diff --git a/.flake8 b/.flake8
index 35bb985..c826cfb 100644
--- a/.flake8
+++ b/.flake8
@@ -1,2 +1,3 @@
 [flake8]
-ignore = W191
\ No newline at end of file
+ignore = W191, E501
+max-line-length = 120
diff --git a/pathfinder/gradient_descent.py b/pathfinder/gradient_descent.py
new file mode 100644
index 0000000..446cc79
--- /dev/null
+++ b/pathfinder/gradient_descent.py
@@ -0,0 +1,25 @@
+import numpy
+
+
+def find_sols(cost_array, jacobian, step_size=0.001, max_iterations=5, initial=(0, 0), desired_cost=1e-6, step_size_tries=10):
+	desired_cost_squared = desired_cost**2
+	current = numpy.array(initial)
+	iterations = 0
+	curr_cost = numpy.array(cost_array(current))
+	while iterations < max_iterations:
+		curr_cost = numpy.array(cost_array(current))
+		if curr_cost.dot(curr_cost) < desired_cost_squared:
+			return ("Finished early", current)
+		gradient = .5 * numpy.matmul(numpy.transpose(jacobian(current)), curr_cost)
+		next = current - step_size * gradient
+		next_cost = numpy.array(cost_array(next))
+		tries = step_size_tries
+		current_step = step_size
+		while tries > 0 and next_cost.dot(next_cost) > curr_cost.dot(curr_cost):
+			current_step = current_step / 10
+			next = current - current_step / 10 * gradient
+			next_cost = numpy.array(cost_array(next))
+			tries -= 1
+		current = next
+		iterations += 1
+	return ("Ran out of iterations", current)
diff --git a/pathfinder/pathfinder.py b/pathfinder/pathfinder.py
index e69de29..64abe4c 100644
--- a/pathfinder/pathfinder.py
+++ b/pathfinder/pathfinder.py
@@ -0,0 +1,9 @@
+import numpy  # type: ignore
+
+
+def circle_cost(x: float, y: float) -> float:
+	return 4 - x**2 - y**2
+
+
+def circle_gradient(x: float, y: float) -> numpy.ndarray:
+	return numpy.array([-2 * x, -2 * y])
diff --git a/poetry.lock b/poetry.lock
index a48a80f..7907376 100644
--- a/poetry.lock
+++ b/poetry.lock
@@ -1,107 +1,80 @@
 [[package]]
-category = "dev"
-description = "Atomic file writes."
-marker = "sys_platform == \"win32\""
 name = "atomicwrites"
+version = "1.4.0"
+description = "Atomic file writes."
+category = "dev"
 optional = false
 python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*"
-version = "1.4.0"
 
 [[package]]
-category = "dev"
-description = "Classes Without Boilerplate"
 name = "attrs"
+version = "21.2.0"
+description = "Classes Without Boilerplate"
+category = "dev"
 optional = false
 python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*"
-version = "21.2.0"
 
 [package.extras]
-dev = ["coverage (>=5.0.2)", "hypothesis", "pympler", "pytest (>=4.3.0)", "six", "mypy", "pytest-mypy-plugins", "zope.interface", "furo", "sphinx", "sphinx-notfound-page", "pre-commit"]
+dev = ["coverage[toml] (>=5.0.2)", "hypothesis", "pympler", "pytest (>=4.3.0)", "six", "mypy", "pytest-mypy-plugins", "zope.interface", "furo", "sphinx", "sphinx-notfound-page", "pre-commit"]
 docs = ["furo", "sphinx", "zope.interface", "sphinx-notfound-page"]
-tests = ["coverage (>=5.0.2)", "hypothesis", "pympler", "pytest (>=4.3.0)", "six", "mypy", "pytest-mypy-plugins", "zope.interface"]
-tests_no_zope = ["coverage (>=5.0.2)", "hypothesis", "pympler", "pytest (>=4.3.0)", "six", "mypy", "pytest-mypy-plugins"]
+tests = ["coverage[toml] (>=5.0.2)", "hypothesis", "pympler", "pytest (>=4.3.0)", "six", "mypy", "pytest-mypy-plugins", "zope.interface"]
+tests_no_zope = ["coverage[toml] (>=5.0.2)", "hypothesis", "pympler", "pytest (>=4.3.0)", "six", "mypy", "pytest-mypy-plugins"]
 
