ó ˽÷Xc@sdZddljjZddlZedƒZd„Z d„Z d„Z d„Z d„Z d „Zd „Zd „Zd „Zd „Zd„Zd„Zd„Zdd„Zdd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Z d„Z!d„Z"d„Z#d „Z$d!„Z%d"„Z&d#„Z'd$„Z(d%„Z)d&„Z*d'„Z+d(„Z,d)„Z-d*„Z.dd+„Z/dd,„Z0d-„Z1d.„Z2d/„Z3d0„Z4d1„Z5d2„Z6d3„Z7d4„Z8d5„Z9d6„Z:d7„Z;d8„Z<d9„Z=dS(:s0 Direct wrappers for Fortran `id_dist` backend. iÿÿÿÿNsnonzero return codecCs tj|ƒS(s  Generate standard uniform pseudorandom numbers via a very efficient lagged Fibonacci method. :param n: Number of pseudorandom numbers to generate. :type n: int :return: Pseudorandom numbers. :rtype: :class:`numpy.ndarray` (t_idtid_srand(tn((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyR,s cCs tj|ƒ}tj|ƒdS(s¹ Initialize seed values for :func:`id_srand` (any appropriately random numbers will do). :param t: Array of 55 seed values. :type t: :class:`numpy.ndarray` N(tnptasfortranarrayRt id_srandi(tt((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyR<s cCstjƒdS(s5 Reset seed values to their original values. N(Rt id_srando(((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyRIscCstj|||ƒS(s| Transform real vector via a composition of Rokhlin's random transform, random subselection, and an FFT. In contrast to :func:`idd_sfrm`, this routine works best when the length of the transformed vector is the power-of-two integer output by :func:`idd_frmi`, or when the length is not specified but instead determined a posteriori from the output. The returned transformed vector is randomly permuted. :param n: Greatest power-of-two integer satisfying `n <= x.size` as obtained from :func:`idd_frmi`; `n` is also the length of the output vector. :type n: int :param w: Initialization array constructed by :func:`idd_frmi`. :type w: :class:`numpy.ndarray` :param x: Vector to be transformed. :type x: :class:`numpy.ndarray` :return: Transformed vector. :rtype: :class:`numpy.ndarray` (Rtidd_frm(Rtwtx((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyRTscCstj||||ƒS(sê Transform real vector via a composition of Rokhlin's random transform, random subselection, and an FFT. In contrast to :func:`idd_frm`, this routine works best when the length of the transformed vector is known a priori. :param l: Length of transformed vector, satisfying `l <= n`. :type l: int :param n: Greatest power-of-two integer satisfying `n <= x.size` as obtained from :func:`idd_sfrmi`. :type n: int :param w: Initialization array constructed by :func:`idd_sfrmi`. :type w: :class:`numpy.ndarray` :param x: Vector to be transformed. :type x: :class:`numpy.ndarray` :return: Transformed vector. :rtype: :class:`numpy.ndarray` (Rtidd_sfrm(tlRR R ((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyR qscCs tj|ƒS(sC Initialize data for :func:`idd_frm`. :param m: Length of vector to be transformed. :type m: int :return: Greatest power-of-two integer `n` satisfying `n <= m`. :rtype: int :return: Initialization array to be used by :func:`idd_frm`. :rtype: :class:`numpy.ndarray` (Rtidd_frmi(tm((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyR ŽscCstj||ƒS(s• Initialize data for :func:`idd_sfrm`. :param l: Length of output transformed vector. :type l: int :param m: Length of the vector to be transformed. :type m: int :return: Greatest power-of-two integer `n` satisfying `n <= m`. :rtype: int :return: Initialization array to be used by :func:`idd_sfrm`. :rtype: :class:`numpy.ndarray` (Rt idd_sfrmi(R R((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyR scCsxtj|ƒ}tj||ƒ\}}}|jd}|jjƒ||| j|||fddƒ}|||fS(sž Compute ID of a real matrix to a specified relative precision. :param eps: Relative precision. :type eps: float :param A: Matrix. :type A: :class:`numpy.ndarray` :return: Rank of ID. :rtype: int :return: Column index array. :rtype: :class:`numpy.ndarray` :return: Interpolation coefficients. :rtype: :class:`numpy.ndarray` itordertF(RRRtiddp_idtshapetTtraveltreshape(tepstAtktidxtrnormsRtproj((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyR¹s  