B Z @sdZddlmZddlmZmZddlZddlm Z ddl m Z ddlm Z mZmZmZmZmZddlZddlmZmZdd lmZdd d Zdd d ZeejZeejZdddddZdddZdddZddZ e!dkrej"#ddZ$e$ddddfej"#ddZ%ee$e%ee$ee$ee$Z&e'j(e$Z)e*e+e,e&e)ee$Z&e'j(e$Z)e*e+e,e&e)dS)zylocal, adjusted version from scipy.linalg.basic.py changes: The only changes are that additional results are returned )print_function)lmaprangeN)svd)get_lapack_funcs)asarrayzerossum conjugatedot transpose)asarray_chkfinitesingle) LinAlgErrorcCstt||f\}}|jdkr$td|j\}}|jdkrD|jd} nd} ||jdkr^tdtd||f\} ||krt|| f| jd} |jdkr|| d|ddf<n|| d|df<| }|p||k ot|d  }|p||k ot|d  }| j dd d krF| ||d d d} | dj t j } | |||| ||d\}}}}} }ntd| j |dkrftd|dkr~td| tg|jd}||kr|d|}||krt||dddd}|}||||fS)aCompute least-squares solution to equation :m:`a x = b` Compute a vector x such that the 2-norm :m:`|b - a x|` is minimised. Parameters ---------- a : array, shape (M, N) b : array, shape (M,) or (M, K) cond : float Cutoff for 'small' singular values; used to determine effective rank of a. Singular values smaller than rcond*largest_singular_value are considered zero. overwrite_a : boolean Discard data in a (may enhance performance) overwrite_b : boolean Discard data in b (may enhance performance) Returns ------- x : array, shape (N,) or (N, K) depending on shape of b Least-squares solution residues : array, shape () or (1,) or (K,) Sums of residues, squared 2-norm for each column in :m:`b - a x` If rank of matrix a is < N or > M this is an empty array. If b was 1-d, this is an (1,) shape array, otherwise the shape is (K,) rank : integer Effective rank of matrix a s : array, shape (min(M,N),) Singular values of a. The condition number of a is abs(s[0]/s[-1]). Raises LinAlgError if computation does not converge zexpected matrixrzincompatible dimensions)gelss)dtypeNZ __array__Zflapack)lwork)condr overwrite_a overwrite_bzcalling gelss from %sz,SVD did not converge in Linear Least Squaresz0illegal value in %-th argument of internal gelss)axis)rr ndim ValueErrorshaperrrhasattrZ module_namerealZastypenpintNotImplementedErrorrrr )abrrrZa1Zb1mnZnrhsrZb2ZworkrvxsZrankinfoZresidsZx1r,7lib/python3.7/site-packages/statsmodels/tools/linalg.pylstsqsL"             r.cCs<t|}tj|jd|jd}|dk r*|}t|||ddS)aCompute the (Moore-Penrose) pseudo-inverse of a matrix. Calculate a generalized inverse of a matrix using a least-squares solver. Parameters ---------- a : array, shape (M, N) Matrix to be pseudo-inverted cond, rcond : float Cutoff for 'small' singular values in the least-squares solver. Singular values smaller than rcond*largest_singular_value are considered zero. Returns ------- B : array, shape (N, M) Raises LinAlgError if computation does not converge Examples -------- >>> from numpy import * >>> a = random.randn(9, 6) >>> B = linalg.pinv(a) >>> allclose(a, dot(a, dot(B, a))) True >>> allclose(B, dot(B, dot(a, B))) True r)rN)r)r numpyZidentityrrr.)r$rrcondr%r,r,r-pinvhs r1r)fdFDc Cst|}t|\}}}|jj}|dk r*|}|dkrLtdtddt|}|j\}}|tj |} t ||f|} x8t t |D](} || | krdt|| | | | f<qWtttt|| |S)aSCompute the (Moore-Penrose) pseudo-inverse of a matrix. Calculate a generalized inverse of a matrix using its singular-value decomposition and including all 'large' singular values. Parameters ---------- a : array, shape (M, N) Matrix to be pseudo-inverted cond, rcond : float or None Cutoff for 'small' singular values. Singular values smaller than rcond*largest_singular_value are considered zero. If None or -1, suitable machine precision is used. Returns ------- B : array, shape (N, M) Raises LinAlgError if SVD computation does not converge Examples -------- >>> from numpy import * >>> a = random.randn(9, 6) >>> B = linalg.pinv2(a) >>> allclose(a, dot(a, dot(B, a))) True >>> allclose(B, dot(B, dot(a, B))) True N)Nrg@@g.A)rrg?)r decomp_svdrcharfepseps_array_precisionrr/Zmaximumreducerrlenr r r ) r$rr0ur*Zvhtr&r'cutoffZpsigmair,r,r-pinv2s#  rAFcCsRddlm}|r(t||jks(td|j|dd\}}dtt| S)z Return log(det(m)) asserting positive definiteness of m. Parameters ---------- m : array-like 2d array that is positive-definite (and symmetric) Returns ------- logdet : float The log-determinant of m. r)linalgzm is not symmetric.T)lowerr) scipyrBr!allTrZ cho_factorr logZdiagonal)r&Z check_symmrBc_r,r,r- logdet_symms  rJc Csj|dd}|j}|jdkr,|dddf}|ddddf}xtdt|D]}|d|ddd}||ddft||dt||ddd}|t|ddd|}tj||dddffdd}|t|dkrP||} | t||dt||ddd}|||ddd}t|tj|f}qRW|dkrf|dddf}|S)aH Solve a linear system for a Toeplitz correlation matrix. A Toeplitz correlation matrix represents the covariance of a stationary series with unit variance. Parameters ---------- r : array-like A vector describing the coefficient matrix. r[0] is the first band next to the diagonal, r[1] is the second band, etc. b : array-like The right-hand side for which we are solving, i.e. we solve Tx = b and return b, where T is the Toeplitz coefficient matrix. Returns ------- The solution to the linear system. rrNr)r)rrr<r!r ZouterZ concatenateZr_) rr%ZdbZdimr)jZrfr$zZrnr,r,r-stationary_solves&  6* rN__main__d )Nrr)NN)NN)F)-__doc__Z __future__rZstatsmodels.compat.pythonrrr/r!Z scipy.linalgrr6Zscipy.linalg.lapackrrrr r r r r rZ numpy.linalgrr.r1Zfinfofloatr9r8r:rArJrN__name__ZrandomZrandnZa0Zb0r)rDrBZx2printmaxabsr,r,r,r-s:      S '   4 1 $