtained by
    // convolution, having the same number of points in the z direction as the axes variables (eta, lambda_e, etc)
//    double pad_value_a = minus_t2wa(minus_t2wa.rows()-1);
//    double pad_value_b = minus_t2wb(minus_t2wb.rows()-1);
//
//    auto last_n = lambda_e.rows() - minus_t2wa.rows();
//    minus_t2wa.conservativeResize(lambda_e.rows(),1);
//    minus_t2wb.conservativeResize(lambda_e.rows(),1);
//    minus_t2wa.tail(last_n) = pad_value_a;
//    minus_t2wb.tail(last_n) = pad_value_b;

    // Store in the data object
    data.lambda_fine = lambda_fine;
    data.r13a_analytic_fine = r13a_fine;
    data.r13b_analytic_fine = r13b_fine;
    data.minus_t2wa_fine = minus_t2wa_fine;
    data.minus_t2wb_fine = minus_t2wb_fine;
    data.ja_fine = ja_fine;
    data.jb_fine = jb_fine;
    data.eta_fine = eta_fine;
    data.eta = eta_fine;

}


void get_mean_speed(AdemData& data) {
    data.u_horizontal = lewkowicz_speed(data.eta, data.pi_coles, data.kappa, data.u_inf, data.u_tau);
}


void get_reynolds_stresses(AdemData& data, const EddySignature& signature_a, const EddySignature& signature_b){

    // Allocate the output and set zero
    data.reynolds_stress_a = Eigen::ArrayXXd(data.lambda_fine.rows(), 6);
    data.reynolds_stress_b = Eigen::ArrayXXd(data.lambda_fine.rows(), 6);
    data.reynolds_stress_a.setZero();
    data.reynolds_stress_b.setZero();

    // Column-wise convolution of T2w with J
    for (int k = 0; k < 6; k++) {
        data.reynolds_stress_a.col(k) = conv(data.minus_t2wa_fine.matrix(), data.ja_fine.col(k).matrix());
        data.reynolds_stress_b.col(k) = conv(data.minus_t2wb_fine.matrix(), data.jb_fine.col(k).matrix());
    }

    // Trim the zero-padded ends
    data.reynolds_stress = data.reynolds_stress_a + data.reynolds_stress_b;

    // Check that R13 stacks up against the analytical solution
    Figure fig = Figure();
    Layout lay = Layout();
    ScatterPlot paa = ScatterPlot();
    paa.x = data.eta_fine;
    paa.y = -1.0*data.r13a_analytic_fine;
    paa.name = "Type A - analytic";
    ScatterPlot pba = ScatterPlot();
    pba.x = data.eta_fine;
    pba.y = -1.0*data.r13b_analytic_fine;
    pba.name = "Type B - analytic";
    ScatterPlot par = ScatterPlot();
    par.x = data.eta_fine;
    par.y = -1.0*(data.reynolds_stress_a.col(2));
    par.name = "Type A - reconstructed";
    ScatterPlot pbr = ScatterPlot();
    pbr.x = data.eta_fine;
    pbr.y = -1.0*(data.reynolds_stress_b.col(2));
    pbr.name = "Type B - reconstructed";
    fig.add(paa);
    fig.add(pba);
    fig.add(par);
    fig.add(pbr);
    lay.xTitle("$z/\\delta_{c}$");
    lay.yTitle("$-\\overline{u_1u_3}/U_\\tau^2$");
    fig.setLayout(lay);
    fig.write("check_r13_analytic_and_reconstructed.json");
}


void get_spectra(AdemData& data, const EddySignature& signature_a, const EddySignature& signature_b){

    // Initialise the output spectrum tensors
    Eigen::array<Eigen::Index, 3> dims = signature_a.g.dimensions();
    Eigen::array<Eigen::Index, 3> psi_dims = {data.t2wa.rows(), dims[1], dims[2]};
    Eigen::Tensor<double, 3> psi_a(psi_dims);
    Eigen::Tensor<double, 3> psi_b(psi_dims);

    // Map the t2w arrays as vectors, for use with the conv function
    Eigen::Map<Eigen::VectorXd> t2wa_vec(data.t2wa.data(), data.t2wa.rows());
    Eigen::Map<Eigen::VectorXd> t2wb_vec(data.t2wb.data(), data.t2wb.rows());

    std::cout << "DIMS " << dims[0] << " " << dims[1] << " " << dims[2] << std::endl;
    std::cout << "PSI_DIMS " << psi_dims[0] << " " << psi_dims[1] << " " << psi_dims[2] << std::endl;

    // For each of the 6 auto / cross spectra terms
    for (Eigen::Index j = 0; j < dims[2]; j++) {

        auto page_offset_sig = j * dims[0] * dims[1];
        auto page_offset_psi = j * psi_dims[0] * psi_dims[1];

        // For each of the wavenumbers
        for (Eigen::Index i = 0; i < dims[1]; i++) {

            auto elements_offset_sig = (page_offset_sig + i * dims[0]);
            auto elements_offset_psi = (page_offset_psi + i * psi_dims[0]);

            Eigen::Map<Eigen::VectorXd> g_a_vec((double *)signature_a.g.data() + elements_offset_sig, dims[0]);
            Eigen::Map<Eigen::VectorXd> g_b_vec((double *)signature_b.g.data() + elements_offset_sig, dims[0]);

            Eigen::Map<Eigen::VectorXd> psi_a_vec((double *)psi_a.data() + elements_offset_psi, psi_dims[0]);
            Eigen::Map<Eigen::VectorXd> psi_b_vec((double *)psi_b.data() + elements_offset_psi, psi_dims[0]);

            psi_a_vec = conv(t2wa_vec, g_a_vec).reverse();
            psi_b_vec = conv(t2wb_vec, g_b_vec).reverse();

        }
    }

    // Don't store the sum of the spectra - they're memory hungry and we can always add the two together

    // Premultiply by the u_tau^2 term (see eq. 43)
    // auto u_tau_sqd = pow(data.u_tau, 2.0);
    // data.psi_a = u_tau_sqd * psi_a;
    // data.psi_b = u_tau_sqd * psi_b;
    data.psi_a = psi_a;
    data.psi_b = psi_b;

}


AdemData adem(const double beta,
              const double delta_c,
              const double kappa,
              const double pi_coles,
              const double shear_ratio,
              const double u_inf,
              const double zeta,
              const EddySignature& signature_a,
              const EddySignature& signature_b,
              bool compute_spectra=true){

    // Data will contain computed outputs and useful small variables from the large signature files
    AdemData data = AdemData();

    // Add parameter inputs to data structure
    data.beta = beta;
    data.delta_c = delta_c;
    data.kappa = kappa;
    data.pi_coles = pi_coles;
    data.shear_ratio = shear_ratio;
    data.u_inf = u_inf;
    data.u_tau = data.u_inf / data.shear_ratio;
    data.zeta = zeta;

    // Deconvolve for T^2w and update the data structure with the outputs
    get_t2w(data, signature_a, signature_b);

    // Get vertical points through the boundary layer (for which the convolution functions were defined)
    data.z = data.eta.array() * data.delta_c;

    // Add k1z to the data structure
    Eigen::ArrayXd eta = data.eta.array();
    data.k1z = signature_a.k1z(eta);

    // Get the mean speed profile at the same vertical points and update the data structure
    get_mean_speed(data);

    // Determine Reynolds Stresses by convolution and add them to the data structure
    get_reynolds_stresses(data, signature_a, signature_b);

    // Determine Spectra by convolution and add them to the data structure
    if (compute_spectra) {
        get_spectra(data, signature_a, signature_b);
    }

    return data;

}

} /* namespace es */

#endif /* SOURCE_ADEM_H_ */

Includes¶

Eigen/Core
Eigen/Dense
adem/signature.h (File signature.h)
boost/algorithm/string/classification.hpp
boost/algorithm/string/split.hpp
cpplot.h
io/variable_readers.h (File variable_readers.h)
iostream
profile.h (File profile.h)
relations/stress.h (File stress.h)
relations/velocity.h (File velocity.h)
stdexcept
unsupported/Eigen/CXX11/Tensor
unsupported/Eigen/FFT
unsupported/Eigen/Splines
utilities/conv.h (File conv.h)
utilities/filter.h (File filter.h)
utilities/interp.h (File interp.h)
utilities/tensors.h (File tensors.h)
vector

Namespaces¶

Classes¶

Class AdemData

Functions¶

File biot_savart.h¶

↰ Parent directory (source/adem)

Contents

Definition (source/adem/biot_savart.h)
Includes
Included By
Namespaces
Functions
Defines

Definition (source/adem/biot_savart.h)¶

Program Listing for File biot_savart.h¶

↰ Return to documentation for file (source/adem/biot_savart.h)

/*
 * biot_savart.h A parallelised biot-savart function for use with the Attached-Detached Eddy Method
 *
 * Author:              Tom Clark  (thclark @ github)
 *
 * Copyright (c) 2014-2019 Octue Ltd. All Rights Reserved.
 *
 */

#ifndef ES_FLOW_BIOT_SAVART_H
#define ES_FLOW_BIOT_SAVART_H

#include <tbb/tbb.h>
#include <tbb/blocked_range.h>
#include <tbb/parallel_for.h>
#include <tbb/atomic.h>
#include <math.h>
#include <stdio.h>
#include <string.h>
#include <time.h>
#include <iostream>
#include <Eigen/Dense>


using namespace Eigen;
using namespace std;


#define pi          3.14159265358979323846264;
#define fourpi      12.5663706143592172953851;
#define invfourpi   0.079577471545948;


namespace es {


// @cond - Don't document these convenience inline functions or the kernel

// Inverse magnitude of a Vector3d element
static inline double InvMagnitude(Vector3d vec){
    return 1 / vec.norm();
}


// Inverse magnitude of a Vector3d element handling /0 errors to return 0 always
static inline double InvMagnitudeZero(Vector3d vec)
{
    double a = vec.norm();
    if (a == 0.) {
        return 0.;
    } else {
        return 1 / a;
    }
}


// Kernel that applies induction from one vortex line to one control point
static inline Vector3d BiotElementalKernel(Vector3d control_locations, Vector3d start_nodes, Vector3d end_nodes, double gamma, double effective_core_radius_squared)
{

    Vector3d l12 = end_nodes - start_nodes;

    Vector3d r1 = control_locations - start_nodes;

    Vector3d r2 = control_locations - end_nodes;

    Vector3d cross1 = l12.cross(r1);

    // Used invmagnitudezero to solve the problem where the cross product is {0,0,0} due to point p being on the line defined by l12 (r1 collinear with l12)
    Vector3d induction;
    induction = InvMagnitudeZero(cross1) * cross1;
    double mag_l12 = InvMagnitude(l12);
    double mag_r1 = InvMagnitudeZero(r1);
    double mag_r2 = InvMagnitudeZero(r2);
    double costheta_1 = l12.dot(r1) * (mag_l12 * mag_r1);
    double costheta_2 = l12.dot(r2) * (mag_l12 * mag_r2);
    double h = (cross1.norm()) * (mag_l12);
    double magu = gamma * h * (costheta_1 - costheta_2) * invfourpi;
    magu /= sqrt(pow(effective_core_radius_squared, 2) + pow(h, 4));
    induction = induction * magu;

    return induction;

};


// @endcond


Matrix3Xd NaiveBiotSavart(Matrix3Xd startNodes, Matrix3Xd endNodes, Matrix3Xd locations, VectorXd gamma, VectorXd effective_core_radius_squared){

    assert (startNodes.cols() == gamma.size());
    assert (startNodes.cols() == endNodes.cols());
    assert (startNodes.cols() == effective_core_radius_squared.size());
    Index start = 0;
    Index n_control_point = locations.cols();
    Index n_vortex = gamma.size();
    Index n = n_control_point * n_vortex;

    Matrix3Xd induction(3, n_control_point);
    induction.setZero();

    // Parallel version
    tbb::affinity_partitioner partitioner1;
    tbb::affinity_partitioner partitioner2;

    tbb::parallel_for(start, n_control_point, [&](Index control_i){

        Vector3d p = locations.col(control_i);

        Vector3d induction_accumulator;
        induction_accumulator.setZero();
        tbb::spin_mutex induction_mutex;

        tbb::parallel_for(start, n_vortex, [&](Index vortex_i){
            Vector3d A1 = startNodes.col(vortex_i);
            Vector3d B1 = endNodes.col(vortex_i);
            double a = gamma(vortex_i);
            double rc4 = effective_core_radius_squared(vortex_i);
            Vector3d induction_elemental = BiotElementalKernel(p, A1, B1, a, rc4);
            {
                tbb::spin_mutex::scoped_lock lock(induction_mutex);
                induction_accumulator += induction_elemental;
            }
        }, partitioner1);
        induction.block(0, control_i, 3, 1) = induction_accumulator;

    }, partitioner2);

    /* Serial version
    for (long control_i = 0; control_i < n_control_point; control_i++)
    {
        Vector3d p = locations.block(0,control_i,3,1);
        long vortex_i;
        for (vortex_i = 0; vortex_i < n_vortex; vortex_i++) {
            Vector3d A1 = startNodes.block(0, vortex_i, 3, 1);
            Vector3d B1 = endNodes.block(0, vortex_i, 3, 1);
            double a = gamma(vortex_i);
            double rc4 = effective_core_radius_squared(vortex_i);
            induction.block(0, control_i, 3, 1) = induction.block(0, control_i, 3, 1) + BiotElementalKernel(p, A1, B1, a, rc4);
        };

    }
    */

    return induction;
};

};

#endif

Includes¶

Eigen/Dense
iostream
math.h
stdio.h
string.h
tbb/atomic.h
tbb/blocked_range.h
tbb/parallel_for.h
tbb/tbb.h
time.h

Included By¶

File signature.h

Namespaces¶

Functions¶

Function es::NaiveBiotSavart

Defines¶

File conv.h¶

↰ Parent directory (source/utilities)

Contents

Definition (source/utilities/conv.h)
Includes
Included By
Namespaces
Functions

Definition (source/utilities/conv.h)¶

Program Listing for File conv.h¶

↰ Return to documentation for file (source/utilities/conv.h)

/*
 * conv.h Matlab-like convolution
 *
 * Author:              Tom Clark  (thclark @ github)
 *
 * Copyright (c) 2019 Octue Ltd. All Rights Reserved.
 *
 */

#ifndef ES_FLOW_CONV_H
#define ES_FLOW_CONV_H

#include <Eigen/Dense>
#include <Eigen/Core>
#include <unsupported/Eigen/FFT>
#include <math.h>

//#include "cpplot.h"
//using namespace cpplot;

namespace utilities {


template<typename T>
T fft_next_good_size(const T n) {
    T result = n;
    if (n <= 2) {
        result = 2;
        return result;
    }
    while (true) {
        T m = result;
        while ((m % 2) == 0) m = m / 2;
        while ((m % 3) == 0) m = m / 3;
        while ((m % 5) == 0) m = m / 5;
        if (m <= 1) {
            return (result);
        }
        result = result + 1;
    }
}


Eigen::VectorXd conv(const Eigen::VectorXd &input, const Eigen::VectorXd &kernel) {

    // TODO template this function signature to also accept arrays

    // Map the input signature data to tensors (shared memory)
    auto input_len = input.rows();
    auto kernel_len = kernel.rows();

    // Compute cumulative length of input and kernel;
    auto N = input_len + kernel_len - 1;
    auto M = fft_next_good_size(N);

    // Create padded FFT inputs
    Eigen::FFT<double> fft;
    Eigen::VectorXd input_padded(M);
    Eigen::VectorXd kernel_padded(M);
    input_padded.setZero();
    kernel_padded.setZero();
    input_padded.topRows(input_len) = input;
    kernel_padded.topRows(kernel_len) = kernel;

    // Take the forward ffts
    Eigen::VectorXcd input_transformed(M);
    Eigen::VectorXcd kernel_transformed(M);
    fft.fwd(input_transformed, input_padded);
    fft.fwd(kernel_transformed, kernel_padded);

    // Convolve by element-wise multiplication
    Eigen::VectorXcd inter = input_transformed.array() * kernel_transformed.array();

    // Inverse FFT
    Eigen::VectorXd out(M);
    out.setZero();
    fft.inv(out, inter);

    // Crop to the size of the input vector
    out = out.topRows(input_len);
    return out;
}


Eigen::MatrixXd convolution_matrix(const Eigen::VectorXd &k, const Eigen::Index n) {

    Eigen::Index mk = k.rows();
    Eigen::VectorXd toeplitz_col = Eigen::VectorXd::Zero(mk + n - 1);
    toeplitz_col.topRows(mk) = k;

    Eigen::Index mt = toeplitz_col.rows();
    Eigen::MatrixXd toeplitz = Eigen::MatrixXd::Zero(mt, n);

    // Fill the lower diagonal of a toeplitz matrix.
    // If it's fat rectangular we don't need to fill the right-most columns.
    Eigen::Index nt_limit = Eigen::Vector2i(n, mt).minCoeff();
    for (Eigen::Index j = 0; j < nt_limit; j++) {
        Eigen::Index extent = Eigen::Vector2i(mt-j, k.rows()).minCoeff();
        toeplitz.block(j,j, extent, 1) = toeplitz_col.topRows(extent);
    }
    return toeplitz;
}


Eigen::VectorXd diagonal_loading_deconv(const Eigen::VectorXd &input, const Eigen::VectorXd &kernel, const double alpha=0.1) {
    Eigen::Index n = input.rows();
    Eigen::MatrixXd eye(n, n);
    eye.setIdentity();
    Eigen::MatrixXd c = convolution_matrix(kernel, n).topRows(n);
    Eigen::MatrixXd ct = c.transpose();
    Eigen::BDCSVD<Eigen::MatrixXd> svd(ct * c + alpha * eye, Eigen::ComputeThinU | Eigen::ComputeThinV);
    Eigen::VectorXd x = svd.solve(ct * input);
    return x;
}


Eigen::VectorXd lowpass_fft_deconv(const Eigen::VectorXd &input, const Eigen::VectorXd &kernel, const std::string &flag, double stab=0.01) {

    // Map the input signature data to tensors (shared memory)
    auto input_len = input.rows();
    auto kernel_len = kernel.rows();

    // Compute cumulative length of input and kernel;
    auto N = input_len + kernel_len - 1;
    auto M = fft_next_good_size(N);

    // Create padded FFT inputs
    Eigen::FFT<double> fft;
    Eigen::VectorXd input_padded(M);
    Eigen::VectorXd kernel_padded(M);
    input_padded.setZero();
    kernel_padded.setZero();
    input_padded.topRows(input_len) = input;
    kernel_padded.topRows(kernel_len) = kernel;

    // Take the forward ffts
    Eigen::VectorXcd input_transformed(M);
    Eigen::VectorXcd kernel_transformed(M);
    fft.fwd(input_transformed, input_padded);
    fft.fwd(kernel_transformed, kernel_padded);

    // Magnitude of the transformed kernel and input
    Eigen::ArrayXd input_mag = pow(input_transformed.array().real(), 2.0) + pow(input_transformed.array().imag(), 2.0);
    input_mag = pow(input_mag, 0.5);
    Eigen::ArrayXd kernel_mag = pow(kernel_transformed.array().real(), 2.0) + pow(kernel_transformed.array().imag(), 2.0);
    kernel_mag = pow(kernel_mag, 0.5);

    // Double check plot
//    Figure fig = Figure();
//    ScatterPlot p3 = ScatterPlot();
//    p3.x = Eigen::ArrayXd::LinSpaced(M, 1, M);
//    p3.y = input_mag;
//    p3.name = "input mag";
//    fig.add(p3);
//    ScatterPlot p2 = ScatterPlot();
//    p2.x = Eigen::ArrayXd::LinSpaced(M, 1, M);
//    p2.y = kernel_mag;
//    p2.name = "kernel mag";
//    fig.add(p2);

    // Deconvolve by element-wise division, stabilising divide-by-0 errors based on the 1% of magnitude of the kernel
    Eigen::VectorXcd inter(M);
    inter.setZero();

    if (stab > 0) {
        double kernel_cutoff_magnitude = kernel_mag.maxCoeff() * stab;
        Eigen::Index ctr = 0;
        Eigen::Index location = -1;
        for (ctr = 0; ctr < M; ctr++) {
            if (kernel_mag(ctr) > kernel_cutoff_magnitude) {
                inter(ctr) = input_transformed(ctr) / kernel_transformed(ctr);
            } else {
                if (location == -1) {
                    location = ctr;
                };
//                break;
                inter(ctr) = 0;
            }
        }
        std::cout << "LOCATION " << location << std::endl;

