package scipy

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val get_py : string -> Py.Object.t

Get an attribute of this module as a Py.Object.t. This is useful to pass a Python function to another function.

val dct : ?type_:[ `Three | `One | `Four | `Two ] -> ?n:int -> ?axis:int -> ?norm:string -> ?overwrite_x:bool -> x:[> `Ndarray ] Np.Obj.t -> unit -> Py.Object.t

Return the Discrete Cosine Transform of arbitrary type sequence x.

Parameters ---------- x : array_like The input array. type :

, 2, 3, 4

, optional Type of the DCT (see Notes). Default type is 2. n : int, optional Length of the transform. If ``n < x.shapeaxis``, `x` is truncated. If ``n > x.shapeaxis``, `x` is zero-padded. The default results in ``n = x.shapeaxis``. axis : int, optional Axis along which the dct is computed; the default is over the last axis (i.e., ``axis=-1``). norm : None, 'ortho', optional Normalization mode (see Notes). Default is None. overwrite_x : bool, optional If True, the contents of `x` can be destroyed; the default is False.

Returns ------- y : ndarray of real The transformed input array.

See Also -------- idct : Inverse DCT

Notes ----- For a single dimension array ``x``, ``dct(x, norm='ortho')`` is equal to MATLAB ``dct(x)``.

There are theoretically 8 types of the DCT, only the first 4 types are implemented in scipy. 'The' DCT generally refers to DCT type 2, and 'the' Inverse DCT generally refers to DCT type 3.

**Type I**

There are several definitions of the DCT-I; we use the following (for ``norm=None``)

.. math::

y_k = x_0 + (-1)^k x_N-1 + 2 \sum_n=1^N-2 x_n \cos\left( \frac\pi k nN-1 \right)

If ``norm='ortho'``, ``x0`` and ``xN-1`` are multiplied by a scaling factor of :math:`\sqrt

`, and ``yk`` is multiplied by a scaling factor ``f``

.. math::

f = \begincases \frac

\sqrt\frac{1N-1

}

& \textfk=0\text or N-1, \\ \frac

\sqrt\frac{2N-1

}

& \textotherwise \endcases

.. versionadded:: 1.2.0 Orthonormalization in DCT-I.

.. note:: The DCT-I is only supported for input size > 1.

**Type II**

There are several definitions of the DCT-II; we use the following (for ``norm=None``)

.. math::

y_k = 2 \sum_n=0^N-1 x_n \cos\left(\frac\pi k(2n+1)

N

\right)

If ``norm='ortho'``, ``yk`` is multiplied by a scaling factor ``f``

.. math:: f = \begincases \sqrt\frac{1

N

}

& \textfk=0, \\ \sqrt\frac{1

N

}

& \textotherwise \endcases

Which makes the corresponding matrix of coefficients orthonormal (``O @ O.T = np.eye(N)``).

**Type III**

There are several definitions, we use the following (for ``norm=None``)

.. math::

y_k = x_0 + 2 \sum_n=1^N-1 x_n \cos\left(\frac\pi(2k+1)n

N

\right)

or, for ``norm='ortho'``

.. math::

y_k = \fracx_0\sqrt{N

}

  1. \sqrt\frac{2N

}

\sum_n=1^N-1 x_n \cos\left(\frac\pi(2k+1)n

N

\right)

The (unnormalized) DCT-III is the inverse of the (unnormalized) DCT-II, up to a factor `2N`. The orthonormalized DCT-III is exactly the inverse of the orthonormalized DCT-II.

**Type IV**

There are several definitions of the DCT-IV; we use the following (for ``norm=None``)

.. math::

y_k = 2 \sum_n=0^N-1 x_n \cos\left(\frac\pi(2k+1)(2n+1)

N

\right)

If ``norm='ortho'``, ``yk`` is multiplied by a scaling factor ``f``

.. math::

f = \frac

\sqrt{2N

}

.. versionadded:: 1.2.0 Support for DCT-IV.

References ---------- .. 1 'A Fast Cosine Transform in One and Two Dimensions', by J. Makhoul, `IEEE Transactions on acoustics, speech and signal processing` vol. 28(1), pp. 27-34, :doi:`10.1109/TASSP.1980.1163351` (1980). .. 2 Wikipedia, 'Discrete cosine transform', https://en.wikipedia.org/wiki/Discrete_cosine_transform

Examples -------- The Type 1 DCT is equivalent to the FFT (though faster) for real, even-symmetrical inputs. The output is also real and even-symmetrical. Half of the FFT input is used to generate half of the FFT output:

>>> from scipy.fftpack import fft, dct >>> fft(np.array(4., 3., 5., 10., 5., 3.)).real array( 30., -8., 6., -2., 6., -8.) >>> dct(np.array(4., 3., 5., 10.), 1) array( 30., -8., 6., -2.)

val dctn : ?type_:[ `Three | `One | `Four | `Two ] -> ?shape:[ `I of int | `Array_like_of_ints of Py.Object.t ] -> ?axes:[ `I of int | `Array_like_of_ints of Py.Object.t ] -> ?norm:string -> ?overwrite_x:bool -> x:[> `Ndarray ] Np.Obj.t -> unit -> Py.Object.t

Return multidimensional Discrete Cosine Transform along the specified axes.

