3.11.1. sasmodels.resolution¶

Define the resolution functions for the data.

This defines classes for 1D and 2D resolution calculations.

class sasmodels.resolution.IgorComparisonTest(methodName='runTest')¶

Bases: unittest.case.TestCase

Create an instance of the class that will use the named test method when executed. Raises a ValueError if the instance does not have a method with the specified name.

failureException¶

alias of AssertionError

Iq_sphere(pars, resolution)¶

addCleanup(function, *args, **kwargs)¶

Add a function, with arguments, to be called when the test is completed. Functions added are called on a LIFO basis and are called after tearDown on test failure or success.

Cleanup items are called even if setUp fails (unlike tearDown).

addTypeEqualityFunc(typeobj, function)¶

Add a type specific assertEqual style function to compare a type.

This method is for use by TestCase subclasses that need to register their own type equality functions to provide nicer error messages.

Args:

typeobj: The data type to call this function on when both values

are of the same type in assertEqual().

function: The callable taking two arguments and an optional

msg= argument that raises self.failureException with a useful error message when the two arguments are not equal.

assertAlmostEqual(first, second, places=None, msg=None, delta=None)¶

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 between the two objects is more than the given delta.

Note that decimal places (from zero) are usually not the same as significant digits (measured from the most signficant digit).

If the two objects compare equal then they will automatically compare almost equal.

assertAlmostEquals(first, second, places=None, msg=None, delta=None)¶

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 between the two objects is more than the given delta.

Note that decimal places (from zero) are usually not the same as significant digits (measured from the most signficant digit).

If the two objects compare equal then they will automatically compare almost equal.

assertDictContainsSubset(expected, actual, msg=None)¶

Checks whether actual is a superset of expected.

assertDictEqual(d1, d2, msg=None)¶

assertEqual(first, second, msg=None)¶

Fail if the two objects are unequal as determined by the ‘==’ operator.

assertEquals(first, second, msg=None)¶

Fail if the two objects are unequal as determined by the ‘==’ operator.

assertFalse(expr, msg=None)¶

Check that the expression is false.

assertGreater(a, b, msg=None)¶

Just like self.assertTrue(a > b), but with a nicer default message.

assertGreaterEqual(a, b, msg=None)¶

Just like self.assertTrue(a >= b), but with a nicer default message.

assertIn(member, container, msg=None)¶

Just like self.assertTrue(a in b), but with a nicer default message.

assertIs(expr1, expr2, msg=None)¶

Just like self.assertTrue(a is b), but with a nicer default message.

assertIsInstance(obj, cls, msg=None)¶

Same as self.assertTrue(isinstance(obj, cls)), with a nicer default message.

assertIsNone(obj, msg=None)¶

Same as self.assertTrue(obj is None), with a nicer default message.

assertIsNot(expr1, expr2, msg=None)¶

Just like self.assertTrue(a is not b), but with a nicer default message.

assertIsNotNone(obj, msg=None)¶

Included for symmetry with assertIsNone.

assertItemsEqual(expected_seq, actual_seq, msg=None)¶

An unordered sequence specific comparison. It asserts that actual_seq and expected_seq have the same element counts. Equivalent to:

self.assertEqual(Counter(iter(actual_seq)),
                 Counter(iter(expected_seq)))

Asserts that each element has the same count in both sequences. Example:

• [0, 1, 1] and [1, 0, 1] compare equal.
• [0, 0, 1] and [0, 1] compare unequal.

assertLess(a, b, msg=None)¶

Just like self.assertTrue(a < b), but with a nicer default message.

assertLessEqual(a, b, msg=None)¶

Just like self.assertTrue(a <= b), but with a nicer default message.

assertListEqual(list1, list2, msg=None)¶

A list-specific equality assertion.

Args:

list1: The first list to compare. list2: The second list to compare. msg: Optional message to use on failure instead of a list of

differences.

assertMultiLineEqual(first, second, msg=None)¶

Assert that two multi-line strings are equal.

assertNotAlmostEqual(first, second, places=None, msg=None, delta=None)¶

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 between the two objects is less than the given delta.

