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Diffstat (limited to '.venv/lib/python3.12/site-packages/numpy/polynomial/_polybase.py')
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diff --git a/.venv/lib/python3.12/site-packages/numpy/polynomial/_polybase.py b/.venv/lib/python3.12/site-packages/numpy/polynomial/_polybase.py new file mode 100644 index 00000000..9730574c --- /dev/null +++ b/.venv/lib/python3.12/site-packages/numpy/polynomial/_polybase.py @@ -0,0 +1,1206 @@ +""" +Abstract base class for the various polynomial Classes. + +The ABCPolyBase class provides the methods needed to implement the common API +for the various polynomial classes. It operates as a mixin, but uses the +abc module from the stdlib, hence it is only available for Python >= 2.6. + +""" +import os +import abc +import numbers + +import numpy as np +from . import polyutils as pu + +__all__ = ['ABCPolyBase'] + +class ABCPolyBase(abc.ABC): + """An abstract base class for immutable series classes. + + ABCPolyBase provides the standard Python numerical methods + '+', '-', '*', '//', '%', 'divmod', '**', and '()' along with the + methods listed below. + + .. versionadded:: 1.9.0 + + Parameters + ---------- + coef : array_like + Series coefficients in order of increasing degree, i.e., + ``(1, 2, 3)`` gives ``1*P_0(x) + 2*P_1(x) + 3*P_2(x)``, where + ``P_i`` is the basis polynomials of degree ``i``. + domain : (2,) array_like, optional + Domain to use. The interval ``[domain[0], domain[1]]`` is mapped + to the interval ``[window[0], window[1]]`` by shifting and scaling. + The default value is the derived class domain. + window : (2,) array_like, optional + Window, see domain for its use. The default value is the + derived class window. + symbol : str, optional + Symbol used to represent the independent variable in string + representations of the polynomial expression, e.g. for printing. + The symbol must be a valid Python identifier. Default value is 'x'. + + .. versionadded:: 1.24 + + Attributes + ---------- + coef : (N,) ndarray + Series coefficients in order of increasing degree. + domain : (2,) ndarray + Domain that is mapped to window. + window : (2,) ndarray + Window that domain is mapped to. + symbol : str + Symbol representing the independent variable. + + Class Attributes + ---------------- + maxpower : int + Maximum power allowed, i.e., the largest number ``n`` such that + ``p(x)**n`` is allowed. This is to limit runaway polynomial size. + domain : (2,) ndarray + Default domain of the class. + window : (2,) ndarray + Default window of the class. + + """ + + # Not hashable + __hash__ = None + + # Opt out of numpy ufuncs and Python ops with ndarray subclasses. + __array_ufunc__ = None + + # Limit runaway size. T_n^m has degree n*m + maxpower = 100 + + # Unicode character mappings for improved __str__ + _superscript_mapping = str.maketrans({ + "0": "⁰", + "1": "¹", + "2": "²", + "3": "³", + "4": "⁴", + "5": "⁵", + "6": "⁶", + "7": "⁷", + "8": "⁸", + "9": "⁹" + }) + _subscript_mapping = str.maketrans({ + "0": "₀", + "1": "₁", + "2": "₂", + "3": "₃", + "4": "₄", + "5": "₅", + "6": "₆", + "7": "₇", + "8": "₈", + "9": "₉" + }) + # Some fonts don't support full unicode character ranges necessary for + # the full set of superscripts and subscripts, including common/default + # fonts in Windows shells/terminals. Therefore, default to ascii-only + # printing on windows. + _use_unicode = not os.name == 'nt' + + @property + def symbol(self): + return self._symbol + + @property + @abc.abstractmethod + def domain(self): + pass + + @property + @abc.abstractmethod + def window(self): + pass + + @property + @abc.abstractmethod + def basis_name(self): + pass + + @staticmethod + @abc.abstractmethod + def _add(c1, c2): + pass + + @staticmethod + @abc.abstractmethod + def _sub(c1, c2): + pass + + @staticmethod + @abc.abstractmethod + def _mul(c1, c2): + pass + + @staticmethod + @abc.abstractmethod + def _div(c1, c2): + pass + + @staticmethod + @abc.abstractmethod + def _pow(c, pow, maxpower=None): + pass + + @staticmethod + @abc.abstractmethod + def _val(x, c): + pass + + @staticmethod + @abc.abstractmethod + def _int(c, m, k, lbnd, scl): + pass + + @staticmethod + @abc.abstractmethod + def _der(c, m, scl): + pass + + @staticmethod + @abc.abstractmethod + def _fit(x, y, deg, rcond, full): + pass + + @staticmethod + @abc.abstractmethod + def _line(off, scl): + pass + + @staticmethod + @abc.abstractmethod + def _roots(c): + pass + + @staticmethod + @abc.abstractmethod + def _fromroots(r): + pass + + def has_samecoef(self, other): + """Check if coefficients match. + + .. versionadded:: 1.6.0 + + Parameters + ---------- + other : class instance + The other class must have the ``coef`` attribute. + + Returns + ------- + bool : boolean + True if the coefficients are the same, False otherwise. + + """ + if len(self.coef) != len(other.coef): + return False + elif not np.all(self.coef == other.coef): + return False + else: + return True + + def has_samedomain(self, other): + """Check if domains match. + + .. versionadded:: 1.6.0 + + Parameters + ---------- + other : class instance + The other class must have the ``domain`` attribute. + + Returns + ------- + bool : boolean + True if the domains are the same, False otherwise. + + """ + return np.all(self.domain == other.domain) + + def has_samewindow(self, other): + """Check if windows match. + + .. versionadded:: 1.6.0 + + Parameters + ---------- + other : class instance + The other class must have the ``window`` attribute. + + Returns + ------- + bool : boolean + True if the windows are the same, False otherwise. + + """ + return np.all(self.window == other.window) + + def has_sametype(self, other): + """Check if types match. + + .. versionadded:: 1.7.0 + + Parameters + ---------- + other : object + Class instance. + + Returns + ------- + bool : boolean + True if other is same class as self + + """ + return isinstance(other, self.__class__) + + def _get_coefficients(self, other): + """Interpret other as polynomial coefficients. + + The `other` argument is checked to see if it is of the same + class as self with identical domain and window. If so, + return its coefficients, otherwise return `other`. + + .. versionadded:: 1.9.0 + + Parameters + ---------- + other : anything + Object to be checked. + + Returns + ------- + coef + The coefficients of`other` if it is a compatible instance, + of ABCPolyBase, otherwise `other`. + + Raises + ------ + TypeError + When `other` is an incompatible instance of ABCPolyBase. + + """ + if isinstance(other, ABCPolyBase): + if not isinstance(other, self.__class__): + raise TypeError("Polynomial types differ") + elif not np.all(self.domain == other.domain): + raise TypeError("Domains differ") + elif not np.all(self.window == other.window): + raise TypeError("Windows differ") + elif self.symbol != other.symbol: + raise ValueError("Polynomial symbols differ") + return other.coef + return other + + def __init__(self, coef, domain=None, window=None, symbol='x'): + [coef] = pu.as_series([coef], trim=False) + self.coef = coef + + if domain is not None: + [domain] = pu.as_series([domain], trim=False) + if len(domain) != 2: + raise ValueError("Domain has wrong number of elements.") + self.domain = domain + + if window is not None: + [window] = pu.as_series([window], trim=False) + if len(window) != 2: + raise ValueError("Window has wrong number of elements.") + self.window = window + + # Validation for symbol + try: + if not symbol.isidentifier(): + raise ValueError( + "Symbol string must be a valid Python identifier" + ) + # If a user passes in something other than a string, the above + # results in an AttributeError. Catch this and raise a more + # informative exception + except AttributeError: + raise TypeError("Symbol must be a non-empty string") + + self._symbol = symbol + + def __repr__(self): + coef = repr(self.coef)[6:-1] + domain = repr(self.domain)[6:-1] + window = repr(self.window)[6:-1] + name = self.__class__.__name__ + return (f"{name}({coef}, domain={domain}, window={window}, " + f"symbol='{self.symbol}')") + + def __format__(self, fmt_str): + if fmt_str == '': + return self.__str__() + if fmt_str not in ('ascii', 'unicode'): + raise ValueError( + f"Unsupported format string '{fmt_str}' passed to " + f"{self.__class__}.