        // The above works on its own, but produces high frequency ringing, because of the sharp cutoff low pass filter.
        // The ctr is now set at the point where we want the lowpass filter to fade out entirely, so determine a
        // gaussian form between position 0 and here

//        inter = input_transformed.array() / kernel_transformed.array();

        // TODO this can be done in-place to avoid duplicating memory but we want to plot for the time being
        Eigen::ArrayXd map_frequency = Eigen::ArrayXd::LinSpaced(location, -5.0, 5);
        Eigen::ArrayXd low_pass(M);
        low_pass.setZero();
        for (auto i = 0; i < map_frequency.rows(); i++) {
            low_pass(i) = 0.5 * (1.0 - std::erf(map_frequency(i)));
        }

        // We're working with a dual-sided FFT so mirror the filter
        low_pass = low_pass + low_pass.reverse();

        // Apply the low pass filter
        inter = inter.array() * low_pass;

        // Debug plot
//        ScatterPlot p5 = ScatterPlot();
//        p5.x = Eigen::ArrayXd::LinSpaced(low_pass.rows(), 1, low_pass.rows());
//        p5.y = low_pass;
//        p5.name = "lowpass magnitude";
//        fig.add(p5);

    } else {
        inter = input_transformed.array() / kernel_transformed.array();
    }

//    for (auto k = 0; k<M; k++) {
//        if ((k > 4) && (k < M-5)) {
//            inter(k) = 0.0;
//        }
//    }

//    std::cout << "Smoothing the inter" <<std::endl;
//    Eigen::ArrayXd inter_sm_imag(inter.size());
//    inter_sm_imag.segment(2, M-5) = (inter.imag().segment(0, M-5) + inter.imag().segment(1, M-5) + inter.imag().segment(2, M-5) + inter.imag().segment(3, M-5)  + inter.imag().segment(4, M-5)) / 5.0;
//    inter_sm_imag(1) = (inter.imag()(0) + inter.imag()(1) + inter.imag()(2))/3.0;
//    inter_sm_imag(M-2) = (inter.imag()(M-3) + inter.imag()(M-2) + inter.imag()(M-1))/3.0;
//    inter.imag() = inter_sm_imag;
//    Eigen::ArrayXd inter_sm_real(inter.size());
//    inter_sm_real.segment(2, M-5) = (inter.real().segment(0, M-5) + inter.real().segment(1, M-5) + inter.real().segment(2, M-5) + inter.real().segment(3, M-5)  + inter.real().segment(4, M-5)) / 5.0;
//    inter_sm_real(1) = (inter.real()(0) + inter.real()(1) + inter.real()(2))/3.0;
//    inter_sm_real(M-2) = (inter.real()(M-3) + inter.real()(M-2) + inter.real()(M-1))/3.0;
//    inter.real() = inter_sm_real;


//    Eigen::ArrayXd inter_mag = pow(inter.array().real(), 2.0) + pow(inter.array().imag(), 2.0);
//    inter_mag = pow(inter_mag, 0.5);
    Eigen::ArrayXd inter_mag = inter.array().imag();
//    ScatterPlot p4 = ScatterPlot();
//    p4.x = Eigen::ArrayXd::LinSpaced(M, 1, M);
//    p4.y = inter_mag;
//    p4.name = "inter mag";
//    fig.add(p4);
//
//    fig.write("check_that_fft_deconv_behaves_" + flag + ".json");
    // Inverse FFT
    Eigen::VectorXd out(M);
    out.setZero();
    fft.inv(out, inter);

    // Smooth the output
    std::cout << "Smoothing the out" <<std::endl;
    Eigen::ArrayXd inter_sm_imag(out.size());
    Eigen::ArrayXd out_sm(out.size());
    out_sm.segment(2, M-5) = (out.segment(0, M-5) + out.segment(1, M-5) + out.segment(2, M-5) + out.segment(3, M-5)  + out.segment(4, M-5)) / 5.0;
    out_sm(1) = (out(0) + out(1) + out(2))/3.0;
    out_sm(M-2) = (out(M-3) + out(M-2) + out(M-1))/3.0;
    out = out_sm;

    // Crop to the size of the input vector
    out = out.topRows(input_len);

    return out;
}

}  /* namespace utilities */



#endif //ES_FLOW_CONV_H

Includes¶

Eigen/Core
Eigen/Dense
math.h
unsupported/Eigen/FFT

Included By¶

Namespaces¶

Namespace utilities

Functions¶

File cumsum.h¶

↰ Parent directory (source/utilities)

Contents

Definition (source/utilities/cumsum.h)
Includes
Namespaces
Functions

Definition (source/utilities/cumsum.h)¶

Program Listing for File cumsum.h¶

↰ Return to documentation for file (source/utilities/cumsum.h)

/*
 * cumsum.h Cumulative sum of a vector
 *
 * Author:              Tom Clark  (thclark @ github)
 *
 * Copyright (c) 2019 Octue Ltd. All Rights Reserved.
 *
 * ---
 *
 * This file is adapted from part of libigl, a simple c++ geometry processing library.
 *
 * Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
 *
 * This Source Code Form is subject to the terms of the Mozilla Public License
 * v. 2.0. If a copy of the MPL was not distributed with this file, You can
 * obtain one at http://mozilla.org/MPL/2.0/.
 *
 */

#ifndef ES_FLOW_CUMSUM_H
#define ES_FLOW_CUMSUM_H

#include <Eigen/Core>
#include <Eigen/Dense>


namespace utilities {

/* Computes a cumulative sum down the columns (or across the rows) of X
 *
 * @tparam DerivedX Type of matrix/array X
 * @tparam DerivedY Type of matrix/array Y
 * @param[in] X    m by n Matrix to be cumulatively summed.
 * @param[in] dim  dimension to take cumulative sum (1 goes down columns, 2 across rows). Default 1.
 * @param[out] Y   m by n Matrix containing cumulative sum.
 */
template <typename DerivedX, typename DerivedY>
EIGEN_STRONG_INLINE void cumsum(Eigen::PlainObjectBase<DerivedY > & y, const Eigen::MatrixBase<DerivedX > & x, const int dim=1) {

    y.resizeLike(x);

    Eigen::Index num_outer = (dim == 1 ? x.cols() : x.rows() );
    Eigen::Index num_inner = (dim == 1 ? x.rows() : x.cols() );

    // This has been optimized so that dim = 1 or 2 is roughly the same cost.
    // (Optimizations assume ColMajor order)
    if (dim == 1) {
        // TODO multithread the outer loop
        for(int o = 0; o<num_outer; o++)
        {
            typename DerivedX::Scalar sum = 0;
            for (int i = 0;i<num_inner;i++) {
                sum += x(i,o);
                y(i,o) = sum;
            }
        }
    } else {
        for (int i = 0; i<num_inner; i++) {
            // TODO multithread the inner loop
            for (int o = 0; o<num_outer; o++) {
                if (i == 0) {
                    y(o,i) = x(o,i);
                } else {
                    y(o,i) = y(o,i-1) + x(o,i);
                }
            }
        }
    }
}

}

#endif //ES_FLOW_CUMSUM_H

Includes¶

Eigen/Core
Eigen/Dense

Namespaces¶

Namespace utilities

Functions¶

Template Function utilities::cumsum

File cumtrapz.h¶

↰ Parent directory (source/utilities)

Contents

Definition (source/utilities/cumtrapz.h)
Includes

Definition (source/utilities/cumtrapz.h)¶

Program Listing for File cumtrapz.h¶

↰ Return to documentation for file (source/utilities/cumtrapz.h)

/*
 * cumtrapz.h Cumulative Trapezoidal Numerical Integration for Eigen
 *
 * Author:              Tom Clark  (thclark @ github)
 *
 * Copyright (c) 2019 Octue Ltd. All Rights Reserved.
 *
 */

#ifndef ES_FLOW_CUMTRAPZ_H
#define ES_FLOW_CUMTRAPZ_H

#include <Eigen/Dense>


namespace utilities {


template<typename Derived, typename OtherDerived>
EIGEN_STRONG_INLINE void cumsum(Eigen::ArrayBase<OtherDerived> const & out, const Eigen::ArrayBase<Derived>& in)
{
    Eigen::ArrayBase<OtherDerived>& out_ = const_cast< Eigen::ArrayBase<OtherDerived>& >(out);
    out_ = in;
    for (int i = 0 ; i < out_.cols() ; ++i)
    {
        for (int j = 1 ; j < out_.rows() ; ++j)
        {
            out_.coeffRef(j,i) += out_.coeff(j-1,i);
        }
    }
}
// Remove template specialisation from doc (causes duplicate) @cond
template<typename Derived>
EIGEN_STRONG_INLINE Eigen::Array<typename Eigen::ArrayBase<Derived>::Scalar, Eigen::ArrayBase<Derived>::RowsAtCompileTime, Eigen::ArrayBase<Derived>::ColsAtCompileTime> cumsum(const Eigen::ArrayBase<Derived>& y)
{
    Eigen::Array<typename Eigen::ArrayBase<Derived>::Scalar, Eigen::ArrayBase<Derived>::RowsAtCompileTime, Eigen::ArrayBase<Derived>::ColsAtCompileTime> z;
    cumsum(z,y);
    return z;
}
// @endcond


template<typename Derived, typename OtherDerived>
EIGEN_STRONG_INLINE void cumtrapz(Eigen::ArrayBase<OtherDerived> const & out, const Eigen::ArrayBase<Derived>& in)
{
    Eigen::ArrayBase<OtherDerived>& out_ = const_cast< Eigen::ArrayBase<OtherDerived>& >(out);
    out_.derived().setZero(in.rows(), in.cols());
    cumsum(out_.bottomRows(out_.rows()-1), (in.topRows(in.rows()-1) + in.bottomRows(in.rows()-1)) * 0.5);
}
// Remove template specialisation from doc (causes duplicate) @cond
template<typename Derived>
EIGEN_STRONG_INLINE Eigen::Array<typename Eigen::ArrayBase<Derived>::Scalar, Eigen::ArrayBase<Derived>::RowsAtCompileTime, Eigen::ArrayBase<Derived>::ColsAtCompileTime> cumtrapz(const Eigen::ArrayBase<Derived>& y)
{
    Eigen::Array<typename Eigen::ArrayBase<Derived>::Scalar, Eigen::ArrayBase<Derived>::RowsAtCompileTime, Eigen::ArrayBase<Derived>::ColsAtCompileTime> z;
    cumtrapz(z,y);
    return z;
}
// @endcond


template<typename DerivedX, typename DerivedY, typename DerivedOut>
EIGEN_STRONG_INLINE void cumtrapz(Eigen::ArrayBase<DerivedOut> const & out, const Eigen::ArrayBase<DerivedX>& in_x, const Eigen::ArrayBase<DerivedY>& in_y)
{
    // Input size check
    eigen_assert(in_x.rows() == in_y.rows());
    eigen_assert(in_x.cols() == 1);

    // Get dx for each piece of the integration
    Eigen::Array<typename Eigen::ArrayBase<DerivedX>::Scalar, Eigen::ArrayBase<DerivedX>::RowsAtCompileTime, Eigen::ArrayBase<DerivedX>::ColsAtCompileTime> dx;
    dx = (in_x.bottomRows(in_x.rows()-1) - in_x.topRows(in_x.rows()-1));

    // Get the average heights of the trapezoids
    Eigen::Array<typename Eigen::ArrayBase<DerivedY>::Scalar, Eigen::ArrayBase<DerivedY>::RowsAtCompileTime, Eigen::ArrayBase<DerivedY>::ColsAtCompileTime> inter;
    inter = (in_y.topRows(in_y.rows()-1) + in_y.bottomRows(in_y.rows()-1)) * 0.5;

    // Multiply by trapezoid widths to give areas of the trapezoids.
    // NB Broadcasting with *= only works for arrayX types, not arrayXX types like dx
    //  inter *= dx;
    for (int i = 0 ; i < inter.cols() ; ++i)
    {
        for (int j = 0 ; j < inter.rows() ; ++j)
        {
            inter(j,i) *= dx(j,0);
        }
    }

    // Initialise output
    Eigen::ArrayBase<DerivedOut>& out_ = const_cast< Eigen::ArrayBase<DerivedOut>& >(out);
    out_.derived().setZero(in_y.rows(), in_y.cols());

    // Perform the cumulative sum down the columns
    cumsum(out_.bottomRows(out_.rows()-1), inter);
}
// Remove template specialisation from doc (causes duplicate) @cond
template<typename DerivedX, typename DerivedY, typename DerivedOut>
EIGEN_STRONG_INLINE Eigen::Array<typename Eigen::ArrayBase<DerivedOut>::Scalar, Eigen::ArrayBase<DerivedOut>::RowsAtCompileTime, Eigen::ArrayBase<DerivedOut>::ColsAtCompileTime> cumtrapz(const Eigen::ArrayBase<DerivedX>& x, const Eigen::ArrayBase<DerivedY>& y)
{
    Eigen::Array<typename Eigen::ArrayBase<DerivedOut>::Scalar, Eigen::ArrayBase<DerivedOut>::RowsAtCompileTime, Eigen::ArrayBase<DerivedOut>::ColsAtCompileTime> z;
    cumtrapz(z, x, y);
    return z;
}

}  /* namespace utilities */

#endif //ES_FLOW_CUMTRAPZ_H

Includes¶

Eigen/Dense

File data_types.h¶

↰ Parent directory (source)

Contents

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Definition (source/data_types.h)¶

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/*
 * data_types.h Definitions for different input data types
 *
 * Author:              Tom Clark  (thclark @ github)
 *
 * Copyright (c) 2019 Octue Ltd. All Rights Reserved.
 *
 */

#ifndef ES_FLOW_DATA_TYPES_H
#define ES_FLOW_DATA_TYPES_H

#include <string>
#include "matio.h"
#include <eigen3/Eigen/Core>
#include "io/variable_readers.h"


namespace es {


class BasicLidar {
public:
    const std::string type = "lidar_basic";
    VectorXd t;
    VectorXd z;
    Eigen::Array<double, Eigen::Dynamic, Eigen::Dynamic> u;
    Eigen::Array<double, Eigen::Dynamic, Eigen::Dynamic> v;
    Eigen::Array<double, Eigen::Dynamic, Eigen::Dynamic> w;
    Eigen::Vector3d position;
    double half_angle;
    struct {
        std::string t;
        std::string z;
        std::string u;
        std::string v;
        std::string w;
        std::string position;
        std::string half_angle;
    }units;

    void read(mat_t *matfp, bool print_var = true) {

        // Straightforward reads
        t = readVectorXd(matfp, "t", print_var);
        z = readVectorXd(matfp, "z", print_var);
        u = readArrayXXd(matfp, "u", print_var);
        v = readArrayXXd(matfp, "v", print_var);
        w = readArrayXXd(matfp, "w", print_var);
        half_angle = readDouble(matfp, "half_angle", print_var);

        // Handle initialisation of position as a two element vector, zero padded (elevation = 0) and as a three
        // element vector.
        Eigen::VectorXd pos = readVectorXd(matfp, "position", print_var);
        if (pos.size() == 2) {
            position = Vector3d(pos(0), pos(1), 0.0);
        }else {
            position = Vector3d(pos(0), pos(1), pos(2));
        }

        // TODO read in and tests on units structure

    }

};

} /* namespace es */

#endif // ES_FLOW_DATA_TYPES_H

Includes¶

eigen3/Eigen/Core
io/variable_readers.h (File variable_readers.h)
matio.h
string

Included By¶

File readers.h

Namespaces¶

Namespace es

Classes¶

Class BasicLidar

File definitions.h¶

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Definition (source/definitions.h)
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Definition (source/definitions.h)¶

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/*
 * definitions.h Constants, definitions and identities
 *
 * Author:              Tom Clark  (thclark @ github)
 *
 * Copyright (c) 2019 Octue Ltd. All Rights Reserved.
 *
 */

#ifndef ES_FLOW_DEFINITIONS_H
#define ES_FLOW_DEFINITIONS_H

// Rotational speed of the world in rad/s
#define OMEGA_WORLD 7.2921159e-05

// von Karman constant
#define KAPPA_VON_KARMAN 0.41

// Degrees based trigonometry
#define sind(x) (sin(fmod((x), 360.0) * M_PI / 180.0))
#define cosd(x) (cos(fmod((x), 360.0) * M_PI / 180.0))
#define asind(x) (asin(x) * 180.0 / M_PI)
#define acosd(x) (acos(x) * 180.0 / M_PI)
#define tand(x) (tan(x * M_PI / 180.0) * M_PI / 180.0)

#endif // ES_FLOW_DEFINITIONS_H

Included By¶

Defines¶

File exceptions.h¶

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Definition (source/exceptions.h)
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Definition (source/exceptions.h)¶

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/*
 * exceptions.h Customised exceptions for appropriate and fine grained error handling
 *
 * Author:              Tom Clark  (thclark@github)
 *
 * Copyright (c) 2017-9 Octue Ltd. All Rights Reserved.
 *
 */

#ifndef ES_FLOW_EXCEPTIONS_H
#define ES_FLOW_EXCEPTIONS_H


#include <exception>


namespace es {


struct NotImplementedException : public std::exception {
    std::string message = "Not yet implemented";
    const char *what() const throw() {
        return message.c_str();
    }
};

struct InvalidEddyTypeException : public std::exception {
    std::string message = "Unknown eddy type. Eddy type string must be one of 'A', 'B1', 'B2', 'B3' or 'B4'.";
    const char *what() const throw() {
        return message.c_str();
    }

};

}

#endif // ES_FLOW_EXCEPTIONS_H

Includes¶

exception (File exceptions.h)

Namespaces¶

Namespace es

Classes¶

File filter.h¶

↰ Parent directory (source/utilities)

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Definition (source/utilities/filter.h)
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Definition (source/utilities/filter.h)¶

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/*
 * filter.h One-dimensional polynomial based digital filter for eigen arrayXd
 *
 * Author:              Tom Clark  (thclark @ github)
 *
 * Copyright (c) 2019 Octue Ltd. All Rights Reserved.
 *
 */

#ifndef ES_FLOW_FILTER_H
#define ES_FLOW_FILTER_H

#include <vector>
#include <iostream>
#include <Eigen/Dense>
#include <Eigen/Core>
#include <stdexcept>


namespace utilities {


template<typename DerivedOut, typename DerivedIn>
void filter(Eigen::ArrayBase<DerivedOut> &y,
            const Eigen::ArrayBase<DerivedIn> &b,
            const Eigen::ArrayBase<DerivedIn> &a,
            const Eigen::ArrayBase<DerivedIn> &x) {

    // Check for 1D inputs
    eigen_assert((a.cols() == 1) || (a.rows() == 1));
    eigen_assert((b.cols() == 1) || (a.rows() == 1));
    eigen_assert((x.cols() == 1) || (a.rows() == 1));

    // Initialise output
    Eigen::ArrayBase<DerivedOut> &y_ = const_cast< Eigen::ArrayBase<DerivedOut> & >(y);
    y_.derived().setZero(x.rows(), x.cols());

    // Direct Form II transposed standard difference equation
    typename DerivedOut::Scalar tmp;
    Eigen::Index i;
    Eigen::Index j;
    for (i = 0; i < x.size(); i++) {
        tmp = 0.0;
        j = 0;
        y_(i) = 0.0;

        for (j = 0; j < b.size(); j++) {
            if (i - j < 0) continue;
            tmp += b(j) * x(i - j);
        }

        for (j = 1; j < a.size(); j++) {
            if (i - j < 0) continue;
            tmp -= a(j) * y_(i - j);
        }

        tmp /= a(0);
        y_(i) = tmp;
    }
}

template<typename T>
void filter(std::vector<T> &y, const std::vector<T> &b, const std::vector<T> &a, const std::vector<T> &x) {

    y.resize(0);
    y.resize(x.size());

    for (int i = 0; i < x.size(); i++) {
        T tmp = 0.0;
        int j = 0;
        y[i] = 0.0;
        for (j = 0; j < b.size(); j++) {
            if (i - j < 0) continue;
            tmp += b[j] * x[i - j];
        }

        for (j = 1; j < a.size(); j++) {
            if (i - j < 0) continue;
            tmp -= a[j] * y[i - j];
        }

        tmp /= a[0];
        y[i] = tmp;
    }
}

template<typename DerivedIn, typename DerivedOut>
void deconv(Eigen::ArrayBase<DerivedOut> &z,
            const Eigen::ArrayBase<DerivedIn> &b,
            const Eigen::ArrayBase<DerivedIn> &a) {

    eigen_assert(a(0) != 0);
    eigen_assert((a.cols() == 1) || (a.rows() == 1));
    eigen_assert((b.cols() == 1) || (b.rows() == 1));

    auto na = a.size();
    auto nb = b.size();

