{
  "__type": "IngestedDoc",
  "__tag": 4010,
  "_content": {
    "Notes": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "An RBF is a scalar valued function in N-dimensional space whose value at "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "x"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " can be expressed in terms of "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "r=||x - c||"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", where "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "c"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " is the center of the RBF."
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "An RBF interpolant for the vector of data values "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "d"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", which are from locations "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "y"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", is a linear combination of RBFs centered at "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "y"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " plus a polynomial with a specified degree. The RBF interpolant is written as"
            }
          ]
        },
        {
          "__type": "Math",
          "__tag": 4058,
          "value": "f(x) = K(x, y) a + P(x) b,"
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "where "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "K(x, y)"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " is a matrix of RBFs with centers at "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "y"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " evaluated at the points "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "x"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", and "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "P(x)"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " is a matrix of monomials, which span polynomials with the specified degree, evaluated at "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "x"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ". The coefficients "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "a"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " and "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "b"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " are the solution to the linear equations"
            }
          ]
        },
        {
          "__type": "Math",
          "__tag": 4058,
          "value": "(K(x, y) + \\lambda I) a + P(y) b = d"
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "and"
            }
          ]
        },
        {
          "__type": "Math",
          "__tag": 4058,
          "value": "P(y)^T a = 0,"
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "where "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "\\lambda"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " is a non-negative smoothing parameter that controls how well we want to fit the data. The data are fit exactly when the smoothing parameter is 0."
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "The above system is uniquely solvable if the following requirements are met:"
            }
          ]
        },
        {
          "__type": "Blockquote",
          "__tag": 4059,
          "children": [
            {
              "__type": "BulletList",
              "__tag": 4053,
              "ordered": false,
              "start": 1,
              "children": [
                {
                  "__type": "ListItem",
                  "__tag": 4054,
                  "children": [
                    {
                      "__type": "Paragraph",
                      "__tag": 4045,
                      "children": [
                        {
                          "__type": "InlineMath",
                          "__tag": 4057,
                          "value": "P(y)"
                        },
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": " must have full column rank. "
                        },
                        {
                          "__type": "InlineMath",
                          "__tag": 4057,
                          "value": "P(y)"
                        },
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": " always has full       column rank when "
                        },
                        {
                          "__type": "ParamRef",
                          "__tag": 4071,
                          "name": "degree"
                        },
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": " is -1 or 0. When "
                        },
                        {
                          "__type": "ParamRef",
                          "__tag": 4071,
                          "name": "degree"
                        },
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": " is 1,       "
                        },
                        {
                          "__type": "InlineMath",
                          "__tag": 4057,
                          "value": "P(y)"
                        },
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": " has full column rank if the data point locations are not       all collinear (N=2), coplanar (N=3), etc."
                        }
                      ]
                    }
                  ]
                },
                {
                  "__type": "ListItem",
                  "__tag": 4054,
                  "children": [
                    {
                      "__type": "Paragraph",
                      "__tag": 4045,
                      "children": [
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": "If "
                        },
                        {
                          "__type": "ParamRef",
                          "__tag": 4071,
                          "name": "kernel"
                        },
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": " is 'multiquadric', 'linear', 'thin_plate_spline',       'cubic', or 'quintic', then "
                        },
                        {
                          "__type": "ParamRef",
                          "__tag": 4071,
                          "name": "degree"
                        },
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": " must not be lower than the       minimum value listed above."
                        }
                      ]
                    }
                  ]
                },
                {
                  "__type": "ListItem",
                  "__tag": 4054,
                  "children": [
                    {
                      "__type": "Paragraph",
                      "__tag": 4045,
                      "children": [
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": "If "
                        },
                        {
                          "__type": "ParamRef",
                          "__tag": 4071,
                          "name": "smoothing"
                        },
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": " is 0, then each data point location must be distinct."
                        }
                      ]
                    }
                  ]
                }
              ]
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "When using an RBF that is not scale invariant ('multiquadric', 'inverse_multiquadric', 'inverse_quadratic', or 'gaussian'), an appropriate shape parameter must be chosen (e.g., through cross validation). Smaller values for the shape parameter correspond to wider RBFs. The problem can become ill-conditioned or singular when the shape parameter is too small."
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "The memory required to solve for the RBF interpolation coefficients increases quadratically with the number of data points, which can become impractical when interpolating more than about a thousand data points. To overcome memory limitations for large interpolation problems, the "
            },
            {
              "__type": "ParamRef",
              "__tag": 4071,
              "name": "neighbors"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " argument can be specified to compute an RBF interpolant for each evaluation point using only the nearest data points."