 [[package]]
-category = "dev"
-description = "Cross-platform colored terminal text."
-marker = "sys_platform == \"win32\""
 name = "colorama"
+version = "0.4.4"
+description = "Cross-platform colored terminal text."
+category = "dev"
 optional = false
 python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*"
-version = "0.4.4"
 
 [[package]]
-category = "dev"
-description = "Code coverage measurement for Python"
 name = "coverage"
+version = "5.5"
+description = "Code coverage measurement for Python"
+category = "dev"
 optional = false
 python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*, <4"
-version = "5.5"
 
 [package.extras]
 toml = ["toml"]
 
 [[package]]
-category = "dev"
-description = "the modular source code checker: pep8 pyflakes and co"
 name = "flake8"
+version = "3.9.2"
+description = "the modular source code checker: pep8 pyflakes and co"
+category = "dev"
 optional = false
 python-versions = "!=3.0.*,!=3.1.*,!=3.2.*,!=3.3.*,!=3.4.*,>=2.7"
-version = "3.9.2"
 
 [package.dependencies]
 mccabe = ">=0.6.0,<0.7.0"
 pycodestyle = ">=2.7.0,<2.8.0"
 pyflakes = ">=2.3.0,<2.4.0"
 
-[package.dependencies.importlib-metadata]
-python = "<3.8"
-version = "*"
-
 [[package]]
-category = "dev"
-description = "Read metadata from Python packages"
-marker = "python_version < \"3.8\""
-name = "importlib-metadata"
-optional = false
-python-versions = ">=3.6"
-version = "4.6.1"
-
-[package.dependencies]
-zipp = ">=0.5"
-
-[package.dependencies.typing-extensions]
-python = "<3.8"
-version = ">=3.6.4"
-
-[package.extras]
-docs = ["sphinx", "jaraco.packaging (>=8.2)", "rst.linker (>=1.9)"]
-perf = ["ipython"]
-testing = ["pytest (>=4.6)", "pytest-checkdocs (>=2.4)", "pytest-flake8", "pytest-cov", "pytest-enabler (>=1.0.1)", "packaging", "pep517", "pyfakefs", "flufl.flake8", "pytest-perf (>=0.9.2)", "pytest-black (>=0.3.7)", "pytest-mypy", "importlib-resources (>=1.3)"]
-
-[[package]]
-category = "dev"
-description = "iniconfig: brain-dead simple config-ini parsing"
 name = "iniconfig"
-optional = false
-python-versions = "*"
 version = "1.1.1"
-
-[[package]]
+description = "iniconfig: brain-dead simple config-ini parsing"
 category = "dev"
-description = "McCabe checker, plugin for flake8"
-name = "mccabe"
 optional = false
 python-versions = "*"
-version = "0.6.1"
 
 [[package]]
+name = "mccabe"
+version = "0.6.1"
+description = "McCabe checker, plugin for flake8"
 category = "dev"
-description = "Optional static typing for Python"
+optional = false
+python-versions = "*"
+
+[[package]]
 name = "mypy"
+version = "0.790"
+description = "Optional static typing for Python"
+category = "dev"
 optional = false
 python-versions = ">=3.5"
-version = "0.790"
 
 [package.dependencies]
 mypy-extensions = ">=0.4.3,<0.5.0"
@@ -112,104 +85,103 @@ typing-extensions = ">=3.7.4"
 dmypy = ["psutil (>=4.0)"]
 
