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+# Sphinx build info version 1
+# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
+config: 80e4a40933bfdc4bb51210288adb974d
+tags: 645f666f9bcd5a90fca523b33c5a78b7

pull/9/_sources/blog.rst.txt

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+====
+Blog
+====

pull/9/_sources/developers.rst.txt

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+.. _dipy_developers:
+
+Developers
+==========
+
+The core development team consists of the following individuals:
+
+- **Eleftherios Garyfallidis**, Indiana University, IN, USA
+- **Ariel Rokem**, University of Washington, WA, USA
+- **Matthew Brett**, Birmingham University, Birmingham, UK
+- **Bago Amirbekian**, Databricks, San Francisco, CA, USA
+- **Omar Ocegueda**, Google, San Francisco, CA
+- **Marc-Alexandre Côté**,  Microsoft Research, Montreal, QC, CA
+- **Serge Koudoro**, Indiana University, IN, USA
+- **Gabriel Girard**, Swiss Federal Institute of Technology (EPFL), Lausanne, CH
+- **Rafael Neto Henriques**, Cambridge University, UK
+- **Matthieu Dumont**, Imeka, Sherbrooke, QC, CA
+- **Ranveer Aggarwal**, Microsoft, Hyderabad, Telangana, India
+
+And here is the rest of the wonderful contributors:
+
+- **Ian Nimmo-Smith**, retired, formerly at MRC Cognition and Brain Sciences Unit, Cambridge, UK
+- **Maxime Descoteaux**, University of Sherbrooke, QC, CA
+- **Stefan Van der Walt**, University of California, Berkeley, CA, USA
+- **Jean-Christophe Houde**, University of Sherbrooke, QC, CA and Imeka, Sherbrooke, QC, CA
+- **Francois Rhéault**, University of Sherbrooke, QC, CA
+- **Samuel St-Jean**, University Medical Center (UMC) Utrecht, Utrecht, NL
+- **Michael Paquette**, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, DE
+- **Christopher Nguyen**,  Massachusetts General Hospital, MA, USA
+- **Emanuele Olivetti**, NeuroInformatics Laboratory (NILab), Trento, IT
+- **Yaroslav Halchenco**, PBS Department, Dartmouth, NH, USA
+- **Emmanuel Caruyer**, Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), University of Rennes I, Rennes, FR
+- **Sylvain Merlet**, INRIA, Sophia-Antipolis, FR
+- **Erick Ziegler**, Université de Liège, BE
+- **Kimberly Chan**, Stanford University, CA, USA
+- **Chantal Tax**, Cardiff University, Cardiff, UK
+- **Demian Wassermann**, INRIA, Sophia Antipolis, FR
+- **Mauro Zucchelli**, INRIA, Sophia-Antipolis, France
+- **Rutger Fick**, INRIA, Sophia Antipolis, FR
+- **Gregory R. Lee**, Cincinnati Children's Hospital Medical Center, Cincinnati, OH, USA
+- **Endolith**, New-York, NY, USA
+- **Matthias Ekman**, Donders Institute for Brain, Cognition and Behaviour, Nijmegen, NL
+- **Andrew Lawrence**, University of Cambridge, Cambridge, UK
+- **Kesshi Jordan**, University of California, San Francisco, CA, USA
+- **Maria Luisa Mandelli**, University of California, San Francisco, CA, USA
+- **Adam Rybinski**, Jagiellonian University, Krakow, PL
+- **Qiyuan Tian**, Stanford University, Stanford, CA, USA
+- **Jon Haitz Legarreta Gorroño**, University of Sherbrooke, QC, CA
+- **Rafael Neto Henriques**, Champalimaud Neuroscience Programme, Champalimaud Centre for the Unknown, Lisbon, PT
+- **Stephan Meesters**, Eindhoven University of Technology, NL
+- **Himanshu Mishra**, Indian Institute of Technology, Karaghpur, IN
+- **Alexander Gauvin**, University of Sherbrooke, QC, CA
+- **Oscar Esteban**, Stanford University, CA, US
+- **Bishakh Ghosh**, National Institute of Technology, Durgapur, IN
+- **Dimitris Rozakis**, Tomotech, Athens, GR
+- **Rohan Prinja**, Indian Institute of Technology, Bombay, IN
+- **Sagun Pai**, Indian Institute of Technology, Bombay, IN
+- **Vatsala Swaroop**, Mombai, IN
+- **Shahnawaz Ahmed**, Birla Institute of Technology and Science, Pilani, Goa, IN
+- **Nil Goyette**, Imeka, Sherbrooke, QC, CA
+- **Scott Trinkle**, University of Chicago, IL, USA
+- **Kevin R. Sitek**, MIT McGovern Institute for Brain Research, MA, USA
+- **Derek Pisner**, University of Texas at Austin, USA
+- **Ross Lawrence**, Johns Hopkins University, USA
+- **Eric Larson**, University of Washington, USA
+- **Jakob Wasserthal**, German Cancer Research Center, DE
+- **Bramsh Qamar Chandio**, Indiana University, IN, USA
+- **Javier Guaje**, Indiana University, IN, USA
+- **Shreyas Fadnavis**, Indiana University,  IN, USA
+- **Matt Cieslak**, University of Pennsylvania, USA
+- **Sven Dorkenwald**, Princeton University, USA
+
+
+
+Boundless collaboration is in the heart of DIPY_. We encourage everyone from anywhere in the world to join the team. You can start sharing your code `here`__. If you want to contribute but you don't know in area to focus, please send us an e-mail. We will be more than happy to help.
+
+__ `dipy github`_
+
+.. include:: links_names.inc

