Vpf;ddlmZddlmZddlmZddlZddlmZddl m Z ddl m Z ddlmZddlmZd%dZd&dZd'dZ d(d)dZd*dZ d+d,d!Z d(d)d"Z d+d,d#Zd&d$ZdS)-) annotations)Sequence)partialN)lax)canonicalize_axis)promote_dtypes_complex)ArrayNintkr returncvt||\}}tjdtjz|z|z S)Ny)rjnpexppi)r r N_arrs R/var/www/html/nettyfy-visnx/env/lib/python3.11/site-packages/jax/_src/scipy/fft.py_W4rs5 #Aq ) )(% "U* + ++xaxisc tj|ddd|}tjtj|ddd||f}tj||g|SN)r slice_in_dimrev concatenate)rrv0v1s r_dct_interleaver!sV 4q$//" ws1dAt44tg>>" "b4 ( ((routcdtjtjdd|jtj|jdz fd|jgd}tj|fdt |jD}|tj||jzz S)N)rrrrc g|] }|k| Sr&.0ars r z#_dct_ortho_norm..&s#L#L#L!!t))A)))r) rrfulldtypeshape expand_dimsrangendimsqrt)r"rfactors ` r_dct_ortho_normr3$s ?CHT1ci88#(CIdOVWDWCY[\^a^g:h:hikl m m& ?6#L#L#L#LuSX#L#L#L M M& sx4011 11rrtypen int | Nonenorm str | Nonec|dkrtd||dvrtd|dtjNt jt jdjfdtjDj }t}t j | }t j t j||jj fd tjD}|t!||z} d| jz} |d krt#| } | S) 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)) [[-0.58 -0.33 -1.08] [-0.88 -1.01 -1.79] [-1.06 -2.43 1.24]] When ``n`` smaller than ``x.shape[axis]`` >>> with jnp.printoptions(precision=2, suppress=True): ... print(jax.scipy.fft.dct(x, n=2)) [[-0.22 -0.9 ] [-0.57 -1.68] [-2.52 -0.11]] 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)) [[-2.22 1.43 -0.67] [ 0.52 -0.26 -0.04]] 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)) [[-0.58 -0.35 -0.64 -1.11] [-0.88 -0.9 -1.46 -1.68] [-1.06 -2.25 -1.15 1.93]] rOnly DCT type 2 is implemented.Nbackwardorthozjax.scipy.fft.dct: norm= is not implementedrcFg|]}d|krjz nddfSrr-r(r)rr6rs rr*zdct..lH)))!t))Q&&A>)))rrr,c g|] }|k| Sr&r&r's rr*zdct..rs%9`9`9`VW[_V_V_!V_V_V_rr>)NotImplementedError ValueErrorrr0rpadrarrayr,r/r-r!fftr.arangerealrr3) rr5r6rr8r vVr r"s ` `` rdctrQ-sin QYY ? @ @@ $&;;; G4GGG H HH 4 ( ($] 39Q(())))))--))) * *Agdm!a! gkk!$k! ocj!&,7779`9`9`9`U16]]9`9`9`aa! C1II # CH # W__ #t $ $C *raxes Sequence[int]c d ttt|j|\ |j |j }}t t |  }t j||}tj t j ||j  fdt|jD}tj t j ||j  fdt|jD}t||t|||zt|| t jt j| d zzz} d | jz} |d krt%t%|  S| S) N)num_dims)rRrFc g|] }|k| Sr&r&)r(r)axis1s rr*z_dct2..???aAJJJJJrc g|] }|k| Sr&r&)r(r)axis2s rr*z_dct2..rXrrEr)shiftrrr>)maprrr0r-r!rrLfftnrr.rMr,r/rrollfliprNr3) rrRr8N1N2rOrPk1k2r"rWrZs @@r_dct2rdzs~W.@@@$GG,% 75>175>b"oa//77! gll14l  ! sz"AG444????5==???AA" sz"AG444????5==???AA" B s2r{{QR"!RWAXAXAX`ahm8n8n8n)nno# CH # W__ ?366 > >> *rsSequence[int] | Nonec|dkrtd||dvrtd|dtjt dkr#t ||dndd| S|lt t|fd tjD}tj tj dj |t dkrt| Sfd tdt dDD]}t|| S) 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)) [[-5.04 -7.54 -3.26] [ 0.83 3.64 -4.03] [ 0.12 -0.73 3.74]] 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])) [[-2.92 -2.68 -5.74] [ 0.42 0.97 1. ]] 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])) [[-0.22 -0.9 ] [-0.57 -1.68] [-2.52 -0.11]] 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])) [[-2.92 -2.49 -4.21 -5.57] [ 0.42 0.79 1.16 0.8 ]] rr;Nr<zjax.scipy.fft.dctn: norm=r?rrr6rr8cNg|]!}d|vr|j|z nddf"SrArBr(r)nsrs rr*zdctn..< P P PQQa2gg1 ""1a 8 P P Pr)rRr8c*g|]}||dzS)rr&)r(irRs rr*zdctn..s%AAAQT!AaC%[AAAr)rHrIr/r0lenrQdictziprrJrrKr,rddctn)rr5rerRr8pads axes_blockrks` ` @rrrrrsi~ QYY ? @ @@ $&;;; HDHHH I II \ ==DYY!