 [[package]]
-category = "dev"
-description = "Experimental type system extensions for programs checked with the mypy typechecker."
 name = "mypy-extensions"
+version = "0.4.3"
+description = "Experimental type system extensions for programs checked with the mypy typechecker."
+category = "dev"
 optional = false
 python-versions = "*"
-version = "0.4.3"
 
 [[package]]
-category = "dev"
-description = "Core utilities for Python packages"
+name = "numpy"
+version = "1.21.1"
+description = "NumPy is the fundamental package for array computing with Python."
+category = "main"
+optional = false
+python-versions = ">=3.7"
+
+[[package]]
 name = "packaging"
+version = "21.0"
+description = "Core utilities for Python packages"
+category = "dev"
 optional = false
 python-versions = ">=3.6"
-version = "21.0"
 
 [package.dependencies]
 pyparsing = ">=2.0.2"
 
 [[package]]
-category = "dev"
-description = "plugin and hook calling mechanisms for python"
 name = "pluggy"
+version = "0.13.1"
+description = "plugin and hook calling mechanisms for python"
+category = "dev"
 optional = false
 python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*"
-version = "0.13.1"
-
-[package.dependencies]
-[package.dependencies.importlib-metadata]
-python = "<3.8"
-version = ">=0.12"
 
 [package.extras]
 dev = ["pre-commit", "tox"]
 
 [[package]]
-category = "dev"
-description = "library with cross-python path, ini-parsing, io, code, log facilities"
 name = "py"
-optional = false
-python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*"
 version = "1.10.0"
+description = "library with cross-python path, ini-parsing, io, code, log facilities"
+category = "dev"
+optional = false
+python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*"
 
 [[package]]
-category = "dev"
-description = "Python style guide checker"
 name = "pycodestyle"
-optional = false
-python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*"
 version = "2.7.0"
-
-[[package]]
+description = "Python style guide checker"
 category = "dev"
-description = "passive checker of Python programs"
-name = "pyflakes"
 optional = false
 python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*"
-version = "2.3.1"
 
 [[package]]
+name = "pyflakes"
+version = "2.3.1"
+description = "passive checker of Python programs"
 category = "dev"
-description = "Python parsing module"
+optional = false
+python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*"
+
+[[package]]
 name = "pyparsing"
+version = "2.4.7"
+description = "Python parsing module"
+category = "dev"
 optional = false
 python-versions = ">=2.6, !=3.0.*, !=3.1.*, !=3.2.*"
-version = "2.4.7"
 
 [[package]]
-category = "dev"
-description = "pytest: simple powerful testing with Python"
 name = "pytest"
+version = "6.2.4"
+description = "pytest: simple powerful testing with Python"
+category = "dev"
 optional = false
 python-versions = ">=3.6"
-version = "6.2.4"
 
 [package.dependencies]
-atomicwrites = ">=1.0"
+atomicwrites = {version = ">=1.0", markers = "sys_platform == \"win32\""}
 attrs = ">=19.2.0"
-colorama = "*"
+colorama = {version = "*", markers = "sys_platform == \"win32\""}
 iniconfig = "*"
 packaging = "*"
 pluggy = ">=0.12,<1.0.0a1"
 py = ">=1.8.2"
 toml = "*"
 
-[package.dependencies.importlib-metadata]
-python = "<3.8"
-version = ">=0.12"
-
 [package.extras]
 testing = ["argcomplete", "hypothesis (>=3.56)", "mock", "nose", "requests", "xmlschema"]
 
 [[package]]
-category = "dev"
-description = "Pytest plugin for measuring coverage."
 name = "pytest-cov"
+version = "2.12.1"
+description = "Pytest plugin for measuring coverage."
+category = "dev"
 optional = false
 python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*"
-version = "2.12.1"
 
 [package.dependencies]
 coverage = ">=5.2.1"
@@ -220,45 +192,33 @@ toml = "*"
 testing = ["fields", "hunter", "process-tests", "six", "pytest-xdist", "virtualenv"]
 
