fiery.bounds.realtransforms

This module implements discrete transforms for real signals:

The implementation relies on the FFT under the hood, with memory-saving tricks (borrowed from cupy).

The table below lists all functions implemented in the module. In addition to these, wrappers of the form FUNCTYPE = partial(FUNC, type=TYPE) are defined. For example:

dct1 = partial(dct, type=1)
idct1 = partial(idct, type=1)
dctn1 = partial(dctn, type=1)

Functions:

Name	Description
`dct`	One-dimensional Discrete Cosine Transform (DCT)
`dst`	One-dimensional Discrete Sine Transform (DST)
`idct`	One-dimensional Inverse Discrete Cosine Transform (DCT)
`idst`	One-dimensional Inverse Discrete Sine Transform (DST)
`dctn`	N-dimensional Discrete Cosine Transform (DCT)
`dstn`	N-dimensional Discrete Sine Transform (DST)
`idctn`	N-dimensional Inverse Discrete Cosine Transform (IDCT)
`idstn`	N-dimensional Inverse Discrete Sine Transform (IDST)

Functions:

dct

dct(x: Tensor, dim: int = -1, norm: str = 'backward', type: int = 2) -> Tensor

Return the Discrete Cosine Transform

Type IV not implemented

Parameters:

Name	Type	Description	Default
`x`	`tensor`	The input tensor	required
`dim`	`int`	Dimension along which the DCT is computed. Default is the last one.	`-1`
`norm`	`(backward, ortho, forward)`	Normalization mode. Default is "backward".	`"backward"`
`type`	`int`	Type of the DCT. Default type is 2.	`2`

Returns:

Name	Type	Description
`y`	`tensor`	The transformed tensor.

idct

idct(x: Tensor, dim: int = -1, norm: str = 'backward', type: int = 2) -> Tensor

Return the Inverse Discrete Cosine Transform

Warning

Type IV not implemented

Parameters:

Name	Type	Description	Default
`x`	`tensor`	The input tensor	required
`dim`	`int`	Dimension along which the DCT is computed. Default is the last one.	`-1`
`norm`	`(backward, ortho, forward)`	Normalization mode. Default is "backward".	`"backward"`
`type`	`int`	Type of the DCT. Default type is 2.	`2`

Returns:

Name	Type	Description
`y`	`tensor`	The transformed tensor.

dst

dst(x: Tensor, dim: int = -1, norm: str = 'backward', type: int = 2) -> Tensor

Return the Discrete Sine Transform

Type IV not implemented

Warning

dst(..., norm="ortho") yields a different result than scipy and cupy for types 2 and 3. This is because their DST is not properly orthogonalized. Use norm="ortho_scipy" to get results matching their implementation.

Parameters:

Name	Type	Description	Default
`x`	`tensor`	The input tensor	required
`dim`	`int`	Dimension along which the DST is computed. Default is the last one.	`-1`
`norm`	`(backward, ortho, forward, ortho_scipy)`	Normalization mode. Default is "backward".	`"backward"`
`type`	`int`	Type of the DST. Default type is 2.	`2`

Returns:

Name	Type	Description
`y`	`tensor`	The transformed tensor.

idst

idst(x: Tensor, dim: int = -1, norm: str = 'backward', type: int = 2) -> Tensor

Return the Inverse Discrete Sine Transform

Type IV not implemented

Warning

idst(..., norm="ortho") yields a different result than scipy and cupy for types 2 and 3. This is because their DST is not properly orthogonalized. Use norm="ortho_scipy" to get results matching their implementation.

Parameters:

Name	Type	Description	Default
`x`	`tensor`	The input tensor	required
`dim`	`int`	Dimension along which the DST is computed. Default is the last one.	`-1`
`norm`	`(backward, ortho, forward, ortho_scipy)`	Normalization mode. Default is "backward".	`"backward"`
`type`	`int`	Type of the DST. Default type is 2.	`2`

Returns:

Name	Type	Description
`y`	`tensor`	The transformed tensor.

dctn

dctn(x: Tensor, dim: SequenceOrScalar[int] | None = None, norm: str = 'backward', type: int = 2) -> Tensor

Return multidimensional Discrete Cosine Transform along the specified axes.

Type IV not implemented

Parameters:

Name	Type	Description	Default
`x`	`tensor`	The input tensor	required
`dim`	`[sequence of] int`	Dimensions over which the DCT is computed. If not given, all dimensions are used.	`None`
`norm`	`(backward, ortho, forward)`	Normalization mode. Default is "backward".	`"backward"`
`type`	`int`	Type of the DCT. Default type is 2.	`2`

Returns:

Name	Type	Description
`y`	`tensor`	The transformed tensor.

idctn

idctn(x: Tensor, dim: SequenceOrScalar[int] | None = None, norm: str = 'backward', type: int = 2) -> Tensor

Return multidimensional Inverse Discrete Cosine Transform along the specified axes.

Type IV not implemented

Parameters:

Name	Type	Description	Default
`x`	`tensor`	The input tensor	required
`dim`	`[sequence of] int`	Dimensions over which the DCT is computed. If not given, all dimensions are used.	`None`
`norm`	`(backward, ortho, forward)`	Normalization mode. Default is "backward".	`"backward"`
`type`	`int`	Type of the DCT. Default type is 2.	`2`

Returns:

Name	Type	Description
`y`	`tensor`	The transformed tensor.

dstn

dstn(x: Tensor, dim: SequenceOrScalar[int] | None = None, norm: str = 'backward', type: int = 2) -> Tensor

Return multidimensional Discrete Sine Transform along the specified axes.

Type IV not implemented

Warning

dstn(..., norm="ortho") yields a different result than scipy and cupy for types 2 and 3. This is because their DST is not properly orthogonalized. Use norm="ortho_scipy" to get results matching their implementation.

Parameters:

Name	Type	Description	Default
`x`	`tensor`	The input tensor	required
`dim`	`[sequence of] int`	Dimensions over which the DST is computed. If not given, all dimensions are used.	`None`
`norm`	`(backward, ortho, forward, ortho_scipy)`	Normalization mode. Default is "backward".	`"backward"`
`type`	`int`	Type of the DST. Default type is 2.	`2`

Returns:

Name	Type	Description
`y`	`tensor`	The transformed tensor.

idstn

idstn(x: Tensor, dim: SequenceOrScalar[int] | None = None, norm: str = 'backward', type: int = 2) -> Tensor

Return multidimensional Inverse Discrete Sine Transform along the specified axes.

Type IV not implemented

Warning

idstn(..., norm="ortho") yields a different result than scipy and cupy for types 2 and 3. This is because their DST is not properly orthogonalized. Use norm="ortho_scipy" to get results matching their implementation.

Parameters:

Name	Type	Description	Default
`x`	`tensor`	The input tensor	required
`dim`	`[sequence of] int`	Dimensions over which the DST is computed. If not given, all dimensions are used.	`None`
`norm`	`(backward, ortho, forward, ortho_scipy)`	Normalization mode. Default is "backward".	`"backward"`
`type`	`int`	Type of the DST. Default type is 2.	`2`

Returns:

Name	Type	Description
`y`	`tensor`	The transformed tensor.