Merge pull request #82 from brocksam/add-differentiation-benchmarks

Add differentiation benchmarks

asv.conf.conda.slow.json

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+{
+    // The version of the config file format.  Do not change, unless
+    // you know what you are doing.
+    "version": 1,
+
+    // The name of the project being benchmarked
+    "project": "sympy",
+
+    // The project's homepage
+    "project_url": "http://sympy.org/",
+
+    // The URL or local path of the source code repository for the
+    // project being benchmarked
+    "repo": "https://github.com/sympy/sympy.git",
+
+    // List of branches to benchmark. If not provided, defaults to "master"
+    // (for git) or "tip" (for mercurial).
+    // "branches": ["master"], // for git
+    // "branches": ["tip"],    // for mercurial
+
+    // The DVCS being used.  If not set, it will be automatically
+    // determined from "repo" by looking at the protocol in the URL
+    // (if remote), or by looking for special directories, such as
+    // ".git" (if local).
+    // "dvcs": "git",
+
+    // The tool to use to create environments.  May be "conda",
+    // "virtualenv" or other value depending on the plugins in use.
+    // If missing or the empty string, the tool will be automatically
+    // determined by looking for tools on the PATH environment
+    // variable.
+    "environment_type": "conda",
+
+    // the base URL to show a commit for the project.
+    "show_commit_url": "http://github.com/sympy/sympy/commit/",
+
+    // The Pythons you'd like to test against.  If not provided, defaults
+    // to the current version of Python used to run `asv`.
+    // "pythons": ["2.7", "3.6"],
+
+    // The matrix of dependencies to test.  Each key is the name of a
+    // package (in PyPI) and the values are version numbers.  An empty
+    // list indicates to just test against the default (latest)
+    // version.
+    "matrix": {
+        "fastcache": [],
+        "mpmath": [],
+        "numpy": [],
+    },
+
+    // The directory (relative to the current directory) that benchmarks are
+    // stored in.  If not provided, defaults to "benchmarks"
+    "benchmark_dir": "slow_benchmarks",
+
+    // The directory (relative to the current directory) to cache the Python
+    // environments in.  If not provided, defaults to "env"
+    // "env_dir": "env",
+
+
+    // The directory (relative to the current directory) that raw benchmark
+    // results are stored in.  If not provided, defaults to "results".
+    // "results_dir": "results",
+
+    // The directory (relative to the current directory) that the html tree
+    // should be written to.  If not provided, defaults to "html".
+    // "html_dir": "html",
+
+    // The number of characters to retain in the commit hashes.
+    // "hash_length": 8,
+
+    // `asv` will cache wheels of the recent builds in each
+    // environment, making them faster to install next time.  This is
+    // number of builds to keep, per environment.
+    // "wheel_cache_size": 0
+}

asv.conf.venv.slow.json

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+{
+    // The version of the config file format.  Do not change, unless
+    // you know what you are doing.
+    "version": 1,
+
+    // The name of the project being benchmarked
+    "project": "sympy",
+
+    // The project's homepage
+    "project_url": "http://sympy.org/",
+
+    // The URL or local path of the source code repository for the
+    // project being benchmarked
+    "repo": "https://github.com/sympy/sympy.git",
+
+    // List of branches to benchmark. If not provided, defaults to "master"
+    // (for git) or "tip" (for mercurial).
+    // "branches": ["master"], // for git
+    // "branches": ["tip"],    // for mercurial
+
+    // The DVCS being used.  If not set, it will be automatically
+    // determined from "repo" by looking at the protocol in the URL
+    // (if remote), or by looking for special directories, such as
+    // ".git" (if local).
+    // "dvcs": "git",
+
+    // The tool to use to create environments.  May be "conda",
+    // "virtualenv" or other value depending on the plugins in use.
+    // If missing or the empty string, the tool will be automatically
+    // determined by looking for tools on the PATH environment
+    // variable.
+    "environment_type": "virtualenv",
+
+    // the base URL to show a commit for the project.
+    "show_commit_url": "http://github.com/sympy/sympy/commit/",
+
+    // The Pythons you'd like to test against.  If not provided, defaults
+    // to the current version of Python used to run `asv`.
+    // "pythons": ["2.7", "3.3"],
+
+    // The matrix of dependencies to test.  Each key is the name of a
+    // package (in PyPI) and the values are version numbers.  An empty
+    // list indicates to just test against the default (latest)
+    // version.
+    "matrix": {
+        "fastcache": [],
+        "mpmath": [],
+        "numpy": [],
+    },
+
+    // The directory (relative to the current directory) that benchmarks are
+    // stored in.  If not provided, defaults to "benchmarks"
+    "benchmark_dir": "slow_benchmarks",
+
+    // The directory (relative to the current directory) to cache the Python
+    // environments in.  If not provided, defaults to "env"
+    // "env_dir": "env",
+
+
+    // The directory (relative to the current directory) that raw benchmark
+    // results are stored in.  If not provided, defaults to "results".
+    // "results_dir": "results",
+
+    // The directory (relative to the current directory) that the html tree
+    // should be written to.  If not provided, defaults to "html".
+    // "html_dir": "html",
+
+    // The number of characters to retain in the commit hashes.
+    // "hash_length": 8,
+
+    // `asv` will cache wheels of the recent builds in each
+    // environment, making them faster to install next time.  This is
+    // number of builds to keep, per environment.
+    // "wheel_cache_size": 0
+}