 [[package]]
-category = "dev"
-description = "Python Library for Tom's Obvious, Minimal Language"
 name = "toml"
+version = "0.10.2"
+description = "Python Library for Tom's Obvious, Minimal Language"
+category = "dev"
 optional = false
 python-versions = ">=2.6, !=3.0.*, !=3.1.*, !=3.2.*"
-version = "0.10.2"
 
 [[package]]
-category = "dev"
-description = "a fork of Python 2 and 3 ast modules with type comment support"
 name = "typed-ast"
-optional = false
-python-versions = "*"
 version = "1.4.3"
-
-[[package]]
+description = "a fork of Python 2 and 3 ast modules with type comment support"
 category = "dev"
-description = "Backported and Experimental Type Hints for Python 3.5+"
-name = "typing-extensions"
 optional = false
 python-versions = "*"
-version = "3.10.0.0"
 
 [[package]]
+name = "typing-extensions"
+version = "3.10.0.0"
+description = "Backported and Experimental Type Hints for Python 3.5+"
 category = "dev"
-description = "Backport of pathlib-compatible object wrapper for zip files"
-marker = "python_version < \"3.8\""
-name = "zipp"
 optional = false
-python-versions = ">=3.6"
-version = "3.5.0"
-
-[package.extras]
-docs = ["sphinx", "jaraco.packaging (>=8.2)", "rst.linker (>=1.9)"]
-testing = ["pytest (>=4.6)", "pytest-checkdocs (>=2.4)", "pytest-flake8", "pytest-cov", "pytest-enabler (>=1.0.1)", "jaraco.itertools", "func-timeout", "pytest-black (>=0.3.7)", "pytest-mypy"]
+python-versions = "*"
 
 [metadata]
-content-hash = "b3de1ca8a251edc8dae2c93e878deb3131846055ac2a6d6b34e43ea20a8f1ea2"
-python-versions = "^3.7"
+lock-version = "1.1"
+python-versions = "^3.8"
+content-hash = "1ede17bb5e095a5778c8840f952675b181c00d9c9434f11a16652886a77af0a2"
 