Note that decimal places (from zero) are usually not the same as significant digits (measured from the most signficant digit).

Objects that are equal automatically fail.

assertNotAlmostEquals(first, second, places=None, msg=None, delta=None)¶

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 between the two objects is less than the given delta.

Note that decimal places (from zero) are usually not the same as significant digits (measured from the most signficant digit).

Objects that are equal automatically fail.

assertNotEqual(first, second, msg=None)¶

Fail if the two objects are equal as determined by the ‘!=’ operator.

assertNotEquals(first, second, msg=None)¶

Fail if the two objects are equal as determined by the ‘!=’ operator.

assertNotIn(member, container, msg=None)¶

Just like self.assertTrue(a not in b), but with a nicer default message.

assertNotIsInstance(obj, cls, msg=None)¶

Included for symmetry with assertIsInstance.

assertNotRegexpMatches(text, unexpected_regexp, msg=None)¶

Fail the test if the text matches the regular expression.

assertRaises(excClass, callableObj=None, *args, **kwargs)¶

Fail unless an exception of class excClass is raised by callableObj when invoked with arguments args and keyword arguments kwargs. If a different type of exception is raised, it will not be caught, and the test case will be deemed to have suffered an error, exactly as for an unexpected exception.

If called with callableObj omitted or None, will return a context object used like this:

with self.assertRaises(SomeException):
    do_something()

The context manager keeps a reference to the exception as the ‘exception’ attribute. This allows you to inspect the exception after the assertion:

with self.assertRaises(SomeException) as cm:
    do_something()
the_exception = cm.exception
self.assertEqual(the_exception.error_code, 3)

assertRaisesRegexp(expected_exception, expected_regexp, callable_obj=None, *args, **kwargs)¶

Asserts that the message in a raised exception matches a regexp.

Args:

expected_exception: Exception class expected to be raised. expected_regexp: Regexp (re pattern object or string) expected

to be found in error message.

callable_obj: Function to be called. args: Extra args. kwargs: Extra kwargs.

assertRegexpMatches(text, expected_regexp, msg=None)¶

Fail the test unless the text matches the regular expression.

assertSequenceEqual(seq1, seq2, msg=None, seq_type=None)¶

An equality assertion for ordered sequences (like lists and tuples).

For the purposes of this function, a valid ordered sequence type is one which can be indexed, has a length, and has an equality operator.

Args:

seq1: The first sequence to compare. seq2: The second sequence to compare. seq_type: The expected datatype of the sequences, or None if no

datatype should be enforced.

msg: Optional message to use on failure instead of a list of

differences.

assertSetEqual(set1, set2, msg=None)¶

A set-specific equality assertion.

Args:

set1: The first set to compare. set2: The second set to compare. msg: Optional message to use on failure instead of a list of

differences.

assertSetEqual uses ducktyping to support different types of sets, and is optimized for sets specifically (parameters must support a difference method).

assertTrue(expr, msg=None)¶

Check that the expression is true.

assertTupleEqual(tuple1, tuple2, msg=None)¶

A tuple-specific equality assertion.

Args:

tuple1: The first tuple to compare. tuple2: The second tuple to compare. msg: Optional message to use on failure instead of a list of

differences.

assert_(expr, msg=None)¶

Check that the expression is true.

compare(q, output, answer, tolerance)¶

countTestCases()¶

debug()¶

Run the test without collecting errors in a TestResult

defaultTestResult()¶

doCleanups()¶

Execute all cleanup functions. Normally called for you after tearDown.

fail(msg=None)¶

Fail immediately, with the given message.

failIf(*args, **kwargs)¶

failIfAlmostEqual(*args, **kwargs)¶

failIfEqual(*args, **kwargs)¶

failUnless(*args, **kwargs)¶

failUnlessAlmostEqual(*args, **kwargs)¶

failUnlessEqual(*args, **kwargs)¶

failUnlessRaises(*args, **kwargs)¶

id()¶

run(result=None)¶

setUp()¶

classmethod setUpClass()¶

Hook method for setting up class fixture before running tests in the class.

shortDescription()¶

Returns a one-line description of the test, or None if no description has been provided.