            }
          ]
        },
        {
          "__type": "Admonition",
          "__tag": 4056,
          "kind": "versionadded",
          "base_type": "neutral",
          "children": [
            {
              "__type": "AdmonitionTitle",
              "__tag": 4055,
              "children": [
                {
                  "__type": "Text",
                  "__tag": 4046,
                  "value": "versionadded 1.7.0"
                }
              ]
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Strong",
              "__tag": 4048,
              "children": [
                {
                  "__type": "Text",
                  "__tag": 4046,
                  "value": "Array API Standard Support"
                }
              ]
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "CrossRef",
              "__tag": 4002,
              "value": "RBFInterpolator",
              "reference": {
                "__type": "LocalRef",
                "__tag": 4022,
                "kind": "module",
                "path": "scipy.interpolate._rbfinterp:RBFInterpolator"
              },
              "kind": "module"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "SCIPY_ARRAY_API=1"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported."
            }
          ]
        },
        {
          "__type": "Code",
          "__tag": 4050,
          "value": "====================  ====================  ====================\nLibrary               CPU                   GPU\n====================  ====================  ====================\nNumPy                 ✅                     n/a                 \nCuPy                  n/a                   ✅                   \nPyTorch               ✅                     ✅                   \nJAX                   ✅                     ✅                   \nDask                  ⛔                     n/a                 \n====================  ====================  ====================",
          "execution_status": null
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Only the default "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "neighbors=None"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " is Array API compatible. If a non-default value of "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "neighbors"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " is given, the behavior is NumPy -only."
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "See "
            },
            {
              "__type": "InlineRole",
              "__tag": 4003,
              "value": "dev-arrayapi",
              "domain": null,
              "role": "ref",
              "inventory": null
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " for more information."
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Warns": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Raises": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Yields": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Methods": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Returns": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Radial basis function interpolator in N ≥ 1 dimensions."
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Receives": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Warnings": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Attributes": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Parameters": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Parameters",
          "__tag": 4026,
          "children": [
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "y",
              "annotation": "(npoints, ndims) array_like",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "2-D array of data point coordinates."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "d",
              "annotation": "(npoints, ...) array_like",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "N-D array of data values at "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "y"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": ". The length of "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "d"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " along the first axis must be equal to the length of "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "y"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": ". Unlike some interpolators, the interpolation axis cannot be changed."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "neighbors",
              "annotation": "int, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "If specified, the value of the interpolant at each evaluation point will be computed using only this many nearest data points. All the data points are used by default."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "smoothing",
              "annotation": "float or (npoints, ) array_like, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Smoothing parameter. The interpolant perfectly fits the data when this is set to 0. For large values, the interpolant approaches a least squares fit of a polynomial with the specified degree. Default is 0."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "kernel",
              "annotation": "str, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Type of RBF. This should be one of"
                    }
                  ]
                },
                {
                  "__type": "Blockquote",
                  "__tag": 4059,
                  "children": [
                    {
                      "__type": "BulletList",
                      "__tag": 4053,
                      "ordered": false,
                      "start": 1,
                      "children": [
                        {
                          "__type": "ListItem",
                          "__tag": 4054,
                          "children": [
                            {
                              "__type": "Paragraph",
                              "__tag": 4045,
                              "children": [
                                {
                                  "__type": "Text",
                                  "__tag": 4046,
                                  "value": "'linear'"
                                },
                                {
                                  "__type": "InlineCode",
                                  "__tag": 4051,
                                  "value": "-r"
                                }
                              ]
                            }
                          ]
                        },
                        {
                          "__type": "ListItem",
                          "__tag": 4054,
                          "children": [
                            {
                              "__type": "Paragraph",
                              "__tag": 4045,
                              "children": [
                                {
                                  "__type": "Text",
                                  "__tag": 4046,
                                  "value": "'thin_plate_spline'"
                                },
                                {
                                  "__type": "InlineCode",
                                  "__tag": 4051,
                                  "value": "r**2 * log(r)"
                                }
                              ]
                            }
                          ]
                        },
                        {
                          "__type": "ListItem",
                          "__tag": 4054,
                          "children": [
                            {
                              "__type": "Paragraph",
                              "__tag": 4045,
                              "children": [
                                {
                                  "__type": "Text",
                                  "__tag": 4046,
                                  "value": "'cubic'"
                                },
                                {
                                  "__type": "InlineCode",
                                  "__tag": 4051,
                                  "value": "r**3"
                                }
                              ]
                            }
                          ]
                        },
                        {
                          "__type": "ListItem",
                          "__tag": 4054,
                          "children": [
                            {
                              "__type": "Paragraph",
                              "__tag": 4045,
                              "children": [
                                {
                                  "__type": "Text",
                                  "__tag": 4046,
                                  "value": "'quintic'"
                                },
                                {
