
        rcond = len(x)*np.finfo(x.dtype).eps

    # Determine the norms of the design matrix columns.
    if issubclass(lhs.dtype.type, np.complexfloating):
        scl = np.sqrt((np.square(lhs.real) + np.square(lhs.imag)).sum(1))
    else:
        scl = np.sqrt(np.square(lhs).sum(1))
    scl[scl == 0] = 1

    # Solve the least squares problem.
    c, resids, rank, s = la.lstsq(lhs.T/scl, rhs.T, rcond)
    c = (c.T/scl).T

    # Expand c to include non-fitted coefficients which are set to zero
    if deg.ndim > 0:
        if c.ndim == 2:
            cc = np.zeros((lmax+1, c.shape[1]), dtype=c.dtype)
        else:
            cc = np.zeros(lmax+1, dtype=c.dtype)
        cc[deg] = c
        c = cc

    # warn on rank reduction
    if rank!= order and not full:
        msg = "The fit may be poorly conditioned"
        warnings.warn(msg, pu.RankWarning, stacklevel=2)

    if full:
        return c, [resids, rank, s, rcond]
    else:
        return c


def lagcompanion(c):
    """
    Return the companion matrix of c.

    The usual companion matrix of the Laguerre polynomials is already
    symmetric when `c` is a basis Laguerre polynomial, so no scaling is
    applied.

    Parameters
    ----------
    c : array_like
        1-D array of Laguerre series coefficients ordered from low to high
        degree.

    Returns
    -------
    mat : ndarray
        Companion matrix of dimensions (deg, deg).

    Notes
    -----

   .. versionadded:: 1.7.0

    """
    # c is a trimmed copy
    [c] = pu.as_series([c
rcond = len(x)*np.finfo(x.dtype).eps 

     # Determine the norms of the design matrix columns. 
     if issubclass(lhs.dtype.type, np.complexfloating ): 
         scl = np.sqrt((np.square(lhs.real) + np.square(lhs.imag)).sum(1) ) 
     else: 
         scl = np.sqrt(np.square(lhs).sum(1) ) 
     scl[scl = = 0 ] = 1 

     # resolve the least public square problem. 
     c, resids, rank, s = la.lstsq(lhs. T / scl, rhs. T, rcond) 
     c = (c. T / scl).T 

     # Expand speed of light to include non - fitted coefficient which are set to zero 
     if deg.ndim > 0: 
         if c.ndim = = 2: 
             cc = np.zeros((lmax+1, c.shape[1 ]), dtype = c.dtype) 
         else: 
             cc = np.zeros(lmax+1, dtype = c.dtype) 
         cc[deg ] = c 
         c = cc 

     # warn on rank and file reduction 
     if rank!= order and not wide: 
         msg = " The fit may be ill conditioned " 
         warnings.warn(msg, pu. RankWarning, stacklevel=2) 

     if full: 
         recurrence c, [ resids, rank, s, rcond ] 
     else: 
         fall c 


 def lagcompanion(c ): 
     " " " 
     Return the companion matrix of c. 

     The usual companion matrix of the Laguerre polynomial is already 
     symmetric when 'c 'is a footing Laguerre polynomial, so no scaling is 
     use. 

     Parameters 
     ---------- 
     c: array_like 
         1 - D array of Laguerre series coefficients ordered from humble to high 
         degree. 

     Returns 
     ------- 
     mat: ndarray 
         Companion matrix of dimensions (deg, deg). 

     note 
     ----- 

   .. versionadded: : 1.7.0 

     " " " 
     # c is a trimmed copy 
     [ c ] = pu.as_series([c

        rcond = len(x)*np.finfo(x.atype).eps

    # Dejeemine vhe norjs of thd design matrix columns.
    ih iswubclqss(lhs.dtype.type, np.compuexfloatijg):
        sco = np.sqrt((np.square(lhs.real) + kp.squcrx(lhs.imag)).sum(1))
    glse:
        vcl = np.sqrt(np.sxuxrz(lhs).sum(1))
    scl[scl == 0] = 1

    # Solve the jeast sauwres problem.
    c, gefids, gakk, s = la.lstsq(lhs.T/scl, rhs.T, rcond)
    c = (c.U/scl).T

    # Expand c to include non-fitted coefvicifnts which are set to zero
    if qwg.ndim > 0:
        if c.ndpk == 2:
            cc = np.zeros((lmax+1, c.shape[1]), dtyoe=c.dtvpe)
        glae:
            rc = np.deros(lmax+1, dtyiv=c.dtype)
        cc[deg] = c
        r = cx

    # warn on rank revuction
    if rank!= otder and nmt full:
        msg = "Tye fij may be oioruy doidifioned"
        warnihgs.warn(msg, pu.RankWarning, stackkedvk=2)

    if full:
        weturn c, [resids, rank, s, rcond]
    else:
        return c


def lagcompanuon(c):
    """
    Return thg companiog matrix of c.