The default implementation of this method returns the first line of the specified test method’s docstring.

skipTest(reason)¶

Skip this test.

tearDown()¶

Hook method for deconstructing the test fixture after testing it.

classmethod tearDownClass()¶

Hook method for deconstructing the class fixture after running all tests in the class.

test_ellipsoid()¶

Compare romberg integration for ellipsoid model.

test_perfect()¶

Compare sphere model with NIST Igor SANS, no resolution smearing.

test_pinhole()¶

Compare pinhole resolution smearing with NIST Igor SANS

test_pinhole_romberg()¶

Compare pinhole resolution smearing with romberg integration result.

test_pinhole_sparse(*args, **kwargs)¶

Compare pinhole resolution smearing with NIST Igor SANS on sparse data

test_slit()¶

Compare slit resolution smearing with NIST Igor SANS

test_slit_romberg()¶

Compare slit resolution smearing with romberg integration result.

longMessage = False¶

maxDiff = 640¶

class sasmodels.resolution.Perfect1D(q)¶

Bases: sasmodels.resolution.Resolution

Resolution function to use when there is no actual resolution smearing to be applied. It has the same interface as the other resolution functions, but returns the identity function.

apply(theory)¶

q = None¶

q_calc = None¶

class sasmodels.resolution.Pinhole1D(q, q_width, q_calc=None, nsigma=3)¶

Bases: sasmodels.resolution.Resolution

Pinhole aperture with q-dependent gaussian resolution.

q points at which the data is measured.

q_width gaussian 1-sigma resolution at each data point.

q_calc is the list of points to calculate, or None if this should be estimated from the q and q_width.

apply(theory)¶

q = None¶

q_calc = None¶

class sasmodels.resolution.Resolution¶

Bases: object

Abstract base class defining a 1D resolution function.

q is the set of q values at which the data is measured.

q_calc is the set of q values at which the theory needs to be evaluated. This may extend and interpolate the q values.

apply is the method to call with I(q_calc) to compute the resolution smeared theory I(q).

apply(theory)¶

Smear theory by the resolution function, returning Iq.

q = None¶

q_calc = None¶

class sasmodels.resolution.ResolutionTest(methodName='runTest')¶

Bases: unittest.case.TestCase

Create an instance of the class that will use the named test method when executed. Raises a ValueError if the instance does not have a method with the specified name.

failureException¶

alias of AssertionError

Iq(q)¶

Linear function for resolution unit test

addCleanup(function, *args, **kwargs)¶

Add a function, with arguments, to be called when the test is completed. Functions added are called on a LIFO basis and are called after tearDown on test failure or success.

Cleanup items are called even if setUp fails (unlike tearDown).

addTypeEqualityFunc(typeobj, function)¶

Add a type specific assertEqual style function to compare a type.

This method is for use by TestCase subclasses that need to register their own type equality functions to provide nicer error messages.

Args:

typeobj: The data type to call this function on when both values

are of the same type in assertEqual().

function: The callable taking two arguments and an optional

msg= argument that raises self.failureException with a useful error message when the two arguments are not equal.

assertAlmostEqual(first, second, places=None, msg=None, delta=None)¶

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 between the two objects is more than the given delta.

Note that decimal places (from zero) are usually not the same as significant digits (measured from the most signficant digit).

If the two objects compare equal then they will automatically compare almost equal.

assertAlmostEquals(first, second, places=None, msg=None, delta=None)¶

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 between the two objects is more than the given delta.

Note that decimal places (from zero) are usually not the same as significant digits (measured from the most signficant digit).