Parameters ---------- x : array_like The input array. type :

, 2, 3, 4

, optional Type of the DCT (see Notes). Default type is 2. shape : int or array_like of ints or None, optional The shape of the result. If both `shape` and `axes` (see below) are None, `shape` is ``x.shape``; if `shape` is None but `axes` is not None, then `shape` is ``scipy.take(x.shape, axes, axis=0)``. If ``shapei > x.shapei``, the i-th dimension is padded with zeros. If ``shapei < x.shapei``, the i-th dimension is truncated to length ``shapei``. If any element of `shape` is -1, the size of the corresponding dimension of `x` is used. axes : int or array_like of ints or None, optional Axes along which the DCT is computed. The default is over all axes. norm : None, 'ortho', optional Normalization mode (see Notes). Default is None. overwrite_x : bool, optional If True, the contents of `x` can be destroyed; the default is False.

Returns ------- y : ndarray of real The transformed input array.

See Also -------- idctn : Inverse multidimensional DCT

Notes ----- For full details of the DCT types and normalization modes, as well as references, see `dct`.

Examples -------- >>> from scipy.fftpack import dctn, idctn >>> y = np.random.randn(16, 16) >>> np.allclose(y, idctn(dctn(y, norm='ortho'), norm='ortho')) True

val dst : ?type_:[ `Three | `One | `Four | `Two ] -> ?n:int -> ?axis:int -> ?norm:string -> ?overwrite_x:bool -> x:[> `Ndarray ] Np.Obj.t -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Return the Discrete Sine Transform of arbitrary type sequence x.

Parameters ---------- x : array_like The input array. type :

, 2, 3, 4

, optional Type of the DST (see Notes). Default type is 2. n : int, optional Length of the transform. If ``n < x.shapeaxis``, `x` is truncated. If ``n > x.shapeaxis``, `x` is zero-padded. The default results in ``n = x.shapeaxis``. axis : int, optional Axis along which the dst is computed; the default is over the last axis (i.e., ``axis=-1``). norm : None, 'ortho', optional Normalization mode (see Notes). Default is None. overwrite_x : bool, optional If True, the contents of `x` can be destroyed; the default is False.

Returns ------- dst : ndarray of reals The transformed input array.

See Also -------- idst : Inverse DST

Notes ----- For a single dimension array ``x``.

There are theoretically 8 types of the DST for different combinations of even/odd boundary conditions and boundary off sets 1_, only the first 4 types are implemented in scipy.

**Type I**

There are several definitions of the DST-I; we use the following for ``norm=None``. DST-I assumes the input is odd around `n=-1` and `n=N`.

.. math::

y_k = 2 \sum_n=0^N-1 x_n \sin\left(\frac\pi(k+1)(n+1)N+1\right)

Note that the DST-I is only supported for input size > 1. The (unnormalized) DST-I is its own inverse, up to a factor `2(N+1)`. The orthonormalized DST-I is exactly its own inverse.

**Type II**

There are several definitions of the DST-II; we use the following for ``norm=None``. DST-II assumes the input is odd around `n=-1/2` and `n=N-1/2`; the output is odd around :math:`k=-1` and even around `k=N-1`

.. math::

y_k = 2 \sum_n=0^N-1 x_n \sin\left(\frac\pi(k+1)(2n+1)

N

\right)

if ``norm='ortho'``, ``yk`` is multiplied by a scaling factor ``f``

.. math::

f = \begincases \sqrt\frac{1

N

}

& \textfk = 0, \\ \sqrt\frac{1

N

}

& \textotherwise \endcases

**Type III**

There are several definitions of the DST-III, we use the following (for ``norm=None``). DST-III assumes the input is odd around `n=-1` and even around `n=N-1`

.. math::

y_k = (-1)^k x_N-1 + 2 \sum_n=0^N-2 x_n \sin\left( \frac\pi(2k+1)(n+1)

N

\right)

The (unnormalized) DST-III is the inverse of the (unnormalized) DST-II, up to a factor `2N`. The orthonormalized DST-III is exactly the inverse of the orthonormalized DST-II.