                                  "__type": "InlineCode",
                                  "__tag": 4051,
                                  "value": "-r**5"
                                }
                              ]
                            }
                          ]
                        },
                        {
                          "__type": "ListItem",
                          "__tag": 4054,
                          "children": [
                            {
                              "__type": "Paragraph",
                              "__tag": 4045,
                              "children": [
                                {
                                  "__type": "Text",
                                  "__tag": 4046,
                                  "value": "'multiquadric'"
                                },
                                {
                                  "__type": "InlineCode",
                                  "__tag": 4051,
                                  "value": "-sqrt(1 + r**2)"
                                }
                              ]
                            }
                          ]
                        },
                        {
                          "__type": "ListItem",
                          "__tag": 4054,
                          "children": [
                            {
                              "__type": "Paragraph",
                              "__tag": 4045,
                              "children": [
                                {
                                  "__type": "Text",
                                  "__tag": 4046,
                                  "value": "'inverse_multiquadric'"
                                },
                                {
                                  "__type": "InlineCode",
                                  "__tag": 4051,
                                  "value": "1/sqrt(1 + r**2)"
                                }
                              ]
                            }
                          ]
                        },
                        {
                          "__type": "ListItem",
                          "__tag": 4054,
                          "children": [
                            {
                              "__type": "Paragraph",
                              "__tag": 4045,
                              "children": [
                                {
                                  "__type": "Text",
                                  "__tag": 4046,
                                  "value": "'inverse_quadratic'"
                                },
                                {
                                  "__type": "InlineCode",
                                  "__tag": 4051,
                                  "value": "1/(1 + r**2)"
                                }
                              ]
                            }
                          ]
                        },
                        {
                          "__type": "ListItem",
                          "__tag": 4054,
                          "children": [
                            {
                              "__type": "Paragraph",
                              "__tag": 4045,
                              "children": [
                                {
                                  "__type": "Text",
                                  "__tag": 4046,
                                  "value": "'gaussian'"
                                },
                                {
                                  "__type": "InlineCode",
                                  "__tag": 4051,
                                  "value": "exp(-r**2)"
                                }
                              ]
                            }
                          ]
                        }
                      ]
                    }
                  ]
                },
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Default is 'thin_plate_spline'."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "epsilon",
              "annotation": "float, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Shape parameter that scales the input to the RBF. If "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "kernel"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is 'linear', 'thin_plate_spline', 'cubic', or 'quintic', this defaults to 1 and can be ignored because it has the same effect as scaling the smoothing parameter. Otherwise, this must be specified."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "degree",
              "annotation": "int, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Degree of the added polynomial. For some RBFs the interpolant may not be well-posed if the polynomial degree is too small. Those RBFs and their corresponding minimum degrees are"
                    }
                  ]
                },
                {
                  "__type": "Blockquote",
                  "__tag": 4059,
                  "children": [
                    {
                      "__type": "BulletList",
                      "__tag": 4053,
                      "ordered": false,
                      "start": 1,
                      "children": [
                        {
                          "__type": "ListItem",
                          "__tag": 4054,
                          "children": [
                            {
                              "__type": "Paragraph",
                              "__tag": 4045,
                              "children": [
                                {
                                  "__type": "Text",
                                  "__tag": 4046,
                                  "value": "'multiquadric'0"
                                }
                              ]
                            }
                          ]
                        },
                        {
                          "__type": "ListItem",
                          "__tag": 4054,
                          "children": [
                            {
                              "__type": "Paragraph",
                              "__tag": 4045,
                              "children": [
                                {
                                  "__type": "Text",
                                  "__tag": 4046,
                                  "value": "'linear'0"
                                }
                              ]
                            }
                          ]
                        },
                        {
                          "__type": "ListItem",
                          "__tag": 4054,
                          "children": [
                            {
                              "__type": "Paragraph",
                              "__tag": 4045,
                              "children": [
                                {
                                  "__type": "Text",
                                  "__tag": 4046,
                                  "value": "'thin_plate_spline'1"
                                }
                              ]
                            }
                          ]
                        },
                        {
                          "__type": "ListItem",
                          "__tag": 4054,
                          "children": [
                            {
                              "__type": "Paragraph",
                              "__tag": 4045,
                              "children": [
                                {
                                  "__type": "Text",
                                  "__tag": 4046,
                                  "value": "'cubic'1"
                                }
                              ]
                            }
                          ]
                        },
                        {
                          "__type": "ListItem",
                          "__tag": 4054,
                          "children": [
                            {
                              "__type": "Paragraph",
                              "__tag": 4045,
                              "children": [
                                {
                                  "__type": "Text",
                                  "__tag": 4046,
                                  "value": "'quintic'2"
                                }
                              ]
                            }
                          ]
                        }
                      ]
                    }
                  ]
                },
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "The default value is the minimum degree for "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "kernel"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " or 0 if there is no minimum degree. Set this to -1 for no added polynomial."
