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4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "As noted above, the " }, { "__type": "InlineRole", "__tag": 4003, "value": "poly1d class ", "domain": null, "role": "class", "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " and associated functions defined in " }, { "__type": "InlineCode", "__tag": 4051, "value": "numpy.lib.polynomial" }, { "__type": "Text", "__tag": 4046, "value": ", such as " }, { "__type": "CrossRef", "__tag": 4002, "value": "numpy.polyfit", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "numpy", "version": "*", "kind": "api", "path": "numpy:polyfit" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " and " }, { "__type": "CrossRef", "__tag": 4002, "value": "numpy.poly", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "numpy", "version": "*", "kind": "api", "path": "numpy:poly" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": ", are considered legacy and should " }, { "__type": "Strong", "__tag": 4048, "children": [ { "__type": "Text", "__tag": 4046, "value": "not" } ] }, { "__type": "Text", "__tag": 4046, "value": " be used in new code. Since NumPy version 1.4, the " }, { "__type": "CrossRef", "__tag": 4002, "value": "numpy.polynomial", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "numpy", "version": "*", "kind": "api", "path": "numpy.polynomial" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " package is preferred for working with polynomials." } ] } ], "title": [ { "__type": "Text", "__tag": 4046, "value": "Transitioning from " }, { "__type": "InlineRole", "__tag": 4003, "value": "numpy.poly1d", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " to " }, { "__type": "InlineRole", "__tag": 4003, "value": "numpy.polynomial", "domain": null, "role": null, "inventory": null } ], "level": 1, "target": null }, { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The following table highlights some of the main differences between the legacy polynomial module and the polynomial package for common tasks. The " }, { "__type": "CrossRef", "__tag": 4002, "value": "Polynomial", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "numpy", "version": "*", "kind": "api", "path": "numpy.polynomial.polynomial:Polynomial" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " class is imported for brevity " } ] }, { "__type": "Code", "__tag": 4050, "value": "from numpy.polynomial import Polynomial", "execution_status": null }, { "__type": "Code", "__tag": 4050, "value": "+------------------------+----------------------------------------+---------------------------------------+\n| **How to...** | Legacy (`numpy.poly1d`) | `numpy.polynomial` |\n+------------------------+----------------------------------------+---------------------------------------+\n| Create a | ``p = np.poly1d([1, 2, 3])`` | ``p = Polynomial([3, 2, 1])`` |\n| polynomial object | | |\n| from coefficients [1]_ | | |\n+------------------------+----------------------------------------+---------------------------------------+\n| Create a polynomial | ``r = np.poly([-1, 1])`` | ``p = Polynomial.fromroots([-1, 1])`` |\n| object from roots | ``p = np.poly1d(r)`` | |\n+------------------------+----------------------------------------+---------------------------------------+\n| Fit a polynomial of | | |\n| degree ``deg`` to data | ``np.polyfit(x, y, deg)`` | ``Polynomial.fit(x, y, deg)`` |\n+------------------------+----------------------------------------+---------------------------------------+\n| Evaluate a polynomial | ``p(2.0)`` or | ``p(2.0)`` or ``polyval(2.0, p.coef)``|\n| at a point [2]_ | ``np.polyval([1, 2, 3], 2.0)`` | (use ``p.convert().coef`` after fit) |\n+------------------------+----------------------------------------+---------------------------------------+", "execution_status": null }, { "__type": "Footnote", "__tag": 4067, "label": "1", "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Note the reversed ordering of the coefficients" } ] } ] }, { "__type": "Footnote", "__tag": 4067, "label": "2", "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "When evaluating polynomials created with " }, { "__type": "InlineCode", "__tag": 4051, "value": "fit()" }, { "__type": "Text", "__tag": 4046, "value": ", use " }, { "__type": "InlineCode", "__tag": 4051, "value": "p(x)" }, { "__type": "Text", "__tag": 4046, "value": " or " }, { "__type": "InlineCode", "__tag": 4051, "value": "polyval(x, p.convert().coef)" }, { "__type": "Text", "__tag": 4046, "value": " to handle domain/window scaling correctly." } ] } ] } ], "title": [ { "__type": "Text", "__tag": 4046, "value": "Quick Reference" } ], "level": 2, "target": null }, { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "There are significant differences