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Cholesky Function updated at 4 location -- PR for issue #23048 #23166

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Cholesky Function updated at 4 location -- PR for issue #23048 #23166

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5079186
Update linear_algebra.py
msarmadsohail Sep 6, 2023
4f73142
Update linear_algebra.py
msarmadsohail Sep 6, 2023
22cfec1
Update linear_algebra.py
msarmadsohail Sep 6, 2023
77fc8f7
Update linear_algebra.py
msarmadsohail Sep 6, 2023
81ccdc1
Merge branch 'unifyai:main' into main
msarmadsohail Sep 7, 2023
019eef9
Update linear_algebra.py
msarmadsohail Sep 8, 2023
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Merge branch 'unifyai:main' into main
msarmadsohail Sep 17, 2023
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83 changes: 81 additions & 2 deletions ivy/functional/backends/jax/linear_algebra.py
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Original file line number Diff line number Diff line change
Expand Up @@ -24,8 +24,87 @@
backend_version,
)
def cholesky(
x: JaxArray, /, *, upper: bool = False, out: Optional[JaxArray] = None
) -> JaxArray:
x: Union[jnp.DeviceArray, jnp.ShapedArray],
/,
*,
upper: bool = False,
out: Optional[jnp.DeviceArray] = None,
) -> jnp.DeviceArray:
"""
Compute the Cholesky decomposition of the x matrix.

Parameters
----------
x : jnp.DeviceArray or jnp.ShapedArray
Input array having shape (..., M, M) and whose innermost two dimensions form
square symmetric positive-definite matrices. Should have a floating-point data
type.
upper : bool, optional
If True, the result must be the upper-triangular Cholesky factor U. If False,
the result must be the lower-triangular Cholesky factor L. Default: False.
out : jnp.DeviceArray, optional
Optional output array, for writing the result to. It must have a shape that the
inputs broadcast to.

Returns
-------
jnp.DeviceArray
An array containing the Cholesky factors for each square matrix. If upper is
False, the returned array must contain lower-triangular matrices; otherwise, the
returned array must contain upper-triangular matrices. The returned array must
have a floating-point data type determined by Type Promotion Rules and must have
the same shape as x.

Examples
--------
With jnp.DeviceArray input:

>>> x = jnp.array([[4.0, 1.0, 2.0, 0.5, 2.0],
... [1.0, 0.5, 0.0, 0.0, 0.0],
... [2.0, 0.0, 3.0, 0.0, 0.0],
... [0.5, 0.0, 0.0, 0.625, 0.0],
... [2.0, 0.0, 0.0, 0.0, 16.0]])
>>> l = cholesky(x, upper=False)
>>> print(l)
jnp.array([[ 2. , 0.5 , 1. , 0.25, 1. ],
[ 0. , 0.5 , -1. , -0.25, -1. ],
[ 0. , 0. , 1. , -0.5 , -2. ],
[ 0. , 0. , 0. , 0.5 , -3. ],
[ 0. , 0. , 0. , 0. , 1. ]])

>>> x = jnp.array([[4.0, 1.0, 2.0, 0.5, 2.0],
... [1.0, 0.5, 0.0, 0.0, 0.0],
... [2.0, 0.0, 3.0, 0.0, 0.0],
... [0.5, 0.0, 0.0, 0.625, 0.0],
... [2.0, 0.0, 0.0, 0.0, 16.0]])
>>> y = jnp.zeros([5, 5])
>>> cholesky(x, upper=False, out=y)
>>> print(y)
jnp.array([[ 2. , 0.5 , 1. , 0.25, 1. ],
[ 0. , 0.5 , -1. , -0.25, -1. ],
[ 0. , 0. , 1. , -0.5 , -2. ],
[ 0. , 0. , 0. , 0.5 , -3. ],
[ 0. , 0. , 0. , 0. , 1. ]])

>>> x = jnp.array([[4.0, 1.0, 2.0, 0.5, 2.0],
... [1.0, 0.5, 0.0, 0.0, 0.0],
... [2.0, 0.0, 3.0, 0.0, 0.0],
... [0.5, 0.0, 0.0, 0.625, 0.0],
... [2.0, 0.0, 0.0, 0.0, 16.0]])
>>> cholesky(x, upper=False, out=x)
>>> print(x)
jnp.array([[ 2. , 0.5 , 1. , 0.25, 1. ],
[ 0. , 0.5 , -1. , -0.25, -1. ],
[ 0. , 0. , 1. , -0.5 , -2. ],
[ 0. , 0. , 0. , 0.5 , -3. ],
[ 0. , 0. , 0. , 0. , 1. ]])