4cCsrtj|ƒ}tj||ƒ\}}|jd}|jjƒ||| j|||fddƒ}||fS(sQ Compute ID of a real matrix to a specified rank. :param A: Matrix. :type A: :class:`numpy.ndarray` :param k: Rank of ID. :type k: int :return: Column index array. :rtype: :class:`numpy.ndarray` :return: Interpolation coefficients. :rtype: :class:`numpy.ndarray` iRR(RRRtiddr_idRRRR(RRRRRR((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyRÕs  4cCsRtj|ƒ}|jdkr1tj|||ƒS|dd…tj|ƒfSdS(ss Reconstruct matrix from real ID. :param B: Skeleton matrix. :type B: :class:`numpy.ndarray` :param idx: Column index array. :type idx: :class:`numpy.ndarray` :param proj: Interpolation coefficients. :type proj: :class:`numpy.ndarray` :return: Reconstructed matrix. :rtype: :class:`numpy.ndarray` iN(RRtsizeRt idd_reconidtargsort(tBRR((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyRîscCstj||ƒS(s6 Reconstruct interpolation matrix from real ID. :param idx: Column index array. :type idx: :class:`numpy.ndarray` :param proj: Interpolation coefficients. :type proj: :class:`numpy.ndarray` :return: Interpolation matrix. :rtype: :class:`numpy.ndarray` (Rt idd_reconint(RR((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyR"scCs"tj|ƒ}tj|||ƒS(sN Reconstruct skeleton matrix from real ID. :param A: Original matrix. :type A: :class:`numpy.ndarray` :param k: Rank of ID. :type k: int :param idx: Column index array. :type idx: :class:`numpy.ndarray` :return: Skeleton matrix. :rtype: :class:`numpy.ndarray` (RRRt idd_copycols(RRR((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyR#scCsLtj|ƒ}tj|||ƒ\}}}}|r?t‚n|||fS(s Convert real ID to SVD. :param B: Skeleton matrix. :type B: :class:`numpy.ndarray` :param idx: Column index array. :type idx: :class:`numpy.ndarray` :param proj: Interpolation coefficients. :type proj: :class:`numpy.ndarray` :return: Left singular vectors. :rtype: :class:`numpy.ndarray` :return: Right singular vectors. :rtype: :class:`numpy.ndarray` :return: Singular values. :rtype: :class:`numpy.ndarray` (RRRt idd_id2svdt_RETCODE_ERROR(R!RRtUtVtStier((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyR$3s ! icCs%tj|||||ƒ\}}|S(s Estimate spectral norm of a real matrix by the randomized power method. :param m: Matrix row dimension. :type m: int :param n: Matrix column dimension. :type n: int :param matvect: Function to apply the matrix transpose to a vector, with call signature `y = matvect(x)`, where `x` and `y` are the input and output vectors, respectively. :type matvect: function :param matvec: Function to apply the matrix to a vector, with call signature `y = matvec(x)`, where `x` and `y` are the input and output vectors, respectively. :type matvec: function :param its: Number of power method iterations. :type its: int :return: Spectral norm estimate. :rtype: float (Rt idd_snorm(RRtmatvecttmatvectitstsnormtv((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyR*Vs!cCstj|||||||ƒS(s0 Estimate spectral norm of the difference of two real matrices by the randomized power method. :param m: Matrix row dimension. :type m: int :param n: Matrix column dimension. :type n: int :param matvect: Function to apply the transpose of the first matrix to a vector, with call signature `y = matvect(x)`, where `x` and `y` are the input and output vectors, respectively. :type matvect: function :param matvect2: Function to apply the transpose of the second matrix to a vector, with call signature `y = matvect2(x)`, where `x` and `y` are the input and output vectors, respectively. :type matvect2: function :param matvec: Function to apply the first matrix to a vector, with call signature `y = matvec(x)`, where `x` and `y` are the input and output vectors, respectively. :type matvec: function :param matvec2: Function to apply the second matrix to a vector, with call signature `y = matvec2(x)`, where `x` and `y` are the input and output