codekingpro/portable-devtools
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g)a 4Abstract base class for the various polynomial Classes.5 6The ABCPolyBase class provides the methods needed to implement the common API7for the various polynomial classes. It operates as a mixin, but uses the8abc module from the stdlib, hence it is only available for Python >= 2.6.9 10� N)�Callable� )� polyutils� ABCPolyBasec
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SS.125 r13\R SSSSSSSSSSS.145 r \ R S:X + r\S 5 r\\R$ S 5 5 r\\R$ S 5 5 r\\R$ S 5 5 r\\R$ S 5 5 r\\R$ S 5 5 r\\R$ S! 5 5 r\\R$ S" 5 5 r\\R$ SiS# j5 5 r\\R$ S$ 5 5 r \\R$ S% 5 5 r \\R$ S& 5 5 r \\R$ S' 5 5 r \\R$ S( 5 5 r \\R$ S) 5 5 r!\\R$ S* 5 5 r"S+ r#S, r$S- r%S. r&S/ r'SjS1 jr(S2 r)S3 r*S4 r+S5 r,\-S6 5 r.\-S7 5 r/\-S8 5 r0\SkS9 j5 r1S:\2S;\3S<\34S= jr4S> r5S? r6S@ r7SA r8SB r9SC r:SD r;SE r<SF r=SG r>SH r?SI r@SJ rASK rBSL rCSM rDSN rESO rFSP rGSQ rHSR rISS rJST rKSU rLSV rMSW rNSX rOSY rPSlSZ jrQS[ rRSmS\ jrSS] rTS^/ S4S_ jrUSnS` jrVSa rWSoSb jrX\- SpSc j5 rY\-/ SS04Sd j5 rZ\-SjSe j5 r[\-SjSf j5 r\\-SqSg j5 r]Shr^g)rr � aF An abstract base class for immutable series classes.15 16ABCPolyBase provides the standard Python numerical methods17'+', '-', '*', '//', '%', 'divmod', '**', and '()' along with the18methods listed below.19 20Parameters21----------22coef : array_like23 Series coefficients in order of increasing degree, i.e.,24 ``(1, 2, 3)`` gives ``1*P_0(x) + 2*P_1(x) + 3*P_2(x)``, where25 ``P_i`` is the basis polynomials of degree ``i``.26domain : (2,) array_like, optional27 Domain to use. The interval ``[domain[0], domain[1]]`` is mapped28 to the interval ``[window[0], window[1]]`` by shifting and scaling.29 The default value is the derived class domain.30window : (2,) array_like, optional31 Window, see domain for its use. The default value is the32 derived class window.33symbol : str, optional34 Symbol used to represent the independent variable in string35 representations of the polynomial expression, e.g. for printing.36 The symbol must be a valid Python identifier. Default value is 'x'.37 38 .. versionadded:: 1.2439 40Attributes41----------42coef : (N,) ndarray43 Series coefficients in order of increasing degree.44domain : (2,) ndarray45 Domain that is mapped to window.46window : (2,) ndarray47 Window that domain is mapped to.48symbol : str49 Symbol representing the independent variable.50 51Class Attributes52----------------53maxpower : int54 Maximum power allowed, i.e., the largest number ``n`` such that55 ``p(x)**n`` is allowed. This is to limit runaway polynomial size.56domain : (2,) ndarray57 Default domain of the class.58window : (2,) ndarray59 Default window of the class.60 61N�d u ⁰� ¹� ²� ³u ⁴u ⁵u ⁶u ⁷u ⁸u ⁹)62�0�1�2�3�4�5�6�7�8�9u ₀u ₁u ₂u ₃u ₄u ₅u ₆u ₇u ₈u ₉�ntc � � U R $ �N)�_symbol��selfs �`D:\code\apps\devtools\python\user_packages\Python313\site-packages\numpy/polynomial/_polybase.py�symbol�ABCPolyBase.symboln s � ��|�|�� c � � g r � r s r �domain�ABCPolyBase.domainr � � �
r c � � g r r" r s r �window�ABCPolyBase.windoww r% r c � � g r r" r s r �63basis_name�ABCPolyBase.basis_name| r% r c � � g r r" ��c1�c2s r �_add�ABCPolyBase._add� r% r c � � g r r" r- s r �_sub�ABCPolyBase._sub� r% r c � � g r r" r- s r �_mul�ABCPolyBase._mul� r% r c � � g r r" r- s r �_div�ABCPolyBase._div� r% r c � � g r r" )�c�pow�maxpowers r �_pow�ABCPolyBase._pow� r% r c � � g r r" )�xr< s r �_val�ABCPolyBase._val� r% r c � � g r r" )r< �m�k�lbnd�scls r �_int�ABCPolyBase._int� r% r c � � g r r" )r< rF rI s r �_der�ABCPolyBase._der� r% r c � � g r