__format__. Valid options are " + f"'ascii' and 'unicode'" + ) + if fmt_str == 'ascii': + return self._generate_string(self._str_term_ascii) + return self._generate_string(self._str_term_unicode) + + def __str__(self): + if self._use_unicode: + return self._generate_string(self._str_term_unicode) + return self._generate_string(self._str_term_ascii) + + def _generate_string(self, term_method): + """ + Generate the full string representation of the polynomial, using + ``term_method`` to generate each polynomial term. + """ + # Get configuration for line breaks + linewidth = np.get_printoptions().get('linewidth', 75) + if linewidth < 1: + linewidth = 1 + out = pu.format_float(self.coef[0]) + for i, coef in enumerate(self.coef[1:]): + out += " " + power = str(i + 1) + # Polynomial coefficient + # The coefficient array can be an object array with elements that + # will raise a TypeError with >= 0 (e.g. strings or Python + # complex). In this case, represent the coefficient as-is. + try: + if coef >= 0: + next_term = f"+ " + pu.format_float(coef, parens=True) + else: + next_term = f"- " + pu.format_float(-coef, parens=True) + except TypeError: + next_term = f"+ {coef}" + # Polynomial term + next_term += term_method(power, self.symbol) + # Length of the current line with next term added + line_len = len(out.split('\n')[-1]) + len(next_term) + # If not the last term in the polynomial, it will be two + # characters longer due to the +/- with the next term + if i < len(self.coef[1:]) - 1: + line_len += 2 + # Handle linebreaking + if line_len >= linewidth: + next_term = next_term.replace(" ", "\n", 1) + out += next_term + return out + + @classmethod + def _str_term_unicode(cls, i, arg_str): + """ + String representation of single polynomial term using unicode + characters for superscripts and subscripts. + """ + if cls.basis_name is None: + raise NotImplementedError( + "Subclasses must define either a basis_name, or override " + "_str_term_unicode(cls, i, arg_str)" + ) + return (f"·{cls.basis_name}{i.translate(cls._subscript_mapping)}" + f"({arg_str})") + + @classmethod + def _str_term_ascii(cls, i, arg_str): + """ + String representation of a single polynomial term using ** and _ to + represent superscripts and subscripts, respectively. + """ + if cls.basis_name is None: + raise NotImplementedError( + "Subclasses must define either a basis_name, or override " + "_str_term_ascii(cls, i, arg_str)" + ) + return f" {cls.basis_name}_{i}({arg_str})" + + @classmethod + def _repr_latex_term(cls, i, arg_str, needs_parens): + if cls.basis_name is None: + raise NotImplementedError( + "Subclasses must define either a basis name, or override " + "_repr_latex_term(i, arg_str, needs_parens)") + # since we always add parens, we don't care if the expression needs them + return f"{{{cls.basis_name}}}_{{{i}}}({arg_str})" + + @staticmethod + def _repr_latex_scalar(x, parens=False): + # TODO: we're stuck with disabling math formatting until we handle + # exponents in this function + return r'\text{{{}}}'.format(pu.format_float(x, parens=parens)) + + def _repr_latex_(self): + # get the scaled argument string to the basis functions + off, scale = self.mapparms() + if off == 0 and scale == 1: + term = self.symbol + needs_parens = False + elif scale == 1: + term = f"{self._repr_latex_scalar(off)} + {self.symbol}" + needs_parens = True + elif off == 0: + term = f"{self._repr_latex_scalar(scale)}{self.symbol}" + needs_parens = True + else: + term = ( + f"{self._repr_latex_scalar(off)} + " + f"{self._repr_latex_scalar(scale)}{self.symbol}" + ) + needs_parens = True + + mute = r"\color{{LightGray}}{{{}}}".format + + parts = [] + for i, c in enumerate(self.coef): + # prevent duplication of + and - signs + if i == 0: + coef_str = f"{self._repr_latex_scalar(c)}" + elif not isinstance(c, numbers.Real): + coef_str = f" + ({self._repr_latex_scalar(c)})" + elif not np.signbit(c): + coef_str = f" + {self._repr_latex_scalar(c, parens=True)}" + else: + coef_str = f" - {self._repr_latex_scalar(-c, parens=True)}" + + # produce the string for the term + term_str = self._repr_latex_term(i, term, needs_parens) + if term_str == '1': + part = coef_str + else: + part = rf"{coef_str}\,{term_str}" + + if c == 0: + part = mute(part) + + parts.append(part) + + if parts: + body = ''.join(parts) + else: + # in case somehow there are no coefficients at all + body = '0' + + return rf"${self.symbol} \mapsto {body}$" + + + + # Pickle and copy + + def __getstate__(self): + ret = self.