uki=,ddlmZddlmZddlmZddlZddlZddlZ ddl m Z ddl mZ ddl mZddlmZmZmZdd lmZmZdd lmZdd Zdd Zdd Z d ddZddZ d ddZ d ddZ d ddZ ddZ!y)) annotations)Sequence)partialN)lax)numpy)fft)promote_dtypes_complexpromote_dtypes_inexactensure_arraylike)canonicalize_axiscanonicalize_axis_tuple)Arraycxt||\}}tjdtjz|z|z S)Ny)r jnpexpnppi)NkN_arrs M/home/cdr/jupyterlab/.venv/lib/python3.12/site-packages/jax/_src/scipy/fft.py_W4r s3 #Aq )(% !E) **c tj|ddd|}tjtj|ddd||f}tj||g|SN)r slice_in_dimrev concatenate)xaxisv0v1s r_dct_interleaver%$sT 4q$/" wws1dAt4tg>" "b4 ((rctjtjdd|jtj|j|dz fd|jgd}tj |t |jDcgc] }||k7s | c}}|tj||j|zz Scc}w)N)rrrr) rr fulldtypeshape expand_dimsrangendimsqrt)outr"factoras r_dct_ortho_normr2)s ??CHHT1cii8#((CIIdOVWDWCY[\^a^g^g:hikl m& ??6uSXX#L!!t)A#L M& sxx401 11$Ms  C C c td|}|dk7r td||dvrtd|dt||j}|pt j |tjd|jt|jDcgc]}d||k(r||j|z nddf c}}|j|}t||}tj||}t jtj ||j"j t|jDcgc] }||k7s | c}} |t%|| z} d| j"z} |d k(r t'| |} | Scc}wcc}w) aComputes the discrete cosine transform of the input JAX implementation of :func:`scipy.fft.dct`. Args: x: array type: integer, default = 2. Currently only type 2 is supported. n: integer, default = x.shape[axis]. The length of the transform. If larger than ``x.shape[axis]``, the input will be zero-padded, if smaller, the input will be truncated. axis: integer, default=-1. The axis along which the dct will be performed. norm: string. The normalization mode: one of ``[None, "backward", "ortho"]``. The default is ``None``, which is equivalent to ``"backward"``. Returns: array containing the discrete cosine transform of x See Also: - :func:`jax.scipy.fft.dctn`: multidimensional DCT - :func:`jax.scipy.fft.idct`: inverse DCT - :func:`jax.scipy.fft.idctn`: multidimensional inverse DCT Examples: >>> x = jax.random.normal(jax.random.key(0), (3, 3)) >>> with jnp.printoptions(precision=2, suppress=True): ... print(jax.scipy.fft.dct(x)) [[ 6.43 3.56 -2.86] [-1.75 1.55 -1.4 ] [ 1.33 -2.01 -0.82]] When ``n`` smaller than ``x.shape[axis]`` >>> with jnp.printoptions(precision=2, suppress=True): ... print(jax.scipy.fft.dct(x, n=2)) [[ 7.3 -0.57] [ 0.19 -0.36] [-0. -1.4 ]] When ``n`` smaller than ``x.shape[axis]`` and ``axis=0`` >>> with jnp.printoptions(precision=2, suppress=True): ... print(jax.scipy.fft.dct(x, n=2, axis=0)) [[ 3.09 4.4 -2.81] [ 2.41 2.62 0.76]] When ``n`` larger than ``x.shape[axis]`` and ``axis=1`` >>> with jnp.printoptions(precision=2, suppress=True): ... print(jax.scipy.fft.dct(x, n=4, axis=1)) [[ 6.43 4.88 0.04 -3.3 ] [-1.75 0.73 1.01 -2.18] [ 1.33 -1.05 -2.34 -0.07]] idctnrOnly DCT type 2 is implemented.backwardorthozjax.scipy.fft.dct: norm= is not implementedrr"r)r8)r NotImplementedError ValueErrorr r-rpadrarrayr)r,r*r%jnp_fftrr+arangerealrr2) r!typenr"normr1rvVrr/s rdctrH2sanw"! QY ? @@ $&;; 04)3FG HH 4 ($] 399Q(-)!t)Q&A>) *Aggdm!a! kk!$! oocjj!