r" )rB �y�deg�rcond�fulls r �_fit�ABCPolyBase._fit� r% r c � � g r r" )�offrI s r �_line�ABCPolyBase._line� r% r c � � g r r" )r< s r �_roots�ABCPolyBase._roots� r% r c � � g r r" )�rs r �64_fromroots�ABCPolyBase._fromroots� r% r c �� � [ U R 5 [ UR 5 :H =( a- [ R " U R UR :H 5 $ )z�Check if coefficients match.65 66Parameters67----------68other : class instance69 The other class must have the ``coef`` attribute.70 71Returns72-------73bool : boolean74 True if the coefficients are the same, False otherwise.75 76)�len�coef�np�all�r �others r � has_samecoef�ABCPolyBase.has_samecoef� s? � �
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0����t�y�y�E�J�J�.�/� 77r c �\ � [ R " U R UR :H 5 $ )z�Check if domains match.78 79Parameters80----------81other : class instance82 The other class must have the ``domain`` attribute.83 84Returns85-------86bool : boolean87 True if the domains are the same, False otherwise.88 89)rd re r# rf s r �has_samedomain�ABCPolyBase.has_samedomain� � � � �v�v�d�k�k�U�\�\�1�2�2r c �\ � [ R " U R UR :H 5 $ )z�Check if windows match.90 91Parameters92----------93other : class instance94 The other class must have the ``window`` attribute.95 96Returns97-------98bool : boolean99 True if the windows are the same, False otherwise.100 101)rd re r' rf s r �has_samewindow�ABCPolyBase.has_samewindow� rm r c �, � [ XR 5 $ )z�Check if types match.102 103Parameters104----------105other : object106 Class instance.107 108Returns109-------110bool : boolean111 True if other is same class as self112 113)�114isinstance� __class__rf s r � has_sametype�ABCPolyBase.has_sametype� s � � �%� � �0�0r c �� � [ U[ 5 ( a� [ XR 5 ( d [ S5 e[ R115 " U R UR :H 5 ( d [ S5 e[ R116 " U R UR :H 5 ( d [ S5 eU R UR :w a [ S5 eUR $ U$ )a� Interpret other as polynomial coefficients.117 118The `other` argument is checked to see if it is of the same119class as self with identical domain and window. If so,120return its coefficients, otherwise return `other`.121 122Parameters123----------124other : anything125 Object to be checked.126 127Returns128-------129coef130 The coefficients of`other` if it is a compatible instance,131 of ABCPolyBase, otherwise `other`.132 133Raises134------135TypeError136 When `other` is an incompatible instance of ABCPolyBase.137 138zPolynomial types differzDomains differzWindows differzPolynomial symbols differ) rr r rs � TypeErrorrd re r# r' r �139ValueErrorrc rf s r �_get_coefficients� ABCPolyBase._get_coefficients s� � �0 �e�[� )� )� �e�^�^�4�4� � 9�:�:��V�V�D�K�K�5�<�<� 7�8�8� � 0�1�1��V�V�D�K�K�5�<�<� 7�8�8� � 0�1�1����� � �,� �!<�=�=��:�:� �� r rB c � � [ R " U/SS9u nXl Ub8 [ R " U/SS9u n[ U5 S:w a [ S5 eX l Ub8 [ R " U/SS9u n[ U5 S:w a [ S5 eX0l UR 5 ( d [ S5 e X@l140 g ! [ a [ S5 ef = f)NF��trim� z$Domain has wrong number of elements.z$Window has wrong number of elements.z/Symbol string must be a valid Python identifierz!Symbol must be a non-empty string) �pu� as_seriesrc rb rx r# r' � isidentifier�AttributeErrorrw r )r rc r# r' r s r �__init__�ABCPolyBase.__init__$ s� � �� � �t�f�5�1���� � � ��|�|�V�H�5�9�H�V��6�{�a� � �!G�H�H� �K� � ��|�|�V�H�5�9�H�V��6�{�a� � �!G�H�H� �K� A��&�&�(�(� �E�� � )� � �� � A�� ?�@� @� A�s � B> �>Cc 141 �� � [ U R 5 SS n[ U R 5 SS n[ U R 5 SS nU R R142 nU SU SU SU SU R S3143$ )N� ������(z , domain=z , window=z144, symbol='z'))�reprrc r# r' rs �__name__r )r rc r# r' �names r �__repr__�ABCPolyBase.__repr__B s� � ��D�I�I��q��$���d�k�k�"�1�R�(���d�k�k�"�1�R�(���~�~�&�&���&��$��y��� �&�� B� �;�;�-�r�+� ,r c �� � US:X a U R 5 $ US; a [ SU SU R S35 eUS:X a U R U R 5 $ U R U R145 5 $ )N� )�ascii�unicodezUnsupported format string 'z ' passed to z4.__format__. Valid options are 'ascii' and 'unicode'r� )�__str__rx rs �_generate_string�_str_term_ascii�_str_term_unicode)r �fmt_strs r �146__format__�ABCPolyBase.__format__J s� � � �b�=��<�<�>� !� �.� .� �-�g�Y�l��>�>�"� #(�)��
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scalar_formatrW r� c �168 � US:X a US:X a U R nSnXE4$ US:X a U" U5 SU R 3nSnXE4$ US:X a U" U5 U R 3nSnXE4$ U" U5 SU" U5 U R 3nSnXE4$ )z&Format a single term in the expansion r r F� + T)r )r r� rW r� �termr� s r r� �ABCPolyBase._format_term� s� � � �!�8���169��;�;�D� �L� �!�!� �a�Z�#�C�(�)��T�[�[�M�:�D� �L� �!�!� �A�X�#�E�*�+�D�K�K�=�9�D� �L� �!�!� !��%�&�c� ��'�(����
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r c �D � U R U5 nU[ L a U$ US $ r r8 r s r �__rmod__�ABCPolyBase.__rmod__r r< r c �H � U R XR 5 u p#U R X R U R U R 5 nU R X0R U R U R 5 nX#4$ ! [ a e [ a [ s $ f = fr ) r9 rc r! r� r� rs r# r' r )r rg r" r# s r r9 �ABCPolyBase.__rdivmod__x s� � � "��y�y�� � �2�H�C�192 �n�n�S�+�+�t�{�{�D�K�K�H���n�n�S�+�+�t�{�{�D�K�K�H���x���
!� � �� "�!� !� "�s � B �B!� B!c � � [ XR 5 =( a� [ R " U R UR :H 5 =( a� [ R " U R193 UR194 :H 5 =( a� U R R UR R :H =( aM [ R " U R UR :H 5 =( a U R UR :H nU$ r ) rr rs rd re r# r' rc �shaper r s r �__eq__�ABCPolyBase.__eq__� s� � ��%� � �0� -��v�v�d�k�k�U�\�\�1�2�-��v�v�d�k�k�U�\�\�1�2�-� � � ���5�:�:�#3�#3�3�-� �v�v�d�i�i�5�:�:�-�.� -�195 � � �u�|�|�+� � �196r c �. � U R U5 ( + $ r )rD rf s r �__ne__�ABCPolyBase.__ne__� s � ��;�;�u�%�%�%r c �z � U R U R U R U R U R 5 $ )zGReturn a copy.197 198Returns199-------200new_series : series201 Copy of self.202 203r� r s r r� �ABCPolyBase.copy� s) � � �~�~�d�i�i����d�k�k�4�;�;�O�Or c � � [ U 5 S-204 $ )uj The degree of the series.205 206Returns207-------208degree : int209 Degree of the series, one less than the number of coefficients.210 211Examples212--------213 214Create a polynomial object for ``1 + 7*x + 4*x**2``:215 216>>> np.polynomial.set_default_printstyle("unicode")217>>> poly = np.polynomial.Polynomial([1, 7, 4])218>>> print(poly)2191.0 + 7.0·x + 4.0·x²220>>> poly.degree()2212222 223Note that this method does not check for non-zero coefficients.224You must trim the polynomial to remove any trailing zeroes:225 226>>> poly = np.polynomial.Polynomial([1, 7, 0])227>>> print(poly)2281.0 + 7.0·x + 0.0·x²229>>> poly.degree()2302231>>> poly.trim().degree()2321233 234r )rb r s r �degree�ABCPolyBase.degree� s � �@ �4�y�1�}� r c �* � U R US- 5 $ )a9 Truncate series to the given degree.235 236Reduce the degree of the series to `deg` by discarding the237high order terms. If `deg` is greater than the current degree a238copy of the current series is returned. This can be useful in least239squares where the coefficients of the high degree terms may be very240small.241 242Parameters243----------244deg : non-negative int245 The series is reduced to degree `deg` by discarding the high246 order terms. The value of `deg` must be a non-negative integer.247 248Returns249-------250new_series : series251 New instance of series with reduced degree.252 253r )�truncate)r rQ s r �cutdeg�ABCPolyBase.cutdeg� s � �* �}�}�S�1�W�%�%r c � � [ R " U R U5 nU R X R U R254 U R 5 $ )a' Remove trailing coefficients255 256Remove trailing coefficients until a coefficient is reached whose257absolute value greater than `tol` or the beginning of the series is258reached. If all the coefficients would be removed the series is set259to ``[0]``. A new series instance is returned with the new260coefficients. The current instance remains unchanged.261 262Parameters263----------264tol : non-negative number.265 All trailing coefficients less than `tol` will be removed.266 267Returns268-------269new_series : series270 New instance of series with trimmed coefficients.271 272)r �trimcoefrc rs r# r' r )r �tolrc s r r} �ABCPolyBase.trim� s7 � �( �{�{�4�9�9�c�*���~�~�d�K�K����d�k�k�J�Jr c � � [ U5 nX!:w d US: a [ S5 eU[ U R 5 :� a
