Stddev calculations #5

enritoomey · 2017-11-08T20:41:02Z

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enritoomey · 2017-11-08T21:29:01Z

@Juanlu001 @gilgamezh como arreglo esto?

matiasg · 2017-11-08T22:00:13Z

@enritoomey , creo que hay que mergear primero el PR de @gilgamezh para que travis sepa de qué se trata el proyecto.

gilgamezh · 2017-11-09T00:45:04Z

@henry-aocs please merge master to this branch to get the tests working

coveralls · 2017-11-09T14:15:56Z

Coverage decreased (-5.0%) to 85.185% when pulling 9896d78 on stddev_calculations into 28dba2a on master.

coveralls · 2017-11-09T14:15:56Z

Coverage decreased (-5.0%) to 85.185% when pulling 9896d78 on stddev_calculations into 28dba2a on master.

coveralls · 2017-11-09T14:15:56Z

Coverage decreased (-5.0%) to 85.185% when pulling 9896d78 on stddev_calculations into 28dba2a on master.

coveralls · 2017-11-09T14:15:56Z

Coverage decreased (-5.0%) to 85.185% when pulling 9896d78 on stddev_calculations into 28dba2a on master.

enritoomey · 2017-11-09T14:36:24Z

el covarage da bajo porque agregue una funcion que no testeo.... en el proximo commit le agrego el test y saco el wip

coveralls · 2017-11-09T19:05:10Z

Coverage increased (+1.8%) to 91.981% when pulling c85723c on stddev_calculations into 28dba2a on master.

enritoomey · 2017-11-09T21:27:36Z

@gilgamezh @matiasg estoy esperando su +1

enritoomey · 2017-11-13T13:58:02Z

@Juanlu001, queres darle una mirada a este MR?

astrojuanlu

Despite some minor comments and typos this looks good to me, however bear in mind that I didn't review the math in depth. There are lots of tests against MATLAB though, which is very nice.

astrojuanlu · 2017-11-13T14:05:15Z

quaternions/quaternions.py

@@ -1,7 +1,7 @@
 import functools
 import numpy as np
 from collections import Iterable
-
+from quaternions.utils import (covariance_matrix_from_angles, sigma_lerner, orthogonal_matrix)


No need to have parentheses here

yes, but i was @matiasg style to put then anyway

parentheses there are needed when you need to split into multiple lines. Otherwise, they are not.
I'm not saying that I always go by this rule, but it's the best rule I can produce ;-)

astrojuanlu · 2017-11-13T14:06:56Z

quaternions/quaternions.py

        '''
        Return the quaternion such that its matrix minimizes the square distance
        to the matrices of the quaternions in the argument list.

        See Averaging Quaternions, by Markley, Cheng, Crassidis, Oschman.
        '''
        B = np.array([q.coordinates for q in quaternions])
-        if not weights:
+        if not any(True for _ in weights):


Why this instead of the empty list/tuple?

I'll change it to: use None as default value for weights, and then check if weights is None.

astrojuanlu · 2017-11-13T14:07:03Z

quaternions/quaternions.py

+        Naive implementation of std. dev. calculation, assuming small angles between quaternions
+        and average. Returns average quaternion and stddev of input quaternion list in deg
+        """
+        if not any(True for _ in weights):


Same as above

astrojuanlu · 2017-11-13T14:07:18Z

quaternions/quaternions.py

+            weights = np.ones(len(quaternions))
+        q_average = Quaternion.average(*quaternions, weights=weights)
+        diffs = np.array([q_average.distance(quat) for quat in quaternions])
+        # TODO: check that this way of taking into account weights in stddev calculation is ok


I'd say it's ok!

astrojuanlu · 2017-11-13T14:07:37Z

quaternions/quaternions.py

+        called sigma lerner. This covariance matriz is the one asociated with the rotation angles of
+        each input quaternion agains the average one. Returns the average quaternion anf the sigma lerner
+        in deg.
+        :param quaternions: lista de objetos Quaternion


Se escapó un comentario en español :)

Yo no hablar español... jajja, ahora lo corrigo

astrojuanlu · 2017-11-13T14:13:23Z

quaternions/quaternions.py

+    @staticmethod
+    def average_and_std_lerner(*quaternions, weights=()):
+        """
+        Calculates the std. dev. as 1.87 of the root of the maximum eigenvalue of the covariance matrix,


I am not an expert on quaternions, but Google didn't show any relevant results on "quaternions" "sigma lerner" and variations. Perhaps it's coming from some article by Gerald M. Lerner? Is there a chance we can document this a bit more?

certainly, i have to track down the paper from which this way of condensing a correlation matrix to a single value was taken...

