ó àÆ÷Xc@`sˆddlmZmZmZddlZddlZddlmZddlZddl m Z ddl m Z m Z ddlmZddl mZejeƒZde fd „ƒYZeƒZd e fd „ƒYZeƒZd „Zd e fd„ƒYZeƒZde fd„ƒYZeƒZd„Zd„Zde fd„ƒYZ e ƒZ!de fd„ƒYZ"e"ƒZ#de"fd„ƒYZ$d„Z%de fd„ƒYZ&dd„Z'de fd„ƒYZ(d e fd!„ƒYZ)d"d#„Z*d$e fd%„ƒYZ+d&d&d'„Z,d(e fd)„ƒYZ-d*„Z.d+„Z/d,e fd-„ƒYZ0d.d/„Z1d0e fd1„ƒYZ2dd2„Z4dS(3i(tabsolute_importtprint_functiontdivisionN(txrange(tas_tensor_variable(tOptApply(tDisconnectedType(tbasict MatrixPinvcB`s/eZdZdZd„Zd„Zd„ZRS(s¹Computes the pseudo-inverse of a matrix :math:`A`. The pseudo-inverse of a matrix :math:`A`, denoted :math:`A^+`, is defined as: "the matrix that 'solves' [the least-squares problem] :math:`Ax = b`," i.e., if :math:`\bar{x}` is said solution, then :math:`A^+` is that matrix such that :math:`\bar{x} = A^+b`. Note that :math:`Ax=AA^+b`, so :math:`AA^+` is close to the identity matrix. This method is not faster than `matrix_inverse`. Its strength comes from that it works for non-square matrices. If you have a square matrix though, `matrix_inverse` can be both more exact and faster to compute. Also this op does not get optimized into a solve op. cC`sdS(N((tself((s5/tmp/pip-build-X4mzal/theano/theano/tensor/nlinalg.pyt__init__$scC`s=t|ƒ}|jdks!t‚t||g|jƒgƒS(Ni(RtndimtAssertionErrorRttype(R tx((s5/tmp/pip-build-X4mzal/theano/theano/tensor/nlinalg.pyt make_node's cC`s8|\}|\}tjj|ƒj|jƒ|d`_, one can deduce that the relation corresponds to .. math:: (X^{-1} \cdot V^{T} \cdot X^{-1})^T. (t matrix_dottT(R Rt g_outputsRtxitgz((s5/tmp/pip-build-X4mzal/theano/theano/tensor/nlinalg.pytgradQs   cC`sE|\}||ƒ}|\}|dkr1dgSt|||ƒ gS(s›The gradient function should return .. math:: \frac{\partial X^{-1}}{\partial X}V, where :math:`V` corresponds to ``g_outputs`` and :math:`X` to ``inputs``. Using the `matrix cookbook `_, one can deduce that the relation corresponds to .. math:: X^{-1} \cdot V \cdot X^{-1}. N(tNoneR!(R Rt eval_pointsRR$tev((s5/tmp/pip-build-X4mzal/theano/theano/tensor/nlinalg.pytR_opds    cC`s|S(N((R Rtshapes((s5/tmp/pip-build-X4mzal/theano/theano/tensor/nlinalg.pyt infer_shapexs(( RRRRR RRR&R*R,(((s5/tmp/pip-build-X4mzal/theano/theano/tensor/nlinalg.pyR4s      cG`s8|d}x'|dD]}tjj||ƒ}qW|S(sþ Shorthand for product between several dots. Given :math:`N` matrices :math:`A_0, A_1, .., A_N`, ``matrix_dot`` will generate the matrix product between all in the given order, namely :math:`A_0 \cdot A_1 \cdot A_2 \cdot .. \cdot A_N`. ii(ttheanottensortdot(targstrvalta((s5/tmp/pip-build-X4mzal/theano/theano/tensor/nlinalg.pyR!~s t AllocDiagcB`s8eZdZdZd„Zd„Zd„Zd„ZRS(sJ Allocates a square matrix with the given vector as its diagonal. cC`s[t|ƒ}|jjdkr0td|ƒ‚nt||gtjjd|jjƒgƒS(NisAllocDiag only works on vectorsR( RRR t TypeErrorRR-R.tmatrixR(R t_xR((s5/tmp/pip-build-X4mzal/theano/theano/tensor/nlinalg.pyR“s cC`st|dƒgS(Ni(t extract_diag(R RR#((s5/tmp/pip-build-X4mzal/theano/theano/tensor/nlinalg.pyR&™scC`sG|\}|\}|jdkr0t|ƒ‚ntj|ƒ|ds  cC`s!