14. vector

This module is used to manipulate arrays of 3D vectors, assumed to be numpy arrays of shape (..., 3).

mag and dot include alternate versions (mag1 and dot1) which keep the last dimension index. This is useful when you intend to multiply or divide a vector by a result, e.g.:

normed_vector = vector / mag1(vector)

Note that using mag in this case will trigger an error, because the arrays are not aligned.

14.1. Overview

mag(X)	Calculate the length of an array of vectors.
mag1(X)	Calculate the length of an array of vectors, keeping the last dimension index.
dot(X, Y)	Calculate the dot product of two arrays of vectors.
dot1(X, Y)	Calculate the dot product of two arrays of vectors, keeping the last dimension index
norm(X)	Computes a normalized version of an array of vectors.
plus(X)	Return a shifted version of an array of vectors.
minus(X)	Return a shifted version of an array of vectors.
cross(X, Y)	Return the cross-product of two vectors.
proj(X, Y)	Return the projection of one vector onto another.
apply_basis(X, B)	Transform each vector into the specified basis/bases.
midpoint_delta(X)	Returns center point and vector of each edge of the polygon defined by the points.
arb_perp(V)	For each vector, return an arbitrary vector that is perpendicular.
vec([x, y, z])	Generate a […, 3] vector from seperate x, y, z.
rot(a[, X, cutoff])	Rotate points around an arbitrary axis.
normalize_basis(B)	Create right-handed orthonormal basis/bases from input basis.

14.2. Functions

ilpm.vector.mag(X)

Calculate the length of an array of vectors.

ilpm.vector.mag1(X)

Calculate the length of an array of vectors, keeping the last dimension index.

ilpm.vector.dot(X, Y)

Calculate the dot product of two arrays of vectors.

ilpm.vector.dot1(X, Y)

Calculate the dot product of two arrays of vectors, keeping the last dimension index

ilpm.vector.norm(X)

Computes a normalized version of an array of vectors.

ilpm.vector.plus(X)

Return a shifted version of an array of vectors.

ilpm.vector.minus(X)

Return a shifted version of an array of vectors.

ilpm.vector.cross(X, Y)

Return the cross-product of two vectors.

ilpm.vector.proj(X, Y)

Return the projection of one vector onto another.

Parameters

X, Yvector array

Returns

Zvector array

\(\vec{Z} = \frac{\vec{X} \cdot \vec{Y}}{|Y|^2} \vec{Y}\)

ilpm.vector.midpoint_delta(X)

Returns center point and vector of each edge of the polygon defined by the points.

ilpm.vector.arb_perp(V)

For each vector, return an arbitrary vector that is perpendicular.

Note: arbitrary does not mean random!

ilpm.vector.apply_basis(X, B)

Transform each vector into the specified basis/bases.

Parameters

Xvector array, shape […, 3]

Borthonormal basis array, shape […, 3, 3]

Returns

Yvector array, shape […, 3]

X transformed into the basis given by B

ilpm.vector.vec(x=[0], y=[0], z=[0])

Generate a […, 3] vector from seperate x, y, z.

Parameters

x, y, z: array

coordinates; default to 0, may have any shape

Returns

X[…, 3] array

ilpm.vector.rot(a, X=None, cutoff=1e-10)

Rotate points around an arbitrary axis.

Parameters

a[…, 3] array

Rotation vector, will rotate counter-clockwise around axis by an amount given be the length of the vector (in radians). May be a single vector or an array of vectors if each point is rotated separately.

X[…, 3] array

Vectors to rotate; if not specified generates a rotation basis instead.

cutofffloat

If length of vector less than this value (1E-10 by default), no rotation is performed. (Used to avoid basis errors)

Returns

Y[…, 3] array

Rotated vectors or rotation basis.

ilpm.vector.normalize_basis(B)

Create right-handed orthonormal basis/bases from input basis.

Parameters

B[…, 1-3, 3] array

input basis, should be at least 2d. If the second to last axis has 1 vectors, it will automatically create an arbitrary orthonormal basis with the specified first vector. (note: even if three bases are specified, the last is always ignored, and is generated by a cross product of the first two.)