U R nOU R SU nU R X0R273 U R U R 5 $ )a Truncate series to length `size`.274 275Reduce the series to length `size` by discarding the high276degree terms. The value of `size` must be a positive integer. This277can be useful in least squares where the coefficients of the278high degree terms may be very small.279 280Parameters281----------282size : positive int283 The series is reduced to length `size` by discarding the high284 degree terms. The value of `size` must be a positive integer.285 286Returns287-------288new_series : series289 New instance of series with truncated coefficients.290 291r z size must be a positive integerN)�intrx rb rc rs r# r' r )r �size�isizerc s r rO �ABCPolyBase.truncate� sl � �( �D� �� �=�E�A�I� � >�?� ?� �C�� � �N� "��9�9�D��9�9�V�e�$�D��~�~�d�K�K����d�k�k�J�Jr c � � Uc U R nUc UR nUc UR nU " UR XU R S95 $ )a1 Convert series to a different kind and/or domain and/or window.292 293Parameters294----------295domain : array_like, optional296 The domain of the converted series. If the value is None,297 the default domain of `kind` is used.298kind : class, optional299 The polynomial series type class to which the current instance300 should be converted. If kind is None, then the class of the301 current instance is used.302window : array_like, optional303 The window of the converted series. If the value is None,304 the default window of `kind` is used.305 306Returns307-------308new_series : series309 The returned class can be of different type than the current310 instance and/or have a different domain and/or different311 window.312 313Notes314-----315Conversion between domains and class types can result in316numerically ill defined series.317 318)r' r )rs r# r' �identityr )r r# �kindr' s r �convert�ABCPolyBase.convert sJ � �: �<��>�>�D� �>��[�[�F� �>��[�[�F��D�M�M�&�� � �M�L�M�Mr c �X � [ R " U R U R 5 $ )a# Return the mapping parameters.319 320The returned values define a linear map ``off + scl*x`` that is321applied to the input arguments before the series is evaluated. The322map depends on the ``domain`` and ``window``; if the current323``domain`` is equal to the ``window`` the resulting map is the324identity. If the coefficients of the series instance are to be325used by themselves outside this class, then the linear function326must be substituted for the ``x`` in the standard representation of327the base polynomials.328 329Returns330-------331off, scl : float or complex332 The mapping function is defined by ``off + scl*x``.333 334Notes335-----336If the current domain is the interval ``[l1, r1]`` and the window337is ``[l2, r2]``, then the linear mapping function ``L`` is338defined by the equations::339 340 L(l1) = l2341 L(r1) = r2342 343)r r� r# r' r s r r� �ABCPolyBase.mapparms0 s � �6 �{�{�4�;�;�� � �4�4r r c �� � U R 5 u pEUc SnOXEU- - nU R U R XUSU- 5 nU R X`R U R344 U R 5 $ )ay Integrate.345 346Return a series instance that is the definite integral of the347current series.348 349Parameters350----------351m : non-negative int352 The number of integrations to perform.353k : array_like354 Integration constants. The first constant is applied to the355 first integration, the second to the second, and so on. The356 list of values must less than or equal to `m` in length and any357 missing values are set to zero.358lbnd : Scalar359 The lower bound of the definite integral.360 361Returns362-------363new_series : series364 A new series representing the integral. The domain is the same365 as the domain of the integrated series.366 367r g �?)r� rJ rc rs r# r' r )r rF rG rH rW rI rc s r �integ�ABCPolyBase.integM sb � �2 �=�=�?