|dd}|f||fgS(Ni((R RR+tn((s5/tmp/pip-build-X4mzal/theano/theano/tensor/nlinalg.pyR,Cs(( RRRt staticmethodRRteigR`RRRR,(((s5/tmp/pip-build-X4mzal/theano/theano/tensor/nlinalg.pyR\.s   tEighcB`sMeZdZeejjƒZdZdd„Z d„Z d„Z d„Z RS(sV Return the eigenvalues and eigenvectors of a Hermitian or symmetric matrix. tUPLOtLcC`s|dkst‚||_dS(NRftU(RfRg(R Re(R Re((s5/tmp/pip-build-X4mzal/theano/theano/tensor/nlinalg.pyR SscC`s˜t|ƒ}|jdks!t‚|jtj|jƒjƒggƒdjj}tj j d|ƒ}tj j d|jƒ}t ||g||gƒS(NiiR( RR R R`RRRtnameR-R.R]R5R(R Rtw_dtypeR^R_((s5/tmp/pip-build-X4mzal/theano/theano/tensor/nlinalg.pyRWs  1cC`s<|\}|\}}|j||jƒ\|d<|dRRtappendRJ(RtgradstlRVtg((s5/tmp/pip-build-X4mzal/theano/theano/tensor/nlinalg.pyRjˆs RkcB`s;eZdZdZdd„Zd„Zd„Zd„ZRS(s< Gradient of an eigensystem of a Hermitian matrix. ReRfcC`s^|dkst‚||_|dkrBtj|_d„|_ntj|_d„|_dS(NRfRgcS`stj|dƒS(Ni(Rttriu(R2((s5/tmp/pip-build-X4mzal/theano/theano/tensor/nlinalg.pytŸscS`stj|dƒS(Niÿÿÿÿ(Rttril(R2((s5/tmp/pip-build-X4mzal/theano/theano/tensor/nlinalg.pyRu¢s(RfRg(R ReRRvttri0ttri1Rt(R Re((s5/tmp/pip-build-X4mzal/theano/theano/tensor/nlinalg.pyR šs    cC`sútt|||||fƒ\}}}}}|jdksBt‚|jdksWt‚|jdkslt‚|jdkst‚|jdks–t‚tjj|j|j|j|j|jƒ}tjj d|ƒ}t ||||||g|gƒS(NiiR( tmapRR R R-RUtupcastRR.R5R(R RR^R_RlRmt out_dtypetout((s5/tmp/pip-build-X4mzal/theano/theano/tensor/nlinalg.pyR¤s-c`s¸|\}‰‰‰‰|jd‰tj‰‡‡‡‡fd†‰t‡‡‡‡fd†tˆƒDƒƒ}|j|ƒ|j|ƒj}tj|d|j dj ƒ|dd»s(RQR(Ra(tNRR_R^(Ras5/tmp/pip-build-X4mzal/theano/theano/tensor/nlinalg.pytGºsc3`sP|]F}ˆˆdd…|fˆdd…|fˆ|ˆ|ƒƒVqdS(N((R}Ra(RtWtouterR_(s5/tmp/pip-build-X4mzal/theano/theano/tensor/nlinalg.pys ¾sRN( RCRRƒRQRRwRxR"RWRR(R RRRRRsR|((RR€RR‚RƒR_R^s5/tmp/pip-build-X4mzal/theano/theano/tensor/nlinalg.pyR°s   cC`s |dgS(Ni((R RR+((s5/tmp/pip-build-X4mzal/theano/theano/tensor/nlinalg.pyR,Ïs(sUPLO(RRRRR RRR,(((s5/tmp/pip-build-X4mzal/theano/theano/tensor/nlinalg.pyRk’s  RfcC`st|ƒ|ƒS(N(Rd(R2Re((s5/tmp/pip-build-X4mzal/theano/theano/tensor/nlinalg.pyRnÓstQRFullcB`sAeZdZeejjƒZdZd„Z d„Z d„Z RS(s¦ Full QR Decomposition. Computes the QR decomposition of a matrix. Factor the matrix a as qr, where q is orthonormal and r is upper-triangular. tmodecC`s ||_dS(N(R…(R R…((s5/tmp/pip-build-X4mzal/theano/theano/tensor/nlinalg.pyR äscC`sšt|ƒ}|jdks'tdƒ‚tjjd|jƒ}|jdkritjjd|jƒ}ntjjd|jƒ}t ||g||gƒS(Nis,The input of qr function should be a matrix.Rtraw( RR R R-R.R5RR…R]R(R Rtqtr((s5/tmp/pip-build-X4mzal/theano/theano/tensor/nlinalg.pyRçs cC`sW|\}|\}}|jdks0tdƒ‚|j||jƒ\|d<|dRRR‰ttupleR„RŠ(R2R…R((s5/tmp/pip-build-X4mzal/theano/theano/tensor/nlinalg.pyR‰s+tSVDcB`sGeZdZeejjƒZdZe e d„Z d„Z d„Z RS(sy Parameters ---------- full_matrices : bool, optional If True (default), u and v have the shapes (M, M) and (N, N), respectively. Otherwise, the shapes are (M, K) and (K, N), respectively, where K = min(M, N). compute_uv : bool, optional Whether or not to compute u and v in addition to s. True by default. t full_matricest compute_uvcC`s||_||_dS(N(RŽR(R RŽR((s5/tmp/pip-build-X4mzal/theano/theano/tensor/nlinalg.pyR \s cC`s‹t|ƒ}|jdks'tdƒ‚tjjd|jƒ}tjjd|jƒ}tjjd|jƒ}t||g|||gƒS(Nis-The input of svd function should be a matrix.R( RR R R-R.R5RR]R(R RR^tuR_((s5/tmp/pip-build-X4mzal/theano/theano/tensor/nlinalg.pyR`s  cC`sg|\}|\}}}|jdks3tdƒ‚|j||j|jƒ\|d<|d<|d 2( RR t ValueErrorR'R.RQtmaxtabsRNtnonzeroRCR4tNotImplementedError(RtordR R((s5/tmp/pip-build-X4mzal/theano/theano/tensor/nlinalg.pytnorm«s@        %       t TensorInvcB`sMeZdZeejjƒZdZdd„Z d„Z d„Z d„Z RS(sc Class wrapper for tensorinv() function; Theano utilization of numpy.linalg.tensorinv; tindicC`s ||_dS(N(R§(R R§((s5/tmp/pip-build-X4mzal/theano/theano/tensor/nlinalg.pyR ØscC`s.t|ƒ}|jƒ}t||g|gƒS(N(RRR(R R2R|((s5/tmp/pip-build-X4mzal/theano/theano/tensor/nlinalg.pyRÛs  cC`s/|\}|\}|j||jƒ|dsP    G   ?   !  > A " 2)  % !