.. versionadded:: 0.11.0

**Type IV**

There are several definitions of the DST-IV, we use the following (for ``norm=None``). DST-IV assumes the input is odd around `n=-0.5` and even around `n=N-0.5`

.. math::

y_k = 2 \sum_n=0^N-1 x_n \sin\left(\frac\pi(2k+1)(2n+1)

N

\right)

The (unnormalized) DST-IV is its own inverse, up to a factor `2N`. The orthonormalized DST-IV is exactly its own inverse.

.. versionadded:: 1.2.0 Support for DST-IV.

References ---------- .. 1 Wikipedia, 'Discrete sine transform', https://en.wikipedia.org/wiki/Discrete_sine_transform

val dstn : ?type_:[ `Three | `One | `Four | `Two ] -> ?shape:[ `I of int | `Array_like_of_ints of Py.Object.t ] -> ?axes:[ `I of int | `Array_like_of_ints of Py.Object.t ] -> ?norm:string -> ?overwrite_x:bool -> x:[> `Ndarray ] Np.Obj.t -> unit -> Py.Object.t

Return multidimensional Discrete Sine Transform along the specified axes.

Parameters ---------- x : array_like The input array. type :

, 2, 3, 4

, optional Type of the DST (see Notes). Default type is 2. shape : int or array_like of ints or None, optional The shape of the result. If both `shape` and `axes` (see below) are None, `shape` is ``x.shape``; if `shape` is None but `axes` is not None, then `shape` is ``scipy.take(x.shape, axes, axis=0)``. If ``shapei > x.shapei``, the i-th dimension is padded with zeros. If ``shapei < x.shapei``, the i-th dimension is truncated to length ``shapei``. If any element of `shape` is -1, the size of the corresponding dimension of `x` is used. axes : int or array_like of ints or None, optional Axes along which the DCT is computed. The default is over all axes. norm : None, 'ortho', optional Normalization mode (see Notes). Default is None. overwrite_x : bool, optional If True, the contents of `x` can be destroyed; the default is False.

Returns ------- y : ndarray of real The transformed input array.

See Also -------- idstn : Inverse multidimensional DST

Notes ----- For full details of the DST types and normalization modes, as well as references, see `dst`.

Examples -------- >>> from scipy.fftpack import dstn, idstn >>> y = np.random.randn(16, 16) >>> np.allclose(y, idstn(dstn(y, norm='ortho'), norm='ortho')) True

val idct : ?type_:[ `Three | `One | `Four | `Two ] -> ?n:int -> ?axis:int -> ?norm:string -> ?overwrite_x:bool -> x:[> `Ndarray ] Np.Obj.t -> unit -> Py.Object.t

Return the Inverse Discrete Cosine Transform of an arbitrary type sequence.

Parameters ---------- x : array_like The input array. type :

, 2, 3, 4

, optional Type of the DCT (see Notes). Default type is 2. n : int, optional Length of the transform. If ``n < x.shapeaxis``, `x` is truncated. If ``n > x.shapeaxis``, `x` is zero-padded. The default results in ``n = x.shapeaxis``. axis : int, optional Axis along which the idct is computed; the default is over the last axis (i.e., ``axis=-1``). norm : None, 'ortho', optional Normalization mode (see Notes). Default is None. overwrite_x : bool, optional If True, the contents of `x` can be destroyed; the default is False.

Returns ------- idct : ndarray of real The transformed input array.

See Also -------- dct : Forward DCT

Notes ----- For a single dimension array `x`, ``idct(x, norm='ortho')`` is equal to MATLAB ``idct(x)``.

'The' IDCT is the IDCT of type 2, which is the same as DCT of type 3.

IDCT of type 1 is the DCT of type 1, IDCT of type 2 is the DCT of type 3, and IDCT of type 3 is the DCT of type 2. IDCT of type 4 is the DCT of type 4. For the definition of these types, see `dct`.

Examples -------- The Type 1 DCT is equivalent to the DFT for real, even-symmetrical inputs. The output is also real and even-symmetrical. Half of the IFFT input is used to generate half of the IFFT output:

>>> from scipy.fftpack import ifft, idct >>> ifft(np.array( 30., -8., 6., -2., 6., -8.)).real array( 4., 3., 5., 10., 5., 3.) >>> idct(np.array( 30., -8., 6., -2.), 1) / 6 array( 4., 3., 5., 10.)

val idctn : ?type_:[ `Three | `One | `Four | `Two ] -> ?shape:[ `I of int | `Array_like_of_ints of Py.Object.t ] -> ?axes:[ `I of int | `Array_like_of_ints of Py.Object.t ] -> ?norm:string -> ?overwrite_x:bool -> x:[> `Ndarray ] Np.Obj.t -> unit -> Py.Object.t

Return multidimensional Discrete Cosine Transform along the specified axes.

