IntelPython / dpnp / 38276469894

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Commit Message

Use computation dtype in dpnp.linalg.pinv for default tolerance and empty input (#3090)

This PR updates `dpnp.linalg.pinv` to take the data type for the default
tolerance and for the result of an empty input from the data type the
SVD is computed in. This aligns `dpnp.linalg.pinv` with NumPy 2.6
behavior.

### Default tolerance
When `rtol=None` (the default) and `rcond` is not given, the cutoff is
`max(M, N) * eps`. Previously `eps` was taken from
`dpnp.result_type(a.dtype, dpnp.default_float_type(a.device))`, which
gives `float64`:
- for `float32`/`complex64` input on devices with fp64 support;
- for integer input on devices without fp64 support, since `result_type`
called with dtypes only does not know the device.

In both cases the SVD runs in single precision, so the cutoff was about
10⁹ times too small. Singular values at the level of single-precision
rounding noise were therefore inverted instead of discarded. The
tolerance now uses `eps` of `_common_type(a)`, which also matches the
docstring (`max(M, N) * dpnp.finfo(a.dtype).eps`).

Note that `dpnp.linalg.pinv(a)` called without a tolerance now uses the
larger cutoff for `float32`/`complex64` input on devices with fp64
support.

### Empty input
The empty-input shortcut returned an array of the input data type. An
empty integer or boolean array therefore produced an integer/boolean
result, while a non-empty one produced a floating-point result. The
shortcut now returns the computation data type: `float64`, or `float32`
on devices without fp64 support.

```python
import dpnp as np

a = np.diag(np.array([1.0, 1e-9], dtype=np.float32))
np.linalg.pinv(a)  # was [[1, 0], [0, 1e9]], now [[1, 0], [0, 0]]

np.linalg.pinv(np.empty((0, 3), dtype=np.int64)).dtype  # was int64, now float64
```

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