Returns

NB[…, 3, 3] array

orthonormal basis

class ilpm.vector.TestCases(methodName='runTest')

Bases: unittest.case.TestCase

Methods

__call__(self, \*args, \*\*kwds)	Call self as a function.
addCleanup(self, function, \*args, \*\*kwargs)	Add a function, with arguments, to be called when the test is completed.
addTypeEqualityFunc(self, typeobj, function)	Add a type specific assertEqual style function to compare a type.
assertAlmostEqual(self, first, second[, …])	Fail if the two objects are unequal as determined by their difference rounded to the given number of decimal places (default 7) and comparing to zero, or by comparing that the difference between the two objects is more than the given delta.
assertCountEqual(self, first, second[, msg])	An unordered sequence comparison asserting that the same elements, regardless of order.
assertDictContainsSubset(self, subset, …)	Checks whether dictionary is a superset of subset.
assertEqual(self, first, second[, msg])	Fail if the two objects are unequal as determined by the ‘==’ operator.
assertFalse(self, expr[, msg])	Check that the expression is false.
assertGreater(self, a, b[, msg])	Just like self.assertTrue(a > b), but with a nicer default message.
assertGreaterEqual(self, a, b[, msg])	Just like self.assertTrue(a >= b), but with a nicer default message.
assertIn(self, member, container[, msg])	Just like self.assertTrue(a in b), but with a nicer default message.
assertIs(self, expr1, expr2[, msg])	Just like self.assertTrue(a is b), but with a nicer default message.
assertIsInstance(self, obj, cls[, msg])	Same as self.assertTrue(isinstance(obj, cls)), with a nicer default message.
assertIsNone(self, obj[, msg])	Same as self.assertTrue(obj is None), with a nicer default message.
assertIsNot(self, expr1, expr2[, msg])	Just like self.assertTrue(a is not b), but with a nicer default message.
assertIsNotNone(self, obj[, msg])	Included for symmetry with assertIsNone.
assertLess(self, a, b[, msg])	Just like self.assertTrue(a < b), but with a nicer default message.
assertLessEqual(self, a, b[, msg])	Just like self.assertTrue(a <= b), but with a nicer default message.
assertListEqual(self, list1, list2[, msg])	A list-specific equality assertion.
assertLogs(self[, logger, level])	Fail unless a log message of level level or higher is emitted on logger_name or its children.
assertMultiLineEqual(self, first, second[, msg])	Assert that two multi-line strings are equal.
assertNotAlmostEqual(self, first, second[, …])	Fail if the two objects are equal as determined by their difference rounded to the given number of decimal places (default 7) and comparing to zero, or by comparing that the difference between the two objects is less than the given delta.
assertNotEqual(self, first, second[, msg])	Fail if the two objects are equal as determined by the ‘!=’ operator.
assertNotIn(self, member, container[, msg])	Just like self.assertTrue(a not in b), but with a nicer default message.
assertNotIsInstance(self, obj, cls[, msg])	Included for symmetry with assertIsInstance.
assertNotRegex(self, text, unexpected_regex)	Fail the test if the text matches the regular expression.
assertRaises(self, expected_exception, …)	Fail unless an exception of class expected_exception is raised by the callable when invoked with specified positional and keyword arguments.
assertRaisesRegex(self, expected_exception, …)	Asserts that the message in a raised exception matches a regex.
assertRegex(self, text, expected_regex[, msg])	Fail the test unless the text matches the regular expression.
assertSequenceEqual(self, seq1, seq2[, msg, …])	An equality assertion for ordered sequences (like lists and tuples).
assertSetEqual(self, set1, set2[, msg])	A set-specific equality assertion.
assertTrue(self, expr[, msg])	Check that the expression is true.
assertTupleEqual(self, tuple1, tuple2[, msg])	A tuple-specific equality assertion.
assertWarns(self, expected_warning, \*args, …)	Fail unless a warning of class warnClass is triggered by the callable when invoked with specified positional and keyword arguments.
assertWarnsRegex(self, expected_warning, …)	Asserts that the message in a triggered warning matches a regexp.
debug(self)	Run the test without collecting errors in a TestResult
doCleanups(self)	Execute all cleanup functions.
fail(self[, msg])	Fail immediately, with the given message.
failureException	alias of builtins.AssertionError
setUp(self)	Hook method for setting up the test fixture before exercising it.
setUpClass()	Hook method for setting up class fixture before running tests in the class.
shortDescription(self)	Returns a one-line description of the test, or None if no description has been provided.
skipTest(self, reason)	Skip this test.
subTest(self[, msg])	Return a context manager that will return the enclosed block of code in a subtest identified by the optional message and keyword parameters.
tearDown(self)	Hook method for deconstructing the test fixture after testing it.
tearDownClass()	Hook method for deconstructing the class fixture after running all tests in the class.

assertAlmostEquals
assertDictEqual
assertEquals
assertNotAlmostEquals
assertNotEquals
assertNotRegexpMatches
assertRaisesRegexp
assertRegexpMatches
assert_
countTestCases
defaultTestResult
failIf
failIfAlmostEqual
failIfEqual
failUnless
failUnlessAlmostEqual
failUnlessEqual
failUnlessRaises
id
run
test_construct_vec
test_normalize
test_rotation