__dict__.copy() + ret['coef'] = self.coef.copy() + ret['domain'] = self.domain.copy() + ret['window'] = self.window.copy() + ret['symbol'] = self.symbol + return ret + + def __setstate__(self, dict): + self.__dict__ = dict + + # Call + + def __call__(self, arg): + off, scl = pu.mapparms(self.domain, self.window) + arg = off + scl*arg + return self._val(arg, self.coef) + + def __iter__(self): + return iter(self.coef) + + def __len__(self): + return len(self.coef) + + # Numeric properties. + + def __neg__(self): + return self.__class__( + -self.coef, self.domain, self.window, self.symbol + ) + + def __pos__(self): + return self + + def __add__(self, other): + othercoef = self._get_coefficients(other) + try: + coef = self._add(self.coef, othercoef) + except Exception: + return NotImplemented + return self.__class__(coef, self.domain, self.window, self.symbol) + + def __sub__(self, other): + othercoef = self._get_coefficients(other) + try: + coef = self._sub(self.coef, othercoef) + except Exception: + return NotImplemented + return self.__class__(coef, self.domain, self.window, self.symbol) + + def __mul__(self, other): + othercoef = self._get_coefficients(other) + try: + coef = self._mul(self.coef, othercoef) + except Exception: + return NotImplemented + return self.__class__(coef, self.domain, self.window, self.symbol) + + def __truediv__(self, other): + # there is no true divide if the rhs is not a Number, although it + # could return the first n elements of an infinite series. + # It is hard to see where n would come from, though. + if not isinstance(other, numbers.Number) or isinstance(other, bool): + raise TypeError( + f"unsupported types for true division: " + f"'{type(self)}', '{type(other)}'" + ) + return self.__floordiv__(other) + + def __floordiv__(self, other): + res = self.__divmod__(other) + if res is NotImplemented: + return res + return res[0] + + def __mod__(self, other): + res = self.__divmod__(other) + if res is NotImplemented: + return res + return res[1] + + def __divmod__(self, other): + othercoef = self._get_coefficients(other) + try: + quo, rem = self._div(self.coef, othercoef) + except ZeroDivisionError: + raise + except Exception: + return NotImplemented + quo = self.__class__(quo, self.domain, self.window, self.symbol) + rem = self.__class__(rem, self.domain, self.window, self.symbol) + return quo, rem + + def __pow__(self, other): + coef = self._pow(self.coef, other, maxpower=self.maxpower) + res = self.__class__(coef, self.domain, self.window, self.symbol) + return res + + def __radd__(self, other): + try: + coef = self._add(other, self.coef) + except Exception: + return NotImplemented + return self.__class__(coef, self.domain, self.window, self.symbol) + + def __rsub__(self, other): + try: + coef = self._sub(other, self.coef) + except Exception: + return NotImplemented + return self.__class__(coef, self.domain, self.window, self.symbol) + + def __rmul__(self, other): + try: + coef = self._mul(other, self.coef) + except Exception: + return NotImplemented + return self.__class__(coef, self.domain, self.window, self.symbol) + + def __rdiv__(self, other): + # set to __floordiv__ /. + return self.__rfloordiv__(other) + + def __rtruediv__(self, other): + # An instance of ABCPolyBase is not considered a + # Number. + return NotImplemented + + def __rfloordiv__(self, other): + res = self.__rdivmod__(other) + if res is NotImplemented: + return res + return res[0] + + def __rmod__(self, other): + res = self.__rdivmod__(other) + if res is NotImplemented: + return res + return res[1] + + def __rdivmod__(self, other): + try: + quo, rem = self._div(other, self.coef) + except ZeroDivisionError: + raise + except Exception: + return NotImplemented + quo = self.__class__(quo, self.domain, self.window, self.symbol) + rem = self.