pull/9/_sources/documentation.rst.txt

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+.. _documentation:
+
+Documentation
+===============
+
+.. This tree is helping populate the side navigation panel
+.. toctree::
+   :maxdepth: 2
+
+   introduction
+   mission
+   installation
+   faq
+   developers
+
+.. Main content will be displayed using the jinja template
+
+

pull/9/_sources/faq.rst.txt

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+.. _faq:
+
+==========================
+Frequently Asked Questions
+==========================
+
+-----------
+Theoretical
+-----------
+
+1. **What is a b-value?**
+
+  The b-value $b$ or *diffusion weighting* is a function of the
+  strength, duration and temporal spacing and timing parameters of the
+  specific paradigm. This function is derived from the Bloch-Torrey
+  equations. In the case of the classical Stejskal-Tanner
+  pulsed gradient spin-echo (PGSE) sequence, at the time of readout
+  $b=\gamma^{2}G^{2}\delta^{2}\left(\Delta-\frac{\delta}{3}\right)$
+  where $\gamma$ is the gyromagnetic ratio, $\delta$ denotes the pulse
+  width, $G$ is the gradient amplitude and $\Delta$ the center-to-center
+  spacing. $\gamma$ is a constant, but we can change the other
+  three parameters and in that way control the b-value.
+
+2. **What is q-space?**
+
+  Q-space is the space of one or more 3D spin displacement wave vectors
+  $\mathbf{q}$. The vector $\mathbf{q}$
+  parametrizes the space of diffusion gradients. It is related to the
+  applied magnetic gradient $\mathbf{g}$ by the formula
+  $\mathbf{q}=(2\pi)^{-1}\gamma\delta\mathbf{g}$.
+  Every single vector $\mathbf{q}$ has the same orientation as the
+  direction of diffusion gradient $\mathbf{g}$ and length proportional
+  to the strength $g$ of the gradient field. Every single point in
+  q-space corresponds to a possible 3D volume of the MR signal for a specific
+  gradient direction and strength. Therefore if, for example, we have
+  programmed the scanner to apply 60 gradient directions, then our data
+  should have 60 diffusion volumes, with each volume obtained for a specific
+  gradient. A Diffusion Weighted Image (DWI) is the volume acquired
+  from only one direction gradient.
+
+3. **What does DWI stand for?**
+
+  Diffusion Weighted Imaging (DWI) is MRI imaging designed to be sensitive
+  to diffusion. A diffusion weighted image is a volume of voxel data gathered
+  by applying only one gradient direction
+  using a diffusion sequence. We expect that the signal in any voxel
+  should be low if there is greater mobility of water molecules along
+  the specified gradient direction and it should be high if there is
+  less movement in that direction. Yes, it is counterintuitive but correct!
+  However, greater mobility gives greater opportunity for the proton spins to
+  be dephased, producing a smaller RF signal.
+
+4. **Why dMRI and not DTI?**
+
+  Diffusion MRI (dMRI or dwMRI) are the preferred terms if you want to speak
+  about diffusion weighted MRI in general. DTI (diffusion tensor imaging) is
+  just one of the many ways you can reconstruct the voxel from your measured
+  signal. There are plenty of others, for example DSI, GQI, QBI, etc.
+
+5. **What is the difference between Image coordinates and World coordinates?**
+
+  Image coordinates have positive integer values and represent the centres
+  $(i, j, k)$ of the voxels. There is an affine transform (stored in the
+  nifti file) that takes the image coordinates and transforms them into
+  millimeter (mm) in real world space. World coordinates have floating point