between " }, { "__type": "InlineCode", "__tag": 4051, "value": "numpy.lib.polynomial" }, { "__type": "Text", "__tag": 4046, "value": " and " }, { "__type": "CrossRef", "__tag": 4002, "value": "numpy.polynomial", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "numpy", "version": "*", "kind": "api", "path": "numpy.polynomial" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": ". The most significant difference is the ordering of the coefficients for the polynomial expressions. The various routines in " }, { "__type": "CrossRef", "__tag": 4002, "value": "numpy.polynomial", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "numpy", "version": "*", "kind": "api", "path": "numpy.polynomial" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " all deal with series whose coefficients go from degree zero upward, which is the " }, { "__type": "Emphasis", "__tag": 4047, "children": [ { "__type": "Text", "__tag": 4046, "value": "reverse order" } ] }, { "__type": "Text", "__tag": 4046, "value": " of the poly1d convention. The easy way to remember this is that indices correspond to degree, i.e., " }, { "__type": "InlineCode", "__tag": 4051, "value": "coef[i]" }, { "__type": "Text", "__tag": 4046, "value": " is the coefficient of the term of degree " }, { "__type": "Emphasis", "__tag": 4047, "children": [ { "__type": "Text", "__tag": 4046, "value": "i" } ] }, { "__type": "Text", "__tag": 4046, "value": "." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Though the difference in convention may be confusing, it is straightforward to convert from the legacy polynomial API to the new. For example, the following demonstrates how you would convert a " }, { "__type": "CrossRef", "__tag": 4002, "value": "numpy.poly1d", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "numpy", "version": "*", "kind": "api", "path": "numpy:poly1d" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " instance representing the expression " }, { "__type": "InlineMath", "__tag": 4057, "value": "x^{2} + 2x + 3" }, { "__type": "Text", "__tag": 4046, "value": " to a " }, { "__type": "CrossRef", "__tag": 4002, "value": "Polynomial", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "numpy", "version": "*", "kind": "api", "path": "numpy.polynomial.polynomial:Polynomial" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " instance representing the same expression:" } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "See the documentation for the " }, { "__type": "InlineRole", "__tag": 4003, "value": "convenience classes ", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " for further details on the " }, { "__type": "InlineCode", "__tag": 4051, "value": "domain" }, { "__type": "Text", "__tag": 4046, "value": " and " }, { "__type": "InlineCode", "__tag": 4051, "value": "window" }, { "__type": "Text", "__tag": 4046, "value": " attributes." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Another major difference between the legacy polynomial module and the polynomial package is polynomial fitting. In the old module, fitting was done via the " }, { "__type": "CrossRef", "__tag": 4002, "value": "polyfit", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "numpy", "version": "*", "kind": "api", "path": "numpy:polyfit" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " function. In the polynomial package, the " }, { "__type": "CrossRef", "__tag": 4002, "value": "fit", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "numpy", "version": "*", "kind": "api", "path": "numpy.polynomial._polybase:ABCPolyBase.fit" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " class method is preferred. For example, consider a simple linear fit to the following data:" } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "With the legacy polynomial module, a linear fit (i.e. polynomial of degree 1) could be applied to these data with " }, { "__type": "CrossRef", "__tag": 4002, "value": "polyfit", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "numpy", "version": "*", "kind": "api", "path": "numpy:polyfit" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": ":" } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "With the new polynomial API, the " }, { "__type": "CrossRef", "__tag": 4002, "value": "fit", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "numpy", "version": "*", "kind": "api", "path": "numpy.polynomial._polybase:ABCPolyBase.fit" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " class method is preferred:" } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Note that the coefficients are given " }, { "__type": "Emphasis", "__tag": 4047, "children": [ { "__type": "Text", "__tag": 4046, "value": "in the scaled domain" } ] }, { "__type": "Text", "__tag": 4046, "value": " defined by the