    // Initialise output
    Eigen::ArrayBase<DerivedOut> &z_ = const_cast< Eigen::ArrayBase<DerivedOut> & >(z);

    // Cannot deconvolve a longer signal out of a smaller one
    if (na > nb) {
        std::cout << "Warning! You cannot deconvolve a longer signal (a) out of a shorter one (b)!!" << std::endl;
        z_.derived().setZero(1, 1);
        return;
    }
    z_.derived().setZero(nb - na + 1, 1);

    // Deconvolution and polynomial division are the same operations as a digital filter's impulse response B(z)/A(z):
    Eigen::Array<typename DerivedOut::Scalar, Eigen::Dynamic, 1> impulse;
    impulse.setZero(nb - na + 1, 1);
    impulse(0) = 1;
    filter(z_, b, a, impulse);
}

}  /* namespace utilities */

#endif //ES_FLOW_FILTER_H

Includes¶

Eigen/Core
Eigen/Dense
iostream
stdexcept
vector

Included By¶

Namespaces¶

Namespace utilities

Functions¶

File fit.h¶

↰ Parent directory (source)

Contents

Definition (source/fit.h)
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Definition (source/fit.h)¶

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/*
 * Fit.h Use ceres-solver to fit mean speed and spectra to measured data
 *
 * Author:              Tom Clark  (thclark @ github)
 *
 * Copyright (c) 2019 Octue Ltd. All Rights Reserved.
 *
 */

#ifndef ES_FLOW_FIT_H
#define ES_FLOW_FIT_H

#include <stdio.h>
#include "ceres/ceres.h"
#include <Eigen/Core>

#include "relations/velocity.h"
#include "definitions.h"

using ceres::AutoDiffCostFunction;
using ceres::DynamicAutoDiffCostFunction;
using ceres::CostFunction;
using ceres::Problem;
using ceres::Solver;
using ceres::Solve;
using ceres::CauchyLoss;


typedef Eigen::Array<bool, 5, 1> Array5b;
typedef Eigen::Array<double, 5, 1> Array5d;


namespace es {


struct PowerLawSpeedResidual {
    PowerLawSpeedResidual(double z, double u, double z_ref=1.0, double u_ref=1.0) : z_(z), u_(u), u_ref_(u_ref), z_ref_(z_ref) {}
    template <typename T> bool operator()(const T* const alpha, T* residual) const {

        residual[0] = u_ - power_law_speed(T(z_), u_ref_, z_ref_, alpha[0]);
        return true;
    }
private:
    // Observations for a sample
    const double u_;
    const double z_;
    const double u_ref_;
    const double z_ref_;
};


double fit_power_law_speed(const Eigen::ArrayXd &z, const Eigen::ArrayXd &u, const double z_ref=1.0, const double u_ref=1.0) {

    // Define the variable to solve for with its initial value. It will be mutated in place by the solver.
    double alpha = 0.3;

    // TODO Assert that z.size() == u.size()

    // Build the problem
    Problem problem;
    Solver::Summary summary;
    Solver::Options options;

    options.max_num_iterations = 400;
    options.linear_solver_type = ceres::DENSE_QR;
    options.minimizer_progress_to_stdout = true;
//std::cout << options << std::endl;
    // Set up the only cost function (also known as residual), using cauchy loss function for
    // robust fitting and auto-differentiation to obtain the derivative (jacobian)
    for (auto i = 0; i < z.size(); i++) {
        CostFunction *cost_function = new AutoDiffCostFunction<PowerLawSpeedResidual, 1, 1>(
            new PowerLawSpeedResidual(z[i], u[i], z_ref, u_ref));
        problem.AddResidualBlock(cost_function, new CauchyLoss(0.5), &alpha);
    }

    // Run the solver
    Solve(options, &problem, &summary);
    std::cout << summary.BriefReport() << "\n";
    std::cout << "Initial alpha: " << 0.3 << "\n";
    std::cout << "Final   alpha: " << alpha << "\n";

    return alpha;
}


struct LewkowiczSpeedResidual {

    LewkowiczSpeedResidual(double z, double u, const Array5b &fixed_params, const Array5d &initial_params) : z_(z), u_(u), fixed_params_(fixed_params), initial_params_(initial_params) { }

    template <typename T> bool operator()(T const* const* parameters, T* residual) const {

        // Mask out fixed and variable parameters
        // TODO Once Eigen 3.4.x comes out, reduce this code to use the parameter mask as a logical index.
        //  See this issue which will allow such indexing in eigen: http://eigen.tuxfamily.org/bz/show_bug.cgi?id=329#c27
        int param_ctr = 0;
        std::vector<T> params(5);
        for (auto i = 0; i < 5; i++) {
            if (fixed_params_(i)) {
                params[i] = T(initial_params_(i));
            } else {
                params[i] = parameters[param_ctr][0];
                param_ctr += 1;
            }
        }
        T spd = lewkowicz_speed(T(z_), params[0], params[1], params[2], params[3], params[4]);
        residual[0] = u_ - spd;
        return true;
    }
private:
    const double u_;
    const double z_;
    Array5b fixed_params_;
    Array5d initial_params_;
};


Array5d fit_lewkowicz_speed(const Eigen::ArrayXd &z, const Eigen::ArrayXd &u, const Array5b &fixed_params, const Array5d &initial_params, bool print_report = true) {

    // Initialise a results array, and get a vector of pointers to the 'unfixed' parameters (the ones to optimise)
    Array5d final_params(initial_params);
    std::vector<double *> unfixed_param_ptrs;
    for (int p_ctr = 0; p_ctr <5; p_ctr++) {
        if (!fixed_params(p_ctr)) { unfixed_param_ptrs.push_back(final_params.data()+p_ctr); };
    }

    // Build the problem
    Problem problem;
    Solver::Summary summary;
    Solver::Options options;
    options.max_num_iterations = 400;
    options.minimizer_progress_to_stdout = print_report;

    for (auto i = 0; i < z.size(); i++) {

        // Set the stride such that the entire set of derivatives is computed at once (since we have maximum 5)
        auto cost_function = new DynamicAutoDiffCostFunction<LewkowiczSpeedResidual, 5>(
            new LewkowiczSpeedResidual(z[i], u[i], fixed_params, initial_params)
        );

        // Add N parameters, where N is the number of free parameters in the problem
        auto pc = 0;
        for (auto p_ctr = 0; p_ctr < 5; p_ctr++) {
            if (!fixed_params(p_ctr)) {
                cost_function->AddParameterBlock(1);
                pc += 1;
            }
        }
        cost_function->SetNumResiduals(1);
        problem.AddResidualBlock(cost_function, new CauchyLoss(0.5), unfixed_param_ptrs);
    }

    Solve(options, &problem, &summary);

    if (print_report) {
        std::cout << summary.FullReport() << std::endl;
        std::cout << "Initial values: " << initial_params.transpose() << std::endl;
        std::cout << "Final   values: " << final_params.transpose() << std::endl;
    }

    return final_params;
}


Array5d fit_lewkowicz_speed(const Eigen::ArrayXd &z, const Eigen::ArrayXd &u, bool print_report = true) {

    // Set default initial parameters
    double pi_coles = 0.5;
    double kappa = KAPPA_VON_KARMAN;
    double shear_ratio = 20;
    double u_inf = u.maxCoeff();
    double delta_c = 1000;
    Array5d initial_params;
    initial_params << pi_coles, kappa, u_inf, shear_ratio, delta_c;

    // Set default fixed parameters (von karman constant and boundary layer thickness)
    Array5b fixed_params;
    fixed_params << false, true, false, false, true;

    return fit_lewkowicz_speed(z, u, fixed_params, initial_params, print_report);

}

} /* namespace es */


#endif // ES_FLOW_FIT_H

Includes¶

Eigen/Core
ceres/ceres.h
definitions.h (File definitions.h)
relations/velocity.h (File velocity.h)
stdio.h

Namespaces¶

Namespace es

Classes¶

Functions¶

Typedefs¶

File flow.h¶

↰ Parent directory (source)

Contents

Definition (source/flow.h)

Definition (source/flow.h)¶

Program Listing for File flow.h¶

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/*
 * flow.h Sketching out public api for the flow library
 *
 * Author:              Tom Clark  (thclark @ github)
 *
 * Copyright (c) 2019 Octue Ltd. All Rights Reserved.
 *
 */

#ifndef ES_FLOW_FLOW_H
#define ES_FLOW_FLOW_H




#endif //ES_FLOW_FLOW_H

File how_to.h¶

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Definition (source/how_to.h)

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/*
 * how_to.h  Chunks of code that show us how to do things
 *
 *  May not be complete, may not compile. Not included in any build targets. Just copy, paste, adapt to our own uses.
 *
 * Author:              Tom Clark  (thclark @ github)
 *
 * Copyright (c) 2019 Octue Ltd. All Rights Reserved.
 *
 */


// Remove template specialisation from doc (causes duplicate) @cond

/***********************************************************************************************************************
 * HOW TO DO PIECEWISE CUBIC HERMITE INTERPOLATION
 **********************************************************************************************************************/


// TODO This is a work in progress. It gives a pchip spline, but not one which is shape preserving. Need gradient
//  conditions at the maxima, minima and endpoints.
#include <iostream>
#include <algorithm>
#include <math.h>
#include <Eigen/Core>
#include <Eigen/Dense>
double evaluate(const double xi, const Eigen::VectorXd &x, const ceres::CubicInterpolator<ceres::Grid1D<double> > &interpolator){

    const Eigen::Index k = x.rows();
    Eigen::Index n_rows = x.rows()-1;
    Eigen::VectorXd x_percent;
    Eigen::VectorXd diff = x.bottomRows(n_rows) - x.topRows(n_rows);
//    if ((diff <= 0.0).any()) {
//        throw std::invalid_argument("Input values x must be strictly increasing");
//    }
    cumsum(x_percent, diff);
    x_percent = x_percent / x_percent(n_rows-1);
    double x_max = x.maxCoeff();
    double x_min = x.minCoeff();

    // Out of range xi values are constrained to the endpoints
    double bounded_target = std::max(std::min(xi, x_max), x_min);

    // Run a binary search for where the node is in the grid. This makes the algorithm O(log(N)) to evaluate one location
// Thanks to: https://stackoverflow.com/questions/6553970/find-the-first-element-in-a-sorted-array-that-is-greater-than-the-target
    Eigen::Index low = 0, high = k; // numElems is the size of the array i.e arr.size()
    while (low != high) {
        Eigen::Index mid = (low + high) / 2; // Or a fancy way to avoid int overflow
        if (x[mid] <= bounded_target) {
            /* This index, and everything below it, must not be the first element
             * greater than what we're looking for because this element is no greater
             * than the element.
             */
            low = mid + 1;
        }
        else {
            /* This element is at least as large as the element, so anything after it can't
             * be the first element that's at least as large.
             */
            high = mid;
        }
    }
    low = low - 1;

    /* Now, low and high surround to the element in question. */

    std::cout << low << " " << high << std::endl;

    double node_low = x[low];
    double node_high = x[high];

    std::cout << "node_low " << node_low << std::endl;
    std::cout << "node_high " << node_low << std::endl;
    std::cout << "low " << low << std::endl;
    std::cout << "high " << high << std::endl;


    double proportion = (bounded_target - node_low) / (node_high - node_low);
    double xi_mapped = double(low) + proportion;

    std::cout << "proportion " << proportion << std::endl;
    std::cout << "xi_mapped " << xi_mapped << std::endl;
    double f, dfdx;

    interpolator.Evaluate(xi_mapped, &f, &dfdx);
    std::cout << "evaluated: " << f << std::endl;

    return f;
}

double evaluateDirect(const double xi, const ceres::CubicInterpolator<ceres::Grid1D<double> > &interpolator){
    // This doesn't work because it doesn't map the proportion of the way through correctly
    double f, dfdx;

    interpolator.Evaluate(xi, &f, &dfdx);
    std::cout << "evaluated: " << f << std::endl;

    return f;
}

TEST_F(InterpTest, test_pchip_interp_double) {

Eigen::VectorXd x(5);
Eigen::VectorXd y(5);
Eigen::VectorXd xi = Eigen::VectorXd::LinSpaced(100, 0, 5);
Eigen::VectorXd yi(100);
x << 2, 4.5, 8, 9, 10;
y << 6, 1, 10, 12, 19;

const Eigen::Index k = y.rows();
ceres::Grid1D<double> grid(y.data(), 0, k);
// TODO the interpolator, unlike MATLAB's routine, isn't shape preserving, nor does it adjust for non-monotonic x.
//  So this works as an interpolant, but is pretty horrid.
ceres::CubicInterpolator<ceres::Grid1D<double> > interpolator(grid);

double x_max = x.maxCoeff();
double x_min = x.minCoeff();
for (Eigen::Index i=0; i<xi.rows(); i++) {
//yi[i] = evaluateDirect(xi[i], interpolator);
//xi[i] = xi[i] * ((x_max - x_min) / k) + x_min;
yi[i] = evaluate(xi[i], x, interpolator);
}


Figure fig = Figure();
ScatterPlot p_xy = ScatterPlot();
p_xy.x = x;
p_xy.y = y;
p_xy.name = "xy";
fig.add(p_xy);
ScatterPlot p_xiyi = ScatterPlot();
p_xiyi.x = xi;
p_xiyi.y = yi;
p_xiyi.name = "xiyi";
fig.add(p_xiyi);

// Add axis labeling
Layout lay = Layout("pchip check");
lay.xTitle("$x$");
lay.yTitle("$y$");
fig.setLayout(lay);

// Write figures
fig.write("check_pchip.json");

}

// TODO Once done, you can wrap this up into an interpolant much like in the interp.h file:



#include "ceres/ceres.h"
#include "ceres/cubic_interpolation.h"
#include "glog/logging.h"
#include "utilities/cumsum.h"

ceres::CubicInterpolator<ceres::Grid1D<double> > getInterpolator(Eigen::VectorXd const &x_vec, Eigen::VectorXd const &y_vec) {
    const Eigen::Index k = y_vec.rows();
    // TODO file an issue over at ceres-solver. Grid1D is deeply unhelpful. At the very least it should accept Eigen::Index instead of int.
    std::cout << "k: " << k << std::endl;
    ceres::Grid1D<double> grid(y_vec.data(), 0, k);
    ceres::CubicInterpolator<ceres::Grid1D<double> > interpolator(grid);
    return interpolator;

}

class PiecewiseCubicHermiteInterpolant {
public:
    // TODO template for arrays
    PiecewiseCubicHermiteInterpolant(Eigen::VectorXd const &x_vec, Eigen::VectorXd const &y_vec)
        : k_(y_vec.rows()),
          interpolator_(getInterpolator(x_vec, y_vec)) {
        // TODO assert that x is strictly ascending or strictly descending
        std::cout << "HEREbf" <<std::endl;
        Eigen::Index n_rows = x_vec.rows();
        Eigen::VectorXd x_percent;
        cumsum(x_percent, x_vec.bottomRows(n_rows-1) - x_vec.topRows(n_rows-1));
    }


    double operator()(double xi) const {
        // x values need to be scaled down in extraction as well.
        std::cout << "evaluating" << std::endl;
        //
        double f, dfdx;
        interpolator_.Evaluate(xi, &f, &dfdx);
        std::cout << "evaluated" << std::endl;

        return f;
    }

    Eigen::VectorXd operator()(Eigen::VectorXd const &xi_vec) {
        Eigen::VectorXd yi_vec(xi_vec.rows());
        yi_vec = xi_vec.unaryExpr([this](double xi) { return this->operator()(xi); }).transpose();
        return yi_vec;
    }

private:


//    double scaled_value(double x) const {
//        return (x - x_min) / (x_max - x_min);
//    }

//    Eigen::RowVectorXd scaled_values(Eigen::VectorXd const &x_vec) const {
//        return x_vec.unaryExpr([this](double x) { return scaled_value(x); }).transpose();
//    }

    // Number of samples in the input data
    Eigen::Index k_;

    // Interpolator, initialised with the grid of values
    const ceres::CubicInterpolator<ceres::Grid1D<double> > interpolator_;
};







/***********************************************************************************************************************
 * HOW TO DIFFERENTIATE USING EIGEN::AUTODIFF
 **********************************************************************************************************************/


#include <unsupported/Eigen/AutoDiff>
template <typename T>
T myfun2(const double a, T const & b){
    T c = pow(sin(a),2.) + pow(cos(b),2.) + 1.;
    return c;
}

void test_scalar() {
    std::cout << "== test_scalar() ==" << std::endl;
    double a;
    a = 0.3;
    typedef Eigen::AutoDiffScalar<Eigen::VectorXd> AScalar;
    AScalar Ab;
    Ab.value() = 0.5;
    Ab.derivatives() = Eigen::VectorXd::Unit(1,0);
    AScalar Ac = myfun2(a,Ab);
    std::cout << "Result: " << Ac.value() << std::endl;
    std::cout << "Gradient: " << Ac.derivatives().transpose() << std::endl;
}


template <typename T>
T myfun(T const & a, T const & b){
    T c = pow(sin(a),2.) + pow(cos(b),2.) + 1.;
    return c;
}

void test_scalar(){
    std::cout << "== test_scalar() ==" << std::endl;
    // use with normal floats
    double a,b;
    a = 0.3;
    b = 0.5;
    double c = myfun(a,b);
    std::cout << "Result: " << c << std::endl;

    // use with AutoDiffScalar
    typedef Eigen::AutoDiffScalar<Eigen::VectorXd> AScalar;
    AScalar Aa,Ab;
    Aa.value() = 0.3;
    Ab.value() = 0.5;
    Aa.derivatives() = Eigen::VectorXd::Unit(2,0); // This is a unit vector [1, 0]
    Ab.derivatives() = Eigen::VectorXd::Unit(2,1); // This is a unit vector [0, 1]
    AScalar Ac = myfun(Aa,Ab);
    std::cout << "Result: " << Ac.value() << std::endl;
    std::cout << "Gradient: " << Ac.derivatives().transpose() << std::endl;
}


/***********************************************************************************************************************
 * HOW TO INTEGRATE USING THE NUMERICALINTEGRATION LIBRARY
 **********************************************************************************************************************/

#include <Eigen/Dense>
#include <Eigen/Core>
#include <iostream>
#include "NumericalIntegration.h"

/* Integrator for the velocity deficit
 *  We consider the example from:
 *
 *       http://www.gnu.org/software/gsl/manual/html_node/Numerical-integration-examples.html
 *
 *       int_0^1 x^{-1/2} log(x) dx = -4
 *
 *  The integrator expects the user to provide a functor as shown below.
 */

template<typename Scalar>
class IntegrandExampleFunctor
{
public:
    IntegrandExampleFunctor(const Scalar alpha):m_alpha(alpha)
    {
        assert(alpha>0);
    }

    Scalar operator()(const Scalar x) const
    {
        assert(x>0);
        return log(m_alpha*x) / sqrt(x);
    }

    void setAlpha(const Scalar alpha)
    {
        m_alpha = alpha;
    }
private:
    Scalar m_alpha;
};

double do_something(const double arg)
{
    // Define the scalar
    typedef double Scalar;

    // Define the functor
    Scalar alpha=1.;
    IntegrandExampleFunctor<Scalar> inFctr(alpha);

    //define the integrator
    Eigen::Integrator<Scalar> eigIntgtor(200);

    //define a quadrature rule
    Eigen::Integrator<Scalar>::QuadratureRule quadratureRule = Eigen::Integrator<Scalar>::GaussKronrod61;

    //define the desired absolute and relative errors
    Scalar desAbsErr = Scalar(0.);
    Scalar desRelErr = Eigen::NumTraits<Scalar>::epsilon() * 50.;

    //integrate
    Scalar result = eigIntgtor.quadratureAdaptive(inFctr, Scalar(0.),Scalar(1.), desAbsErr, desRelErr, quadratureRule);

    //expected result
    Scalar expected = Scalar(-4.);

    //print output
    size_t outputPrecision  = 18;
    std::cout<<std::fixed;
    std::cout<<"result          = "<<std::setprecision(outputPrecision)<<result<<std::endl;
    std::cout<<"exact result    = "<<std::setprecision(outputPrecision)<<expected<<std::endl;
    std::cout<<"actual error    = "<<std::setprecision(outputPrecision)<<(expected-result)<<std::endl;

    return 0.0;
}

TEST_F(MyTest, test_integrator_example) {

// Test a basic integrator out
double arg = 0.0;
double res = do_something(arg);

}



/***********************************************************************************************************************
 * HOW TO FIT USING CERES-SOLVER
 **********************************************************************************************************************/


