# Examples of design matrices#

Three examples of design matrices specification and computation for first-level fMRI data analysis (event-related design, block design, FIR design).

This examples requires matplotlib.

```try:
import matplotlib.pyplot as plt
except ImportError:
raise RuntimeError("This script needs the matplotlib library")
```

## Define parameters#

At first, we define parameters related to the images acquisition.

```import numpy as np
tr = 1.0  # repetition time is 1 second
n_scans = 128  # the acquisition comprises 128 scans
frame_times = np.arange(n_scans) * tr  # here are the corresponding frame times
```

Then we define parameters related to the experimental design.

```# these are the types of the different trials
conditions = ['c0', 'c0', 'c0', 'c1', 'c1', 'c1', 'c3', 'c3', 'c3']
duration = [1., 1., 1., 1., 1., 1., 1., 1., 1.]
# these are the corresponding onset times
onsets = [30., 70., 100., 10., 30., 90., 30., 40., 60.]
# Next, we simulate 6 motion parameters jointly observed with fMRI acquisitions
motion = np.cumsum(np.random.randn(n_scans, 6), 0)
# The 6 parameters correspond to three translations and three
# rotations describing rigid body motion
add_reg_names = ['tx', 'ty', 'tz', 'rx', 'ry', 'rz']
```

## Create design matrices#

The same parameters allow us to obtain a variety of design matrices. We first create an events object.

```import pandas as pd
events = pd.DataFrame({'trial_type': conditions, 'onset': onsets,
'duration': duration})
```

We sample the events into a design matrix, also including additional regressors.

```hrf_model = 'glover'
from nilearn.glm.first_level import make_first_level_design_matrix
X1 = make_first_level_design_matrix(
frame_times, events, drift_model='polynomial', drift_order=3,
```

Now we compute a block design matrix. We add duration to create the blocks. For this we first define an event structure that includes the duration parameter.

```duration = 7. * np.ones(len(conditions))
events = pd.DataFrame({'trial_type': conditions, 'onset': onsets,
'duration': duration})
```

Then we sample the design matrix.

```X2 = make_first_level_design_matrix(frame_times, events,
drift_model='polynomial', drift_order=3,
hrf_model=hrf_model)
```

Finally we compute a FIR model

```events = pd.DataFrame({'trial_type': conditions, 'onset': onsets,
'duration': duration})
hrf_model = 'FIR'
X3 = make_first_level_design_matrix(frame_times, events, hrf_model='fir',
drift_model='polynomial', drift_order=3,
fir_delays=np.arange(1, 6))
```

Here are the three designs side by side.

```from nilearn.plotting import plot_design_matrix
fig, (ax1, ax2, ax3) = plt.subplots(figsize=(10, 6), nrows=1, ncols=3)
plot_design_matrix(X1, ax=ax1)
ax1.set_title('Event-related design matrix', fontsize=12)
plot_design_matrix(X2, ax=ax2)
ax2.set_title('Block design matrix', fontsize=12)
plot_design_matrix(X3, ax=ax3)
ax3.set_title('FIR design matrix', fontsize=12)
```
```Text(0.5, 1.1753015208063937, 'FIR design matrix')
```

Let’s improve the layout and show the result.

```plt.subplots_adjust(left=0.08, top=0.9, bottom=0.21, right=0.96, wspace=0.3)
plt.show()
```

Total running time of the script: ( 0 minutes 6.634 seconds)

Estimated memory usage: 9 MB

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