astrojuanlu · 2017-11-13T14:13:39Z

quaternions/quaternions.py

+    def average_and_std_lerner(*quaternions, weights=()):
+        """
+        Calculates the std. dev. as 1.87 of the root of the maximum eigenvalue of the covariance matrix,
+        called sigma lerner. This covariance matriz is the one asociated with the rotation angles of


"matriz", "anf"

astrojuanlu · 2017-11-13T14:15:14Z

quaternions/quaternions.py

+            orthogonal_matrix_sum += orthogonal_matrix(q).dot(
+                R_inverse.dot(orthogonal_matrix(q).T))
+
+        cov_dev_matrix = np.linalg.inv(orthogonal_matrix(q_average).T.dot(


I guess the code is required to run in Python 3.4? Otherwise you could use orthogonal_matrix(q_average).T @ orthogonal_matrix_sum @ orthogonal_matrix(q_average).

yeap, I still fun python 3.4 in my debian8 installation 😳 Do we have a requisite on the python version?

We have travis now, that tests the code from python 3.4 until 3.6.
And 3.4 is needed, sadly.

astrojuanlu · 2017-11-13T14:16:10Z

quaternions/utils.py

+    """
+    covariance_matrix = np.zeros((3, 3))
+    for angles in angles_list:
+        covariance_matrix += np.outer(angles.T, angles)


I guess angles_list is a list of NumPy arrays, right?

astrojuanlu · 2017-11-13T14:16:37Z

tests/test_quaternions.py

+                        * np.sqrt(len(quat_diff_matlab_quats)-1)
+
+            assert abs(sigma_lerner_in_deg - sigma_lerner_out_deg ) \
+                   < self.tolerance_deg


Missing newline

coveralls · 2017-11-15T10:57:22Z

Coverage increased (+1.8%) to 91.981% when pulling 5616a6e on stddev_calculations into 28dba2a on master.

astrojuanlu

Although it would be nice to know from which Lerner paper does the covariance come, I'm approving these changes.

astrojuanlu · 2017-11-15T11:00:48Z

...although some tests fail in Python 3.6 :)

matiasg

We should first merge the PR splitting quaternions into two classes and then merge this one. Anyway, there should be almost no changes in this PR for that.
Mostly, I'd like some function names to change.

matiasg · 2017-11-21T21:24:00Z

quaternions/utils.py

@@ -0,0 +1,38 @@
+import numpy as np


please, add the reference to the paper(s) you are implementing here.
Also, in the methods, there could be a line like equation 2.3 from (1), or any other citation like this one.

Still missing the reference paper to the sigma lerner calculation

matiasg · 2017-11-21T21:25:51Z

quaternions/utils.py

+                     [-quaternion.qj, quaternion.qi, 0]])
+
+
+def orthogonal_matrix(quaternion):


I strongly oppose to this name :-P
This matrix is not square, so it is not an orthogonal matrix.

matiasg · 2017-11-21T21:27:48Z

quaternions/utils.py

+    return 1.87 * np.sqrt(max(values))
+
+
+def rotation_matrix(quaternion):


this is not a rotation matrix, but the matrix of a cross product with the vector [qi, qj, qk].
The name cross_product_matrix might be better. It could also have the same name it has in the paper where it comes from.

coveralls · 2017-11-28T21:38:23Z

Coverage increased (+1.009%) to 96.899% when pulling 881db4f on stddev_calculations into 8f57a95 on master.

coveralls · 2017-11-28T21:47:16Z

Coverage increased (+1.009%) to 96.899% when pulling 88800e8 on stddev_calculations into 8f57a95 on master.

coveralls · 2017-11-28T21:47:16Z

Coverage increased (+1.009%) to 96.899% when pulling 88800e8 on stddev_calculations into 8f57a95 on master.

coveralls · 2017-11-29T03:24:36Z

Coverage increased (+1.009%) to 96.899% when pulling d12da5d on stddev_calculations into 8f57a95 on master.

coveralls · 2017-11-29T03:24:36Z

Coverage increased (+1.009%) to 96.899% when pulling d12da5d on stddev_calculations into 8f57a95 on master.

matiasg

Ok for me after a few changes are made.

matiasg · 2017-11-29T12:27:31Z

quaternions/quaternion.py

+            weights = np.ones(len(quaternions))
+        q_average = Quaternion.average(*quaternions, weights=weights)
+        diffs = np.array([q_average.distance(quat) for quat in quaternions])
+        # TODO: check that this way of taking into account weights in stddev calculation is ok


this is what you do with any zero-mean random variable to compute its standard deviation:
sqrt( sum ( x ** 2 * p(x) ) )

matiasg · 2017-11-29T12:33:03Z

quaternions/quaternion.py

+    @staticmethod
+    def average_and_std_naive(*quaternions, weights=None):
+        """
+        Naive implementation of std. dev. calculation, assuming small angles between quaternions


why do you need small angles?

