# Linear OT mapping estimation

```# Author: Remi Flamary <remi.flamary@unice.fr>
#

# sphinx_gallery_thumbnail_number = 2
import os
from pathlib import Path

import numpy as np
from matplotlib import pyplot as plt
import ot
```

## Generate data

```n = 1000
d = 2
sigma = .1

rng = np.random.RandomState(42)

# source samples
angles = rng.rand(n, 1) * 2 * np.pi
xs = np.concatenate((np.sin(angles), np.cos(angles)),
axis=1) + sigma * rng.randn(n, 2)
xs[:n // 2, 1] += 2

# target samples
anglet = rng.rand(n, 1) * 2 * np.pi
xt = np.concatenate((np.sin(anglet), np.cos(anglet)),
axis=1) + sigma * rng.randn(n, 2)
xt[:n // 2, 1] += 2

A = np.array([[1.5, .7], [.7, 1.5]])
b = np.array([[4, 2]])
xt = xt.dot(A) + b
```

## Plot data

```plt.figure(1, (5, 5))
plt.plot(xs[:, 0], xs[:, 1], '+')
plt.plot(xt[:, 0], xt[:, 1], 'o')
```

Out:

```[<matplotlib.lines.Line2D object at 0x7f5cdcd24d90>]
```

## Estimate linear mapping and transport

```Ae, be = ot.da.OT_mapping_linear(xs, xt)

xst = xs.dot(Ae) + be
```

## Plot transported samples

```plt.figure(1, (5, 5))
plt.clf()
plt.plot(xs[:, 0], xs[:, 1], '+')
plt.plot(xt[:, 0], xt[:, 1], 'o')
plt.plot(xst[:, 0], xst[:, 1], '+')

plt.show()
```

```def im2mat(img):
"""Converts and image to matrix (one pixel per line)"""
return img.reshape((img.shape[0] * img.shape[1], img.shape[2]))

def mat2im(X, shape):
"""Converts back a matrix to an image"""
return X.reshape(shape)

def minmax(img):
return np.clip(img, 0, 1)

this_file = os.path.realpath('__file__')
data_path = os.path.join(Path(this_file).parent.parent.parent, 'data')

I1 = plt.imread(os.path.join(data_path, 'ocean_day.jpg')).astype(np.float64) / 256
I2 = plt.imread(os.path.join(data_path, 'ocean_sunset.jpg')).astype(np.float64) / 256

X1 = im2mat(I1)
X2 = im2mat(I2)
```

```mapping = ot.da.LinearTransport()

mapping.fit(Xs=X1, Xt=X2)

xst = mapping.transform(Xs=X1)
xts = mapping.inverse_transform(Xt=X2)

I1t = minmax(mat2im(xst, I1.shape))
I2t = minmax(mat2im(xts, I2.shape))
```

## Plot transformed images

```plt.figure(2, figsize=(10, 7))

plt.subplot(2, 2, 1)
plt.imshow(I1)
plt.axis('off')
plt.title('Im. 1')

plt.subplot(2, 2, 2)
plt.imshow(I2)
plt.axis('off')
plt.title('Im. 2')

plt.subplot(2, 2, 3)
plt.imshow(I1t)
plt.axis('off')
plt.title('Mapping Im. 1')

plt.subplot(2, 2, 4)
plt.imshow(I2t)
plt.axis('off')
plt.title('Inverse mapping Im. 2')
```

Out:

```Text(0.5, 1.0, 'Inverse mapping Im. 2')
```

Total running time of the script: ( 0 minutes 0.884 seconds)

Gallery generated by Sphinx-Gallery