 [metadata.files]
 atomicwrites = [
@@ -331,10 +291,6 @@ flake8 = [
     {file = "flake8-3.9.2-py2.py3-none-any.whl", hash = "sha256:bf8fd333346d844f616e8d47905ef3a3384edae6b4e9beb0c5101e25e3110907"},
     {file = "flake8-3.9.2.tar.gz", hash = "sha256:07528381786f2a6237b061f6e96610a4167b226cb926e2aa2b6b1d78057c576b"},
 ]
-importlib-metadata = [
-    {file = "importlib_metadata-4.6.1-py3-none-any.whl", hash = "sha256:9f55f560e116f8643ecf2922d9cd3e1c7e8d52e683178fecd9d08f6aa357e11e"},
-    {file = "importlib_metadata-4.6.1.tar.gz", hash = "sha256:079ada16b7fc30dfbb5d13399a5113110dab1aa7c2bc62f66af75f0b717c8cac"},
-]
 iniconfig = [
     {file = "iniconfig-1.1.1-py2.py3-none-any.whl", hash = "sha256:011e24c64b7f47f6ebd835bb12a743f2fbe9a26d4cecaa7f53bc4f35ee9da8b3"},
     {file = "iniconfig-1.1.1.tar.gz", hash = "sha256:bc3af051d7d14b2ee5ef9969666def0cd1a000e121eaea580d4a313df4b37f32"},
@@ -363,6 +319,36 @@ mypy-extensions = [
     {file = "mypy_extensions-0.4.3-py2.py3-none-any.whl", hash = "sha256:090fedd75945a69ae91ce1303b5824f428daf5a028d2f6ab8a299250a846f15d"},
     {file = "mypy_extensions-0.4.3.tar.gz", hash = "sha256:2d82818f5bb3e369420cb3c4060a7970edba416647068eb4c5343488a6c604a8"},
 ]
+numpy = [
+    {file = "numpy-1.21.1-cp37-cp37m-macosx_10_9_x86_64.whl", hash = "sha256:38e8648f9449a549a7dfe8d8755a5979b45b3538520d1e735637ef28e8c2dc50"},
+    {file = "numpy-1.21.1-cp37-cp37m-manylinux_2_12_i686.manylinux2010_i686.whl", hash = "sha256:fd7d7409fa643a91d0a05c7554dd68aa9c9bb16e186f6ccfe40d6e003156e33a"},
+    {file = "numpy-1.21.1-cp37-cp37m-manylinux_2_12_x86_64.manylinux2010_x86_64.whl", hash = "sha256:a75b4498b1e93d8b700282dc8e655b8bd559c0904b3910b144646dbbbc03e062"},
+    {file = "numpy-1.21.1-cp37-cp37m-manylinux_2_17_aarch64.manylinux2014_aarch64.whl", hash = "sha256:1412aa0aec3e00bc23fbb8664d76552b4efde98fb71f60737c83efbac24112f1"},
+    {file = "numpy-1.21.1-cp37-cp37m-manylinux_2_5_i686.manylinux1_i686.whl", hash = "sha256:e46ceaff65609b5399163de5893d8f2a82d3c77d5e56d976c8b5fb01faa6b671"},
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+    {file = "numpy-1.21.1-cp37-cp37m-win32.whl", hash = "sha256:73101b2a1fef16602696d133db402a7e7586654682244344b8329cdcbbb82172"},
+    {file = "numpy-1.21.1-cp37-cp37m-win_amd64.whl", hash = "sha256:7a708a79c9a9d26904d1cca8d383bf869edf6f8e7650d85dbc77b041e8c5a0f8"},
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+    {file = "numpy-1.21.1-cp38-cp38-manylinux_2_17_aarch64.manylinux2014_aarch64.whl", hash = "sha256:0318c465786c1f63ac05d7c4dbcecd4d2d7e13f0959b01b534ea1e92202235c5"},