linear mapping between the " }, { "__type": "InlineCode", "__tag": 4051, "value": "window" }, { "__type": "Text", "__tag": 4046, "value": " and " }, { "__type": "InlineCode", "__tag": 4051, "value": "domain" }, { "__type": "Text", "__tag": 4046, "value": ". " }, { "__type": "CrossRef", "__tag": 4002, "value": "convert", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "numpy", "version": "*", "kind": "api", "path": "numpy.polynomial._polybase:ABCPolyBase.convert" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " can be used to get the coefficients in the unscaled data domain." } ] } ], "title": [ { "__type": "Text", "__tag": 4046, "value": "Transition Guide" } ], "level": 2, "target": null }, { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "In addition to standard power series polynomials, the polynomial package provides several additional kinds of polynomials including Chebyshev, Hermite (two subtypes), Laguerre, and Legendre polynomials. Each of these has an associated " }, { "__type": "InlineRole", "__tag": 4003, "value": "convenience class ", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " available from the " }, { "__type": "CrossRef", "__tag": 4002, "value": "numpy.polynomial", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "numpy", "version": "*", "kind": "api", "path": "numpy.polynomial" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " namespace that provides a consistent interface for working with polynomials regardless of their type." } ] }, { "__type": "BulletList", "__tag": 4053, "ordered": false, "start": 1, "children": [ { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "CrossRef", "__tag": 4002, "value": "Using the convenience classes", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "docs", "path": "reference:routines.polynomials.classes" }, "kind": "exists" } ] } ] } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Documentation pertaining to specific functions defined for each kind of polynomial individually can be found in the corresponding module documentation:" } ] }, { "__type": "BulletList", "__tag": 4053, "ordered": false, "start": 1, "children": [ { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "CrossRef", "__tag": 4002, "value": "routines.polynomials.polynomial", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "docs", "path": "reference:routines.polynomials.polynomial" }, "kind": "exists" } ] } ] }, { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "CrossRef", "__tag": 4002, "value": "routines.polynomials.chebyshev", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "docs", "path": "reference:routines.polynomials.chebyshev" }, "kind": "exists" } ] } ] }, { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "CrossRef", "__tag": 4002, "value": "routines.polynomials.hermite", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "docs", "path": "reference:routines.polynomials.hermite" }, "kind": "exists" } ] } ] }, { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "CrossRef", "__tag": 4002, "value": "routines.polynomials.hermite_e", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "docs", "path": "reference:routines.polynomials.hermite_e" }, "kind": "exists" } ] } ] }, { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "CrossRef", "__tag": 4002, "value": "routines.polynomials.laguerre", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "docs", "path": "reference:routines.polynomials.laguerre" }, "kind": "exists" } ] } ] }, { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "CrossRef", "__tag": 4002, "value": "routines.polynomials.legendre", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "docs", "path": "reference:routines.polynomials.legendre" }, "kind": "exists" } ] } ] }, { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "CrossRef", "__tag": 4002, "value": "Polyutils", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "docs", "path": "reference:routines.polynomials.polyutils" }, "kind": "exists" } ] } ] } ] } ], "title": [ { "__type": "Text", "__tag": 4046, "value": "Documentation for the " }, { "__type": "InlineRole", "__tag": 4003, "value": "~numpy.polynomial", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " package" } ], "level": 1, "target": null }, { "__type": "Section", "__tag": 4015, "children": [ { "__type": "BulletList", "__tag": 4053, "ordered": false, "start": 1, "children": [ { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "CrossRef", "__tag": 4002, "value": "Poly1d", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "docs", "path": "reference:routines.polynomials.poly1d" }, "kind": "exists" } ] } ] } ] } ], "title": [ { "__type": "Text", "__tag": 4046, "value": "Documentation for legacy polynomials" } ], "level": 1, "target": null } ], "local_refs": [] }