��� �<��D��t��#�D��y�y����A�$��S��9���~�~�d�K�K����d�k�k�J�Jr c �� � U R 5 u p#U R U R X5 nU R X@R U R368 U R 5 $ )aG Differentiate.369 370Return a series instance of that is the derivative of the current371series.372 373Parameters374----------375m : non-negative int376 Find the derivative of order `m`.377 378Returns379-------380new_series : series381 A new series representing the derivative. The domain is the same382 as the domain of the differentiated series.383 384)r� rM rc rs r# r' r )r rF rW rI rc s r �deriv�ABCPolyBase.derivn sD � �$ �=�=�?����y�y����A�+���~�~�d�K�K����d�k�k�J�Jr c � � U R U R 5 n[ R " XR U R385 5 $ )z�Return the roots of the series polynomial.386 387Compute the roots for the series. Note that the accuracy of the388roots decreases the further outside the `domain` they lie.389 390Returns391-------392roots : ndarray393 Array containing the roots of the series.394 395)r[ rc r r� r' r# )r �rootss r ri �ABCPolyBase.roots� s/ � � � � �D�I�I�&���|�|�E�;�;�� � �<�<r c �r � Uc U R n[ R " US US U5 nU " U5 nX44$ )a
Return x, y values at equally spaced points in domain.396 397Returns the x, y values at `n` linearly spaced points across the398domain. Here y is the value of the polynomial at the points x. By399default the domain is the same as that of the series instance.400This method is intended mostly as a plotting aid.401 402Parameters403----------404n : int, optional405 Number of point pairs to return. The default value is 100.406domain : {None, array_like}, optional407 If not None, the specified domain is used instead of that of408 the calling instance. It should be of the form ``[beg,end]``.409 The default is None which case the class domain is used.410 411Returns412-------413x, y : ndarray414 x is equal to linspace(self.domain[0], self.domain[1], n) and415 y is the series evaluated at element of x.416 417r r )r# rd �linspace)r �nr# rB rP s r rl �ABCPolyBase.linspace� s< � �0 �>��[�[�F� �K�K��q� �6�!�9�a� 0�� ��G���t� r c418 � � Uc= [ R " U5 nUS US :X a US== S- ss' US== S-
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4$ U n U " X�X�S9$ )a Least squares fit to data.421 422Return a series instance that is the least squares fit to the data423`y` sampled at `x`. The domain of the returned instance can be424specified and this will often result in a superior fit with less425chance of ill conditioning.426 427Parameters428----------429x : array_like, shape (M,)430 x-coordinates of the M sample points ``(x[i], y[i])``.431y : array_like, shape (M,)432 y-coordinates of the M sample points ``(x[i], y[i])``.433deg : int or 1-D array_like434 Degree(s) of the fitting polynomials. If `deg` is a single integer435 all terms up to and including the `deg`'th term are included in the436 fit. For NumPy versions >= 1.11.0 a list of integers specifying the437 degrees of the terms to include may be used instead.438domain : {None, [beg, end], []}, optional439 Domain to use for the returned series. If ``None``,440 then a minimal domain that covers the points `x` is chosen. If441 ``[]`` the class domain is used. The default value was the442 class domain in NumPy 1.4 and ``None`` in later