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+    {file = "numpy-1.21.1-cp38-cp38-manylinux_2_5_x86_64.manylinux1_x86_64.whl", hash = "sha256:91c6f5fc58df1e0a3cc0c3a717bb3308ff850abdaa6d2d802573ee2b11f674a8"},
+    {file = "numpy-1.21.1-cp38-cp38-win32.whl", hash = "sha256:978010b68e17150db8765355d1ccdd450f9fc916824e8c4e35ee620590e234cd"},
+    {file = "numpy-1.21.1-cp38-cp38-win_amd64.whl", hash = "sha256:9749a40a5b22333467f02fe11edc98f022133ee1bfa8ab99bda5e5437b831214"},
+    {file = "numpy-1.21.1-cp39-cp39-macosx_10_9_universal2.whl", hash = "sha256:d7a4aeac3b94af92a9373d6e77b37691b86411f9745190d2c351f410ab3a791f"},
+    {file = "numpy-1.21.1-cp39-cp39-macosx_10_9_x86_64.whl", hash = "sha256:d9e7912a56108aba9b31df688a4c4f5cb0d9d3787386b87d504762b6754fbb1b"},
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+    {file = "numpy-1.21.1-cp39-cp39-manylinux_2_12_x86_64.manylinux2010_x86_64.whl", hash = "sha256:05a0f648eb28bae4bcb204e6fd14603de2908de982e761a2fc78efe0f19e96e1"},
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+    {file = "numpy-1.21.1-cp39-cp39-win32.whl", hash = "sha256:88c0b89ad1cc24a5efbb99ff9ab5db0f9a86e9cc50240177a571fbe9c2860ac2"},
+    {file = "numpy-1.21.1-cp39-cp39-win_amd64.whl", hash = "sha256:01721eefe70544d548425a07c80be8377096a54118070b8a62476866d5208e33"},
+    {file = "numpy-1.21.1-pp37-pypy37_pp73-manylinux_2_12_x86_64.manylinux2010_x86_64.whl", hash = "sha256:2d4d1de6e6fb3d28781c73fbde702ac97f03d79e4ffd6598b880b2d95d62ead4"},
+    {file = "numpy-1.21.1.zip", hash = "sha256:dff4af63638afcc57a3dfb9e4b26d434a7a602d225b42d746ea7fe2edf1342fd"},
+]
 packaging = [
     {file = "packaging-21.0-py3-none-any.whl", hash = "sha256:c86254f9220d55e31cc94d69bade760f0847da8000def4dfe1c6b872fd14ff14"},
     {file = "packaging-21.0.tar.gz", hash = "sha256:7dc96269f53a4ccec5c0670940a4281106dd0bb343f47b7471f779df49c2fbe7"},
@@ -436,7 +422,3 @@ typing-extensions = [
     {file = "typing_extensions-3.10.0.0-py3-none-any.whl", hash = "sha256:779383f6086d90c99ae41cf0ff39aac8a7937a9283ce0a414e5dd782f4c94a84"},
     {file = "typing_extensions-3.10.0.0.tar.gz", hash = "sha256:50b6f157849174217d0656f99dc82fe932884fb250826c18350e159ec6cdf342"},
 ]
-zipp = [
-    {file = "zipp-3.5.0-py3-none-any.whl", hash = "sha256:957cfda87797e389580cb8b9e3870841ca991e2125350677b2ca83a0e99390a3"},
-    {file = "zipp-3.5.0.tar.gz", hash = "sha256:f5812b1e007e48cff63449a5e9f4e7ebea716b4111f9c4f9a645f91d579bf0c4"},
-]
diff --git a/pyproject.toml b/pyproject.toml
index b95c79a..778df52 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -5,7 +5,8 @@ description = ""
 authors = ["Deepak <dmallubhotla+github@gmail.com>"]
 