vectors, respectively. :type matvec2: function :param its: Number of power method iterations. :type its: int :return: Spectral norm estimate of matrix difference. :rtype: float (Rt idd_diffsnorm(RRR+tmatvect2R,tmatvec2R-((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyR0vs'cCsItj|ƒ}tj||ƒ\}}}}|r<t‚n|||fS(s› Compute SVD of a real matrix to a specified rank. :param A: Matrix. :type A: :class:`numpy.ndarray` :param k: Rank of SVD. :type k: int :return: Left singular vectors. :rtype: :class:`numpy.ndarray` :return: Right singular vectors. :rtype: :class:`numpy.ndarray` :return: Singular values. :rtype: :class:`numpy.ndarray` (RRRtiddr_svdR%(RRR&R'R(R)((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyR3¤s  c CsÛtj|ƒ}|j\}}tj||ƒ\}}}}}} | rQt‚n||d|||d!j||fddƒ} ||d|||d!j||fddƒ} ||d||d!} | | | fS(s¶ Compute SVD of a real matrix to a specified relative precision. :param eps: Relative precision. :type eps: float :param A: Matrix. :type A: :class:`numpy.ndarray` :return: Left singular vectors. :rtype: :class:`numpy.ndarray` :return: Right singular vectors. :rtype: :class:`numpy.ndarray` :return: Singular values. :rtype: :class:`numpy.ndarray` iRR(RRRRtiddp_svdR%R( RRRRRtiUtiVtiSR R)R&R'R(((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyR4Às$ 22c Cs²tj|ƒ}|j\}}t|ƒ\}}tj|d|d|dddƒ}tj||||ƒ\}}}|||| j|||fddƒ}|||fS(s¸ Compute ID of a real matrix to a specified relative precision using random sampling. :param eps: Relative precision. :type eps: float :param A: Matrix. :type A: :class:`numpy.ndarray` :return: Rank of ID. :rtype: int :return: Column index array. :rtype: :class:`numpy.ndarray` :return: Interpolation coefficients. :rtype: :class:`numpy.ndarray` iiRR(RRRR temptyRtiddp_aidR( RRRRtn2R RRR((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyR9äs)!+cCs{tj|ƒ}|j\}}t|ƒ\}}tj|||d|dddƒ}tj||||ƒ\}}|S(se Estimate rank of a real matrix to a specified relative precision using random sampling. The output rank is typically about 8 higher than the actual rank. :param eps: Relative precision. :type eps: float :param A: Matrix. :type A: :class:`numpy.ndarray` :return: Rank estimate. :rtype: int iRR(RRRR R8Rt idd_estrank(RRRRR:R traR((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyR;s )cCsZtj|ƒ}|j\}}tj|ƒ\}}tjtt||ƒdd|d|ddt||ƒdd|d|dƒddƒ}tj||||ƒ\}}} } }} | rÐt ‚n||d|||d!j ||fddƒ} || d| ||d!j ||fddƒ} || d| |d!}| | |fS(sÐ Compute SVD of a real matrix to a specified relative precision using random sampling. :param eps: Relative precision. :type eps: float :param A: Matrix. :type A: :class:`numpy.ndarray` :return: Left singular vectors. :rtype: :class:`numpy.ndarray` :return: Right singular vectors. :rtype: :class:`numpy.ndarray` :return: Singular values. :rtype: :class:`numpy.ndarray` iiiiiRR( RRRRR R8tmaxtmint iddp_asvdR%R(RRRRR:twinitR RR5R6R7R)R&R'R(((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyR?!s< * 22cCs¦tj|dd|t||ƒdddƒ}tj|||||ƒ\}}}}|dkrnt‚n|||| j|||fddƒ}|||fS(së Compute ID of a real matrix to a specified relative precision using random matrix-vector multiplication. :param eps: Relative precision. :type eps: float :param m: Matrix row dimension. :type m: int :param n: Matrix column dimension. :type n: int :param matvect: Function to apply the matrix transpose to a vector, with call signature `y = matvect(x)`, where `x` and `y` are the input and output vectors, respectively. :type matvect: function :return: Rank of ID. :rtype: int :return: Column index array. :rtype: :class:`numpy.ndarray` :return: Interpolation coefficients. :rtype: :class:`numpy.ndarray` iiRRi(RR8R>Rtiddp_ridR%R(RRRR+RRRR)((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyRAKs 2'  +cCs4tj||||ƒ\}}}|r0t‚n|S(sQ Estimate rank of a real matrix to a specified relative precision using random matrix-vector multiplication. :param eps: Relative precision. :type eps: float :param m: Matrix row dimension. :type m: int :param n: Matrix column dimension. :type n: int :param matvect: Function to apply the matrix transpose to a vector, with call signature `y = matvect(x)`, where `x` and `y` are the input and output vectors, respectively. :type matvect: function :return: Rank estimate. :rtype: int (Rt idd_findrankR%(RRRR+RR<R)((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyRBqs! cCsÆtj|||||ƒ\}}}}} } | r<t‚n| |d|||d!j||fddƒ} | |d|||d!j||fddƒ} | |d||d!