If the two objects compare equal then they will automatically compare almost equal.

assertDictContainsSubset(expected, actual, msg=None)¶

Checks whether actual is a superset of expected.

assertDictEqual(d1, d2, msg=None)¶

assertEqual(first, second, msg=None)¶

Fail if the two objects are unequal as determined by the ‘==’ operator.

assertEquals(first, second, msg=None)¶

Fail if the two objects are unequal as determined by the ‘==’ operator.

assertFalse(expr, msg=None)¶

Check that the expression is false.

assertGreater(a, b, msg=None)¶

Just like self.assertTrue(a > b), but with a nicer default message.

assertGreaterEqual(a, b, msg=None)¶

Just like self.assertTrue(a >= b), but with a nicer default message.

assertIn(member, container, msg=None)¶

Just like self.assertTrue(a in b), but with a nicer default message.

assertIs(expr1, expr2, msg=None)¶

Just like self.assertTrue(a is b), but with a nicer default message.

assertIsInstance(obj, cls, msg=None)¶

Same as self.assertTrue(isinstance(obj, cls)), with a nicer default message.

assertIsNone(obj, msg=None)¶

Same as self.assertTrue(obj is None), with a nicer default message.

assertIsNot(expr1, expr2, msg=None)¶

Just like self.assertTrue(a is not b), but with a nicer default message.

assertIsNotNone(obj, msg=None)¶

Included for symmetry with assertIsNone.

assertItemsEqual(expected_seq, actual_seq, msg=None)¶

An unordered sequence specific comparison. It asserts that actual_seq and expected_seq have the same element counts. Equivalent to:

self.assertEqual(Counter(iter(actual_seq)),
                 Counter(iter(expected_seq)))

Asserts that each element has the same count in both sequences. Example:

• [0, 1, 1] and [1, 0, 1] compare equal.
• [0, 0, 1] and [0, 1] compare unequal.

assertLess(a, b, msg=None)¶

Just like self.assertTrue(a < b), but with a nicer default message.

assertLessEqual(a, b, msg=None)¶

Just like self.assertTrue(a <= b), but with a nicer default message.

assertListEqual(list1, list2, msg=None)¶

A list-specific equality assertion.

Args:

list1: The first list to compare. list2: The second list to compare. msg: Optional message to use on failure instead of a list of

differences.

assertMultiLineEqual(first, second, msg=None)¶

Assert that two multi-line strings are equal.

assertNotAlmostEqual(first, second, places=None, msg=None, delta=None)¶

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 between the two objects is less than the given delta.

Note that decimal places (from zero) are usually not the same as significant digits (measured from the most signficant digit).

Objects that are equal automatically fail.

assertNotAlmostEquals(first, second, places=None, msg=None, delta=None)¶

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 between the two objects is less than the given delta.

Note that decimal places (from zero) are usually not the same as significant digits (measured from the most signficant digit).

Objects that are equal automatically fail.

assertNotEqual(first, second, msg=None)¶

Fail if the two objects are equal as determined by the ‘!=’ operator.

assertNotEquals(first, second, msg=None)¶

Fail if the two objects are equal as determined by the ‘!=’ operator.

assertNotIn(member, container, msg=None)¶

Just like self.assertTrue(a not in b), but with a nicer default message.

assertNotIsInstance(obj, cls, msg=None)¶

Included for symmetry with assertIsInstance.

assertNotRegexpMatches(text, unexpected_regexp, msg=None)¶

Fail the test if the text matches the regular expression.

assertRaises(excClass, callableObj=None, *args, **kwargs)¶

Fail unless an exception of class excClass is raised by callableObj when invoked with arguments args and keyword arguments kwargs. If a different type of exception is raised, it will not be caught, and the test case will be deemed to have suffered an error, exactly as for an unexpected exception.

If called with callableObj omitted or None, will return a context object used like this:

with self.assertRaises(SomeException):
    do_something()

The context manager keeps a reference to the exception as the ‘exception’ attribute. This allows you to inspect the exception after the assertion:

with self.assertRaises(SomeException) as cm:
    do_something()
the_exception = cm.exception
self.assertEqual(the_exception.error_code, 3)

assertRaisesRegexp(expected_exception, expected_regexp, callable_obj=None, *args, **kwargs)¶

Asserts that the message in a raised exception matches a regexp.