+  precision and your dataset has 3 real dimensions e.g. $(x, y, z)$.
+
+6. **We generated dMRI datasets with nonisotropic voxel sizes. What do we do?**
+
+  You need to resample your raw data to an isotropic size. Have a look at
+  the module ``dipy.align.aniso2iso``. (We think it is a mistake to
+  acquire nonisotropic data because the directional resolution of the data
+  will depend on the orientation of the gradient with respect to the
+  voxels, being lower when aligned with a longer voxel dimension.)
+
+7. **Why are non-isotropic voxel sizes a bad idea in diffusion?**
+
+  If, for example, you have $2 \times 2 \times 4\ \textrm{mm}^3$ voxels, the
+  last dimension will be averaged over the double distance and less detail
+  will be captured compared to the other two dimensions. Furthermore, with
+  very anisotropic voxels the uncertainty on orientation estimates will
+  depend on the position of the subject in the scanner.
+
+---------
+Practical
+---------
+
+1. **Why Python and not MATLAB or some other language?**
+
+  Python is free, batteries included, very well-designed, painless to read
+  and easy to use.
+  There is nothing else like it. Give it a go.
+  Once with Python, always with Python.
+
+2. **Isn't Python slow?**
+
+  True, sometimes Python can be slow if you are using multiple nested
+  ``for`` loops, for example.
+  In that case, we use Cython_, which takes execution up to C speed.
+
+3. **What numerical libraries do you use in Python?**
+
+  The best ever designed numerical library - NumPy_.
+
+2. **Which Python console do you recommend?**
+
+  IPython_
+
+3. **What do you use for visualization?**
+
+  For 3D visualization, we use ``dipy.viz`` which depends in turn on ``FURY``::
+
+    from dipy.viz import window, actor
+
+  For 2D visualization we use matplotlib_.
+
+4. **Which file formats do you support?**
+
+  Nifti (.nii), Dicom (Siemens(read-only)), Trackvis (.trk), DIPY (.dpy),
+  Numpy (.npy, ,npz), text and any other formats supported by nibabel and
+  pydicom.
+
+  You can also read/save in Matlab version v4 (Level 1.0), v6 and v7 to 7.2,
+  using `scipy.io.loadmat`. For higher versions >= 7.3, you can use pytables_
+  or any other python-to-hdf5 library e.g. h5py.
+
+  For object serialization, you can use ``dipy.io.pickles`` functions
+  ``load_pickle``, ``save_pickle``.
+
+5. **What is dpy**?
+
+  ``dpy`` is an ``hdf5`` file format that we use in DIPY to store
+  tractography and other information. This allows us to store huge
+  tractography and load different parts of the datasets
+  directly from the disk as if it were in memory.
+
+6. **Which python editor should I use?**
+
+  Any text editor would do the job but we prefer the following: PyCharm, Sublime, Aptana, Emacs, Vim and Eclipse (with PyDev).
+
+7. **I have problems reading my dicom files using nibabel, what should I do?**
+
+  Use Chris Rorden's dcm2nii to transform them into nifti files.
+  http://www.cabiatl.com/mricro/mricron/dcm2nii.html
+  Or you can make your own reader using pydicom.
+  http://code.google.com/p/pydicom/
+  and then use nibabel to store the data as nifti.
+
+8. **Where can I find diffusion data?**
+
+  There are many sources for openly available diffusion MRI. the :mod:`dipy.data` module can be used to download some sample datasets that we use in our examples. In addition there are a lot of large research-grade datasets available through the following sources:
+
+    - http://fcon_1000.projects.nitrc.org/
+    - https://www.humanconnectome.org/
+    - https://openneuro.org/
+
+.. include:: links_names.inc