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Extended Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Other Parameters": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    }
  },
  "_ordered_sections": [
    "Summary",
    "Extended Summary",
    "Parameters",
    "Attributes",
    "Methods",
    "Returns",
    "Yields",
    "Receives",
    "Other Parameters",
    "Raises",
    "Warns",
    "Warnings",
    "Notes"
  ],
  "item_file": "/scipy/interpolate/_rbfinterp.py",
  "item_line": 62,
  "item_type": "class",
  "aliases": [
    "scipy.interpolate.RBFInterpolator"
  ],
  "example_section_data": {
    "__type": "Section",
    "__tag": 4015,
    "children": [
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "Demonstrate interpolating scattered data to a grid in 2-D.\n\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "import numpy as np\nimport matplotlib.pyplot as plt\nfrom scipy.interpolate import RBFInterpolator\nfrom scipy.stats.qmc import Halton\n",
        "execution_status": "success"
      },
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "rng = np.random.default_rng()\nxobs = 2*Halton(2, seed=rng).random(100) - 1\nyobs = np.sum(xobs, axis=1)*np.exp(-6*np.sum(xobs**2, axis=1))\n",
        "execution_status": "success"
      },
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "x1 = np.linspace(-1, 1, 50)\nxgrid = np.asarray(np.meshgrid(x1, x1, indexing='ij'))\nxflat = xgrid.reshape(2, -1).T     # make it a 2-D array\nyflat = RBFInterpolator(xobs, yobs)(xflat)\nygrid = yflat.reshape(50, 50)\n",
        "execution_status": "success"
      },
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "fig, ax = plt.subplots()\n",
        "execution_status": "success"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "ax.pcolormesh(*xgrid, ygrid, vmin=-0.25, vmax=0.25, shading='gouraud')\n",
        "execution_status": "failure"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "p = ax.scatter(*xobs.T, c=yobs, s=50, ec='k', vmin=-0.25, vmax=0.25)\n",
        "execution_status": "success"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "fig.colorbar(p)\n",
        "execution_status": "failure"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "plt.show()\n",
        "execution_status": "success"
      },
      {
        "__type": "Figure",
        "__tag": 4024,
        "value": {
          "__type": "RefInfo",
          "__tag": 4000,
          "module": "scipy",
          "version": "1.17.1",
          "kind": "assets",
          "path": "fig-3852f3f74fa85402.png"
        }
      }
    ],
    "title": [],
    "level": 0,
    "target": null
  },
  "see_also": [
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "CloughTocher2DInterpolator",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "scipy.interpolate._interpnd:CloughTocher2DInterpolator"
        },
        "kind": "module"
      },
      "descriptions": [],
      "type": "func"
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "LinearNDInterpolator",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "scipy.interpolate._interpnd:LinearNDInterpolator"
        },
        "kind": "module"
      },
      "descriptions": [],
      "type": "func"
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "NearestNDInterpolator",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "scipy.interpolate._ndgriddata:NearestNDInterpolator"
        },
        "kind": "module"
      },
      "descriptions": [],
      "type": "func"
    }
  ],
  "signature": {
    "__type": "SignatureNode",
    "__tag": 4029,
    "kind": "function",
    "parameters": [
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "y",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": {
          "__type": "Empty",
          "__tag": 4031
        }
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "d",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": {
          "__type": "Empty",
          "__tag": 4031
        }
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "neighbors",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "None"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "smoothing",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "0.0"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "kernel",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "thin_plate_spline"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "epsilon",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "None"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "degree",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "None"
      }
    ],
    "return_annotation": {
      "__type": "Empty",
      "__tag": 4031
    },
    "target_name": "RBFInterpolator"
  },
  "references": [
    ".. [1] Fasshauer, G., 2007. Meshfree Approximation Methods with Matlab.",
    "    World Scientific Publishing Co.",
    "",
    ".. [2] http://amadeus.math.iit.edu/~fass/603_ch3.pdf",
    "",
    ".. [3] Wahba, G., 1990. Spline Models for Observational Data. SIAM.",
    "",
    ".. [4] http://pages.stat.wisc.edu/~wahba/stat860public/lect/lect8/lect8.pdf"
  ],
  "qa": "scipy.interpolate._rbfinterp:RBFInterpolator",
  "arbitrary": [],
  "local_refs": [
    "d",
    "degree",
    "epsilon",
    "kernel",
    "neighbors",
    "smoothing",
    "y"
  ]
}