Includes tests with scipy methods

pathfinder/model/__init__.py

@@ -0,0 +1,16 @@
+
+
+class DipoleModel():
+	'''
+	Model object represents a physical dipole finding problem.
+
+	Parameters
+	----------
+	n : int
+		The number of dipoles expected.
+	m: int
+		The number of dots used to sample the potential.
+	'''
+	def __init__(self, n, m):
+		self.n = n
+		serf.m = m

poetry.lock

@@ -191,6 +191,17 @@ toml = "*"
 [package.extras]
 testing = ["fields", "hunter", "process-tests", "six", "pytest-xdist", "virtualenv"]
 
+[[package]]
+name = "scipy"
+version = "1.5.4"
+description = "SciPy: Scientific Library for Python"
+category = "main"
+optional = false
+python-versions = ">=3.6"
+
+[package.dependencies]
+numpy = ">=1.14.5"
+
 [[package]]
 name = "toml"
 version = "0.10.2"
@@ -217,8 +228,8 @@ python-versions = "*"
 
 [metadata]
 lock-version = "1.1"
-python-versions = "^3.8"
+python-versions = "^3.8,<3.10"
-content-hash = "1ede17bb5e095a5778c8840f952675b181c00d9c9434f11a16652886a77af0a2"
+content-hash = "bde9b5d449e7257dc8c24675658295cf82950d7ec381d873e936ad7cc4bcf6d8"
 