//#include <stdlib.h>
//#include <stdio.h>
//#include <unistd.h>
//#include <stdbool.h>
//#include "matio.h"
#include "ceres/ceres.h"

#include <Eigen/Core>


using ceres::AutoDiffCostFunction;
using ceres::CostFunction;
using ceres::Problem;
using ceres::Solver;
using ceres::Solve;

// A templated cost functor that implements the residual r = 10 -
// x. The method operator() is templated so that we can then use an
// automatic differentiation wrapper around it to generate its
// derivatives.
struct CostFunctor {
    template <typename T> bool operator()(const T* const x, T* residual) const {
        residual[0] = T(10.0) - x[0];
        return true;
    }
};

void my_fitting_func() {

    // Run the ceres solver

    // Define the variable to solve for with its initial value. It will be mutated in place by the solver.
    double x = 0.5;
    const double initial_x = x;

    // Build the problem.
    Problem problem;

    // Set up the only cost function (also known as residual). This uses
    // auto-differentiation to obtain the derivative (jacobian).
    CostFunction *cost_function = new AutoDiffCostFunction<CostFunctor, 1, 1>(new CostFunctor);
    problem.AddResidualBlock(cost_function, NULL, &x);

    // Run the solver!
    Solver::Options ceroptions;
    ceroptions.minimizer_progress_to_stdout = true;
    Solver::Summary summary;
    Solve(ceroptions, &problem, &summary);
    std::cout << summary.BriefReport() << "\n";
    std::cout << "x : " << initial_x << " -> " << x << "\n";

}


/***********************************************************************************************************************
 * HOW TO DO AN FFT USING EIGEN
 **********************************************************************************************************************/


#include <Eigen/Core>
#include <unsupported/Eigen/FFT>


void my_fft_func() {
    size_t dim_x = 28, dim_y = 126;
    Eigen::FFT<float> fft;
    Eigen::MatrixXf in = Eigen::MatrixXf::Random(dim_x, dim_y);
    Eigen::MatrixXcf out;
    out.setZero(dim_x, dim_y);

    for (int k = 0; k < in.rows(); k++) {
        Eigen::VectorXcf tmpOut(dim_x);
        fft.fwd(tmpOut, in.row(k));
        out.row(k) = tmpOut;
    }

    for (int k = 0; k < in.cols(); k++) {
        Eigen::VectorXcf tmpOut(dim_y);
        fft.fwd(tmpOut, out.col(k));
        out.col(k) = tmpOut;
    }
}


/***********************************************************************************************************************
 * HOW TO DO AN FFT USING MKL DIRECTLY
 **********************************************************************************************************************/

#include "mkl_dfti.h"

void my_mkl_fft() {
    // Run an example FFT

    // Make meaningless data and a size vector
    float xf[200][100];
    MKL_LONG len[2] = {200, 100};

    // Create a decriptor, which is a pattern for what operation an FFT will undertake
    DFTI_DESCRIPTOR_HANDLE fft;
    DftiCreateDescriptor (&fft, DFTI_SINGLE, DFTI_REAL, 2, len);
    DftiCommitDescriptor(fft);

    // Compute a forward transform, in-place on the data
    DftiComputeForward(fft, xf);

    // Free the descriptor
    DftiFreeDescriptor(&fft);

    std::cout << "FFT COMPLETE\n";
}


/***********************************************************************************************************************
 * HOW TO PLOT REYNOLDS STRESS PROFILES, EDDY SIGNATURES AND STRENGTH / SCALE DISTRIBUTIONS WITH CPPLOT
 **********************************************************************************************************************/

#include "cpplot.h"

void my_rs_plotting_func() {

    // Plot the Reynolds Stress profiles (comes from get_spectra)
    cpplot::Figure figa = cpplot::Figure();
    for (auto i = 0; i < 6; i++) {
        cpplot::ScatterPlot p = cpplot::ScatterPlot();
        p.x = Eigen::VectorXd::LinSpaced(data.reynolds_stress_a.rows(), 1, data.reynolds_stress_a.rows());
        p.y = data.reynolds_stress_a.col(i).matrix();
        figa.add(p);
    }
    figa.write("test_t2w_rij_a.json");
    //    legend({'R13A'; 'R13B'})
    //    xlabel('\lambda_E')

    cpplot::Figure figb = cpplot::Figure();
    for (auto i = 0; i < 6; i++) {
        cpplot::ScatterPlot p = cpplot::ScatterPlot();
        p.x = Eigen::VectorXd::LinSpaced(data.reynolds_stress_b.rows(), 1, data.reynolds_stress_b.rows());
        p.y = data.reynolds_stress_b.col(i).matrix();
        figb.add(p);
    }
    figb.write("test_t2w_rij_b.json");
    //    legend({'R13A'; 'R13B'})
    //    xlabel('\lambda_E')


    // Plot the eddy signatures
    cpplot::Figure fig2 = cpplot::Figure();
    cpplot::ScatterPlot ja = cpplot::ScatterPlot();
    ja.x = Eigen::VectorXd::LinSpaced(j13a.rows(), 1, j13a.rows());
    ja.y = j13a.matrix();
    fig2.add(ja);
    cpplot::ScatterPlot jb = cpplot::ScatterPlot();
    jb.x = ja.x;
    jb.y = j13b.matrix();
    fig2.add(jb);
    fig2.write("test_t2w_j13ab.json");
    //    legend({'J13A'; 'J13B'})

    // Plot strength and scale distributions
    cpplot::Figure fig3 = cpplot::Figure();
    cpplot::ScatterPlot twa = cpplot::ScatterPlot();
    twa.x = Eigen::VectorXd::LinSpaced(minus_t2wa.rows(), 1, minus_t2wa.rows());
    twa.y = minus_t2wa.matrix();
    fig3.add(twa);
    cpplot::ScatterPlot twb = cpplot::ScatterPlot();
    twb.x = twa.x;
    twb.y = minus_t2wb.matrix();
    fig3.add(twb);
    fig3.write("test_t2w_t2wab.json");
    //    legend({'T^2\omegaA'; 'T^2\omegaB'})

}

/***********************************************************************************************************************
 * HOW TO DO MAT FILE READ WRITE
 **********************************************************************************************************************/

#include "matio.h"

// Create the output file
mat_t *matfp;
matfp = Mat_CreateVer(options["o"].as<std::string>().c_str(), NULL, MAT_FT_MAT73);
if ( NULL == matfp ) {
std::string msg = "Error creating MAT file: ";
throw  msg + options["o"].as<std::string>();
}

// We haven't written any data - just close the file
Mat_Close(matfp);

std::cout << "MATIO TEST COMPLETE" << std::endl;




// @endcond

File integration.h¶

↰ Parent directory (source/utilities)

Contents

Definition (source/utilities/integration.h)
Includes
Included By
Namespaces
Functions

Definition (source/utilities/integration.h)¶

Program Listing for File integration.h¶

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/*
 * integration.h Convenient wrappers around tbs1980's Numerical Integration module for Eigen
 *
 * Author:              Tom Clark  (thclark @ github)
 *
 * Copyright (c) 2019 Octue Ltd. All Rights Reserved.
 *
 */

#ifndef ES_FLOW_INTEGRATION_H
#define ES_FLOW_INTEGRATION_H

#include <Eigen/Dense>
#include <Eigen/Core>
#include "NumericalIntegration.h"


namespace utilities {


template<typename T_functor>
Eigen::ArrayXd cumulative_integrate(const Eigen::ArrayXd &x, const T_functor &functor, const int max_subintervals=200)
{
    typedef double ScalarType;
    Eigen::ArrayXd integral(x.rows());
    integral.setZero();

    // Define the integrator and quadrature rule
    Eigen::Integrator<ScalarType> eigIntgtor(max_subintervals);
    Eigen::Integrator<ScalarType>::QuadratureRule quadratureRule = Eigen::Integrator<ScalarType>::GaussKronrod61;

    // Define the desired absolute and relative errors
    auto desAbsErr = ScalarType(0.0);
    ScalarType desRelErr = Eigen::NumTraits<ScalarType>::epsilon() * 50.;

    // Integrate to each value in eta
    for (Eigen::Index i = 0; i < x.rows()-1; i++) {
        integral[i+1] = eigIntgtor.quadratureAdaptive(functor, ScalarType(x[i]), ScalarType(x[i+1]), desAbsErr, desRelErr, quadratureRule) + integral[i];
    }
    return integral;
}


}  /* namespace utilities */

#endif //ES_FLOW_INTEGRATION_H

Includes¶

Eigen/Core
Eigen/Dense
NumericalIntegration.h

Included By¶

File stress.h

Namespaces¶

Namespace utilities

Functions¶

Template Function utilities::cumulative_integrate

File interp.h¶

↰ Parent directory (source/utilities)

Contents

Definition (source/utilities/interp.h)
Includes
Included By
Namespaces
Classes

Definition (source/utilities/interp.h)¶

Program Listing for File interp.h¶

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/*
 * interp.h Interpolation tools
 *
 * Author:              Tom Clark  (thclark @ github)
 *
 * Copyright (c) 2019 Octue Ltd. All Rights Reserved.
 *
 */

#ifndef ES_FLOW_INTERP_H
#define ES_FLOW_INTERP_H

#include <iostream>
#include <math.h>
#include <Eigen/Core>
#include <Eigen/Dense>
#include <unsupported/Eigen/Splines>


namespace utilities {


class LinearInterpolant {
public:
    LinearInterpolant(const Eigen::ArrayXd x_vec, const Eigen::ArrayXd y_vec)
      : x_min(x_vec.minCoeff()), x_max(x_vec.maxCoeff()), x(x_vec), y(y_vec) {}

    double operator()(double xi) const {
        double bounded_xi = std::max(std::min(xi, x_max), x_min);
        Eigen::Index node = findNode(bounded_xi);
        if (node == x.size()-1) {
            return y[node];
        }
        double proportion = (bounded_xi - x[node]) / (x[node + 1] - x[node]);
        return proportion * (y[node + 1] - y[node]) + y[node];
    }

    Eigen::ArrayXd operator()(Eigen::ArrayXd const &xi_vec) {
        Eigen::ArrayXd yi_vec(xi_vec.rows());
        yi_vec = xi_vec.unaryExpr([this](double xi) { return this->operator()(xi); }).transpose();
        return yi_vec;
    }

private:

    // Find the index of the data value in x_vec immediately before the required xi value
    Eigen::Index findNode(const double bounded_xi) const {

        // Run a binary search to find the adjacent node in the grid. This is O(log(N)) to evaluate one location.
        // https://stackoverflow.com/questions/6553970/find-the-first-element-in-a-sorted-array-that-is-greater-than-the-target
        Eigen::Index low = 0;
        Eigen::Index high = x.size();
        while (low != high) {
            Eigen::Index mid = (low + high) / 2; // Or a fancy way to avoid int overflow
            if (x[mid] <= bounded_xi) {
                low = mid + 1;
            } else {
                high = mid;
            }
        }
        return low - 1;
    }

    // Boundaries of the vector
    double x_min;
    double x_max;

    // Hold a copy of the data in case it changes outside during the life of the interpolant
    Eigen::ArrayXd x;
    Eigen::ArrayXd y;
};


class CubicSplineInterpolant {
public:
    CubicSplineInterpolant(Eigen::VectorXd const &x_vec, Eigen::VectorXd const &y_vec)
        : x_min(x_vec.minCoeff()),
          x_max(x_vec.maxCoeff()),
          spline_(Eigen::SplineFitting<Eigen::Spline<double, 1>>::Interpolate(
              y_vec.transpose(),
              // No more than cubic spline, but accept short vectors.
              std::min<long>(x_vec.rows() - 1, 3),
              scaled_values(x_vec))) {}

    double operator()(double xi) const {
        // x values need to be scaled down in extraction as well.
        return spline_(scaled_value(xi))(0);
    }

    Eigen::VectorXd operator()(Eigen::VectorXd const &xi_vec) {
        Eigen::VectorXd yi_vec(xi_vec.rows());
        yi_vec = xi_vec.unaryExpr([this](double xi) { return spline_(scaled_value(xi))(0); }).transpose();
        return yi_vec;
    }

private:
    double scaled_value(double x) const {
        return (x - x_min) / (x_max - x_min);
    }

    Eigen::RowVectorXd scaled_values(Eigen::VectorXd const &x_vec) const {
        return x_vec.unaryExpr([this](double x) { return scaled_value(x); }).transpose();
    }

    double x_min;
    double x_max;

    // Spline of one-dimensional "points."
    Eigen::Spline<double, 1> spline_;
};


}  /* namespace utilities */


#endif //ES_FLOW_INTERP_H

Includes¶

Eigen/Core
Eigen/Dense
iostream
math.h
unsupported/Eigen/Splines

Included By¶

Namespaces¶

Namespace utilities

Classes¶

File main.cpp¶

↰ Parent directory (source)

Contents

Definition (source/main.cpp)
Includes
Functions

Definition (source/main.cpp)¶

Program Listing for File main.cpp¶

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/*
 * main.cpp Command line executable for es-flow
 *
 * Author:              Tom Clark  (thclark @ github)
 *
 * Copyright (c) 2016-9 Octue Ltd. All Rights Reserved.
 *
 */

#include <stdlib.h>
#include <stdio.h>
#include <unistd.h>
#include <stdbool.h>
#include "glog/logging.h"
#include "cxxopts.hpp"


int main(int argc, char* argv[]) {

    try {

        // Handle the input parsing and create the program help page

        // Set the program name (for --help option display) and default option behaviour
        cxxopts::Options options("es-flow", "EnvironmentSTUDIO flow library wrapper");
        bool logging = false;

        // Define the command line options, arranged visually (in the --help output) in two groups:
        options.add_options()
                ("l,log-file",
                 "Switch on logging, optionally specify the directory to save logfiles.",
                 cxxopts::value<std::string>()->implicit_value("logs"), "FILE")
                ("h,help",
                 "Display program help.",
                 cxxopts::value<bool>(), "BOOL");

        options.add_options("Input / output file")
                ("i,input-file", "Name of the input file (read only).", cxxopts::value<std::string>(), "FILE")
                ("o,output-file",
                 "Name of the output results file. Warning - this file will be overwritten if it already exists.",
                 cxxopts::value<std::string>(), "FILE");

        // Parse the input options
        options.parse(argc, argv);

        if (options.count("help")) {
            std::cout << options.help({"", "Input / output file"}) << std::endl;
            exit(0);
        }

        if (options.count("l")) {
            logging = true;
        }

        if (logging) {
            FLAGS_logtostderr = false;
            FLAGS_minloglevel = 0;
            FLAGS_log_dir = options["l"].as<std::string>();
            std::cout << "Logging to: " << FLAGS_log_dir << std::endl;
            google::InitGoogleLogging(argv[0]);
        }


    } catch (const cxxopts::OptionException &e) {
        std::cout << "Error parsing options: " << e.what() << std::endl;
        exit(1);

    } catch (...) {
        // Handle logging of general exceptions
        auto eptr = std::current_exception();
        try {
            // This deliberately rethrows the caught exception in the current scope, so we can log it
            if (eptr) {
                std::rethrow_exception(eptr);
            }
        } catch(const std::exception& e) {
            std::cout << "Caught exception: " << e.what() << std::endl;
        }
        exit(1);

    }

    exit(0);

}

Includes¶

cxxopts.hpp
glog/logging.h
stdbool.h
stdio.h
stdlib.h
unistd.h

Functions¶

Function main

File profile.cpp¶

↰ Parent directory (source)

Contents

Definition (source/profile.cpp)
Includes
Namespaces
Functions

Definition (source/profile.cpp)¶

Program Listing for File profile.cpp¶

↰ Return to documentation for file (source/profile.cpp)

/*
 * profile.cpp Profile handling for (e.g.) Velocity, Reynolds Stress and Spectral Tensor Profile management
 *
 * Function definitions are included in the .h file, because of the templating constraint. See http://stackoverflow.com/questions/495021/why-can-templates-only-be-implemented-in-the-header-file
 *
 * Author:                   Tom Clark (thclark @ github)
 *
 * Copyright (c) 2016-9 Octue Ltd. All Rights Reserved.
 *
 */
#include "profile.h"
#include "math.h"
#include "definitions.h"


namespace es {

Bins::Bins(std::vector<double> z): z_ctrs(z) {
    // Construct from a spacing with default bin size from central difference of the spacing
    int i;
    n_bins = z_ctrs.size();
    dx = std::vector<double>(n_bins);
    dy = std::vector<double>(n_bins);
    dz = std::vector<double>(n_bins);
    dz[0] = fabs(z[1]-z[0]);
    for (i = 1; i < n_bins-1; i++) {
        dz[i] = 0.5*fabs(z[i+1]-z[i-1]);
    }
    dz[n_bins-1] = fabs(z[n_bins-1]-z[n_bins-2]);
    for (i = 0; i < n_bins-1; i++) {
        dx[i] = dz[i];
        dy[i] = dz[i];
    }
}

Bins::Bins(std::vector<double> z, std::vector<double> d_x, std::vector<double> d_y, std::vector<double> d_z): Bins(z) {
    // Construct from a spacing and bin size in x, y, z
    dx = d_x;
    dy = d_y;
    dz = d_z;
    if ((dx.size() != n_bins) ||  (dy.size() != n_bins) || (dz.size() != n_bins)){
        throw std::range_error("Length of dx, dy or dz does not match the number of bins");
    }
}

Bins::Bins(std::vector<double> z, double half_angle_degrees): Bins(z) {
    // Construct from spacing, with bin height from central differencing of the spacing and bin widths using a half angle
    int i;
    double tha;
    tha = tand(half_angle_degrees);
    dx = std::vector<double>(z_ctrs.size());
    dy = std::vector<double>(z_ctrs.size());
    for (i = 0; i < n_bins - 1; i++) {
        dx[i] = 2.0 * z[i] * tha;
        dy[i] = dx[i];
    }
}

Bins::Bins(std::vector<double> z, double half_angle_degrees, std::vector<double> d_z): Bins(z, half_angle_degrees) {
    // Construct from spacing, with bin height given and bin widths using a half angle
    int i;
    dz = d_z;
    if (dz.size() != n_bins){
        throw std::range_error("Length of dx, dy or dz does not match the number of bins");
    }
}

Bins::~Bins() {
    //Destructor
}

::std::ostream& operator<<(::std::ostream& os, const Bins& bins) {
    // Represent in logs or ostream
    return os << "debug statement for bins class";
}


/* Use profile base class constructor and destructor
VelocityProfile::VelocityProfile() {
// TODO Auto-generated constructor stub
}

VelocityProfile::~VelocityProfile() {
// TODO Auto-generated destructor stub
}

VectorXd VelocityProfile::AutoDiff() {
// Differentiate the velocity profile wrt z

    typedef Eigen::AutoDiffScalar<Eigen::VectorXd> AScalar;
    // AScalar stores a scalar and a derivative vector.

