Add files for genz intergration benchmark

benchmarks/genz-integration/Dockerfile

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+FROM ubuntu:latest
+
+RUN apt-get update && \
+    apt-get install -y python3-pip
+
+RUN update-ca-certificates && \
+    pip3 config set global.trusted-host "pypi.org files.pythonhosted.org pypi.python.org"
+
+RUN pip3 install umbridge
+
+RUN pip3 install pyapprox
+
+COPY minimal_server.py /
+
+CMD python3 minimal_server.py

benchmarks/genz-integration/README.md

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+# Genz Integration Functions
+
+## Overview
+This benchmark consists of fix families of analytical functions $F_i:\mathbb{R}^D\to\mathbb{R}$, $i=1,\ldots,6$, with means $\mathbb{E}[F(\theta)]$ that can be computed analytically. The number of inputs $D$ and the anisotropy (relative importance of each variable and interactions) of the functions can be adjusted.
+
+## Authors
+John D. Jakeman
+
+## Run
+docker run -it -p 4243:4243 linusseelinger/benchmark-genz
+
+## Properties
+
+Model | Description
+---|---
+forward | Forward model
+
+### forward
+Mapping | Dimensions | Description
+---|---|---
+input | [D] | 2D coordinates $x \in \mathbb{R}^D$
+output | [1] | Function $F(x)$ evaluated at $x$
+
+Feature | Supported
+---|---
+Evaluate | True
+Gradient | False
+ApplyJacobian | False
+ApplyHessian | False
+
+Config | Type | Default | Description
+---|---|---|---
+nvars | int | D | Number of inputs
+c_factor | double | 1.0 | Normalization parameter
+w_factor | double | 0. | shift parameter
+coef_type | string | "sqexp" | Coefficient decay type
+name | string | "oscillatory" | Name of the test function
+
+The supported values of the coef_type and name config variables are:
+
+name=["oscillatory", "product_peak", "corner_peak", "gaussian", "c0continuous",  "discontinuous"]
+coef_type=["none", "quadratic", "quartic", "exp", "sqexp"]
+
+
+## Mount directories
+Mount directory | Purpose
+---|---
+None |
+
+## Source code
+
+[Model sources here.](https://github.com/sandialabs/pyapprox/blob/master/pyapprox/benchmarks/genz.py)
+
+
+## Description
+The six Genz test function are:
+
+Oscillatory ('oscillatory')
+
+$$ f(z) = \cos\left(2\pi w_1 + \sum_{d=1}^D c_dz_d\right)$$
+
+Product Peak ('product_peak')
+
+$$ f(z) = \prod_{d=1}^D \left(c_d^{-2}+(z_d-w_d)^2\right)^{-1}$$
+
+Corner Peak ('corner_peak')
+
+$$ f(z)=\left( 1+\sum_{d=1}^D c_dz_d\right)^{-(D+1)}$$
+
+Gaussian Peak ('gaussian')
+
+$$ f(z) = \exp\left( -\sum_{d=1}^D c_d^2(z_d-w_d)^2\right)$$
+
+C0 Continuous ('c0continuous')
+
+$$ f(z) = \exp\left( -\sum_{d=1}^D c_d\lvert z_d-w_d\rvert\right)$$
+
+Discontinuous ('discontinuous')
+
+$$ f(z) = \begin{cases}
+0 & z_1>w_1 \;\mathrm{or}\; z_2>w_2\\
+\exp\left(\sum_{d=1}^D c_dz_d\right) & \mathrm{otherwise}
+\end{cases}$$
+
+Increasing $\lVert c \rVert$ will in general make
+the integrands more difficult.
+
+The $0\le w_d \le 1$ parameters do not affect the difficulty
+of the integration problem. We set $w_1=w_2=\ldots=W_D$.
+
+The coefficient types implement different decay rates for $c_d$.
+This allows testing of methods that can identify and exploit anisotropy.
+They are as follows:
+
+No decay (none)
+
+$$ \hat{c}_d=\frac{d+0.5}{D}$$
+
+Quadratic decay (qudratic)
+
+$$ \hat{c}_d = \frac{1}{(D + 1)^2}$$
+
+Quartic decay (quartic)
+
+$$ \hat{c}_d = \frac{1}{(D + 1)^4}$$
+
+Exponential decay (exp)
+
+$$ \hat{c}_d=\exp\left(\log(c_\mathrm{min})\frac{d+1}{D}\right)$$
+
+Squared-exponential decay (sqexp)
+
+$$ \hat{c}_d=10^{\left(\log_{10}(c_\mathrm{min})\frac{(d+1)^2}{D}\right)}$$
+
+Here $c_\mathrm{min}$ is argument that sets the minimum value of $c_D$.
+
+Once the formula are used the coefficients are normalized such that
+
+$$ c_d = c_\text{factor}\frac{\hat{c}_d}{\sum_{d=1}^D \hat{c}_d}.$$
+
+## References
+This benchmark was first proposed [here.](https://doi.org/10.1007/978-94-009-3889-2_33)

benchmarks/genz-integration/minimal_server.py

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+import umbridge
+import numpy as np
+
+from pyapprox.benchmarks.genz import GenzFunction
+
+
+class GenzModel(umbridge.Model):
+    def __init__(self):
+        super().__init__("genz")
+        self._model = GenzFunction()
+
+    def get_input_sizes(self, config):
+        return [config.get("nvars", 5)]
+
+    def get_output_sizes(self, config):
+        return [1]
+
+    def __call__(self, parameters, config):
+        sample = np.asarray(parameters).T
+        assert sample.shape[0] == config.get("nvars", 5)
+        self._model.set_coefficients(
+            sample.shape[0],
+            config.get("c_factor", 1),
+            config.get("coef_type", "sqexp"),
+            config.get("w_factor", 0.5))
+        name = config.get("name", "oscillatory")
+        val = self._model(name, sample)[0, 0]
+        return [[val]]
+
+    def supports_evaluate(self):
+        return True
+
+
+models = [GenzModel()]
+umbridge.serve_models(models, 4242)

benchmarks/genz-integration/test_output.py

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+#!/usr/bin/env python3
+import argparse
+import itertools
+
+import umbridge
+import numpy as np
+
+
+parser = argparse.ArgumentParser(description='Model output test.')
+parser.add_argument(
+    'url', metavar='url', type=str,
+    help='the ULR on which the model is running, for example {0}'.format(
+        'http://localhost:4242'))
+args = parser.parse_args()
+print(f"Connecting to host URL {args.url}")
+
+model = umbridge.HTTPModel(args.url, "genz")
+
+assert model.get_input_sizes({"nvars": 4}) == [4]
+assert model.get_output_sizes() == [1]
+
+# check all combinations of config runs
+names = ["oscillatory", "product_peak", "corner_peak", "gaussian",
+         "c0continuous", "discontinuous"]
+nvars = np.arange(2, 7).astype(float)
+decays = ["none", "quadratic", "quartic", "exp", "sqexp"]
+test_scenarios = itertools.product(*[names, nvars, decays])
+for test_scenario in test_scenarios:
+    np.random.seed(1)
+    parameters = [np.random.uniform(0, 1, (int(test_scenario[1]))).tolist()]
+    config = {"name": test_scenario[0], "nvars": test_scenario[1],
+              "coef_type": test_scenario[2]}
+    value = model(parameters, config)