__class__(rem, self.domain, self.window, self.symbol) + return quo, rem + + def __eq__(self, other): + res = (isinstance(other, self.__class__) and + np.all(self.domain == other.domain) and + np.all(self.window == other.window) and + (self.coef.shape == other.coef.shape) and + np.all(self.coef == other.coef) and + (self.symbol == other.symbol)) + return res + + def __ne__(self, other): + return not self.__eq__(other) + + # + # Extra methods. + # + + def copy(self): + """Return a copy. + + Returns + ------- + new_series : series + Copy of self. + + """ + return self.__class__(self.coef, self.domain, self.window, self.symbol) + + def degree(self): + """The degree of the series. + + .. versionadded:: 1.5.0 + + Returns + ------- + degree : int + Degree of the series, one less than the number of coefficients. + + Examples + -------- + + Create a polynomial object for ``1 + 7*x + 4*x**2``: + + >>> poly = np.polynomial.Polynomial([1, 7, 4]) + >>> print(poly) + 1.0 + 7.0·x + 4.0·x² + >>> poly.degree() + 2 + + Note that this method does not check for non-zero coefficients. + You must trim the polynomial to remove any trailing zeroes: + + >>> poly = np.polynomial.Polynomial([1, 7, 0]) + >>> print(poly) + 1.0 + 7.0·x + 0.0·x² + >>> poly.degree() + 2 + >>> poly.trim().degree() + 1 + + """ + return len(self) - 1 + + def cutdeg(self, deg): + """Truncate series to the given degree. + + Reduce the degree of the series to `deg` by discarding the + high order terms. If `deg` is greater than the current degree a + copy of the current series is returned. This can be useful in least + squares where the coefficients of the high degree terms may be very + small. + + .. versionadded:: 1.5.0 + + Parameters + ---------- + deg : non-negative int + The series is reduced to degree `deg` by discarding the high + order terms. The value of `deg` must be a non-negative integer. + + Returns + ------- + new_series : series + New instance of series with reduced degree. + + """ + return self.truncate(deg + 1) + + def trim(self, tol=0): + """Remove trailing coefficients + + Remove trailing coefficients until a coefficient is reached whose + absolute value greater than `tol` or the beginning of the series is + reached. If all the coefficients would be removed the series is set + to ``[0]``. A new series instance is returned with the new + coefficients. The current instance remains unchanged. + + Parameters + ---------- + tol : non-negative number. + All trailing coefficients less than `tol` will be removed. + + Returns + ------- + new_series : series + New instance of series with trimmed coefficients. + + """ + coef = pu.trimcoef(self.coef, tol) + return self.__class__(coef, self.domain, self.window, self.symbol) + + def truncate(self, size): + """Truncate series to length `size`. + + Reduce the series to length `size` by discarding the high + degree terms. The value of `size` must be a positive integer. This + can be useful in least squares where the coefficients of the + high degree terms may be very small. + + Parameters + ---------- + size : positive int + The series is reduced to length `size` by discarding the high + degree terms. The value of `size` must be a positive integer. + + Returns + ------- + new_series : series + New instance of series with truncated coefficients. + + """ + isize = int(size) + if isize != size or isize < 1: + raise ValueError("size must be a positive integer") + if isize >= len(self.coef): + coef = self.coef + else: + coef = self.coef[:isize] + return self.__class__(coef, self.domain, self.window, self.symbol) + + def convert(self, domain=None, kind=None, window=None): + """Convert series to a different kind and/or domain and/or window. + + Parameters + ---------- + domain : array_like, optional + The domain of the converted series. If the value is None, + the default domain of `kind` is used. + kind : class, optional + The polynomial series type class to which the current instance + should be converted. If kind is None, then the class of the + current instance is used. + window : array_like, optional + The window of the converted series. If the value is None, + the default window of `kind` is used. + + Returns + ------- + new_series : series + The returned class can be of different type than the current + instance and/or have a different domain and/or different + window. + + Notes + ----- + Conversion between domains and class types can result in + numerically ill defined series. + + """ + if kind is None: + kind = self.