versions.443 The ``[]`` option was added in numpy 1.5.0.444rcond : float, optional445 Relative condition number of the fit. Singular values smaller446 than this relative to the largest singular value will be447 ignored. The default value is ``len(x)*eps``, where eps is the448 relative precision of the float type, about 2e-16 in most449 cases.450full : bool, optional451 Switch determining nature of return value. When it is False452 (the default) just the coefficients are returned, when True453 diagnostic information from the singular value decomposition is454 also returned.455w : array_like, shape (M,), optional456 Weights. If not None, the weight ``w[i]`` applies to the unsquared457 residual ``y[i] - y_hat[i]`` at ``x[i]``. Ideally the weights are458 chosen so that the errors of the products ``w[i]*y[i]`` all have459 the same variance. When using inverse-variance weighting, use460 ``w[i] = 1/sigma(y[i])``. The default value is None.461window : {[beg, end]}, optional462 Window to use for the returned series. The default463 value is the default class domain464symbol : str, optional465 Symbol representing the independent variable. Default is 'x'.466 467Returns468-------469new_series : series470 A series that represents the least squares fit to the data and471 has the domain and window specified in the call. If the472 coefficients for the unscaled and unshifted basis polynomials are473 of interest, do ``new_series.convert().coef``.474 475[resid, rank, sv, rcond] : list476 These values are only returned if ``full == True``477 478 - resid -- sum of squared residuals of the least squares fit479 - rank -- the numerical rank of the scaled Vandermonde matrix480 - sv -- singular values of the scaled Vandermonde matrix481 - rcond -- value of `rcond`.482 483 For more details, see `linalg.lstsq`.484 485r r )�wrR rS �r# r' r ) r � getdomainrr �listrb r# r' r� rT )r� rB rP rQ r# rR rS rp r' r �xnewr rc �statuss r �fit�ABCPolyBase.fit� s� � �J �>��\�\�!�_�F��a�y�F�1�I�%��q� �Q�� ��q� �Q�� ��
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� �D��t�6�I� Ir c �r � [ R " U/SS9u nUc [ R " U5 nO0[ U[ 5 ( a [ U5 S:X a U R nUc U R n[ U5 n[ R " X#5 u pgXgU- - nU R U5 Xu- - n U " X�X4S9$ )a� Return series instance that has the specified roots.486 487Returns a series representing the product488``(x - r[0])*(x - r[1])*...*(x - r[n-1])``, where ``r`` is a489list of roots.490 491Parameters492----------493roots : array_like494 List of roots.495domain : {[], None, array_like}, optional496 Domain for the resulting series. If None the domain is the497 interval from the smallest root to the largest. If [] the498 domain is the class domain. The default is [].499window : {None, array_like}, optional500 Window for the returned series. If None the class window is501 used. The default is None.502symbol : str, optional503 Symbol representing the independent variable. Default is 'x'.504 505Returns506-------507new_series : series508 Series with the specified roots.509 510Fr| r rq )511r r� rr rr rs rb r# r' r� r_ )512r� ri r# r' r rQ rW rI �rnewrc s513 r � fromroots�ABCPolyBase.fromroots s� � �8 �,�,��w�U�3��� �>��\�\�%�(�F�
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%�#�f�+��*:��Z�Z�F� �>��Z�Z�F��%�j���;�;�v�.����5�[� ���~�~�d�#�c�h�.���4�v�E�Er c � � Uc U R nUc U R n[ R " X!5 u pEU R XE5 nU " XaX#5 $ )a� Identity function.514 515If ``p`` is the returned series, then ``p(x) == x`` for all516values of x.517 518Parameters519----------520domain : {None, array_like}, optional521 If given, the array must be of the form ``[beg, end]``, where522 ``beg`` and ``end`` are the endpoints of the domain. If None is523 given then the class domain is used. The default is None.524window : {None, array_like}, optional525 If given, the resulting array must be if the form526 ``[beg, end]``, where ``beg`` and ``end`` are the endpoints of527 the window. If None is given then the class window is used. The528 default is None.529symbol : str, optional530 Symbol representing the independent variable. Default is 'x'.531 532Returns533-------534new_series : series535 Series of representing the identity.536 537)r# r' r r� rX )r� r# r' r rW rI rc s r r\ �ABCPolyBase.identity7 sK � �6 �>��Z�Z�F� �>��Z�Z�F��;�;�v�.����y�y��"���4��0�0r c � � Uc U R nUc U R n[ U5 nXQ:w d US: a [ S5 eU " S/U- S/- X#U5 $ )a� Series basis polynomial of degree `deg`.538 539Returns the series representing the basis polynomial of degree `deg`.540 541Parameters542----------543deg : int544 Degree of the basis polynomial for the series. Must be >= 0.545domain : {None, array_like}, optional546 If given, the array must be of the form ``[beg, end]``, where547 ``beg`` and ``end`` are the endpoints of the domain. If None is548 given then the class domain is used. The default is None.549window : {None, array_like}, optional550 If given, the resulting array must be if the form551 ``[beg, end]``, where ``beg`` and ``end`` are the endpoints of552 the window. If None is given then the class window is used. The553 default is None.554symbol : str, optional555 Symbol representing the independent variable. Default is 'x'.556 557Returns558-------559new_series : series560 A series with the coefficient of the `deg` term set to one and561 all others zero.562 563r z deg must be non-negative integerr )r# r' rW rx )r� rQ r# r' r �idegs r �basis�ABCPolyBase.basisZ s\ � �: �>��Z�Z�F� �>��Z�Z�F��3�x�� �;�$��(� � ?�@� @��A�3��:���#�V�V�<�<r c �b � Uc U R nUc U R nUR X U5 $ )a� Convert series to series of this class.564 565The `series` is expected to be an instance of some polynomial566series of one of the types supported by by the numpy.polynomial567module, but could be some other class that supports the convert568method.569 570Parameters571----------572series : series573 The series instance to be converted.574domain : {None, array_like}, optional575 If given, the array must be of the form ``[beg, end]``, where576 ``beg`` and ``end`` are the endpoints of the domain. If None is577 given then the class domain is used. The default is None.578window : {None, array_like}, optional579 If given, the resulting array must be if the form580 ``[beg, end]``, where ``beg`` and ``end`` are the endpoints of581 the window. If None is given then the class window is used. The582 default is None.583 584Returns585-------586new_series : series587 A series of the same kind as the calling class and equal to588 `series` when evaluated.589 590See Also591--------592convert : similar instance method593 594)r# r' r^ )r� �seriesr# r' s r �cast�ABCPolyBase.cast� s2 � �D �>��Z�Z�F� �>��Z�Z�F��~�~�f�6�2�2r )r� r rc r# r' r )NNrB )F)r )NNN)r )r N)NNFNNrB )NN)_r� �595__module__� __qualname__�__firstlineno__�__doc__�__hash__�__array_ufunc__r> r� � maketrans�_superscript_mappingr� �osr� r� �propertyr �abc�abstractmethodr# r' r* � staticmethodr0 r3 r6 r9 r? rC rJ rM rT rX r[ r_ rh rk ro rt ry r� r� r� r� r� � classmethodr� r� r� r� r �floatr� r� r� r� r� r� r� r� r� r r r596 r r r r r& r* r/ r2 r5 r: r> r9 rD rG r� rL rP r} rO r^ r� rc rf ri rl rv rz r\ r� r� �__static_attributes__r" r r r r s� � �/�d �H� �O� �H� �=�=�
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