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librosa.util.nnls

librosa.util.nnls(A, B, **kwargs)[source]

Non-negative least squares.

Given two matrices A and B, find a non-negative matrix X that minimizes the sum squared error:

```err(X) = sum_i,j ((AX)[i,j] - B[i, j])^2
```
Parameters:
Anp.ndarray [shape=(m, n)]

The basis matrix

Bnp.ndarray [shape=(…, m, N)]

**kwargs

Additional keyword arguments to `scipy.optimize.fmin_l_bfgs_b`

Returns:
Xnp.ndarray [shape=(…, n, N), non-negative]

A minimizing solution to `|AX - B|^2`

Examples

Approximate a magnitude spectrum from its mel spectrogram

```>>> y, sr = librosa.load(librosa.ex('trumpet'), duration=3)
>>> S = np.abs(librosa.stft(y, n_fft=2048))
>>> M = librosa.feature.melspectrogram(S=S, sr=sr, power=1)
>>> mel_basis = librosa.filters.mel(sr=sr, n_fft=2048, n_mels=M.shape[0])
>>> S_recover = librosa.util.nnls(mel_basis, M)
```

Plot the results

```>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(nrows=3, sharex=True, sharey=True)
>>> librosa.display.specshow(librosa.amplitude_to_db(S, ref=np.max),
...                          y_axis='log', x_axis='time', ax=ax[2])
>>> ax[2].set(title='Original spectrogram (1025 bins)')
>>> ax[2].label_outer()
>>> librosa.display.specshow(librosa.amplitude_to_db(M, ref=np.max),
...                          y_axis='mel', x_axis='time', ax=ax[0])
>>> ax[0].set(title='Mel spectrogram (128 bins)')
>>> ax[0].label_outer()
>>> img = librosa.display.specshow(librosa.amplitude_to_db(S_recover, ref=np.max(S)),
...                          y_axis='log', x_axis='time', ax=ax[1])
>>> ax[1].set(title='Reconstructed spectrogram (1025 bins)')
>>> ax[1].label_outer()
>>> fig.colorbar(img, ax=ax, format="%+2.0f dB")
```