__class__ + if domain is None: + domain = kind.domain + if window is None: + window = kind.window + return self(kind.identity(domain, window=window, symbol=self.symbol)) + + def mapparms(self): + """Return the mapping parameters. + + The returned values define a linear map ``off + scl*x`` that is + applied to the input arguments before the series is evaluated. The + map depends on the ``domain`` and ``window``; if the current + ``domain`` is equal to the ``window`` the resulting map is the + identity. If the coefficients of the series instance are to be + used by themselves outside this class, then the linear function + must be substituted for the ``x`` in the standard representation of + the base polynomials. + + Returns + ------- + off, scl : float or complex + The mapping function is defined by ``off + scl*x``. + + Notes + ----- + If the current domain is the interval ``[l1, r1]`` and the window + is ``[l2, r2]``, then the linear mapping function ``L`` is + defined by the equations:: + + L(l1) = l2 + L(r1) = r2 + + """ + return pu.mapparms(self.domain, self.window) + + def integ(self, m=1, k=[], lbnd=None): + """Integrate. + + Return a series instance that is the definite integral of the + current series. + + Parameters + ---------- + m : non-negative int + The number of integrations to perform. + k : array_like + Integration constants. The first constant is applied to the + first integration, the second to the second, and so on. The + list of values must less than or equal to `m` in length and any + missing values are set to zero. + lbnd : Scalar + The lower bound of the definite integral. + + Returns + ------- + new_series : series + A new series representing the integral. The domain is the same + as the domain of the integrated series. + + """ + off, scl = self.mapparms() + if lbnd is None: + lbnd = 0 + else: + lbnd = off + scl*lbnd + coef = self._int(self.coef, m, k, lbnd, 1./scl) + return self.__class__(coef, self.domain, self.window, self.symbol) + + def deriv(self, m=1): + """Differentiate. + + Return a series instance of that is the derivative of the current + series. + + Parameters + ---------- + m : non-negative int + Find the derivative of order `m`. + + Returns + ------- + new_series : series + A new series representing the derivative. The domain is the same + as the domain of the differentiated series. + + """ + off, scl = self.mapparms() + coef = self._der(self.coef, m, scl) + return self.__class__(coef, self.domain, self.window, self.symbol) + + def roots(self): + """Return the roots of the series polynomial. + + Compute the roots for the series. Note that the accuracy of the + roots decreases the further outside the `domain` they lie. + + Returns + ------- + roots : ndarray + Array containing the roots of the series. + + """ + roots = self._roots(self.coef) + return pu.mapdomain(roots, self.window, self.domain) + + def linspace(self, n=100, domain=None): + """Return x, y values at equally spaced points in domain. + + Returns the x, y values at `n` linearly spaced points across the + domain. Here y is the value of the polynomial at the points x. By + default the domain is the same as that of the series instance. + This method is intended mostly as a plotting aid. + + .. versionadded:: 1.5.0 + + Parameters + ---------- + n : int, optional + Number of point pairs to return. The default value is 100. + domain : {None, array_like}, optional + If not None, the specified domain is used instead of that of + the calling instance. It should be of the form ``[beg,end]``. + The default is None which case the class domain is used. + + Returns + ------- + x, y : ndarray + x is equal to linspace(self.domain[0], self.domain[1], n) and + y is the series evaluated at element of x. + + """ + if domain is None: + domain = self.domain + x = np.linspace(domain[0], domain[1], n) + y = self(x) + return x, y + + @classmethod + def fit(cls, x, y, deg, domain=None, rcond=None, full=False, w=None, + window=None, symbol='x'): + """Least squares fit to data. + + Return a series instance that is the least squares fit to the data + `y` sampled at `x`. The domain of the returned instance can be + specified and this will often result in a superior fit with less + chance of ill conditioning. + + Parameters + ---------- + x : array_like, shape (M,) + x-coordinates of the M sample points ``(x[i], y[i])``. + y : array_like, shape (M,) + y-coordinates of the M sample points ``(x[i], y[i])``. + deg : int or 1-D array_like + Degree(s) of the fitting polynomials. If `deg` is a single integer + all terms up to and including the `deg`'th term are included in the + fit. For NumPy versions >= 1.11.0 a list of integers specifying the + degrees of the terms to include may be used instead. + domain : {None, [beg, end], []}, optional + Domain to use for the returned series. If ``None``, + then a minimal domain that covers the points `x` is chosen. If + ``[]`` the class domain is used. The default value was the + class domain in NumPy 1.4 and ``None`` in later versions. + The ``[]`` option was added in numpy 1.5.0. + rcond : float, optional + Relative condition number of the fit. Singular values smaller + than this relative to the largest singular value will be + ignored. The default value is len(x)*eps, where eps is the + relative precision of the float type, about 2e-16 in most + cases. + full : bool, optional + Switch determining nature of return value. When it is False + (the default) just the coefficients are returned, when True + diagnostic information from the singular value decomposition is + also returned. + w : array_like, shape (M,), optional + Weights. If not None, the weight ``w[i]`` applies to the unsquared + residual ``y[i] - y_hat[i]`` at ``x[i]``. Ideally the weights are + chosen so that the errors of the products ``w[i]*y[i]`` all have + the same variance. When using inverse-variance weighting, use + ``w[i] = 1/sigma(y[i])``. The default value is None. + + .. versionadded:: 1.5.0 + window : {[beg, end]}, optional + Window to use for the returned series. The default + value is the default class domain + + .. versionadded:: 1.6.0 + symbol : str, optional + Symbol representing the independent variable. Default is 'x'. + + Returns + ------- + new_series : series + A series that represents the least squares fit to the data and + has the domain and window specified in the call. If the + coefficients for the unscaled and unshifted basis polynomials are + of interest, do ``new_series.convert().coef``. + + [resid, rank, sv, rcond] : list + These values are only returned if ``full == True`` + + - resid -- sum of squared residuals of the least squares fit + - rank -- the numerical rank of the scaled Vandermonde matrix + - sv -- singular values of the scaled Vandermonde matrix + - rcond -- value of `rcond`. + + For more details, see `linalg.lstsq`. + + """ + if domain is None: + domain = pu.getdomain(x) + elif type(domain) is list and len(domain) == 0: + domain = cls.domain + + if window is None: + window = cls.window + + xnew = pu.mapdomain(x, domain, window) + res = cls._fit(xnew, y, deg, w=w, rcond=rcond, full=full) + if full: + [coef, status] = res + return ( + cls(coef, domain=domain, window=window, symbol=symbol), status + ) + else: + coef = res + return cls(coef, domain=domain, window=window, symbol=symbol) + + @classmethod + def fromroots(cls, roots, domain=[], window=None, symbol='x'): + """Return series instance that has the specified roots. + + Returns a series representing the product + ``(x - r[0])*(x - r[1])*...