    // Instantiate an AutoDiffScalar variable with a normal Scalar
    double s = 0.3;
    AScalar As(s);

    // Get the value from the Instance
    std::cout << "value: " << As.value() << std::endl;

    // The derivative vector is As.derivatives();

    // Resize the derivative vector to the number of dependent variables
    As.derivatives().resize(2);

    // Set the initial derivative vector
    As.derivatives() = Eigen::VectorXd::Unit(2,0);
    std::cout << "Derivative vector : " << As.derivatives().transpose() << std::endl;

    // Instantiate another AScalar
    AScalar Ab(4);
    Ab.derivatives() = Eigen::VectorXd::Unit(2,1);

    // Do the most simple calculation
    AScalar Ac = As * Ab;

    std::cout << "Result/Ac.value()" << Ac.value() << std::endl;
    std::cout << "Gradient: " << Ac.derivatives().transpose() << std::endl;

    Eigen::VectorXd a(1);
    return a;
}
*/

} /* namespace es */

Includes¶

definitions.h (File definitions.h)
math.h
profile.h (File profile.h)

Namespaces¶

Namespace es

Functions¶

Function es::operator<<(::std::ostream&, const Bins&)

File profile.h¶

↰ Parent directory (source)

Contents

Definition (source/profile.h)
Includes
Included By
Namespaces
Classes
Functions

Definition (source/profile.h)¶

Program Listing for File profile.h¶

↰ Return to documentation for file (source/profile.h)

/*
 * profile.h Profile handling for (e.g.) Velocity, Reynolds Stress and Spectral Tensor Profile management
 *
 * Function definitions are included here, rather than the cpp file, because of the templating constraint. See http://stackoverflow.com/questions/495021/why-can-templates-only-be-implemented-in-the-header-file
 *
 * Author:                   Tom Clark (thclark @ github)
 *
 * Copyright (c) 2016-9 Octue Ltd. All Rights Reserved.
 *
 */

#ifndef ES_FLOW_PROFILE_H
#define ES_FLOW_PROFILE_H

#include <iostream>
#include <vector>
#include <cstdlib>
#include <string>
#include <stdexcept>


namespace es {


class Bins {
public:

    // Construct from a spacing with bin sizes set by central differencing of spacing
    Bins(std::vector<double> z);

    // Construct from spacing with bin sizes specified
    Bins(std::vector<double> z, std::vector<double> dx, std::vector<double> dy, std::vector<double> dz);

    // Construct from spacing and a half angle in degrees, dz set by central differencing of spacing
    Bins(std::vector<double> z, double half_angle_degrees);

    // Construct from spacing and a half angle in degrees, with dz specified
    Bins(std::vector<double> z, double half_angle_degrees, std::vector<double> dz);

    // Destroy
    ~Bins();

    // Vectors of z locations and bin dimensions
    unsigned long n_bins;
    std::vector<double> z_ctrs;
    std::vector<double> dx;
    std::vector<double> dy;
    std::vector<double> dz;

};

// Represent Bins class in logs or ostream
::std::ostream& operator<<(::std::ostream& os, const Bins& bins);

template <class ProfileType>
class Profile {
private:
    std::vector<ProfileType> values;

public:

    // Construct using bins only (zero values and position)
    Profile(const Bins &bins);

    // Construct using bins and a global origin location
    Profile(const Bins &bins, double x, double y, double z);

    // Destroy
    virtual ~Profile();

    // Get the values, whatever type they might be
    const std::vector<ProfileType> &getValues() const;

    void setValues(const std::vector<ProfileType> &values);

    // Properties
    double position[3];
    Bins bins;

};

// Represent Profiles class in logs or ostream
template <class ProfileType>
::std::ostream& operator<<(::std::ostream& os, const Profile<ProfileType>& profile);

template <class ProfileType>
Profile<ProfileType>::Profile(const Bins &bins) : bins(bins) {
    // Construct from just bins, with default position {0.0, 0.0, 0.0}
    position[0] = 0.0;
    position[1] = 0.0;
    position[2] = 0.0;
}

template <class ProfileType>
Profile<ProfileType>::~Profile() {
    // Destructor
}

template <class ProfileType>
Profile<ProfileType>::Profile(const Bins &bins, double x, double y, double z): bins(bins) {
    // Construct from bins and a position
    position[0] = x;
    position[1] = y;
    position[2] = z;
}

template <class ProfileType>
void Profile<ProfileType>::setValues(const std::vector<ProfileType> &values) {
    if (values.size() != bins.n_bins) {
        throw std::out_of_range("size of vector 'values' does not equal the number of bins for this profile");
    }
    Profile::values = values;
}

template <class ProfileType>
const std::vector<ProfileType> &Profile<ProfileType>::getValues() const {
    return values;
}

//template <class ProfileType>
//const std::vector<ProfileType> &Profile<ProfileType>::getZDerivative() const {
//    // Get the first derivative with respect to Z location using Eigen's Autodiff
//    // Some examples can be found in eigen/unsupported/doc/examples/AutoDiff.cpp
//
//
//    return derivatives;
//}

template <class ProfileType>
::std::ostream& operator<<(::std::ostream& os, const Profile<ProfileType>& profile) {
    // Represent in logs or ostream
    return os << "debug statement for profile class";
}


class VelocityProfile: public Profile<double> {
public:
    VelocityProfile();
    virtual ~VelocityProfile();

//    VectorXd AutoDiff();
};


} /* namespace es */


#endif // ES_FLOW_PROFILE_H

Includes¶

cstdlib
iostream
stdexcept
string
vector

Included By¶

Namespaces¶

Namespace es

Classes¶

Functions¶

Template Function es::operator<<(::std::ostream&, const Profile<ProfileType>&)

File readers.h¶

↰ Parent directory (source/io)

Contents

Definition (source/io/readers.h)
Includes
Namespaces
Classes
Enums
Functions

Definition (source/io/readers.h)¶

Program Listing for File readers.h¶

↰ Return to documentation for file (source/io/readers.h)

/*
 * readers.h File readers for timeseries instrument data
 *
 * Author:                   Tom Clark (thclark @ github)
 *
 * Copyright (c) 2016-9 Octue Ltd. All Rights Reserved.
 *
 */
#ifndef ES_FLOW_READERS_H
#define ES_FLOW_READERS_H

#include <stdlib.h>
#include <stdio.h>
#include <unistd.h>
#include <stdbool.h>
#include <iostream>
#include <vector>
#include <cstdlib>
#include <string>
#include <stdexcept>
#include "matio.h"
#include "glog/logging.h"
#include <iostream>
#include <vector>
#include <cstdlib>
#include <string>
#include <stdexcept>
#include <eigen3/Eigen/Core>
#include "data_types.h"


namespace es {


// Level of data validation applied to timeseries. Exception is thrown if checks fail
enum timeseries_check_level {
    PRESENT             = 0,    // Checks that data is present and of correct type. Extracts start and end timestamps.
    INCREASING          = 1,    // As PRESENT + checks that the timestamp always increases.
    MONOTONIC           = 2,    // As INCREASING + checks that timestamp uniformly increases, allows data skip (e.g. instrument turned off then back on later). Extracts sampling frequency.
    STRICTLY_MONOTONIC  = 3,    // AS INCREASING + checks that timestamp uniformly increases, data skipping causes errors. Extracts sampling frequency.
};

// Level of data validation applied to file type. Exception is thrown if checks fail
enum file_type_check_level {
    NONE                = 0,    // No checks
    OAS_STANDARD        = 1,    // Checks that the file contains the 'type' string variable
};

template <class DataType>
class Reader {
public:

    Reader(const std::string &file);

    ~Reader();

    std::string logString() const;

    DataType *read(bool print=false);

    void checkFileType(int level);

    void checkTimeseries(int level);

    double getWindowDuration() const;

    void setWindowDuration(double windowDuration);

    int getWindowSize() const;

    void setWindowSize(int windowSize);

    void readWindow(const int index);

protected:

    std::string file;
    mat_t *matfp;
    std::string file_type = std::string("none");
    int windowSize;
    double windowDuration;
    DataType data;

};

template <class DataType>
Reader<DataType>::Reader(const std::string &file) : file(file) {

    // Open the MAT file for reading and save the pointer
    matfp = Mat_Open(file.c_str(), MAT_ACC_RDONLY);
    if (matfp == NULL) {
        std::string msg = "Error reading MAT file: ";
        throw std::invalid_argument(msg + file);
    }

}

template <class DataType>
Reader<DataType>::~Reader() {

    // Close the file on destruction of the Reader
    Mat_Close(matfp);

}

template <class DataType>
void Reader<DataType>::checkFileType(int level){

    // Get the file type from the reserved 'type' variable in the mat file
    matvar_t *type_var = Mat_VarRead(matfp, "type");
    if (type_var == NULL) {
        if (level == OAS_STANDARD) {
            throw std::invalid_argument("Error reading mat file (most likely not an OAS standard file format - 'type' variable is missing)");
        }
    } else {
        if (type_var->class_type != MAT_C_CHAR) {
            throw std::invalid_argument("Error reading mat file ('type' variable must be a character array)");
        }
        file_type = std::string((const char*)type_var->data, type_var->dims[1]);
    }

}

template <class DataType>
void Reader<DataType>::checkTimeseries(int level) {

    // Check the integrity of the timeseries, automatically determine dt and frequency where possible

}

template <class DataType>
double Reader<DataType>::getWindowDuration() const {
    return windowDuration;
}

template <class DataType>
void Reader<DataType>::setWindowDuration(double windowDuration) {
    Reader<DataType>::windowDuration = windowDuration;
}

template <class DataType>
int Reader<DataType>::getWindowSize() const {
    return windowSize;
}

template <class DataType>
void Reader<DataType>::setWindowSize(int windowSize) {
    Reader<DataType>::windowSize = windowSize;
}

template <class DataType>
std::string Reader<DataType>::logString() const {
    return std::string("Object Reader for type ") + file_type + std::string(", attached to file ") + file;
}

template <class DataType>
DataType *Reader<DataType>::read(bool print) {
    // Simply invoke the read method of the DataType class.
    if (std::strcmp(data.type.c_str(), file_type.c_str())) {
        std::string msg = "Mat file type '" + file_type + "' incompatible with the specified data type '" + data.type + "'";
        throw std::invalid_argument(msg);
    }
    data.read(matfp, print);
    return &data;
}

template <class DataType>
void Reader<DataType>::readWindow(const int index) {
    //<DataType>.read(file_type, matfp);
}

// Represent Reader classes in logs or ostream
template <class DataType>
::std::ostream& operator<<(::std::ostream& os, const Reader<DataType>& reader) {
    // Represent in logs or ostream
    return os << reader.logString();
}

} /* namespace es */



#endif // ES_FLOW_READERS_H

Includes¶

cstdlib
data_types.h (File data_types.h)
eigen3/Eigen/Core
glog/logging.h
iostream
matio.h
stdbool.h
stdexcept
stdio.h
stdlib.h
string
unistd.h
vector

Namespaces¶

Namespace es

Classes¶

Template Class Reader

Enums¶

Functions¶

Template Function es::operator<<(::std::ostream&, const Reader<DataType>&)

File signature.h¶

↰ Parent directory (source/adem)

Contents

Definition (source/adem/signature.h)
Includes
Included By
Namespaces
Classes
Typedefs

Definition (source/adem/signature.h)¶

Program Listing for File signature.h¶

↰ Return to documentation for file (source/adem/signature.h)

/*
 * signature.h Eddy Signatures for use with the Attached-Detached Eddy Method
 *
 * Author:              Tom Clark  (thclark @ github)
 *
 * Copyright (c) 2019 Octue Ltd. All Rights Reserved.
 *
 */

#ifndef SOURCE_ADEM_SIGNATURE_H_
#define SOURCE_ADEM_SIGNATURE_H_

#include <boost/algorithm/string/classification.hpp> // Include boost::for is_any_of
#include <boost/algorithm/string/split.hpp> // Include for boost::split
#include <Eigen/Dense>
#include <Eigen/Core>
#include <math.h>
#include <stdexcept>
#include <unsupported/Eigen/CXX11/Tensor>
#include <unsupported/Eigen/FFT>

#include "adem/biot_savart.h"
#include "profile.h"
#include "relations/stress.h"
#include "relations/velocity.h"
#include "utilities/filter.h"
#include "utilities/conv.h"
#include "utilities/interp.h"
#include "utilities/tensors.h"
#include "utilities/trapz.h"
#include "io/variable_readers.h"
#include "io/variable_writers.h"

#include "cpplot.h"


typedef Eigen::Array<double, 5, 3> Array53d;
typedef Eigen::Array<double, 3, 3> Array33d;


using namespace utilities;
namespace es {


class EddySignature {
public:

    std::string eddy_type;

    Eigen::ArrayXd lambda;

    Eigen::ArrayXd eta;

    Eigen::Tensor<double, 3> g;

    Eigen::Array<double, Eigen::Dynamic, 6> j;

    Eigen::Array3d domain_spacing;

    Eigen::Array<double, 3, 2> domain_extents;

    void load(std::string file_name, bool print_var = false) {
        std::cout << "Reading eddy signature data from file " << file_name << std::endl;

        // Open the MAT file for reading
        mat_t *matfp = Mat_Open(file_name.c_str(), MAT_ACC_RDONLY);
        if (matfp == NULL) {
            std::string msg = "Error reading MAT file: ";
            throw std::invalid_argument(msg + file_name);
        }

        // Use the variable readers to assist
        eddy_type = readString(matfp, "eddy_type", print_var);
        lambda = readArrayXd(matfp, "lambda", print_var);
        eta = readArrayXd(matfp, "eta", print_var);
        domain_spacing = readArray3d(matfp, "domain_spacing", print_var);
        domain_extents = readArray32d(matfp, "domain_extents", print_var);
        g = readTensor3d(matfp, "g", print_var);
        j = readArrayXXd(matfp, "j", print_var);

        // Close the file
        Mat_Close(matfp);
        std::cout << "Finished reading eddy signature (Type " + eddy_type + ")" << std::endl;
    }

    void save(std::string file_name) {
        std::cout << "Writing signature data to file " << file_name << std::endl;

        mat_t *matfp = Mat_CreateVer(file_name.c_str(), NULL, MAT_FT_MAT73);
        if ( NULL == matfp ) {
            throw std::runtime_error("Unable to create/overwrite MAT file '" + file_name + "'");
        }

        // Use the variable writers to assist
        writeString(matfp, "eddy_type", eddy_type);
        writeArrayXd(matfp, "lambda", lambda);
        writeArrayXd(matfp, "eta", eta);
        writeArray3d(matfp, "domain_spacing", domain_spacing);
        writeArray32d(matfp, "domain_extents", domain_extents);
        writeTensor3d(matfp, "g", g);
        writeArrayXXd(matfp, "j", j);

        // Close the file
        Mat_Close(matfp);
        std::cout << "Finished writing eddy signature (Type " + eddy_type + ")" << std::endl;

    }

    EddySignature operator+(const EddySignature& c) const
    {
        EddySignature result;
        result.eddy_type = this->eddy_type + "+" + c.eddy_type;
        result.eta = this->eta;
        result.lambda = this->lambda;
        result.domain_spacing = this->domain_spacing;
        result.domain_extents = this->domain_extents;
        result.g = (this->g + c.g);
        result.j = (this->j + c.j);
        return result;
    }

    EddySignature operator*(double a) const
    {
        EddySignature result;
        result.eddy_type = "(" + this->eddy_type + ")*" + std::to_string(a);
        result.eta = this->eta;
        result.lambda = this->lambda;
        result.domain_spacing = this->domain_spacing;
        result.domain_extents = this->domain_extents;
        result.g = this->g;
        result.j = this->j;
        result.g = result.g * a;
        result.j = result.j * a;
        return result;
    }

    EddySignature operator/(double denom) const
    {
        EddySignature result;
        result.eddy_type = "(" + this->eddy_type + ")/" + std::to_string(denom);
        result.eta = this->eta;
        result.lambda = this->lambda;
        result.domain_spacing = this->domain_spacing;
        result.domain_extents = this->domain_extents;
        result.g = this->g;
        result.j = this->j;
        result.g = result.g / denom;
        result.j = result.j / denom;
        return result;
    }

    Eigen::ArrayXXd k1z(Eigen::ArrayXd &eta) const {

        double dx = domain_spacing[0];
        auto nx = Eigen::Index((domain_extents(0,1) - domain_extents(0,0)) / dx) + 1;
        Eigen::ArrayXd k1_delta = Eigen::ArrayXd::LinSpaced(nx, 0, nx-1) * 2.0 * M_PI / dx;
        Eigen::ArrayXXd k1z = k1_delta.replicate(1, eta.rows()) * eta.transpose().replicate(k1_delta.rows(), 1);

        std::cout << "k1_delta_start " << k1_delta(0) << std::endl;
        std::cout << "k1_delta_end " << k1_delta(nx-1) << std::endl;
        std::cout << "eta_start " << eta(0) << std::endl;
        std::cout << "eta_end " << eta(eta.rows()-1) << std::endl;
        std::cout << "k1z_n_rows " << k1z.rows() << std::endl;
        std::cout << "k1z_n_cols " << k1z.cols() << std::endl;

        return k1z;
    }

    Eigen::ArrayXXd getJ(const Eigen::ArrayXd & locations, const bool linear=false) const {
        Eigen::ArrayXXd j_fine(locations.rows(), 6);
        if (linear) {
            // The new locations are values of eta

            // Assert locations are in the valid range...
            if ((locations < 0.0).any()) {
                throw std::invalid_argument("Input locations (eta values) must be defined for eta >= 0.0");
            }

            // Interpolate on an eta basis
            for (int k = 0; k < 6; k++) {
                utilities::CubicSplineInterpolant s(this->eta.matrix(), this->j.col(k).matrix());
                j_fine.col(k) = s(locations);
            }

        } else {
            // The new locations are values of lambda

            // Interpolate on a lambda basis
            for (int k = 0; k < 6; k++) {
                utilities::CubicSplineInterpolant s(this->lambda.matrix(), this->j.col(k).matrix());
                j_fine.col(k) = s(locations);
            }
        }
        return j_fine;
     };

    void computeSignature(const std::string &type, const int n_lambda=200, const double dx=0.002) {

        // Set the type string
        eddy_type = type;

        // Express eddy structure as line vortices.  See Figure 13 Perry and Marusic 1995.
        Array33d eddy;
        if (type == "A") {
            eddy << 0, -0.8, 0,
                    1,  0,   1,
                    0,  0.8, 0;

        } else if (type == "B1") {
            eddy << 0.2, -0.15, 1,
                    0,    0,    0.5,
                    0.09, 0.15, 1;

        } else if (type == "B2") {
            eddy << 0,     0.15, 0.5,
                    0.2,   0,    1,
                    0.11, -0.15, 0.5;

        } else if (type == "B3") {
            eddy << 0.09, -0.15, 1,
                    0,     0,    0.5,
                    0.2,   0.15, 1;

        } else if (type == "B4") {
            eddy << 0.11, 0.15, 0.5,
                    0.20, 0,    1,
                    0,   -0.15, 0.5;
        } else {
            // TODO sort out cpplot import ordering so that I can import exceptions from our own damn library!
//            es::InvalidEddyTypeException e;
//            throw(e);
        }

        // Determine start and end nodes of the eddy...
        Eigen::Array3Xd startNodes(3,4);
        Eigen::Array3Xd endNodes(3,4);
        startNodes.leftCols(2) = eddy.topRows(2).transpose();
        endNodes.leftCols(2) = eddy.bottomRows(2).transpose();

        // ... and its reflection in the wall
        eddy.col(2) *= -1;
        startNodes.rightCols(2) = eddy.bottomRows(2).transpose();
        endNodes.rightCols(2) = eddy.topRows(2).transpose();

        //    % PLOT EDDY STRUCTURE SHAPE
        //    raiseFigure(['Type ' type ' Eddy Structure'])
        //    clf
        //    subplot(1,3,1)
        //    plot3([startNodes(:,1)'; endNodes(:,1)'],[startNodes(:,2)'; endNodes(:,2)'],[startNodes(:,3)'; endNodes(:,3)'],'k-')
        //    axis equal
        //    xlabel('x/\delta')
        //    ylabel('y/\delta')
        //    zlabel('z/\delta')

        // Set up influence domain

        /* Let's just think a second about frequency. For an ABL, the boundary layer is (say) delta = 1km thick,
         * and the wind speed is (say) 20m/s, and we want to resolve spectra to a frequency of (say) 10Hz,
         * then what eddy scale do we need to go down to?
         *      20/10 = 2 m ...
         * nondimensionalising, that's an eddy scale z/delta of 0.002. So our largest value of lambda_e (the eddy scale,
         * smaller as lambda_e increases) should correspond to this z/delta (or even finer scale).
         *
         * We thus choose z/delta = 0.002 as our finest eddy scale - that's why input param dx is set at 0.002.
         *
         */
        //double lambda_max = log(1/dx);
        std::cout << "UNBODGE THIS" << std::endl;
        double lambda_max = log(500);
        double lambda_min = log(1/1.5);

        // The domain extents are set accordingly
        domain_extents = Eigen::Array<double, 3, 2>::Zero();
        domain_extents << -4, 4,
                          -2, 2,
                           (1.0 / exp(lambda_max)), (1.0 / exp(lambda_min));

        // Logarithmically space the lambda coordinates
        lambda = Eigen::ArrayXd::LinSpaced(n_lambda, lambda_min, lambda_max);
        double d_lambda = lambda(1)-lambda(0);

        // Store real space vertical coordinates too
        eta = lambda.exp().inverse();

        /* So now we need to set the spacing in the physical domain
         * Wavenumber k1 2*pi/L = 2*pi*f/U
         *
         * So for the above estimated parameters of f = 10Hz, U = 20m/s, L = 2. Normalised to x/delta, this is 0.002.
         * So we need the grid spacing to be of a similar order in order to capture the appropriate wavenumbers...
         */
        domain_spacing << dx, dx, d_lambda;

        // A constant expression used for scaling the Reynolds Stress contributions
        constexpr double u0_sqd = 1.0 / (4.0 * M_PI * M_PI);