 [metadata.files]
 atomicwrites = [
@@ -381,6 +392,33 @@ pytest-cov = [
     {file = "pytest-cov-2.12.1.tar.gz", hash = "sha256:261ceeb8c227b726249b376b8526b600f38667ee314f910353fa318caa01f4d7"},
     {file = "pytest_cov-2.12.1-py2.py3-none-any.whl", hash = "sha256:261bb9e47e65bd099c89c3edf92972865210c36813f80ede5277dceb77a4a62a"},
 ]
+scipy = [
+    {file = "scipy-1.5.4-cp36-cp36m-macosx_10_9_x86_64.whl", hash = "sha256:4f12d13ffbc16e988fa40809cbbd7a8b45bc05ff6ea0ba8e3e41f6f4db3a9e47"},
+    {file = "scipy-1.5.4-cp36-cp36m-manylinux1_i686.whl", hash = "sha256:a254b98dbcc744c723a838c03b74a8a34c0558c9ac5c86d5561703362231107d"},
+    {file = "scipy-1.5.4-cp36-cp36m-manylinux1_x86_64.whl", hash = "sha256:368c0f69f93186309e1b4beb8e26d51dd6f5010b79264c0f1e9ca00cd92ea8c9"},
+    {file = "scipy-1.5.4-cp36-cp36m-manylinux2014_aarch64.whl", hash = "sha256:4598cf03136067000855d6b44d7a1f4f46994164bcd450fb2c3d481afc25dd06"},
+    {file = "scipy-1.5.4-cp36-cp36m-win32.whl", hash = "sha256:e98d49a5717369d8241d6cf33ecb0ca72deee392414118198a8e5b4c35c56340"},
+    {file = "scipy-1.5.4-cp36-cp36m-win_amd64.whl", hash = "sha256:65923bc3809524e46fb7eb4d6346552cbb6a1ffc41be748535aa502a2e3d3389"},
+    {file = "scipy-1.5.4-cp37-cp37m-macosx_10_9_x86_64.whl", hash = "sha256:9ad4fcddcbf5dc67619379782e6aeef41218a79e17979aaed01ed099876c0e62"},
+    {file = "scipy-1.5.4-cp37-cp37m-manylinux1_i686.whl", hash = "sha256:f87b39f4d69cf7d7529d7b1098cb712033b17ea7714aed831b95628f483fd012"},
+    {file = "scipy-1.5.4-cp37-cp37m-manylinux1_x86_64.whl", hash = "sha256:25b241034215247481f53355e05f9e25462682b13bd9191359075682adcd9554"},
+    {file = "scipy-1.5.4-cp37-cp37m-manylinux2014_aarch64.whl", hash = "sha256:fa789583fc94a7689b45834453fec095245c7e69c58561dc159b5d5277057e4c"},
+    {file = "scipy-1.5.4-cp37-cp37m-win32.whl", hash = "sha256:d6d25c41a009e3c6b7e757338948d0076ee1dd1770d1c09ec131f11946883c54"},
+    {file = "scipy-1.5.4-cp37-cp37m-win_amd64.whl", hash = "sha256:2c872de0c69ed20fb1a9b9cf6f77298b04a26f0b8720a5457be08be254366c6e"},
+    {file = "scipy-1.5.4-cp38-cp38-macosx_10_9_x86_64.whl", hash = "sha256:e360cb2299028d0b0d0f65a5c5e51fc16a335f1603aa2357c25766c8dab56938"},
+    {file = "scipy-1.5.4-cp38-cp38-manylinux1_i686.whl", hash = "sha256:3397c129b479846d7eaa18f999369a24322d008fac0782e7828fa567358c36ce"},
+    {file = "scipy-1.5.4-cp38-cp38-manylinux1_x86_64.whl", hash = "sha256:168c45c0c32e23f613db7c9e4e780bc61982d71dcd406ead746c7c7c2f2004ce"},
+    {file = "scipy-1.5.4-cp38-cp38-manylinux2014_aarch64.whl", hash = "sha256:213bc59191da2f479984ad4ec39406bf949a99aba70e9237b916ce7547b6ef42"},
+    {file = "scipy-1.5.4-cp38-cp38-win32.whl", hash = "sha256:634568a3018bc16a83cda28d4f7aed0d803dd5618facb36e977e53b2df868443"},
+    {file = "scipy-1.5.4-cp38-cp38-win_amd64.whl", hash = "sha256:b03c4338d6d3d299e8ca494194c0ae4f611548da59e3c038813f1a43976cb437"},
+    {file = "scipy-1.5.4-cp39-cp39-macosx_10_9_x86_64.whl", hash = "sha256:3d5db5d815370c28d938cf9b0809dade4acf7aba57eaf7ef733bfedc9b2474c4"},
+    {file = "scipy-1.5.4-cp39-cp39-manylinux1_i686.whl", hash = "sha256:6b0ceb23560f46dd236a8ad4378fc40bad1783e997604ba845e131d6c680963e"},
+    {file = "scipy-1.5.4-cp39-cp39-manylinux1_x86_64.whl", hash = "sha256:ed572470af2438b526ea574ff8f05e7f39b44ac37f712105e57fc4d53a6fb660"},
+    {file = "scipy-1.5.4-cp39-cp39-manylinux2014_aarch64.whl", hash = "sha256:8c8d6ca19c8497344b810b0b0344f8375af5f6bb9c98bd42e33f747417ab3f57"},
+    {file = "scipy-1.5.4-cp39-cp39-win32.whl", hash = "sha256:d84cadd7d7998433334c99fa55bcba0d8b4aeff0edb123b2a1dfcface538e474"},
+    {file = "scipy-1.5.4-cp39-cp39-win_amd64.whl", hash = "sha256:cc1f78ebc982cd0602c9a7615d878396bec94908db67d4ecddca864d049112f2"},
+    {file = "scipy-1.5.4.tar.gz", hash = "sha256:4a453d5e5689de62e5d38edf40af3f17560bfd63c9c5bd228c18c1f99afa155b"},
+]
 toml = [
     {file = "toml-0.10.2-py2.py3-none-any.whl", hash = "sha256:806143ae5bfb6a3c6e736a764057db0e6a0e05e338b5630894a5f779cabb4f9b"},
     {file = "toml-0.10.2.tar.gz", hash = "sha256:b3bda1d108d5dd99f4a20d24d9c348e91c4db7ab1b749200bded2f839ccbe68f"},

pyproject.toml

@@ -5,8 +5,9 @@ description = ""
 authors = ["Deepak <dmallubhotla+github@gmail.com>"]
 
 [tool.poetry.dependencies]
-python = "^3.8"
+python = "^3.8,<3.10"
 numpy = "^1.21.1"
+scipy = "~1.5"
 
 [tool.poetry.dev-dependencies]
 pytest = ">=6"

tests/test_gradient_descent.py

@@ -108,7 +108,10 @@ def test_actual_dipole_finding():
 			jac_row(5)(pt),
 		])
 