*(x - r[n-1])``, where ``r`` is a + list of roots. + + Parameters + ---------- + roots : array_like + List of roots. + domain : {[], None, array_like}, optional + Domain for the resulting series. If None the domain is the + interval from the smallest root to the largest. If [] the + domain is the class domain. The default is []. + window : {None, array_like}, optional + Window for the returned series. If None the class window is + used. The default is None. + symbol : str, optional + Symbol representing the independent variable. Default is 'x'. + + Returns + ------- + new_series : series + Series with the specified roots. + + """ + [roots] = pu.as_series([roots], trim=False) + if domain is None: + domain = pu.getdomain(roots) + elif type(domain) is list and len(domain) == 0: + domain = cls.domain + + if window is None: + window = cls.window + + deg = len(roots) + off, scl = pu.mapparms(domain, window) + rnew = off + scl*roots + coef = cls._fromroots(rnew) / scl**deg + return cls(coef, domain=domain, window=window, symbol=symbol) + + @classmethod + def identity(cls, domain=None, window=None, symbol='x'): + """Identity function. + + If ``p`` is the returned series, then ``p(x) == x`` for all + values of x. + + Parameters + ---------- + domain : {None, array_like}, optional + If given, the array must be of the form ``[beg, end]``, where + ``beg`` and ``end`` are the endpoints of the domain. If None is + given then the class domain is used. The default is None. + window : {None, array_like}, optional + If given, the resulting array must be if the form + ``[beg, end]``, where ``beg`` and ``end`` are the endpoints of + the window. If None is given then the class window is used. The + default is None. + symbol : str, optional + Symbol representing the independent variable. Default is 'x'. + + Returns + ------- + new_series : series + Series of representing the identity. + + """ + if domain is None: + domain = cls.domain + if window is None: + window = cls.window + off, scl = pu.mapparms(window, domain) + coef = cls._line(off, scl) + return cls(coef, domain, window, symbol) + + @classmethod + def basis(cls, deg, domain=None, window=None, symbol='x'): + """Series basis polynomial of degree `deg`. + + Returns the series representing the basis polynomial of degree `deg`. + + .. versionadded:: 1.7.0 + + Parameters + ---------- + deg : int + Degree of the basis polynomial for the series. Must be >= 0. + domain : {None, array_like}, optional + If given, the array must be of the form ``[beg, end]``, where + ``beg`` and ``end`` are the endpoints of the domain. If None is + given then the class domain is used. The default is None. + window : {None, array_like}, optional + If given, the resulting array must be if the form + ``[beg, end]``, where ``beg`` and ``end`` are the endpoints of + the window. If None is given then the class window is used. The + default is None. + symbol : str, optional + Symbol representing the independent variable. Default is 'x'. + + Returns + ------- + new_series : series + A series with the coefficient of the `deg` term set to one and + all others zero. + + """ + if domain is None: + domain = cls.domain + if window is None: + window = cls.window + ideg = int(deg) + + if ideg != deg or ideg < 0: + raise ValueError("deg must be non-negative integer") + return cls([0]*ideg + [1], domain, window, symbol) + + @classmethod + def cast(cls, series, domain=None, window=None): + """Convert series to series of this class. + + The `series` is expected to be an instance of some polynomial + series of one of the types supported by by the numpy.polynomial + module, but could be some other class that supports the convert + method. + + .. versionadded:: 1.7.0 + + Parameters + ---------- + series : series + The series instance to be converted. + domain : {None, array_like}, optional + If given, the array must be of the form ``[beg, end]``, where + ``beg`` and ``end`` are the endpoints of the domain. If None is + given then the class domain is used. The default is None. + window : {None, array_like}, optional + If given, the resulting array must be if the form + ``[beg, end]``, where ``beg`` and ``end`` are the endpoints of + the window. If None is given then the class window is used. The + default is None. + + Returns + ------- + new_series : series + A series of the same kind as the calling class and equal to + `series` when evaluated. + + See Also + -------- + convert : similar instance method + + """ + if domain is None: + domain = cls.domain + if window is None: + window = cls.window + return series.convert(domain, cls, window) |