        // Streamwise and transverse grids (eta is z)
        Eigen::Index nx = ceil((domain_extents(0,1) - domain_extents(0,0)) / domain_spacing(0));
        Eigen::Index ny = ceil((domain_extents(1,1) - domain_extents(1,0)) / domain_spacing(1));
        Eigen::ArrayXXd x_vec = Eigen::ArrayXd::LinSpaced(nx, domain_extents(0,0), domain_extents(0,1));
        Eigen::ArrayXXd y_vec = Eigen::ArrayXd::LinSpaced(ny, domain_extents(1,0), domain_extents(1,1));

        // Produce x, y matrices, with y being the quickest changing (down columns)
        // Eigen syntax to replicate and interleave like this is v. awkward, so we have to write a loop. Sigh.
        Eigen::Index n_locations = x_vec.rows() * y_vec.rows();
        Eigen::Array3Xd locations(3, n_locations);
        Eigen::Index ctr = 0;
        for (auto i=0; i<x_vec.rows(); i++) {
            for (auto j=0; j<y_vec.rows(); j++) {
                locations(0, ctr) = x_vec(i);
                locations(1, ctr) = y_vec(j);
                ctr++;
            };
        };

        // Set unit circulation and the core radius of 0.05 as recommended by Perry and Marusic.
        Eigen::VectorXd gamma = Eigen::VectorXd::Ones(4);
        Eigen::VectorXd effective_core_radius_squared = Eigen::VectorXd::Ones(4) * pow(0.05, 2.0);

        j = Eigen::ArrayXXd(n_lambda,6);
        j.setZero();

        // For each vertical coordinate, determine the contribution to the eddy signature and spectra
        for (Eigen::Index lam_ctr=0; lam_ctr<n_lambda; lam_ctr++) {
            locations.row(2) = Eigen::ArrayXXd::Constant(1, n_locations, eta(lam_ctr));
            std::cout << "Computing signature at eta=" << eta(lam_ctr) << " (" << lam_ctr+1 << " of " << n_lambda << ")" << std::endl;
            Eigen::Array3Xd induction = NaiveBiotSavart(
                startNodes.matrix(),
                endNodes.matrix(),
                locations.matrix(),
                gamma,
                effective_core_radius_squared
            );

            // We don't want to copy or reallocate the memory... map into the induction
            Eigen::Map<Eigen::ArrayXXd, 0, Eigen::InnerStride<3>> u (induction.data(), y_vec.rows(), x_vec.rows());
            Eigen::Map<Eigen::ArrayXXd, 0, Eigen::InnerStride<3>> v (induction.data()+1, y_vec.rows(), x_vec.rows());
            Eigen::Map<Eigen::ArrayXXd, 0, Eigen::InnerStride<3>> w (induction.data()+2, y_vec.rows(), x_vec.rows());

            // Compute and plot Reynolds Stresses produced by a single eddy
            Eigen::ArrayXXd uu = u * u / u0_sqd;
            Eigen::ArrayXXd uv = u * v / u0_sqd;
            Eigen::ArrayXXd uw = u * w / u0_sqd;
            Eigen::ArrayXXd vv = v * v / u0_sqd;
            Eigen::ArrayXXd vw = v * w / u0_sqd;
            Eigen::ArrayXXd ww = w * w / u0_sqd;

            // We have constant spacing, so use quick version of trapz to integrate first across X, then down Y
            j.block<1,1>(lam_ctr, 0) = trapz(trapz(uu,2) * domain_spacing(0),1) * domain_spacing(1);
            j.block<1,1>(lam_ctr, 1) = trapz(trapz(uv,2) * domain_spacing(0),1) * domain_spacing(1);
            j.block<1,1>(lam_ctr, 2) = trapz(trapz(uw,2) * domain_spacing(0),1) * domain_spacing(1);
            j.block<1,1>(lam_ctr, 3) = trapz(trapz(vv,2) * domain_spacing(0),1) * domain_spacing(1);
            j.block<1,1>(lam_ctr, 4) = trapz(trapz(vw,2) * domain_spacing(0),1) * domain_spacing(1);
            j.block<1,1>(lam_ctr, 5) = trapz(trapz(ww,2) * domain_spacing(0),1) * domain_spacing(1);
        };


    }

    void applySignature(const std::string &type, const int n_lambda=200) {

        // Set the type string
        eddy_type = type;

        // Set arbitrary domain extents
        double lambda_max = log(500);
        double lambda_min = log(1/1.5);
        domain_extents = Eigen::Array<double, 3, 2>::Zero();
        domain_extents << -4, 4,
            -2, 2,
            (1.0 / exp(lambda_max)), (1.0 / exp(lambda_min));

        // Logarithmically space lambda coordinates
        lambda = Eigen::ArrayXd::LinSpaced(n_lambda, lambda_min, lambda_max);
        domain_spacing << 1.0, 1.0, lambda(1)-lambda(0);

        // Store real space vertical coordinates too
        eta = lambda.exp().inverse();

        // Interpolate the signatures that are given.
        j = Eigen::ArrayXXd(n_lambda,6);
        j.setZero();
        Eigen::ArrayXXd i11;
        Eigen::ArrayXXd i13;
        Eigen::ArrayXXd i22;
        Eigen::ArrayXXd i33;
        if (type == "A") {
            i11 = Eigen::ArrayXXd(2, 26);
            i11 << 0, 0.012710542, 0.030316638, 0.05182384, 0.08898147, 0.1300581, 0.18483716, 0.2357049, 0.29636374, 0.35898846, 0.41573855, 0.4783607, 0.5585967, 0.6368718, 0.7073141, 0.76600707, 0.82468724, 0.87943816, 0.91658044, 0.9419913, 0.97133654, 1.0007021, 1.0516082, 1.1260028, 1.2239062, 1.50,
                1.6593906, 1.6418779, 1.611259, 1.5544281, 1.4713508, 1.3926289, 1.3051336, 1.2263831, 1.1476042, 1.08192, 1.0162529, 0.94620186, 0.8586324, 0.7667018, 0.6747941, 0.5829205, 0.469213, 0.33368298, 0.22440498, 0.1457287, 0.09760853, 0.084422655, 0.07117407, 0.040389933, 0.027004533, 0.0;

            i13 = Eigen::ArrayXXd(2, 21);
            i13 << 0, 0.023503713, 0.05093406, 0.08618198, 0.12728672, 0.17620902, 0.22121488, 0.28186864, 0.3620689, 0.45790172, 0.55568004, 0.64367235, 0.7238267, 0.80006206, 0.86259496, 0.90362066, 0.93487054, 0.9700394, 0.9993566, 1.0423712, 1.50,
                0, -0.061066702, -0.14832275, -0.22682244, -0.2878379, -0.340097, -0.38363394, -0.43149212, -0.4618262, -0.4702808, -0.46126255, -0.43917242, -0.39090434, -0.32954726, -0.24639612, -0.17204118, -0.102081485, -0.045210768, -0.014557855, -0.0030345472, -0.004372481;

            i22 = Eigen::ArrayXXd(2, 23);
            i22 << 0, 0.018947192, 0.03648182, 0.054011352, 0.0754471, 0.10665094, 0.17303112, 0.21991083, 0.28439146, 0.34693173, 0.41142765, 0.48179564, 0.57952243, 0.65573704, 0.7202125, 0.788579, 0.8452064, 0.9115866, 0.9701798, 1.0483195, 1.1304111, 1.2340457, 1.50,
                1.176464, 1.150218, 1.0934712, 1.0323671, 0.966883, 0.8926276, 0.79638124, 0.74817854, 0.6998736, 0.6646518, 0.6294187, 0.5985088, 0.5500107, 0.5016375, 0.4489753, 0.37886125, 0.3044581, 0.20821178, 0.14251183, 0.067983694, 0.028291034, 0.014617034, 0.0043686354;

            i33 = Eigen::ArrayXXd(2, 32);
            i33 << 0.0, 0.023483196, 0.041119818, 0.06269325, 0.09603633, 0.12936921, 0.17444114, 0.21754721, 0.25868744, 0.30175778, 0.35461667, 0.4133425, 0.46618098, 0.5346596, 0.608995, 0.6696255, 0.73806334, 0.7908406, 0.83576465, 0.8884807, 0.92553115, 0.95087314, 0.9898843, 1.0288852, 1.0737991, 1.1304673, 1.1793332, 1.2321156, 1.2849082, 1.3552966, 1.4374342, 1.50,
                0.0, 0.012935479, 0.043334138, 0.095496446, 0.1780915, 0.251972, 0.3301416, 0.39960802, 0.46037126, 0.49933675, 0.54696, 0.5945491, 0.6247433, 0.6504893, 0.6674866, 0.6714917, 0.66237944, 0.6402863, 0.59209496, 0.51771456, 0.42599595, 0.35613185, 0.26875913, 0.17267188, 0.115766004, 0.07622104, 0.05415063, 0.036414765, 0.027393447, 0.013912599, 0.013435401, 0.0043572737;

        } else if (type == "B") {
            i11 = Eigen::ArrayXXd(2, 23);
            i11 << 0, 0.07068844, 0.1666695, 0.27835685, 0.36659724, 0.4334307, 0.48672056, 0.5342177, 0.5837344, 0.62532634, 0.67665803, 0.74737716, 0.8137505, 0.8545449, 0.8894136, 0.93391985, 0.9706649, 1.00945, 1.0521617, 1.1184429, 1.2122818, 1.3199301, 1.50,
                0.016322415, 0.016322415, 0.018703382, 0.024518738, 0.03472676, 0.056264196, 0.091715895, 0.13412246, 0.18173045, 0.22154763, 0.25700384, 0.27592924, 0.25842202, 0.23056176, 0.19837682, 0.15315433, 0.11402357, 0.08182956, 0.050494146, 0.025177978, 0.011945607, 0.0073581133, 0.0017353186;

            i13 = Eigen::ArrayXXd(2, 14);
            i13 << 0, 0.2741542, 0.34076267, 0.42109883, 0.47993597, 0.56440324, 0.6233631, 0.7057494, 0.7918987, 0.8779049, 0.94425774, 1.0145372, 1.1240618, 1.50,
                0, -2.3333919E-4, -0.002682268, -0.0068347994, -0.014507807, -0.036872122, -0.054957043, -0.06691398, -0.06584696, -0.05263271, -0.033390157, -0.015006201, -0.0034729026, -8.676593E-4;

            i22 = Eigen::ArrayXXd(2, 23);
            i22 << 0, 0.14884579, 0.29180932, 0.4054613, 0.46828458, 0.515565, 0.5411826, 0.5746176, 0.6335705, 0.6963938, 0.74149364, 0.7689007, 0.8080032, 0.8490102, 0.89000964, 0.93290585, 0.9660264, 0.99715817, 1.0224689, 1.049784, 1.0810461, 1.1632366, 1.50,
                0, 0.0023498295, 0.0038403252, 0.012338308, 0.030489888, 0.06258152, 0.08079781, 0.09726137, 0.12063707, 0.13878864, 0.14566672, 0.14474949, 0.13772498, 0.12461021, 0.110625885, 0.08968175, 0.07049375, 0.047830947, 0.031265218, 0.019913385, 0.012032943, 0.005803057, 0.0026086513;

            i33 = Eigen::ArrayXXd(2, 20);
            i33 << 0, 0.21936293, 0.31337926, 0.39961416, 0.44083738, 0.48011523, 0.5254081, 0.56480104, 0.64147526, 0.64147526, 0.70819265, 0.7767404, 0.8334498, 0.8939988, 0.9446548, 0.9952725, 1.0459669, 1.0967507, 1.1632637, 1.5000255,
                0, 0.002830162, 0.004290453, 0.009236455, 0.016043989, 0.023722952, 0.0409085, 0.05637945, 0.07693768, 0.07693768, 0.08626908, 0.08693706, 0.081578515, 0.07101401, 0.053551547, 0.033491757, 0.018626625, 0.009821928, 0.0053009023, 0.0017315528;

        } else {
            throw std::invalid_argument("You can only apply signatures for type 'A' or type 'B' eddies");
        }

        utilities::LinearInterpolant s11(i11.row(0).transpose(), i11.row(1).transpose());
        utilities::LinearInterpolant s13(i13.row(0).transpose(), i13.row(1).transpose());
        utilities::LinearInterpolant s22(i22.row(0).transpose(), i22.row(1).transpose());
        utilities::LinearInterpolant s33(i33.row(0).transpose(), i33.row(1).transpose());

        j.col(0) = s11(eta);
        j.col(2) = s13(eta);
        j.col(3) = s22(eta);
        j.col(5) = s33(eta);
    }
};

} /* namespace es */

#endif /* SOURCE_ADEM_SIGNATURE_H_ */

Includes¶

Eigen/Core
Eigen/Dense
adem/biot_savart.h (File biot_savart.h)
boost/algorithm/string/classification.hpp
boost/algorithm/string/split.hpp
cpplot.h
io/variable_readers.h (File variable_readers.h)
io/variable_writers.h (File variable_writers.h)
math.h
profile.h (File profile.h)
relations/stress.h (File stress.h)
relations/velocity.h (File velocity.h)
stdexcept
unsupported/Eigen/CXX11/Tensor
unsupported/Eigen/FFT
utilities/conv.h (File conv.h)
utilities/filter.h (File filter.h)
utilities/interp.h (File interp.h)
utilities/tensors.h (File tensors.h)
utilities/trapz.h (File trapz.h)

Included By¶

File adem.h

Namespaces¶

Namespace es

Classes¶

Class EddySignature

Typedefs¶

File smear.h¶

↰ Parent directory (source/utilities)

Contents

Definition (source/utilities/smear.h)

Definition (source/utilities/smear.h)¶

Program Listing for File smear.h¶

↰ Return to documentation for file (source/utilities/smear.h)

/*
 * smear.h Brief overview sentence
 *
 * Author:              Tom Clark  (thclark @ github)
 *
 * Copyright (c) 2019 Octue Ltd. All Rights Reserved.
 *
 */

#ifndef ES_FLOW_SMEAR_H
#define ES_FLOW_SMEAR_H

#endif //ES_FLOW_SMEAR_H

File spectra.cpp¶

↰ Parent directory (source/relations)

Contents

Definition (source/relations/spectra.cpp)
Includes

Definition (source/relations/spectra.cpp)¶

Program Listing for File spectra.cpp¶

↰ Return to documentation for file (source/relations/spectra.cpp)

/*
 * spectra.cpp Brief overview sentence
 *
 * Author:              Tom Clark  (thclark @ github)
 *
 * Copyright (c) 2019 Octue Ltd. All Rights Reserved.
 *
 */

#include "spectra.h"

Includes¶

spectra.h (File spectra.h)

File spectra.h¶

↰ Parent directory (source/relations)

Contents

Definition (source/relations/spectra.h)
Included By
Classes

Definition (source/relations/spectra.h)¶

Program Listing for File spectra.h¶

↰ Return to documentation for file (source/relations/spectra.h)

/*
 * spectra.h Brief overview sentence
 *
 * Author:              Tom Clark  (thclark @ github)
 *
 * Copyright (c) 2019 Octue Ltd. All Rights Reserved.
 *
 */

#ifndef ES_FLOW_SPECTRA_H
#define ES_FLOW_SPECTRA_H

class spectra {

};

#endif //ES_FLOW_SPECTRA_H

Included By¶

File spectra.cpp

Classes¶

Class spectra

File stress.h¶

↰ Parent directory (source/relations)

Contents

Definition (source/relations/stress.h)
Includes
Included By
Namespaces
Classes
Functions

Definition (source/relations/stress.h)¶

Program Listing for File stress.h¶

↰ Return to documentation for file (source/relations/stress.h)

/*
 * stress.h Atmospheric Boundary Layer Reynolds Stress relations
 *
 * Author:              Tom Clark  (thclark @ github)
 *
 * Copyright (c) 2019 Octue Ltd. All Rights Reserved.
 *
 */

#ifndef ES_FLOW_STRESS_H_
#define ES_FLOW_STRESS_H_

#include <Eigen/Dense>
#include <Eigen/Core>
#include <iostream>
#include <iomanip>
#include <math.h>
#include "NumericalIntegration.h"
#include "profile.h"
#include "relations/velocity.h"
#include "utilities/integration.h"

#include "definitions.h"
#include "cpplot.h"

using namespace utilities;
using namespace cpplot;


namespace es {


template<typename T_scalar, typename T_param>
class DeficitFunctor {
private:
    double m_kappa, m_shear_ratio;
    T_param m_pi_coles;
    bool m_lewkowicz, m_deficit_squared;

public:
    DeficitFunctor(const double kappa, const T_param pi_coles, const double shear_ratio, const bool lewkowicz, const bool deficit_squared=false) : m_kappa(kappa), m_pi_coles(pi_coles), m_shear_ratio(shear_ratio), m_lewkowicz(lewkowicz), m_deficit_squared(deficit_squared) {};
    T_scalar operator() (T_scalar eta) const{
        if (m_deficit_squared){
            return pow(deficit(eta, m_kappa, m_pi_coles, m_shear_ratio, m_lewkowicz), 2.0);

        }
        return deficit(eta, m_kappa, m_pi_coles, m_shear_ratio, m_lewkowicz);
    };
};


void reynolds_stress_13(Eigen::ArrayXd &r13_a, Eigen::ArrayXd &r13_b, const double beta, const Eigen::ArrayXd &eta, const double kappa, const double pi_coles, const double shear_ratio, const double zeta){

    // Check the input has a valid range; the integration will be messed up otherwise.
    if ((eta(eta.rows()-1) != 1.0) || (eta(0) != 0.0)) {
        throw std::invalid_argument("Input eta must be defined in the range 0, 1 exactly");
    }

    // TODO Improved control of models - see #61.
    bool lewkowicz = true;

    // Get f between eta = 0 and eta = 1
    Eigen::ArrayXd f = deficit(eta, kappa, pi_coles, shear_ratio, lewkowicz);
    const double d_pi = 0.001 * pi_coles;

    // Do the integrations for ei, with central differencing for numerical differentiation of e coefficients 5-7
    DeficitFunctor<double, double> deficit_functor(KAPPA_VON_KARMAN, pi_coles, shear_ratio, true, false);
    DeficitFunctor<double, double> deficit_functor_plus(KAPPA_VON_KARMAN, pi_coles+d_pi, shear_ratio, true, false);
    DeficitFunctor<double, double> deficit_functor_minus(KAPPA_VON_KARMAN, pi_coles-d_pi, shear_ratio, true, false);
    DeficitFunctor<double, double> deficit_squared_functor(KAPPA_VON_KARMAN, pi_coles, shear_ratio, true, true);
    DeficitFunctor<double, double> deficit_squared_functor_plus(KAPPA_VON_KARMAN, pi_coles+d_pi, shear_ratio, true, true);
    DeficitFunctor<double, double> deficit_squared_functor_minus(KAPPA_VON_KARMAN, pi_coles-d_pi, shear_ratio, true, true);
    Eigen::ArrayXd e1 = utilities::cumulative_integrate(eta, deficit_functor);
    Eigen::ArrayXd e1_plus = utilities::cumulative_integrate(eta, deficit_functor_plus);
    Eigen::ArrayXd e1_minus = utilities::cumulative_integrate(eta, deficit_functor_minus);
    Eigen::ArrayXd e2 = utilities::cumulative_integrate(eta, deficit_squared_functor);
    Eigen::ArrayXd e2_plus = utilities::cumulative_integrate(eta, deficit_squared_functor_plus);
    Eigen::ArrayXd e2_minus = utilities::cumulative_integrate(eta, deficit_squared_functor_minus);
    Eigen::ArrayXd e3 = f * e1;
    Eigen::ArrayXd e4 = eta * f;
    Eigen::ArrayXd e5 = (e1_plus - e1_minus) / (2.0 * d_pi);
    Eigen::ArrayXd e6 = (e2_plus - e2_minus) / (2.0 * d_pi);
    Eigen::ArrayXd e7 = f * e5;

    // Get C1 value (eqn 14) which is the end value of the e1 distribution
    double c1 = e1[e1.rows()-1];

    // Get A coefficients from equations A2 a-d
    Eigen::ArrayXd a1 = e2 - e3 + shear_ratio * (e4 - e1);
    Eigen::ArrayXd a2 = (-2.0 * e2) + e3 + (shear_ratio * e1);
    Eigen::ArrayXd a3 = e6 - e7 - (shear_ratio * e5);
    Eigen::ArrayXd a4 = (2.0 * e2) - e3 + (shear_ratio * e4) - (shear_ratio * 3.0 * e1);

    // B coefficients are simply evaluated at eta = 1 (eqn A6)
    double b1 = a1(eta.rows()-1);
    double b2 = a2(eta.rows()-1);
    double b3 = a3(eta.rows()-1);
    double b4 = a4(eta.rows()-1);