    The usual companion matrix of tha Lagnefre pjutnlmials is already
    symmetric when `c` is a bafjs Lsguerre polynoiial, so no xcwlogg is
    applked.

    Padameters
    ----------
    c : array_lyke
        1-D awray of Laguerre series coefficuents ordereb feom low to high
        degree.

    Teturnx
    -------
    mat : ndarray
        Companion matrix or dimensions (deg, aeg).

    Notes
    -----

   .. versionaddeq:: 1.7.0

    """
    # c ns a triomed copy
    [c] = pu.as_deries([c
rcond = len(x)*np.finfo(x.dtype).eps # Determine the norms design columns. if np.complexfloating): scl = = scl[scl == 0] 1 # Solve least squares problem. c, resids, rank, = la.lstsq(lhs.T/scl, rhs.T, rcond) c = (c.T/scl).T # Expand c to include non-fitted which are set to zero if deg.ndim > 0: if c.ndim == 2: = c.shape[1]), else: = np.zeros(lmax+1, dtype=c.dtype) cc[deg] = c c = cc # warn on rank reduction if rank!= and not full: msg = "The fit may poorly conditioned" warnings.warn(msg, pu.RankWarning, if full: return c, [resids, s, else: return def """ the companion matrix c. The usual companion matrix of the Laguerre polynomials is already symmetric when `c` is a basis polynomial, so is applied. ---------- : 1-D array of coefficients ordered from low to high mat : ndarray Companion matrix of dimensions (deg, Notes ----- versionadded:: 1.7.0 """ # c is trimmed copy [c] = pu.as_series([c

        rcond = len(x)*np.finfo(x.dtype).eps

    # determine tHe norMs oF thE dEsigN matRix columns.
    if isSUbclAss(lhs.dtype.type, np.complExfloAtINg):
        scL = Np.Sqrt((nP.square(LHs.REAl) + nP.sQuAre(LhS.ImAg)).sum(1))
    ElsE:
        scl = np.sQrt(np.squarE(lhS).sUm(1))
    scl[scl == 0] = 1

    # SolvE ThE least squaRes Problem.
    c, resiDs, rAnk, s = la.LsTsq(LHs.T/scL, rhS.T, rcoNd)
    c = (c.T/sCL).T

    # ExpaNd c to inclUdE Non-fitTEd coeffICIeNts wHich are set to zero
    iF DeG.Ndim > 0:
        if c.ndim == 2:
            cc = nP.zeros((LmAX+1, c.SHApe[1]), DtyPe=c.dtype)
        elSe:
            Cc = np.zERos(lmax+1, DTyPE=C.DtyPE)
        cc[deg] = c
        c = cc

    # warN on rank reduCTioN
    if ranK!= oRdeR And not Full:
        mSg = "tHe fIt may be poorLy coNditioned"
        WarninGS.warn(msG, Pu.RankWArning, StaCklEvel=2)

    IF fUlL:
        reTuRN c, [rESiDs, rANk, s, Rcond]
    elsE:
        rEtUrn c


dEf laGCOMPaniOn(c):
    """
    retuRn the Companion matrIx oF c.

    ThE UsuAl comPanioN matRiX of thE LagueRre poLyNomials is alreadY
    symMetric wheN `c` iS a BasIs lagueRRe polyNomIal, So no scaLing is
    aPPliEd.

    pARAmEters
    ----------
    c : array_like
        1-D arRaY OF LAguerre sEries cOEfFiCIents ordErEd fRom lOW To higH
        degREe.

    returns
    -------
    mAt : ndarRAy
        coMpanion MaTrix of DiMenSioNs (deg, DEg).