} | | | fS(sÚ Compute SVD of a real matrix to a specified relative precision using random matrix-vector multiplication. :param eps: Relative precision. :type eps: float :param m: Matrix row dimension. :type m: int :param n: Matrix column dimension. :type n: int :param matvect: Function to apply the matrix transpose to a vector, with call signature `y = matvect(x)`, where `x` and `y` are the input and output vectors, respectively. :type matvect: function :param matvec: Function to apply the matrix to a vector, with call signature `y = matvec(x)`, where `x` and `y` are the input and output vectors, respectively. :type matvec: function :return: Left singular vectors. :rtype: :class:`numpy.ndarray` :return: Right singular vectors. :rtype: :class:`numpy.ndarray` :return: Singular values. :rtype: :class:`numpy.ndarray` iRR(Rt iddp_rsvdR%R(RRRR+R,RR5R6R7R R)R&R'R(((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyRC“s#- 22cCsžtj|ƒ}|j\}}t|||ƒ}tj|||ƒ\}}||krutjgddddƒ}n|j|||fddƒ}||fS(sg Compute ID of a real matrix to a specified rank using random sampling. :param A: Matrix. :type A: :class:`numpy.ndarray` :param k: Rank of ID. :type k: int :return: Column index array. :rtype: :class:`numpy.ndarray` :return: Interpolation coefficients. :rtype: :class:`numpy.ndarray` tdtypetfloat64RR(RRRt iddr_aidiRtiddr_aidtarrayR(RRRRR RR((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyRGÃs cCstj|||ƒS(sO Initialize array for :func:`iddr_aid`. :param m: Matrix row dimension. :type m: int :param n: Matrix column dimension. :type n: int :param k: Rank of ID. :type k: int :return: Initialization array to be used by :func:`iddr_aid`. :rtype: :class:`numpy.ndarray` (RRF(RRR((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyRFàsc CsÁtj|ƒ}|j\}}tjd|d|d|d|d|ddddƒ}t|||ƒ}|||j*tj|||ƒ\}}}} | d kr´t‚n|||fS( s± Compute SVD of a real matrix to a specified rank using random sampling. :param A: Matrix. :type A: :class:`numpy.ndarray` :param k: Rank of SVD. :type k: int :return: Left singular vectors. :rtype: :class:`numpy.ndarray` :return: Right singular vectors. :rtype: :class:`numpy.ndarray` :return: Singular values. :rtype: :class:`numpy.ndarray` iiiiiidRRi( RRRR8RFRRt iddr_asvdR%( RRRRR tw_R&R'R(R)((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyRIùsA !  cCsStj||||ƒ\}}|||| j|||fddƒ}||fS(sž Compute ID of a real matrix to a specified rank using random matrix-vector multiplication. :param m: Matrix row dimension. :type m: int :param n: Matrix column dimension. :type n: int :param matvect: Function to apply the matrix transpose to a vector, with call signature `y = matvect(x)`, where `x` and `y` are the input and output vectors, respectively. :type matvect: function :param k: Rank of ID. :type k: int :return: Column index array. :rtype: :class:`numpy.ndarray` :return: Interpolation coefficients. :rtype: :class:`numpy.ndarray` RR(Rtiddr_ridR(RRR+RRR((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyRKs+c CsItj|||||ƒ\}}}}|dkr<t‚n|||fS(s¿ Compute SVD of a real matrix to a specified rank using random matrix-vector multiplication. :param m: Matrix row dimension. :type m: int :param n: Matrix column dimension. :type n: int :param matvect: Function to apply the matrix transpose to a vector, with call signature `y = matvect(x)`, where `x` and `y` are the input and output vectors, respectively. :type matvect: function :param matvec: Function to apply the matrix to a vector, with call signature `y = matvec(x)`, where `x` and `y` are