benchmarks/core/diff.py

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+"""Benchmarks for symbolic differentiation."""
+
+from sympy import exp, sin, symbols, tan, Matrix
+
+
+class GriewankBabyExampleDerivatives:
+    """Simple test function in two variables.
+
+    Function is the "baby example" taken from Griewank, A., & Walther, A.
+    (2008). Evaluating derivatives: principles and techniques of algorithmic
+    differentiation. SIAM.
+
+    """
+
+    def setup(self):
+        """Create the required symbols (x1, x2) and the expression (y)."""
+        x1, x2 = symbols("x1, x2")
+        self.x = Matrix([x1, x2])
+        self.y = (sin(x1 / x2) + (x1 / x2) - exp(x2)) * ((x1 / x2) - exp(x2))
+
+    def time_jacobian(self):
+        """Time differentiation of the baby example."""
+        self.G = self.y.diff(self.x)
+
+
+class GriewankLighthouseExampleDerivatives:
+    """Simple matrix test function in four variables.
+
+    Function is the "lighthouse example" taken from Griewank, A., & Walther, A.
+    (2008). Evaluating derivatives: principles and techniques of algorithmic
+    differentiation. SIAM.
+    
+    """
+
+    def setup(self):
+        """Create the required symbols (nu, gamma, omega, t) and the expression
+        (y).
+
+        """
+        nu, gamma, omega, t = symbols("nu, gamma, omega, t")
+        self.x = Matrix([nu, gamma, omega, t])
+        self.y = Matrix([
+            nu * tan(omega * t) / (gamma - tan(omega * t)),
+            nu * gamma * tan(omega * t) / (gamma - tan(omega * t)),
+        ])
+
+    def time_jacobian(self):
+        """Time differentation of the lighthouse example."""
+        self.G = self.y.jacobian(self.x)

slow_benchmarks/core/artifacts/partials.txt

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+(Symbol('qaxi'), Symbol('qayi'), Symbol('qai'), Symbol('qbi'), Symbol('qci'), Symbol('qdi'), Symbol('qei'), Symbol('qfi'), Symbol('qgi'), Symbol('uaxi'), Symbol('uayi'), Symbol('uai'), Symbol('ubi'), Symbol('uci'), Symbol('udi'), Symbol('uei'), Symbol('ufi'), Symbol('ugi'), Symbol('qaxp'), Symbol('qayp'), Symbol('qap'), Symbol('qbp'), Symbol('qcp'), Symbol('qdp'), Symbol('qep'), Symbol('qfp'), Symbol('qgp'), Symbol('uaxp'), Symbol('uayp'), Symbol('uap'), Symbol('ubp'), Symbol('ucp'), Symbol('udp'), Symbol('uep'), Symbol('ufp'), Symbol('ugp'), Symbol('Tbi'), Symbol('Tci'), Symbol('Tdi'), Symbol('Tei'), Symbol('Tfi'), Symbol('Tgi'))

slow_benchmarks/core/diff.py

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+"""Benchmarks for symbolic differentiation."""
+
+import pathlib
+
+from sympy import sympify
+
+
+class Gait2DDerivatives:
+    """Large real-world example equations of motion in 42 variables.
+
+    The equations of motion (EoMs) are derived from the Gait2D dynamic model of
+    gait (see here: https://github.com/csu-hmc/gait2d). This specific benchmark,
+    involving the derivation of the 18x42 Jacobian matrix, was highlighted in
+    SymPy issue #8191 (see here: https://github.com/sympy/sympy/issues/8191).
+
+    """
+
+    def setup(self):
+        """Read the equation of motion and variables from artifact files.
+
+        The 18 equations of motion are specified in `dis_eom.txt` while the 42
+        variables are specified in `partials.txt`. Copies of both `dis_eom.txt`
+        and `partials.txt` are in the `artifacts` subdirectory.
+
+        """
+        artifacts_dir_path = pathlib.Path(__file__).parents[0] / "artifacts"
+        dis_eom_path = pathlib.Path(artifacts_dir_path, "dis_eom.txt")
+        with open(dis_eom_path, "r") as A_file:
+            self.A = sympify(A_file.read())
+        partials_path = pathlib.Path(artifacts_dir_path, "partials.txt")
+        with open(partials_path, "r") as x_file:
+            self.x = sympify(x_file.read())
+
+    def time_jacobian(self):
+        """Time differentiation to construct the 18x42 Jacobian matrix."""
+        self.A.jacobian(self.x)