Args:

expected_exception: Exception class expected to be raised. expected_regexp: Regexp (re pattern object or string) expected

to be found in error message.

callable_obj: Function to be called. args: Extra args. kwargs: Extra kwargs.

assertRegexpMatches(text, expected_regexp, msg=None)¶

Fail the test unless the text matches the regular expression.

assertSequenceEqual(seq1, seq2, msg=None, seq_type=None)¶

An equality assertion for ordered sequences (like lists and tuples).

For the purposes of this function, a valid ordered sequence type is one which can be indexed, has a length, and has an equality operator.

Args:

seq1: The first sequence to compare. seq2: The second sequence to compare. seq_type: The expected datatype of the sequences, or None if no

datatype should be enforced.

msg: Optional message to use on failure instead of a list of

differences.

assertSetEqual(set1, set2, msg=None)¶

A set-specific equality assertion.

Args:

set1: The first set to compare. set2: The second set to compare. msg: Optional message to use on failure instead of a list of

differences.

assertSetEqual uses ducktyping to support different types of sets, and is optimized for sets specifically (parameters must support a difference method).

assertTrue(expr, msg=None)¶

Check that the expression is true.

assertTupleEqual(tuple1, tuple2, msg=None)¶

A tuple-specific equality assertion.

Args:

tuple1: The first tuple to compare. tuple2: The second tuple to compare. msg: Optional message to use on failure instead of a list of

differences.

assert_(expr, msg=None)¶

Check that the expression is true.

countTestCases()¶

debug()¶

Run the test without collecting errors in a TestResult

defaultTestResult()¶

doCleanups()¶

Execute all cleanup functions. Normally called for you after tearDown.

fail(msg=None)¶

Fail immediately, with the given message.

failIf(*args, **kwargs)¶

failIfAlmostEqual(*args, **kwargs)¶

failIfEqual(*args, **kwargs)¶

failUnless(*args, **kwargs)¶

failUnlessAlmostEqual(*args, **kwargs)¶

failUnlessEqual(*args, **kwargs)¶

failUnlessRaises(*args, **kwargs)¶

id()¶

run(result=None)¶

setUp()¶

classmethod setUpClass()¶

Hook method for setting up class fixture before running tests in the class.

shortDescription()¶

Returns a one-line description of the test, or None if no description has been provided.

The default implementation of this method returns the first line of the specified test method’s docstring.

skipTest(reason)¶

Skip this test.

tearDown()¶

Hook method for deconstructing the test fixture after testing it.

classmethod tearDownClass()¶

Hook method for deconstructing the class fixture after running all tests in the class.

test_perfect()¶

Perfect resolution and no smearing.

test_pinhole()¶

Pinhole smearing with dQ = 0.001 [Note: not dQ/Q = 0.001]

test_pinhole_zero()¶

Pinhole smearing with perfect resolution

test_slit_both_high(*args, **kwargs)¶

Slit smearing with width < 100*height.

test_slit_both_wide(*args, **kwargs)¶

Slit smearing with width > 100*height.

test_slit_high(*args, **kwargs)¶

Slit smearing with height 0.005

test_slit_wide(*args, **kwargs)¶

Slit smearing with width 0.0002

test_slit_zero()¶

Slit smearing with perfect resolution.

longMessage = False¶

maxDiff = 640¶

class sasmodels.resolution.Slit1D(q, width, height, q_calc=None)¶

Bases: sasmodels.resolution.Resolution

Slit aperture with a complicated resolution function.

q points at which the data is measured.

qx_width slit width

qy_height slit height

q_calc is the list of points to calculate, or None if this should be estimated from the q and q_width.

The weight_matrix is computed by slit1d_resolution()

apply(theory)¶

q = None¶

q_calc = None¶

sasmodels.resolution.apply_resolution_matrix(weight_matrix, theory)¶

Apply the resolution weight matrix to the computed theory function.

sasmodels.resolution.bin_edges(x)¶

Determine bin edges from bin centers, assuming that edges are centered between the bins.