the input and output vectors, respectively. :type matvec: function :param k: Rank of SVD. :type k: int :return: Left singular vectors. :rtype: :class:`numpy.ndarray` :return: Right singular vectors. :rtype: :class:`numpy.ndarray` :return: Singular values. :rtype: :class:`numpy.ndarray` i(Rt iddr_rsvdR%( RRR+R,RR&R'R(R)((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyRLAs#'  cCstj|||ƒS(s Transform complex vector via a composition of Rokhlin's random transform, random subselection, and an FFT. In contrast to :func:`idz_sfrm`, this routine works best when the length of the transformed vector is the power-of-two integer output by :func:`idz_frmi`, or when the length is not specified but instead determined a posteriori from the output. The returned transformed vector is randomly permuted. :param n: Greatest power-of-two integer satisfying `n <= x.size` as obtained from :func:`idz_frmi`; `n` is also the length of the output vector. :type n: int :param w: Initialization array constructed by :func:`idz_frmi`. :type w: :class:`numpy.ndarray` :param x: Vector to be transformed. :type x: :class:`numpy.ndarray` :return: Transformed vector. :rtype: :class:`numpy.ndarray` (Rtidz_frm(RR R ((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyRMnscCstj||||ƒS(sí Transform complex vector via a composition of Rokhlin's random transform, random subselection, and an FFT. In contrast to :func:`idz_frm`, this routine works best when the length of the transformed vector is known a priori. :param l: Length of transformed vector, satisfying `l <= n`. :type l: int :param n: Greatest power-of-two integer satisfying `n <= x.size` as obtained from :func:`idz_sfrmi`. :type n: int :param w: Initialization array constructed by :func:`idd_sfrmi`. :type w: :class:`numpy.ndarray` :param x: Vector to be transformed. :type x: :class:`numpy.ndarray` :return: Transformed vector. :rtype: :class:`numpy.ndarray` (Rtidz_sfrm(R RR R ((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyRN‹scCs tj|ƒS(sC Initialize data for :func:`idz_frm`. :param m: Length of vector to be transformed. :type m: int :return: Greatest power-of-two integer `n` satisfying `n <= m`. :rtype: int :return: Initialization array to be used by :func:`idz_frm`. :rtype: :class:`numpy.ndarray` (Rtidz_frmi(R((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyRO¨scCstj||ƒS(s• Initialize data for :func:`idz_sfrm`. :param l: Length of output transformed vector. :type l: int :param m: Length of the vector to be transformed. :type m: int :return: Greatest power-of-two integer `n` satisfying `n <= m`. :rtype: int :return: Initialization array to be used by :func:`idz_sfrm`. :rtype: :class:`numpy.ndarray` (Rt idz_sfrmi(R R((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyRPºscCsxtj|ƒ}tj||ƒ\}}}|jd}|jjƒ||| j|||fddƒ}|||fS(s¡ Compute ID of a complex matrix to a specified relative precision. :param eps: Relative precision. :type eps: float :param A: Matrix. :type A: :class:`numpy.ndarray` :return: Rank of ID. :rtype: int :return: Column index array. :rtype: :class:`numpy.ndarray` :return: Interpolation coefficients. :rtype: :class:`numpy.ndarray` iRR(RRRtidzp_idRRRR(RRRRRRR((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyRQÓs  4cCsrtj|ƒ}tj||ƒ\}}|jd}|jjƒ||| j|||fddƒ}||fS(sT Compute ID of a complex matrix to a specified rank. :param A: Matrix. :type A: :class:`numpy.ndarray` :param k: Rank of ID. :type k: int :return: Column index array. :rtype: :class:`numpy.ndarray` :return: Interpolation coefficients. :rtype: :class:`numpy.ndarray` iRR(RRRtidzr_idRRRR(RRRRRR((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyRRïs  4cCsRtj|ƒ}|jdkr1tj|||ƒS|dd…tj|ƒfSdS(sv Reconstruct matrix from complex ID. :param B: Skeleton matrix. :type B: :class:`numpy.ndarray` :param idx: Column index array. :type idx: :class:`numpy.ndarray` :param proj: Interpolation coefficients. :type proj: :class:`numpy.ndarray` :return: Reconstructed matrix. :rtype: :class:`numpy.ndarray` iN(RRRRt idz_reconidR (R!RR((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyRSscCstj||ƒS(s9 Reconstruct interpolation matrix from complex ID. :param idx: Column index array. :type idx: :class:`numpy.ndarray` :param proj: Interpolation coefficients. :type proj: :class:`numpy.ndarray` :return: Interpolation matrix. :rtype: :class:`numpy.ndarray` (Rt idz_reconint(RR((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyRT!scCs"tj|ƒ}tj|||ƒS(sQ Reconstruct skeleton matrix from complex ID. :param A: Original matrix. :type A: :class:`numpy.ndarray` :param k: Rank of ID. :type k: int :param idx: Column index array. :type idx: :class:`numpy.ndarray` :return: Skeleton matrix. :rtype: :class:`numpy.ndarray` (RRRt idz_copycols(RRR((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyRU3scCsLtj|ƒ}tj|||ƒ\}}}}|r?t‚n|||fS(s Convert complex ID to SVD. :param B: Skeleton matrix. :type B: :class:`numpy.ndarray` :param idx: Column index array. :type idx: :class:`numpy.ndarray` :param proj: Interpolation coefficients. :type proj: :class:`numpy.ndarray` :return: Left singular vectors. :rtype: :class:`numpy.ndarray` :return: Right singular vectors. :rtype: :class:`numpy.ndarray` :return: Singular values. :rtype: :class:`numpy.ndarray` (RRRt idz_id2svdR%(R!RRR&R'R(R)((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyRVMs ! cCs%tj|||||ƒ\}}|S(s Estimate spectral norm of a complex matrix by the randomized power method. :param m: Matrix row dimension. :type m: int :param n: Matrix column dimension. :type n: int :param matveca: Function to apply the matrix adjoint to a vector, with call signature `y = matveca(x)`, where `x` and `y` are the input and output vectors, respectively. :type matveca: function :param matvec: Function to apply the matrix to a vector, with call signature `y = matvec(x)`, where `x` and `y` are the input and output vectors, respectively. :type matvec: function :param its: Number of power method iterations. :type its: int :return: Spectral norm estimate. :rtype: float (Rt idz_snorm(RRtmatvecaR,R-R.R/((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyRWps!cCstj|||||||ƒS(s/ Estimate spectral norm of the difference of two complex matrices by the randomized power method. :param m: Matrix row dimension. :type m: int :param n: Matrix column dimension. :type n: int :param matveca: Function to apply the adjoint of the first matrix to a vector, with call signature `y = matveca(x)`, where `x` and `y` are the input and output vectors, respectively. :type matveca: function :param matveca2: Function to apply the adjoint of the second matrix to a vector, with call signature `y = matveca2(x)`, where `x` and `y` are the input and output vectors, respectively. :type matveca2: function :param matvec: Function to apply the first matrix to a vector, with call signature `y = matvec(x)`, where `x` and `y` are the input and output vectors, respectively. :type matvec: function :param matvec2: Function to apply the second matrix to a vector, with call signature `y = matvec2(x)`, where `x` and `y` are the input and output vectors, respectively. :type matvec2: function :param its: Number of power method iterations. :type its: int :return: Spectral norm estimate of matrix difference. :rtype: float (Rt idz_diffsnorm(RRRXtmatveca2R,R2R-((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyRYs'cCsItj|ƒ}tj||ƒ\}}}}|r<t‚n|||fS(sž Compute SVD of a complex matrix to a specified rank. :param A: Matrix. :type A: :class:`numpy.ndarray` :param k: Rank of SVD. :type k: int :return: Left singular vectors. :rtype: :class:`numpy.ndarray` :return: Right singular vectors. :rtype: :class:`numpy.ndarray` :return: Singular values. :rtype: :class:`numpy.ndarray` (RRRtidzr_svdR%(RRR&R'R(R)((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyR[¾s  c CsÛtj|ƒ}|j\}}tj||ƒ\}}}}}} | rQt‚n||d|||d!j||fddƒ} ||d|||d!j||fddƒ} ||d||d!