I really don't know why I put that docstring.

matiasg · 2017-11-29T12:50:52Z

quaternions/quaternion.py

+        """
+        q_average = Quaternion.average(*quaternions, weights=weights)
+        diffs = [quat / q_average for quat in quaternions]
+        angles_list = np.array([[2 * diff.coordinates[i] for i in [1, 2, 3]] for diff in diffs])


I think you can do here

angles_list = [2 * diff.coordinates[1:] for diff in diffs]

You don't need it to be a numpy array, anyway

actually, the RAX paper works with Gibbs vectors, which are

diff.coordinates[1:] / diff.qr

yes, actually there's a factor of two. I'll open an issue

matiasg · 2017-11-29T12:51:12Z

quaternions/quaternion.py

+        """
+        Calculates the std. dev. as 1.87 of the root of the maximum eigenvalue of the covariance matrix,
+        called sigma lerner. This covariance matrix is the one asociated with the rotation angles of
+        each input quaternion agains the average one. Returns the average quaternion and the sigma lerner


matiasg · 2017-11-29T12:58:02Z

quaternions/utils.py

+    """
+    covariance_matrix = np.zeros((3, 3))
+    for angles in angles_list:
+        covariance_matrix += np.outer(angles.T, angles)


it seems that these three lines can be

covariance_matrix = sum(np.outer(angles, angles) for angles in angles_list)

or, if you already receive a numpy.array, by

covariance_matrix = angles_list.T.dot(angles_list)

matiasg · 2017-11-29T14:20:00Z

quaternions/quaternion.py

+        Returns the quaternion such that its matrix minimizes the square distance
+        to the matrices of the quaternions in the argument list, and the resulting
+        covariance matrix asociated with that quaternion. Input matrix R (3x3) is
+        assume to be the same for all input quaternions, and in rads**2


matiasg · 2017-11-29T14:20:47Z

quaternions/quaternion.py

+        '''
+        Returns the quaternion such that its matrix minimizes the square distance
+        to the matrices of the quaternions in the argument list, and the resulting
+        covariance matrix asociated with that quaternion. Input matrix R (3x3) is


associated

coveralls · 2017-11-29T15:19:21Z

Coverage increased (+1.0%) to 96.875% when pulling df4485f on stddev_calculations into 8f57a95 on master.

coveralls · 2017-11-29T15:26:55Z

Coverage increased (+1.0%) to 96.875% when pulling 5fa4f58 on stddev_calculations into 8f57a95 on master.

coveralls · 2017-11-29T15:26:55Z

Coverage increased (+1.0%) to 96.875% when pulling 5fa4f58 on stddev_calculations into 8f57a95 on master.

coveralls · 2017-11-29T15:26:55Z

Coverage increased (+1.0%) to 96.875% when pulling 5fa4f58 on stddev_calculations into 8f57a95 on master.

coveralls · 2017-11-29T15:26:55Z

Coverage increased (+1.0%) to 96.875% when pulling 5fa4f58 on stddev_calculations into 8f57a95 on master.

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henry-aocs added 5 commits November 8, 2017 16:21

add methods to calculate average and stddev

cef2154

add tests to stddev calculation methods

496e4ca

add estxa functions to utils

69f0802

minor changes

0050ba8

change way of checking if weights input is empty

69f0939

Merge remote-tracking branch 'origin/master' into stddev_calculations

9896d78

enriquecarlostoomey added 3 commits November 9, 2017 15:53

refactor average_and_std_teoretical method to average_and_covariance

0c8c65c

add test for average_and_covariance method

e89ed1a

small refactor in average_and_naive and average_and_sigma_lener methods

c85723c

enritoomey changed the title ~~[WIP] Stddev calculations~~ Stddev calculations Nov 9, 2017

astrojuanlu suggested changes Nov 13, 2017

View reviewed changes

junlu's review

5616a6e

astrojuanlu approved these changes Nov 15, 2017

View reviewed changes

matiasg reviewed Nov 21, 2017

View reviewed changes

Merge branch 'master' into stddev_calculations

881db4f

rename auxiliary functions and improve docstring

88800e8

add reference paper for sigma lerner calculation docstring

d12da5d

matiasg approved these changes Nov 29, 2017

View reviewed changes

enriquecarlostoomey added 3 commits November 29, 2017 12:13

fix docstrings

f765db2

refactor covariance_matrix usage to make code more compact and clear

df4485f

bug in sigma_lerner calculation

5fa4f58

enritoomey merged commit 10a0adc into master Nov 29, 2017

enritoomey deleted the stddev_calculations branch March 19, 2020 23:54

		[-quaternion.qj, quaternion.qi, 0]])


		def orthogonal_matrix(quaternion):

		return 1.87 * np.sqrt(max(values))


		def rotation_matrix(quaternion):

Stddev calculations #5

Stddev calculations #5

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enritoomey commented Nov 8, 2017

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