^^ qAMAaDDt$q' M M MM] c$ll  B P P P P P%-- P P PD 39Q(($//AYY!^^ D ) ) ))BAAA%3t99a*@*@AAA,,j QZd+++AA (rcr|dkrtd||dvrtd|dtjNt jt jdjfdtjDj } t j ||d krttt jt j|t j fd tjD}t!||} |jt!||z dz|zt j t'j}|S) 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)) [[-0.02 -0. -0.17] [-0.02 -0.07 -0.28] [-0.16 -0.36 0.18]] When ``n`` smaller than ``x.shape[axis]`` >>> with jnp.printoptions(precision=2, suppress=True): ... print(jax.scipy.fft.idct(x, n=2)) [[ 0. -0.19] [-0.03 -0.34] [-0.38 0.04]] 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)) [[-0.35 0.23 -0.1 ] [ 0.17 -0.09 0.01]] 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)) [[-0.34 0.03 0.07] [ 0. 0.18 -0.17] [ 0.14 0.09 -0.14] [ 0. -0.18 0.14]] ``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) rr;Nr<zjax.scipy.fft.idct: norm=r?rcFg|]}d|krjz nddfSrArBrCs rr*zidct..*rDrr=rFc g|] }|k| Sr&r&r's rr*zidct..2s%8_8_8_qUVZ^U^U^U^U^U^rrE)rHrIrr0rrJrrKr,r/r-astypefloat32r3r.rMrrLifft_dct_deinterleaverN) rr5r6rr8r r w4r"s ` `` ridctr}s@ QYY ? @ @@ $&;;; HDHHH I II 4 ( ($] 39Q(())))))--))) * *Agdm!hhs{! \TZ''4  Aa! ocj#+6668_8_8_8_E!&MM8_8_8_``! 1Qxx"hhrx!3q!99o!!eai! gll14l  !!&$''# *rc|dkrtd||dvrtd|d|tj}t |dkr#t ||dnd|d| S|lt t||fd tjD}tj tj dj ||D]}t || S) 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)) [[-0.03 -0.08 -0.08] [ 0.05 0.12 -0.09] [-0.02 -0.04 0.08]] 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])) [[-0.01 -0.03 -0.14] [ 0. 0.03 0.06]] 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.idctn(x, s=[2], axes=[1])) [[ 0. -0.19] [-0.03 -0.34] [-0.38 0.04]] 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])) [[-0.01 -0.01 -0.05 -0.11] [ 0. 0.01 0.03 0.04]] ``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) rr;Nr<zjax.scipy.fft.idctn: norm=r?rrrhcNg|]!}d|vr|j|z nddf"SrArBrjs rr*zidctn..rlr)rr8) rHrIr/r0ror}rprqrrJrrKr,)rr5rerRr8rsrrks` @ridctnr?sL QYY ? @ @@ $&;;; ITIII J JJ \ ==DYY!^^ Q]QqTT47 N N NN] c$ll  B P P P P P%-- P P PD 39Q(($//A&&d QT%%%AA (rc tddd t fdttjD}t fdttjD}|}t j|f}tjjj }t fdttjD}t fdttjD}|j | |}|j | |}|S)Nc3K|]=}|kr1tdtjjdz dnV>dSrslicemathceilr-r(rnr empty_slicers r z$_dct_deinterleave..sd$$ 56IIeD$)AGDM!O,,a000;$$$$$$rc3K|]=}|kr1ttjjdz ddnV>dS)rNrrrs rrz$_dct_deinterleave..sd$$ 56IIeDIagdmAo & &a000;$$$$$$rrFc3JK|]}|krtdddnVdS)Nrrr(rnrrs rrz$_dct_deinterleave..sUWW=>a4iieD$[WWWWWWrc3JK|]}|krtdddnVdS)rNrrrs rrz$_dct_deinterleave..sUTT:;199eAtQ+TTTTTTr) rtupler/ror-rrrzerosr,atset) rrix0ix1rr r"evensoddsrs `` @rr{r{sdD$''+ $$$$$$S\\""$$$ $ $# $$$$$$S\\""$$$ $ $# v" wqvw" !')))# WWWWWBGAG BUBUWWW W W% TTTTT?DS\\?R?RTTT T T$   2  # t # *r)r r r r r r )rr rr r r )r"r rr r r )rNr4N) rr r5r r6r7rr r8r9r r )rr rRrSr8r9r r )rNNN) rr r5r rerfrRrfr8r9r r ) __future__rcollections.abcr functoolsrrjaxr jax.numpynumpyr jax._src.utilrjax._src.numpy.utilrjax._src.typingr rr!r3rQrdrrr}rr{r&rrrs#"""""$$$$$$ ++++++666666!!!!!!,,,,)))) 222226+/J J J J J Z     !!%&* U U U U U p37+/Z Z Z Z Z z!""&'+!Y Y Y Y Y x      r