} | | | fS(s¹ Compute SVD of a complex matrix to a specified relative precision. :param eps: Relative precision. :type eps: float :param A: Matrix. :type A: :class:`numpy.ndarray` :return: Left singular vectors. :rtype: :class:`numpy.ndarray` :return: Right singular vectors. :rtype: :class:`numpy.ndarray` :return: Singular values. :rtype: :class:`numpy.ndarray` iRR(RRRRtidzp_svdR%R( RRRRRR5R6R7R R)R&R'R(((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyR\Ús$ 22c Cs¸tj|ƒ}|j\}}t|ƒ\}}tj|d|d|dddddƒ}tj||||ƒ\}}}|||| j|||fddƒ}|||fS(s» Compute ID of a complex matrix to a specified relative precision using random sampling. :param eps: Relative precision. :type eps: float :param A: Matrix. :type A: :class:`numpy.ndarray` :return: Rank of ID. :rtype: int :return: Column index array. :rtype: :class:`numpy.ndarray` :return: Interpolation coefficients. :rtype: :class:`numpy.ndarray` iiRDt complex128RR(RRRROR8Rtidzp_aidR( RRRRR:R RRR((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyR^þs/!+cCstj|ƒ}|j\}}t|ƒ\}}tj|||d|dddddƒ}tj||||ƒ\}}|S(sh Estimate rank of a complex matrix to a specified relative precision using random sampling. The output rank is typically about 8 higher than the actual rank. :param eps: Relative precision. :type eps: float :param A: Matrix. :type A: :class:`numpy.ndarray` :return: Rank estimate. :rtype: int iRDR]RR(RRRROR8Rt idz_estrank(RRRRR:R R<R((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyR_s /cCsctj|ƒ}|j\}}tj|ƒ\}}tjtt||ƒdd|d|ddt||ƒdd|d|dƒdtjdd ƒ}tj ||||ƒ\}}} } }} | rÙt ‚n||d|||d!j ||fdd ƒ} || d| ||d!j ||fdd ƒ} || d| |d!}| | |fS( sÓ Compute SVD of a complex matrix to a specified relative precision using random sampling. :param eps: Relative precision. :type eps: float :param A: Matrix. :type A: :class:`numpy.ndarray` :return: Left singular vectors. :rtype: :class:`numpy.ndarray` :return: Right singular vectors. :rtype: :class:`numpy.ndarray` :return: Singular values. :rtype: :class:`numpy.ndarray` iiii iiRDRR( RRRRROR8R=R>R]t idzp_asvdR%R(RRRRR:R@R RR5R6R7R)R&R'R(((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyR`;s<* 22cCs©tj|dd|t||ƒddtjddƒ}tj|||||ƒ\}}}}|rqt‚n|||| j|||fddƒ}|||fS(sì Compute ID of a complex matrix to a specified relative precision using random matrix-vector multiplication. :param eps: Relative precision. :type eps: float :param m: Matrix row dimension. :type m: int :param n: Matrix column dimension. :type n: int :param matveca: Function to apply the matrix adjoint to a vector, with call signature `y = matveca(x)`, where `x` and `y` are the input and output vectors, respectively. :type matveca: function :return: Rank of ID. :rtype: int :return: Column index array. :rtype: :class:`numpy.ndarray` :return: Interpolation coefficients. :rtype: :class:`numpy.ndarray` iiRDRR(RR8R>R]Rtidzp_ridR%R(RRRRXRRRR)((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyRaes#' +cCs4tj||||ƒ\}}}|r0t‚n|S(sR Estimate rank of a complex matrix to a specified relative precision using random matrix-vector multiplication. :param eps: Relative precision. :type eps: float :param m: Matrix row dimension. :type m: int :param n: Matrix column dimension. :type n: int :param matveca: Function to apply the matrix adjoint to a vector, with call signature `y = matveca(x)`, where `x` and `y` are the input and output vectors, respectively. :type matveca: function :return: Rank estimate. :rtype: int (Rt idz_findrankR%(RRRRXRR<R)((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyRbs! cCsÆtj|||||ƒ\}}}}} } | r<t‚n| |d|||d!j||fddƒ} | |d|||d!j||fddƒ} | |d||d!