    // E1 from (eqn A4). Can't call it E1 due to name conflict with above.
    double e1_coeff = 1.0 / (kappa * shear_ratio + 1.0);

    // TODO Resolve issue #59 here.
    double n = coles_wake(1.0, pi_coles);

    // Compile f_i terms
    Eigen::ArrayXd f1;
    Eigen::ArrayXd f2;
    Eigen::ArrayXd f3;
    f1 = 1.0
        - a1 / (b1 + e1_coeff * b2)
        - e1_coeff * a2 / (b1 + e1_coeff * b2);

    f2 = (e1_coeff * n * a2 * b1
        + a3 * b1
        - e1_coeff * n * a1 * b2
        + e1_coeff * a3 * b2
        - a1 * b3
        - e1_coeff * a2 * b3) / (b1 + e1_coeff * b2);

    f3 = (e1_coeff * a2 * b1
        + a4 * b1
        - e1_coeff * a1 * b2
        + e1_coeff * a4 * b2
        - a1 * b4
        - e1_coeff * a2 * b4) / (b1 + e1_coeff * b2);

    // Convert f2 and f3 into g1 and g2, apply eq. 15
    Eigen::ArrayXd g1 = f2 / shear_ratio;
    Eigen::ArrayXd g2 = -f3 / (c1 * shear_ratio);
    Eigen::ArrayXd minus_r13 = f1 + g1 * zeta + g2 * beta;

    // As a validation check, reproduce figure
    Figure fig = Figure();
    ScatterPlot p1 = ScatterPlot();
    p1.x = eta;
    p1.y = f1;
    p1.name = "f1";
    ScatterPlot p2 = ScatterPlot();
    p2.x = eta;
    p2.y = g1*zeta;
    p2.name = "g1*zeta";
    ScatterPlot p3 = ScatterPlot();
    p3.x = eta;
    p3.y = g2*beta;
    p3.name = "g2*beta";
    ScatterPlot p4 = ScatterPlot();
    p4.x = eta;
    p4.y = minus_r13;
    p4.name = "tau / tau_0 (= -r13)";
    fig.add(p1);
    fig.add(p2);
    fig.add(p3);
    fig.add(p4);
    Layout lay = Layout("Check reproduction of Perry & Marusic 1995 Figure 1");
    lay.xTitle("$\\eta$");
    fig.setLayout(lay);
    fig.write("check_perry_marusic_fig_1");

    Eigen::ArrayXd minus_r13_a(eta.rows());
    if (lewkowicz) {
        // Lewkowicz 1982 shear stress for equilibrium sink flow, Perry and Marusic eqn. 51
        minus_r13_a = 1.0
            - (60.0 / 59.0) * eta
            - (20.0 / 59.0) * eta.pow(3.0)
            + (45.0 / 59.0) * eta.pow(4.0)
            - (24.0 / 59.0) * eta.pow(5.0)
            + (60.0 / 59.0) * eta * eta.log();
    } else {
        // Shear stress for `pure` equilibrium sink flow with no correction, Perry and Marusic eqn. 53
        minus_r13_a = 1.0 - eta + eta * eta.log();
    }

    // Handle the log(0) singularity
    for (int i = 0; i < minus_r13_a.size(); i++) {
        if (std::isinf(minus_r13_a(i)) || std::isnan(minus_r13_a(i))) {
            minus_r13_a(i) = 1.0;
        }
    }

    // Output correctly signed reynolds stress components
    r13_a = -1.0 * minus_r13_a;
    r13_b = -1.0 * (minus_r13 - minus_r13_a);

}

} /* namespace es */

#endif /* ES_FLOW_STRESS_H_ */

Includes¶

Eigen/Core
Eigen/Dense
NumericalIntegration.h
cpplot.h
definitions.h (File definitions.h)
iomanip
iostream
math.h
profile.h (File profile.h)
relations/velocity.h (File velocity.h)
utilities/integration.h (File integration.h)

Included By¶

Namespaces¶

Namespace es

Classes¶

Template Class DeficitFunctor

Functions¶

Function es::reynolds_stress_13

File tensors.h¶

↰ Parent directory (source/utilities)

Contents

Definition (source/utilities/tensors.h)
Includes
Included By
Namespaces
Functions
Typedefs

Definition (source/utilities/tensors.h)¶

Program Listing for File tensors.h¶

↰ Return to documentation for file (source/utilities/tensors.h)

/*
 * tensors.h Utilities to help with Eigen::Tensors
 *
 * Author:              Tom Clark  (thclark @ github)
 *
 * Copyright (c) 2019 Octue Ltd. All Rights Reserved.
 *
 */

#ifndef ES_FLOW_TENSORS_H
#define ES_FLOW_TENSORS_H

#include <unsupported/Eigen/CXX11/Tensor>
#include <iostream>
#include <string>


namespace utilities {


template<typename T>
using  MatrixType = Eigen::Matrix<T,Eigen::Dynamic, Eigen::Dynamic>;


template<typename T>
using  ArrayType = Eigen::Array<T,Eigen::Dynamic, Eigen::Dynamic>;


template<typename Scalar,int rank, typename sizeType>
auto tensor_to_matrix(const Eigen::Tensor<Scalar,rank> &tensor,const sizeType rows,const sizeType cols)
{
    return Eigen::Map<const MatrixType<Scalar>> (tensor.data(), rows,cols);
}


template<typename Scalar, typename... Dims>
auto matrix_to_tensor(const MatrixType<Scalar> &matrix, Dims... dims)
{
    constexpr int rank = sizeof... (Dims);
    return Eigen::TensorMap<Eigen::Tensor<const Scalar, rank>>(matrix.data(), {dims...});
}


template<typename Scalar,int rank, typename sizeType>
auto tensor_to_array(const Eigen::Tensor<Scalar,rank> &tensor,const sizeType rows,const sizeType cols)
{
    return Eigen::Map<const ArrayType<Scalar>> (tensor.data(), rows,cols);
}


template<typename Scalar, typename... Dims>
auto array_to_tensor(const ArrayType<Scalar> &matrix, Dims... dims)
{
    constexpr int rank = sizeof... (Dims);
    return Eigen::TensorMap<Eigen::Tensor<const Scalar, rank>>(matrix.data(), {dims...});
}


template<typename T>
std::string tensor_dims(T &tensor) {
    std::stringstream dims;
    for (auto i = tensor.dimensions().begin(); i != tensor.dimensions().end(); ++i) {
        dims << *i << " x ";
    }
    std::string dim_str = dims.str();
    dim_str.pop_back();
    dim_str.pop_back();
    dim_str.pop_back();
    return dim_str;
}

} /* namespace utilities */

#endif //ES_FLOW_TENSORS_H

Includes¶

iostream
string
unsupported/Eigen/CXX11/Tensor

Included By¶

Namespaces¶

Namespace utilities

Functions¶

Typedefs¶

File trapz.h¶

↰ Parent directory (source/utilities)

Contents

Definition (source/utilities/trapz.h)
Includes
Included By
Namespaces
Functions

Definition (source/utilities/trapz.h)¶

Program Listing for File trapz.h¶

↰ Return to documentation for file (source/utilities/trapz.h)

/*
 * trapz.h Trapezoidal Numerical Integration for Eigen
 *
 * Author:              Tom Clark  (thclark @ github)
 *
 * Copyright (c) 2019 Octue Ltd. All Rights Reserved.
 *
 */

#ifndef ES_FLOW_TRAPZ_H
#define ES_FLOW_TRAPZ_H

#include <Eigen/Dense>
#include <stdexcept>


namespace utilities {


template<typename Derived, typename OtherDerived>
EIGEN_STRONG_INLINE void trapz(Eigen::ArrayBase<OtherDerived> const & out, const Eigen::ArrayBase<Derived>& in, Eigen::Index direction=1) {
    Eigen::ArrayBase<OtherDerived> &out_ = const_cast< Eigen::ArrayBase<OtherDerived> & >(out);
    Eigen::Array<typename Eigen::ArrayBase<Derived>::Scalar,
                 Eigen::ArrayBase<Derived>::RowsAtCompileTime,
                 Eigen::ArrayBase<Derived>::ColsAtCompileTime> inter;

    if (direction == 1) {
        if (in.rows() == 1) {
            out_.derived().setZero(1, in.cols());
        } else {
            inter = (in.topRows(in.rows() - 1) + in.bottomRows(in.rows() - 1)) * 0.5;
            out_.derived() = inter.colwise().sum();
        }
    } else if (direction == 2) {
        if (in.cols() == 1) {
            out_.derived().setZero(in.rows(), 1);
        } else {
            inter = (in.leftCols(in.cols() - 1) + in.rightCols(in.cols() - 1)) * 0.5;
            out_.derived() = inter.rowwise().sum();
        }
    } else {
        assert(((direction == 1) || (direction == 2)));
    }

}

/*
 * Overload method to return result by value.
 */
template<typename Derived>
EIGEN_STRONG_INLINE Eigen::Array<typename Eigen::ArrayBase<Derived>::Scalar, Eigen::ArrayBase<Derived>::RowsAtCompileTime, Eigen::ArrayBase<Derived>::ColsAtCompileTime> trapz(const Eigen::ArrayBase<Derived>& y, Eigen::Index dimension=1)
{
    Eigen::Array<typename Eigen::ArrayBase<Derived>::Scalar, Eigen::ArrayBase<Derived>::RowsAtCompileTime, Eigen::ArrayBase<Derived>::ColsAtCompileTime> z;
    trapz(z,y, dimension);
    return z;
}

template<typename DerivedX, typename DerivedY, typename DerivedOut>
EIGEN_STRONG_INLINE void trapz(Eigen::ArrayBase<DerivedOut> const & out, const Eigen::ArrayBase<DerivedX>& in_x, const Eigen::ArrayBase<DerivedY>& in_y)
{
    // Input size check
    eigen_assert(in_x.rows() == in_y.rows());
    eigen_assert(in_x.cols() == 1);

    // Get dx for each piece of the integration
    Eigen::Array<typename Eigen::ArrayBase<DerivedX>::Scalar, Eigen::ArrayBase<DerivedX>::RowsAtCompileTime, Eigen::ArrayBase<DerivedX>::ColsAtCompileTime> dx;
    dx = (in_x.bottomRows(in_x.rows()-1) - in_x.topRows(in_x.rows()-1));


    // Get the average heights of the trapezoids
    Eigen::Array<typename Eigen::ArrayBase<DerivedY>::Scalar, Eigen::ArrayBase<DerivedY>::RowsAtCompileTime, Eigen::ArrayBase<DerivedY>::ColsAtCompileTime> inter;
    inter = (in_y.topRows(in_y.rows()-1) + in_y.bottomRows(in_y.rows()-1)) * 0.5;

    // Multiply by trapezoid widths. NB Broadcasting with *= only works for arrayX types, not arrayXX types like dx
    //  inter *= dx;
    for (int i = 0 ; i < inter.cols() ; ++i)
    {
        for (int j = 0 ; j < inter.rows() ; ++j)
        {
            inter(j,i) *= dx(j,0);
        }
    }

    // Initialise output
    Eigen::ArrayBase<DerivedOut>& out_ = const_cast< Eigen::ArrayBase<DerivedOut>& >(out);
    out_.derived().setZero(1, in_y.cols());

    // Output the column-wise sum
    out_.derived() = inter.colwise().sum();
}

/* @brief Trapezoidal numerical integration with non-unit spacing
 * Overload method to return result by value.
 * TODO add dimension argument, for optional integration along the second dimension.
 */
template<typename DerivedX, typename DerivedY, typename DerivedOut>
EIGEN_STRONG_INLINE Eigen::Array<typename Eigen::ArrayBase<DerivedOut>::Scalar, Eigen::ArrayBase<DerivedOut>::RowsAtCompileTime, Eigen::ArrayBase<DerivedOut>::ColsAtCompileTime> trapz(const Eigen::ArrayBase<DerivedX>& x, const Eigen::ArrayBase<DerivedY>& y)
{
    Eigen::Array<typename Eigen::ArrayBase<DerivedOut>::Scalar, Eigen::ArrayBase<DerivedOut>::RowsAtCompileTime, Eigen::ArrayBase<DerivedOut>::ColsAtCompileTime> z;
    trapz(z, x, y);
    return z;
}

}  /* namespace utilities */

#endif //ES_FLOW_TRAPZ_H

Includes¶

Eigen/Dense
stdexcept

Included By¶

File signature.h

Namespaces¶

Namespace utilities

Functions¶

File variable_readers.h¶

↰ Parent directory (source/io)

Contents

Definition (source/io/variable_readers.h)
Includes
Included By
Namespaces
Functions
Typedefs

Definition (source/io/variable_readers.h)¶

Program Listing for File variable_readers.h¶

↰ Return to documentation for file (source/io/variable_readers.h)

/*
 * variable_readers.h Helper functions for reading data from mat files to Eigen arrays and vectors.
 *
 * References:
 *
 *   [1] Eigen: http://eigen.tuxfamily.org/dox/index.html
 *
 *   [2] matio: https://sourceforge.net/projects/matio/
 *
 *   [3] eigen-matio: https://github.com/tesch1/eigen-matio
 *
 * Future Improvements:
 *
 *   [1] Extension to structs and a range of different types
 *
 *   [2] More elegant implementation based on type, or possibly use of eigen-matio (ref [3])
 *
 * Author:                   Tom Clark (thclark @ github)
 *
 * Copyright (c) 2019 Octue Ltd. All Rights Reserved.
 *
 */

#ifndef ES_FLOW_VARIABLE_READERS_H
#define ES_FLOW_VARIABLE_READERS_H

#include <iostream>
#include <string>
#include "matio.h"
#include <eigen3/Eigen/Core>
#include <unsupported/Eigen/CXX11/Tensor>

using Eigen::Array;
using Eigen::ArrayXd;
using Eigen::Array3d;
using Eigen::ArrayXXd;
using Eigen::Vector3d;
using Eigen::VectorXd;
using Eigen::Tensor;
using Eigen::Dynamic;
typedef Eigen::Array<double, 3, 2> Array32d;


// TODO the Eigen variable readers are getting very unwieldy. Template them!

namespace es {


template<size_t SIZE, class T> inline size_t array_size(T (&arr)[SIZE]) {
    return SIZE;
}

void checkVariableType(matvar_t *mat_var, int matvar_type) {

    // Throw error if the requested data type does not match the saved data type
    if (mat_var->class_type != matvar_type) {
        std::string msg = "Error reading mat file (" + std::string(mat_var->name) + " incorrect variable type)";
        throw std::invalid_argument(msg);
    }

}

matvar_t * getVariable(mat_t *matfp, const std::string var_name, bool print_var = true, int max_rank = 2) {

    // Get the variable's structure pointer and check validity
    matvar_t *mat_var = Mat_VarRead(matfp, var_name.c_str());
    if (mat_var == NULL) {
        std::string msg = "Error reading mat file (most likely incorrect file type: " + var_name + " variable is missing)";
        throw std::invalid_argument(msg);
    }

    // Optionally print the variable information to terminal
    if (print_var) {
        std::cout << "Reading variable: " << std::endl;
        Mat_VarPrint(mat_var, true);
    }

    // Check the rank
    if (mat_var->rank > max_rank) {
        std::string msg = "Rank of variable " + var_name + " exceeds required rank of " + std::to_string(max_rank) ;
        throw std::invalid_argument(msg);
    }

    return mat_var;
}

std::string readString(mat_t *matfp, const std::string var_name, bool print_var) {

    // Get the variable's structure pointer and check validity
    matvar_t *mat_var = getVariable(matfp, var_name, print_var);

    // Read the const char from the file, instantiate as std::string
    std::string var = std::string((const char *) mat_var->data, mat_var->dims[1]);

    // Free the data pointer and return the new variable
    Mat_VarFree(mat_var);
    return var;
}

Vector3d readVector3d(mat_t *matfp, const std::string var_name, bool print_var) {

    // Get the variable's structure pointer and check validity
    matvar_t *mat_var = getVariable(matfp, var_name, print_var);

    // Check for three elements always
    if (mat_var->dims[1]*mat_var->dims[0] != 3) {
        std::string msg = "Number of elements in variable '" + var_name + "' not equal to 3";
        throw std::invalid_argument(msg);
    }

    // Read a vector, with automatic transpose to column vector always.
    Vector3d var;
    if (mat_var->dims[0] == 1) {
        if (print_var) std::cout << "Converting row vector '" << mat_var->name << "' to column vector" << std::endl;
    }
    var = Vector3d();
    double *var_d = (double *) mat_var->data;
    long int i = 0;
    for (i = 0; i < 3; i++) {
        var[i] = var_d[i];
    }

    // Free the data pointer and return the new variable
    Mat_VarFree(mat_var);
    return var;

}


Array3d readArray3d(mat_t *matfp, const std::string var_name, bool print_var) {
    return readVector3d(matfp, var_name, print_var).array();
}


VectorXd readVectorXd(mat_t *matfp, const std::string var_name, bool print_var) {

    // Get the variable's structure pointer and check validity
    matvar_t *mat_var = getVariable(matfp, var_name, print_var);

    // Read a vector, with automatic transpose to column vector always.
    VectorXd var;
    if (mat_var->dims[0] == 1) {
        if (print_var) std::cout << "Converting row vector '" << mat_var->name << "' to column vector" << std::endl;
        var = VectorXd(mat_var->dims[1], mat_var->dims[0]);
    } else {
        var = VectorXd(mat_var->dims[0], mat_var->dims[1]);
    }

    // Copy the data into the native Eigen types. However, we can also map to data already in
    // memory which avoids a copy. Read about mapping here:
    // http://eigen.tuxfamily.org/dox/group__TutorialMapClass.html
    // TODO consider mapping to reduce peak memory overhead
    double *var_d = (double *) mat_var->data;
    long int i = 0;
    for (i = 0; i < var.rows()*var.cols(); i++) {
        var[i] = var_d[i];
    }

    // Free the data pointer and return the new variable
    Mat_VarFree(mat_var);
    return var;

}


ArrayXd readArrayXd(mat_t *matfp, const std::string var_name, bool print_var) {
    return readVectorXd(matfp, var_name, print_var).array();
}


Array32d readArray32d(mat_t *matfp, const std::string var_name, bool print_var) {

    // Get the variable's structure pointer and check validity
    matvar_t *mat_var = getVariable(matfp, var_name, print_var);

    // Check for three elements always
    if ((mat_var->dims[0] != 3) || (mat_var->dims[1] != 2)) {
        std::string msg = "Variable '" + var_name + "' must be of size 3 x 2";
        throw std::invalid_argument(msg);
    }

    // Declare and size the array
    Eigen::Array<double, 3, 2> var;
    var = Eigen::Array<double, 3, 2>();

    // Copy the data into the native Eigen types. However, we can also map to data already in
    // memory which avoids a copy. Read about mapping here:
    // http://eigen.tuxfamily.org/dox/group__TutorialMapClass.html
    // TODO consider mapping to reduce peak memory overhead
    double *var_d = (double *) mat_var->data;
    long int i = 0;
    for (i = 0; i < var.rows()*var.cols(); i++) {
        var(i) = var_d[i];
    }

    // Free the data pointer and return the new variable
    Mat_VarFree(mat_var);
    return var;

}


ArrayXXd readArrayXXd(mat_t *matfp, const std::string var_name, bool print_var) {

    // Get the variable's structure pointer and check validity
    matvar_t *mat_var = getVariable(matfp, var_name, print_var);

    // Read an array. We always read as eigen arrays, not matrices, as these are far more flexible.
    // Can easily cast to matrix type later if linear algebra functionality is needed.