>>> x = jnp.array([[1., -2.], [2., 5.]])
>>> u = cholesky(x, upper=False)
>>> print(u)
jnp.array([[ 1., -2.],
[ 0., 1.]])
"""
if not upper:
ret = jnp.linalg.cholesky(x)
else:
Expand Down
75 changes: 75 additions & 0 deletions ivy/functional/backends/numpy/linear_algebra.py
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Original file line number Diff line number Diff line change
Expand Up @@ -23,6 +23,81 @@
def cholesky(
x: np.ndarray, /, *, upper: bool = False, out: Optional[np.ndarray] = None
) -> np.ndarray:
"""
Compute the Cholesky decomposition of the x matrix.

Parameters
----------
x : np.ndarray
Input array having shape (..., M, M) and whose innermost two dimensions form
square symmetric positive-definite matrices. Should have a floating-point data
type.
upper : bool, optional
If True, the result must be the upper-triangular Cholesky factor U. If False,
the result must be the lower-triangular Cholesky factor L. Default: False.
out : np.ndarray, optional
Optional output array, for writing the result to. It must have a shape that the
inputs broadcast to.

Returns
-------
np.ndarray
An array containing the Cholesky factors for each square matrix. If upper is
False, the returned array must contain lower-triangular matrices; otherwise, the
returned array must contain upper-triangular matrices. The returned array must
have a floating-point data type determined by Type Promotion Rules and must have
the same shape as x.

Examples
--------
With np.ndarray input:

>>> x = np.array([[4.0, 1.0, 2.0, 0.5, 2.0],
... [1.0, 0.5, 0.0, 0.0, 0.0],
... [2.0, 0.0, 3.0, 0.0, 0.0],
... [0.5, 0.0, 0.0, 0.625, 0.0],
... [2.0, 0.0, 0.0, 0.0, 16.0]])
>>> l = cholesky(x, upper=False)
>>> print(l)
np.array([[ 2. , 0.5 , 1. , 0.25, 1. ],
[ 0. , 0.5 , -1. , -0.25, -1. ],
[ 0. , 0. , 1. , -0.5 , -2. ],
[ 0. , 0. , 0. , 0.5 , -3. ],
[ 0. , 0. , 0. , 0. , 1. ]])

>>> x = np.array([[4.0, 1.0, 2.0, 0.5, 2.0],
... [1.0, 0.5, 0.0, 0.0, 0.0],
... [2.0, 0.0, 3.0, 0.0, 0.0],
... [0.5, 0.0, 0.0, 0.625, 0.0],
... [2.0, 0.0, 0.0, 0.0, 16.0]])
>>> y = np.zeros([5, 5])
>>> cholesky(x, upper=False, out=y)
>>> print(y)
np.array([[ 2. , 0.5 , 1. , 0.25, 1. ],
[ 0. , 0.5 , -1. , -0.25, -1. ],
[ 0. , 0. , 1. , -0.5 , -2. ],
[ 0. , 0. , 0. , 0.5 , -3. ],
[ 0. , 0. , 0. , 0. , 1. ]])

>>> x = np.array([[4.0, 1.0, 2.0, 0.5, 2.0],
... [1.0, 0.5, 0.0, 0.0, 0.0],
... [2.0, 0.0, 3.0, 0.0, 0.0],
... [0.5, 0.0, 0.0, 0.625, 0.0],
... [2.0, 0.0, 0.0, 0.0, 16.0]])
>>> cholesky(x, upper=False, out=x)
>>> print(x)
np.array([[ 2. , 0.5 , 1. , 0.25, 1. ],
[ 0. , 0.5 , -1. , -0.25, -1. ],
[ 0. , 0. , 1. , -0.5 , -2. ],
[ 0. , 0. , 0. , 0.5 , -3. ],
[ 0. , 0. , 0. , 0. , 1. ]])

>>> x = np.array([[1., -2.], [2., 5.]])
>>> u = cholesky(x, upper=False)
>>> print(u)
np.array([[ 1., -2.],
[ 0., 1.]])
"""
if not upper:
ret = np.linalg.cholesky(x)
else:
Expand Down
83 changes: 79 additions & 4 deletions ivy/functional/backends/torch/linear_algebra.py
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Original file line number Diff line number Diff line change
Expand Up @@ -25,8 +25,82 @@
def cholesky(
x: torch.Tensor, /, *, upper: bool = False, out: Optional[torch.Tensor] = None
) -> torch.Tensor:
"""
Compute the Cholesky decomposition of the x matrix.