pull/9/_sources/gimbal_lock.rst.txt

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+.. _gimbal-lock:
+
+=============
+ Gimbal lock
+=============
+
+See also: http://en.wikipedia.org/wiki/Gimbal_lock
+
+Euler angles have a major deficiency, and that is, that it is possible,
+in some rotation sequences, to reach a situation where two of the three
+Euler angles cause rotation around the same axis of the object.  In the
+case below, rotation around the $x$ axis becomes indistinguishable in
+its effect from rotation around the $z$ axis, so the $z$ and $x$ axis
+angles collapse into one transformation, and the rotation reduces from
+three degrees of freedom to two.
+
+Imagine that we are using the Euler angle convention of starting with a
+rotation around the $x$ axis, followed by the $y$ axis, followed by the
+$z$ axis.
+
+Here we see a Spitfire aircraft, flying across the screen.  The $x$ axis
+is left to right (tail to nose), the $y$ axis is from the left wing tip
+to the right wing tip (going away from the screen), and the $z$ axis is
+from bottom to top:
+
+.. image:: images/spitfire_0.png
+
+Imagine we wanted to do a slight roll with the left wing tilting down
+(rotation about $x$) like this:
+
+.. image:: images/spitfire_x.png
+
+followed by a violent pitch so we are pointing straight up (rotation
+around $y$ axis):
+
+.. image:: images/spitfire_y.png
+
+Now we'd like to do a turn of the nose towards the viewer (and the tail
+away from the viewer):
+
+.. image:: images/spitfire_hoped.png
+
+But, wait, let's go back over that again.  Look at the result of the
+rotation around the $y$ axis.  Notice that the $x$ axis, as was, is now
+aligned with the $z$ axis, as it is now.  Rotating around the $z$ axis
+will have exactly the same effect as adding an extra rotation around the
+$x$ axis at the beginning.  That means that when there is a $y$ axis
+rotation that rotates the $x$ axis onto the $z$ axis (a rotation of
+$\pm\pi/2$ around the $y$ axis) - the $x$ and $y$ axes are "locked"
+together.
+
+Mathematics of gimbal lock
+==========================
+
+We see gimbal lock for this type of Euler axis convention, when
+$\cos(\beta) = 0$, where $\beta$ is the angle of rotation around the $y$
+axis.  By "this type of convention" we mean using rotation around all 3
+of the $x$, $y$ and $z$ axes, rather than using the same axis twice -
+e.g. the physics convention of $z$ followed by $x$ followed by $z$ axis
+rotation (the physics convention has different properties to its gimbal
+lock).
+
+We can show how gimbal lock works by creating a rotation matrix for the
+three component rotations. Recall that, for a rotation of $\alpha$
+radians around $x$, followed by a rotation $\beta$ around $y$, followed
+by rotation $\gamma$ around $z$, the rotation matrix $R$ is:
+
+.. math::
+
+   R = \left(\begin{smallmatrix}\operatorname{cos}\left(\beta\right) \operatorname{cos}\left(\gamma\right) & - \operatorname{cos}\left(\alpha\right) \operatorname{sin}\left(\gamma\right) + \operatorname{cos}\left(\gamma\right) \operatorname{sin}\left(\alpha\right) \operatorname{sin}\left(\beta\right) & \operatorname{sin}\left(\alpha\right) \operatorname{sin}\left(\gamma\right) + \operatorname{cos}\left(\alpha\right) \operatorname{cos}\left(\gamma\right) \operatorname{sin}\left(\beta\right)\\\operatorname{cos}\left(\beta\right) \operatorname{sin}\left(\gamma\right) & \operatorname{cos}\left(\alpha\right) \operatorname{cos}\left(\gamma\right) + \operatorname{sin}\left(\alpha\right) \operatorname{sin}\left(\beta\right) \operatorname{sin}\left(\gamma\right) &- \operatorname{cos}\left(\gamma\right) \operatorname{sin}\left(\alpha\right) + \operatorname{cos}\left(\alpha\right) \operatorname{sin}\left(\beta\right) \operatorname{sin}\left(\gamma\right)\\- \operatorname{sin}\left(\beta\right) & \operatorname{cos}\left(\beta\right) \operatorname{sin}\left(\alpha\right) & \operatorname{cos}\left(\alpha\right) \operatorname{cos}\left(\beta\right)\end{smallmatrix}\right)