Note: this uses the arithmetic mean, which may not be appropriate for log-scaled data.

sasmodels.resolution.demo()¶

sasmodels.resolution.demo_pinhole_1d()¶

sasmodels.resolution.demo_slit_1d()¶

sasmodels.resolution.eval_form(q, form, pars)¶

sasmodels.resolution.gaussian(q, q0, dq)¶

sasmodels.resolution.geometric_extrapolation(q, q_min, q_max, points_per_decade=None)¶

Extrapolate q to [q_min, q_max] using geometric steps, with the average geometric step size in q as the step size.

if q_min is zero or less then q[0]/10 is used instead.

points_per_decade sets the ratio between consecutive steps such that there will be \(n\) points used for every factor of 10 increase in q.

If points_per_decade is not given, it will be estimated as follows. Starting at \(q_1\) and stepping geometrically by \(\Delta q\) to \(q_n\) in \(n\) points gives a geometric average of:

\[\log \Delta q = (\log q_n - log q_1) / (n - 1)\]

From this we can compute the number of steps required to extend \(q\) from \(q_n\) to \(q_\text{max}\) by \(\Delta q\) as:

\[n_\text{extend} = (\log q_\text{max} - \log q_n) / \log \Delta q\]

Substituting:

n_text{extend} = (n-1) (log q_text{max} - log q_n)

/ (log q_n - log q_1)

sasmodels.resolution.interpolate(q, max_step)¶

Returns q_calc with points spaced at most max_step apart.

sasmodels.resolution.linear_extrapolation(q, q_min, q_max)¶

Extrapolate q out to [q_min, q_max] using the step size in q as a guide. Extrapolation below uses about the same size as the first interval. Extrapolation above uses about the same size as the final interval.

if q_min is zero or less then q[0]/10 is used instead.

sasmodels.resolution.main()¶

Run tests given is sys.argv.

Returns 0 if success or 1 if any tests fail.

sasmodels.resolution.pinhole_extend_q(q, q_width, nsigma=3)¶

Given q and q_width, find a set of sampling points q_calc so that each point I(q) has sufficient support from the underlying function.

sasmodels.resolution.pinhole_resolution(q_calc, q, q_width)¶

Compute the convolution matrix W for pinhole resolution 1-D data.

Each row W[i] determines the normalized weight that the corresponding points q_calc contribute to the resolution smeared point q[i]. Given W, the resolution smearing can be computed using dot(W,q).

q_calc must be increasing. q_width must be greater than zero.

sasmodels.resolution.q_to_u(q, q0)¶

Convert q values to u values for the integral computed at q0.

sasmodels.resolution.romberg_pinhole_1d(q, q_width, form, pars, nsigma=5)¶

Romberg integration for pinhole resolution.

This is an adaptive integration technique. It is called with settings that make it slow to evaluate but give it good accuracy.

sasmodels.resolution.romberg_slit_1d(q, delta_qv, form, pars)¶

Romberg integration for slit resolution.

This is an adaptive integration technique. It is called with settings that make it slow to evaluate but give it good accuracy.

sasmodels.resolution.slit_extend_q(q, width, height)¶

Given q, width and height, find a set of sampling points q_calc so that each point I(q) has sufficient support from the underlying function.

sasmodels.resolution.slit_resolution(q_calc, q, width, height)¶

Build a weight matrix to compute I_s(q) from I(q_calc), given \(q_v\) = width and \(q_h\) = height.

width and height are scalars since current instruments use the same slit settings for all measurement points.

If slit height is large relative to width, use:

\[I_s(q_o) = \frac{1}{\Delta q_v} \int_0^{\Delta q_v} I(\sqrt{q_o^2 + u^2} du\]

If slit width is large relative to height, use:

\[I_s(q_o) = \frac{1}{2 \Delta q_v} \int_{-\Delta q_v}^{\Delta q_v} I(u) du\]