 [tool.poetry.dependencies]
-python = "^3.7"
+python = "^3.8"
+numpy = "^1.21.1"
 
 [tool.poetry.dev-dependencies]
 pytest = ">=6"
@@ -16,3 +17,6 @@ mypy = "^0.790"
 [build-system]
 requires = ["poetry>=0.12"]
 build-backend = "poetry.masonry.api"
+
+[tool.pytest.ini_options]
+testpaths = ["tests"]
diff --git a/scripts/patch.sh b/scripts/patch.sh
new file mode 100644
index 0000000..e67ca06
--- /dev/null
+++ b/scripts/patch.sh
@@ -0,0 +1,29 @@
+#!/usr/bin/env bash
+set -Eeuo pipefail
+
+if [ -z "$(git status --porcelain)" ]; then 
+	# Working directory clean
+	branch_name=$(git symbolic-ref -q HEAD)
+	branch_name=${branch_name##refs/heads/}
+	branch_name=${branch_name:-HEAD}
+	
+	poetry version patch
+	version=`sed 's/version = "\([0-9]*.[0-9]*.[0-9]*\)"/\1/p' -n <pyproject.toml`
+	read -p "Create commit for version $version? " -n 1 -r
+	echo    # (optional) move to a new line
+	if [[ $REPLY =~ ^[Yy]$ ]]
+	then
+		# do dangerous stuff
+		echo "Creating a new patch"
+		git add pyproject.toml
+		git commit -m "Created version $version"
+		git tag -a "$version" -m "patch.sh created version $version"
+		git push --tags
+	else
+		echo "Surrendering, clean up by reverting pyproject.toml..."
+		exit 2
+	fi
+else 
+	echo "Can't create patch version, working tree unclean..."
+	exit 1
+fi
diff --git a/tests/test_gradient_descent.py b/tests/test_gradient_descent.py
new file mode 100644
index 0000000..dc7406e
--- /dev/null
+++ b/tests/test_gradient_descent.py
@@ -0,0 +1,110 @@
+import numpy
+import pathfinder.gradient_descent
+
+
+def circ_cost(radius, center=(0, 0)):
+
+	def cf(pt):
+		pt2 = numpy.array(pt) - numpy.array(center)
+		return (radius**2 - pt2.dot(pt2))
+
+	return cf
+
+
+def test_circ_cost():
+	cost = circ_cost(5)
+	actual = cost([3, 4])
+	expected = 0
+	assert actual == expected
+
+	cost = circ_cost(13, [12, 5])
+	actual = cost([0, 0])
+	expected = 0
+	assert actual == expected
+
+
+def test_find_sols():
+	c1 = circ_cost(5)
+	c2 = circ_cost(13, [8, -8])
+
+	def costs(pt):
+		return numpy.array(
+			[c1(pt), c2(pt)]
+		)
+
+	def jac(pt):
+		x, y = pt
+		return numpy.array([[-2 * x, -2 * y], [-2 * (x - 8), -2 * (y + 8)]])
+
+	print(costs([3, 4]))
+	result = pathfinder.gradient_descent.find_sols(costs, jac, step_size=0.01, max_iterations=5000, initial=(2, 10), desired_cost=1e-6)
+	print(result)
+
+
+def dipole_cost(vn, xn_raw):
+	xn = numpy.array(xn_raw)
+
+	def dc(pt):
+		p = pt[0:3]
+		s = pt[3:6]
+
+		diff = xn - s
+		return (vn * (numpy.linalg.norm(diff)**3)) - p.dot(diff)
+
+	return dc
+
+
+def test_actual_dipole_finding():
+	def c0(pt):
+		p = pt[0:3]
+		return (p.dot(p) - 35)
+
+	v1 = -0.0554777
+	v2 = -0.0601857
+	v3 = -0.0636403
+	v4 = -0.0648838
+	v5 = -0.0629715
+
+	# the 0 here is a red herring for index purposes later
+	vns = [0, v1, v2, v3, v4, v5]
+	# the 0 here is a red herring
+	xns = [numpy.array([0, 0, n]) for n in range(0, 6)]
+
+	c1 = dipole_cost(v1, [0, 0, 1])
+	c2 = dipole_cost(v2, [0, 0, 2])
+	c3 = dipole_cost(v3, [0, 0, 3])
+	c4 = dipole_cost(v4, [0, 0, 4])
+	c5 = dipole_cost(v5, [0, 0, 5])
+
+	def costs(pt):
+		return numpy.array(
+			[c0(pt), c1(pt), c2(pt), c3(pt), c4(pt), c5(pt)]
+		)
+
+	def jac_row(n):
+		def jr(pt):
+			p = pt[0:3]
+			s = pt[3:6]
+			vn = vns[n]
+			xn = xns[n]
+			diff = xn - s
+			return [
+				-diff[0], -diff[1], -diff[2],
+				p[0] - vn * 3 * numpy.linalg.norm(diff) * (diff)[0],
+				p[1] - vn * 3 * numpy.linalg.norm(diff) * (diff)[1],
+				p[2] - vn * 3 * numpy.linalg.norm(diff) * (diff)[2]
+			]
+		return jr
+
+	def jac(pt):
+		return numpy.array([
+			[2 * pt[0], 2 * pt[1], 2 * pt[2], 0, 0, 0],
+			jac_row(1)(pt),
+			jac_row(2)(pt),
+			jac_row(3)(pt),
+			jac_row(4)(pt),
+			jac_row(5)(pt),
+		])
+
+	result = pathfinder.gradient_descent.find_sols(costs, jac, step_size=0.01, max_iterations=10000, initial=(1, 2, 3, 4, 5, 6), desired_cost=1e-6, step_size_tries=25)
+	print(result)