-	_, _, result = pathfinder.gradient_descent.find_sols(costs, jac, step_size=1, max_iterations=10000, initial=(1, 2, 3, 4, 5, 6), desired_cost=1e-6, step_size_tries=30)
+	_, iterations, result = pathfinder.gradient_descent.find_sols(costs, jac, step_size=1, max_iterations=10000, initial=(1, 2, 3, 4, 5, 6), desired_cost=1e-6, step_size_tries=30)
+	print(f"\n\n{iterations} iterations")
+	print(result)
+	print("\n")
 	numpy.testing.assert_allclose(
 		result, (1, 3, 5, 5, 6, 7),
 		rtol=5e-2, err_msg='the result was off', verbose=True

tests/test_scipy_optimize.py

@@ -0,0 +1,165 @@
+import numpy
+import scipy.optimize
+
+import pytest
+
+
+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(scipy.optimize.minimize(lambda x: costs(x).dot(costs(x)), numpy.array([1, 2])))
+	#
+	# message, iterations, result = pathfinder.gradient_descent.find_sols(costs, jac, step_size=0.01, max_iterations=5000, initial=(2, 10), desired_cost=1e-6)
+	# numpy.testing.assert_almost_equal(
+	# 	result, (3, 4),
+	# 	decimal=7, err_msg='the result was off', verbose=True
+	# )
+
+
+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 = -0.05547767706400186526225414
+	v2 = -0.06018573388098888319642888
+	v3 = -0.06364032191901859480476888
+	v4 = -0.06488383879243851188402150
+	v5 = -0.06297148063759813929659130
+	v6 = -0.05735489606460216
+	v7 = -0.07237320672886623
+
+	# 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)]
+
+	# the 0 here is a red herring for index purposes later
+	vns2 = [0, v1, v2, v3, v4, v5, v6, v7]
+	# the 0 here is a red herring
+	xns2 = [numpy.array([0, 0, n]) for n in range(0, 7)]
+	xns2.append([1, 1, 7])
+
+	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])
+	c6 = dipole_cost(v6, [0, 0, 6])
+	c6 = dipole_cost(v6, [0, 0, 6])
+	c7 = dipole_cost(v7, [1, 1, 7])
+
+	def costs(pt):
+		return numpy.array(
+			[c0(pt), c1(pt), c2(pt), c3(pt), c4(pt), c5(pt)]
+		)
+	def costs2(pt):
+		return numpy.array(
+			[c0(pt), c1(pt), c2(pt), c3(pt), c4(pt), c5(pt), c6(pt), c7(pt)]
+		)
+
+	def jac_row(n):
+		def jr(pt):
+			p = pt[0:3]
+			s = pt[3:6]
+			vn = vns2[n]
+			xn = xns2[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),
+		])
+
+	def jac2(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),
+			jac_row(6)(pt),
+			jac_row(7)(pt),
+		])
+
+	def print_result(msg, result):
+		print(msg)
+		print(f"\tResult: {result.x}")
+		print(f"\tSuccess: {result.success}. {result.message}")
+		try:
+			print(f"\tFunc evals: {result.nfev}")
+		except AttributeError as e:
+			pass
+		try:
+			print(f"\tJacb evals: {result.njev}")
+		except AttributeError as e:
+			pass
+	print("Minimising the squared costs")
+	print(scipy.optimize.minimize(lambda x: costs(x).dot(costs(x)), numpy.array([1, 2, 3, 4, 5, 6])))
+	# print(scipy.optimize.broyden1(costs, numpy.array([1, 2, 3, 4, 5, 6])))
+	# print(scipy.optimize.newton_krylov(costs, numpy.array([1, 2, 3, 4, 5, 6])))
+	# print(scipy.optimize.anderson(costs, numpy.array([1, 2, 3, 4, 5, 6])))
+	print_result("Using root", scipy.optimize.root(costs, numpy.array([1, 2, 3, 4, 5, 6])))
+	print_result("Using root with jacobian", scipy.optimize.root(costs, numpy.array([1, 2, 3, 4, 5, 6]), jac=jac, tol=1e-12))
+	print_result("Using least squares", scipy.optimize.least_squares(costs, numpy.array([1, 2, 3, 4, 5, 6]), gtol=1e-12))
+	print_result("Using least squares, with jacobian", scipy.optimize.least_squares(costs, numpy.array([1, 2, 3, 4, 5, 6]), jac=jac, ftol=3e-16, gtol=3e-16, xtol=3e-16))
+	print_result("Using least squares, with jacobian, lm", scipy.optimize.least_squares(costs, numpy.array([1, 2, 3, 4, 5, 6]), jac=jac, ftol=3e-16, gtol=3e-16, xtol=3e-16, method="lm"))
+	print_result("Using least squares extra dot", scipy.optimize.least_squares(costs2, numpy.array([1, 2, 3, 4, 5, 6])))
+	print_result("Using least squares extra dot, with jacobian", scipy.optimize.least_squares(costs2, numpy.array([1, 2, 3, 4, 5, 6]), jac=jac2, ftol=1e-12))
+	print(scipy.optimize.least_squares(costs2, numpy.array([1, 2, 3, 4, 5, 6]), jac=jac2, ftol=1e-12).x[0])