} | | | fS(sÛ Compute SVD of a complex matrix to a specified relative precision using random matrix-vector multiplication. :param eps: Relative precision. :type eps: float :param m: Matrix row dimension. :type m: int :param n: Matrix column dimension. :type n: int :param matveca: Function to apply the matrix adjoint to a vector, with call signature `y = matveca(x)`, where `x` and `y` are the input and output vectors, respectively. :type matveca: function :param matvec: Function to apply the matrix to a vector, with call signature `y = matvec(x)`, where `x` and `y` are the input and output vectors, respectively. :type matvec: function :return: Left singular vectors. :rtype: :class:`numpy.ndarray` :return: Right singular vectors. :rtype: :class:`numpy.ndarray` :return: Singular values. :rtype: :class:`numpy.ndarray` iRR(Rt idzp_rsvdR%R(RRRRXR,RR5R6R7R R)R&R'R(((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyRc¯s#- 22cCsžtj|ƒ}|j\}}t|||ƒ}tj|||ƒ\}}||krutjgddddƒ}n|j|||fddƒ}||fS(sj Compute ID of a complex matrix to a specified rank using random sampling. :param A: Matrix. :type A: :class:`numpy.ndarray` :param k: Rank of ID. :type k: int :return: Column index array. :rtype: :class:`numpy.ndarray` :return: Interpolation coefficients. :rtype: :class:`numpy.ndarray` RDR]RR(RRRt idzr_aidiRtidzr_aidRHR(RRRRR RR((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyReßs cCstj|||ƒS(sO Initialize array for :func:`idzr_aid`. :param m: Matrix row dimension. :type m: int :param n: Matrix column dimension. :type n: int :param k: Rank of ID. :type k: int :return: Initialization array to be used by :func:`idzr_aid`. :rtype: :class:`numpy.ndarray` (RRd(RRR((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyRdüsc CsÉtj|ƒ}|j\}}tjd|d|d|d|d|dd|ddd d d ƒ}t|||ƒ}|||j*tj|||ƒ\}}}} | r¼t‚n|||fS( s´ Compute SVD of a complex matrix to a specified rank using random sampling. :param A: Matrix. :type A: :class:`numpy.ndarray` :param k: Rank of SVD. :type k: int :return: Left singular vectors. :rtype: :class:`numpy.ndarray` :return: Right singular vectors. :rtype: :class:`numpy.ndarray` :return: Singular values. :rtype: :class:`numpy.ndarray` iiiiii iZRDR]RR( RRRR8RdRRt idzr_asvdR%( RRRRR RJR&R'R(R)((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyRfs: ! cCsStj||||ƒ\}}|||| j|||fddƒ}||fS(sŸ Compute ID of a complex matrix to a specified rank using random matrix-vector multiplication. :param m: Matrix row dimension. :type m: int :param n: Matrix column dimension. :type n: int :param matveca: Function to apply the matrix adjoint to a vector, with call signature `y = matveca(x)`, where `x` and `y` are the input and output vectors, respectively. :type matveca: function :param k: Rank of ID. :type k: int :return: Column index array. :rtype: :class:`numpy.ndarray` :return: Interpolation coefficients. :rtype: :class:`numpy.ndarray` RR(Rtidzr_ridR(RRRXRRR((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyRg;s+c CsCtj|||||ƒ\}}}}|r6t‚n|||fS(sÀ Compute SVD of a complex matrix to a specified rank using random matrix-vector multiplication. :param m: Matrix row dimension. :type m: int :param n: Matrix column dimension. :type n: int :param matveca: Function to apply the matrix adjoint to a vector, with call signature `y = matveca(x)`, where `x` and `y` are the input and output vectors, respectively. :type matveca: function :param matvec: Function to apply the matrix to a vector, with call signature `y = matvec(x)`, where `x` and `y` are the input and output vectors, respectively. :type matvec: function :param k: Rank of SVD. :type k: int :return: Left singular vectors. :rtype: :class:`numpy.ndarray` :return: Right singular vectors. :rtype: :class:`numpy.ndarray` :return: Singular values. :rtype: :class:`numpy.ndarray` (Rt idzr_rsvdR%( RRRXR,RR&R'R(R)((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyRh_s#' (>t__doc__tscipy.linalg._interpolativetlinalgt_interpolativeRtnumpyRt RuntimeErrorR%RRRRR R RRRRR"R#R$R*R0R3R4R9R;R?RARBRCRGRFRIRKRLRMRNRORPRQRRRSRTRURVRWRYR[R\R^R_R`RaRbRcReRdRfRgRh(((sB/tmp/pip-build-7oUkmx/scipy/scipy/linalg/_interpolative_backend.pyt sp             # .  $   * & " 0   $ $ -          # .  $   * ( " 0   & $