+
+When $\cos(\beta) = 0$, $\sin(\beta) = \pm1$ and $R$ simplifies to:
+
+.. math::
+
+     R = \left(\begin{smallmatrix}0 & - \operatorname{cos}\left(\alpha\right) \operatorname{sin}\left(\gamma\right) + \pm{1} \operatorname{cos}\left(\gamma\right) \operatorname{sin}\left(\alpha\right) & \operatorname{sin}\left(\alpha\right) \operatorname{sin}\left(\gamma\right) + \pm{1} \operatorname{cos}\left(\alpha\right) \operatorname{cos}\left(\gamma\right)\\0 & \operatorname{cos}\left(\alpha\right) \operatorname{cos}\left(\gamma\right) + \pm{1} \operatorname{sin}\left(\alpha\right) \operatorname{sin}\left(\gamma\right) & - \operatorname{cos}\left(\gamma\right) \operatorname{sin}\left(\alpha\right) + \pm{1} \operatorname{cos}\left(\alpha\right) \operatorname{sin}\left(\gamma\right)\\- \pm{1} & 0 & 0\end{smallmatrix}\right)
+
+When $\sin(\beta) = 1$:
+
+.. math::
+
+   R = \left(\begin{smallmatrix}0 & \operatorname{cos}\left(\gamma\right) \operatorname{sin}\left(\alpha\right) - \operatorname{cos}\left(\alpha\right) \operatorname{sin}\left(\gamma\right) & \operatorname{cos}\left(\alpha\right) \operatorname{cos}\left(\gamma\right) + \operatorname{sin}\left(\alpha\right) \operatorname{sin}\left(\gamma\right)\\0 & \operatorname{cos}\left(\alpha\right) \operatorname{cos}\left(\gamma\right) + \operatorname{sin}\left(\alpha\right) \operatorname{sin}\left(\gamma\right) & \operatorname{cos}\left(\alpha\right) \operatorname{sin}\left(\gamma\right) - \operatorname{cos}\left(\gamma\right) \operatorname{sin}\left(\alpha\right)\\-1 & 0 & 0\end{smallmatrix}\right)
+
+From the `angle sum and difference identities
+<http://en.wikipedia.org/wiki/List_of_trigonometric_identities#Angle_sum_and_difference_identities>`_
+(see also `geometric proof
+<http://www.themathpage.com/atrig/sum-proof.htm>`_, `Mathworld treatment
+<http://mathworld.wolfram.com/TrigonometricAdditionFormulas.html>`_) we
+remind ourselves that, for any two angles $\alpha$ and $\beta$:
+
+.. math::
+
+   \sin(\alpha \pm \beta) = \sin \alpha \cos \beta \pm \cos \alpha \sin \beta \,
+
+   \cos(\alpha \pm \beta) = \cos \alpha \cos \beta \mp \sin \alpha \sin \beta
+
+We can rewrite $R$ as:
+
+.. math::
+
+    R = \left(\begin{smallmatrix}0 & V_{1} & V_{2}\\0 & V_{2} & - V_{1}\\-1 & 0 & 0\end{smallmatrix}\right)
+
+where:
+
+.. math::
+
+    V_1 = \operatorname{cos}\left(\gamma\right) \operatorname{sin}\left(\alpha\right) - \operatorname{cos}\left(\alpha\right) \operatorname{sin}\left(\gamma\right) = \sin(\alpha - \gamma) \,
+
+    V_2 =  \operatorname{cos}\left(\alpha\right) \operatorname{cos}\left(\gamma\right) + \operatorname{sin}\left(\alpha\right) \operatorname{sin}\left(\gamma\right) = \cos(\alpha - \gamma)
+
+We immediately see that $\alpha$ and $\gamma$ are going to lead the same
+transformation - the mathematical expression of the observation on the
+spitfire above, that rotation around the $x$ axis is equivalent to
+rotation about the $z$ axis.
+
+It's easy to do the same set of reductions, with the same conclusion,
+for the case where $\sin(\beta) = -1$ - see
+http://www.gregslabaugh.name/publications/euler.pdf.
+