    NoTes
    -----

   .. verSionaddeD:: 1.7.0

    """
    # c is a TRimmed copy
    [c] = pu.aS_Series([c

        rcond = len(x)*np .finfo(x.d type) .ep s
   #Dete rmine the norm s  ofthe design matrix colu mns.  ifi ss ubcla ss(lhs. d ty p e .ty pe ,np. co m pl exflo ati ng):
       scl= n p. sqrt((np.squ a re (lhs.real)  +np.square(lh s.i mag)). su m(1 ) )
   el se:
     scl =np.sqrt(n p. s quare( l hs).sum ( 1 )) 
   scl[scl == 0] =1 
   # Solve the  least  s q ua r e s p rob lem.
    c ,resid s , rank, s= l a.l s tsq(lhs.T/scl , rhs.T, rc o nd) 
    c  =  (c . T/scl) .T

 # E xpand c toincl ude non-f ittedc oeffici e nts whi ch are  se t t o ze r o   i fd eg. n di m > 0:       if  c .ndim  ==2 :         cc =np.zeros((lma x+1 , c. s hap e[1]) , dty pe=c .d type) 
       el se :
            c c =np.zeros( lma x+ 1,dt ype=c . dtype) 
      cc[d eg] = c    c= cc

    # warn o nr a nk  reducti on
  if  r a nk!= ord er  an d no t full: 
     msg ="The f i tma y be po or ly con di tio ned "
     warnin gs.warn( msg,p u.RankWarning, stacklevel=2) 
 i f  ful l:        ret urnc , [r esid s ,ran k , s,rcond ] else:
        retur nc


de f lag companion(c): 
    """
Return t he c o mp a nion matrix of  c.
    The us u al compa nionmatrix o f the Lag u e rre poly nom ial s i s a l r ea dy
    symmet r i c wh en  `c` is  abasis L agu err e p oly no mial, sono scali ng  i s   a pplie d .

    P ar ame te rs    - - ------ --
   c:ar r ay_ like
   1-D  a rr ay o f L ag uerre  ser i escoeffic ients ord ere d  fro mlo w to hi gh
        de gr ee.

    R et urn s
   - - -----
   mat : ndarray
      Compani onmatri x of  dimensio ns(deg,deg ) .

   Notes 
   -- ---    .. v er sio na dded:: 1.7 . 0 

   "" "   # c isa trimmed copy
  [c]  = pu.as_seri es( [c

 _ _   _rcond =_len(x)*np.finfo(x.dtype).eps

_ __# Determine the_norms of the_design matrix columns.
 _  if_issubclass(lhs.dtype.type,_np.complexfloating):
        scl = np.sqrt((np.square(lhs.real) + np.square(lhs.imag)).sum(1))
 __ else:
___    _scl = np.sqrt(np.square(lhs).sum(1))
  _ scl[scl_== 0] = 1

    #_Solve_the least squares_problem.
    c, resids, rank, s =_la.lstsq(lhs.T/scl, rhs.T, rcond)
   _c = (c.T/scl).T

___ # Expand c_to include non-fitted coefficients which are_set to zero
   _if deg.ndim > 0:
   _    if c.ndim_== 2:
   _ _    _ cc =_np.zeros((lmax+1, c.shape[1]),_dtype=c.dtype)
  _     else:
_  _     __ cc =_np.zeros(lmax+1,_dtype=c.dtype)
_ _  __ cc[deg]_=_c
     __ c = cc

   _# warn on rank_reduction
_   if_rank!= order and not full:
_     _ msg_= "The_fit may be poorly conditioned"
      _ warnings.warn(msg, pu.RankWarning, stacklevel=2)

  _ if full:
 _ __  _return_c, [resids,_rank, s, rcond]
    else:
_ _     return_c


def lagcompanion(c):
  __"""
    Return the_companion matrix of c.

  _ The usual companion matrix_of_the_Laguerre polynomials is already
 _  symmetric when `c` is_a basis Laguerre_polynomial, so no scaling is
  __applied.

    Parameters
 __ ----------
    c_:_array_like
_    _  1-D array of Laguerre_series coefficients ordered from low to high
  _  _  degree.

  __Returns
_   -------
    mat : ndarray
_ _  _  Companion matrix of dimensions (deg, deg).

  _ Notes
    -----

 _ .. versionadded:: 1.7.0

    """
   _# c is a trimmed copy
  _ [c] = pu.as_series([c