    ArrayXXd var;
    var = ArrayXXd(mat_var->dims[0],  mat_var->dims[1]);

    // Copy the data into the native Eigen types. However, we can also map to data already in
    // memory which avoids a copy. Read about mapping here:
    // http://eigen.tuxfamily.org/dox/group__TutorialMapClass.html
    // TODO consider mapping to reduce peak memory overhead
    double *var_d = (double *) mat_var->data;
    long int i = 0;
    long int j = 0;
    long int ind = 0;
    for (j = 0; j < var.cols(); j++) {
        for (i = 0; i < var.rows(); i++) {
            var(i, j) = var_d[ind];
            ind = ind+1;
        }
    }

    // Free the data pointer and return the new variable
    Mat_VarFree(mat_var);
    return var;

}

Tensor<double, 3> readTensor3d(mat_t *matfp, const std::string var_name, bool print_var) {

    // Get the variable's structure pointer and check validity for rank 3
    matvar_t *mat_var = getVariable(matfp, var_name, print_var, 3);

    // Read the tensor
    // TODO this code typecasts from size_t to long int, meaning possible data loss for very large arrays. Add a check.
    Eigen::Index dim0 = mat_var->dims[0];
    Eigen::Index dim1 = mat_var->dims[1];
    Eigen::Index dim2 = mat_var->dims[2];
    // std::cout  << "Initialising Tensor of size: " << dim0 << ", " << dim1 << ", "  << dim2 << std::endl;
    Eigen::Tensor<double, 3> var = Eigen::Tensor<double, 3>(dim0, dim1, dim2);
    var.setZero();

    // Copy the data into the native Eigen types. However, we can also map to data already in
    // memory which avoids a copy. Read about mapping here:
    // http://eigen.tuxfamily.org/dox/group__TutorialMapClass.html
    // TODO consider mapping to reduce peak memory overhead
    double *var_d = (double *) mat_var->data;
    long int i = 0;
    long int j = 0;
    long int k = 0;
    long int ind = 0;
    for (k = 0; k < var.dimensions()[2]; k++) {
        for (j = 0; j < var.dimensions()[1]; j++) {
            for (i = 0; i < var.dimensions()[0]; i++) {
                var(i, j, k) = var_d[ind];
                ind = ind + 1;
            }
        }
    }

    // Free the data pointer and return the new variable
    Mat_VarFree(mat_var);
    return var;

}

double readDouble(mat_t *matfp, const std::string var_name, bool print_var){

    // Get the variable's structure pointer and check validity
    matvar_t *mat_var = getVariable(matfp, var_name, print_var);

    // Read a single element double
    double *var_d = (double *) mat_var->data;
    double var = var_d[0];

    // Free the data pointer and return the new variable
    Mat_VarFree(mat_var);
    return var;
}


} /* end namespace */


#endif // ES_FLOW_VARIABLE_READERS_H

Includes¶

eigen3/Eigen/Core
iostream
matio.h
string
unsupported/Eigen/CXX11/Tensor

Included By¶

Namespaces¶

Namespace es

Functions¶

Typedefs¶

Typedef Array32d

File variable_writers.h¶

↰ Parent directory (source/io)

Contents

Definition (source/io/variable_writers.h)
Includes
Included By
Namespaces
Functions
Typedefs

Definition (source/io/variable_writers.h)¶

Program Listing for File variable_writers.h¶

↰ Return to documentation for file (source/io/variable_writers.h)

/*
 * variable_writers.h Helper functions for writing data to mat files from Eigen arrays and vectors.
 *
 * References:
 *
 *   [1] Eigen: http://eigen.tuxfamily.org/dox/index.html
 *
 *   [2] matio: https://sourceforge.net/projects/matio/
 *
 *   [3] eigen-matio: https://github.com/tesch1/eigen-matio
 *
 * Future Improvements:
 *
 *   [1] Extension to structs and a range of different types
 *
 *   [2] More elegant implementation based on type, or possibly use of eigen-matio (ref [3])
 *
 * Author:                   Tom Clark (thclark @ github)
 *
 * Copyright (c) 2019 Octue Ltd. All Rights Reserved.
 *
 */

#ifndef ES_FLOW_VARIABLE_WRITERS_H
#define ES_FLOW_VARIABLE_WRITERS_H

#include <iostream>
#include <string>
#include <Eigen/Dense>
#include <Eigen/Core>
#include <Eigen/Dense>
#include <unsupported/Eigen/CXX11/Tensor>

#include "matio.h"

using Eigen::Array;
using Eigen::Array3d;
using Eigen::ArrayXXd;
using Eigen::Vector3d;
using Eigen::VectorXd;
using Eigen::Tensor;
using Eigen::Dynamic;


typedef Eigen::Array<double, 3, 2> Array32d;


// TODO the Eigen variable writers are getting very unwieldy. Template them!


namespace es {


void writeString(mat_t *mat_fp, const std::string &var_name, std::string &var) {

    // Create the variable
    size_t dims[2] = {1, var.length()};
    matvar_t *mat_var = Mat_VarCreate(
        var_name.c_str(),
        MAT_C_CHAR,
        MAT_T_UTF8,
        2,
        dims,
        static_cast<void*>(const_cast<char*>(var.data())),
        0
    );
    if (nullptr == mat_var ) {
        throw std::runtime_error("Unable to write variable '" + var_name + "' to file.");
    }

    // Write the data and free the pointer
    Mat_VarWrite(mat_fp, mat_var, MAT_COMPRESSION_NONE);
    Mat_VarFree(mat_var);

}


void writeArray3d(mat_t *mat_fp, const std::string &var_name, const Eigen::Array3d &var) {

    // Create the variable
    size_t dims[2] = {3, 1};
    matvar_t *mat_var = Mat_VarCreate(
        var_name.c_str(),
        MAT_C_DOUBLE,
        MAT_T_DOUBLE,
        2,
        dims,
        static_cast<void*>(const_cast<double*>(var.data())),
        0
    );
    if (nullptr == mat_var ) {
        throw std::runtime_error("Unable to write variable '" + var_name + "' to file.");
    }

    // Write the data and free the pointer
    Mat_VarWrite(mat_fp, mat_var, MAT_COMPRESSION_NONE);
    Mat_VarFree(mat_var);

}


void writeArrayXd(mat_t *mat_fp, const std::string &var_name, const Eigen::ArrayXd &var) {

    // Create the variable
    size_t dims[2];
    dims[0] = var.rows();
    dims[1] = 1;
    matvar_t *mat_var = Mat_VarCreate(
        var_name.c_str(),
        MAT_C_DOUBLE,
        MAT_T_DOUBLE,
        2,
        dims,
        static_cast<void*>(const_cast<double*>(var.data())),
        0
    );
    if (nullptr == mat_var ) {
        throw std::runtime_error("Unable to write variable '" + var_name + "' to file.");
    }

    // Write the data and free the pointer
    Mat_VarWrite(mat_fp, mat_var, MAT_COMPRESSION_NONE);
    Mat_VarFree(mat_var);

}


void writeArrayXXd(mat_t *mat_fp, const std::string &var_name, const Eigen::ArrayXXd &var) {

    // Create the variable
    size_t dims[2];
    dims[0] = var.rows();
    dims[1] = var.cols();
    matvar_t *mat_var = Mat_VarCreate(
        var_name.c_str(),
        MAT_C_DOUBLE,
        MAT_T_DOUBLE,
        2,
        dims,
        static_cast<void*>(const_cast<double*>(var.data())),
        0
    );
    if (nullptr == mat_var ) {
        throw std::runtime_error("Unable to write variable '" + var_name + "' to file.");
    }

    // Write the data and free the pointer
    Mat_VarWrite(mat_fp, mat_var, MAT_COMPRESSION_NONE);
    Mat_VarFree(mat_var);

}


void writeArray32d(mat_t *mat_fp, const std::string &var_name, const Eigen::Array<double, 3, 2> &var) {

    // Create the variable
    size_t dims[2] = {3, 2};
    matvar_t *mat_var = Mat_VarCreate(
        var_name.c_str(),
        MAT_C_DOUBLE,
        MAT_T_DOUBLE,
        2,
        dims,
        static_cast<void*>(const_cast<double*>(var.data())),
        0
    );
    if (nullptr == mat_var ) {
        throw std::runtime_error("Unable to write variable '" + var_name + "' to file.");
    }

    // Write the data and free the pointer
    Mat_VarWrite(mat_fp, mat_var, MAT_COMPRESSION_NONE);
    Mat_VarFree(mat_var);

}


void writeTensor3d(mat_t *mat_fp, const std::string &var_name, const Tensor<double, 3> &var) {

    // Create the variable
    size_t dims[3];
    dims[0] = var.dimensions()[0];
    dims[1] = var.dimensions()[1];
    dims[2] = var.dimensions()[2];
    matvar_t *mat_var = Mat_VarCreate(
        var_name.c_str(),
        MAT_C_DOUBLE,
        MAT_T_DOUBLE,
        3,
        dims,
        static_cast<void*>(const_cast<double*>(var.data())),
        0
    );
    if (nullptr == mat_var ) {
        throw std::runtime_error("Unable to write variable '" + var_name + "' to file.");
    }

    // Write the data and free the pointer
    Mat_VarWrite(mat_fp, mat_var, MAT_COMPRESSION_NONE);
    Mat_VarFree(mat_var);

}


void writeDouble(mat_t *mat_fp, const std::string &var_name, const double var){

    // Create the variable
    size_t dims[2] = {1, 1};
    matvar_t *mat_var = Mat_VarCreate(
        var_name.c_str(),
        MAT_C_DOUBLE,
        MAT_T_DOUBLE,
        3,
        dims,
        static_cast<void*>(const_cast<double*>(&var)),
        0
    );
    if (nullptr == mat_var ) {
        throw std::runtime_error("Unable to write variable '" + var_name + "' to file.");
    }

    // Write the data and free the pointer
    Mat_VarWrite(mat_fp, mat_var, MAT_COMPRESSION_NONE);
    Mat_VarFree(mat_var);

}


} /* end namespace */


#endif // ES_FLOW_VARIABLE_WRITERS_H

Includes¶

Eigen/Core
Eigen/Dense
iostream
matio.h
string
unsupported/Eigen/CXX11/Tensor

Included By¶

File signature.h

Namespaces¶

Namespace es

Functions¶

Typedefs¶

Typedef Array32d

File veer.h¶

↰ Parent directory (source/relations)

Contents

Definition (source/relations/veer.h)
Includes
Namespaces
Functions

Definition (source/relations/veer.h)¶

Program Listing for File veer.h¶

↰ Return to documentation for file (source/relations/veer.h)

/*
 * veer.h Atmospheric Boundary Layer Veer relations
 *
 * Author:              Tom Clark  (thclark @ github)
 *
 * Copyright (c) 2015-9 Octue Ltd. All Rights Reserved.
 *
 */

#ifndef ES_FLOW_VEER_H_
#define ES_FLOW_VEER_H_

#include <Eigen/Dense>
#include <Eigen/Core>

#include "definitions.h"
#include "profile.h"


namespace es {


template <typename T>
T veer_lhs(T const & ui, const double ui_g, const double phi){
    T lhs = 2.0*OMEGA_WORLD*sind(phi)*(ui_g - ui);
    return lhs;
}


template <typename T>
T veer_rhs(T & ui, T & uiu3_bar, const double nu){
    T rhs, mixing_term;
    mixing_term = nu*ui.getZDerivative() + uiu3_bar;
    rhs = mixing_term.getZDerivative();
    return rhs;
}

} /* namespace es */

#endif /* ES_FLOW_VEER_H_ */

Includes¶

Eigen/Core
Eigen/Dense
definitions.h (File definitions.h)
profile.h (File profile.h)

Namespaces¶

Namespace es

Functions¶

File velocity.h¶

↰ Parent directory (source/relations)

Contents

Definition (source/relations/velocity.h)
Includes
Included By
Namespaces
Functions

Definition (source/relations/velocity.h)¶

Program Listing for File velocity.h¶

↰ Return to documentation for file (source/relations/velocity.h)

/*
 * velocity.h Atmospheric Boundary Layer velocity profile relations
 *
 * Author:              Tom Clark  (thclark @ github)
 *
 * Copyright (c) 2013-9 Octue Ltd. All Rights Reserved.
 *
 */

#ifndef ES_FLOW_VELOCITY_H_
#define ES_FLOW_VELOCITY_H_

#include <Eigen/Dense>
#include <Eigen/Core>
#include "profile.h"
#include <iostream>


namespace es {

template <typename T, typename Talf>
T power_law_speed(T const & z, const double u_ref, const double z_ref, Talf const & alpha){
    T z_norm = z / z_ref;
    T speed = pow(z_norm, alpha) * u_ref;
    return speed;
};

// Remove template specialisations from doc (causes duplicate) @cond
Eigen::VectorXd power_law_speed(Eigen::VectorXd const & z, const double u_ref, const double z_ref, const double alpha) {
    Eigen::VectorXd z_norm = z.array() / z_ref;
    Eigen::VectorXd speed = pow(z_norm.array(), alpha) * u_ref;
    return speed;
};
// @endcond


template <typename T>
T most_law_speed(T const & z, const double kappa, const double d, const double z0, const double L){
    std::cout << "MOST Law not implemented yet" << std::endl;
    T speed;
    return speed;
}

// Remove template specialisation from doc (causes duplicate) @cond
Eigen::VectorXd most_law_speed(Eigen::VectorXd const & z, const double kappa, const double d, const double z0, const double L){
    std::cout << "MOST Law not implemented yet" << std::endl;
    Eigen::VectorXd speed;
    return speed;
};
// @endcond


template <typename T_z, typename T_pi_j>
T_z marusic_jones_speed(T_z const & z, T_pi_j const pi_j, const double kappa, const double z_0,
                      const double delta, const double u_inf, const double u_tau){
    T_z eta = (z + z_0) / (delta + z_0);
    T_z eta_cubed = pow(eta, 3.0);
    T_z term1 = log(eta) / kappa;
    T_z term2 = (eta_cubed - 1.0) / (3.0 * kappa);
    T_z term3 = 2.0 * pi_j * (1.0 - pow(eta, 2.0) * 3.0 + eta_cubed * 2.0) / kappa;
    T_z u_deficit = term2 - term1 + term3;
    T_z speed = u_inf - u_deficit * u_tau;
    return speed;
};

// Remove template specialisation from doc (causes duplicate) @cond
template <typename T_pi_j>
Eigen::VectorXd marusic_jones_speed(Eigen::VectorXd const & z, T_pi_j const pi_j, const double kappa, const double z_0,
                             const double delta, const double u_inf, const double u_tau){
    Eigen::VectorXd eta = (z.array() + z_0) / (delta + z_0);
    Eigen::VectorXd eta_cubed = eta.array().cube();
    Eigen::VectorXd term1 = eta.array().log() / kappa;
    Eigen::VectorXd term2 = (eta_cubed.array() - 1.0) / (3.0 * kappa);
    Eigen::VectorXd term3 = 2.0 * pi_j * (1.0 - eta.array().square() * 3.0 + eta_cubed.array() * 2.0) / kappa;
    Eigen::VectorXd u_deficit = term2 - term1 + term3;
    Eigen::VectorXd speed = u_inf - u_deficit.array() * u_tau;
    return speed;
};
//@endcond


template <typename T_z, typename T_param>
T_z coles_wake(T_z const &eta, T_param const &pi_coles, const bool corrected=true){
    T_z wake_param, eta_sqd;
    eta_sqd = pow(eta, 2.0);
    if (corrected) {
        wake_param = 2.0 * eta_sqd * (3.0 - 2.0 * eta)
            - eta_sqd * (1.0 - eta) * (1.0 - 2.0 * eta) / pi_coles;
    } else {
        wake_param = 2.0 * eta_sqd * (3.0 - 2.0 * eta);
    }
    return wake_param;
};

// Remove template specialisation from doc (causes duplicate) @cond
template <typename T_param>
Eigen::VectorXd coles_wake(Eigen::VectorXd const &eta, T_param const &pi_coles, const bool corrected=true){
    Eigen::VectorXd wake_param, eta_sqd;
    eta_sqd = eta.array().pow(2.0);
    if (corrected) {
        wake_param = 2.0 * eta_sqd.array() * (3.0 - 2.0 * eta.array())
            - eta_sqd.array() * (1.0 - eta.array()) * (1.0 - 2.0*eta.array()) / pi_coles;
    } else {
        wake_param = 2.0 * eta_sqd.array() * (3.0 - 2.0 * eta.array());
    }
    return wake_param;
};
//@endcond


// Do not document @cond
/* Template wrapper for std::isinf to kill off problems where ceres::Jet is used (autodifferentiation) instead of
 * a double. Call it is_dbl_inf rather than isinf to avoid accidental use.
 */
bool is_double_inf(double in) {
    return std::isinf(in);
};

template <typename T>
bool is_double_inf(T in) {
    return false;
};
// @endcond


template <typename T_eta, typename T_param>
T_eta deficit(T_eta const &eta, const double kappa, T_param const & pi_coles, const double shear_ratio, const bool lewkowicz=false) {
    T_eta f, ones;
    ones = 1.0;
    f = -1.0 * log(eta)/ kappa;
    if (lewkowicz) {
        f = f + (pi_coles/kappa) * coles_wake(ones, pi_coles)
              - (pi_coles/kappa) * coles_wake(eta, pi_coles);
    } else {
        f = f + (pow(eta, 3.0) - 1.0)/(3.0*kappa)
              + 2.0*pi_coles*(1.0 - 3.0*pow(eta, 2.0) + 2.0*pow(eta, 3.0))/kappa;
    }
    if (is_double_inf(f)) {
        f = shear_ratio;
    };
    return f;
}
// Remove template specialisation from doc (causes duplicate) @cond
template <typename T_param>
Eigen::ArrayXd deficit(const Eigen::ArrayXd &eta, const double kappa, T_param const & pi_coles, const double shear_ratio, const bool lewkowicz=false) {
    Eigen::ArrayXd f;
    Eigen::ArrayXd ones;
    ones.setOnes(eta.size());
    f = -1.0 * log(eta)/ kappa;
    if (lewkowicz) {
        f = f + (pi_coles/kappa) * coles_wake(ones, pi_coles)
            - (pi_coles/kappa) * coles_wake(eta, pi_coles);
    } else {
        f = f + (eta.pow(3.0) - 1.0)/(3.0*kappa)
            + 2.0*pi_coles*(1.0 - 3.0*eta.pow(2.) + 2.0*eta.pow(3.0))/kappa;
    }
    for (int k = 0; k < f.size(); k++) {
        if (std::isinf(f[k])) {
            f(k) = shear_ratio;
        }
    }
    return f;
}
// @endcond


template <typename T_z, typename T_param>
T_z lewkowicz_speed(T_z const & z, T_param const & pi_coles, T_param const & kappa, T_param const & u_inf, T_param const & shear_ratio, T_param const &delta_c) {
    T_z f, speed, eta;
    eta = z / delta_c;
    T_param u_tau = u_inf / shear_ratio;
    T_z term1 = log(eta) / (-1.0*kappa);
    T_z term2 = pi_coles * coles_wake(T_z(1.0), pi_coles, true) / kappa;
    T_z term3 = pi_coles * coles_wake(eta, pi_coles, true) / kappa;
    f = term1 + term2 - term3;
    // TODO why isn't this set directly to shear_ratio?
    if (is_double_inf(f)) {
        f = u_inf / u_tau;
    };
    speed = u_inf - f * u_tau;
    return speed;
};

// Remove template specialisation from doc (causes duplicate) @cond
template <typename T_param>
Eigen::VectorXd lewkowicz_speed(Eigen::VectorXd const & z, T_param const &pi_coles, T_param const &kappa, T_param const &u_inf, T_param const &shear_ratio, T_param const &delta_c=1.0){
    Eigen::VectorXd f, speed, eta;
    eta = z.array() / delta_c;
    T_param u_tau = u_inf/shear_ratio;
    Eigen::VectorXd term1 = eta.array().log() / (-1.0*kappa);
    double term2 = pi_coles * coles_wake(1.0, pi_coles) / kappa;
    Eigen::VectorXd term3 = pi_coles * coles_wake(eta, pi_coles).array() / kappa;
    f = term1.array() + term2 - term3.array();
    for (int k = 0; k < f.size(); k++) {
        if (std::isinf(f[k])) {
            f(k) = u_inf / u_tau;
        }
    }
    speed = u_inf - f.array() * u_tau;
    return speed;
};

template <typename T_param>
Eigen::ArrayXd lewkowicz_speed(Eigen::ArrayXd const & z, T_param const &pi_coles, T_param const &kappa, T_param const &u_inf, T_param const &shear_ratio, T_param const &delta_c=1.0){
    Eigen::ArrayXd f, speed, eta;
    eta = z / delta_c;
    T_param u_tau = u_inf/shear_ratio;
    Eigen::ArrayXd term1 = eta.log() / (-1.0*kappa);
    double term2 = pi_coles * coles_wake(1.0, pi_coles) / kappa;
    Eigen::ArrayXd term3 = pi_coles * coles_wake(eta, pi_coles) / kappa;
    f = term1 + term2 - term3;
    for (int k = 0; k < f.size(); k++) {
        if (std::isinf(f[k])) {
            f(k) = u_inf / u_tau;
        }
    }
    speed = u_inf - f * u_tau;
    return speed;
};
// @endcond


} /* namespace es */


#endif /* ES_FLOW_VELOCITY_H_ */

Includes¶

Eigen/Core
Eigen/Dense
iostream
profile.h (File profile.h)

Included By¶

Namespaces¶

Namespace es

Functions¶

Footnotes

[1]	Not all of this functionality is implemented yet!