&&,,7U166]9`VW[_V_!9`a! C1I # CHH # W_ #t $C *) :as#F < F F c tttt|j|\}}|j||j|}}t t |||}t j||}tjtj||jt|jD cgc] } | |k7s |  c} } tjtj||jt|jD cgc] } | |k7s |  c} } t|| t|| |zt|| tjtj ||d|zzz} d| j"z} |dk(rt%t%| ||S| Scc} wcc} w) N)num_dims)axesr;r:r)shiftr"rr8)maprr r-r*r%r@fftnrr+rrAr)r,rrollfliprBr2) r!rKrEaxis1axis2N1N2rFrGr1k1k2r/s r_dct2rWsOW.@$G,% 775>1775>b"oa/7! ll14 ! szz"AGG4#(=?aAJ?A" szz"AGG4#(=?aAJ?A" B s2r{QR"!RWAX`ahm8n)nno# CHH # W_ ?36 >> *@?s: F0 F0  F5 !F5 cHtd|}|dk7r td||dvrtd|d| t|}t||j}t|dk(rt|||d nd|d | S|tt||}t|jDcgc] }d ||vr|||j |z nd d f"}}t#j$|t'j(d |j*|}t|dk(rt-||| Std t|dDcgc] }|||dz c}D]} t/|| | }|S#t$r,t |t rJtj|g}YVwxYwcc}wcc}w) aComputes the multidimensional discrete cosine transform of the input JAX implementation of :func:`scipy.fft.dctn`. Args: x: array type: integer, default = 2. Currently only type 2 is supported. s: integer or sequence of integers. Specifies the shape of the result. If not specified, it will default to the shape of ``x`` along the specified ``axes``. axes: integer or sequence of integers. Specifies the axes along which the transform will be computed. norm: string. The normalization mode: one of ``[None, "backward", "ortho"]``. The default is ``None``, which is equivalent to ``"backward"``. Returns: array containing the discrete cosine transform of x See Also: - :func:`jax.scipy.fft.dct`: one-dimensional DCT - :func:`jax.scipy.fft.idct`: one-dimensional inverse DCT - :func:`jax.scipy.fft.idctn`: multidimensional inverse DCT Examples: ``jax.scipy.fft.dctn`` computes the transform along both the axes by default when ``axes`` argument is ``None``. >>> x = jax.random.normal(jax.random.key(0), (3, 3)) >>> with jnp.printoptions(precision=2, suppress=True): ... print(jax.scipy.fft.dctn(x)) [[ 12.01 6.2 -10.17] [ 8.84 9.65 -3.54] [ 11.25 -1.54 -0.88]] When ``s=[2]``, dimension of the transform along ``axis 0`` will be ``2`` and dimension along ``axis 1`` will be same as that of input. >>> with jnp.printoptions(precision=2, suppress=True): ... print(jax.scipy.fft.dctn(x, s=[2])) [[ 9.36 10.22 -8.53] [11.57 2.85 -2.06]] When ``s=[2]`` and ``axes=[1]``, dimension of the transform along ``axis 1`` will be ``2`` and dimension along ``axis 0`` will be same as that of input. Also when ``axes=[1]``, transform will be computed only along ``axis 1``. >>> with jnp.printoptions(precision=2, suppress=True): ... print(jax.scipy.fft.dctn(x, s=[2], axes=[1])) [[ 7.3 -0.57] [ 0.19 -0.36] [-0. -1.4 ]] When ``s=[2, 4]``, shape of the transform will be ``(2, 4)``. >>> with jnp.printoptions(precision=2, suppress=True): ... print(jax.scipy.fft.dctn(x, s=[2, 4])) [[ 9.36 11.23 2.12 -10.97] [ 11.57 5.86 -1.37 -1.58]] r4rr5Nr6zjax.scipy.fft.dctn: norm=r9rrrDr"rE)rKrE)r r<r=list TypeError isinstanceroperatorindexr r-lenrHdictzipr,r*rr>rr?r)rWdctn) r!rCsrKrEnsr1padsi axes_blocks rrbrbs~w"! QY ? @@ $&;; 1D94GH II] q'a !qvv .$Y!^ qAMAaDt$q' MM] c$l BBG- PQQa2g1 "1a 8 PD P 399Q($/AY!^ D ))+03t9a*@AQT!AaC[A,j QZd+A, () Ax(( ( >>!  