Parameters
----------
x : torch.Tensor
Input tensor having shape (..., M, M) and whose innermost two dimensions form
square symmetric positive-definite matrices. Should have a floating-point data
type.
upper : bool, optional
If True, the result must be the upper-triangular Cholesky factor U. If False,
the result must be the lower-triangular Cholesky factor L. Default: False.
out : torch.Tensor, optional
Optional output tensor, for writing the result to. It must have a shape that the
inputs broadcast to.

Returns
-------
torch.Tensor
A tensor containing the Cholesky factors for each square matrix. If upper is
False, the returned tensor must contain lower-triangular matrices; otherwise, the
returned tensor must contain upper-triangular matrices. The returned tensor must
have a floating-point data type and the same shape as x.

Examples
--------
With torch.Tensor input:

>>> x = torch.tensor([[4.0, 1.0, 2.0, 0.5, 2.0],
... [1.0, 0.5, 0.0, 0.0, 0.0],
... [2.0, 0.0, 3.0, 0.0, 0.0],
... [0.5, 0.0, 0.0, 0.625, 0.0],
... [2.0, 0.0, 0.0, 0.0, 16.0]])
>>> l = cholesky(x, upper=False)
>>> print(l)
torch.Tensor([[ 2. , 0.5 , 1. , 0.25, 1. ],
[ 0. , 0.5 , -1. , -0.25, -1. ],
[ 0. , 0. , 1. , -0.5 , -2. ],
[ 0. , 0. , 0. , 0.5 , -3. ],
[ 0. , 0. , 0. , 0. , 1. ]])

>>> x = torch.tensor([[4.0, 1.0, 2.0, 0.5, 2.0],
... [1.0, 0.5, 0.0, 0.0, 0.0],
... [2.0, 0.0, 3.0, 0.0, 0.0],
... [0.5, 0.0, 0.0, 0.625, 0.0],
... [2.0, 0.0, 0.0, 0.0, 16.0]])
>>> y = torch.zeros([5, 5])
>>> cholesky(x, upper=False, out=y)
>>> print(y)
torch.Tensor([[ 2. , 0.5 , 1. , 0.25, 1. ],
[ 0. , 0.5 , -1. , -0.25, -1. ],
[ 0. , 0. , 1. , -0.5 , -2. ],
[ 0. , 0. , 0. , 0.5 , -3. ],
[ 0. , 0. , 0. , 0. , 1. ]])

>>> x = torch.tensor([[4.0, 1.0, 2.0, 0.5, 2.0],
... [1.0, 0.5, 0.0, 0.0, 0.0],
... [2.0, 0.0, 3.0, 0.0, 0.0],
... [0.5, 0.0, 0.0, 0.625, 0.0],
... [2.0, 0.0, 0.0, 0.0, 16.0]])
>>> cholesky(x, upper=False, out=x)
>>> print(x)
torch.Tensor([[ 2. , 0.5 , 1. , 0.25, 1. ],
[ 0. , 0.5 , -1. , -0.25, -1. ],
[ 0. , 0. , 1. , -0.5 , -2. ],
[ 0. , 0. , 0. , 0.5 , -3. ],
[ 0. , 0. , 0. , 0. , 0. , 1. ]])

>>> x = torch.tensor([[1., -2.], [2., 5.]])
>>> u = cholesky(x, upper=False)
>>> print(u)
torch.Tensor([[ 1., -2.],
[ 0., 1.]])
"""
if not upper:
return torch.linalg.cholesky(x, out=out)
ret = torch.linalg.cholesky(x, out=out)
else:
ret = torch.transpose(
torch.linalg.cholesky(
Expand All @@ -35,9 +109,10 @@ def cholesky(
dim0=len(x.shape) - 1,
dim1=len(x.shape) - 2,
)
if ivy.exists(out):
return ivy.inplace_update(out, ret)
return ret
if out is not None:
out.copy_(ret)
return out
return ret


cholesky.support_native_out = True
Expand Down
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