Parameters ---------- x : array_like The input array. type :

, 2, 3, 4

, optional Type of the DCT (see Notes). Default type is 2. shape : int or array_like of ints or None, optional The shape of the result. If both `shape` and `axes` (see below) are None, `shape` is ``x.shape``; if `shape` is None but `axes` is not None, then `shape` is ``scipy.take(x.shape, axes, axis=0)``. If ``shapei > x.shapei``, the i-th dimension is padded with zeros. If ``shapei < x.shapei``, the i-th dimension is truncated to length ``shapei``. If any element of `shape` is -1, the size of the corresponding dimension of `x` is used. axes : int or array_like of ints or None, optional Axes along which the IDCT is computed. The default is over all axes. norm : None, 'ortho', optional Normalization mode (see Notes). Default is None. overwrite_x : bool, optional If True, the contents of `x` can be destroyed; the default is False.

Returns ------- y : ndarray of real The transformed input array.

See Also -------- dctn : multidimensional DCT

Notes ----- For full details of the IDCT types and normalization modes, as well as references, see `idct`.

Examples -------- >>> from scipy.fftpack import dctn, idctn >>> y = np.random.randn(16, 16) >>> np.allclose(y, idctn(dctn(y, norm='ortho'), norm='ortho')) True

val idst : ?type_:[ `Three | `One | `Four | `Two ] -> ?n:int -> ?axis:int -> ?norm:string -> ?overwrite_x:bool -> x:[> `Ndarray ] Np.Obj.t -> unit -> Py.Object.t

Return the Inverse Discrete Sine Transform of an arbitrary type sequence.

Parameters ---------- x : array_like The input array. type :

, 2, 3, 4

, optional Type of the DST (see Notes). Default type is 2. n : int, optional Length of the transform. If ``n < x.shapeaxis``, `x` is truncated. If ``n > x.shapeaxis``, `x` is zero-padded. The default results in ``n = x.shapeaxis``. axis : int, optional Axis along which the idst is computed; the default is over the last axis (i.e., ``axis=-1``). norm : None, 'ortho', optional Normalization mode (see Notes). Default is None. overwrite_x : bool, optional If True, the contents of `x` can be destroyed; the default is False.

Returns ------- idst : ndarray of real The transformed input array.

See Also -------- dst : Forward DST

Notes ----- 'The' IDST is the IDST of type 2, which is the same as DST of type 3.

IDST of type 1 is the DST of type 1, IDST of type 2 is the DST of type 3, and IDST of type 3 is the DST of type 2. For the definition of these types, see `dst`.

.. versionadded:: 0.11.0

val idstn : ?type_:[ `Three | `One | `Four | `Two ] -> ?shape:[ `I of int | `Array_like_of_ints of Py.Object.t ] -> ?axes:[ `I of int | `Array_like_of_ints of Py.Object.t ] -> ?norm:string -> ?overwrite_x:bool -> x:[> `Ndarray ] Np.Obj.t -> unit -> Py.Object.t

Return multidimensional Discrete Sine Transform along the specified axes.

Parameters ---------- x : array_like The input array. type :

, 2, 3, 4

, optional Type of the DST (see Notes). Default type is 2. shape : int or array_like of ints or None, optional The shape of the result. If both `shape` and `axes` (see below) are None, `shape` is ``x.shape``; if `shape` is None but `axes` is not None, then `shape` is ``scipy.take(x.shape, axes, axis=0)``. If ``shapei > x.shapei``, the i-th dimension is padded with zeros. If ``shapei < x.shapei``, the i-th dimension is truncated to length ``shapei``. If any element of `shape` is -1, the size of the corresponding dimension of `x` is used. axes : int or array_like of ints or None, optional Axes along which the IDST is computed. The default is over all axes. norm : None, 'ortho', optional Normalization mode (see Notes). Default is None. overwrite_x : bool, optional If True, the contents of `x` can be destroyed; the default is False.

Returns ------- y : ndarray of real The transformed input array.

See Also -------- dstn : multidimensional DST

Notes ----- For full details of the IDST types and normalization modes, as well as references, see `idst`.

Examples -------- >>> from scipy.fftpack import dstn, idstn >>> y = np.random.randn(16, 16) >>> np.allclose(y, idstn(dstn(y, norm='ortho'), norm='ortho')) True

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