a QBs E"+%F;F"1FFc td|}|dk7r td||dvrtd|dt||j}|pt j |tjd|jt|jDcgc]}d||k(r||j|z nddf c}}|j|}t|\}||dk(r t||}t||}t jtj||j t|jDcgc] }||k7s | c}}t!||}|j#|j}|t!||z }|dz|z}t%j&|| }t)|j*|} | Scc}wcc}w) aComputes the inverse discrete cosine transform of the input JAX implementation of :func:`scipy.fft.idct`. Args: x: array type: integer, default = 2. Currently only type 2 is supported. n: integer, default = x.shape[axis]. The length of the transform. If larger than ``x.shape[axis]``, the input will be zero-padded, if smaller, the input will be truncated. axis: integer, default=-1. The axis along which the dct will be performed. norm: string. The normalization mode: one of ``[None, "backward", "ortho"]``. The default is ``None``, which is equivalent to ``"backward"``. Returns: array containing the inverse discrete cosine transform of x See Also: - :func:`jax.scipy.fft.dct`: DCT - :func:`jax.scipy.fft.dctn`: multidimensional DCT - :func:`jax.scipy.fft.idctn`: multidimensional inverse DCT Examples: >>> x = jax.random.normal(jax.random.key(0), (3, 3)) >>> with jnp.printoptions(precision=2, suppress=True): ... print(jax.scipy.fft.idct(x)) [[ 0.78 0.41 -0.39] [-0.12 0.31 -0.23] [ 0.17 -0.3 -0.11]] When ``n`` smaller than ``x.shape[axis]`` >>> with jnp.printoptions(precision=2, suppress=True): ... print(jax.scipy.fft.idct(x, n=2)) [[ 1.12 -0.31] [ 0.04 -0.08] [ 0.05 -0.3 ]] When ``n`` smaller than ``x.shape[axis]`` and ``axis=0`` >>> with jnp.printoptions(precision=2, suppress=True): ... print(jax.scipy.fft.idct(x, n=2, axis=0)) [[ 0.38 0.57 -0.45] [ 0.43 0.44 0.24]] When ``n`` larger than ``x.shape[axis]`` and ``axis=0`` >>> with jnp.printoptions(precision=2, suppress=True): ... print(jax.scipy.fft.idct(x, n=4, axis=0)) [[ 0.1 0.38 -0.16] [ 0.28 0.18 -0.26] [ 0.3 0.15 -0.08] [ 0.13 0.3 0.29]] ``jax.scipy.fft.idct`` can be used to reconstruct ``x`` from the result of ``jax.scipy.fft.dct`` >>> x_dct = jax.scipy.fft.dct(x) >>> jnp.allclose(x, jax.scipy.fft.idct(x_dct)) Array(True, dtype=bool) idctrr5r6zjax.scipy.fft.idct: norm=r9rr7r;r:)r r<r=r r-rr>rr?r)r,r*r r2r+rArastyper@ifft_dct_deinterleaverB) r!rCrDr"rEr1rrw4r/s rriris@vq!! QY ? @@ $&;; 1D94GH II 4 ($] 399Q(-)!t)Q&A>) *Aggdm!a "! \TZ'4 Aa! oocjj!''2aff 4[1QRVZQZQ4[\! 1Qx"hhrxx!3q!9o!!eai! ll14 !!&&$'# *%)5\s#F> ; G G ctd|}|dk7r td||dvrtd|d| t|}t||j}t|dk(rt|||d nd|d | S|tt||}t|jDcgc] }d ||vr|||j |z nd d f"}}t#j$|t'j(d |j*|}|D]}t||| }|S#t$r,t |t rJtj|g}YwxYwcc}w) a Computes the multidimensional inverse discrete cosine transform of the input JAX implementation of :func:`scipy.fft.idctn`. Args: x: array type: integer, default = 2. Currently only type 2 is supported. s: integer or sequence of integers. Specifies the shape of the result. If not specified, it will default to the shape of ``x`` along the specified ``axes``. axes: integer or sequence of integers. Specifies the axes along which the transform will be computed. norm: string. The normalization mode: one of ``[None, "backward", "ortho"]``. The default is ``None``, which is equivalent to ``"backward"``. Returns: array containing the inverse discrete cosine transform of x See Also: - :func:`jax.scipy.fft.dct`: one-dimensional DCT - :func:`jax.scipy.fft.dctn`: multidimensional DCT - :func:`jax.scipy.fft.idct`: one-dimensional inverse DCT Examples: ``jax.scipy.fft.idctn`` computes the transform along both the axes by default when ``axes`` argument is ``None``. >>> x = jax.random.normal(jax.random.key(0), (3, 3)) >>> with jnp.printoptions(precision=2, suppress=True): ... print(jax.scipy.fft.idctn(x)) [[ 0.12 0.11 -0.15] [ 0.07 0.17 -0.03] [ 0.19 -0.07 -0.02]] When ``s=[2]``, dimension of the transform along ``axis 0`` will be ``2`` and dimension along ``axis 1`` will be the same as that of input. >>> with jnp.printoptions(precision=2, suppress=True): ... print(jax.scipy.fft.idctn(x, s=[2])) [[ 0.15 0.21 -0.18] [ 0.24 -0.01 -0.02]] When ``s=[2]`` and ``axes=[1]``, dimension of the transform along ``axis 1`` will be ``2`` and dimension along ``axis 0`` will be same as that of input. Also when ``axes=[1]``, transform will be computed only along ``axis 1``. >>> with jnp.printoptions(precision=2, suppress=True): ... print(jax.scipy.fft.idctn(x, s=[2], axes=[1])) [[ 1.12 -0.31] [ 0.04 -0.08] [ 0.05 -0.3 ]] When ``s=[2, 4]``, shape of the transform will be ``(2, 4)`` >>> with jnp.printoptions(precision=2, suppress=True): ... print(jax.scipy.fft.idctn(x, s=[2, 4])) [[ 0.1 0.18 0.07 -0.16] [ 0.2 0.06 -0.03 -0.01]] ``jax.scipy.fft.idctn`` can be used to reconstruct ``x`` from the result of ``jax.scipy.fft.dctn`` >>> x_dctn = jax.scipy.fft.dctn(x) >>> jnp.allclose(x, jax.scipy.fft.idctn(x_dctn)) Array(True, dtype=bool) r4rr5Nr6zjax.scipy.fft.idctn: norm=r9rrrY)r"rE)r r<r=rZr[r\rr]r^r r-r_rir`rar,r*rr>rr?r)) r!rCrcrKrErdr1rer"s rr4r4PscLw"! QY ? @@ $&;; 2TI5HI JJ] q'a !qvv .$Y!^ Q]QqT47 NN] c$l BBG- PQQa2g1 "1a 8 PD P 399Q($/A&d QT%A& (# Ax(( ( >>!  a Qs D+%E1EEc tddd t fdttjD}t fdttjD}|}t j |f}tjjj}t fdttjD}t fdttjD}|j|j|}|j|j|}|S)Nc3K|];}|k(r0tdtjjdz dn=ywrslicemathceilr*.0rfr" empty_slicer!s r z$_dct_deinterleave..sB$ 56IeD$))AGGDM!O,a0;N$AAc3K|];}|k(r0ttjjdz ddn=yw)rNrrqrus rrxz$_dct_deinterleave..sB$ 56IeDIIaggdmAo &a0;N$ryr;c3FK|]}|k(r tdddnyw)Nrrrrvrfr"rws rrxz$_dct_deinterleave..s,W=>a4ieD$[8W!c3FK|]}|k(r tdddnyw)rNrr|r}s rrxz$_dct_deinterleave..s,T:;19eAtQ+5Tr~) rrtupler,r_r*rrrzerosr)atset) r!r"ix0ix1r#r$r/evensoddsrws `` @rrlrlsdD$'+ $S\"$ $# $S\"$ $# v" wwqvw" !'')# WBGAGG BUW W% T?DS\?RT T$   2 # t # *r)rintrrreturnr)r!rr"rrr)r/rr"rrr)rNN) r!rrCrrDz int | Noner"rrE str | Nonerr)r!rrKz Sequence[int]rErrr)rNNN) r!rrCrrcSequence[int] | NonerKrrErrr)" __future__rcollections.abcr functoolsrrsr]rrjax._srcrrjax._src.numpyrr@jax._src.numpy.utilr r r jax._src.utilr r jax._src.typingrrr%r2rHrWrbrir4rlrrrs#$ !)FFD!+) 226+/L L (L 49L ^  !!%&* ] ] #] ] &+] @37,0\ \ )\ 5:\ ~!""&'+!a !a $a a ',a H r