.. vim: ft=rst

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Basic linear modeling
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* For code template see: :download:`multi_model_code.py`;
* For solution see: :doc:`multi_model_solution`.

In this exercise we will run a simple regression on all voxels in a 4D
FMRI image :download:`ds114_sub009_t2r1.nii`:

.. nbplot::

    >>> #: Import some standard librares
    >>> import numpy as np
    >>> # Print to 4 DP
    >>> np.set_printoptions(precision=4)
    >>> import numpy.linalg as npl
    >>> import matplotlib.pyplot as plt
    >>> # Set default imshow parameters
    >>> plt.rcParams['image.interpolation'] = 'nearest'
    >>> plt.rcParams['image.cmap'] = 'gray'

.. nbplot::

    >>> #: Load the image as an image object
    >>> import nibabel as nib
    >>> img = nib.load('ds114_sub009_t2r1.nii')

.. nbplot::

    >>> #: Load the image data as an array
    >>> # Drop the first 4 3D volumes from the array
    >>> # (We already saw that these were abnormal)
    >>> data = img.get_data()[..., 4:]

We make the design matrix from the convolved regressor from
:doc:`convolution_background`:

.. nbplot::

    >>> #- Load the pre-written convolved time course
    >>> #- Knock off the first four elements

.. nbplot::

    >>> #- Compile the design matrix
    >>> #- First column is convolved regressor
    >>> #- Second column all ones
    >>> #- Hint: investigate "aspect" keyword to ``plt.imshow`` for a nice
    >>> #- looking image.

.. nbplot::

    >>> #- Reshape the 4D data to voxel by time 2D
    >>> #- Transpose to give time by voxel 2D
    >>> #- Calculate the pseudoinverse of the design
    >>> #- Apply to time by voxel array to get betas

.. nbplot::

    >>> #- Transpose betas to give voxels by 2 array
    >>> #- Reshape into 4D array, with same 3D shape as original data,
    >>> #- last dimension length 2

.. nbplot::

    >>> #- Show the middle slice from the first beta volume

.. nbplot::

    >>> #- Show the middle slice from the second beta volume